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Fuzzy logic in polder flood control operations in Bangkok Agsorn, Songkran 1995

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FUZZY LOGIC IN FOLDER FLOOD CONTROL OPERATIONS IN BANGKOKbySONGKRAN AGSORNB. S. (Meteorology), North Carolina State University, 1980M. S. (Meteorology), The University of Wisconsin-Madison, 1982M. Sc. (Hydrology), The National University of Ireland, 1988A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUTREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIES(Department of Civil Engineering)We accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAJune, 1995.© Songkran Agsorn, 1995In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature)Department of Civil EngineeringThe University of British ColumbiaVancouver, CanadaDate June 26, 1995DE-6 (2/88)ABSTRACTThe flood situation in Bangkok and the way in which it has evolved is described in thisstudy. The present approach to flood control involves use of the polder concept. Sinceexcess water in a polder has to be disposed of either through gravity drainage or pumping,the way in which the gates and/or pumps are operated becomes very important. In practice,operators of such facilities tend to be risk averse and favor operating according to fixedrules.Fuzzy logic programming was investigated as a way to improve operations, while notdeparting too far from the fixed rule operation that operators prefer. Some simpleexperiments were first done to find the most suitable alternative to present methods ofincorporating fuzzy information. A new fuzzy algorithm was proposed and tested.Due to unavailability of actual data, a simple, but reasonably representative floodcontrol situation, typical of those in Bangkok was used. Operating procedures weredeveloped based on synthetic rainfalls and runoffs. Then, fuzzy operating rules werederived, and a fuzzy rule base was set up. Next, simulations were used in which floodhydrographs were generated and the system was “operated” using fuzzy logic programmingand the fuzzy rule base which was developed. The results were compared with three othersystems: fixed rule system, a time varying rule curve, and “optimal” operation. Besides themain experiments, which involved only pump operations, additional sets of experimentswere conducted for the cases with combined pump and gate operations and with tides.11Fuzzy logic programming was demonstrated to be a very promising tool for improvingflood control operating procedures for polder systems such as those in use in Bangkok. Theprocedure can be looked upon as an extension of the fixed rule operating procedurespresently being used by the operators. Further extensions are possible, including the use offlow forecasts. However, the main purpose of this study was to investigate the feasibility ofusing fuzzy logic programming to improve on existing operating procedures.111CONTENTSABSTRACT iiCONTENTS ivTABLES viiFIGURES xACKNOWLEDGMENTS xiiiDEDICATION xiv1 INTRODUCTION 11.1 Background 11.2 Objectives of the Study 31.3 Structure of the Thesis 52 REVIEW OF BANGKOK’S FLOOD SITUATION 72.1 Background 72.1.1 History 72.1.2 The Chao Pbraya River Basin 132.1.3 Bangkok’s Floods 222.2 Flood Control Approaches 272.2.1 Background 272.2.2 Flood Control in Bangkok 292.2.2.1 Background 29iv2.2.2.2 Folder Flood Control 322.2.2.3 Flood Control Development 362.3 Approaches to Flood Control Operation 382.3.1 Background 382.3.2 Bangkok’s Practice 432.4 Alternative Way to Improve the Existing Flood Control Operations 443 FUZZY LOGIC 463.1 Background 463.2 Fuzzy System as Model-free Estimator 544 EXPERIMENTS WITH FUZZY LOGIC PROGRAMMING 564.1 General 564.2 Experimental Procedure 584.3 Setting up the Rule Bases from Known Output Functions 624.4 Setting up the Rule Base from Training Data 654.5 Results of the Experiments 664.5.1 With Accurate Rule Base 664.5.2 With FAM (Fuzzy Associative Memory) Rule Base Derivedfrom Training Data 694.6 Robustness 734.7 Conclusions 755 NUMERICAL EXPERIMENTS 775.1 Introduction 77V5.2 Experimental Polders 795.3 Simulating Flows 815.4 Time Varying Rule Curve 865.5 Fuzzy Estimating System 885.5.1 Fuzzy Membership Function 915.5.2 Derivation of Fuzzy Associative Memories 936 RESULTS AND DISCUSSION 986.1 Introduction 986.2 Main Experiments 1006.3 Additional Experiments 1096.3.1 Experiments with Independent Rainfall Intensity-Duration 1096.3.2 Experiments with Pump and Gate Discharges 1146.3.3 Experiments with Tides 1196.4 Discussion 1287 CONCLUSIONS 1327.1 Summary 1327.2 Conclusions 1357.3 Implementation Considerations 1387.4 Further Research 139REFERENCES 141viTABLESTABLE 4.1. Fuzzy Rule Base in the Conventional Form for the First Test Function. 60TABLE 4.2. Fuzzy Rule Base Used in the Direct Method for the First Test Function. 60TABLE 4.3. Fuzzy Rule Base in the Conventional Form for the Second Test Function. 63TABLE 4.4. Fuzzy Rule Base Used in the Direct Method for the Second Test Function. 63TABLE 4.5. Fuzzy Rule Base Used in the Conventional Form for the Third TestFunction. 64TABLE 4.6. Fuzzy Rule Base Used in the Direct Method for the Third Test Function. 64TABLE 4.7. Standard Errors of Estimation for the First Test Function by VariousAlternatives. 67TABLE 4.8. Standard Errors of Estimation for the Second Test Function by Various FuzzyAlternatives. 68TABLE 4.9. Standard Errors of Estimation for the Third Test Function by Various FuzzyAlternatives. 68TABLE 4.10. Standard Errors of Estimates of the First Test Function by the Direct Method,Based on the Training Data. 71TABLE 4.11. Standard Errors of Estimates of the Second Test Function by the DirectMethod, Based on the Training Data. 72TABLE 4.12. Standard Errors of Estimates of the Third Test Function by the DirectMethod, Based on the Training Data. 72viiTABLE 4.13.TABLE 4.14.TABLE 4.15.TABLE 5.1.TABLE 5.2.TABLE 5.3.TABLE 6.1.TABLE 6.2.TABLE 6.3.TABLE 6.4.TABLE 6.5.TABLE 6.6.TABLE 6.7.Standard Errors as Rules Are Randomly Omitted for the First TestFunction. 73Standard Errors as Rules Are Randomly Omitted for the Second Function. 74Standard Errors as Rules Are Randomly Omitted for the Third Function. 75Set-up of the Polders in the Experiments. 81First Fuzzy Associative Memory (FAM) for Polder #2—for Use DuringRainstorm. (Correlated Rainfall Intensity-Duration Relationship). 97Second Fuzzy Associative Memory (FAM) for Polder #2—for UseFollowing the End of Rainstorm. (Correlated Rainfall Intensity-DurationRelationship). 97Flood Volumes with Alternative Operating Methods. 102Pumping Volumes with Alternative Operating Methods. 103Fixed Rule Curve Operation with Different Fixed Rules—Polder #2. 106First Fuzzy Associative Memory (FAM) for Polder #2—for Use DuringRainstorm (Independent Rainfall Intensity-Duration Relationship). 110Second Fuzzy Associative Memory (FAM) for Polder #2—for Use Following the End of Rainstorm (Independent Rainfall Intensity-Duration Relationship). 110Flood Volumes with Alternative Operating Methods for Different SimulatedRainfalls. 111Pumping Volumes with Alternative Operating Methods for DifferentSimulated Rainfalls. 112viiiTABLE 6.8. Flood Volumes with Alternative Operating Methods for Pump/GateOperation. 115TABLE 6.9. Pumping Volumes with Alternative Operating Methods for Pump/GateOperation. 116TABLE 6.10. First Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2—for Use During Rainstorm (Correlated Rainfall Intensity-DurationRelationship). 122TABLE 6.11 Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2—for Use Following the End of Rainstorm (Correlated Rainfall Intensity-Duration Relationship). 123TABLE 6.12. First Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2—for Use During Rainstorm (Independent Rainfall Intensity-DurationRelationship). 123TABLE 6.13. Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2—for Use Following the End of Rainstorm (Independent Rainfall Intensity-Duration Relationship). 124TABLE 6.14. Flood Volumes with Different Operating Alternatives with Tides. 124TABLE 6.15. Pumping Volumes with Different Operating Alternatives with Tides. 125TABLE 6.16. Summary of Improvement of the Various Operations Using DifferentAlternatives. 130ixFIGURESFig. 1.1. Polder flood control concept (adapted from New York Times, Feb. 2, 1995). 2Fig. 2.1. Lay-out of Old Bangkok. 8Fig. 2.2. The Chao Phraya River Basin. 14Fig. 2.3. Details of The Lower Chao Phraya River Basin. 15Fig. 2.4. Ground subsidence rates of Bangkok (after Foster 1993). 25Fig. 2.5. River diversion schemes. 31Fig. 2.6. City Core project’s polders (after AlT 1986). 34Fig. 2.7. Eastern Suburb project’s polders (after JICA 1986). 35Fig. 2.8. Various flood protection and related studies and proposal. 36Fig. 3.1. Diagram of crisp characteristic membership function. 47Fig. 3.2. Example of fuzzy membership functions. (Crisp variable X = 6.3 has amembership in TALL of 0.7 and AVERAGE 0.3). 48Fig. 3.3. Fuzzfication of crisp input values of X1 and X2 and correspondingrulestriggered. 50Fig. 3.4. Input inference of the example fuzzy rule. 51Fig. 3.5. Output inference on Y for the example rule. A). Clipped. B). Scaled. 52Fig. 3.6. Center-of-Area (COA) defuzzfication. 52Fig. 3.7. Height defuz4fication. 53Fig. 4.1. Fuzzy membership functions of inputs X for test functions. 58xFig. 4.2. Fuzzy membership functions of outputs Y for the test functions. 59Fig. 4.3. Development of the Direct method’s nile structure. 61Fig. 5.1. Rainfall depth-duration mass curve used in the simulation. 83Fig. 5.2. Example of a simulated inflow used in this study. 85Fig. 5.3. Required empty storage derived with perfect knowledge of hydrograph. 86Fig. 5.4. Rule curve derivation. 87Fig. 5.5. Membership function of time from the beginning of a storm. 92Fig. 5.6. Membership function of rain intensity. 93Fig. 5.7. Membership function of rain depth. 93Fig. 6.1. Typical operation in Case 1 (Pump). 104Fig. 6.2. Typical operation in Case 2 (Pump). 104Fig. 6.3. Typical operation in Case 3 (Pump). 105Fig. 6.4. Mean flood volumes for Polder #2 (Pump). 107Fig. 6.5. Mean pumping volumes for Folder #2 (Pump). 108Fig. 6.6. Mean flood volumes for the independent intensity-duration, Folder #2(Pump). 113Fig. 6.7. Mean pumping volumes for the independent intensity-duration, Folder #2(Pump). 114Fig. 6.8. Mean flood volumes for the correlated intensity-duration, Folder #2(Pump/Gate). 117Fig. 6.9. Mean pumping volumes for the correlated intensity-duration, Folder #2(Pump! Gate). 118xiFig. 6.10. Mean flood volumes for the independent intensity-duration, Polder #2(Pump/Gate). 118Fig. 6.11. Mean pumping volumes for the independent intensity-duration, Polder #2(Pump/Gate). 119Fig. 6.12. Time varying rule curve with tidal effects for Polder #2 with the correlated rainintensity-relation. 120Fig. 6.13.Time varying rule curve with tidal effects for Polder #2 with the independentrainintensity-relation. 121Fig. 6.14.Membership finction of time of low tides. 122Fig. 6.15.Mean flood volumes for the correlated intensity-duration, Polder #2 (Tide). 126Fig. 6.16. Mean pumping volumes for the correlated intensity-duration, Polder #2(Tide). 127Fig. 6.17. Mean flood volumes for the independent intensity-duration, Polder #2(Tide). 127Fig. 6.18.Mean pumping volumes for the independent intensity-duration, Polder #2(Tide). 128xiiACKNOWLEDGMENTSThe author wishes to express his sincere gratitude to his major professor, Professor Samuel0. Dennis Russell for his enthusiasm, professionalism, and his incessant patience andpositive attitude in guiding this research. This thesis would not have been made possible inits final form without his brilliant advises.The author would also like to thank all the members of his supervisory committee.Professors William F. Caselton and John A. Meech are gratefully acknowledged for theircandid remarks and criticisms, and constructive suggestions on the research. Encouragingcomments by Professor Michael C. Quick are also invaluable throughout the course of thestudy.The author is deeply indebted to Dr. Dave W. Martin, Senior Scientist of Space Scienceand Engineering Center (SSEC) at the University of Wisconsin-Madison, formerly hisresearch supervisor at Madison, later a long-time colleague and friend for his endless andtimely encouragement and supports in the author’s decades of searching for the diverseeducation. His correspondences through E-mails are most valuable and helpful.The author would like to thank all members of his family, especially his mother, towhom the thesis is dedicated, for the unfailingly supports for all the years of his study.Special thanks are extended to Dr. Sombat Charoenwongse, Deputy Director-General ofTMD, Mr. Nattapong Bunjing, the Director of Thai Trade Center-Singapore and Mr. NatSrisukhonthanon, Senior Engineer of Public Works Department for their courteousassistance. Miss. Boossarasiri Thana is gratefully acknowledged for her kindlyunderstanding.Funding for the study was generously provided by the Government of Canada, inpromoting human resource development for Thailand, through THAILAND CANADARattanakosin Scholarship on the occasion of the Bangkok Bicentennial in 1982 (CIDA906/10569).xliiDedicated toMy Mother,who always believes that there is alwaysan opportunity to learn and improve things.xiv1INTRODUCTION1.1 BackgroundOwing to its location in a floodplain and near the sea, Bangkok Metropolis has naturallyinherited flood related problems. The floodplain is a part of the large Chao Phraya RiverBasin, which experiences floods annually. Flat topography, tidal action and heavy tropicalrainfalls have influenced the floods in the area. In the past, living with floods was acceptedas a fact of life by the residents. Rice, the major crop for livelihood, has been grown to takeadvantage of wet season flooding. The network of canals was an integrating part of theriverine settlement. It provided transportation, drainage and irrigation to the area. Bangkok,however, like other great cities has been changing through time. Many adjustments,considered to be appropriate at the time, have been made to cope with the growth of the city.Such changes have also affected the flood problems of Bangkok. Rapid urbanization sincethe 1950s has increased the exposure of the present population to flood problems. The canaldrainage system, once spread extensively throughout the city for irrigation and drainagepurposes, has become insufficient and ineffective as a result of modifications to the system.For example, several canals have been filled in and used as roads, to take advantage of theirright of way. Flood magnitudes and frequencies have been increasing. Flood protection hasbecome essential to the city. Although recent developments in flood studies (e.g., Williams1994) suggest integrated floodplain management as the most appropriate way to institutesustainable development of a floodplain, the sense of urgency after major floods in Bangkokhas influenced the authority to pursue a more traditional, structural flood control approach.1Many studies of flooding and flood control have been made in recent years, resulting in anumber of alternative proposals. Most of these can be categorized into two broadapproaches: major river-diversions, and land-drainage or diking or polder schemes. Thelatest river-diversion scheme is considered by some engineers to be the most technicallycomprehensive and effective way of tackling the flood situation. It is, however, regarded byothers as too expensive, time-consuming, and socially and politically impractical. On theother hand, the land-drainage and diking or polder flood-control approach offers a phaseddevelopment. It requires less capital to implement and allows setting priorities for the landsto be protected. The present flood control scheme has evolved around the polder floodcontrol concept, and the Bangkok Metropolitan Administration (BMA) has opted for this asthe basis for its protection scheme.Fig. 1.1. Polder flood control concept (adapted from New York Times, Feb. 2, 1995).2The polder flood-control concept (Fig. 1.1) is based on independent drainage-management of the floodwater in each designed unit. It divides the protected lands into self-contained plots of land or polders. A polder is an area of land surrounded by a river or canaland flood barriers. The barriers form a line of protection against external floodwaters.Internal excess stormwater has to be pumped or drained by gravity to canals or a river. Sinceexcess water in a polder has to be disposed of either through gravity drainage or pumping,the way in which the gates and/or pumps are operated becomes very important. If the pumpsor gates are not operated effectively, it may not be possible to prevent serious flooding. Onthe other hand, if they are used too often and for too long, the cost of operation can becomeexcessive. A strategy for timely release of the excess water should improve the effectivenessof the existing polder system if it can be practically implemented.1.2 Objectives of the StudyThe main objective of this study was to understand the flood situation in Bangkok anddetermine how it could be improved. To achieve the first goal, factors influencing the floodproblem in Bangkok were identified and reviewed. The historical development ofsettlements in Bangkok’s area was reviewed for background understanding of the changingland use in the city. A study of the river basin was conducted to gain knowledge about theriver and its floodplain. Causes of floods were identified. The various approaches used tomitigate or control floods were also reviewed. Current practices in operating flood controlsystems were investigated and used as background knowledge for the second goal of thestudy.The second objective of the study was to fmd the way to mitigate the existing floodproblems in Bangkok; once they were identified. As mentioned in Section 1.1, Bangkok’scurrent flood protection has been relying mainly on structural flood control and following3the polder flood control concept. Improvements to the control system could be achieved byusing a more effective strategy in releasing excess water from within the polder. Besidesimproving the flood prevention performance, better operation could also reduce the cost ofoperating and maintaining the flood control system.There have been many studies of flood operating procedures. Academic studies tend toemphasize “optimization”—operating the gates and pumps in such a way as to optimizesome objective, such as minimizing the total expected cost of flood damage and the cost ofoperation. However, in practice, operators tend to be more risk averse and favor operatingaccording to fixed rules, such as opening the gates and starting the pumps should the waterlevel exceed some pre-specified value. Recognizing this operational reality, a practicalalternative to derive a strategy for a release of excess floodwater from within a poldersystem was sought. The simplified time varying rule curve was introduced as an initial stepto improve the current operation. In anticipating the more variable and flexible nature of thereal situation, fuzzy logic was introduced as a way to improve the time varying rule curve.Fuzzy logic programming offered a way to improve operations, while not departing too farfrom the fixed rule operation that operators prefer. Fuzzy control systems and algorithmswere investigated, and a new fuzzy algorithm was developed and tested. The procedure canbe looked upon as an extension of the fixed rule operating procedures presently being usedby the operators. Thus, fuzzy logic programming should probably be acceptable to them.A numerical experiment was set up to examine the fuzzy logic concept as compared tothe fixed rule, time varying rule curve, and “optimum” alternatives. A simple, butreasonably representative flood control situation was defmed and operating procedures weredeveloped. The control situation was simplified as an operation of a single polder,equivalent to a single reservoir. Flood flows were generated by a Monte Carlo procedure,but set up such that the resulting flows were reasonably realistic. After typical floodhydrographs were derived, optimal operating rules for each one were developed withhindsight. The operating rule was defmed by the water level below which the pumps should4be off and above which they should be on. After a large number of optimal rules forindividual flood events had been developed, these rules were related to information whichwould have been available at the time. Two simple items of information were found to bemost useful—the time since the storm had begun and the average rainfall up to that time.From these, fuzzy operating rules were derived, and a fuzzy rule base set up. Next,simulations were used in which flood hydrographs were generated and the system was“operated” using fuzzy logic programming and the fuzzy rule base which had beendeveloped. Since the main experiments involved rainstorms generated with the correlatedrelationship between rain intensity and duration, which was frequently used for flood designand planning in Bangkok, additional sets of experiments reflecting more variable floods andflood control operations were also conducted. The experiments included rainfall generatedfrom an independent intensity-duration relationship, a combination of pump and gateoperations, and tidal effects. The results, in terms of total release volumes, were comparedwith results from operations of the various alternatives to evaluate the performance of thefuzzy logic programming. These showed that fuzzy logic programming provides aneffective flood control system, but its potential to achieve greater improvement of theoperation increases as the system becomes more variable.1.3 Structure of the ThesisChapter 2 describes the flood problems in Bangkok and the current approach to theseproblems. The historical background concerning the flood problem is first presented. It isfollowed by a description of the Chao Phraya River Basin, in which Bangkok is situated.The geographical setting and hydrological characteristics of the basin are described. Thecauses of the floods in Bangkok and the flood prevention approach being taken by the cityare discussed. The current operating practice of the city of Bangkok in coping with its flood5problems is described. A review of recent research and practice in flood control and relatedoperations in water resources follows.In Chapter 3, a review of fuzzy logic programming is given. It introduces the mainideas of fuzzy logic and the concept of the “black-box” estimation approach by fuzzy logicsystem is discussed. Use of Fuzzy Associative Memories (FAM’s) as an input-outputtranslation mechanism is also explained.Chapter 4 describes simple experiments to fmd the most suitable of the many possibleways of combining the available information. Various ways to construct a fuzzy estimatingsystem are examined and compared. A simple extension algorithm for building a fuzzysystem is presented for further use in the study.In Chapter 5, the numerical experiments used to test the feasibility of the fuzzy logicapproach to the polder flood problem are presented. The development of rule curves andfuzzy logic programming proposed for the study are shown in this chapter. Thedevelopment of the fuzzy logic programming algorithm used to decide when to releaseexcess water in the polder system is described. Details of the fuzzy programmingtechniques, such as its rule structure, rule base and membership functions are given.In Chapter 6, the results of the operations by the fuzzy logic programming are presentedand compared with alternative operating systems.In the last Chapter, a brief summary, a discussion of the experiments and conclusionsare presented. It includes suggestions for further research.62REVIEW OF BANGKOK’S FLOODS2.1 Background2.1.1 HistoryModem Bangkok has evolved from a small fishing village in the early Ayutthaya period(1350-1767) of Thailand’s history. During this period, Bangkok remained small in size, butits strategic importance increased with expanding interactions between Thailand and theoutside world. By the mid sixteenth century, Bangkok’s status was officially raised from avillage to a town. The original walled town of Bangkok was built around 1557 to guard aby-pass canal in an ox-bow of the river. Measuring only 260 m by 480 m and containingtwo canals and six bridges, it was officially called Thonburi (Jumsai 1988). This new namereceived little acceptance and came to mean only the settlement on the west side of the river,which was located about 25 km from the mouth of the Chao Phraya River. The river was theonly access by water from the Gulf of Siam (Thailand) to the capital, Ayutthaya, upriver.This