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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 BANGKOK by SONGKRAN AGSORN B. S. (Meteorology), North Carolina State University, 1980 M. S. (Meteorology), The University of Wisconsin-Madison, 1982 M. Sc. (Hydrology), The National University of Ireland, 1988 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUTREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Civil Engineering)  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA June, 1995 © Songkran Agsorn, 1995  In presenting this thesis in partial fulfilment of the requirements for degree at the University of British Columbia, I agree that the Library freely available for reference and study. I further agree that permission copying of this thesis for scholarly purposes may be granted by the department  or by  his  or  her  representatives.  It  is  understood  an advanced shall make it for extensive  head of my that copying or  publication of this thesis for financial gain shall not be allowed without my written permission.  (Signature)  Department of Civil Engineering The University of British Columbia Vancouver, Canada Date  DE-6 (2/88)  June 26, 1995  ABSTRACT  The flood situation in Bangkok and the way in which it has evolved is described in this study. The present approach to flood control involves use of the polder concept. Since excess 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 fixed rules. Fuzzy logic programming was investigated as a way to improve operations, while not departing too far from the fixed rule operation that operators prefer.  Some simple  experiments were first done to find the most suitable alternative to present methods of incorporating fuzzy information. A new fuzzy algorithm was proposed and tested. Due to unavailability of actual data, a simple, but reasonably representative flood control situation, typical of those in Bangkok was used. developed based on synthetic rainfalls and runoffs.  Operating procedures were  Then, fuzzy operating rules were  derived, and a fuzzy rule base was 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 was developed. The results were compared with three other systems: fixed rule system, a time varying rule curve, and “optimal” operation. Besides the main experiments, which involved only pump operations, additional sets of experiments were conducted for the cases with combined pump and gate operations and with tides.  11  Fuzzy logic programming was demonstrated to be a very promising tool for improving flood control operating procedures for polder systems such as those in use in Bangkok. The procedure can be looked upon as an extension of the fixed rule operating procedures presently being used by the operators. Further extensions are possible, including the use of flow forecasts. However, the main purpose of this study was to investigate the feasibility of using fuzzy logic programming to improve on existing operating procedures.  111  CONTENTS ABSTRACT  ii  CONTENTS  iv  TABLES  vii  FIGURES  x  ACKNOWLEDGMENTS DEDICATION  xiii  xiv  1 INTRODUCTION 1.1 Background  1 1 3  1.2 Objectives of the Study 1.3 Structure of the Thesis  5  2 REVIEW OF BANGKOK’S FLOOD SITUATION 2.1 Background  7  7  2.1.1 History  7  2.1.2 The Chao Pbraya River Basin 2.1.3 Bangkok’s Floods  22  2.2 Flood Control Approaches  27  2.2.1 Background  13  27  2.2.2 Flood Control in Bangkok 2.2.2.1 Background  29  29  iv  2.2.2.2 Folder Flood Control  32  2.2.2.3 Flood Control Development 2.3 Approaches to Flood Control Operation 2.3.1 Background  36  38  38 43  2.3.2 Bangkok’s Practice  2.4 Alternative Way to Improve the Existing Flood Control Operations 3 FUZZY LOGIC  46  3.1 Background  46  3.2 Fuzzy System as Model-free Estimator  54  4 EXPERIMENTS WITH FUZZY LOGIC PROGRAMMING 4.1 General  44  56  56  4.2 Experimental Procedure  58  4.3 Setting up the Rule Bases from Known Output Functions 4.4 Setting up the Rule Base from Training Data  62  65  66  4.5 Results of the Experiments  4.5.1 With Accurate Rule Base  66  4.5.2 With FAM (Fuzzy Associative Memory) Rule Base Derived from Training Data 4.6 Robustness 4.7 Conclusions  73 75  5 NUMERICAL EXPERIMENTS 5.1 Introduction  69  77  77  V  5.2 Experimental Polders 5.3 Simulating Flows  79  81  5.4 Time Varying Rule Curve  86  5.5 Fuzzy Estimating System  88  5.5.1 Fuzzy Membership Function  91  5.5.2 Derivation of Fuzzy Associative Memories 6 RESULTS AND DISCUSSION 6.1 Introduction  93  98  98  6.2 Main Experiments  100  6.3 Additional Experiments  109  6.3.1 Experiments with Independent Rainfall Intensity-Duration 6.3.2 Experiments with Pump and Gate Discharges 6.3.3 Experiments with Tides  114  119  128  6.4 Discussion 7 CONCLUSIONS  132  7.1 Summary  132  7.2 Conclusions  135  7.3 Implementation Considerations 7.4 Further Research REFERENCES  109  138  139  141  vi  TABLES  60  TABLE 4.1.  Fuzzy Rule Base in the Conventional Form for the First Test Function.  TABLE 4.2.  Fuzzy Rule Base Used in the Direct Method for the First Test Function.  TABLE 4.3.  Fuzzy Rule Base in the Conventional Form for the Second Test Function. 63  TABLE 4.4.  Fuzzy Rule Base Used in the Direct Method for the Second Test Function. 63  TABLE 4.5.  Fuzzy Rule Base Used in the Conventional Form for the Third Test Function.  60  64  TABLE 4.6.  Fuzzy Rule Base Used in the Direct Method for the Third Test Function. 64  TABLE 4.7.  Standard Errors of Estimation for the First Test Function by Various Alternatives.  TABLE 4.8.  Standard Errors of Estimation for the Second Test Function by Various Fuzzy Alternatives.  TABLE 4.9.  67  68  Standard Errors of Estimation for the Third Test Function by Various Fuzzy Alternatives.  68  TABLE 4.10. Standard Errors of Estimates of the First Test Function by the Direct Method, Based on the Training Data.  71  TABLE 4.11. Standard Errors of Estimates of the Second Test Function by the Direct Method, Based on the Training Data.  72  TABLE 4.12. Standard Errors of Estimates of the Third Test Function by the Direct Method, Based on the Training Data.  72  vii  TABLE 4.13. Standard Errors as Rules Are Randomly Omitted for the First Test Function.  73  TABLE 4.14. Standard Errors as Rules Are Randomly Omitted for the Second Function. 74 75  TABLE 4.15. Standard Errors as Rules Are Randomly Omitted for the Third Function. 81  TABLE 5.1.  Set-up of the Polders in the Experiments.  TABLE 5.2.  First Fuzzy Associative Memory (FAM) for Polder #2—for Use During Rainstorm. (Correlated Rainfall Intensity-Duration Relationship).  TABLE 5.3.  97  Second Fuzzy Associative Memory (FAM) for Polder #2—for Use Following the End of Rainstorm. Relationship).  (Correlated Rainfall Intensity-Duration  97 102  TABLE 6.1.  Flood Volumes with Alternative Operating Methods.  TABLE 6.2.  Pumping Volumes with Alternative Operating Methods.  TABLE 6.3.  Fixed Rule Curve Operation with Different Fixed Rules—Polder #2.  TABLE 6.4.  First Fuzzy Associative Memory (FAM) for Polder #2—for Use During  103  Rainstorm (Independent Rainfall Intensity-Duration Relationship). TABLE 6.5.  Second  Fuzzy  Associative  Memory  (FAM)  for  Polder  106  110 #2—  for Use Following the End of Rainstorm (Independent Rainfall IntensityDuration Relationship). TABLE 6.6.  Flood Volumes with Alternative Operating Methods for Different Simulated Rainfalls.  TABLE 6.7.  110  111  Pumping Volumes with Alternative Operating Methods for Different Simulated Rainfalls.  112  viii  TABLE 6.8.  Flood Volumes with Alternative Operating Methods for Pump/Gate 115  Operation. TABLE 6.9.  Pumping Volumes with Alternative Operating Methods for Pump/Gate 116  Operation.  TABLE 6.10. First Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2— for  Use  During  Relationship). TABLE 6.11  Rainstorm  (Correlated  Rainfall  Intensity-Duration  122  Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2— for Use Following the End of Rainstorm (Correlated Rainfall IntensityDuration Relationship).  123  TABLE 6.12. First Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2— for Use  During Rainstorm  Relationship).  (Independent  Rainfall  Intensity-Duration  123  TABLE 6.13. Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2— for Use Following the End of Rainstorm (Independent Rainfall IntensityDuration Relationship).  124  TABLE 6.14. Flood Volumes with Different Operating Alternatives with Tides.  124  TABLE 6.15. Pumping Volumes with Different Operating Alternatives with Tides. 125 TABLE 6.16. Summary of Improvement of the Various Operations Using Different Alternatives.  130  ix  FIGURES  Fig. 1.1. Polder flood control concept (adapted from New York Times, Feb. 2, 1995). 8  Fig. 2.1. Lay-out of Old Bangkok.  Fig. 2.2. The Chao Phraya River Basin.  14 15  Fig. 2.3. Details of The Lower Chao Phraya River Basin.  Fig. 2.4. Ground subsidence rates of Bangkok (after Foster 1993).  25  31  Fig. 2.5. River diversion schemes.  34  Fig. 2.6. City Core project’s polders (after AlT 1986).  35  Fig. 2.7. Eastern Suburb project’s polders (after JICA 1986).  36  Fig. 2.8. Various flood protection and related studies and proposal. 47  Fig. 3.1. Diagram of crisp characteristic membership function.  Fig. 3.2. Example of fuzzy membership functions. (Crisp variable X membership in TALL of 0.7 and AVERAGE 0.3). Fig. 3.3. Fuzzfication of crisp input values of rulestriggered.  2  1 X  =  6.3 has a  48 and  2 X  and corresponding  50  Fig. 3.4. Input inference of the example fuzzy rule.  51  Fig. 3.5. Output inference on Y for the example rule. A). Clipped. B). Scaled. Fig. 3.6. Center-of-Area (COA) defuzzfication. Fig. 3.7. Height defuz4fication.  52  52  53  Fig. 4.1. Fuzzy membership functions of inputs X for test functions.  58  x  Fig. 4.2. Fuzzy membership functions of outputs Y for the test functions. 61  Fig. 4.3. Development of the Direct method’s nile structure.  Fig. 5.1. Rainfall depth-duration mass curve used in the simulation. Fig. 5.2. Example of a simulated inflow used in this study.  59  83  85  Fig. 5.3. Required empty storage derived with perfect knowledge of hydrograph. Fig. 5.4. Rule curve derivation.  86  87  Fig. 5.5. Membership function of time from the beginning of a storm. 93  Fig. 5.6. Membership function of rain intensity. Fig. 5.7. Membership function of rain depth.  92  93  Fig. 6.1. Typical operation in Case 1 (Pump).  104  Fig. 6.2. Typical operation in Case 2 (Pump).  104  Fig. 6.3. Typical operation in Case 3 (Pump).  105  Fig. 6.4. Mean flood volumes for Polder #2 (Pump).  107  Fig. 6.5. Mean pumping volumes for Folder #2 (Pump).  108  Fig. 6.6. Mean flood volumes for the independent intensity-duration, Folder #2 (Pump).  113  Fig. 6.7. Mean pumping volumes for the independent intensity-duration, Folder #2 (Pump). Fig. 6.8. Mean  114 flood  (Pump/Gate).  volumes  for  the  correlated  intensity-duration,  Folder  #2  117  Fig. 6.9. Mean pumping volumes for the correlated intensity-duration, Folder #2 (Pump! Gate).  118  xi  Fig. 6.10. Mean flood volumes (Pump/Gate).  for the independent intensity-duration, Polder #2  118  Fig. 6.11. Mean pumping volumes for the independent intensity-duration, Polder #2 (Pump/Gate).  119  Fig. 6.12. Time varying rule curve with tidal effects for Polder #2 with the correlated rain intensity-relation.  120  Fig. 6.13.Time varying rule curve with tidal effects for Polder #2 with the independentrain intensity-relation.  121  Fig. 6.14.Membership finction of time of low tides.  122  Fig. 6.15.Mean flood volumes for the correlated intensity-duration, Polder #2 (Tide).  126  Fig. 6.16. Mean pumping volumes for the correlated intensity-duration, Polder #2 (Tide).  127  Fig. 6.17. Mean flood volumes for the independent intensity-duration, Polder #2 (Tide).  127  Fig. 6.18.Mean pumping volumes for the independent intensity-duration, Polder #2 (Tide).  128  xii  ACKNOWLEDGMENTS  The author wishes to express his sincere gratitude to his major professor, Professor Samuel 0. Dennis Russell for his enthusiasm, professionalism, and his incessant patience and positive attitude in guiding this research. This thesis would not have been made possible in its 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 their candid remarks and criticisms, and constructive suggestions on the research. Encouraging comments by Professor Michael C. Quick are also invaluable throughout the course of the study. The author is deeply indebted to Dr. Dave W. Martin, Senior Scientist of Space Science and Engineering Center (SSEC) at the University of Wisconsin-Madison, formerly his research supervisor at Madison, later a long-time colleague and friend for his endless and timely encouragement and supports in the author’s decades of searching for the diverse education. His correspondences through E-mails are most valuable and helpful. The author would like to thank all members of his family, especially his mother, to whom 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 of TMD, Mr. Nattapong Bunjing, the Director of Thai Trade Center-Singapore and Mr. Nat Srisukhonthanon, Senior Engineer of Public Works Department for their courteous Miss. Boossarasiri Thana is gratefully acknowledged for her kindly assistance. understanding. Funding for the study was generously provided by the Government of Canada, in promoting human resource development for Thailand, through THAILAND CANADA Rattanakosin Scholarship on the occasion of the Bangkok Bicentennial in 1982 (CIDA 906/10569).  xlii  Dedicated to My Mother, who always believes that there is always an opportunity to learn and improve things.  xiv  1 INTRODUCTION  1.1 Background Owing to its location in a floodplain and near the sea, Bangkok Metropolis has naturally inherited flood related problems. The floodplain is a part of the large Chao Phraya River Basin, which experiences floods annually. Flat topography, tidal action and heavy tropical rainfalls have influenced the floods in the area. In the past, living with floods was accepted as a fact of life by the residents. Rice, the major crop for livelihood, has been grown to take advantage of wet season flooding. The network of canals was an integrating part of the riverine 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 since the 1950s has increased the exposure of the present population to flood problems. The canal drainage system, once spread extensively throughout the city for irrigation and drainage purposes, 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 their right of way. Flood magnitudes and frequencies have been increasing. Flood protection has become essential to the city. Although recent developments in flood studies (e.g., Williams 1994) suggest integrated floodplain management as the most appropriate way to institute sustainable development of a floodplain, the sense of urgency after major floods in Bangkok has influenced the authority to pursue a more traditional, structural flood control approach. 1  Many studies of flooding and flood control have been made in recent years, resulting in a number of alternative proposals.  Most of these can be categorized into two broad  approaches: major river-diversions, and land-drainage or diking or polder schemes. The latest river-diversion scheme is considered by some engineers to be the most technically comprehensive and effective way of tackling the flood situation. It is, however, regarded by others as too expensive, time-consuming, and socially and politically impractical. On the other hand, the land-drainage and diking or polder flood-control approach offers a phased development. It requires less capital to implement and allows setting priorities for the lands to be protected. The present flood control scheme has evolved around the polder flood control concept, and the Bangkok Metropolitan Administration (BMA) has opted for this as the basis for its protection scheme.  Fig. 1.1. Polder flood control concept (adapted from New York Times, Feb. 2, 1995).  2  The polder flood-control concept (Fig. 1.1) is based on independent drainagemanagement of the floodwater in each designed unit. It divides the protected lands into selfcontained plots of land or polders. A polder is an area of land surrounded by a river or canal and 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. Since excess 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 pumps or gates are not operated effectively, it may not be possible to prevent serious flooding. On the other hand, if they are used too often and for too long, the cost of operation can become excessive. A strategy for timely release of the excess water should improve the effectiveness of the existing polder system if it can be practically implemented.  1.2 Objectives of the Study The main objective of this study was to understand the flood situation in Bangkok and determine how it could be improved. To achieve the first goal, factors influencing the flood problem in Bangkok were identified and reviewed.  The historical development of  settlements in Bangkok’s area was reviewed for background understanding of the changing land use in the city. A study of the river basin was conducted to gain knowledge about the river and its floodplain. Causes of floods were identified. The various approaches used to mitigate or control floods were also reviewed. Current practices in operating flood control systems were investigated and used as background knowledge for the second goal of the study. The second objective of the study was to fmd the way to mitigate the existing flood problems in Bangkok; once they were identified. As mentioned in Section 1.1, Bangkok’s current flood protection has been relying mainly on structural flood control and following 3  the polder flood control concept. Improvements to the control system could be achieved by using a more effective strategy in releasing excess water from within the polder. Besides improving the flood prevention performance, better operation could also reduce the cost of operating and maintaining the flood control system. There have been many studies of flood operating procedures. Academic studies tend to emphasize “optimization”—operating the gates and pumps in such a way as to optimize some objective, such as minimizing the total expected cost of flood damage and the cost of operation. However, in practice, operators tend to be more risk averse and favor operating according to fixed rules, such as opening the gates and starting the pumps should the water level exceed some pre-specified value.  Recognizing this operational reality, a practical  alternative to derive a strategy for a release of excess floodwater from within a polder system was sought. The simplified time varying rule curve was introduced as an initial step to improve the current operation. In anticipating the more variable and flexible nature of the real 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 far from the fixed rule operation that operators prefer. Fuzzy control systems and algorithms were investigated, and a new fuzzy algorithm was developed and tested. The procedure can be looked upon as an extension of the fixed rule operating procedures presently being used by 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 to the fixed rule, time varying rule curve, and “optimum” alternatives.  A simple, but  reasonably representative flood control situation was defmed and operating procedures were developed.  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 flood  hydrographs were derived, optimal operating rules for each one were developed with hindsight. The operating rule was defmed by the water level below which the pumps should 4  be off and above which they should be on.  After a large number of optimal rules for  individual flood events had been developed, these rules were related to information which would have been available at the time. Two simple items of information were found to be most 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 been developed. Since the main experiments involved rainstorms generated with the correlated relationship between rain intensity and duration, which was frequently used for flood design and planning in Bangkok, additional sets of experiments reflecting more variable floods and flood control operations were also conducted. The experiments included rainfall generated from an independent intensity-duration relationship, a combination of pump and gate operations, and tidal effects. The results, in terms of total release volumes, were compared with results from operations of the various alternatives to evaluate the performance of the fuzzy logic programming.  These showed that fuzzy logic programming provides an  effective flood control system, but its potential to achieve greater improvement of the operation increases as the system becomes more variable.  1.3 Structure of the Thesis Chapter 2 describes the flood problems in Bangkok and the current approach to these problems. The historical background concerning the flood problem is first presented. It is followed 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. The causes of the floods in Bangkok and the flood prevention approach being taken by the city are discussed. The current operating practice of the city of Bangkok in coping with its flood 5  problems is described. A review of recent research and practice in flood control and related operations in water resources follows. In Chapter 3, a review of fuzzy logic programming is given. It introduces the main ideas of fuzzy logic and the concept of the “black-box” estimation approach by fuzzy logic system is discussed.  Use of Fuzzy Associative Memories (FAM’s) as an input-output  translation mechanism is also explained. Chapter 4 describes simple experiments to fmd the most suitable of the many possible ways of combining the available information. Various ways to construct a fuzzy estimating system are examined and compared. A simple extension algorithm for building a fuzzy system is presented for further use in the study. In Chapter 5, the numerical experiments used to test the feasibility of the fuzzy logic approach to the polder flood problem are presented. The development of rule curves and fuzzy logic programming proposed for the study are shown in this chapter.  The  development of the fuzzy logic programming algorithm used to decide when to release excess water in the polder system is described.  Details of the fuzzy programming  techniques, 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 presented and compared with alternative operating systems. In the last Chapter, a brief summary, a discussion of the experiments and conclusions are presented. It includes suggestions for further research.  6  2 REVIEW OF BANGKOK’S FLOODS  2.1 Background 2.1.1 History  Modem 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, but its strategic importance increased with expanding interactions between Thailand and the outside world. By the mid sixteenth century, Bangkok’s status was officially raised from a village to a town. The original walled town of Bangkok was built around 1557 to guard a by-pass canal in an ox-bow of the river. Measuring only 260 m by 480 m and containing two canals and six bridges, it was officially called Thonburi (Jumsai 1988). This new name received 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 the only 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. By the 17th century, strategic forts were built at Bangkok to protect Ayutthaya against sea-borne invasion. The town was later transformed into a busy trade center occupied largely by an immigrant Chinese community.  7  A: 1687. Adapted from Simon de la Loubere (1693), A New Historical Relation ofthe Kingdom ofSiam. London. B: 1895. Adapted from Jumsai (1988), based on the Royal Survey Department’s map 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 new capital. This was based mainly on its strategic location as its surrounding waterways were thought to provide a strategic advantage for defending the city. However, in 1782 the capital was moved to the eastern bank (Fig. 2.1) which was considered to be more defensible than Thonburi. The main river named the Chao Phraya, located on the west and a swampy plain on 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 wide  8  moats to the north, south and west; the latter direction being toward hostile Burma, while the eastern 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 cities were on riverine, man-made islands full of canals. Initially, an old canal (Kiong Lord) was enlarged and extended to join the bends of the river, forming an artificial island for the palace ground. King Rama I (1782-1809), the first king of Thailand after Bangkok became the capital, built many kiongs (canals) to facilitate communication in the expanding city. He drafted laborers to excavate a crescent-shaped canal, forming a new moat (Kiong Ong ang/Bang Lumpoo). This second moat and wall were realigned further to the east, parallel to the Klong Lord. Canal construction was completed in 1785. It linked with the Chao Phraya River to form an oval moat surrounding the man-made river island on which Bangkok was originally built (Fig. 2.1). Fortified walls and gates with a total length of approximately 2 formed the early boundary of the capital. 8 km enclosing an area about 3.46 km  Its  population at the end of the eighteenth century was estimated to be 70 000-80 000 (Bunnak et. al. 1982). Following the practice at Ayutthaya, water transportation was considered as the main mode of communication of the new capital. During the nineteenth century, the city was rapidly 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 somewhat parallel to the first and second, was dug and became a new canal which was linked to the rest of the city’s water network. Other main canals, Kiong Samsen and Klong Saenseap,  9  were later dug in the east-west direction, connecting the river with the former eastern marshland.  Malay prisoners, captured during the southern war campaign, were used as  laborers in digging these two canals. The construction of canals reached its peak during the reign of King Rama V (1868-1910). Almost half of Bangkok’s canals were built in this period. Most canals were originally constructed for transportation and irrigation purposes. Eventually, they aided in expanding the capital boundary. Their function as a large storm drainage system also offered immense benefits to the city. During a storm, it conveyed storm waters, connected with sub-drainage and retention areas, and stored excess rain waters. The life-style of the population adapted well to this waterway environment. Most houses were concentrated near the river or canals, where small boats were available to households. Bangkok’s houses, except the palaces and some commercial compounds, were wooden structures built on stilts or bamboo rafts to protect them from seasonal floods. Near the bank of the river, some houses also were built on stilts with their heights approximately 2 to 2.5 m above the bank (Sternstein 1982). It was more common for houses to be floated on the river or canals.  The aquatic or float house was a unique amphibious settlement  indigenously adopted by the natives for living in the floodplain environment. Similar in style from floor to roof to the house on stilts, it differed only in being built on bamboo rafts and moored in the river or canals. The float house was flexible and mobile. It could be moved up and down the slope of the river bank following tidal action.  The greatest  concentration of float houses occurred from the end of the eighteenth century to the beginning of the twentieth century (Jumsai 1988). It was estimated that by the middle of the  10  nineteenth century, the float house population in Bangkok was 350 000 out of the total population 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 along roads, canals and rivers into surrounding rice fields and orchards. Between 1900 and 1978, 2 while the population swelled from 460 000 to the metropolis spread out from 13 to 290 km 4.73 million (Office of Prime Minister 1979). A road system was first introduced to the city in the early nineteenth century. Roads appeared in many sections of the city as did modem stormwater management and facilities, such as sewers.  Stormwater conveyances were  placed in many parts of the city. Then from a short period after the World War II, the urban development in Bangkok was meteoric.  The population was increasing, resulting partly  from economic immigration from rural areas. More new roads were built, often by filling up the canals, thereby replacing them. The network of roads inevitably changed the discharge characteristics of the canals. It often transformed their function to serve largely as storm sewers.  Furthermore, illegal construction of buildings and garbage disposal into the  waterways continued to limit the discharge capacity of the canals. They became smaller and shallower.  The old network of waterways was altered so much that their once, useful  function as a major storm drainage network system was greatly reduced. The original use of the canals as a transportation system has been superseded by roadways, especially on the east side of the river. As the important contributions of the canals have been overlooked, severe flood 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.  Old  accounts of a vast flood over the great floodplain of the Chao Phraya River were often  11  mentioned by earlier travelers or residents (e.g., Leonowens 1870).  As previously  mentioned, an adaptation to the floodplain, such as a float house, was accomplished in the early era of the city.  However, through decades of neglecting appropriate land-use,  uncontrolled urban expansions and inadequate infrastructure for drainage and sanitary systems, modern Bangkok is burdened with a very severe, large-scale flood problem. In this case, fast-paced development of the city, inadequate attention to associated problems of flood dynamics, and the nature of the floodplain are costing inhabitants of the great city of Bangkok more and more. Flood occurrences and magnitudes have increased and caused much hardship to the population who prefer a western life style. During the 1970s, floods occurred 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 and 1986. In 1983, the largest flood since 1942 took place. The floodwater was higher than 90 cm in some areas (JICA 1986). It lasted up to four months in many areas of eastern Bangkok, which received the most damage from this flood. This prolonged flood caused damage, estimated at more than U.S. $260 million’ (the income per capita of Bangkok’s residents was about U.S. $500). After the major floods of 1980 and 1983, more permanenttype, large-scale flood protection projects have been undertaken. Most of them rely much on available 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 residents of the city although such living does still exist in less urbanized communities, such as in a village near the southern coastline of Thailand. To catch up with the changing nature of  ‘In 1985 price unless otherwise stated. 12  flood dynamics, a polder system was adopted for its flexibility in creating a phased protection of the city. As this development has occurred, the Greater Bangkok area has also 2 of land, covering both banks of the Chao Phraya expanded to enclose more than 1700 km River. The current population of the city is a little over 9 million (more than 10 percent of the total population of the country).  