was the first entry stop for Europeans seeking permission to proceed to the capital. Bythe 17th century, strategic forts were built at Bangkok to protect Ayutthaya against sea-borneinvasion. The town was later transformed into a busy trade center occupied largely by animmigrant Chinese community.7A: 1687. Adapted from Simon de la Loubere (1693), A New Historical Relationofthe Kingdom ofSiam. London.B: 1895. Adapted from Jumsai (1988), based on the Royal Survey Department’smap of 1895.Fig. 2.1. Lay-out of Old Bangkok.After the fall of Ayutthaya to the Burmese in 1767, Thonburi was chosen as the newcapital. This was based mainly on its strategic location as its surrounding waterways werethought to provide a strategic advantage for defending the city. However, in 1782 the capitalwas moved to the eastern bank (Fig. 2.1) which was considered to be more defensible thanThonburi. The main river named the Chao Phraya, located on the west and a swampy plainon the east known as “the Sea of Mud” could be used as natural defense lines for the city.The city was purposely located at a bend of the river to utilize the natural and extra wide8moats to the north, south and west; the latter direction being toward hostile Burma, while theeastern side was marshland, which could be a good defense line especially in the wet season(Jumsai 1988).From early maps, Bangkok appeared to resemble 17th-century Ayutthaya. Both citieswere on riverine, man-made islands full of canals. Initially, an old canal (Kiong Lord) wasenlarged and extended to join the bends of the river, forming an artificial island for thepalace ground. King Rama I (1782-1809), the first king of Thailand after Bangkok becamethe capital, built many kiongs (canals) to facilitate communication in the expanding city. Hedrafted laborers to excavate a crescent-shaped canal, forming a new moat (Kiong Ongang/Bang Lumpoo). This second moat and wall were realigned further to the east, parallel tothe Klong Lord. Canal construction was completed in 1785. It linked with the Chao PhrayaRiver to form an oval moat surrounding the man-made river island on which Bangkok wasoriginally built (Fig. 2.1). Fortified walls and gates with a total length of approximately8 km enclosing an area about 3.46 km2 formed the early boundary of the capital. Itspopulation at the end of the eighteenth century was estimated to be 70 000-80 000 (Bunnaket. al. 1982).Following the practice at Ayutthaya, water transportation was considered as the mainmode of communication of the new capital. During the nineteenth century, the city wasrapidly expanding, and a network of canals was built in various sections of the city.Between 1851 and 1854, a third moat (Kiong Pradung Krung Kasem), running somewhatparallel to the first and second, was dug and became a new canal which was linked to therest of the city’s water network. Other main canals, Kiong Samsen and Klong Saenseap,9were later dug in the east-west direction, connecting the river with the former easternmarshland. Malay prisoners, captured during the southern war campaign, were used aslaborers in digging these two canals. The construction of canals reached its peak during thereign of King Rama V (1868-1910). Almost half of Bangkok’s canals were built in thisperiod. Most canals were originally constructed for transportation and irrigation purposes.Eventually, they aided in expanding the capital boundary. Their function as a large stormdrainage system also offered immense benefits to the city. During a storm, it conveyedstorm waters, connected with sub-drainage and retention areas, and stored excess rainwaters. The life-style of the population adapted well to this waterway environment. Mosthouses were concentrated near the river or canals, where small boats were available tohouseholds. Bangkok’s houses, except the palaces and some commercial compounds, werewooden structures built on stilts or bamboo rafts to protect them from seasonal floods. Nearthe bank of the river, some houses also were built on stilts with their heights approximately2 to 2.5 m above the bank (Sternstein 1982). It was more common for houses to be floatedon the river or canals. The aquatic or float house was a unique amphibious settlementindigenously adopted by the natives for living in the floodplain environment. Similar instyle from floor to roof to the house on stilts, it differed only in being built on bamboo raftsand moored in the river or canals. The float house was flexible and mobile. It could bemoved up and down the slope of the river bank following tidal action. The greatestconcentration of float houses occurred from the end of the eighteenth century to thebeginning of the twentieth century (Jumsai 1988). It was estimated that by the middle of the10nineteenth century, the float house population in Bangkok was 350 000 out of the totalpopulation of 400 000. This made Bangkok mostly a floating city at that time.As Thailand’s dealings with the West grew, Bangkok kept expanding outwards alongroads, canals and rivers into surrounding rice fields and orchards. Between 1900 and 1978,the metropolis spread out from 13 to 290 km2 while the population swelled from 460 000 to4.73 million (Office of Prime Minister 1979). A road system was first introduced to the cityin the early nineteenth century. Roads appeared in many sections of the city as did modemstormwater management and facilities, such as sewers. Stormwater conveyances wereplaced in many parts of the city. Then from a short period after the World War II, the urbandevelopment in Bangkok was meteoric. The population was increasing, resulting partlyfrom economic immigration from rural areas. More new roads were built, often by filling upthe canals, thereby replacing them. The network of roads inevitably changed the dischargecharacteristics of the canals. It often transformed their function to serve largely as stormsewers. Furthermore, illegal construction of buildings and garbage disposal into thewaterways continued to limit the discharge capacity of the canals. They became smaller andshallower. The old network of waterways was altered so much that their once, usefulfunction as a major storm drainage network system was greatly reduced. The original use ofthe canals as a transportation system has been superseded by roadways, especially on the eastside of the river. As the important contributions of the canals have been overlooked, severeflood problems in Bangkok appear to be the result of the hasty development of the city.Floods have existed since before the establishment of Bangkok settlement. Oldaccounts of a vast flood over the great floodplain of the Chao Phraya River were often11mentioned by earlier travelers or residents (e.g., Leonowens 1870). As previouslymentioned, an adaptation to the floodplain, such as a float house, was accomplished in theearly era of the city. However, through decades of neglecting appropriate land-use,uncontrolled urban expansions and inadequate infrastructure for drainage and sanitarysystems, modern Bangkok is burdened with a very severe, large-scale flood problem. In thiscase, fast-paced development of the city, inadequate attention to associated problems offlood dynamics, and the nature of the floodplain are costing inhabitants of the great city ofBangkok more and more. Flood occurrences and magnitudes have increased and causedmuch hardship to the population who prefer a western life style. During the 1970s, floodsoccurred in Bangkok more frequently than before. Large floods occurred in 1975 and 1978.In the 1 980s, floods occurred almost every year with severe floods in 1980, 1982, 1983 and1986. In 1983, the largest flood since 1942 took place. The floodwater was higher than90 cm in some areas (JICA 1986). It lasted up to four months in many areas of easternBangkok, which received the most damage from this flood. This prolonged flood causeddamage, estimated at more than U.S. $260 million’ (the income per capita of Bangkok’sresidents was about U.S. $500). After the major floods of 1980 and 1983, more permanent-type, large-scale flood protection projects have been undertaken. Most of them rely much onavailable technologies, which can be fitted to the current problem and available resource.Indigenous ideas such as those of float houses seemed far from acceptance by the residentsof the city although such living does still exist in less urbanized communities, such as in avillage near the southern coastline of Thailand. To catch up with the changing nature of‘In 1985 price unless otherwise stated.12flood dynamics, a polder system was adopted for its flexibility in creating a phasedprotection of the city. As this development has occurred, the Greater Bangkok area has alsoexpanded to enclose more than 1700 km2 of land, covering both banks of the Chao PhrayaRiver. The current population of the city is a little over 9 million (more than 10 percent ofthe total population of the country).2.1.2 The Chao Phraya River BasinThe Chao Phraya River Basin, in which Bangkok is located, is the largest river basin of thecountry (Fig. 2.2 and Fig. 2.3). It has an over-all drainage area of 162 600 km2 or about one-third of the total area of the country. It covers the area between 13.5°-20.0° N and 98.0°-101.50 E. Its longest river channel length is about 980 km. The basin is usually divided intotwo basins: the Upper Basin (106 600 km2) and the Lower Basin (56 000 km2). In theUpper Basin, there are four tributary rivers: the Ping, the Wang, the Yom, and the Nan.They merge to form the Chao Phraya at Nakom Sawan (350 km upstream from the Gulf ofThailand). Most of the Upper Basin is characterized by mountains or hills with forest cover.Two major dams are located in the basin: Bhumipol Dam (effective storage volume of9662 Mm3)on the Ping River, and Sirikit Dam (6600 Mm3) in the Nan River. The averagedetention time of Bhumipol is 2.57 years and that of Sirikit is 1.71 years. These two dams1398E 100E 120E1 8N16N14NFig. 2.2. The Chao Phraya River Basin.have been built for hydropower generation, irrigation and flood control purposes. Prior tothe drought of 1979 in the basin when the reservoirs could not meet irrigation demands, thetop priority was given to hydropower generation. After that drought, irrigation took thepriority over power generation. Hydropower generation has then become the secondarypriority. This has led to a more conservative release of water during the wet season. The20N12N14water is needed for rice irrigation only in the dry season. The other purpose of the reservoirsis for flood control. The reservoirs can, however, only regulate small parts of the floodflows. The other large dam is Kiu Lom Dam (108 Mm3) on the Wang, used mainly forirrigation purposes.[] River KilometerFig. 2.3. Details of the Lower Chao Phraya River Basin.GULF OF THAILANDLEGEND—‘-C River or Canal%% River Basin Boundary15The area from Nakorn Sawan to the Gulf of Thailand has been designated as the LowerBasin. South of Chainat (250 km north of the Gulf) is the alluvial plain of the Chao PhrayaRiver. The plain area from Chainat to the Gulf of Thailand has a very flat overall-gradient.At its apex near Chainat, the elevation is only 15 m above the mean sea level (JICA 1986).Downstream of Chainat, many effluent branches come off the main river channel. One ofthem, the Suphan River, does not again join the Chao Phraya, but discharges into the Gulf ofThailand near Samut Prakan, 35 km west of the main Chao Phraya River. In the middle ofthe basin near Ayutthaya (130 km upstream from the Gulf), the fifth influent tributary, thePasak River meets the Chao Phraya. There are two main barrages: Chao Phraya or ChainatBarrage (Dam) in the main channel and Rama VI Barrage in the Pasak River. Both of themare parts of a large irrigation project, “the Great Chao Pbraya”. The project includes areasaround and north of Bangkok. Water is diverted by canals from Chao Phraya Barrage atChainat. The canals are connected with the Rama IV Barrage on the Pasak River.Extensive, distributing canals have been built in the central floodplain around Bangkok.Their main purpose is for irrigating paddy rice. The density of the canals is about1 km km2. Furthermore, both sides of the Chao Pbraya have been embanked extensively.This includes the river reach from Chainat to Bang Sai (110 km upstream). They extend onthe western bank down to Pak Kret (80 km upstream). Newer dikes have also been placedon the east side of the river at Pak Kret. Downstream from Bang Sai to Bangkok, the topwidth of the river varies from 200 to 500 m (JICA 1985). The overall gradient of the river inthis reach is roughly 5 to 6 centimeters per kilometer. The gradient of the Chao Phraya fromBangkok to the river mouth is very flat, about 2 centimeters per kilometer. The elevation of16the river bank upstream near Bangkok is approximately 1.5 m above mean sea level (MSL).In a normal flood period the river discharges range from 1500 m3 s1 to 4000 m3 s1 (JICA1985). The water level in the Chao Phraya usually experiences the first rise in May or Juneover a period of 1-3 weeks. The second rise occurs gradually and reaches its maximum inthe upper reach in October and in the lower reach in November.In the Lower Basin, most lands are afready heavily irrigated and cultivated. Rice grainsproduced here account for more than half of the country’s total rice production. The mainirrigating water source is surface water from the Chao Phraya River system. Connecting tothe Chao Phraya River throughout the Lower Basin is an extensive network of canals, mostlyfor irrigation as a part of the Great Chao Phraya project. During the flood period, this deltaarea is usually inundated with floodwaters. Overland flow has been a part of wet rice-irrigation practices in the basin. Floodwater is needed for the rice irrigation. It is usedprimarily for controlling weeds which would otherwise choke the crop (Jackson 1989). Therice has long been grown in the basin and is basically a rain-fed crop. Unless artificiallyirrigated, only one harvest of rice is possible. By irrigating the crop, multiple harvestingbecomes possible. The large amount of irrigated land in the Chao Phraya River basindemands a large allocation of water, which is usually met by reservoirs and canal storagewithin the basin.The area between Chainat and Ayutthaya plays an important role as a retention basin. Ina regular wet season, it often acts as a large reservoir to hold floodwaters back from reachingBangkok. One-third of the flood discharge is estimated to be retained in this area.Discharge spills of the Chao Phraya River spreads over the agricultural lands north of17Bangkok. If there are heavy rains in the wet season, then the overland floodwater may flowinto the Bangkok area. The overflow is helped by the north-south slope of the floodplainand spills-over from the extensive irrigating canals. These spreading floodwaters threatenBangkok from the north and northeast areas during the high flood season. The water level inthe plain starts to rise around May and reaches a peak in October. Flooding in the floodplainfrom Chainat to Bang Sai usually occurs from September to October. In the river reachbetween Bang Sai and the Gulf, floods may occur from mid-October to the beginning ofDecember. The flood in the area is partly influenced by tidal situations.Tidal effects have a strong influence on the water levels in the main river channel,especially in the Lower Basin. Effects of tides can sometimes be felt upriver at Ayutthaya.The effects are more pronounced in a flood season if the discharge of the Chao Phrayareaches 1500 m3 s’ (JICA 1986). During a high tide, the tide influx is comparable inmagnitude to the river discharge. The estimated 100-year return period tidal influx to theriver is 3500 m3 s’. The outflow of the river is 3600 m3 s’ for the same return period (Zotti1987). A relatively high tide period usually occurs in November through January. InNovember, if a high river discharge occurs, then it will usually coincide with one or twospring tides. Seasonal variation of a water level in the Chao Pbraya River rises graduallynear the end of August. It reaches a peak in November and falls slowly until the end ofDecember. This phenomenon is mainly caused by run-off from the upper reach of the riverand the tides in the Gulf of Thailand.Within the Lower Basin, the Chao Phraya River cuts through the city of Bangkok, wherethe eastern bank is more urbanized than the western. The river is characterized by its18meandering nature when passing Bangkok. The city extends from about 27 to 56 km northof the Gulf of Thailand. The main drainage system is the network of canals, which even intheir reduced states, are still an important component of the drainage system. They comeunder BMA and Royal Irrigation Department (RID) jurisdiction. Canals in the outer areas,mostly dominated by agriculture use, are regulated by RID. Most of the main canals on thewest bank connect the Tachin (Suphan) River with the Chao Pbraya River. Main canals onthe west bank run mostly in the east-west direction while most canals on the east bank runboth in north-south and east-west directions. Most canals drain into the Chao Phraya River.Their typical dimensions range from 5 to 15 m wide and 1 to 2 m deep (JICA 1986). Thecross-sectional area is in the order of 10 m2. The discharge capacity ranges from2 to 3 m3 The main-canal dimensions range from 10 to 40 m wide and 1 to 2 m deep.The average gradient of a main canal is about 1:15 000 to 1:20 000. Their dischargecapacities range from 10 to 80 m3s1.Most of the Lower Basin areas around and including Bangkok are covered by a layer ofso-called Bangkok Dark Heavy Clay. The layer is approximately 2 m thick. This soil underyearly flooding is extremely well suited for wet-rice production. On the other hand, themain soil type of the Bangkok metropolis is a deep silty clay, 30-40 m thick (JICA 1985). Asoft clay layer extends from the surface to a depth of 10 to 15 m below MSL, with a stiff claylayer 10-15 m thick underneath. The clay layers lie on a dense sand layer, locatedapproximately 30 m below MSL. The city of Bangkok is situated overlying a multi-aquiferalluvial sequence with interbedded clayey aquitards (Foster 1993). The ground level of theBangkok area ranges from slightly below MSL to 1 to 2 m above MSL. Such low levels of19land make gravity drainage of overland flow or intense monsoon rainfalls during the wetseason very difficult.Climatically, the Chao Phraya River Basin belongs to the tropical Savannah region.Distinguished wet and dry seasons are typical in this climatic region. The area is heavilyinfluenced by the monsoon circulations. The north-west monsoon brings a dry cool air massto the basin generally from November through May. During this period, sporadic, isolatedthunderstorms may occur at the edge of the incoming air mass. Relatively small amounts ofrainfall result from such storms. On the other hand, the south-west monsoon brings a muchlarger portion of the annual rainfall in the basin. Its onset usually signifies the beginning ofthe rainy season. The south-west monsoon usually begins in May or June. It brings warmmoist air from the Indian Ocean to the area. The associated complex convective activitiesbring rainstorm systems into the area. Most rain patterns are a concentrated heavy frontalmoving storm type. The rain bands often move following a convergence zone across thefloodplain in the north-south direction during the south-west monsoon season. Therainstorms are strongly diurnal in character and often occur in early morning or evening.Later in the wet season, rains can also result from the passage of an afready degradedtropical storm or depression through the Central Plain. Such tropical storms usually occur inAugust, September and October. Since most of these systems are usually weakened over theland passage, the resulting rainfalls is much less intense than from rainstorms associatedwith the south-west monsoon. Often, they are characterized by wide-spread frontal rainbands with occasional heavy-spells. Such rains may fall intermittently for a couple of daysduring a storm passage.20Rain-making clouds over Bangkok are high water-content warm clouds, resulting fromhigh temperature and humidity of the tropical atmosphere. Thus, a small convective cloudmay sometimes produce a heavy shower. A single cumulonimbus cloud often produces ashort duration, but heavy shower. More lengthy precipitation is from cloud systems relatedto the monsoon-induced convergence zone and tropical storms. More precipitation comesfrom tropical cloud masses organized on the meso-scale with a dimension of 25-100 km(Riehl 1979). Their average area tends to be in the order of 1000 km2. The areaconcentration of rain is about 10% of a synoptic rainstorm envelope. The majority of thetropical rainstorm events are characterized by a single shower, rarely by two showers, andmost rain falls at the forward edge of the cloud. After the rain area has built up to maximumsize, heavy rain ceases within 15-30 mm. “Late precipitation” falling at a lighter rate maycontinue for an hour or more.The total duration of any monsoon rainfall in the Chao Phraya’s Lower Basin is less than9 hours. The average duration of the storm is 1 hour. Rainstorms have an average raindepth of about 30 mm. Rainstorms, except those associated with the tropical storms, usuallyoccur only once within 24 hours. They are usually followed by periods of clear sky. Mostrain falls in a short period, driven by convective activities and are strongly diurnalinfluenced. A single rain event usually accounts for the total rainfall within 24 hours, exceptduring a tropical storm passage, when it may rain intermittently for several hours. Thesediurnal patterns of rainfall are well recognized in the Bangkok area, similar to othermonsoon regions.21Rainfall events in the river basin are concentrated in the wet season. During the rainyseason, about 85% of the annual rainfall depth occurs. The rainy season in the Upper Basinoccurs from May through September. The annual rainfall in the region is about 1230 nun.The average annual evapotranspiration rate is around 1000 mm. The rainy season in theLower Basin usually occurs from mid-May to mid-October. The mean annual rainfall overthe Lower Basin is about 1340 mm with an average annual evapotranspiration rate alsoaround 1000 mm. About 80% of the annual precipitation in the basin evaporates. Incomparison, Bangkok appears to be a little wetter than the average for the surrounding area.Maximum monthly rainfall in Bangkok occurs in September. The average rain depth in thatmonth is around 300 mm. It ranges from 150 to 200 mm, in the other months of a wetseason. The annual rainfall of Bangkok varies from 900 mm to more than 2000 mm with anaverage of 1400 mm. The number of rainy days in Bangkok ranges from 90 to 130 days peryear. It should also be noted that rains in Bangkok concentrate more on the eastern side ofthe river.2.1.3 Bangkok’s FloodsMost floods in lowland river basins develop differently from ones in the upper valleys. Asingle flood wave in an upper tributary may cause a sudden flash flood locally, but it oftenhas much a smaller effect in a wider, lower branch of the main river. Floods in a lowlandriver-basin, such as the Chao Phraya’s Lower Basin, require a large accumulated excess22surface-water volume. The contribution of the entire river basin is usually needed to cause amajor flood.Regular seasonal flooding is an inherent characteristic of low-lying river basins. Floodsoverflow the banks and spread across a large area of a basin annually in the time of highwater. The Lower Basin of the Chao Phraya River is partly flooded for one-third of the yearduring the wet season. By living in a flood-prone area of the Chao Pbraya Basin, Bangkokresidents have to live with unavoidable flood phenomena. Modifications of the riverenvironment might induce an unforeseen or undesired flood response. At one time thereplacement of canals by roads was a desirable idea to planners for urban development sincethe canal right of way was publicly owned. Bangkok, like other emerging metropolises indeveloping countries, such as Jakarta, the capital of Indonesia, seems to have difficulty incoping with rapid growth. Its crowded population requires large resources to deal withinadequate infrastructures. Floodplain management often comes rather late to solve theunderlying flood problem.Technically, various factors affecting Bangkok’s floods can be identified as follows:overland inflow from the floodplain in the north, high water levels and tidal actions in themain river, topographic features resulting from