2.1.2 The Chao Phraya River Basin  The Chao Phraya River Basin, in which Bangkok is located, is the largest river basin of the 2 or about onecountry (Fig. 2.2 and Fig. 2.3). It has an over-all drainage area of 162 600 km 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 into  ). In the 2 ) and the Lower Basin (56 000 km 2 two basins: the Upper Basin (106 600 km Upper 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 of Thailand). 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 of ) in the Nan River. The average 3 9662 Mm ) on the Ping River, and Sirikit Dam (6600 Mm 3 detention time of Bhumipol is 2.57 years and that of Sirikit is 1.71 years. These two dams  13  98E  100E  120E  20N  1 8N  16N  14N  12N  Fig. 2.2. The Chao Phraya River Basin.  have been built for hydropower generation, irrigation and flood control purposes. Prior to the drought of 1979 in the basin when the reservoirs could not meet irrigation demands, the top priority was given to hydropower generation. After that drought, irrigation took the  priority over power generation. Hydropower generation has then become the secondary priority. This has led to a more conservative release of water during the wet season. The  14  water is needed for rice irrigation only in the dry season. The other purpose of the reservoirs is for flood control. The reservoirs can, however, only regulate small parts of the flood ) on the Wang, used mainly for 3 flows. The other large dam is Kiu Lom Dam (108 Mm irrigation purposes.  GULF OF THAILAND LEGEND  —‘-C River or Canal %%  River Basin Boundary  []  River Kilometer  Fig. 2.3. Details of the Lower Chao Phraya River Basin.  15  The area from Nakorn Sawan to the Gulf of Thailand has been designated as the Lower Basin. South of Chainat (250 km north of the Gulf) is the alluvial plain of the Chao Phraya River. 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 of them, the Suphan River, does not again join the Chao Phraya, but discharges into the Gulf of Thailand near Samut Prakan, 35 km west of the main Chao Phraya River. In the middle of the basin near Ayutthaya (130 km upstream from the Gulf), the fifth influent tributary, the Pasak River meets the Chao Phraya. There are two main barrages: Chao Phraya or Chainat Barrage (Dam) in the main channel and Rama VI Barrage in the Pasak River. Both of them are parts of a large irrigation project, “the Great Chao Pbraya”. The project includes areas around and north of Bangkok. Water is diverted by canals from Chao Phraya Barrage at Chainat.  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 about  . Furthermore, both sides of the Chao Pbraya have been embanked extensively. 2 1 km km This includes the river reach from Chainat to Bang Sai (110 km upstream). They extend on the western bank down to Pak Kret (80 km upstream). Newer dikes have also been placed on the east side of the river at Pak Kret. Downstream from Bang Sai to Bangkok, the top width of the river varies from 200 to 500 m (JICA 1985). The overall gradient of the river in this reach is roughly 5 to 6 centimeters per kilometer. The gradient of the Chao Phraya from Bangkok to the river mouth is very flat, about 2 centimeters per kilometer. The elevation of  16  the river bank upstream near Bangkok is approximately 1.5 m above mean sea level (MSL). 1 (JICA 1 to 4000 m 3s 3 s In a normal flood period the river discharges range from 1500 m 1985). The water level in the Chao Phraya usually experiences the first rise in May or June over a period of 1-3 weeks. The second rise occurs gradually and reaches its maximum in the upper reach in October and in the lower reach in November. In the Lower Basin, most lands are afready heavily irrigated and cultivated. Rice grains produced here account for more than half of the country’s total rice production. The main irrigating water source is surface water from the Chao Phraya River system. Connecting to the Chao Phraya River throughout the Lower Basin is an extensive network of canals, mostly for irrigation as a part of the Great Chao Phraya project. During the flood period, this delta area is usually inundated with floodwaters. Overland flow has been a part of wet riceirrigation practices in the basin. Floodwater is needed for the rice irrigation. It is used primarily for controlling weeds which would otherwise choke the crop (Jackson 1989). The rice has long been grown in the basin and is basically a rain-fed crop. Unless artificially irrigated, only one harvest of rice is possible. By irrigating the crop, multiple harvesting becomes possible.  The large amount of irrigated land in the Chao Phraya River basin  demands a large allocation of water, which is usually met by reservoirs and canal storage within the basin. The area between Chainat and Ayutthaya plays an important role as a retention basin. In a regular wet season, it often acts as a large reservoir to hold floodwaters back from reaching Bangkok.  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 of  17  Bangkok. If there are heavy rains in the wet season, then the overland floodwater may flow into the Bangkok area. The overflow is helped by the north-south slope of the floodplain and spills-over from the extensive irrigating canals. These spreading floodwaters threaten Bangkok from the north and northeast areas during the high flood season. The water level in the plain starts to rise around May and reaches a peak in October. Flooding in the floodplain from Chainat to Bang Sai usually occurs from September to October. In the river reach between Bang Sai and the Gulf, floods may occur from mid-October to the beginning of December. 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 Phraya 3 s’ (JICA 1986). reaches 1500 m  During a high tide, the tide influx is comparable in  magnitude to the river discharge. The estimated 100-year return period tidal influx to the 3 s’ for the same return period (Zotti 3 s’. The outflow of the river is 3600 m river is 3500 m 1987).  A relatively high tide period usually occurs in November through January.  In  November, if a high river discharge occurs, then it will usually coincide with one or two spring tides. Seasonal variation of a water level in the Chao Pbraya River rises gradually near the end of August. It reaches a peak in November and falls slowly until the end of December. This phenomenon is mainly caused by run-off from the upper reach of the river and the tides in the Gulf of Thailand. Within the Lower Basin, the Chao Phraya River cuts through the city of Bangkok, where the eastern bank is more urbanized than the western.  The river is characterized by its  18  meandering nature when passing Bangkok. The city extends from about 27 to 56 km north of the Gulf of Thailand. The main drainage system is the network of canals, which even in their reduced states, are still an important component of the drainage system. They come under 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 the west bank connect the Tachin (Suphan) River with the Chao Pbraya River. Main canals on the west bank run mostly in the east-west direction while most canals on the east bank run both 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). The . 2 cross-sectional area is in the order of 10 m 3 2 to 3 m  The discharge capacity ranges from  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 discharge  . 1 3s capacities range from 10 to 80 m  Most of the Lower Basin areas around and including Bangkok are covered by a layer of so-called Bangkok Dark Heavy Clay. The layer is approximately 2 m thick. This soil under yearly flooding is extremely well suited for wet-rice production. On the other hand, the main soil type of the Bangkok metropolis is a deep silty clay, 30-40 m thick (JICA 1985). A soft clay layer extends from the surface to a depth of 10 to 15 m below MSL, with a stiff clay layer 10-15 m thick underneath.  The clay layers lie on a dense sand layer, located  approximately 30 m below MSL. The city of Bangkok is situated overlying a multi-aquifer alluvial sequence with interbedded clayey aquitards (Foster 1993). The ground level of the Bangkok area ranges from slightly below MSL to 1 to 2 m above MSL. Such low levels of  19  land make gravity drainage of overland flow or intense monsoon rainfalls during the wet season 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 heavily influenced by the monsoon circulations. The north-west monsoon brings a dry cool air mass to the basin generally from November through May. During this period, sporadic, isolated thunderstorms may occur at the edge of the incoming air mass. Relatively small amounts of rainfall result from such storms. On the other hand, the south-west monsoon brings a much larger portion of the annual rainfall in the basin. Its onset usually signifies the beginning of the rainy season. The south-west monsoon usually begins in May or June. It brings warm moist air from the Indian Ocean to the area. The associated complex convective activities bring rainstorm systems into the area. Most rain patterns are a concentrated heavy frontal moving storm type. The rain bands often move following a convergence zone across the floodplain in the north-south direction during the south-west monsoon season.  The  rainstorms 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 degraded tropical storm or depression through the Central Plain. Such tropical storms usually occur in August, September and October. Since most of these systems are usually weakened over the land passage, the resulting rainfalls is much less intense than from rainstorms associated with the south-west monsoon.  Often, they are characterized by wide-spread frontal rain  bands with occasional heavy-spells. Such rains may fall intermittently for a couple of days during a storm passage.  20  Rain-making clouds over Bangkok are high water-content warm clouds, resulting from high temperature and humidity of the tropical atmosphere. Thus, a small convective cloud may sometimes produce a heavy shower. A single cumulonimbus cloud often produces a short duration, but heavy shower. More lengthy precipitation is from cloud systems related to the monsoon-induced convergence zone and tropical storms. More precipitation comes from tropical cloud masses organized on the meso-scale with a dimension of 25-100 km (Riehl 1979).  . 2 Their average area tends to be in the order of 1000 km  The area  concentration of rain is about 10% of a synoptic rainstorm envelope. The majority of the tropical rainstorm events are characterized by a single shower, rarely by two showers, and most rain falls at the forward edge of the cloud. After the rain area has built up to maximum size, heavy rain ceases within 15-30 mm. “Late precipitation” falling at a lighter rate may continue for an hour or more. The total duration of any monsoon rainfall in the Chao Phraya’s Lower Basin is less than 9 hours. The average duration of the storm is 1 hour. Rainstorms have an average rain depth of about 30 mm. Rainstorms, except those associated with the tropical storms, usually occur only once within 24 hours. They are usually followed by periods of clear sky. Most rain falls in a short period, driven by convective activities and are strongly diurnal influenced. A single rain event usually accounts for the total rainfall within 24 hours, except during a tropical storm passage, when it may rain intermittently for several hours. These diurnal patterns of rainfall are well recognized in the Bangkok area, similar to other monsoon regions.  21  Rainfall events in the river basin are concentrated in the wet season. During the rainy season, about 85% of the annual rainfall depth occurs. The rainy season in the Upper Basin occurs 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 the Lower Basin usually occurs from mid-May to mid-October. The mean annual rainfall over the Lower Basin is about 1340 mm with an average annual evapotranspiration rate also around 1000 mm.  About 80% of the annual precipitation in the basin evaporates.  In  comparison, 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 that month is around 300 mm. It ranges from 150 to 200 mm, in the other months of a wet season. The annual rainfall of Bangkok varies from 900 mm to more than 2000 mm with an average of 1400 mm. The number of rainy days in Bangkok ranges from 90 to 130 days per year. It should also be noted that rains in Bangkok concentrate more on the eastern side of the river.  2.1.3 Bangkok’s Floods  Most floods in lowland river basins develop differently from ones in the upper valleys. A single flood wave in an upper tributary may cause a sudden flash flood locally, but it often has much a smaller effect in a wider, lower branch of the main river. Floods in a lowland river-basin, such as the Chao Phraya’s Lower Basin, require a large accumulated excess  22  surface-water volume. The contribution of the entire river basin is usually needed to cause a major flood. Regular seasonal flooding is an inherent characteristic of low-lying river basins. Floods overflow the banks and spread across a large area of a basin annually in the time of high water. The Lower Basin of the Chao Phraya River is partly flooded for one-third of the year during the wet season. By living in a flood-prone area of the Chao Pbraya Basin, Bangkok residents have to live with unavoidable flood phenomena.  Modifications of the river  environment might induce an unforeseen or undesired flood response.  At one time the  replacement of canals by roads was a desirable idea to planners for urban development since the canal right of way was publicly owned. Bangkok, like other emerging metropolises in developing countries, such as Jakarta, the capital of Indonesia, seems to have difficulty in coping with rapid growth. Its crowded population requires large resources to deal with inadequate infrastructures. Floodplain management often comes rather late to solve the underlying 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 the main river, topographic features resulting from land subsidence, unorganized land uses, and insufficient drainage and heavy rainfall in the wet monsoon season. The overland flow from the river basin and tidal actions interfering with the river outflows were described in the previous section. The overflow through the irrigated canals threatens the city from the north and north-east. It often occurs sometime from mid-October to December. Also, a high tide may cause high water levels in the river to persist for a long period of time. Thus the  23  drainage of a low area, such as Bangkok can be difficult. High tides affecting the Chao Phraya River and Bangkok can occur from November until the end of December. While flooding is necessary for rice farming in the vast area surrounding Bangkok, floods in the capital cause disruption in the activities of urban dwellers.  In the 1983 flood, about  1800 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 rains  continued to fall in September and October. The entire year was an unusually wet one, with 1560 mm compared to the average of 1400 mm.  The whole river basin received  considerable amounts of rain throughout the season. The dams upstream could not cope with the high water volume and tended to release more water to afready full river channels downstream. By the end of October, a tropical depression passed through the river basin and brought more rain to the city. At the time the water level in the river kept rising and coincidentally matched the rising tide. The drainage system of the city failed, and parts of the city were flooded for a long time. Other important factors that complicate the flood problem are the progressive subsidence of the soils beneath Bangkok (Fig. 2.4) and its reduced retention and drainage capacity resulting from rapid urbanization. The underlying foundation, the soils beneath the city, have been sinking at an alarming rate. Through many years of excessive groundwater abstraction for the increasing demand of water supply for the expanding city, the aquifer underneath the clay layer becomes progressively lower. Large-scale development of the aquifers underneath Bangkok for public water supply began in 1954.  