land subsidence, unorganized land uses, andinsufficient drainage and heavy rainfall in the wet monsoon season. The overland flow fromthe river basin and tidal actions interfering with the river outflows were described in theprevious section. The overflow through the irrigated canals threatens the city from the northand north-east. It often occurs sometime from mid-October to December. Also, a high tidemay cause high water levels in the river to persist for a long period of time. Thus the23drainage of a low area, such as Bangkok can be difficult. High tides affecting the ChaoPhraya River and Bangkok can occur from November until the end of December. Whileflooding is necessary for rice farming in the vast area surrounding Bangkok, floods in thecapital cause disruption in the activities of urban dwellers. In the 1983 flood, about1800 mm of rainfall was recorded in Bangkok in only four months, from July to October.Rainfall in August was 462 mm, more than twice the average (191 mm). Heavy rainscontinued to fall in September and October. The entire year was an unusually wet one, with1560 mm compared to the average of 1400 mm. The whole river basin receivedconsiderable amounts of rain throughout the season. The dams upstream could not copewith the high water volume and tended to release more water to afready full river channelsdownstream. By the end of October, a tropical depression passed through the river basin andbrought more rain to the city. At the time the water level in the river kept rising andcoincidentally matched the rising tide. The drainage system of the city failed, and parts ofthe city were flooded for a long time.Other important factors that complicate the flood problem are the progressivesubsidence of the soils beneath Bangkok (Fig. 2.4) and its reduced retention and drainagecapacity resulting from rapid urbanization. The underlying foundation, the soils beneath thecity, have been sinking at an alarming rate. Through many years of excessive groundwaterabstraction for the increasing demand of water supply for the expanding city, the aquiferunderneath the clay layer becomes progressively lower. Large-scale development of theaquifers underneath Bangkok for public water supply began in 1954. The averageabstraction rate during the 1 970s was around 400 Ml d’, causing the groundwater level to24SCALE10 20 kmDepression (in m) ofpiezometric surface ofconfined Bangkok4 alluvial aquifer in 198720-40 cmb 40-60 cm>60 cmCummulativeland surfacesubsidence to 1987Fig. 2.4. Ground subsidence rates of Bangkok (after Foster 1993).decline at rates of 1-4 m yf’ (Ramnarong and Burapeng 1991). During the l980s,groundwater was a major water source of Bangkok where more than 11 000 deep wells weredrilled by both governmental and private agencies. The demand was caused by the city’sfailure to provide surface water to keep up with the rapid urbanization of the city. Theaverage rate of the groundwater abstraction in the late 1 980s was around 1400 Ml d’ (Foster1993). Besides its use for irrigation, water from the Chao Phraya River has also suppliedBangkok’s need for water supply. Its allocated quantity cannot meet the demand of the city.As a result of such excessive abstraction of the ground water, the underlying clays haveGULF OF THAILAND25consolidated and caused lands to sink. Recent land subsidence in the critical areas (alreadybelow MSL) has a maximum rate of 10 to 15 cm yr4. The rate of subsidence can be as lowas a few centimeters per year in the oldest part of the city. It reaches nearly 15 cm yf’ in theeastern suburb. A large part of eastern Bangkok has already subsided and behaves like alarge lake during a heavy flood. Some high-valued real-estate had to be diked, and the useof pump drainage was implemented. The dikes were often built by elevating surroundingroads. Thus in many areas gravity drainage is no longer possible. To alleviate the problem,the city has prohibited withdrawals of groundwater in most parts of the city for the past fewyears. Metropolitan Water Works Authority (MWWA), the main groundwater supplier inBangkok, also planned to turn its sources to surface water.Besides the land subsidence problem, the urban expansion of Bangkok also makes theflood problem worse. The extensive network of the canals is in a reduced state due to theexpansion and changing land uses. Many canals have been replaced by roads. At present,the canals account for only a little more than 1.4% of the total surface area of Bangkok(Sodsathit 1987). The road network, as a new means of transportation, has stimulated thecity expansion. The expansion has occurred radially and along main roads and highways.The spatial pattern of the development in Bangkok follows the outward expansion, causedby transportation improvements. It is also affected by the intense growth of the inner city,caused by dynamic commercial and cultural activities (NEDECO and SPAN 1985). Landuses in the inner city usually have a mixed commercial and residential pattern. Theconstruction of major highways and the extension of bus routes far from the city center havesupported highly dispersed development along major roads. Rural land uses between the26arterial roads have been adapted to the expanding urban market. The outer suburb areas areoften subjected to housing-estate and industrial-complex development. The developmentgradually replaces the irrigated rice paddies. Thus potential retention areas for excessstormwaters are reduced. Urban development also changes surface permeability of thelands. Natural soil-depressions and reduced infiltration capacity result from impervious landdevelopment. Increasing impervious areas increases run-off and reduces the time ofconcentration. Furthermore, the overcrowded population and inadequate management ofwaste intensify a problem of insufficient drainage of the area. Modification of canals bybuilding obstructions into the waterways is also a result of development. The reserved landsalong the main canals are up to 200 m wide. They are often occupied by low-incomedwellers, and more than 8000 houses are in such areas (Angel 1987). The communities hereare often suspected of interfering with the waterways and obstructing canal improvement andmaintenance. The canal capacity is reduced by the building of houses into the canals, thegrowth of water-vegetables, and garbage disposal into the canals.2.2 Flood Control Approaches2.2.1 BackgroundThrough time, various ways to tackle the flood problems in lowlands have been developedand applied. In a growing urban area, especially in the developing countries, the population27has often encroached upon flood-prone lands without appropriate town planning. Then thearea itself requires not only adequate internal drainage systems but also protection fromexternal riverine flooding. Traditional uses of hydraulic structures to “control” floods havebeen dominantly applied on rivers and their floodplains around the world. Only recently hasa “softer” concept of integrated management become increasingly popular with waterengineers and policy makers in dealing with floods.Flood controls are often classified into two broad approaches: non-structural andstructural measures. Non-structural flood control or flood management includes floodproofing and warning, land-use controls and floodplain insurance. Its goal is to alleviateexisting and future flood hazards in the most cost-effective way. It is designed to reduce theflood-damage potential of a floodplain without incurring heavy capital costs and may requireonly minor civil engineering works. Flood problems in heavily urbanized catchments couldbe treated individually within the framework of an overall integrated catchment plan. Anintegrated catchment plan provides a long-term view of a flood control policy. Structuralflood control, on the other hand, is designed to prevent or eliminate inundation offloodplains by using hydraulic structures such as reservoirs, diversions, levees, dikes, orchannel modifications. Both structural and non-structural approaches produce differentphysical impacts within the catchment and require a compromise on related social, politicaland environment issues for successful implementation. Thampapilai and Musgrave (1985)reviewed both measures in flood mitigation strategies. The combined use of non-structuraland structural measures is often considered as the best approach to tackle flood problems.282.2.2 Flood Control in Bangkok2.2.2.1 BackgroundMany approaches to flood control in Bangkok have been investigated and some have beenimplemented. Non-structural approaches have been under study in Bangkok following theimplementation of structural flood control measures. For example, land-use control iscurrently being experimented on some pilot plots of lands. The idea of flood insurance forinner high-economic valued lands (City Core area) has also been advocated. Most emphasisand investment in flood control in Bangkok have, however, been in structural measures.This is in response to the crucial experience of the past severe floods.As mentioned previously, protection against floods by the structural approach can beaccomplished by the creation of upstream flood detention reservoirs, and also by flooddiversion, channel rectification and embankments. Bhumipol (1964) and Sirikit (1974) arethe two major dams which are located upstream of the Chao Phraya River. At the time thesedams were built, it was anticipated that they would help solve the flood problem in the lowerfloodplain of the river, especially control the flood in Bangkok. Once, in operation, thereservoirs can only regulate small to medium sized floods downstream. The upstreamlocations of the dams in the Upper Basin make them ineffective in controlling floodsdownstream in the elongated catchment. This makes it difficult to manage the reservoirs,which also have other competitive demands for water. The reservoirs are used forgenerating electricity and for irrigation of the lower floodplain. Often, in a wet year, these29reservoirs are already at full or near-full capacity by the middle of the wet season when therain starts to shift to the lower floodplain. This time of the year coincides with high water inthe river and high tides. If heavy rains continue in the upper valley, possibly due to passageof a tropical storm, excess water may have to be released from the reservoirs. The excessrelease complicates the situation of Bangkok’s flood when the high tide, heavy local rainfalland high river water all occur at the same time. To better regulate the floodwater in theLower Basin, a new reservoir has been planned in the Pasak River which merges into theChao Phraya River at Ayutthaya. In the Greater Bangkok area, large available public pondsand the farmlands to the east of the capital are used as retention areas. The large canalsystem is also used for storage of floodwater.Flood diversion and channel rectification have also been investigated as an alternative tosolve the flood problem in Bangkok. The channel diversion scheme was first introduced toby Litchfield, Whiting Browne & Associates, and Adams, Howard and Greeley in theirreport on urban planning for Bangkok (Litchfield & Co. 1960). It was, in fact, the firstflood-control design for Bangkok. Two diversion canals, one on each side of the river, wereproposed for flood control (Fig. 2.5). They were to cut from the Chao Phraya River north ofBangkok to the Gulf of Thailand. However, this part of the plan was rejected by thegovernment. Later, similar plans were brought up again after the great flood of 1983. TheChao Phraya-2 project (MT 1986) was proposed following the fmdings from the FloodRouting Alternative (By-pass) project (MT 1985) which concluded that a flood diversionthrough the existing waterways on the east bank was not economical or effective. In theChao Phraya-2 project (AlT 1986), a diversion channel (capacity of 2000 m3 s’) on the west30bank was proposed with a length of approximately 60 km. A diversion control was to beinstalled at Pak Kret, just north of Bangkok. Also, a group of sophisticated tidal barriers andpumps with capacity of at least 1600 m3 s had to be built near the mouth of the river.Water levels at Bangkok could then be kept near the mean sea level. The proposed planshould eliminate the need for smaller pumps along the main canals or river. Both sides ofthe river still require embankment works. The west bank embankment was to be created bysoil materials from the excavation. Although the river diversion scheme seems to betechnically viable and economical, it cannot be put in place because of the huge investmentrequired and the political problems that would result from the large land procurement. Thus,the river-diversion scheme is considered to be impractical by many.Fig. 2.5. River diversion schemes.Gulfof Thailand1—Litchfield Diversion Plan (Litchileld & Co. 1960)2—Flood Routing Alternative (By-pass) Plan (AlT 1985)3—Chao Phraya 2 River Diversion Plan (AlT 1986)31The flood control schemes which have been implemented in Bangkok have been usingthe polder system. This allows a phased-development of protection. The polder system ofBangkok has been developed over many years. Its first design was proposed in 1969 byCamp, Dresser and Mckee Inc. (CDM 1969). The total protected area under the plan was370 2 The plan was only partially implemented due to insufficient funding. However,other later developments in flood control for the city have mostly used polder control.2.2.2.2 Folder Flood ControlA polder is usually created to isolate an area from exterior high water levels. It permitscontrol of water levels in the interior drainage system by drainage facilities (Fig. 1.1). Abasic polder system consists of a peripheral flood barrier high enough to prevent theoverflow of floodwater from outside the protected area. It has at least one boundary whichconnects to a waterway. Drains, sluices, gates and pumps control the excess surface waterand seepage inside the protected area. The excess water is discharged into either a canaldirectly connected to open water or a so-called, reservoir system. The system can be asimple or more complicated network of canals. By dividing the flood-prone land intoseveral polders, a phased development of flood control for the protected land can beplanned. Different water level controls can be adapted to each polder environment and thepriority of flood protection in each polder can be determined. Polder designs can beclassified into two broad groups: small multi-polders and a large polder (JICA 1985). Inthe small multi-polder design, a main pump is located at the lowest point of each polder.32The water level in the main canal is controlled by the river itself. In contrast, main pumps inthe large-polder design are located near the river. The water level in the canal is thenmanipulated by the pump and/or control gate discharge.An urban Bangkok polder is characterized by its large population, intensive land-useand expensive price of lands. The flood protection has given greater focus to the morepopulated, urbanized, eastern section of the city. The river embankment on the east bankcan be viewed as a large enclosing dike. The long earthen-dike along the north and east ofthe city effectively helps create a large polder surrounding Bangkok. Small multi-polders ofthe City Core project (Fig. 2.6) have been operated for the more sensitive inner city. Thepolder approach used in the eastern Bangkok suburb (Fig. 2.7) followed the large polderapproach. It consisted of a large outer polder and smaller inner polders. The outer poldersystem protects the city area against overland flows from the northeast area and floodingfrom the Chao Phraya River. The inner polder system protects high-priority areas, inside theouter one. Pumping and gate stations in the system consist of main stations, sub-stations andmobile units. Flood barriers consist of roads, highways, railway walls, dikes and floodwalls. Extensive dikes, both concrete and earthen, have been constructed throughout thecity. The long, earthen dike (King’s dike) in the north and northeast section of the suburb ofBangkok was built to prevent the overland-flows.33] PUMPING STATION() POLDER NUMBERI 1OT,5S 1OYEARSRETURNPERIODOF WATER LEVEL ANDEXPECTED LAND SUBSIDENCE5 YEARS RETURN PERIOD OFRAIN STORMFig. 2.6. City Core project’s polders (after AlT 1986).34‘:“—7..i;v.’/7 V NL,. -:-.J RG II) / i--.. __.J..H — - RG R/ ‘1 I‘—. / %..$ . ,1/‘I f / I / :i .1 RGL.RGç cr,i‘‘iJ_ RG___f-_, iJ I . L.’, --I - • .. .-----i. / --. - -... I ...,.I--rz7-ç’q•’ /_I)•••/; 7.:..tz:__*.1/ \ 4z._ i// ‘y) / EASTERN SUBURBIi / ...• %-. 1 POLDERS® PUMPiNG STATION REGULATE GATEA CONTROL GATE EMBANKMENTPOLDER NUMBERFig. 2.7. Eastern Suburb project’s polders (after JICA 1986).352.2.2.3 Flood Control DevelopmentVarious flood protection proposals have been considered by the city administration after thegreat flood of 1983. At least 13 flood studies or proposals have been made (Fig. 2.8).Different agencies and engineering consulting firms, with diverse flood-control expertise,were hired to prepare such studies. The proposals were designed to protect Bangkok from aflood with a 100-year return period. The design-tide was for a 100-year return period, andthe design-rainfall for a 2-year return period. The area to be protected was about 1400 km2.Most proposals could be broadly classified as a river-diversion, land drainage, or a polderscheme.1—City Core (NEDECO)2—Eastern Suburb (JICA)3—Samut Prakan (TISTR)4—Thonburi-Samut Prakan (NEDECO)5—West Bank (Tawee Wattana) (AlT)6—Green Belt (King’s)7—Canal Improvement Zone (RID)8—Nonthaburi Flood Protection (RID)9—Chao Phraya-2 (AlT & TAC)10—Flood Routing Alternative (By-pass) (AlT)Fig. 2.8. Various flood protection and related studies and proposals.Gulf of Thailand36As mentioned previously, most actual flood control works follow the polder concept.Thus, land drainage has been the focal point of the flood control in Bangkok. Canals havebeen significantly improved in their storm conveyance capacities. Embankments along theChao Pbraya River from the north of Bangkok were constructed to extend to the coastline ofthe Gulf of Thailand in Samut Prakan, south of Bangkok. Some lands are used forstormwater retention. Many pumps and gates have been installed in main canals and somesecondary canals next to the river.To control overflows from the north and northeast of the city, long earthen dikes werebuilt along the north and east outer boundaries of the city. The overflows are to be routedthrough the improved existing canals southward to the Gulf of Thailand. The designdischarge was estimated at 75 to 100 m3 s’. Parts of agricultural lands in the farther, easternareas of Bangkok were designed to serve as the retention areas.The area between the long earthen dike and the more populated city core, or the easternsuburb area (260 km2)where the heaviest damages occurred in the floods of 1983, was dikedinto three large polders and one inner polder. The protected area is divided into urban andrural areas. The urban section is drained by pumps. Farther east, in the rural outer areawhich is considered as lower-valued land, flooding is allowed to occur, leaving the area withpoor drainage and as a retention area. A few main pump stations in the canals next to theriver were built in addition to more than 10 tidal gates along the river.In a dense business area of 92 km2 in the inner city, flood protection works are moreextensive (City Core project). They were built following the reviewed and updated design ofthe multi-polder, CDM plan. The area was divided into eight polders. About 50 km of37flood barriers were built, as was a drainage conduit of 12 km. New pumps and gates werealso installed.On the west bank of the Chao Phraya river, where the population is less dense, the floodcontrol facilities were built following the multiple polder approach (NEDECO and SPAN1987). The total protected area was 135 1cm2, with the majority of the land beingagriculturally related. A total of 108 km of flood barriers were built to form multi-polders inthe area. Pumps with a total capacity of 125 m3 s1 and 45 regulators were installed.2.3 Approaches to Flood Control Operation2.3.1 BackgroundThe focus of real-time operations in Bangkok’s flood control is mainly in pump/gateoperations. Pumps are an important component of the polder system because of the flatnature of the floodplain. Though the cost of pumping during a risky storm event is often farless than its potential flood damages, the long-term cost of operating and maintaining pumpsis relatively high. The city’s flood control planners and engineers realize there is potentialfor the improvement of the system by adjusting the pump operations. Improving the realtime operation of main pumps should reduce the over-all cost of flood control. The presentrules for operating pumping stations involve pre-determined set-levels. If the water level ina canal upstream of the station exceeds its set level, the pumps are started. When it fallsbelow, they are stopped. Although such strict rules are easy to follow, they have been found38to be insensitive to a storms’ pattern. Thus, to improve the operation, a more responsiveoperating policy is sought to replace the current one. The current available technologies onreal-time flood control have been investigated. One of the alternatives is to automate thewhole drainage system to attain an optimal performance. This involves the use of amathematical model to simulate behavior of the system, flow forecasts and the use ofvarious optimization techniques. The goal is to create an optimal operation by a globalcontrol approach.Global control is a centralized control in which a control center is established todetermine the appropriate operation actions for various points in the system. The globalcontrol can be a manual, supervision, or automatic control. There has been research inimproving global control in combined sewer overflow (CSO) problems. A main objective isto equalize the spatial utilization of stormwater storage within a large distributed, networksystem of sewers (e.g., Neugebauer et a!. 1991).In flood control, engineering designs and controls are normally aimed to maximize anexpected utility function. This approach is well defined if uncertainty can be handledproperly, or the environment is not under stress. In a real-time operation, a control situationoften differs from those used in design. Optimal operation can be achieved only if theforecast flows are accurate and reliable. Usually, control decisions have to be made withlimited time and information. The decision environment is often under stress. In thissituation, operators are more likely to seek a conservative path to ensure that they can adjustthe control in the next time step. This tendency reflects a long practice in engineering indealing with the uncertainty. Engineers like to “bound” their uncertainty in making39decisions or design and then add a safety margin instead of optimizing to minimize expectedcosts.A review of literature in water resources has indicated the slow acceptance of theoptimal operation goal by field operators in practice. Despite advances in the theory ofmathematical optimization and modeling, many water resources systems are still operatedmanually. Only a few of the large research studies of optimization in water resources havebeen directed to real-time operations. The Task Force on CSO Pollution Abatement ofWater Pollution Control Federation (WPCF 1989) and the Urban Water Resources ResearchCouncil (ASCE/WEF 1992) reported that most existing real-time controls of combinedsewer systems relied primarily on manual manipulation of the systems. Control decisionswere based on the visual inspection of telemetered data. Mathematical optimization modelswere not widely used for automatic control of such systems. Recently, Ormsbee and Lansey(1994) noted that there were severely limited practical applications of mathematicaloptimization techniques in generating policies for water-supply pumping systems. Similarconclusions of limited applications in practical operation were drawn earlier by otherresearchers, especially Yeh (1985) and Wurbs (1991a). Georgakakos and Yao (1993)indicated that the majority of reservoir operators did not usually seek a control policy thatstrictly followed an optimal path. Moreau (1991) noted that a reservoir operator in a watersupply system often operated the system with a goal to reduce the risk of a “worst case”condition to an acceptable level. He also suggested that the failure by many models toaddress the risk and uncertainty arising during operation might be a cause of the slowacceptance of the techniques. Orlouski et al. (1984) concluded that most reservoir operators40tended either to be risk-averse decision makers or to follow pre-determined, well-documented rules of operation. They inclined to choose a conservative path to reduce theirliability. Very often, operators focused their attention and efforts to avoid dramatic failureswhen the system was under stress. In many real-time operations of flood control systems, ahierarchy of simple rules of operations is still used extensively. Common hierarchies ofoperating rules includes rule curve, release schedule, and operating constraints. A rule curveis defined by elevations in a reservoir which define ideal (desirable or target) storagevolumes and provide for release rules specified as a function of storage content (Wurbs1991 b). Rule curves are typically expressed as a pool elevation-time diagram. A releaseschedule is composed of sets of rules or curves of releases for various inflows and amountsof remaining storage available. Operational constraints define the limit on release decisions.They may include the minimum required release, the maximum allowable release, and others(Yazicigil et al. 1983). The use of these hierarchies of operating rules offers a greater senseof security to a flood control operator in making a decision. An operator will be relievedfrom any blame if the system fails as long as he or she follows the pre-set rules. Operationunder a strict set of operation rules may, however, be inflexible. While an operation using afixed rule may be able to deal with a major flood, it may miss an opportunity for reducingflood damage during more ordinary floods.In the polder flood control, the emphasis is on the main pump control of each polderunit. The philosophy ofpolder flood drainage is to divide the area into small, independentdrainage management-units that can be assigned priority of flood protection. Thus, thecontrol here can be dealt with as a local control. The main objective of pump control of the41polder is to reduce the long-term, operating time and hence cost of the pumps, yet avoidflooding of the protected area as long as pump capacity is available. This can be achieved bymanipulating the pump control strategy during the storm. All potential storage capacity ofcanals and retention within the polder should be fully used. Thus, the operation is similar tothat of a single reservoir. Current practice in reservoir operation should provide insightsuseful topolder operation.The use of optimization techniques in reservoir operation has been reviewed by Yeh(1985). Although various optimization techniques have been applied to the long-term aspectof reservoir operation, very few have been applied to the real-time operation. Thedependence on accurate forecasts makes the techniques less applicable to practical real-timeoperations. Sophisticated control systems linked by radio or land-line telemetry monitoringand operated by computers also lack the robustness and comparative simplicity of localcontrols (Hall et al. 1993). Wurbs (1991 b), in his review of reservoir operations under theU.S. Corps of Engineers, noted dominant use of pre-specified rules of operations. Rulecurves and regulating schedules are among the most prevalent rule structures commonlyused in reservoir operations. Some detailed discussions on rule curve construction can befound in Toebes and Rukvichai (1978), USACE (1987), or Votruba and Broza (1988).422.3.2 Bangkok’s PracticeUsual procedures of the city in preparing for drainage operations during floods are asfollows. Before the rainy season, storm-sewer conduits are cleaned up and repaired. Canalsmay be dredged. Plants and garbage in the canals are removed. This waterway cleaningcovers all the urban areas before the first rainstorm.In a wet season, Flood Control Operation Center under the Department of Drainage andSewerage (DDS) of BMA operates fully. During a rainstorm, the center will act as a maincontrol and monitoring center. It supervises, controls and plans the flood operating system.The center coordinates various agencies involved, and issues necessary operational policiesor guidance to pump/gate operators. The center receives real-time weather information,provided by the Meteorological Department. The department controls a radar and rain gagenetwork. Although, a dense network of rain gages over the city exists, most of these gagesare non-automatic. Moreover, the water-levels and tidal conditions are processed by RID,Hydrographic Department and BMA. Monitoring and inspecting teams are sent out toobserve flood situations and conditions of dikes. The hydrological information andmonitoring data are transmitted to the center. A group of senior experts at the center willdetermine a specific operational plan besides a pre-determined one. The pre-determinedplan is to be modified based on real-time information on hydrological, meteorological andflood situation data. Gate and pump operations during a storm event usually follow a predetermined rule. The operation can, however, be overruled by the center. The underlyingdrainage approach is that the canals should flow by gravity, through open gates when the43river is at a low stage. When the river stage is too high to permit gravity flow through thegates, the gates are closed, and pumping is required. For a normal operational procedure,DDS issues pre-determined operating orders to each pump/gate station. The orders requirethat the water level in the reach of the canal upstream of the station be maintained at somepre-set level. Different levels are used for dry weather, a storm, or a cleaning-flushingperiod. The central control coordinating group decides whether the standard operatingorders should be modified based on continuously updated hydrological information. Thecurrent overall flood control operation, thus, depends upon the personal knowledge of thesystem by a few key people.2.4 Alternative Way to Improve the Existing Flood ControlOperationsThe above discussion indicates that a greater amount of refinement of the mathematicaloptimization techniques is needed for real-time operation. However, the persisting use ofrule-curves also suggests an importance of uncertainty which is an influence in real-timecontrol. Pursuing the “academic” approach to the automated global control does not have agood chance of being utilized in practice. Alternative local control that includes sometreatment of uncertainty in operation may be more appropriate. This study of the floodcontrol operation seeks to find such alternatives.44A relatively new concept, fuzzy logic, was tested to see if it could improve on theexisting strict rule curve operation. Due to difficulties in accessing real flood controloperational data for testing the new concept, a simple simulating model was chosen in orderto justify further investigation of the application of the concept. Once the concept wasproven satisfactory, either the flood model can be improved and calibrated with the polderenvironment, or available field data can be sought and collected once the operators concerncould be convinced by the results. The following chapters (Chapter 3 and 4) concentrate onthe fuzzy concept and the extension technique of fuzzy programming proposed in the study.Chapter 5 describes the numerical experiments conducted. Chapter 6 discusses the resultsand is followed by the last chapter, conclusions.453FUZZY LOGIC3.1 BackgroundFuzzy logic is a multi-valued set theory. Fuzzy logic theory and the word fuzzy as atechnical term were first introduced by Zadeh (1965). Since then, the fuzzy logic concepthas been applied in various fields. In principle, fuzzy logic can be used to model anycontinuous system in engineering, physics, biology or economics (Kosko and Isaka 1993).Many of the applications of fuzzy logic have been in control engineering. This branch ofapplications is often called, fuzzy logic control (Lee 1990; Zimmermann 1993). Someexamples of applications include: auto-focus control in cameras and camcorders; loadingcontrols in washing machines; braking-controls of high-speed trains; and process controlsfor cement kilns. A short background on fuzzy logic as an estimating tool, as it is used forthis study, is given here. A complete description of fuzzy logic can be found in many textbooks (e.g., Kosko 1992; Terano et al. 1992).The initial use of fuzzy logic control was based on the expert system approach. In thisapproach, control of the system can be implemented using several operating rules. The rulebase is usually extracted from operators’ control patterns or from verbal rules describing thesystem. The fuzzy system, thus, facilitates qualitative or linguistic representations of an46expert’s knowledge. A fuzzy system can also be used to relate sampled input to output datafrom a system. It then estimates output values of the system based on such relationships andnew inputs. In this way, the fuzzy system performs the same function as statisticalregression or neural networks. However, unlike most other black-box system approaches,such as statistical regression, a fuzzy system estimates an underlying function withoutactually modeling the input-output relations. This approach can be considered as a mode/free estimation.Applications of fuzzy logic in either expert system or model-free approaches takeadvantage of the ability of fuzzy logic to describe a phenomenon or an object as partiallybelonging to one or more sets rather than being completely in or out of a particular set.Uncertainties describing vagueness of an event can be modeled. Although fuzzy logic dealswith vagueness, the logic itself is based on fuzzy set theory, a mathematically rigoroustheory. A fuzzy set is an extension of a conventional crisp set. A crisp set only allows full1.0I0Fig. 3.1. Diagram of crisp characteristic membership function.NOXe X47membership or no membership at all for any element (Fig. 3.1). A fuzzy set allows,however, partial membership for an element. For example, a man whose height is 6.3 ft canbe considered to be either tall or about average (Fig. 3.2). The characteristic membershipfunction in classical set theory which posses precise binary definition (i.e., membership of 1for an element in the set and 0 for an element outside the set) is replaced by the membershipfunction. It defines the membership value for each member of the fuzzy set. Themembership function represents the degree to which a variable with a specific value belongsto a fuzzy set. It can be any shape, such as triangular, trapezoidal or bell-shaped functions.One of the most convenient and computationally efficient shapes for the membershipfunction is the triangular one as shown in Fig. 3.2. The number of fuzzy categories intowhich the range of a variable (universe of discourse) is divided usually is between 3 and 10.The more categories, the greater the accuracy possible (Jordan 1991), but the greater thecomputational burden. If there are n variables and C fuzzy categories, then the number ofrules in the complete rule base is U.AVERAGETALLFig. 3.2. Example of fuzzy membership functions. (Crisp variable X = 6.3 has amembership in TALL of 0.7 and AVERAGE 0.3).1I I0 5.0 5.75 Height (fi)48Since most fuzzy logic applications were initially developed from expert systems, thestructure of the fuzzy system is largely influenced by the approach of an expert system. TheIF-THEN rule-base structure, used widely in expert systems, is also adopted in building thefuzzy system. For example, in a two-input, one-output crisp expert system, the rule basedstructure is of the form:IF X1 > 100.0 AND X2 = 65.0 THEN Y = 40.0IF X1 > 35.0 AND X2 < 10.0 THEN Y = 120.0Typically the values of the variables to describe the system are crisp (e.g., 78.2, 24.0), andonly one rule is “triggered” or “fired” at a time. In contrast a fuzzy system rule base takes theform:IF X1 IS LARGE AND X2 IS MEDIUM THEN Y IS MEDIUMIF X1 IS MEDIUM AND X2 IS SMALL THEN Y IS LARGEwhere SMALL, MEDIUM, LARGE are fuzzy set variables or categories.To operate with a fuzzy system, the fuzzy rule base first has to be set up. Inputs to thesystem, which are typically crisp numbers, have to be “fuzzfled”, that is transformed intofuzzy variables with associated membership values. Typically each crisp input can beassigned membership in two fuzzy categories, as illustrated in Fig. 3.2. These fuzzycategories trigger a number of rules. For example, if there are 2 inputs, this will lead to 4rules being triggered at a time, as illustrated in Fig. 3.3. The rules then have to be givenweights through a process of “input inference”, combined through a process of “outputinference” and reduced to a crisp output by “defuzzWcation “.49Membership Membership1.0ValueInput variable are X1 and X2. Output variable is Y.Rules triggered by specific values ofX and X2:IF X1 IS MEDIUM AND X2 IS SMALL THEN Y IS SMALLIF X1 IS MEDIUM AND X2 IS MEDIUM THEN Y IS MEDIUMIF X1 IS LARGE AND X2 IS SMALL THEN Y IS MEDIUMIF X1 IS LARGE AND X2 IS MEDIUM THEN Y IS LARGEFig. 3.3. Illustration of the fuzzflcation of crisp input values ofcorresponding rules triggered (other rules are not shown).X1 and X2 andThe justification for this elaborate process for transforming a set of crisp input values toa single crisp output is that it allows a smooth response in output to changes in the inputs.Although there may be relatively few fuzzy categories for each input and output variable, thefact that several rules are in operation at any one time and that membership values and ruleweights change smoothly with changes to the input variables results in outputs that alsochange smoothly. Kosko (1993) shows that with fuzzy categories, the output from anyfunction can be modeled to any required degree of accuracy by a fuzzy system.Transforming a set of inputs into an equivalent output can be decomposed into inputinference and output inference. Input inference performs the set operation of matching thefuzzUled input values to the antecedent parts of the IF-THEN rules. The weight or firingstrength of the rule triggered is then computed by combining the membership values of its50input variables. The combination can be done by various ways, including product, minimumor average among many other set operators (e.g., Drainkov et al. 1993). Input inferenceusing the product operator calculates the firing strength of a rule by multiplying themembership values of the input variables within their fuzzy categories (Fig. 3.4). For eachindividual rule, input inference gives the firing strength of its rule.Membership Membership1.0Example of rule triggered:IF X1 IS MEDIUM AND X2 IS SMALL THEN Y IS SMALLInput Inference Product Minimum AverageRule’s Firing Strength 0.56 0.7 0.75Fig. 3.4. Input inference of the example fuzzy rule.To derive the corresponding fuzzy output for each rule, output inference is needed.Most approaches use either the clipped or the scaled inference technique (Fig. 3.5). Theclipped output method is usually associated with the “minimum” input inference operator. Itclips the membership function of values greater than the minimum input membership value.On the other hand, the scaled inference method scales down the corresponding outputmembership function by maintaining the original support of the membership function. This51scaled method of output inference is often associated with the “product” input inferenceoperator.0.7 ClippedRule’s Firing StrengthFig. 3.5. Output inference on Y for the example rule. A). Clipped. B). Scaled.To obtain a single crisp output, as is usually required for operating purposes, the scaledor clipped fuzzy output values have to be transformed to a precise crisp value bydefuzzjflcation. Many defuz4flcation processes have been introduced. These includeCenter-of-Area (COA), Center-of-Sum, Height, Mean-of-Maximum (MOM) and many others.LARGEI I.:4, OutputCrisp OutputCommon area taken onceFig. 3.6. Center-of-Area (COA) defuzzification.A) Membership MEDIIJM B) Membership MEDIUM0.56Rule’s FiringScaledMEDIUMI I1.001Largest weight ofI rule triggered withjoutput LARGE’52The Center-of-Area (COA) is probably the most widely used defuzzjfIcation strategy(Fig. 3.6). It computes the center of gravity of the area under the weighted fuzzy outputs.This method can be used with both clipped and scaled fuzzy output values.The Center-of-Sum differs from the COA only in that it computes the contribution fromeach membership subset independently. The darkened area in Fig. 3.6 is taken twice for theweighting of the output. It is usually used with the clipped method of output inference.The Height defuzzification method represents each output category by the value atwhich its membership is 1.0 and weights each output membership function by its peak valueas determined by the output inference values, determined by either the clipped or the scaledmethod (Fig. 3.7). With this technique, the output categories are essentially represented bysingleton fuzzy sets, i.e., crisp numbers.1’. =where Y*: the final crisp outputY: the crisp value whose fuzzy membership equal 1.0h: the rule’s firing strengthn: the number of fuzzy outputs according to rules fired.Fig. 3.7. Height defuzzification.2nd Rule’s:0 Outputyl533.2 Fuzzy System as Model-free EstimatorThe above discussion of a fuzzy system is based on its development through the expertsystem and control engineering perspective. An important new development in fuzzy logichas recently been the shift from expert system and control perspectives to estimating. Thefuzzy system can also be considered as a black-box or model-free estimating system (Kosko1992). This is the way in which it is used in this thesis. The principle and structure of thesystem remain the same. The emphasis here is on building the rule base for the estimatingsystem based on training data, similar to the neural network approach, rather than obtainingthe rules from an expert. The process of setting the rule base is called “fuzzy mapping”, thatis mapping the input fuzzy set to the output fuzzy set. The advantage of fuzzy mapping isthat it relies on actual data, but gives more insight and understanding of the process than aneural network, which is truly a black-box system. The fuzzy system avoids usingcomplicated mathematical modeling by using symbolic variables and the influence path ofthe decision variables can be traced. In fuzzy mapping, the concept of Fuzzy AssociativeMemory (FAM), that is a way of storing the relationship between fuzzy input and outputvariables, is used as a translation device between inputs and outputs. FAM’s map fuzzy setsto fuzzy sets. Fuzzy associations or “rules” associate output fuzzy sets with input fuzzy sets,thus behave as associative memories. The fuzzy associations can be written as antecedentconsequent pairs or IF-THEN statements. Each FAM rule defines a patch in the inputoutput state space, and the fuzzy system approximates the unknown function by covering itsdomain with FAM-rule patches. The FAM rules can then form the skeleton of a fuzzy54system. In general the FAM system consists of a bank of different FAM associations. Eachassociation corresponds to a different numerical FAM matrix, or a different entry in alinguistic FAM-bank matrix (Kosko 1992). One of the drawbacks of the fuzzy system is thatwhen the number of fuzzy variables or fuzzy subsets increases, the FAM’s also increase anddimensionality becomes a major computational problem. A compromise between thenumber of fuzzy variables and their partitions into categories, has to be reached in buildingup a FAM for fuzzy mapping.In this study, the FAM system is used as a mapping mechanism to relate input-outputtraining data. From the mapping, the required output, in this case the required storage in thepolder system can be derived.As discussed earlier, there are many alternatives in the input inference, output inferenceand defuzzfication processes. Computational demands also dictate the design of the fuzzymapping system. After some preliminary trials with the main problem in the study, somesimple numerical experiments were carried out to help understand the processes ofcomputing with and building a fuzzy mapping system. Number of rules required, choices offuzzy set partitions, robustness of the system and a practical way to derive rules were thesubjects of interest here. These experiments are described in the next chapter.554EXPERIMENTS WITHFUZZY LOGIC PROGRAMMING4.1 GeneralAs outlined in the previous chapter, there are several steps involved in computing therequired output from the set of inputs in an operating fuzzy logic programming system.Typically the inputs and outputs are in the form of crisp numbers. The steps are: inputinference to convert the crisp inputs to fuzzy categories with associated membership values;output inference to combine the membership values of the variables in the rules triggered;and defuz4fication to convert the set of fuzzy outputs from the rules triggered to a singlecrisp output. There are several alternatives to each of the above steps, leading to a largenumber of alternative combinations for the process as a whole. There is no theory orgenerally accepted rules to say which of the alternatives is best, although some alternativeshave been more widely used than others. After some preliminary trials with the mainproblem in this study, a set of numerical experiments were carried out to compare thevarious alternatives in order to determine the most effective method.56The experiments, which are described in this chapter, involved the use of three examplealgebraic functions, with increasing degrees of non-linearity. These are:1) Y=X+X28.O2) Y = X12.X123) Y = X1.X2/(X +X2)°85The first function is linear; the second is non-linear but monotonic and is judged to besomewhat similar to that used later in this thesis for flood control; and the third is arbitrary,but quite non-linear. Each function has two independent input variables and one dependentvariable. With each test function, three methods of input inference: product, minimum andaverage were tried; two methods of output inference: clipped and scaled were tried; and twoconventional defuzzflcation techniques: Center ofArea (COA) and Height were tried. Twomethods for setting up the fuzzy rule base were examined: using accurate values of the inputvariables; and developing FAM’s (Fuzzy Associative Memories) from sets of training dataobtained by randomly generating values of the input variables and computing thecorresponding output values from the test functions. Other experiments involved testingvarious ways of weighting sets of training data to develop the most accurate FAM’s and tocheck the robustness of the fuzzy system approach.574.2 Experimental ProcedureIn all the experiments, triangular membership functions were used for both the input andoutput variables, that is the membership functions were identical sets of symmetrictriangular shapes as shown in Fig. 4.1. The triangular membership functions were chosenbecause of their simple structure and wide use in other fuzzy systems, the computationalease of calculation, and minimal storage requirement.As explained in the previous chapter, the more fuzzy categories used in the membershipfunctions, the more accuracy the estimates can achieve. But this is also associated with morerules and greater computational complexity. Five categories are generally accepted asadequate. In the experiments, the input variables were divided into 5 fuzzy categories, andoutput variables were divided into 5 and 9 fuzzy categories (Fig. 4.1 and Fig. 4.2).A).Y=X,+X2+8.0 [ B).Y=X,2X”N2 Ni ZE P1 P2 Si S2 S3I.-10.0 -5.0 0.0 5.0 10.0X- VariableC). Y =X1*X2/( ,+)°’Si S2 S3 S4 552.0 4.0 6.0 8.0 10.0X -Variablea.IINPUT FT JZZYMEM1ER SHIP FIJNCTTONS0 1.25 2.5 3.75 5.0X-VariableFig. 4.1. Fuzzy membership functions of inputs X for the test functions.58Rule bases were constructed based on known outputs calculated directly from the testfunctions (Section 4.3) and from the randomly generated training data (Section 4.4). Afterthe rule bases (e.g., Table 4.1) had been set up, the more widely used methods of inputinference, output inference and defuzzfIcation were tested. The tested input inferenceoperators were average, minimum and product operators.A). Y =X1+X28.0OUTPUT FUZZY MFM1WRWP F11NCTTON1 Ti T2 T3 T4 T5 T6 T7 T8 T9I.B). Y = X,21120.0 40.0 80.0 120.0 160.0 200.0 240.0 280.0 320.0Y-VariableC) Y = X,X2/(X, + X2)°’5 ZE P1 P2 P3 P4 P5Fig. 4.2. Fuzzy membership functions of outputs Y for the test functions.Y-variable0 0.75 1.5 3.0 4.5 6.0Y-Variable59TABLE 4.1Fuzzy Rule Base in the Conventional Form for the First Test FunctionIF X1 = P1 AND X2 = ZE THEN Y = T6(P1, ZE, etc. are fuzzy input categories as shown in Fig. 4.1 (A);T6, ..., etc. are fuzzy output categories as shown in Fig. 4.2 (A)).Fuzzy Rule Base Used in the Direct Method for the First Test FunctionNote:V = X+X2+8.O Fuzzy Input Categories: X2N2 Ni .