The average  abstraction rate during the 1 970s was around 400 Ml d’, causing the groundwater level to  24  SCALE  10  20  km  Depression (in m) of piezometric surface of confined Bangkok 4 alluvial aquifer in 1987 20-40 cm  b  40-60 cm >60 cm  Cummulative land surface subsidence to 1987  GULF OF THAILAND  Fig. 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 were drilled by both governmental and private agencies. The demand was caused by the city’s failure to provide surface water to keep up with the rapid urbanization of the city. The average rate of the groundwater abstraction in the late 1 980s was around 1400 Ml d’ (Foster 1993). Besides its use for irrigation, water from the Chao Phraya River has also supplied Bangkok’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 have  25  consolidated and caused lands to sink. Recent land subsidence in the critical areas (already . The rate of subsidence can be as low 4 below MSL) has a maximum rate of 10 to 15 cm yr as a few centimeters per year in the oldest part of the city. It reaches nearly 15 cm yf’ in the eastern suburb. A large part of eastern Bangkok has already subsided and behaves like a large lake during a heavy flood. Some high-valued real-estate had to be diked, and the use of pump drainage was implemented. The dikes were often built by elevating surrounding roads. 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 few years. Metropolitan Water Works Authority (MWWA), the main groundwater supplier in Bangkok, also planned to turn its sources to surface water. Besides the land subsidence problem, the urban expansion of Bangkok also makes the flood problem worse. The extensive network of the canals is in a reduced state due to the expansion 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 the city expansion. The expansion has occurred radially and along main roads and highways. The spatial pattern of the development in Bangkok follows the outward expansion, caused by 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). Land uses in the inner city usually have a mixed commercial and residential pattern.  The  construction of major highways and the extension of bus routes far from the city center have supported highly dispersed development along major roads. Rural land uses between the  26  arterial roads have been adapted to the expanding urban market. The outer suburb areas are often subjected to housing-estate and industrial-complex development. The development gradually replaces the irrigated rice paddies. stormwaters are reduced.  Thus potential retention areas for excess  Urban development also changes surface permeability of the  lands. Natural soil-depressions and reduced infiltration capacity result from impervious land development.  Increasing impervious areas increases run-off and reduces the time of  concentration.  Furthermore, the overcrowded population and inadequate management of  waste intensify a problem of insufficient drainage of the area. Modification of canals by building obstructions into the waterways is also a result of development. The reserved lands along the main canals are up to 200 m wide. They are often occupied by low-income dwellers, and more than 8000 houses are in such areas (Angel 1987). The communities here are often suspected of interfering with the waterways and obstructing canal improvement and maintenance. The canal capacity is reduced by the building of houses into the canals, the growth of water-vegetables, and garbage disposal into the canals.  2.2 Flood Control Approaches  2.2.1 Background  Through time, various ways to tackle the flood problems in lowlands have been developed and applied. In a growing urban area, especially in the developing countries, the population  27  has often encroached upon flood-prone lands without appropriate town planning. Then the area itself requires not only adequate internal drainage systems but also protection from external riverine flooding. Traditional uses of hydraulic structures to “control” floods have been dominantly applied on rivers and their floodplains around the world. Only recently has a “softer” concept of integrated management become increasingly popular with water engineers and policy makers in dealing with floods. Flood controls are often classified into two broad approaches: structural measures.  non-structural and  Non-structural flood control or flood management includes flood  proofing and warning, land-use controls and floodplain insurance. Its goal is to alleviate existing and future flood hazards in the most cost-effective way. It is designed to reduce the flood-damage potential of a floodplain without incurring heavy capital costs and may require only minor civil engineering works. Flood problems in heavily urbanized catchments could be treated individually within the framework of an overall integrated catchment plan. An integrated catchment plan provides a long-term view of a flood control policy. Structural flood control, on the other hand, is designed to prevent or eliminate inundation of floodplains by using hydraulic structures such as reservoirs, diversions, levees, dikes, or channel modifications.  Both structural and non-structural approaches produce different  physical impacts within the catchment and require a compromise on related social, political and environment issues for successful implementation. Thampapilai and Musgrave (1985) reviewed both measures in flood mitigation strategies. The combined use of non-structural and structural measures is often considered as the best approach to tackle flood problems.  28  2.2.2 Flood Control in Bangkok  2.2.2.1 Background  Many approaches to flood control in Bangkok have been investigated and some have been implemented. Non-structural approaches have been under study in Bangkok following the implementation of structural flood control measures.  For example, land-use control is  currently being experimented on some pilot plots of lands. The idea of flood insurance for inner high-economic valued lands (City Core area) has also been advocated. Most emphasis and 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 be accomplished by the creation of upstream flood detention reservoirs, and also by flood diversion, channel rectification and embankments. Bhumipol (1964) and Sirikit (1974) are the two major dams which are located upstream of the Chao Phraya River. At the time these dams were built, it was anticipated that they would help solve the flood problem in the lower floodplain of the river, especially control the flood in Bangkok. Once, in operation, the reservoirs can only regulate small to medium sized floods downstream.  The upstream  locations of the dams in the Upper Basin make them ineffective in controlling floods downstream in the elongated catchment. This makes it difficult to manage the reservoirs, which also have other competitive demands for water.  The reservoirs are used for  generating electricity and for irrigation of the lower floodplain. Often, in a wet year, these  29  reservoirs are already at full or near-full capacity by the middle of the wet season when the rain starts to shift to the lower floodplain. This time of the year coincides with high water in the river and high tides. If heavy rains continue in the upper valley, possibly due to passage of a tropical storm, excess water may have to be released from the reservoirs. The excess release complicates the situation of Bangkok’s flood when the high tide, heavy local rainfall and high river water all occur at the same time. To better regulate the floodwater in the Lower Basin, a new reservoir has been planned in the Pasak River which merges into the Chao Phraya River at Ayutthaya. In the Greater Bangkok area, large available public ponds and the farmlands to the east of the capital are used as retention areas. The large canal system is also used for storage of floodwater. Flood diversion and channel rectification have also been investigated as an alternative to solve the flood problem in Bangkok. The channel diversion scheme was first introduced to by Litchfield, Whiting Browne & Associates, and Adams, Howard and Greeley in their report on urban planning for Bangkok (Litchfield & Co. 1960). It was, in fact, the first flood-control design for Bangkok. Two diversion canals, one on each side of the river, were proposed for flood control (Fig. 2.5). They were to cut from the Chao Phraya River north of Bangkok to the Gulf of Thailand.  However, this part of the plan was rejected by the  government. Later, similar plans were brought up again after the great flood of 1983. The Chao Phraya-2 project (MT 1986) was proposed following the fmdings from the Flood Routing Alternative (By-pass) project (MT 1985) which concluded that a flood diversion through the existing waterways on the east bank was not economical or effective. In the 3 s’) on the west Chao Phraya-2 project (AlT 1986), a diversion channel (capacity of 2000 m  30  bank was proposed with a length of approximately 60 km. A diversion control was to be installed at Pak Kret, just north of Bangkok. Also, a group of sophisticated tidal barriers and 3 pumps with capacity of at least 1600 m  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 plan should eliminate the need for smaller pumps along the main canals or river. Both sides of the river still require embankment works. The west bank embankment was to be created by soil materials from the excavation.  Although the river diversion scheme seems to be  technically viable and economical, it cannot be put in place because of the huge investment required and the political problems that would result from the large land procurement. Thus, the river-diversion scheme is considered to be impractical by many.  Gulf of Thailand 1—Litchfield Diversion Plan (Litchileld & Co. 1960) 2—Flood Routing Alternative (By-pass) Plan (AlT 1985) 3—Chao Phraya 2 River Diversion Plan (AlT 1986)  Fig. 2.5. River diversion schemes.  31  The flood control schemes which have been implemented in Bangkok have been using the polder system. This allows a phased-development of protection. The polder system of Bangkok has been developed over many years. Its first design was proposed in 1969 by Camp, Dresser and Mckee Inc. (CDM 1969). The total protected area under the plan was 370  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 Control  A polder is usually created to isolate an area from exterior high water levels. It permits control of water levels in the interior drainage system by drainage facilities (Fig. 1.1). A basic polder system consists of a peripheral flood barrier high enough to prevent the overflow of floodwater from outside the protected area. It has at least one boundary which connects to a waterway. Drains, sluices, gates and pumps control the excess surface water and seepage inside the protected area. The excess water is discharged into either a canal directly connected to open water or a so-called, reservoir system. The system can be a simple or more complicated network of canals.  By dividing the flood-prone land into  several polders, a phased development of flood control for the protected land can be planned. Different water level controls can be adapted to each polder environment and the  priority of flood protection in each polder can be determined.  Polder designs can be  classified into two broad groups: small multi-polders and a large polder (JICA 1985). In the small multi-polder design, a main pump is located at the lowest point of each polder.  32  The water level in the main canal is controlled by the river itself. In contrast, main pumps in the large-polder design are located near the river.  The water level in the canal is then  manipulated by the pump and/or control gate discharge. An urban Bangkok polder is characterized by its large population, intensive land-use and expensive price of lands. The flood protection has given greater focus to the more populated, urbanized, eastern section of the city. The river embankment on the east bank can be viewed as a large enclosing dike. The long earthen-dike along the north and east of the city effectively helps create a large polder surrounding Bangkok. Small multi-polders of the City Core project (Fig. 2.6) have been operated for the more sensitive inner city. The  polder approach used in the eastern Bangkok suburb (Fig. 2.7) followed the large polder approach. It consisted of a large outer polder and smaller inner polders. The outer polder system protects the city area against overland flows from the northeast area and flooding from the Chao Phraya River. The inner polder system protects high-priority areas, inside the outer one. Pumping and gate stations in the system consist of main stations, sub-stations and mobile units. Flood barriers consist of roads, highways, railway walls, dikes and flood walls. Extensive dikes, both concrete and earthen, have been constructed throughout the city. The long, earthen dike (King’s dike) in the north and northeast section of the suburb of Bangkok was built to prevent the overland-flows.  33  ]  PUMPING STATION  ()  POLDER NUMBER  I 1OT,5S  1OYEARSRETURNPERIOD OF WATER LEVEL AND EXPECTED LAND SUBSIDENCE 5 YEARS RETURN PERIOD OF RAIN STORM  Fig. 2.6. City Core project’s polders (after AlT 1986).  34  ‘:“—7 i;v.’  /7 V I) /  H  -:-.J RG ..  NL,.  i--..  —  -  ‘—  /  .  I  RG %..$  /  I  ‘1  .  ,1  / ‘  /  If  __.J..  R  I  :i  /  .1  RG RG  .  L  ç  cr  ___f-_,  ‘‘  iJ I  /  -----i.  i  ,  I  -  L.’,  .  •  --. -  iJ_ .  ..  -...  RG  --  ... ,.  I  I  --rz7 -  ç’q•’  /_I)•••/; 7  .:.  .1  .tz:__*  /  \ 4z._  i  Ii  /  / ...•  ‘y) %-.  / 1  EASTERN SUBURB POLDERS  ®  PUMPiNG STATION  REGULATE GATE  A  CONTROL GATE  EMBANKMENT  POLDER NUMBER  Fig. 2.7. Eastern Suburb project’s polders (after JICA 1986).  35  2.2.2.3 Flood Control Development  Various flood protection proposals have been considered by the city administration after the great 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 a flood with a 100-year return period. The design-tide was for a 100-year return period, and . 2 the design-rainfall for a 2-year return period. The area to be protected was about 1400 km Most proposals could be broadly classified as a river-diversion, land drainage, or a polder scheme.  Gulf of Thailand 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.  36  As 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 have been significantly improved in their storm conveyance capacities. Embankments along the Chao Pbraya River from the north of Bangkok were constructed to extend to the coastline of the Gulf of Thailand in Samut Prakan, south of Bangkok.  Some lands are used for  stormwater retention. Many pumps and gates have been installed in main canals and some secondary canals next to the river. To control overflows from the north and northeast of the city, long earthen dikes were built along the north and east outer boundaries of the city. The overflows are to be routed through the improved existing canals southward to the Gulf of Thailand.  The design  3 s’. Parts of agricultural lands in the farther, eastern discharge was estimated at 75 to 100 m areas 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 eastern ) where the heaviest damages occurred in the floods of 1983, was diked 2 suburb area (260 km into three large polders and one inner polder. The protected area is divided into urban and rural areas. The urban section is drained by pumps. Farther east, in the rural outer area which is considered as lower-valued land, flooding is allowed to occur, leaving the area with poor drainage and as a retention area. A few main pump stations in the canals next to the river were built in addition to more than 10 tidal gates along the river. 