•ZE P1 P2-12.0 -7.0 -2.0 3.0 8.0-7.0 -2.0 3.0 8.0 13.0-2.0 3.0 8.0 13.0 18.03.0 8.0 13.0 18.0 23.08.0 13.0 18.0 23.0 28.0For example, IF X1 = P1 AND X2 = ZE THEN Y = 13.0.(P1, ZE, etc. are fu.zy input categories as shown in Fig. 4.1(A)).xliR’ za,iNote:For example,TABLE 4.2xl60An extension of the Height method was developed in the course of the trials. Instead ofhaving a single fuzzy output associated with each rule, a weighted combination of two fuzzyoutputs per rule was allowed. Then it was realized that a weighted combination of two fuzzyoutputs was mathematically equivalent to a single crisp output, as illustrated by Fig. 4.3.This is called the “Direct” method. The Direct method fuzzy scheme required weightedoutput values—a single crisp value for each rule as shown in Table 4.2.REGULAR FUZZY RULE STRUCTUREinputs outputI I 1ISingle Fuzzy CategoryLXL ‘ x2”,JA:ILDIRECT METHODWeighted Combinationof 2 Fuzzy CategoriesSingle Crisp Value *WIYI + WIY2________ ____________wI+w2Fig. 4.3. Development of the Direct method’s rule structure.inputs outputA’-0 X2DELOPME OF TI DIRECT FUZZY METHOD + output0.7 4’0.3__ __ __ __ ___0614.3 Setting up the Rule Bases from Known Output FunctionsTo set up the “accurate” rule base, values of the output Y were computed for 25combinations of the input variables X1 and X2, which have memberships of 1.0 (i.e., valuesof Xi and X2 of -10.0, -5.0, 0.0, 5.0 and 10.0 for the first test function). When the values forX1 and X2 each have membership of 1.0, only one fuzzy rule is triggered at a time, and hencedo not trigger other rules. The output fuzzy category for each rule is the category in whichthe computed output Y has the largest membership value. For example, in the first testfunction, Y = X1 + X2 + 8.0, if X1 = 5.0 and X2 = 10.0 then Y = 23.0, with maximummembership on fuzzy output category T8. Or, in the second test function, Y X12.X12,ifX1 = 2.0 and X2 = 4.0 then Y = 8.0, with maximum membership on fuzzy category Tl.Two more sets of fuzzy rule bases were constructed for the second and third testfunctions. They were shown in Tables 4.3, 4.4, 4.5 and 4.6. Once the rule bases had beenset up, similar tests on the various alternatives for input inference, output inference anddefuzzflcation were performed. One thousand sets of 25 random combinations of values ofX1 and X2 were generated, and values of the output Y were computed for each of thesecombinations of Xi and X2 by the various alternative fuzzy programming methods. Thecomputed values of Y were compared with values computed directly from the test function.Standard errors were computed for 3 test functions, and results are discussed in Section 4.5.62TABLE 4.3Fuzzy Rule Base in the Conventional Form for the Second Test Functionv =xi2.x1 Fuzzy Input Categories: X2Si S2 S3 S4 S5Si Ti Ti Ti Ti TiS2 T2 T2 T2 T2 T2X1 S3 T2 T3 T3 T4 T4S4 T3 T4 T5 T6 T6S5 T5 T6 T7 T8 T9Note: For the explanation of terms used, see note in Table 4.1 and Figs. 4.1 (B) and 4.2 (B).TABLE 4.4Fuzzy Rule Base Used in the Direct Method for the Second Test FunctionV =X12.X’ Fuzzy Categories: X2Si S2 S3 S4 S5Si 5.7 8.0 9.8 11.3 12.6S2 22.6 32.0 39.2 45.3 50.6X1 S3 50.9 72.0 88.2 101.8 113.8S4 90.5 128.0 156.8 181.0 202.4S5 141.4 200.0 244.9 282.8 316.2Note: For the explanation of terms used, see note In Table 4.2 and Fig. 4.1(B).63TABLE 4.5Fuzzy Rule Base Used in the Conventional Form for the Third Test FunctionY=X1’2/( +X2)°85 Fuzzy categories: X2Si S2 S3 S4 S5Si ZE ZE ZE ZE ZES2 ZE P1 P2 P2 P2Xj S3 ZE P1 P2 P3 P3S4 ZE P1 P2 P3 P4S5 ZE P1 P2 P3 P4Note: For explanation of terms used, see note in Table 4.1 and Figs. 4.1 (C) and 4.2 (C).TABLE 4.6Fuzzy Rule Base Used in the Direct Method for the Third Test FunctionV X1.X2(X +X2)°85 Fuzzy Categories: X2Si S2 S3 S4 S5Si 0.0 0.0 0.0 0.0 0.0S2 0.0 0.74 1.36 1.7 1.92X1 S3 0.0 0.68 1.83 2.7 3.35S4 0.0 0.56 1.81 3.09 4.15S5 0.0 0.48 1.67 3.12 4.49Note: For explanation of terms used, see note in Table 4.2 and Fig. 4.1 (C).644.4 Setting up the Rule Base from Training DataIn the above set of experiments, the fuzzy rule base was obtained from accurate values ofoutput variable Y computed directly from the test function. Some further experiments weremade, in which the rule base was built up from training data sets consisting of randomvalues of the two input variables X1 and X2 and the corresponding output variable Y. Onethousand sets of 25 combinations of the input variables X1 and X2 were randomly generatedand the corresponding output Y computed for each pair of X1 and X2. With each pair of X1and X2, four fuzzy rules were triggered. By input inference (average, minimum or product),the weight of each rule was computed. This weight was then assigned to the output value(already computed) for that particular rule. This corresponded to the Direct method ofdefuz4fication, described previously. Weights and weighted outputs were accumulated fromall the input and output data, and a single weighted output was computed for each rule:= WjkkWiki=1where Yk : Crisp output for rule k,Yjk : Output for rule k from input data set i,wk : Weight of rule k from input data set i.65For the COA and Height methods of defuz4fIcation, a fuzzy output was required foreach rule. For each rule k, the fuzzy category in which Yk had the largest membership valuewas chosen as the output category.4.5 Results of the Experiments4.5.1 With Accurate Rule BaseSets of 1000 pairs of combinations of inputs, X1 and X2 were generated to test theperformance of the fuzzy logic programming with the derived rule bases. The experimentswere repeated several times. Although there were some slight variations, the resultsremained substantially the same from one set of data to the next. Results of the “accurate”case, where the rule bases were derived from the test function were shown in Tables 4.7, 4.8and 4.9. From this it was concluded that the firing strength (weight) of each rule was bestobtained by multiplying the membership function values of the input variables, and the finaloutput was best obtained as the weight average of the crisp outputs associated with the ruletriggered (the Direct method).66TABLE 4.7Standard Errors of Estimation for the First Test Functionby Various Fuzzy AlternativesNote:The standard errors are given as a percentage of the mean value. (Technically, this is the coefficient of variation).where YYoinvalues of Y computed by fuzzy system,accurate value of Y,number of trials.(1) Firing weight of rule computed by averaging the membership function values for each of thevariables as input inference. The corresponding output inference is the scaled method.(2) Minimum of membership values as input inference. The corresponding output inference is theclipped method.(3) Product of membership function values as input inference. The corresponding outputinference is the scaled method.(4) Output defuzzjfled by the Center ofArea (COA) method.(5) Output defuzz(fled by the Height method.(6) Output computed as the weighted average of crisp outputs.Standard Error =_____________-1nYoi100.0%67TABLE 4.8Standard Errors of Estimation for the Second Test Functionby Various Fuzzy AlternativesY = Input Inference MethodDefuz4fication Average Minimum ProductCOA 12.9 10.3 8.5Height 12.8 8.9 8.0Direct 9.8 4.0 1.5Note: For the explanation of terms used, see Table 4.7.TABLE 4.9Standard Errors of Estimation for the Third Test Functionby Various Fuzzy AlternativesY =Xi.X21(X +X2)°85 Input Inference MethodDefuz4fIcation Average Minimum ProductCOA 17.9 13.7 11.7Height 15.2 8.2 7.4Direct 12.6 6.3 4.9Note: For the explanation of terms used, see Table 4.7.684.5.2 With FAM (Fuzzy Associative Memory) Rule Base Derived from Training DataAs mentioned Section 4.4, training data can be used to construct the FAM rule base. Thefuzzy estimating system learns from samples in building its FAM’s. The training data setincludes inputs and their corresponding outputs. Setting up of the FAM rule base fromtraining data is also described in Section 4.4. The fuzzy systems tested in this section are theDirect method.A set of 1000 training data pairs was used to construct each FAM rule base for thecorresponding test function. After the rule bases were created, sets of 1000 pairs of inputvariables, X1 and X2 were generated to test the derived fuzzy systems. In building eachFAM rule base, input data were assigned memberships in corresponding fuzzy sub-sets.Output data were kept as crisp real values. Data pairs were selected if each of their fuzzymembership values of inputs was greater than 0.0 (all pairs selected), 0.5, 0.7, 0.8 asdescribed in Table 4.10. For a selected training data pair, the firing strength of each rule wascomputed for each input inference method. It was defmed as the average, minimum, orproduct of the corresponding fuzzy sub-space membership values of the input variables.This computed value was used as the weighting factor for the corresponding crisp output forthe rule. Weighted outputs were accumulated from all selected training data, and theweighted average for each rule was then computed. For example, if the selected trainingdata set, i, is described as {X1,X21,Y1}, where X11, X2 are crisp inputs, Y, is crisp outputfor i th data pair, and i = 1, 2, 3,..., n, then the firing strength of the i th data set in the k thrule will be69ci, = AVERAGE [J’x1 (X1), (X2)] or= MN {j.Lx1 (X11), JLx2 (X21)] orci PRODUCT [.tx1 (X11), I.tX2 (X21)Jand the weighted output will beFk=1=!whereJ..tx1 (X11) fuzzy membership value ofX11tX2 (X21) fuzzy membership value ofX2is the crisp output value for data set, iFk is the computed value of a cell, k, in the FAM bankOnce the FAM bank was filled with Fk values, the fuzzy program was then used in theanalysis. Results of the applications of fuzzy programming with the training data are shownin Tables 4.10, 4.11 and 4.12. It can be seen that they are not as good as those shown inTables 4.7, 4.8 and 4.9, where the rule bases were accurately computed from the testfunctions. The results were much poorer than the accurate rule base when all training datawere used in generating the rule bases. In other experiments, the rules were developed onlyfrom data where both input membership functions were greater than 0.5 and 0.7. This gavegreater weight to values with large membership numbers. The results computed from theserule bases are shown in Tables 4.10, 4 11 and 4.12. They indicate an improvement of rule70bases up until it was not practical to create enough rule base entries because of the strengthof memberships required. In this experiment, when the membership threshold was set at 0.8,very few training data sets could be used in creating rules, resulting in a significant loss ininformation supporting the rule base.TABLE 4.10Standard Errors of Estimates of the First Test Function by the Direct Method,Based on the Training DataThe standard errors are given as a percentage of the mean value.(1) The input inferences are the same as in Table 4.1.(2) The rule base was derived from computed values- as in Table 4.2 (for the first test function),Table 4.4 (for the second test function) and Table 4.6 (for the third test function).(3) The rule base was derived from “actual” trial data, using all the values generated.(4) The rule base was derived from only the trial data with each input fuzzy membership greaterthan 0.5.(5) The rule base was derived from only the trial data with each input fuzzy membership greaterthan 0.5 and then weighting the output by the square of the firing strength value.(6) The same as (4), but each input membership greater than 0.7.(7) The same as (5), but each input membership greater than 0.7.(8) The same as (4), but each input membership greater than 0.8.Y =X1+X28.0 IDefuzzflcation Average12.7Input In/’rence MethodMinimum Product’4.8 0.020.0 14.9 11.9(Z .Accurate .:•.All (3)Membership > 0.5 4)(Membership > 0.5)1 11Membership > 0.8 ) .. I15.0 9.7 7.514.7 9.2 6.614.0 7.9 5.8Note:14.0 7.8 5.725.5 24.5 24.771TABLE 4.11Standard Errors of Estimates of the Second Test Function by the Direct Method,Based on the Training DataY =X12’X Input Inference MethodDefuzzfication Average Minimum ProductAccurate 9.8 4.0 1.6All 14.6 11.2 9.1Membership> 0.5 11.7 8.0 6.3(Membership > 0.5) 11.4 7.6 5.5Membership>0.7 11.6 6.7 5.1(Membership > 0.7)2 11.6 6.7 4.9Membership > 0.8 27.2 28.2 29.2Note: For the explanation of terms used, see note in Table 4.10.TABLE 4.12Standard Errors of Estimates of the Third Test Function by the Direct Method,Based on the Training DataV=X1.2/( +X2)°85 Input Inference MethodDefuzzification Average Minimum ProductAccurate 12.6 6.3 4.9All 18.7 14.0 12.0Membership>0.5 15.3 10.6 8.7(Membership > 0.5)2 15.1 10.2 8.0Membership>0.7 14.2 8.8 6.9(Membership > 0.7)2 14.2 8.7 6.7Membership>0.8 25.3 25.9 26.5Note: For the explanation of terms used, see Table 4.10.724.6 RobustnessOne of the quoted advantages of fuzzy logic programming is that it is very robust. If someof the rules are omitted, or there are some mistakes in them, the system should still functionreasonably well. To check on this, further experiments were conducted where some of therules were progressively eliminated. The results in Tables 4.13, 4.14 and 4.15 show that asrules are left out, performance of the fuzzy logic system degrades relatively slowly. This canbe a very important practical consideration. It means the fuzzy programming can be usedwhere some faults or missing information of the system are unavoidable. It does not strictlyrequire a high level of precision of all the rule bases or FAM’s. If some structuredknowledge is unavailable or missing, the rules can be estimated and used.TABLE 4.13Standard Errors as Rules Are Randomly Omitted for the First Test FunctionY =X1+X28.O Input Inference MethodNo. ofRulest Omitted Average Minimum Product0 12.3 4.6 0.01 (1) 15.8 10.2 7.72 (2) 17.8 14.5 13.64(3) 21.9 20.1 18.78 (4) 29.5 29.0 28.5Continued on nextpage.73TABLE 4.13—Continued.Note:The standard errors are given as a percentage of the mean value.t The fuzzy rule base is identical to the one used in the Direct method in Table 4.2 (for the firsttest function), Table 4.4 (for the second), and Table 4.6 (for the third). There are 5 categoriesof each of X1 and X2, giving 25 rules in all for each test function.(1) One rule is randomly omitted.(2) Two rules are randomly omitted.(3) Four rules are randomly omitted.(4) Eight rules are randomly omitted.TABLE 4.14Standard Errors as Rules Are Randomly Omitted for the Second FunctionAverage Minimum Product3.811.2 7.6 6.615.5 13.2 12.615.8 14.6 14.119.3 18.5 17.7Note: For the explanation of terms used, see Table 4.13.V = Xi2.X112No. ofRules OmittedInput Inference Method0 I 9.4 1.67413.9 8.2 6.813.7 9.0 7.817.4 16.0 15.320.0 18.5 18.04.7 ConclusionsConclusions drawn from these experiments were:1. The best results were obtained by inferring the firing strength of each rule accordingto the product of the memberships in the categories triggered (i.e., by the productrule of input inference); providing a “crisp” output for each rule, the Direct methodof output inference; and computing the weighted average of these outputs.2. The fuzzy system works best when the outputs corresponding to values of the inputvariables which have memberships of 1.0 can be accurately specified.3. Sets of rules can be developed from experience by fuzzy associative maps - butthese are not quite as good. However, this feature offers the promise of adaptivelearning and adjustment of the rules in the light of experience. In setting up the ruleTABLE 4.15Standard Errors as Rules Are Randomly Omitted for the Third FunctionNo. ofRules OmittedY=X1.X?I(X? +X2) Input Inference Method12.9 6.8 5.1Note: For the explanation of terms used, see Table 4.13.75base, it is best to use only data sets where the input variables have high membershipvalues (i.e., greater than 0.5).4. The system is very robust in that rules can be left out or there can be errors in themwithout seriously compromising performance.5. When, as in the examples tested, there is a rule for each combination of the inputvariables, it is important to keep the number of input variables and fuzzy categoriesto the minimum practical number. Otherwise the number of rules can quicklybecome unmanageably large. This suggests structuring the problem in question withthe minimum number of input variables and keeping the number of fuzzy categoriesto about 5 and certainly less than 10 for each variable.The above conclusions were used in selecting a fuzzy logic operating system forapplication to the polder flood control problem in Bangkok. Details of applications ofthe fuzzy estimators in the polder flood control follow in the next chapter. The actualoperating system is described in Section 5.5.765NUMERICAL EXPERIMENTS5.1 IntroductionAs outlined in Chapter 2, the main feature of Bangkok’s flood control system is polder floodcontrol, which involves independent floodwater releases by gate and/or pumping fromindividual polders. Such releases are necessary to maintain proper water levels within thecanal system of the polders. Current operation of flood release works relies on a fixed rulecurve—generally in the form of a fixed water level. If the water level rises above this level,the gates are opened and/or pumps are started. If below, operation is stopped. After years ofoperating release facilities according to fixed rules, it was realized that improvements couldbe achieved if one could manipulate the releases more flexibly. As described in the systemsengineering literature, this achievement is often sought by using mathematical modeling tooptimize an expected cost function. However, as discussed in Section 2.3.1, fewoptimization studies have been adopted in practice for real-time flood control operations.Several reports on actual flood control operations, including reservoir releases and urbanstorm drainage controls, indicate that an elaborate optimization approach is not yet able tomeet the operators’ needs, and they are not comfortable with it. Even in the Netherlands,where extensive polder systems are in place, use of automatic control optimization has not77yet been accepted in urban storm-drainage of a polder system (Leeuwen and Breur 1993).Manual set-point controls are still mostly in use there. Thus, one of the more realisticalternatives is to improve release operations by enhancing existing technology, such as therule curve.In this chapter, a description of experiments to find better operating procedures withfuzzy logic is given. This involved setting up a flood control situation representative of apolder in Bangkok, but simplified to only include features essential to the study. Sinceactual data were not available, inflows to the polder were simulated with a Monte Carloprocedure. The simulation was conceptually similar to an attempt by Nelen et al. (1987) intheir search for improving internal drainage ofpolder stormwaters. In their study, the polderwas simplified and modeled as a single catchment with a reservoir/canal having a fixedamount of flood storage, and all excess floodwater from the whole polder was discharged bypumping. The rainfall-runoff process was conceptually described by a combination ofreservoirs representing various hydrological components of the polder. Although there wascriticism that the approach was too simplified, satisfactory results of its application to polderdrainage reportedly justified the use of such a simple model. In the present study, a polderwas also treated as a single drainage unit, and its inflows were simulated by using the Clarkmethod (Clark 1945).With the simulated flows, time varying rule curves were first developed for each storm,assuming operation with perfect hindsight, and then these were consolidated into a singlerule curve. Next, a fuzzy rule base was developed with the simulated flows, again assumingoperation with perfect hindsight. Attempts were made to relate the required release to78various items of information likely to be available at the time, such as the time since thestorm began, the total inflows to date and the amount of water already stored. However, itwas found that with too many input variables, the number of rules required became so largethat it became extremely difficult to find any pattern to the rules. Eventually, the problemwas simplified to give the output rule in the form of a desired water level (above which therewould be full discharge, below none) and relate these to just two input variables, time andprecipitation. It was found necessary to have two separate rule bases—one for during therainstorms and the other after the rains had stopped. In this chapter, the simplified poldersituation assumed for the experiment is first described. Next the rainfall-runoff simulation isdescribed. Then the process of rule curve creation is given, followed by the way in whichthe fuzzy rule base was set up. Finally, the procedure used to test and compare the operationof the system using the fuzzy rule base with the rule curve operation is described. Results ofthe comparison are given in the following chapter.5.2 Experimental FoldersThe numerical experiments to check on the usefulness of the fuzzy logic concept inimproving release tactics for floodwater were conducted with assumed polders. Sincepolders are designed to be hydrologically independent, the flood control situation could besimplified and modeled as controlling the release from a simple reservoir. The flood controloperation in each polder catchment was assumed to be independent from other polders. The79release operation was based on the assumption that stonnwaters stored in the polder duringstorms could later be released by gravity after the storms ended.In this section, a description of the assumed polders in the experiments, including size,storage, and capacity of pumps, is presented. Although various polder settings, such asdifferent catcbment sizes were used in the development stage of the experiments, similarresults from the various experiments were obtained. Thus, only the experiments based onthe test polders described in this section (Table 5.1) are presented and discussed in thisthesis.The values describing the test polders were as follows. The catcbment areas of thepolders were 5, 10 and 30 km2 (The polder areas in Bangkok range from 8 km2 in the CityCore project to 165 km2 in the Eastern Bangkok project). Time of concentration (Ta) ofeach catchment was set at 2.5, 3.5 and 4.5 hours for the 5, 10 and 30 km2 polders,respectively. Time of concentration was then allowed to fluctuate within ±30% from themean. The 30% variation was chosen arbitrarily to allow some fluctuation in the parametervalues used. A uniform distribution was used here since it was not possible to determine anexact distribution of the parameters. The Clark’s storage constant (R) mean value was takenas 0.75 x Tc, a value typical of an urban area. The storage constant was allowed to varywithin ±20% of its mean. The maximum floodwater release or pumping rate was 10 m3 sfor the first polder (5 km2), 20 m3 s’ for the second (10 km2), and 60 m3 s’ for the third(30 km2). The release rates were equivalent to the calculated pumping capacity forBangkok’s polders by JICA (1985) using unsteady flow equations. The initial storagevolume of the system was 200 000 m3 for the first test polder (5 km2), 400 000 m3 for the80second (10 km2) and 700 000 m3 for the third (30 km2). For simplicity, tidal actions werenot considered in the main experiments.TABLE 5.1Set-up of the Polders in the ExperimentsPolder #1 Folder #2 Polder #3Area 5 km2 10 km2 30 km2Initial Storage 200 000 m3 400 000 m3 700 000 m3Maximum Release 10 m3 20 m3 s_i 60 m3sT 2.5 hr ±30% 3.5 hr ±30% 4.5 hr ±30%(Uniform) (Uniform) (Uniform)R 0.75 T ±20% (Uniform)5.3 Simulating FlowsRainfalls and corresponding inflows to the assumed polders were generated to simulateflood control situations and operation. The simulation model was composed of two majorparts: a rain generating mechanism and a rainfall-runoff model. Rainfall information wasbased on sequences of random numbers generated under a Monte Carlo procedure.Corresponding run-offs were derived from the generated rainfalls by the Clark hydrographmethod.The rainfall generating mechanism was initialized by a simulation of the duration ofeach rainfall event. An exponential distribution was used to describe the rainfall duration81values (i.e., CDF(t) = 1 - ?. e, where CDF(t) is a cumulative distribution function ofrainfall duration, t, and ?. = (mean of rainfall duration)’). The mean value