2 in the inner city, flood protection works are more In a dense business area of 92 km extensive (City Core project). They were built following the reviewed and updated design of the multi-polder, CDM plan. The area was divided into eight polders. About 50 km of  37  flood barriers were built, as was a drainage conduit of 12 km. New pumps and gates were also installed. On the west bank of the Chao Phraya river, where the population is less dense, the flood control facilities were built following the multiple polder approach (NEDECO and SPAN 1987).  , with the majority of the land being 2 The total protected area was 135 1cm  agriculturally related. A total of 108 km of flood barriers were built to form multi-polders in 1 and 45 regulators were installed. 3s the area. Pumps with a total capacity of 125 m  2.3 Approaches to Flood Control Operation 2.3.1 Background  The focus of real-time operations in Bangkok’s flood control is mainly in pump/gate operations. Pumps are an important component of the polder system because of the flat nature of the floodplain. Though the cost of pumping during a risky storm event is often far less than its potential flood damages, the long-term cost of operating and maintaining pumps is relatively high. The city’s flood control planners and engineers realize there is potential for the improvement of the system by adjusting the pump operations. Improving the real time operation of main pumps should reduce the over-all cost of flood control. The present rules for operating pumping stations involve pre-determined set-levels. If the water level in a canal upstream of the station exceeds its set level, the pumps are started. When it falls below, they are stopped. Although such strict rules are easy to follow, they have been found  38  to be insensitive to a storms’ pattern. Thus, to improve the operation, a more responsive operating policy is sought to replace the current one. The current available technologies on real-time flood control have been investigated. One of the alternatives is to automate the whole drainage system to attain an optimal performance.  This involves the use of a  mathematical model to simulate behavior of the system, flow forecasts and the use of various optimization techniques. The goal is to create an optimal operation by a global control approach. Global control is a centralized control in which a control center is established to determine the appropriate operation actions for various points in the system. The global control can be a manual, supervision, or automatic control.  There has been research in  improving global control in combined sewer overflow (CSO) problems. A main objective is to equalize the spatial utilization of stormwater storage within a large distributed, network system of sewers (e.g., Neugebauer et a!. 1991). In flood control, engineering designs and controls are normally aimed to maximize an expected utility function.  This approach is well defined if uncertainty can be handled  properly, or the environment is not under stress. In a real-time operation, a control situation often differs from those used in design. Optimal operation can be achieved only if the forecast flows are accurate and reliable. Usually, control decisions have to be made with limited time and information.  The decision environment is often under stress.  In this  situation, operators are more likely to seek a conservative path to ensure that they can adjust the control in the next time step. This tendency reflects a long practice in engineering in dealing with the uncertainty.  Engineers like to “bound” their uncertainty in making  39  decisions or design and then add a safety margin instead of optimizing to minimize expected costs. A review of literature in water resources has indicated the slow acceptance of the optimal operation goal by field operators in practice. Despite advances in the theory of mathematical optimization and modeling, many water resources systems are still operated manually. Only a few of the large research studies of optimization in water resources have been directed to real-time operations.  The Task Force on CSO Pollution Abatement of  Water Pollution Control Federation (WPCF 1989) and the Urban Water Resources Research Council (ASCE/WEF 1992) reported that most existing real-time controls of combined sewer systems relied primarily on manual manipulation of the systems. Control decisions were based on the visual inspection of telemetered data. Mathematical optimization models were not widely used for automatic control of such systems. Recently, Ormsbee and Lansey (1994) noted that there were severely limited practical applications of mathematical optimization techniques in generating policies for water-supply pumping systems. Similar conclusions of limited applications in practical operation were drawn earlier by other researchers, especially Yeh (1985) and Wurbs (1991a).  Georgakakos and Yao (1993)  indicated that the majority of reservoir operators did not usually seek a control policy that strictly followed an optimal path. Moreau (1991) noted that a reservoir operator in a water supply 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 to address the risk and uncertainty arising during operation might be a cause of the slow acceptance of the techniques. Orlouski et al. (1984) concluded that most reservoir operators  40  tended either to be risk-averse decision makers or to follow pre-determined, welldocumented rules of operation. They inclined to choose a conservative path to reduce their liability. Very often, operators focused their attention and efforts to avoid dramatic failures when the system was under stress. In many real-time operations of flood control systems, a hierarchy of simple rules of operations is still used extensively. Common hierarchies of operating rules includes rule curve, release schedule, and operating constraints. A rule curve is defined by elevations in a reservoir which define ideal (desirable or target) storage volumes and provide for release rules specified as a function of storage content (Wurbs 1991 b). Rule curves are typically expressed as a pool elevation-time diagram. A release schedule is composed of sets of rules or curves of releases for various inflows and amounts of 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 sense of security to a flood control operator in making a decision. An operator will be relieved from any blame if the system fails as long as he or she follows the pre-set rules. Operation under a strict set of operation rules may, however, be inflexible. While an operation using a fixed rule may be able to deal with a major flood, it may miss an opportunity for reducing flood damage during more ordinary floods. In the polder flood control, the emphasis is on the main pump control of each polder unit. The philosophy of polder flood drainage is to divide the area into small, independent drainage management-units that can be assigned priority of flood protection.  Thus, the  control here can be dealt with as a local control. The main objective of pump control of the  41  polder is to reduce the long-term, operating time and hence cost of the pumps, yet avoid flooding of the protected area as long as pump capacity is available. This can be achieved by manipulating the pump control strategy during the storm. All potential storage capacity of canals and retention within the polder should be fully used. Thus, the operation is similar to that of a single reservoir. Current practice in reservoir operation should provide insights useful 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 aspect of reservoir operation, very few have been applied to the real-time operation.  The  dependence on accurate forecasts makes the techniques less applicable to practical real-time operations. Sophisticated control systems linked by radio or land-line telemetry monitoring and operated by computers also lack the robustness and comparative simplicity of local controls (Hall et al. 1993). Wurbs (1991 b), in his review of reservoir operations under the U.S. Corps of Engineers, noted dominant use of pre-specified rules of operations. Rule curves and regulating schedules are among the most prevalent rule structures commonly used in reservoir operations. Some detailed discussions on rule curve construction can be found in Toebes and Rukvichai (1978), USACE (1987), or Votruba and Broza (1988).  42  2.3.2 Bangkok’s Practice  Usual procedures of the city in preparing for drainage operations during floods are as follows. Before the rainy season, storm-sewer conduits are cleaned up and repaired. Canals may be dredged. Plants and garbage in the canals are removed. This waterway cleaning covers all the urban areas before the first rainstorm. In a wet season, Flood Control Operation Center under the Department of Drainage and Sewerage (DDS) of BMA operates fully. During a rainstorm, the center will act as a main control and monitoring center. It supervises, controls and plans the flood operating system. The center coordinates various agencies involved, and issues necessary operational policies or guidance to pump/gate operators.  The center receives real-time weather information,  provided by the Meteorological Department. The department controls a radar and rain gage network. Although, a dense network of rain gages over the city exists, most of these gages are non-automatic. Moreover, the water-levels and tidal conditions are processed by RID, Hydrographic Department and BMA.  Monitoring and inspecting teams are sent out to  observe flood situations and conditions of dikes.  The hydrological information and  monitoring data are transmitted to the center. A group of senior experts at the center will determine a specific operational plan besides a pre-determined one. The pre-determined plan is to be modified based on real-time information on hydrological, meteorological and flood situation data. Gate and pump operations during a storm event usually follow a pre determined rule. The operation can, however, be overruled by the center. The underlying drainage approach is that the canals should flow by gravity, through open gates when the  43  river is at a low stage. When the river stage is too high to permit gravity flow through the gates, 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 require that the water level in the reach of the canal upstream of the station be maintained at some pre-set level. Different levels are used for dry weather, a storm, or a cleaning-flushing period.  The central control coordinating group decides whether the standard operating  orders should be modified based on continuously updated hydrological information. The current overall flood control operation, thus, depends upon the personal knowledge of the system by a few key people.  2.4  Alternative Way to Improve the Existing Flood Control  Operations  The above discussion indicates that a greater amount of refinement of the mathematical optimization techniques is needed for real-time operation. However, the persisting use of rule-curves also suggests an importance of uncertainty which is an influence in real-time control. Pursuing the “academic” approach to the automated global control does not have a good chance of being utilized in practice.  Alternative local control that includes some  treatment of uncertainty in operation may be more appropriate. This study of the flood control operation seeks to find such alternatives.  44  A relatively new concept, fuzzy logic, was tested to see if it could improve on the existing strict rule curve operation.  Due to difficulties in accessing real flood control  operational data for testing the new concept, a simple simulating model was chosen in order to justify further investigation of the application of the concept.  Once the concept was  proven satisfactory, either the flood model can be improved and calibrated with the polder environment, or available field data can be sought and collected once the operators concern could be convinced by the results. The following chapters (Chapter 3 and 4) concentrate on the fuzzy concept and the extension technique of fuzzy programming proposed in the study. Chapter 5 describes the numerical experiments conducted. Chapter 6 discusses the results and is followed by the last chapter, conclusions.  45  3 FUZZY LOGIC  3.1 Background  Fuzzy logic is a multi-valued set theory.  Fuzzy logic theory and the word fuzzy as a  technical term were first introduced by Zadeh (1965). Since then, the fuzzy logic concept has been applied in various fields.  In principle, fuzzy logic can be used to model any  continuous 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 of applications is often called, fuzzy logic control (Lee 1990; Zimmermann 1993).  Some  examples of applications include: auto-focus control in cameras and camcorders; loading controls in washing machines; braking-controls of high-speed trains; and process controls for cement kilns. A short background on fuzzy logic as an estimating tool, as it is used for this study, is given here. A complete description of fuzzy logic can be found in many text books (e.g., Kosko 1992; Terano et al. 1992). The initial use of fuzzy logic control was based on the expert system approach. In this approach, control of the system can be implemented using several operating rules. The rule base is usually extracted from operators’ control patterns or from verbal rules describing the system. The fuzzy system, thus, facilitates qualitative or linguistic representations of an  46  expert’s knowledge. A fuzzy system can also be used to relate sampled input to output data from a system. It then estimates output values of the system based on such relationships and new inputs.  In this way, the fuzzy system performs the same function as statistical  regression or neural networks. However, unlike most other black-box system approaches, such as statistical regression, a fuzzy system estimates an underlying function without actually 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 take advantage of the ability of fuzzy logic to describe a phenomenon or an object as partially belonging 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 deals with vagueness, the logic itself is based on fuzzy set theory, a mathematically rigorous theory. A fuzzy set is an extension of a conventional crisp set. A crisp set only allows full  1.0  I  NO  0 Xe  X  Fig. 3.1. Diagram of crisp characteristic membership function.  47  membership 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 can be considered to be either tall or about average (Fig. 3.2). The characteristic membership function in classical set theory which posses precise binary definition (i.e., membership of 1 for an element in the set and 0 for an element outside the set) is replaced by the membership function.  It defines the membership value for each member of the fuzzy set.  The  membership function represents the degree to which a variable with a specific value belongs to 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 membership function is the triangular one as shown in Fig. 3.2. The number of fuzzy categories into which 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 the computational burden. If there are n variables and C fuzzy categories, then the number of rules in the complete rule base is U.  I  AVERAGE  I  1  0  5.0  Height (fi)  5.75  TALL Fig. 3.2. Example of fuzzy membership functions. (Crisp variable X membership in TALL of 0.7 and AVERAGE 0.3).  =  6.3 has a  48  Since most fuzzy logic applications were initially developed from expert systems, the structure of the fuzzy system is largely influenced by the approach of an expert system. The IF-THEN rule-base structure, used widely in expert systems, is also adopted in building the fuzzy system. For example, in a two-input, one-output crisp expert system, the rule based structure is of the form: 1 IF X  >  2 100.0 AND X  1 IF X  >  2 35.0 AND X  =  <  65.0 THEN Y 10.0 THEN Y  40.0  =  =  120.0  Typically the values of the variables to describe the system are crisp (e.g., 78.2, 24.0), and only one rule is “triggered” or “fired” at a time. In contrast a fuzzy system rule base takes the form: 2 IS MEDIUM THEN Y IS MEDIUM 1 IS LARGE AND X IF X 2 IS SMALL THEN Y IS LARGE 1 IS MEDIUM AND X IF X where 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 the system, which are typically crisp numbers, have to be “fuzzfled”, that is transformed into fuzzy variables with associated membership values.  Typically each crisp input can be  assigned membership in two fuzzy categories, as illustrated in Fig. 3.2.  These fuzzy  categories trigger a number of rules. For example, if there are 2 inputs, this will lead to 4 rules being triggered at a time, as illustrated in Fig. 3.3. The rules then have to be given weights through a process of “input inference”, combined through a process of “output inference” and reduced to a crisp output by “defuzzWcation  “.  49  Membership  Membership  1.0  Value Input variable are X . Output variable is Y. 2 1 and X : 2 Rules triggered by specific values of X and X IF IF IF IF  X 1 1 X 1 X 1 X  IS IS IS IS  2 IS SMALL THEN Y IS SMALL MEDIUM AND X MEDIUM AND X 2 IS MEDIUM THEN Y IS MEDIUM LARGE AND X 2 IS SMALL THEN Y IS MEDIUM 2 IS MEDIUM THEN Y IS LARGE LARGE AND X  Fig. 3.3. Illustration of the fuzzflcation of crisp input values of corresponding rules triggered (other rules are not shown).  1 X  and  2 and X  The justification for this elaborate process for transforming a set of crisp input values to a 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, the fact that several rules are in operation at any one time and that membership values and rule weights change smoothly with changes to the input variables results in outputs that also change smoothly. Kosko (1993) shows that with fuzzy categories, the output from any function 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 input inference and output inference. Input inference performs the set operation of matching the fuzzUled input values to the antecedent parts of the IF-THEN rules. The weight or firing strength of the rule triggered is then computed by combining the membership values of its  50  input variables. The combination can be done by various ways, including product, minimum or average among many other set operators (e.g., Drainkov et al. 1993). Input inference using the product operator calculates the firing strength of a rule by multiplying the membership values of the input variables within their fuzzy categories (Fig. 3.4). For each individual rule, input inference gives the firing strength of its rule.  Membership  Membership  1.0  Example of rule triggered: 2 IS SMALL THEN Y IS SMALL 1 IS MEDIUM AND X IF X Input Inference  Product  Minimum  Average  Rule’s Firing Strength  0.56  0.7  0.75  Fig. 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). The  clipped output method is usually associated with the “minimum” input inference operator. It clips the membership function of values greater than the minimum input membership value. On the other hand, the scaled inference method scales down the corresponding output membership function by maintaining the original support of the membership function. This  51  scaled method of output inference is often associated with the “product” input inference operator.  A)  MEDIIJM  Membership  B)  Membership  MEDIUM Scaled  Clipped  0.7 Rule’s Firing Strength  0.56 Rule’s Firing  Fig. 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 scaled or clipped fuzzy output values have to be transformed to a precise crisp value by defuzzjflcation.  Many defuz4flcation processes have been introduced.  These include  Center-of-Area (COA), Center-of-Sum, Height, Mean-of-Maximum (MOM) and many others. LARGE I  I  MEDIUM I  I  1.0  argest weight of 1 L I rule triggered with output LARGE’  0  j  .:  4, Common area taken once  Output  Crisp Output  Fig. 3.6. Center-of-Area (COA) defuzzification.  52  The 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 from each membership subset independently. The darkened area in Fig. 3.6 is taken twice for the weighting 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 at which its membership is 1.0 and weights each output membership function by its peak value as determined by the output inference values, determined by either the clipped or the scaled method (Fig. 3.7). With this technique, the output categories are essentially represented by singleton fuzzy sets, i.e., crisp numbers.  1’.  =  2nd Rule’s: 0  Output yl  where  Y*: Y: h: n:  the final crisp output the crisp value whose fuzzy membership equal 1.0 the rule’s firing strength the number of fuzzy outputs according to rules fired.  Fig. 3.7. Height defuzzification.  53  3.2 Fuzzy System as Model-free Estimator  The above discussion of a fuzzy system is based on its development through the expert system and control engineering perspective. An important new development in fuzzy logic has recently been the shift from expert system and control perspectives to estimating. The fuzzy system can also be considered as a black-box or model-free estimating system (Kosko 1992). This is the way in which it is used in this thesis. The principle and structure of the system remain the same. The emphasis here is on building the rule base for the estimating system based on training data, similar to the neural network approach, rather than obtaining the rules from an expert. The process of setting the rule base is called “fuzzy mapping”, that is mapping the input fuzzy set to the output fuzzy set. The advantage of fuzzy mapping is that it relies on actual data, but gives more insight and understanding of the process than a neural network, which is truly a black-box system.  The fuzzy system avoids using  complicated mathematical modeling by using symbolic variables and the influence path of the decision variables can be traced. In fuzzy mapping, the concept of Fuzzy Associative Memory (FAM), that is a way of storing the relationship between fuzzy input and output variables, is used as a translation device between inputs and outputs. FAM’s map fuzzy sets to 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 antecedent consequent pairs or IF-THEN statements. Each FAM rule defines a patch in the input output state space, and the fuzzy system approximates the unknown function by covering its domain with FAM-rule patches. The FAM rules can then form the skeleton of a fuzzy  54  system. In general the FAM system consists of a bank of different FAM associations. Each association corresponds to a different numerical FAM matrix, or a different entry in a linguistic FAM-bank matrix (Kosko 1992). One of the drawbacks of the fuzzy system is that when the number of fuzzy variables or fuzzy subsets increases, the FAM’s also increase and  dimensionality becomes a major computational problem.  A compromise between the  number of fuzzy variables and their partitions into categories, has to be reached in building up a FAM for fuzzy mapping. In this study, the FAM system is used as a mapping mechanism to relate input-output training data. From the mapping, the required output, in this case the required storage in the  polder system can be derived. As discussed earlier, there are many alternatives in the input inference, output inference and defuzzfication processes. Computational demands also dictate the design of the fuzzy mapping system. After some preliminary trials with the main problem in the study, some simple numerical experiments were carried out to help understand the processes of computing with and building a fuzzy mapping system. Number of rules required, choices of fuzzy set partitions, robustness of the system and a practical way to derive rules were the subjects of interest here. These experiments are described in the next chapter.  55  4 EXPERIMENTS WITH FUZZY LOGIC PROGRAMMING  4.1 General  As outlined in the previous chapter, there are several steps involved in computing the required 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: input inference 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 single crisp output. There are several alternatives to each of the above steps, leading to a large number of alternative combinations for the process as a whole.  There is no theory or  generally accepted rules to say which of the alternatives is best, although some alternatives have been more widely used than others.  After some preliminary trials with the main  problem in this study, a set of numerical experiments were carried out to compare the various alternatives in order to determine the most effective method.  56  The experiments, which are described in this chapter, involved the use of three example algebraic functions, with increasing degrees of non-linearity. These are: X 8.O 2 + 1 Y=X 1) + 2) Y  =  12 .X 2 1 X 1  3) Y  =  X .(X 1 X / 2  +  ° 85 ) 2 X  The first function is linear; the second is non-linear but monotonic and is judged to be somewhat 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 dependent variable. With each test function, three methods of input inference: product, minimum and average were tried; two methods of output inference: clipped and scaled were tried; and two conventional defuzzflcation techniques: Center ofArea (COA) and Height were tried. Two methods for setting up the fuzzy rule base were examined: using accurate values of the input variables; and developing FAM’s (Fuzzy Associative Memories) from sets of training data obtained by randomly generating values of the input variables and computing the corresponding output values from the test functions. Other experiments involved testing various ways of weighting sets of training data to develop the most accurate FAM’s and to check the robustness of the fuzzy system approach.  57  4.2 Experimental Procedure  In all the experiments, triangular membership functions were used for both the input and output variables, that is the membership functions were identical sets of symmetric triangular shapes as shown in Fig. 4.1. The triangular membership functions were chosen because of their simple structure and wide use in other fuzzy systems, the computational ease of calculation, and minimal storage requirement. As explained in the previous chapter, the more fuzzy categories used in the membership functions, the more accuracy the estimates can achieve. But this is also associated with more rules and greater computational complexity.  Five categories are generally accepted as  adequate. In the experiments, the input variables were divided into 5 fuzzy categories, and output variables were divided into 5 and 9 fuzzy categories (Fig. 4.1 and Fig. 4.2). ” X 2 [ B).Y=X,  8.0 A).Y=X,+X + 2 N2  Ni  P2  Si  S2  0.0 5.0 10.0 X- Variable  2.0  4.0  ZE  P1  S3  I. -10.0 -5.0  6.0  8.0 10.0 X -Variable  X, X °’ (X, * 1 X / + ) C). Y = 2 Si  S2  S3  S4  55 INPUT FT JZZY  a.  MEM1ER SHIP FIJNCTTONS  I 0  1.25  2.5  3.75 5.0 X-Variable  Fig. 4.1. Fuzzy membership functions of inputs X for the test functions.  58  Rule bases were constructed based on known outputs calculated directly from the test functions (Section 4.3) and from the randomly generated training data (Section 4.4). After the rule bases (e.g., Table 4.1) had been set up, the more widely used methods of input inference, output inference and defuzzfIcation were tested.  The tested input inference  operators were average, minimum and product operators.  OUTPUT FUZZY MFM1WRWP F11NCTTON  1 Ti  8.0 X + 1 X + A). Y = 2  T2  T4  T3  T5  T6  T7  T8  T9  I. Y-variable  12 X, 1 1 X B). Y = 2  0.0  /(X, X,X C) Y = 2  +  °’ 5 ) 2 X  40.0  80.0  120.0 160.0 200.0 240.0 280.0 320.0 Y-Variable  ZE  0  P1  P2  P3  0.75  1.5  3.0  P4  P5  4.5 6.0 Y-Variable  Fig. 4.2. Fuzzy membership functions of outputs Y for the test functions.  59  TABLE 4.1  Fuzzy Rule Base in the Conventional Form for the First Test Function  xl  iR’  za,i  Note: 2 = ZE THEN Y = T6 1 = P1 AND X For example, IF X (P1, ZE, etc. are fuzzy input categories as shown in Fig. 4.1 (A); etc. are fuzzy output categories as shown in Fig. 4.2 (A)). T6, ...,  TABLE 4.2 Fuzzy Rule Base Used in the Direct Method for the First Test Function V  xl  =  2 Fuzzy Input Categories: X  8.O X+X + 2  .•ZE  P1  P2  -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  18.0  3.0  8.0  13.0  18.0  23.0  8.0  13.0  18.0  23.0  28.0  N2  Ni  -12.0  Note: 1 = P1 AND X 2 = ZE THEN Y = 13.0. For example, IF X (P1, ZE, etc. are fu.zy input categories as shown in Fig. 4.1(A)).  60  An extension of the Height method was developed in the course of the trials. Instead of having a single fuzzy output associated with each rule, a weighted combination of two fuzzy  outputs per rule was allowed. Then it was realized that a weighted combination of two fuzzy outputs 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 weighted output values—a single crisp value for each rule as shown in Table 4.2.  REGULAR FUZZY RULE STRUCTURE  inputs I  output 1  I  Single Fuzzy Category  I  L  A:IL XL  ,J x ” 2  ‘  DIRECT METHOD output  inputs  Weighted Combination of 2 Fuzzy Categories A’  0  X2  DELOPME OF TI DIRECT FUZZY METHOD  0.7 0.3 0  +  4’  output Single Crisp Value * WIYI + WIY 2 2 wI+w  Fig. 4.3. Development of the Direct method’s rule structure.  61  4.3 Setting up the Rule Bases from Known Output Functions  To set up the “accurate” rule base, values of the output Y were computed for 25 , which have memberships of 1.0 (i.e., values 2 1 and X combinations of the input variables X 2 of -10.0, -5.0, 0.0, 5.0 and 10.0 for the first test function). When the values for of Xi and X 2 each have membership of 1.0, only one fuzzy rule is triggered at a time, and hence 1 and X X do not trigger other rules. The output fuzzy category for each rule is the category in which the computed output Y has the largest membership value. For example, in the first test function, Y  =  1 X  +  2 X  +  1 8.0, if X  =  2 5.0 and X  =  10.0 then Y  =  23.0, with maximum  membership on fuzzy output category T8. Or, in the second test function, Y 1 X  =  2 2.0 and X  =  X 12 if , . 1 X 1 2  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 test functions. They were shown in Tables 4.3, 4.4, 4.5 and 4.6. Once the rule bases had been set up, similar tests on the various alternatives for input inference, output inference and defuzzflcation were performed. One thousand sets of 25 random combinations of values of 2 were generated, and values of the output Y were computed for each of these 1 and X X X by the various alternative fuzzy programming methods. The combinations of Xi and 2 computed 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.  62  TABLE 4.3 Fuzzy Rule Base in the Conventional Form for the Second Test Function  v  2 Fuzzy Input Categories: X  = 1 .x 2 xi  1 X  Si  S2  S3  S4  S5  Si  Ti  Ti  Ti  Ti  Ti  S2  T2  T2  T2  T2  T2  S3  T2  T3  T3  T4  T4  S4  T3  T4  T5  T6  T6  S5  T5  T6  T7  T8  T9  Note: For the explanation of terms used, see note in Table 4.1 and Figs. 4.1 (B) and 4.2 (B).  