of rainfallduration was 1.0 hour, consistent with the values reported for Bangkok (JICA 1985).Random numbers representing rainfall duration were generated under the definedexponential distribution (i.e., if u is a standard uniform-distributed random number, thenx = -(L’?) in (u) is a random number with an exponential distribution, with ? as definedearlier (Ang and Tang 1984)).The average intensity of the rainfall event was constructed from the generated value ofthe rainfall duration (t (mm)) by using the intensity-duration formula, i a / (7 + t), where iis rainfall intensity (mm hi1); a and b are empirical variables, locally derived for Bangkok.The values of a range from 5690 to 10 040 with a mean of 8230. The values of b range from37 to 44 with a mean of 41 (JICA 1985). Both a and b were randomly chosen from theirranges for each value of duration, t. Then the total rainfall depth (d) was calculated from thedefinition of the rain intensity (i = d/t).After a pair of rain depth and duration was generated, an advanced-skew rainfall (depth-duration) mass curve’ was applied to derive a temporal profile (hyetograph) of the rain. Coordinates of the representative mass curve (Fig. 5.1) were read from the tropical rainfallcurve studied by Colyer (1984) and assigned as mean values. Colyer (1984) derived therainfall mass curve for the application of the design-storm concept to the tropics where dataon temporal patterns of rainfall were limited. The study by JICA (1986) on temporaldistribution of 52 heavy rainstorms in the Bangkok area had a similar advanced-skewed‘Sometimes called Huff’s curve, after Huff (1967).82profile. Very few studies on temporal rainfall intensity were previously conducted in thearea due to a lack of past automatic rain-gage records. Values of the Colyer curve wereallowed to fluctuate uniformly within a range of ±20% of the mean value. To facilitate theselection of an actual rainfall mass curve for a specific pair of the simulated rain depth andduration, outline curves were constructed. The outline curves represented deviations of±20% and formed an outer envelope around the mean Colyer curve. For each rainfallsimulation, another pair of random numbers was generated for the selection of the masscurve. The first number was used to indicate the sign (+ or-) of the variation. The secondnumber was a percentage of the total allowed variation (20%). The two numbers thus gavethe distance as a fraction of the distance between the mean curve and the outline curve(upper or lower one). Reading the co-ordinates according to the fraction gave the rainfallmass curve used in the simulation.I Curve50I100accunimulated rain duration (%)Fig. 5.1. Rainfall depth-duration mass curve used in the simulation.0 5083A sequence of rainfall events was not considered in this study since it was observed thatat most, one rainstorm occurred at one place on any given day in the Bangkok area (Henry1974; JICA 1985). Typical rainstorms in the area exhibit one peak of rain intensity (JICA1986). Thus the inflow simulation in this study was a single-event one.The hyetograph based on the rainfall mass curve was used in determining the run-off atthe release regulating point of a catchment. No abstraction nor loss of rainfall wasconsidered. The generated rainfall was routed by the Clark hydrograph method (Clark1945). The Clark method was used here because of its simplicity and wide applications insimulations of runoff in hydrological studies (Maiclment 1992). The technique is alsoavailable in the well-known hydrological model, HEC- 1 (Hydrological Engineering Center1987). The Clark method includes two important factors characterizing the runoff from acatchment: time of concentration and storage in the basin. It is simply the time-area methodwith a concentrated linear-storage routing at the outlet. The time-area method divides thecatcbment into several sub-drainage areas according to the travel time from each area. Theisochones or lines of equal travel time to the outlet are used in defining such sub-areas. Therunoff at the outlet of a catchment is the flow resulting from the combined contributions ofrainfall excess in each sub-area which is lagged to the outlet of the catchment with a delayequal to the average time of travel of that area. The runoff is not modified in magnitudeuntil it is attenuated by the storage of the catchment assumed to be at the outlet. A linearreservoir is used to represent the lumped effects of storage and resistance in the catchment.In this study, the time-area curve used was adopted from the HEC-1 model’s standard curve,a symmetrical ellipsoid shape represented by the following mathematical equations:84AT = l.414T151-AT = 1.4l4(1-T)’5where0T0.50.5<T< 1.0Al: cumulative contributing area as a fraction of the basin areaT: fraction of time of concentrationThe routing did not take into account loss functions or soil moisture conditions. It wasassumed that the soil was saturated at the time the storm began. A typical simulated inflowhydrograph and its corresponding rainfall hyetograph are shown in Fig. 5.2.Generated rainfalls and runoffs whose peak inflows were greater than the maximumrelease rate of the system (500 pairs) were used in deriving the rule curve (Section 5.4) andfuzzy rules (Section 5.5). An additional set of rainfall events (2000 pairs) was generated fortesting the performance of the fuzzy rules.7060__________________________504030Fig. 5.2. Example of a simulated inflow used in this study.POLDER #210 20 30 40 50 60Time (mm)0 100 200 300 400 500 600 700Time (mm)855.4 Time Varying Rule CurveAs discussed previously, Bangkok’s flood control practice relies mainly on the rule curveapproach—a predetermined, fixed water level. If stormwater in the polder rises above thislevel, gates are to be opened, and/or pumps started; if below, pumps are to be stopped,and/or gates closed. The fixed-level rule curve is a local control which offers relative ease inoperating pumps or gates. However, it renders a sub-optimal performance. One simpleimprovement of the fixed-level rule curve is to have the rule curve level vary with the timesince the rain starts. The time varying rule curve can take information on temporal patternsof storm run-offs into account. By relating the required level to time, the rule curve canoffer an operation more responsive to storms yet still be simple to implement.QmaxFig. 5.3. Required empty storage derived with perfect knowledge of hydrograph.•Required storage at time T0• Required storage at time T1T0 T, time86In the experiments, rule curves were derived for individual floods, assuming that the fullhydrograph was known at the time, and the pumps were operated optimally (that is operationto minimize pumping, yet still avoid flooding). Rule curves were derived for each individualflood by working backwards and at each point in time, computing the storage space required.Fig. 5.3 illustrates the calculation for the amount of storage required at time To to avoidflooding—that is holding the maximum discharge to Qrnax. The shaded area in Fig. 5.3defines the amount of the storage required. This procedure was repeated with all the floods,with the result shown in Fig. 5.4.TIME VARYING RULE CURVE600000_______________500000400000300000200000E1000000YTTTYYTYY!+HHHII.jIIIIIIIIiii.______ _____ ______1111111111111 t11TfT_ _1111111111111111111 B!’1t1111111111IllI llllillr__________11Illll111IllllL1llllllll!111TFii0 50 100 150 200 250 300 350 400 450Time from beginning of storm (mm)Fig. 5.4. Rule curve derivation.In Fig. 5.4, the corresponding values of the empty storage required and the time fromthe beginning of a storm or rule curves of all individual storms were plotted. A final rulecurve was then drawn such that 95% of all points were below the curve. That is if the rule87e Po1 r #2Derived Rule Cuncurve were followed with all floods, only 5% of those large enough to require pumpingwould cause any flooding. In practice, the 5% value would depend on many factors such asthe value of the area being protected; however, 5% was considered a reasonable value forthis study. The upper bound of the rule curve was then limited by the initial storage of thesystem (200 000 m3, 400 000 m3 or 700 000 m3) when operated. In deriving the rule curve,a total of 500 flood inflows whose peaks were greater than the maximum release rate of thesystem (10 m3 s_I, 20 m3 or 60 m3 1) were used.The derived rule curve has an inverse S-shape with a diminishing tail with longer times(Fig. 5.4). Along this rule curve are values of the empty storage that an operator shouldmaintain. If the system has empty storage less than the amount required, then an operatorhas to keep on releasing the stormwater. If the system is afready flooded at that point,whatever information on additional required storage is available to an operator will be of novalue to his decision. The flood situation already forces him to release the excessstormwater.5.5 Fuzzy Estimating SystemIn this study, the fuzzy logic program (Direct method) based on the results of theexperiments described in the previous chapter was used and tested numerically in the polderflood control context. Following is a description of the fuzzy programming approach.881. The flood control problem was set up in a way which reduced the number of theinput variables to two, in order to keep the number of rules in the rule basemanageable and allow patterns to be discerned. Setting up the problem in this waytook considerable experimenting. The input variables are the time since the rainbegan and the average intensity of the rain so far. The output variable is the volumeof storage space required.2. After the input and output control variables were selected, 5 equal triangular fuzzymembership functions were used to partition each of the input variables into fuzzycategories (or values), over the universe of discourse.3. Training data were used to construct the FAM rule base. The process ofconstruction is described previously in Sections 4.4 and 4.5.2. Only those data setswhose input values were assigned relatively strong membership values in theircorresponding partitioned fuzzy categories were used to construct the rules. In thisstudy, a strength of the membership of each input of 0.67 was selected as athreshold. The computer algorithm which was developed for this study,automatically selected the data pairs with such membership strengths. The productmethod of input inference was used in calculating the firing strength or weight ofeach rule.4. The operating fuzzy rule base consists of 25 rules, one for each combination of theinput fuzzy variable categories. The fuzzy rules, used in this study (for a two-input,one-output control system) take the formRi : IF X IS A1 AND Y IS B1 THEN Z IS F1R2 : IF X IS A2 AND Y IS B2 THEN Z IS F289where X and V are fuzzy variables; Ak, Bk are fuzzy categories, and Fk is aweighted crisp output value (FAM value) of the required storage space.5. When specific values of the two input variables are input, their memberships in eachof the fuzzy categories are computed. Four rules are triggered as illustrated inFig. 3.3. The weight of each rule is computed by multiplying the membership valuefor each variable in each category in that rule.6. The fmal crisp output is computed by using the weighed combinationZ(x, ,) = k=iwhereFk: a crisp output of each rule kn: total number of rules triggered (normally 4)the rule number(xk: the strength of rule k, which is defmed ascxk = PRODUCT [j(x), j.t(y)Ji.t(x), j.i(y): membership values of crisp inputs, x, yIn this study, the fuzzy logic program for the polder flood control was constructed,based on training data. The program used available information on rainfall data as inputs.The average rain intensity and the time from the beginning of a storm were used as fuzzyinput variables of the first rule base, for use during the rainstorm. The total rain depth andthe time from the beginning of the storm were the fuzzy input variables for the second rule90base, for use after the storm ended. The output variable was the storage space required for atthat particular time. The operating rule then was to operate the pumps only if the actualstorage space was less than that required. Details of membership functions for the inputvariables and the fuzzy associative memories used in the fuzzy logic program for the polderflood control follow.5.5.1 Fuzzy Membership FunctionIn this study, the triangular membership function was chosen because of its simplicity andcomputational efficiency. The number of fuzzy values or categories for each decisionvariable was minimized as suggested in the experiments in the previous chapter. From thesimulated flows and the derived time varying rule curve, it was found that at a time ofroughly the 8th hour from the beginning of the storm, the required storage space was mostlyclose to nil. Most rainstorms in the experiments had already ended, and their dischargeswere by this time receding. Since the time scale of a storm could often be classified roughlyon an hourly basis, the time membership was partitioned every 2 hours between thebeginning of the storm and the 8th hour into 5 fuzzy values or categories, as illustrated inFig. 5.5. The last fuzzy category (T4) included times over 8 hours. Experimenting with thedata, it was also found that an average rain intensity greater than 120 mm wasinfrequent. For rain intensities greater than 120 mm hr’, the patterns and magnitudes ofrequired storage were closely similar. During a heavy rainstorm, the required storage space91was often large (i.e., FAM cells covering this range of rain intensities would be filled withvalues close to or greater than the total available system storage). The rain intensity fuzzymembership was then partitioned evely 30 mm hr between 0 (zero) and 120 mm hf’ into5 fuzzy values or categories, as illustrated in Fig. 5.6. The last fuzzy value (14) included allintensities over 120 mm hr’. For the case where the rainstorm had already ended, the totaldepth of rainfall was used as a decision fuzzy variable. The total depth over 120 mm wasoften considered to be very heavy. Beyond this value, the pattern of rules were similar—very large empty storage was required initially. The total depth membership was partitionedevery 30 mm between 0 (zero) and 120 mm into 5 fuzzy values, the same way as the averagerain intensity, and was shown in Fig. 5.7.Although more detailed membership functions could be constructed, the larger FAMrule base would be more difficult to manage, and it would be more difficult to fill the FAMcells. The fuzzy categories or values defined are all symmetrical around the peak and haveuniform widths.1I20 2.0 4.0 6.0 8.0 hrtime from the beginning of stormFig. 5.5. Membership function of time from the beginning of a storm.921.E01E0Fig. 5.6. Membership function of rain intensity.Fig. 5.7. Membership function of rain depth.5.5.2 Derivation of Fuzzy Associative MemoriesThe objective of the fuzzy logic programming used here was to give guidance on the emptystorage volume required in a flood reservoir system during a flood. The correspondingstormwater (inflow) volume allowed in the system could be translated into a water level ofthe reservoir by using an established stage-volume curve. Operating instructions were thesame as those used in the rule curve operation. A stormwater release was required whenever30 60 90 120 mm/hraverage rain intensity30 60 90 120 mmtotal rain depth93the remaining empty volume in the reservoir was less than the required volume. The releaseor discharge rate was assumed to be constant (i.e., 10 m3 s_i, 20 m3 s1 or 60 m3 s1). Valuesof the required storage were calculated by the same methodology, described previously in therule curve construction (Section 5.4). A total of 500 inflows were simulated, and thoseinflows which had their peaks greater than the maximum release were used as the trainingdata in determining the fuzzy rules and filling out the FAM’s.Fuzzy rules were derived to create two sets of rule bases or FAM’s. One was for thecase before a rainstorm ended, and the other was for the case after the rain ended. Inputs tothe first FAM set were the average rain intensities up to the time, and the time from thebeginning of storm. Inputs to the second FAM set were the total depth of rainstorm and thetime from the beginning of the storm. The entries in the fuzzy associative memory cellswere weighted crisp real-numbers of the required storage, as described previously inSection 5.5.A standard-FORTRAN program algorithm (similar to the one used in Section 4.5.2) waswritten for use in automatically creating the fuzzy rule matrices. For each pair of inputoutput data (e.g., the time from the beginning of the storm, the average rain intensity as theinputs, and required storage as the output), the corresponding fuzzy set membership valueswere calculated and assigned to input decision variables. The data pair was accepted if eachinput’s membership value was greater than the threshold value. The threshold for thevariables was taken as 0.67, which was close to the optimal membership strength of 0.7found in the experiment in Section 4.5.2. After a pair of data was accepted, its firingstrength was calculated by multiplying the two input membership values. This firing94strength was multiplied by the crisp output value to give a weighted output. Theseindividual weighted outputs were stored for further calculation of a single weighted outputfor each FAM cell. The whole procedure was repeated for each input-output data pair.Finally, for each cell, all the stored data (the firing strength and the corresponding weightedoutput) were added up. The sum of the weighted outputs was divided by the correspondingsum of firing strengths (weights) to render the weighted crisp output for each cell.After setting up the FAM’s, some further calibration and fine-tuning of the rules weredone. There were a few empty FAM cells, where none of the training data fell. Thesemissing FAM cells were filled up with values obtained by interpolation. Also, some of thevalues in the cells were adjusted to give a smoothly changing pattern.Once the FAM’s were established, a simple program was written to “operate” thesystem one time step at a time, given inflows generated as described previously. Threealternative operating rules were used. One was the rule curve, one the fuzzy system and one“optimal.” With the rule curve and fuzzy systems, the required storage space was computedfor each time period. If required storage space exceeded the available storage space, thepumps were assumed to operate during the next time interval. If not, pump discharge wasset to zero. The available storage space was then computed for the next time period byadding the volume discharge (by pumping) and subtracting the volume of inflow during thetime interval. The whole process was repeated for each time step. For “optimal” operation,the complete flow of hydrograph was first generated and then optimal operation computed asdescribed previously.95For each set of experiments, 2000 simulated floods were used in comparisons of thepumping control under the rule curve and fuzzy control guidance. A control decision wasmade every 10 minutes, which was also the time resolution of the storm dischargehydrographs. At each time step, the guidance values were read from both the rule curve andderived from the fuzzy control. The operation of pump was then set, according to thegeneral rules of operation, described in the previous paragraph. The results of thecomparisons are presented and discussed in the following chapter.After some further testing of the derived fuzzy logic program with sets of simulatedinflows, it was found that it allowed some flooding in the case of moderate storms, which ifoperated with optimal (hindsight) information, could have been avoided. This waseliminated by making the rule base slightly more conservative. It was also found that thetotal of the flood volumes from all the simulations was slightly greater with the fuzzy systemthan with the rule curve. The FAM rule was adjusted to make the total accumulated floodvolumes from all simulated flows tested (e.g., 2000 storms) approximately the samemagnitude as with the rule curve. This was done to make the comparison of pumpingvolumes meaningful. The FAM’s used in the Polder #2 are shown in Tables 5.2 and 5.3.96TABLE 5.2First Fuzzy Associative Memory (FAM) for Folder #2—for Use during Rainstorm.(Correlated Rainfall Intensity-Duration Relation)RAIN INTENSITY10 Ii 12 13 14TO 265000 410000 379000 368000 330000T Ti 259000 256000 365000 444000 414000I T2 189000 230000 336000 400000 400000M T3 141000 220000 321000 400000 400000E T4 113000 210000 309000 400000 400000TABLE 5.3Second Fuzzy Associative Memory (FAM) for Folder #2—for Use Following the End ofRainstorm. (Correlated Rainfall Intensity-Duration Relation)TOTAL RAIN DEPTHDO DI D2 D3 D4TO 0 182000 342000 366000 439000T Ti 0 88000 297000 348000 438000I T2 0 15000 97000 130000 305000M T3 0 1000 2000 8000 87000E T4 0 0 0 0 6000976RESULTS AND DISCUSSION6.1 IntroductionAs described in the previous chapter, sets of numerical experiments were conducted withalternative systems for controlling flood releases from a typical polder in Bangkok. Theprimary purpose of the experiments was to compare the performance of an operating systembased on the application of fuzzy logic with the more traditional approach of using a rulecurve to decide on whether or not to use the pumps to discharge floodwaters during the nexttime interval. The rule curve which was used as the basis for comparison shows the amountof desired storage space varying with elapsed time since the beginning of the storm(Fig. 5.4). However, this “time-varying” rule curve is in itself an improvement over thefixed rule system, which is still in general use in Bangkok. Operation with fixed rule curveswas also simulated for comparison with the time varying rule curve. To complete the rangeof alternatives, “optimal operation” was also used.Optimal operation was different from the other alternatives in that it assumed perfectinformation (i.e., that all the flows were known in advance - as could only occur withhindsight). With the other alternatives, real time operation was simulated (i.e., the system98operation at each time interval was determined on the basis of information that would havebeen available at the time). For each set of experiments, 2000 flood hydrographs weresynthetically generated.The results of this main set of experiments, which are presented in the followingsection, showed that the time varying rule curve system was a considerable improvementover the fixed rule curve system, that the fuzzy system was better than the time varying rulecurve approach and that the optimal operation was slightly better again. However, there wasnot much “room” between the time varying rule curve approach, which represented the basecase and the “optimal”, which was the best operation that would be possible even given fulladvance information on the pattern of flows to come.On examining these results, it was realized that the main difference between the fuzzysystem and the base case rule curve approach was with the intermediate storms. With smallfloods, there was no need for pumping as no flooding occurred. Both systems thus gavesimilar results, although a small amount of pumping was required by the rule curveoperation in this case. On the other hand, large floods overwhelmed both systems andcaused flooding regardless of the pump operating system. Thus in this situation, bothsystems provided similar operating patterns. However, with intermediate storms, wheresome pumping was required, there was an opportunity for the application of skill andknowledge in deciding whether and when to pump. In this situation, the fuzzy system didbetter than the more inflexible rule curve approach.Following on this set of experiments, other sets were conducted in which there waslikely to be more room for the fuzzy system to show its merits. In the first set, the99simulation program for generating the flood flows from simulated rainstorms was changed toallow more variability in the flows. In the original approach, the rain duration wascorrelated with the average storm intensity (as is the case in Bangkok) and this results inflood hydrographs which are relatively similar to one another. In this situation, it is notsurprising that a rule curve derived from sets of simulated flows would offer an effectiveapproach to controlling floods generated by the same mechanism. It was thought that if thefloods were more variable, the fuzzy system could have a greater advantage over the rulecurve operation. Other sets of experiments were conducted in which gravity dischargecontrolled by gates was allowed in addition to the pump discharge, and in which tidal effectswere simulated. These experiments and their results are also presented in this chapter.6.2 Main ExperimentsThe experiments discussed in this section used simulated inflows, generated from rainfalls inwhich the average rainfall intensities was correlated with the durations as described inSection 5.3. In this set of experiments, it was assumed that excess stormwater, above whatcould be stored, could only be discharged by pumping. However, it was also assumed thatthe stored floodwaters could be released by gravity after a set period of 15 hours after thestorm began.Summaries of the results of the experiments are given in Tables 6.1 and 6.2. Table 6.1shows the total volume of floodwater (from the 2000 storms investigated), over and above100the volume stored in the available flood storage space and the volumes discharged bypumping. This total volume of floodwaters that cannot be contained or pumped out providesa measure of the overall effectiveness of the flood control system in controlling floods. Asexplained in the previous chapter, the rule base for the fuzzy operating system was adjustedsuch that the total volume of excess floodwater was approximately the same as that with thebase system, the time varying rule curve. Unless those volumes had been closely similar, thecomparison of pumping volumes would have been meaningless. As expected, the total floodvolumes under optimal operation were lower than with the fuzzy system or the time varyingrule curve.It was found convenient to classify the floods into 3 categories in order to betterunderstand the effects of the alternative operating systems being investigated. Thesecategories are: Case 1—no floods and no pumping required; Case 2—no floods butpumping required; and Case 3—floods even with pumping. This classification is similar tothat used by field operators after having had a long experience with pumping operations inBangkok. They classify storms as light, moderate and heaiy (or vely heay), depending ontheir rainfall intensities. Figs. 6.1, 6.2 and 6.3 illustrate typical operations in Case 1, 2and 3, respectively.Flood volume for each storm was defined as the volume of excess stormwater that thesystem could not cope with despite pumping during the storm period. Pump volume foreach storm was defined as the accumulated volume of excess water that was pumped outover that storm. The values of both pump and flood volumes were calculated as totalvolumes over all of the storms.101TABLE 6.1Flood Volumes with Alternative Operating MethodstOOD VOLUME x 106 m3)System Fixed Rule Time-Varying FuzzyOperation Rule Curve0•Case 2 0.2 0.1 0.6 0Case 3 139.0 129.5 129.8 129.3Total 139.2 129.6 130.4 129.3Casel 0 0 0 0Case 2 0.1 0.7 0.6 0Case 3 160.9 156.1 153.9 151.8Total 161.0 156.8 154.5 151.8Casel 0 0 0 0Case 2 0.0 0.1 0.2 0Case 3 606.9 606.1 605.4 605.3Total 606.9 606.2 605.6 605.3OptimumCasel 0 0..102TABLE 6.2Pumping Volumes with Alternative Operating MethodsPUMPING VOLUME (x 1O6mSystem [ Fixed Rule Time-Varying Fuzzy OptimumOperation Rule CurveCase 1 25.2 11.6 4.6 0Case 2 77.6 77.2 63.6 49.0Case 3 405.9 384.1 383.6 382.1Total 508.7 472.9 451.8 431.2% improvement -17.9%t -9.7%t -4.7%t 0Case 1 73.1 20.1 1.9 ‘ 0Case 2 256.8 208.6 180.0 153.3Case 3 613.2 610.7 610.8 610.0Total 943.1 839.3 792.7 763.3% improvement -23.5%t -9.9%f -3.8%t 0Case 1 52.3 12.9 0.5 0Case 2 719.7 627.8 519.5 477.6Case 3 2632.5 2521.7 2519.6 2412.7Total 3404.5 3162.4 3039.6 2890.2% improvement -17.8%t -9.4%t -5.1%t 0t Compared with “optimum” values; minus sign (-) means worse.It should be noted that in practice the “optimum” is not attainable, as it would require perfectforecasts of the flows.Note:10330254 20E02’D 1050time from the beginning of the storm (mm)1000Note: A typical operation under the time varying rule curve requires pumping for a shortperiod as the inflow rises. Operations under fuzzy and optimum alternatives donot require pumping throughout the storm.60Fig. 6.1. Typical operation in Case 1 (Pump).time from the beginning of thestorm (mm)Note: Pumping with the time varying rule curve starts earlier than the other twoalternatives. Pumping with the fuzzy system starts before the optimum and stopsabout the same time as the time varying rule curve.Fig. 6.2. Typical operation in Case 2 (Pump).F - - - -Time Varying Rule CurveO FuzzyOptimum— -- lnflow0 100 200 300 400 500 600 700 800 900\50— 40enE02’I.,• 20100IIIII.‘Time Varying Rule CurveFuzzyOptimum— - -— InflowI’0 100 200 300 400 500 600 700 80010480706050E30201000 100 200 300 400 500 600 700 800time from the beginning of the storm (mm)Note: The optimum and time varying rule curve alternatives have pumps started andstopped about the same time. Pumping with the fuzzy system starts and stops laterthan the other alternatives.Fig. 6.3. Typical operation in Case 3 (Pump).The basic polder system consists of a pump of fixed capacity (described previously inSection 5.2). The pump was turned on if the available storage within the system was lessthan the required value. If the system storage were filled up, and the inflow rates were lessthan the fixed pump rate with no remaining flooding, then the excess inflows would becalculated and added to the total pump volume.As mentioned previously, the fixed rule operating system is generally used incontrolling Bangkok’s flood releases. The fixed rule is a pre-determined, constant waterlevel upstream of a gate or pumping station that the operators have to maintain. The currentfixed levels (maintenance water levels) used in Bangkok were calculated from unsteady flowsimulations for design rainfalls of the 5-year return period. Thus, a comparative fixed levelI ‘/IIII•- + - -Time Varying Rule CurveFuzzyOptimum— - -— mtlowI105was derived from the simulated data. A total of 500 rainstorms of 5-year return periods weregenerated. The empty storage spaces were computed as in Section 5.4. The storage requiredat the beginning of the storms (with 5% probability of exceedance) was then selected as thefixed rule. For Polder #2, the fixed rule value was 265 000 m3 (i.e., empty storage requiredthroughout the storm). Two additional fixed rules of ± 100 000 m3 (365 000 m3 and165 000 m3) of the computed rule were also tested to see the effects of the fixed rules.FixedRule, RuleCurve, orFuzzy Value—” Optimum” Value• 100%“Optimum” ValueTABLE 6.3Fixed Rule Curve Operation with Different Fixed Rules—Folder #2System Operation FIXED RULE RULE CURVE FUZZY165000 m369%f 3%t 2%t12%t l0%t 4%twage Space: 265000i13•43%t 3%t 2%t1 6%t 1 0%t 4%tLule Storage space: 365000 rn36%t 3%t 2%t23%tNote:1• %=1 0%t 4%t106As expected, the fixed rule curve was less effective than the other alternatives used(Table 6.3). The effectiveness of flood prevention by the fixed rule curve operationdepended directly on its value. Setting the fixed rule storage space at a higher value wouldgive better over-all flood reduction. However, it requires more pumping volumes than thelower one, as illustrated in Table 6.3. Thus in comparison with the other alternatives asshown in Tables 6.1 and 6.2, the fixed rule with the higher value of storage space, whichgives total flood volume closer to those of the other alternatives, was used. Fixed rulevalues of 178 000 m3, 365 000 m3 and 662 000 m3 were used for Polder #1, #2 and #3,respectively.500000400000C,E300000-I0‘C2000002Li.1000000Fig. 6.4. Mean flood volumes for Folder #2 (Pump).CASE1 CASE2 CASE3A CASE3B CASE3C107C,ELuz-I0>0z0.0.Figs. 6.4 and 6.5 show the mean flood and pumping volumes in each case for Polder #2.In Case 3, the flood volumes were further divided into 3 categories: less than 100 000 m3(Case 3A), between 100 000 m3 and 300 000 m3 (Case 3B), and over 300 000 m3 (Case 3C).As in Table 6.2, only small fractions of the difference in pumping volume can be seenbetween the time varying rule curve, fuzzy, and optimum alternatives. The fixed ruleoperating alternative involved much more pumping than all other alternatives.10000008000006000004000002000000CASE 1 CASE 2 CASE3A CASE3B CASE3CFig. 6.5. Mean pumping volumes for Polder #2 (Pump).1086.3 Additional ExperimentsSets of experiments were carried out with Polder #2 to evaluate the performance of thefuzzy system in more variable and flexible environments. The first set of the experimentsused the same physical settings as the main experiments, except the rainfalls were generatedfrom the independent rain intensity and rain duration relation. The second set involved thecombined use of a pump and a gate in the flood control operations. The last set ofexperiments dealt with tides by allowing a sudden discharge of floodwaters, simulating theopening of a control gate when the tide level fell below the internal water level. Details ofeach set of experiments are presented in the following sections.6.3.1 Experiments with Independent Rainfall Intensity-DurationIn this set of the experiments, rainfall simulations were based on independent generation ofrain duration and rain intensity. Rain duration was generated as described previously.Average rain intensity was generated from an exponential distribution with a mean of60 mm br, a typical 2-year storm value used in most of Bangkok’s flood studies. Raindepth was then calculated from the rain intensity and duration. Inflows were constructed asdescribed in Section 5.3. Using the same approach as in the main experiment, the rule curveand fuzzy rules were derived. The FAM’s used are shown in Tables 6.4 and 6.5.109TABLE 6.4First Fuzzy Associative Memory (FAM) for Folder #2—for Use during Rainstorm(Independent Rainfall Intensity-Duration Relationship)RAIN INTENSITY10 Ii 12 13 14TO 373000 425000 435000 438000 444000T Ti 345000 319000 414000 400000 422000I T2 154000 243000 400000 400000 400000M T3 92000 186000 400000 400000 400000E T4 83000 123000 400000 400000 400000TABLE 6.5Second Fuzzy Associative Memory (FAM) for Folder #2—for Use Following the End ofRainstorm (Independent Rainfall Intensity-Duration Relationship)TOTAL RAIN DEPTHDO Dl D2 D3 D4TO 0 174000 182000 374000 643000T Ti 0 156000 169000 341000 605000I T2 0 28000 84000 105000 265000M T3 0 1000 12000 6000 43000E T4 0 0 0 0 1000110Tables 6.6 and 6.7 show summaries of the results for the rule curve and fuzzy operatingsystems based on correlated and independent rain durations and intensities. As discussedpreviously, the fuzzy system offered a slight improvement on the rule curve operation whenthe simulated inflows were based on the correlated rainfalls. The improvement increased asthe variability of the inflows increased, with the uncorrelated durations and intensities.However, the time varying rule curve operating policy performed slightly worse than in thecorrelated rain intensity-duration simulations.TABLE 6.6Flood Volumes with Alternative Operating Methods for Different Simulated RainfallsFLOOD VOLUME (x106m3)System Operation Rule Curve Fuzzy OptimumL -Casel 0 0 0Case 2 0.7 0.6 0Case 3 156.1 153.9 151.8All 156.8 154.5 151.8PENDENT INTENSITY AND DURATIONCasel 0 0 0Case 2 0.3 0.5 0Case 3 168.8 166.3 166.1All 169.1 166.8 166.1[ :: :zc* pzpER #2___A TVfl TNTVNTTV A1’JI1 ThTTP A ‘I’TflJ111TABLE 6.7Pumping Volumes with Alternative Operating Methods for Different SimulatedRainfallsI PUMPING VOLUME (x106m3)SystemCC RELATED INTENSITY AND DURATION- r.Case 1 30.1 1.9 0Case 2 198.6 180.0 153.3Case3 610.7 610.8 610.0All 839.3 792.7 763.3% Improvement -9.9%t -3.8%t 0INDEPENDENT INTENSITY AND DURAT. -Case 1 13.0 3.5 — 0Case 2 139.8 101.3 84.6Case 3 442.7 438.8 434.9All 595.6 543.6 519.5% Improvement -14.6%t -4.6%t 0Note:t Compared with “optimum” values; minus sign (-) means worse.It should be noted that in practice the “optimum” is not attainable, as it would require perfectforecasts of the flows.112C,EUI-I0>0U.Figs 6.6 and 6.7 show the mean values of flood and corresponding pumping volumes foreach case. The classification of Case 3 is the same as in the main experiments. Incomparing Fig. 6.7 with Fig. 6.5, there is slight improvement by the fuzzy alternative overthe rule curve, as could be expected. Fig. 6.6 also shows the flood volumes resulting frominflows from rainstorms simulated from the independent rain intensity-duration relation.More large floods occurred with the independent intensity-duration relation than when theywere correlated. There was also slight improvement of the pumping pattern (Case 3A)where floods were less than 100 000 m3 (Fig. 6.7). This did not show in the mainexperiments (Fig. 6.5). However, when all the Case 3 floods were summed up, thisdifference can not be seen in Table 6.7.600000500000400000300000200000100000CASE I CASE 2 CASE 3A CASE 3B CASE 3CFig. 6.6. Mean flood volumes for the independent intensity- duration, Folder #2 (Pump).113C,Ew-I0>0z0.Fig. 6.7. Mean pumping volumes for the independent intensity-duration, Folder #2 (Pump).6.3.2 Experiments with Pump and Gate DischargesIn order to make the polder flood control operation more flexible, the operation of a gatewas introduced in addition to the pumping operation. The gate was allowed to remain openthroughout the storm period. The total discharge capacity of the polder system was kept thesame as in the polder using pumping only. For Folder #2, the gate discharge capacity was 8m3 and pump discharge capacity was 12 m3 s1. Therefore, the total discharge capacitywas equal to the pumping only setting (20 m3 s’). In this set of experiments, the timevarying rule curve and FAM’s used were the same as the ones in the pumping only cases(Sections 6.2 and 6.3.1). Rainfalls simulated from both the correlated and the independentrainfall intensity-duration cases were used in the experiments.CASE 1 CASE 2 CASE3A CASE3B CASE3C114Tables 6.8 and 6.9 show summaries of the results of these experiments. Improvementof the operation by the fuzzy over the rule curve can again be seen as a small percentage oftotal pumping volumes. The fuzzy system shows a greater improvement (13%) over the rulecurve operating system with the independent intensity-duration relation. In this case, thesetting of the experiments is more variable and more operationally flexible. In bothindependent and correlated rain simulations, the flood volumes were compatible (Table 6.8).TABLE 6.8Flood Volumes with Alternative Operating Methods for Pump/Gate Operations115TABLE 6.9Pumping Volumes with Alternative Operating Methods for Pump/Gate OperationsPUMPING VOLUME (x106m3)CORRELATED INTENSI1Y AND DURATIONan...- - - >*-t:c4 - - - - - -Case 1 4.5 0.3 0Case 2 103.2 88.3 83.2Case 3 349.3 354.1 346.9All 461.8 437.9 430.1% Improvement-7.4%t -1.8%t 0: INDEPENDENT INTENSITY AND DURATIONCase 1 10.4 0.1 0Case 2 102.3 74.2 71.4Case 3 260.1 256.6 254.9All 372.8 330.9 326.3% Improvement -14.2%t -1.4%t 0Note:f Compared with “optimum” values; minus sign (-) means worse.It should be noted that in practice the “optimum” is not attainable, as it would require perfectforecasts of the flows.PUMP/GATESystem Operation Rule Curve Fuzzy Optimum116Figs. 6.8 and 6.9, 6.9 and 6.10 show the mean values of flood and correspondingpumping volumes for correlated and uncorrelated rainfalls, respectively. In both cases, thesmall improvement in pumping by the fuzzy operating system over the rule curve is shown.The improvement is in Case 2 and Case 3A, similar to the performance described in theprevious section (Section 6.3.1).C,EuJ-I0‘C02LI.Fig. 6.8. Mean flood volumes for the correlated rainfall intensity-duration Folder #2(Pump/Gate).CASE I CASE 2 CASE3A CASE3B CASE3C117700000600000500000uJ400000-J0>3000000.200000100000CASE I CASE 2 CASE 3A CASE 3B CASE 3CFig. 6.9. Mean pumping volumes the correlated rainfall intensity-duration, Folder #2(Pump/Gate).600000500000C.,! 400000LUz300000>0200000U1000000Fig. 6.10. Mean flood volume for the independent rainfall intensity-duration, Polder #2(Pump/Gate).CASE 1 CASE 2 CASE3A CASE3B CASE3C118$00000700000— 600000nE500000-J4000000300000z- 2000001000000Fig. 6.1l.Mean pumping volumes for the independent rainfall intensity-duration, Polder #2(Pump/Gate).6.3.3 Experiments with TidesTiming of low tides is an important factor in polder flood control operation. At low tide, alarge discharge release can be made in a short period of time. Typically, gates have muchmore discharge capacity than pumps. Including tidal effects increased the complexity of thefuzzy system by adding one more decision variable.Tidal effects were simplified and modeled as a time that the system could suddenlydischarge excess stormwater through an opening gate with unlimited capacity. From thispoint on, the operation of the pumping system is terminated. Initially, the time of low tideswas randomly generated from a uniform distribution within the 12 hour period from the timethe storm began. It was found that the tides had more effect if the large release occurred at aCASE1 CASE2 CASE3A CASE3B CASE3C119time around the peak inflow. If low tides occurred early in the storm event, there was noparticular advantage of an elaborate release strategy. If low tides happened late, theoperations would be the same as those without tidal effects, which had simpler control rules.Thus the experiments were modified and based on low tides occurring within ± 3 hours ofthe time of concentration of the polder. The inflows were simulated as before and requiredrelease computed for various times of low tides. At each time interval, the required storagewas calculated.500000_ 4000004 300000200000‘ 1000000Fig. 6.12. Time varying rule curve with tidal effects for Polder #2 with the correlated rainfallintensity-duration.The polder setting used in this set of experiments was PokIer #2, operated withpumping only (20 m3 1)• The rule curve became a set of curves, one for each time of lowtide at 30 minute intervals (Fig. 6.12 and 6.13). The rule curves were derived in the sameway as described previously in Section 5.4, except that now a set of rule curves wasrequired. For each fixed time of low-tides, the required storage spaces were calculated onlyTime tide occurs0 50 100 150 200 250 300 350 400 450time from the beginning of the storm (mm)120up to such a time. During a simulation run, the operating curve was chosen as the oneclosest to the next time of low tide (e.g., if a low tide occurred at 3.2 hr, the curve at 3.5 hrwould be used). In practice, once the predicted time of low-tides was known, then a specificrule curve would be selected based on the next closest time of low-tide.700000cC 6000006500000D400000C,300000200000°‘ 1000000ENDENT INTENSITY)4 hr Time tide occurs—3 hr rom t e eginningof the storm):30mmRULEcURVjTHjDEP1O ,10 50 90 130 170 210 250 290 330 370 410 450time from the beginning of the storm (mm)Fig. 6.13.Time varying rule curve with tidal effects for Polder #2 with the rainfall intensity-duration.The fuzzy programming also required an additional fuzzy variable, the time that a lowtide occurred. It was incorporated into FAM’s with 3 dimensions. This required morerigorous work to determine the content of the cells. By including the time of the low tide,the total number of FAM cells increased from 2 to 53 Fortunately, the required storage(output) values in the cells were only required at or before the time of low-tides. Largenumbers of cells were filled with 0 (zero) if their time from the beginning storm membershipwas greater than the time of low-tides. The fuzzy membership function of the time of low-tides is shown in Fig. 6.14. Tables 6.10 and 6.11, 6.12 and 6.13 show examples of FAM’s121with tide effects (where the time of low-tide membership is TD3) for the correlated andindependent rain intensity-duration relations, respectively.)/43/TD43.0 4.0 5.0 6.0 hrtime from the beginning of stormFig. 6.14. Membership function of time of low tides.1.0I2.0TABLE 6.10First Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2—for Use during Rainstorm (Correlated Rainfall Intensity-Duration Relationship)TIDE RAIN INTENSITYTD3 Ii 12 13 14)IM290000 264000 229000 235000141000 237000 387000 486000 400000104000 171000 395000 400000 40000014000 24000 400000 400000 4000000 0 0 0 0122TABLE 6.11Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2—for UseFollowing the End of Rainstorm (Correlated Rainfall Intensity-Duration Relationship)TD3 DOTOM_____ _____ __________E____RAIN INTENSITY12.289000388000298000460000fl I ‘271000 336000477000 422000400000 400000400000 4000000 0First Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2—for Useduring Rainstorm. (Independent Rainfall Intensity-Duration Relationship)TD3 IiI TO.... 257000 292000T_____IME T419500086000280000206000170000360000TOTAL RAIN DEPTHD1 D2 D1 D40 137000 181000 334000 3960000 110000 151000 293000 3800000 29000 26000 77000 1560000 6000 2000 6000 210000 0 0 0 0TABLE 6.12123TABLE 6.13Second Fuzzy Associative Memory (FAM) with tides (TD3) for Folder #2—for UseFollowing the End of Rainstorm. (Independent Rainfall Intensity-DurationRelationship)TIDETD3 DO‘ VjrrYrr”M155000 177000 337000 4620000 139000 152000 292000 4300000 62000 29000 76000 1570000 14000 2000 6000 200000 0 0 0 0TABLE 6.14Flood Volumes with Different Operating Alternatives with TidesFLOOD VOLUME (x1O’ m3) I,Iuw—System Operation Rule Curve Optimumf(1DD1’T ATfl TT$JTENSTTV AND DURATIONCasel 0 0 0Case 2 0.2 0.3 0Case 3 14.2 14.4 14.0All 14.4 14.7 14.0Casel 0 0 0Case 2 0.0 0.0 0.0Case 3 74.0 74.4 73.9All 74.0 74.4 73.9TOTAL RAIN DEPTHDi D2124Tables 6.14 and 6.15 show summaries of the results of the experiments with tides. Theflood volumes were reduced significantly in both rain simulating settings. This resultedfrom the opportunity to suddenly release all excess waters at the tide change. Theimprovement by the fuzzy alternative was larger than those of the other sets of experimentsdiscussed before. The percentage improvement with both rain simulations was about thesame magnitude.TABLE 6.15Pumping Volumes with Different Operating Alternatives with TidesPUMPING VOLUME (x106m3)zSystem Operation Rule Curve Fuzzy OptimumA lED INTENSifY AND DURATIONCase 1 30.7 15.4 0Case2 116.2 98.0 79.8Case 3 58.6 56.1 54.2All 205.5 169.5 134.0% Improvement -53.3%t -26.4%t 0INI EPENDENT 1NTE SITY.AND DURAT ONCase 1 36.1 12.0 0Case 2 72.4 53.3 42.4Case 3 155.6 151.8 149.8All 264.1 217.1 192.2% Improvement-37.4%t -l2.9%t 0Note:t Compared with “optimum” values; minus sign (-) means worse.It should be noted that in practice the “optimum” is not attainable, as it would require perfectforecasts of the flows.125Figs. 6.15 and 6.16, 6.17 and 6.18 show time varying rule curves with tidal effects forthe case with the correlated and independent intensity-duration, respectively. As mentionedpreviously, the flood volumes and pumping volumes were significantly reduced by large lowtide discharges. This can be seen in Fig. 6.15, where there was no extreme large flood case(Case 3C) in the correlated rain intensity-duration case. Pumping volume figures show theadvantages of the fuzzy alternative over the rule curve when compared to the optimum ones.ELU-lFig. 6.15. Mean flood volumes for the correlated rainfall intensity-duration, Polder #2(Tide).CASEI CASE2 CASE3A CASE3B CASE3C126Fig. 6.16.Mean pumping volume for the correlated rainfall intensity-duration, Polder #2(Tide).500000400000S300000-200000SLI.1000000Fig. 6.17.Mean flood volumes for the independent rainfall intensity-duration, Polder #2(Tide).S300000-I0C,2000000.a.CASE I CASE 2 CASE3A CASE3B CASE3CCASE 1 CASE 2 CASE 3A CASE 3B CASE 3C127Fig. 6.18.Mean pumping volumes for the independent rainfall intensity-duration, Folder #2(Tide).6.4 DiscussionTable 6.16 shows a comparison of the total volumes of water pumped from Folder #2 during2000 simulated floods with alternative operating policies. The simulated flood flows weretypical of the flood flow regime in Bangkok. Table 6.14 summaries the main results fromthe numerical experiments described in Chapter 5 and this chapter. The operating policiesand parameters were adjusted such that the total amount of flooding (the total volume offloodwaters that could not be either discharged or stored with the available storage) wasapproximately the same with all the alternative operating systems considered. Thus thecomparison of total pumping volumes shown in Table 6.16 gives a direct comparison of theeffectiveness of the alternative flood control operating systems.CASE 1 CASE 2 CASE3A CASE3B CASE3C128The operating systems, which were simulated, were:1. with a fixed rule curve (typical of present day operation in Bangkok);2. with a time varying rule curve;3. with a fuzzy logic system; and4. with an optimal system assuming perfect hindsight knowledge of the flows.In the original set of