TABLE 4.4 Fuzzy Rule Base Used in the Direct Method for the Second Test Function V  1 X  =  2 Fuzzy Categories: X  .X X 2 ’ 1 Si  S2  S3  S4  S5  Si  5.7  8.0  9.8  11.3  12.6  S2  22.6  32.0  39.2  45.3  50.6  S3  50.9  72.0  88.2  101.8  113.8  S4  90.5  128.0  156.8  181.0  202.4  S5  141.4  200.0  244.9  282.8  316.2  Note: For the explanation of terms used, see note In Table 4.2 and Fig. 4.1(B).  63  TABLE 4.5 Fuzzy Rule Base Used in the Conventional Form for the Third Test Function X (X Y2 ’ 1 =X /  Xj  +  2 Fuzzy categories: X  ° 85 ) 2 X Si  S2  S3  S4  S5  Si  ZE  ZE  ZE  ZE  ZE  S2  ZE  P1  P2  P2  P2  S3  ZE  P1  P2  P3  P3  S4  ZE  P1  P2  P3  P4  S5  ZE  P1  P2  P3  P4  Note: For explanation of terms used, see note in Table 4.1 and Figs. 4.1 (C) and 4.2 (C).  TABLE 4.6  Fuzzy Rule Base Used in the Direct Method for the Third Test Function (X .X 1 X 1 V 2  1 X  +  2 Fuzzy Categories: X  ° 85 ) 2 X Si  S2  S3  S4  S5  Si  0.0  0.0  0.0  0.0  0.0  S2  0.0  0.74  1.36  1.7  1.92  S3  0.0  0.68  1.83  2.7  3.35  S4  0.0  0.56  1.81  3.09  4.15  S5  0.0  0.48  1.67  3.12  4.49  Note: For explanation of terms used, see note in Table 4.2 and Fig. 4.1 (C).  64  4.4 Setting up the Rule Base from Training Data  In the above set of experiments, the fuzzy rule base was obtained from accurate values of output variable Y computed directly from the test function. Some further experiments were made, in which the rule base was built up from training data sets consisting of random 2 and the corresponding output variable Y. One 1 and X values of the two input variables X 2 were randomly generated 1 and X thousand sets of 25 combinations of the input variables X 1 . With each pair of X 2 1 and X and the corresponding output Y computed for each pair of X and X , four fuzzy rules were triggered. By input inference (average, minimum or product), 2 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 of  defuz4fication, described previously. Weights and weighted outputs were accumulated from all the input and output data, and a single weighted output was computed for each rule:  =  Wjk k  Wik i=1  where  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.  65  For the COA and Height methods of defuz4fIcation, a fuzzy output was required for each rule. For each rule k, the fuzzy category in which Yk had the largest membership value was chosen as the output category.  4.5 Results of the Experiments 4.5.1 With Accurate Rule Base  1 and X 2 were generated to test the Sets of 1000 pairs of combinations of inputs, X performance of the fuzzy logic programming with the derived rule bases. The experiments were repeated several times.  Although there were some slight variations, the results  remained 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, 4.8 and 4.9. From this it was concluded that the firing strength (weight) of each rule was best obtained by multiplying the membership function values of the input variables, and the final output was best obtained as the weight average of the crisp outputs associated with the rule triggered (the Direct method).  66  TABLE 4.7 Standard Errors of Estimation for the First Test Function by Various Fuzzy Alternatives  Note: The standard errors are given as a percentage of the mean value. (Technically, this is the co efficient of variation).  Standard Error  =  -  100.0%  1nYoi  where  (1)  (2)  (3)  (4) (5) (6)  Y Yoi n  values of Y computed by fuzzy system, accurate value of Y, number of trials.  Firing weight of rule computed by averaging the membership function values for each of the variables as input inference. The corresponding output inference is the scaled method. Minimum of membership values as input inference. The corresponding output inference is the clipped method. Product of membership function values as input inference. The corresponding output inference is the scaled method. Output defuzzjfled by the Center ofArea (COA) method. Output defuzz(fled by the Height method. Output computed as the weighted average of crisp outputs.  67  TABLE 4.8 Standard Errors of Estimation for the Second Test Function by Various Fuzzy Alternatives Y  Note:  Input Inference Method  =  Defuz4fication  Average  Minimum  Product  COA  12.9  10.3  8.5  Height  12.8  8.9  8.0  Direct  9.8  4.0  1.5  For the explanation of terms used, see Table 4.7.  TABLE 4.9 Standard Errors of Estimation for the Third Test Function by Various Fuzzy Alternatives (X 1 1 =Xi.X Y2  Note:  +  Input Inference Method  ° 85 ) 2 X  Defuz4fIcation  Average  Minimum  Product  COA  17.9  13.7  11.7  Height  15.2  8.2  7.4  Direct  12.6  6.3  4.9  For the explanation of terms used, see Table 4.7.  68  4.5.2 With FAM (Fuzzy Associative Memory) Rule Base Derived from Training Data  As mentioned Section 4.4, training data can be used to construct the FAM rule base. The fuzzy estimating system learns from samples in building its FAM’s. The training data set  includes inputs and their corresponding outputs. Setting up of the FAM rule base from training data is also described in Section 4.4. The fuzzy systems tested in this section are the Direct method.  A set of 1000 training data pairs was used to construct each FAM rule base for the corresponding test function. After the rule bases were created, sets of 1000 pairs of input 2 were generated to test the derived fuzzy systems. In building each 1 and X variables, X FAM 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 fuzzy membership values of inputs was greater than 0.0 (all pairs selected), 0.5, 0.7, 0.8 as described in Table 4.10. For a selected training data pair, the firing strength of each rule was computed for each input inference method. It was defmed as the average, minimum, or product 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 for the rule.  Weighted outputs were accumulated from all selected training data, and the  weighted average for each rule was then computed. For example, if the selected training 2 are crisp inputs, Y, is crisp output 1X , 1 , where X Y } 11 , 2 ,X 1 data set, i, is described as {X for i th data pair, and i  =  1, 2, 3,..., n, then the firing strength of the i th data set in the k th  rule will be  69  ci, = =  ), 11 MN {j.Lx 1 (X  2 JLx  )] or 21 (X  ), 11 PRODUCT [.tx 1 (X  ci  ] or (X ) 2  , (X ) AVERAGE [J’x 1 1  2 I.tX  )J 21 (X  and the weighted output will be  Fk= 1=!  where ) 11 1 (X J..tx  11 fuzzy membership value of X  ) 21 (X  2 fuzzy membership value of X  2 tX  is the crisp output value for data set, i Fk  is the computed value of a cell, k, in the FAM bank  Once the FAM bank was filled with Fk values, the fuzzy program was then used in the analysis. Results of the applications of fuzzy programming with the training data are shown in Tables 4.10, 4.11 and 4.12. It can be seen that they  are  not as good as those shown in  Tables 4.7, 4.8 and 4.9, where the rule bases were accurately computed from the test functions. The results were much poorer than the accurate rule base when all training data were used in generating the rule bases. In other experiments, the rules were developed only from data where both input membership functions were greater than 0.5 and 0.7. This gave greater weight to values with large membership numbers. The results computed from these rule bases are shown in Tables 4.10, 4 11 and 4.12. They indicate an improvement of rule  70  bases up until it was not practical to create enough rule base entries because of the strength of 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 in information supporting the rule base.  TABLE 4.10 Standard Errors of Estimates of the First Test Function by the Direct Method, Based on the Training Data Y  =  I  X 8.0 2 + 1 X +  Defuzzflcation Accurate  (Z  .  .:•.  All (3) Membership  >  (Membership  0.5  >  4)  11  0.5)1  Membership > 0.8 )  ..  I  Input In/’rence Method Average  Minimum  Product’  12.7  4.8  0.0  20.0  14.9  11.9  15.0  9.7  7.5  14.7  9.2  6.6  14.0  7.9  5.8  14.0  7.8  5.7  25.5  24.5  24.7  Note: The 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 greater than 0.5. (5) The rule base was derived from only the trial data with each input fuzzy membership greater than 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.  71  TABLE 4.11 Standard Errors of Estimates of the Second Test Function by the Direct Method, Based on the Training Data Y  =  Input Inference Method  ’X X ’ 1 2 Average  Minimum  Product  Accurate  9.8  4.0  1.6  All  14.6  11.2  9.1  Membership> 0.5  11.7  8.0  6.3  11.4  7.6  5.5  11.6  6.7  5.1  11.6  6.7  4.9  27.2  28.2  29.2  Defuzzfication  (Membership  >  0.5)  Membership>0.7 (Membership Membership Note:  > 0.7)2  >  0.8  For the explanation of terms used, see note in Table 4.10.  TABLE 4.12 Standard Errors of Estimates of the Third Test Function by the Direct Method, Based on the Training Data X V2 .(X 1 =X /  +  Input Inference Method  )° 2 X 85 Average  Minimum  Product  Accurate  12.6  6.3  4.9  All  18.7  14.0  12.0  Membership>0.5  15.3  10.6  8.7  15.1  10.2  8.0  14.2  8.8  6.9  14.2  8.7  6.7  25.3  25.9  26.5  Defuzzification  (Membership  >  0.5)2  Membership>0.7 (Membership  >  0.7)2  Membership>0.8 Note:  For the explanation of terms used, see Table 4.10.  72  4.6 Robustness  One of the quoted advantages of fuzzy logic programming is that it is very robust. If some of the rules are omitted, or there are some mistakes in them, the system should still function reasonably well. To check on this, further experiments were conducted where some of the rules were progressively eliminated. The results in Tables 4.13, 4.14 and 4.15 show that as rules are left out, performance of the fuzzy logic system degrades relatively slowly. This can be a very important practical consideration. It means the fuzzy programming can be used where some faults or missing information of the system are unavoidable. It does not strictly require a high level of precision of all the rule bases or FAM’s.  If some structured  knowledge is unavailable or missing, the rules can be estimated and used.  TABLE 4.13 Standard Errors as Rules Are Randomly Omitted for the First Test Function Y  =  Input Inference Method  + 1 X + 2 8.O X  No. ofRulest Omitted  Average  Minimum  Product  0  12.3  4.6  0.0  (1)  15.8  10.2  7.7  2 (2) 4(3)  17.8  14.5  13.6  21.9  20.1  18.7  29.5  29.0  28.5  1  8  (4)  Continued on next page.  73  TABLE 4.13—Continued. Note: The standard errors are given as a percentage of the mean value.  t (1) (2) (3) (4)  The fuzzy rule base is identical to the one used in the Direct method in Table 4.2 (for the first test function), Table 4.4 (for the second), and Table 4.6 (for the third). There are 5 categories , giving 25 rules in all for each test function. 2 1 and X of each of X One rule is randomly omitted. Two rules are randomly omitted. Four rules are randomly omitted. Eight rules are randomly omitted.  TABLE 4.14 Standard Errors as Rules Are Randomly Omitted for the Second Function V  =  Input Inference Method  12 .X 2 Xi 1  No. ofRules Omitted  0  Note:  I  Average  Minimum  Product  9.4  3.8  1.6  11.2  7.6  6.6  15.5  13.2  12.6  15.8  14.6  14.1  19.3  18.5  17.7  For the explanation of terms used, see Table 4.13.  74  TABLE 4.15 Standard Errors as Rules Are Randomly Omitted for the Third Function Y =X .X?I(X? 1  +  Input Inference Method  ) 2 X  No. ofRules Omitted 12.9  6.8  5.1  13.9  8.2  6.8  13.7  9.0  7.8  17.4  16.0  15.3  20.0  18.5  18.0  Note: For the explanation of terms used, see Table 4.13.  4.7 Conclusions  Conclusions drawn from these experiments were: 1. The best results were obtained by inferring the firing strength of each rule according to the product of the memberships in the categories triggered (i.e., by the product rule of input inference); providing a “crisp” output for each rule, the Direct method of output inference; and computing the weighted average of these outputs. 2. The fuzzy system works best when the outputs corresponding to values of the input variables which have memberships of 1.0 can be accurately specified. 3. Sets of rules can be developed from experience by fuzzy associative maps  -  but  these are not quite as good. However, this feature offers the promise of adaptive learning and adjustment of the rules in the light of experience. In setting up the rule  75  base, it is best to use only data sets where the input variables have high membership values (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 them without seriously compromising performance. 5. When, as in the examples tested, there is a rule for each combination of the input variables, it is important to keep the number of input variables and fuzzy categories to the minimum practical number.  Otherwise the number of rules can quickly  become unmanageably large. This suggests structuring the problem in question with the minimum number of input variables and keeping the number of fuzzy categories to about 5 and certainly less than 10 for each variable. The above conclusions were used in selecting a fuzzy logic operating system for application to the polder flood control problem in Bangkok. Details of applications of the fuzzy estimators in the polder flood control follow in the next chapter. The actual operating system is described in Section 5.5.  76  5 NUMERICAL EXPERIMENTS  5.1 Introduction  As outlined in Chapter 2, the main feature of Bangkok’s flood control system is polder flood control, which involves independent floodwater releases by gate and/or pumping from individual polders. Such releases are necessary to maintain proper water levels within the canal system of the polders. Current operation of flood release works relies on a fixed rule curve—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 of operating release facilities according to fixed rules, it was realized that improvements could be achieved if one could manipulate the releases more flexibly. As described in the systems engineering literature, this achievement is often sought by using mathematical modeling to optimize an expected cost function.  However, as discussed in Section 2.3.1, few  optimization studies have been adopted in practice for real-time flood control operations. Several reports on actual flood control operations, including reservoir releases and urban storm drainage controls, indicate that an elaborate optimization approach is not yet able to meet 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 not  77  yet 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 realistic  alternatives is to improve release operations by enhancing existing technology, such as the rule curve. In this chapter, a description of experiments to find better operating procedures with fuzzy logic is given. This involved setting up a flood control situation representative of a  polder in Bangkok, but simplified to only include features essential to the study. Since actual data were not available, inflows to the polder were simulated with a Monte Carlo procedure. The simulation was conceptually similar to an attempt by Nelen et al. (1987) in their search for improving internal drainage of polder stormwaters. In their study, the polder was simplified and modeled as a single catchment with a reservoir/canal having a fixed amount of flood storage, and all excess floodwater from the whole polder was discharged by pumping.  The rainfall-runoff process was conceptually described by a combination of  reservoirs representing various hydrological components of the polder. Although there was criticism that the approach was too simplified, satisfactory results of its application to polder drainage reportedly justified the use of such a simple model. In the present study, a polder was also treated as a single drainage unit, and its inflows were simulated by using the Clark method (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 single rule curve. Next, a fuzzy rule base was developed with the simulated flows, again assuming operation with perfect hindsight.  