experiments (shown as Row 1 - “Correlated”, in Table 6.14), whichinvolved pumping only, the time varying rule curve was significantly more effective than thefixed rule curve. The fuzzy system was about 6% more effective than the time varying rulecurve, and the optimal system was about 4% more effective still. However, the marginbetween the time varying rule curve (which was taken as the base case) and the optimalsystem, which had the most effective possible operation was only about 10%, which did notleave much room for the fuzzy system to demonstrate its merits over the base case, the timevarying rule curve. It is also worth noting that the fuzzy operating system offered littleadvantage over the base case, time varying rule curve approach with small floods, wherelittle pumping was required with any system; and also with very large floods, wherecontinuous pumping was required with all systems. However, with intermediate floods, thefuzzy system did offer a significant improvement over the base case.129TABLE 6.16Summary of Improvement of the Various Operations Using Different Alternatives% IMPROVEMENT OF PUMPING(Polder #2)System Fixed Ru1e f Time VaryliigRule CurvCPUMP. -9.9%t -3.8%t-14.6%t -4.6%t3ATE. -7.4%t -1.8%t-14.2%tTIDESCOj*elatedindependen-53.3%t -26.4%t-37.4%t -12.9%tNote:t Compared with “optimum” values; minus sign (-) means worse.It should be noted that in practice the “optimum” is not attainable, as it would require perfectforecasts of the flows.130In the second set of experiments (shown as Row 2 - “Independent” in Table 6.16), therainfall generating algorithm was changed to eliminate the correlation between the rainfallduration and its average intensity, although in Bangkok, the storm durations and averagerainfall intensities are in fact correlated. This allowed more variability in the flows and asexpected, shows the fuzzy system to be better than the time varying rule curve by about11%. The fuzzy system is more flexible than the time varying rule curve approach and thusis better able to cope with the more variable flood flow regime.The operation of a flood control system involving both pumping and gravity dischargecontrolled by gates was simulated with the same operating systems. (Rows 3 and 4, underPUMP/GATE in Table 6.16). These added a little more variability to the operating system.Again the fuzzy system was somewhat better than the time varying rule curve approach, butby a similar margin to those with only the pump discharges.Finally a flood control system involving the effect of tidal levels was simulated, againwith the same operating systems. It was assumed that there was a large discharge capacity,after the tidal level fell below the water level in the flood control reservoir. The tidal effectwas simulated by assuming that the time between this large increase in discharge and thestart of the rainstorm was a random variable. This introduced a third variable into the fuzzyoperating rule base and required a family of curves instead of a single time varying rulecurve. With the additional variability introduced by the timing of the tide change, there wasa much larger margin (37% to 53%) between the time varying rule curve approach and theoptimal operation. In this situation, the more flexible fuzzy logic operating system showed alarge improvement of about 25% over the base case, time varying operating system.1317CONCLUSIONS7.1 SummaryFloods have been and still are one of the major problems of the riverside city of Bangkok.The city’s location in the floodplain of the Chao Phraya River, tidal actions in the river andheavy tropical rainfalls all influence floods. For decades, the planning of Bangkok’s floodcontrol has been driven by major flood events. Although many studies and consultingreports on comprehensive flood mitigation and control alternatives have been conducted, inpractice incremental flood control measures have been adopted. Presently flood controlrelies mainly on the polder concept. This is mainly due to the flexibility of the polderconcept which allows phased development of the flood control works, which requiresubstantial capital. The unit or “polder” is created by dividing the land into independent,self-drained areas, each protected by a perimeter dike. The essential element of polderflood-control is the independent drainage-management of floodwater in each of the floodprotection units.Polder drainage management mainly deals with the disposal of excess water in polderseither through gravity drainage or pumping. Finding the most effective way to manipulatethe release of the excess water is very important to the successful flood management. The132present operating procedure in a typical Bangkok’s polder depends on a “fixed” rule curve,which requires the operator to maintain a specific, pre-determined water level upstream ofthe pumping or gate station. Through many years of experience, the operators recognize thatthere could be improvements in the operation, but they are reluctant to move away from thecomfort and ease of operation with the fixed rule curve.The literature on flood control operating system was reviewed. It was found that mostof the technical papers came from academic sources and most dealt with the application ofoptimization techniques. However, the papers which described actual flood controloperations, pointed out that almost none of the optimization techniques described in thetechnical literature had found their way into practice. The main explanation was thatoptimization techniques are too complex to be readily understood by the actual operators andthat the operators are reluctant to use tools that they do not fully understand. Rule curves areeasy to understand and apply, and if they are followed, they tend to resolve the operatorsfrom blame, should flooding actually occur.Fuzzy logic offers a relatively new control technology, that could be useful in floodcontrol. Applications both depend and build on experience with the actual system beingcontrolled. It was thought that it could be acceptable to flood control operators, as itrepresents an extension of the present day rule curve approach. Fuzzy logic wasinvestigated, and it was found that although the approach is reasonably straightforward, thereare many alternative ways of combining the available information and deciding on what todo in any given situation. Numerical experiments were carried out with simple functions133(where the “correct” answer could be easily computed) to find a fuzzy logic control systemthat could be used for flood control.The most promising fuzzy logic system was adapted to flood control situations for apolder, typical of those in Bangkok. Ideally, actual data would have been used, but as theywere not available, synthetic simulated data had to be utilized. This involved generatingrainfall and runoff in a Monte Carlo simulation. The resulting synthetic “floods” weretypical of actual floods in Bangkok and were considered sufficiently realistic for developingand testing the fuzzy logic flood control system. Five hundred floods were used as input datafor developing the fuzzy logic rule base; and 2000 additional floods were then used intesting the performance of the system.In addition to the fuzzy logic system, three other systems were tested for purposes of thecomparison. These were the fixed rule system, a time varying rule curve, and “optimal”operation. With the fixed rule curve, a target amount of the flood storage space wasspecified. When the floodwaters encroached upon this space, the pumps were started andkept on until the available space increased to the specific level. With the time varying rulecurve, the amount of storage space was allowed to vary with the time from the beginning ofthe storm. These rule curves were derived from analysis of optimal operation during the 500floods in the data base. The fuzzy logic system was also developed from the same 500floods.For testing the perfonnance of the alternative flood control systems, 2000 floods weregenerated, using the same probability distributions for the parameters as in the 500 floods inthe “design” data base. The alternative operating systems were adjusted so that they all134resulted in the same total volumes of floodwater, that is, surplus water that could not beeither discharged or stored in the available storage space. Comparisons of performance werethen made on the basis of total pumping volumes. These tests showed the time varying rulecurve system to be much better than the fixed rule approach (14% smaller total flood volumepumped); the fuzzy control system to be better than the time varying rule curve (6% smallerflood volume); and the optimal system (operation with hindsight) to be still better (4%smaller flood volume).Although the numerical experiments showed the optimal control system to be best, thefuzzy logic system next and the time varying rule curve third, the differences in performancebetween these three alternatives were relatively small. Other sets of experiments were thenconducted with more variable inflows and more complex systems, one with both pump andgravity discharge controlled, and one that also included tidal effects. These offered more“room” for the more flexible fuzzy operating system to demonstrate better performance thanthe less flexible time varying rule curve. It is worth repeating that the “optimum” system isnot a practical possibility, as it would require perfect flow forecasts.7.2 ConclusionsBangkok, one of the largest and fastest growing cities in East Asia faces very serious floodproblems. Although many comprehensive flood control schemes have been put forward, thecity has in effect settled for an incremental polder based approach in which the city is135divided into a number of independent polders, each protected with surrounding dikes andwith its own canal and flood discharge. Due to the low elevation of much of the city andpossibility of high tides during the rainy season, large pumping stations are needed fordischarging water from the polders into the canal or river system. Operating the pumps in anoptimal or near optimal way to minimize flooding yet also minimize the volume of the waterwhich has to be pumped is important. Traditionally, in Bangkok the operating system hasbeen the fixed rule curve.A logical extension to the fixed rule curve is the time varying rule curve in which thewater level, above which the pumps and/or gates are opened, varies with the time since thebeginning of the storm. In this study, a procedure was developed for deriving such a rulecurve, on the basis of past flow records or, lacking such records, on the basis of synthesizedflows. Operation with these curves showed reductions in the volumes of floodwaters whichhad to be pumped of 14% over that with operation with the fixed rule curves.Fuzzy logic control offers an extension to the time varying rule curve, which providesadditional flexibility, yet should still be explainable to and understandable by operators.From numerical experiments with fuzzy logic systems, it was found that:1. best results were obtained by using the product rule of input inference and theDirect method of output inference;2. in setting up the fuzzy rule base, it was best to only use data sets where inputvariables had membership values greater than 0.6;3. the fuzzy logic system is very robust in that rules can be left out or can containerrors without seriously impairing performance;1364. it is important to keep the number of fuzzy variables and the number of categoriesinto which each is divided as small as possible to keep the problem manageable.On the basis of the above findings, a fuzzy control system was set up for flood control inpolders typical of those in Bangkok. From simulation studies of the operation of the floodcontrol systems, it was found that:1. in the simplest flood control situation, where all floodwaters had to be discharged bypumping, the fuzzy system was 6% better than the time varying rule curve operation(the total volume of the floodwater pumped was 6% less). “Optimal” operation(where perfect knowledge of the flows was assumed) was 4% better than the fuzzysystem. The difference between the various operating systems showed mainly withmoderate floods. With small floods there was no need for pumping, and largefloods overwhelmed all operating systems.2. in more complex situations, where the flow patterns were more variable and wheregate operation and tidal effects were considered as well as pumping, the fuzzysystem had a greater advantage over the time varying rule curve operating system (6-27% better).In summary the main conclusions are:1. time varying rule curves are much more effective for flood control in poldersituations than the traditional fixed rule curve approach;2. an effective approach to develop such rule curves has been demonstrated;1373. fuzzy logic control systems are more flexible and slightly more effective for floodcontrol than the time varying rule curves;4. the more variability in the system components and the flows, the better the fuzzysystem performs relative to other less flexible systems;5. in setting up a fuzzy logic control system, it is important to structure the problemwith as few input variables as possible.7.3 Implementation ConsiderationsPumping stations for polder flood control in Bangkok are presently operated by fixed rules.This is a simple, reliable system, and the operators are familiar and comfortable with it. Asdescribed above, the logical extension to the present system would be to use time varyingrule curves. This would involve the operator in keeping track of the time since the stormbegan and then reading off a curve the rule curve level for that time. If the water level wereabove this level, the pumps should be on; if not they should be off.To go to a fuzzy logic operating system, it would be necessary to provide a computerand get the operators to keep track of the time since the storm began; and also measure theaccumulated rainfall in a simple rain gage. These values would have to be entered into thecomputer, which would then give the rule curve level, or if this level was also entered,would tell the operator what to do with the pumps (i.e., start them, stop them or leave themon or off). Since portable computers are becoming relatively cheap and since inputting the138required information would impose little more burden on the operators than reading a timevarying rule curve, it would seem worth going to the fuzzy operating system almost rightaway. Other advantages of using a computer and fuzzy logic operating system are that itcould be set up to record the input information and the actual operations. With these data, itshould be possible to fine tune the fuzzy logic rule base and operating system, in effectsetting up an adaptive system that would learn from experience.7.4 Further ResearchThe results of the numerical experiments with flood control operations with the fuzzy logiccontrol system are promising and suggest that further exploration of the technique iswarranted. The fuzzy logic system should be tested in more realistic situations where thesimplified methods, such as the time varying rule curve can not well represent the diversepattern of the storms.It is also noted that a flood control system is a system under stress. Furtherimprovement will definitely involve a trade-off between flood damage and pumping energysavings, which has not been included in this study. Penalty costs of flooding are often largein comparison to pumping costs in a storm. However, the accumulated benefits of savings inpumping costs can make the operation attractive. Investigating such trade-off functionsshould be of interest and a topic of further research.139One of ways to incorporate the risk in the fuzzy system is by building a rule base thatreflects the level of preferred risk. The risk associated with flood control operations can bequantitatively included in the fuzzy control by selecting the design storms used in buildingthe fuzzy rules or FAM’s.Another worthwhile improvement to the system would be to incorporate flood forecasts.How to do this most effectively would be another useful research topic.140REFERENCESAlT. 1985. Flood Routing and Control Alternatives of Chao Phraya River of Bangkok.Final project report to the Thai Government by Asian Institute of Technology (AlT).Bangkok.AlT. 1986. Bangkok Flood Protection. Chao Phraya 2. Final project report to the ThaiGovernment by Thai-Australian Consortium and Asian Institute of Technology (AlT).Bangkok.Ang, A., H.-S., and W. H. Tang. 1984. Probability Concepts in Engineering Planning andDesign. Volume II- Decision, Risk, and Reliability. New York: John Wiley & Sons,Inc.Angel, S. 1987. The social impact of single-objective drainage measures: canals andsquatter housing in Bangkok. Proceedings of the International Workshop on UrbanFlood Protection and Drainage in East and Southeast Asia. Bangkok. June 22-25,1987. G1.1-G1.28.ASCE/WEF. 1992. Design and Construction of Urban Stormwater Management Systems.New York: American Society of Civil Engineers.Bunnak, B., D. Nophakhun, and S. Tadamiti. 1982. Canals in Bangkok: History Changesand Their Impact. Bangkok: Chulalongkom University Press. (In Thai language).CDM. 1969. Master Plan, Sewerage, Drainage, and Flood Protection System: Bangkokand Thonburi. Final project report to Thai Government by Camp Dresser & Mckee Inc.Bangkok.Clark, C.O. 1945. Storage and the unit hydrograph. ASCE Transactions of CivilEngineering, 110: 1419-1446.141Colyer, P. J. 1984. A design storm for a tropical location with limited data. Water Scienceand Technology, 16: 63-68.Drainkov, D., H. Hellendoorn, and M. Reinfrank. 1993. An Introduction to Fuzzy Control.New York: Springer-Verlag.Foster, S. S. D. 1993. Groundwater conditions and problems of the humid tropics.Hydrology of Warm Humid Regions. Proceedings of the Yokohama Symposium, July1993. IAHS Pubi. No. 216. 433-449.Georgakakos, A. P., and H. Yao. 1993. New concepts for uncertain water resourcessystems: 1. Theory. Water Resources Research, 29(6): 1505-1516.Hall, M. J., D. J. Hockin, and J. B. Ellis. 1993. Design ofFlood Storage Reservoirs. Oxford:Butterworth-Heinemann.Henry, W. A. 1974. The tropical rainstorm. Monthly Weather Reviews, 102: 7 17-725.Huff, F. A. 1967. Time distribution of rainfall in heavy storms. Water Resources Research,3(4): 1007-1019.Hydrological Engineering Center. 1987. HEC-1. Flood Hydrograph Package Users Manual.U.S. Army Corps of Engineering, Davis, California.Jackson, I. J. 1989. Climate, Water, and Agriculture in the Tropic. 2d ed. London:Longman Group.JICA 1985. Master Plan on Flood Protection/Drainage Project in Eastern SuburbanBangkok. Final project report to Bangkok Metropolitan Administration by JapanInternational Cooperation Agency (JICA). Bangkok. March, 1985.JICA 1986. Feasibility Study on Flood Protection/Drainage Project in Eastern SuburbanBangkok. Final project report to Bangkok Metropolitan Administration by JapanInternational Cooperation Agency (JICA). Bangkok. February, 1986.142Jordan, L. A. 1991. Automating Knowledge Acquisition. Master of Applied Science thesis.University of British Columbia, Vancouver, B.C., Canada.Jumsai, S. 1988. NAGA: Cultural Origins in Siam and the West Pacflc. Oxford: OxfordUniversity Press.Kosko, B. 1992. Neural Networks and Fuzzy System: a Dynamic Systems Approach toMachine Intelligence. Englewood: Prentice-Hall.Kosko, B. 1993. Fuzzy Thinking. New York: Hyperion.Kosko, B., and S. Isaka. 1993. Fuzzy logic. Scien4flc American, July 1993. 76-81.Lee, C. C. 1990. Fuzzy logic in control systems: fuzzy logic controller-part I and II. IEEETransactions on Systems, Man, and Cybernetics, Vol. 20(2): 404-435.Leeuwen, E. van, and K.-J. Breur. 1993. Urban drainage operation control of pumpedsewer systems during heavy storm events. Proceedings of the 6th InternationalConference on Urban Storm Drainage. Niagara Falls, Ontario. September 12-17,1993. IAWPRC. 1639-1650.Leonowens, A. H. 1870. The English Governess at the Siamese Court. London: Trubner&Co.Litchfield & Co. 1960. Greater Bangkok Plan 2533. Report to the Thai Government byLithchfield, Whiting Browne and Associates and Adam Howard and Greeley.Loubere, S. de la. 1693. A New Historical Relation of the Kingdom of Siam. Singapore:Oxford University Press. (Reprint 1986).Maidment, D., ed. 1992. Handbook ofHydrology. New York: McGraw-Hill.Moreau, D. H. 1991. A risk-based model for drought contingency planning. WaterResources Bulletin, 27(1): 117-123.143NEDECO and SPAN. 1985. Bangkok Flood Control Drainage Project (City Core). Finalproject report to Bangkok Metropolitan Administration by NEDECO, the NetherlandsConsultants and SPAN Ltd. Co. Bangkok.NEDECO and SPAN. 1987. Master Plan for Flood Protection and Drainage of Thonburiand Samut Prakan West. Final project report to Bangkok Metropolitan Administrationby NEDECO, the Netherlands Consultants and SPAN Ltd. Co. Bangkok.Nelen, F., B. Sonnenschein, and F. H. M. van de Ven. 1987. Real time control of urbanstorm water to the receiving polder water. In W. Guijer, and V. Krejci (eds.), Topics inUrban Storm Water Quality, Planning and management: Proceedings of theInternational Conference on Urban Storm Drainage. XXII Congress IAHR. Lausanne,Switzerland. 258-263.Neugebauer, K., K. Schilling, and J. Weiss. 1991. A network algorithm for optimumoperation of urban drainage systems. Water Science and Technology, 24(6): 209-2 16.Office of the Prime Minister. 1979. Thailand into the 80’s. Bangkok: Thai Watana PanichPress.Orlouski, S., S. Rinaldi, and R. Soncini-Sessa. 1984. A mm-max approach to reservoirmanagement. Water Resources Research, 20(11): 1506-1514.Ormsbee, L. E., and K. E. Lansey. 1994. Optimal control of water supply pumping systems.Journal of Water Resources Planning and Management, ASCE, 120(2): 237-252.Ramnarong, V., and S. Buapeng, 1991. Mitigation of groundwater crisis and landsubsidence in Bangkok. Proceedings ofAGWSE 4th International Symposium on LandSubsidence. Houston, Taxas. May 1991.Riehi, H. 1979. Climate and Weather in the Tropics. New York: Academic Press.Sodsathit, A. 1987. Development of the flood protection system for the BMA and thevicinity. Proceedings of the International Workshop on Urban Flood Protection andDrainage in East and Southeast Asia. Bangkok. June 1987. B1.1-B1.20.144Sternstein, L. 1982. Portrait of Bangkok. Bangkok Metropolitan Administration.Bangkok: Allied Printers Limited.Terano, T., A. Kiyoji, and M. Sugeno. 1992. Fuzzy Systems Theory and Its Applications.New York: Academic Press.Thampapillai, D. J., and W. F. Musgrave. 1985. Flood damage mitigation: a review ofstructural and non-structural measures and alternative decision frameworks. WaterResources Research, 2 1(4): 4 11-424.Toebes, G., and C. Rukvichai. 1978. Reservoir system operating policy- case study.Journal of Water Resources Planning and Management, ASCE, 1 04(WR1): 175-191.USACE. 1987. USA CE Engineering Manual on Management of Water Control Systems.U.S. Army Corps of Engineers, Hydrological Engineering Center, Davis, California.Votruba, L., and V. Broza. 1989. Water Management in Reservoirs. Amsterdam: ElsevierScience Publishers.Williams, P. B. 1994. Flood control vs flood management. Civil Engineering. May 1994.5 1-54.WPCF. 1989. Combined Sewer Overflow Pollution Abatement. Manual of Practice No.FD-17. Task Force on CSO Pollution Abatement, Water Pollution Control Federation,Alexandria, Virginia.Wurbs, R. A. 1991 a. A review of modeling and analysis approaches for optimization ofreservoir system operations. Hydraulic Engineering: Proceedings of the 1991 NationalConference. Hydraulics Division of the American Society of Civil Engineering.Nashville, Tennessee. July 29- August 2, 1991. 595-600.Wurbs, R. A. 199 lb. Optimization of Multi-Purpose Reservoir System Operations: AReview ofModeling and Analysis Approaches. Research Document 34, U.S. Corps ofEngineers, Hydrologic Engineering Center, Davis, California.145Yazicigil, H., M. H. Houck, and G. H. Toebes. 1983. Daily operation of a multipurposereservoir system. Water Resources Research, Vol. 19(1): 1-13.Yeh, W. 1985. Reservoir management and operation models: a state of art review. WaterResources Research, 21(2): 1797-1818.Zadeh, L. A. 1965. Fuzzy sets. Information and Control, 8: 338-353.Zimmermann, H. 3. 1991. Fuzzy Set Theory and Its Applications. 2d ed. Boston: KiuwerAcademic Publishers.Zottl, H. 1987. Bangkok flood protection, the problem, the objective, the solution.Proceedings of the International Workshop on Urban Flood Protection and Drainagein East and SoutheastAsia. Bangkok. June 22-25, 1987. D2.1-D2.12.146

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