Attempts were made to relate the required release to  78  various items of information likely to be available at the time, such as the time since the storm began, the total inflows to date and the amount of water already stored. However, it was found that with too many input variables, the number of rules required became so large that it became extremely difficult to find any pattern to the rules. Eventually, the problem was simplified to give the output rule in the form of a desired water level (above which there would be full discharge, below none) and relate these to just two input variables, time and precipitation. It was found necessary to have two separate rule bases—one for during the rainstorms and the other after the rains had stopped. In this chapter, the simplified polder situation assumed for the experiment is first described. Next the rainfall-runoff simulation is described. Then the process of rule curve creation is given, followed by the way in which the fuzzy rule base was set up. Finally, the procedure used to test and compare the operation of the system using the fuzzy rule base with the rule curve operation is described. Results of the comparison are given in the following chapter.  5.2 Experimental Folders  The numerical experiments to check on the usefulness of the fuzzy logic concept in improving release tactics for floodwater were conducted with assumed polders.  Since  polders are designed to be hydrologically independent, the flood control situation could be simplified and modeled as controlling the release from a simple reservoir. The flood control operation in each polder catchment was assumed to be independent from other polders. The  79  release operation was based on the assumption that stonnwaters stored in the polder during  storms 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 as different catcbment sizes were used in the development stage of the experiments, similar results from the various experiments were obtained. Thus, only the experiments based on the test polders described in this section (Table 5.1) are presented and discussed in this thesis. The values describing the test polders were as follows. The catcbment areas of the 2 (The polder areas in Bangkok range from 8 km 2 in the City polders were 5, 10 and 30 km 2 in the Eastern Bangkok project). Time of concentration (Ta) of Core project to 165 km 2 polders, each catchment was set at 2.5, 3.5 and 4.5 hours for the 5, 10 and 30 km respectively. Time of concentration was then allowed to fluctuate within ±30% from the mean. The 30% variation was chosen arbitrarily to allow some fluctuation in the parameter values used. A uniform distribution was used here since it was not possible to determine an exact distribution of the parameters. The Clark’s storage constant (R) mean value was taken as 0.75 x Tc, a value typical of an urban area. The storage constant was allowed to vary 3 within ±20% of its mean. The maximum floodwater release or pumping rate was 10 m  s  3 s’ for the third ), 20 m 2 3 s’ for the second (10 km ), and 60 m 2 for the first polder (5 km ). 2 (30 km  The release rates were equivalent to the calculated pumping capacity for  Bangkok’s polders by JICA (1985) using unsteady flow equations.  The initial storage  3 for the first test polder (5 km ), 400 000 m 2 3 for the volume of the system was 200 000 m  80  ). For simplicity, tidal actions were 2 3 for the third (30 km ) and 700 000 m 2 second (10 km not considered in the main experiments.  TABLE 5.1 Set-up of the Polders in the Experiments Polder #1  Folder #2  Polder #3  Area  5 km 2  10 km 2  30 km 2  Initial Storage  3 200 000 m  3 400 000 m  700 000 m 3  20 m 3 s_i  60 m 3s  2.5 hr ±30%  3.5 hr ±30%  4.5 hr ±30%  (Uniform)  (Uniform)  (Uniform)  Maximum Release T  10 m 3  R  0.75 T ±20% (Uniform)  5.3 Simulating Flows  Rainfalls and corresponding inflows to the assumed polders were generated to simulate flood control situations and operation. The simulation model was composed of two major parts: a rain generating mechanism and a rainfall-runoff model. Rainfall information was based on sequences of random numbers generated under a Monte Carlo procedure. Corresponding run-offs were derived from the generated rainfalls by the Clark hydrograph method. The rainfall generating mechanism was initialized by a simulation of the duration of each rainfall event. An exponential distribution was used to describe the rainfall duration  81  values (i.e., CDF(t) = 1  -  ?. e, where CDF(t) is a cumulative distribution function of  rainfall duration, t, and ?. = (mean of rainfall duration)’).  The mean value of rainfall  duration was 1.0 hour, consistent with the values reported for Bangkok (JICA 1985). Random numbers representing rainfall duration were generated under the defined exponential distribution (i.e., if u is a standard uniform-distributed random number, then x = -(L’?) in (u) is a random number with an exponential distribution, with ? as defined earlier (Ang and Tang 1984)). The average intensity of the rainfall event was constructed from the generated value of the rainfall duration (t (mm)) by using the intensity-duration formula, i  a / (7  + t),  where i  ); a and b are empirical variables, locally derived for Bangkok. 1 is rainfall intensity (mm hi The values of a range from 5690 to 10 040 with a mean of 8230. The values of b range from 37 to 44 with a mean of 41 (JICA 1985). Both a and b were randomly chosen from their ranges for each value of duration, t. Then the total rainfall depth (d) was calculated from the definition of the rain intensity (i = d/t). After a pair of rain depth and duration was generated, an advanced-skew rainfall (depthduration) mass curve’ was applied to derive a temporal profile (hyetograph) of the rain. Co ordinates of the representative mass curve (Fig. 5.1) were read from the tropical rainfall curve studied by Colyer (1984) and assigned as mean values. Colyer (1984) derived the rainfall mass curve for the application of the design-storm concept to the tropics where data on temporal patterns of rainfall were limited.  The study by JICA (1986) on temporal  distribution of 52 heavy rainstorms in the Bangkok area had a similar advanced-skewed  ‘Sometimes called Huff’s curve, after Huff (1967).  82  profile. Very few studies on temporal rainfall intensity were previously conducted in the area due to a lack of past automatic rain-gage records. Values of the Colyer curve were allowed to fluctuate uniformly within a range of ±20% of the mean value. To facilitate the selection of an actual rainfall mass curve for a specific pair of the simulated rain depth and duration, outline curves were constructed.  The outline curves represented deviations of  ±20% and formed an outer envelope around the mean Colyer curve.  For each rainfall  simulation, another pair of random numbers was generated for the selection of the mass curve. The first number was used to indicate the sign (+ or  -) of the variation. The second  number was a percentage of the total allowed variation (20%). The two numbers thus gave the 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 rainfall mass curve used in the simulation.  I I  Curve  50  0  100 50 accunimulated rain duration (%)  Fig. 5.1. Rainfall depth-duration mass curve used in the simulation.  83  A sequence of rainfall events was not considered in this study since it was observed that at most, one rainstorm occurred at one place on any given day in the Bangkok area (Henry 1974; JICA 1985). Typical rainstorms in the area exhibit one peak of rain intensity (JICA 1986). 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 at the release regulating point of a catchment. considered.  No abstraction nor loss of rainfall was  The generated rainfall was routed by the Clark hydrograph method (Clark  1945). The Clark method was used here because of its simplicity and wide applications in simulations of runoff in hydrological studies (Maiclment 1992).  The technique is also  available in the well-known hydrological model, HEC- 1 (Hydrological Engineering Center 1987). The Clark method includes two important factors characterizing the runoff from a catchment: time of concentration and storage in the basin. It is simply the time-area method with a concentrated linear-storage routing at the outlet. The time-area method divides the catcbment into several sub-drainage areas according to the travel time from each area. The isochones or lines of equal travel time to the outlet are used in defining such sub-areas. The runoff at the outlet of a catchment is the flow resulting from the combined contributions of rainfall excess in each sub-area which is lagged to the outlet of the catchment with a delay equal to the average time of travel of that area. The runoff is not modified in magnitude until it is attenuated by the storage of the catchment assumed to be at the outlet. A linear reservoir 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:  84  AT 1-AT  =  0T0.5  15 l.414T  =  0.5<T< 1.0  5 1.4l4(1-T)’  where Al: cumulative contributing area as a fraction of the basin area T: fraction of time of concentration The routing did not take into account loss functions or soil moisture conditions. It was assumed that the soil was saturated at the time the storm began. A typical simulated inflow hydrograph and its corresponding rainfall hyetograph are shown in Fig. 5.2. Generated rainfalls and runoffs whose peak inflows were greater than the maximum release rate of the system (500 pairs) were used in deriving the rule curve (Section 5.4) and fuzzy rules (Section 5.5). An additional set of rainfall events (2000 pairs) was generated for testing the performance of the fuzzy rules.  POLDER #2 70 60  10  50  20  40  30 40 50 Time (mm)  60  30  0  100  200  300  400  500  600  700  Time (mm)  Fig. 5.2. Example of a simulated inflow used in this study.  85  5.4 Time Varying Rule Curve  As discussed previously, Bangkok’s flood control practice relies mainly on the rule curve approach—a predetermined, fixed water level. If stormwater in the polder rises above this level, 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 in operating pumps or gates. However, it renders a sub-optimal performance. One simple improvement of the fixed-level rule curve is to have the rule curve level vary with the time since the rain starts. The time varying rule curve can take information on temporal patterns of storm run-offs into account. By relating the required level to time, the rule curve can offer an operation more responsive to storms yet still be simple to implement.  0 • Required storage at time T 1 • Required storage at time T  Qmax  0 T  T,  time  Fig. 5.3. Required empty storage derived with perfect knowledge of hydrograph.  86  In the experiments, rule curves were derived for individual floods, assuming that the full hydrograph was known at the time, and the pumps were operated optimally (that is operation to minimize pumping, yet still avoid flooding). Rule curves were derived for each individual flood 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 avoid flooding—that is holding the maximum discharge to  Qrnax.  The shaded area in Fig. 5.3  defines 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 CURVE 600000_______________  500000 YTTTYYTYY!  +HHHII.j  Po1 r #2  400000  IIIIIIIIiii. e  300000  11Tf 1111111111111tT  1111111111111111111 B!’ 1t1111111111IllI llllillr  Derived Rule Cun  E  200000  100000  0  lL1llllllll!111TF ir 1 11Illll111Illl i  0  50  100  150  200  250  300  350  400  450  Time 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 from the beginning of a storm or rule curves of all individual storms were plotted. A final rule curve was then drawn such that 95% of all points were below the curve. That is if the rule  87  curve were followed with all floods, only 5% of those large enough to require pumping would cause any flooding. In practice, the 5% value would depend on many factors such as the value of the area being protected; however, 5% was considered a reasonable value for this study. The upper bound of the rule curve was then limited by the initial storage of the ) when operated. In deriving the rule curve, 3 3 or 700 000 m , 400 000 m 3 system (200 000 m a total of 500 flood inflows whose peaks were greater than the maximum release rate of the 3 system (10 m  s_I,  20 m 3  3 or 60 m  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 should maintain. If the system has empty storage less than the amount required, then an operator has 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 no value to his decision.  The flood situation already forces him to release the excess  stormwater.  5.5 Fuzzy Estimating System  In this study, the fuzzy logic program (Direct method) based on the results of the experiments described in the previous chapter was used and tested numerically in the polder flood control context. Following is a description of the fuzzy programming approach.  88  1. The flood control problem was set up in a way which reduced the number of the input variables to two, in order to keep the number of rules in the rule base manageable and allow patterns to be discerned. Setting up the problem in this way took considerable experimenting. The input variables are the time since the rain began and the average intensity of the rain so far. The output variable is the volume of storage space required. 2. After the input and output control variables were selected, 5 equal triangular fuzzy membership functions were used to partition each of the input variables into fuzzy categories (or values), over the universe of discourse. 3. Training data were used to construct the FAM rule base.  The process of  construction is described previously in Sections 4.4 and 4.5.2. Only those data sets whose input values were assigned relatively strong membership values in their corresponding partitioned fuzzy categories were used to construct the rules. In this study, a strength of the membership of each input of 0.67 was selected as a threshold.  The computer algorithm which was developed for this study,  automatically selected the data pairs with such membership strengths. The product method of input inference was used in calculating the firing strength or weight of each rule. 4. The operating fuzzy rule base consists of 25 rules, one for each combination of the input fuzzy variable categories. The fuzzy rules, used in this study (for a two-input, one-output control system) take the form 1 1 THEN Z IS F 1 AND Y IS B Ri : IF X IS A 2 2 THEN Z IS F 2 AND Y IS B R2 : IF X IS A  89  where X and V are fuzzy variables; Ak, Bk are fuzzy categories, and Fk is a weighted crisp output value (FAM value) of the required storage space. 5. When specific values of the two input variables are input, their memberships in each of the fuzzy categories are computed.  Four rules are triggered as illustrated in  Fig. 3.3. The weight of each rule is computed by multiplying the membership value for each variable in each category in that rule. 6. The fmal crisp output is computed by using the weighed combination  Z(x, ,)  =  k=i  where Fk:  a crisp output of each rule k  n:  total number of rules triggered (normally 4) the rule number  (xk:  the strength of rule k, which is defmed as cxk =  PRODUCT [j(x), j.t(y)J  i.t(x), j.i(y):  membership values of crisp inputs, x, y  In 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 fuzzy input variables of the first rule base, for use during the rainstorm. The total rain depth and the time from the beginning of the storm were the fuzzy input variables for the second rule  90  base, for use after the storm ended. The output variable was the storage space required for at that particular time. The operating rule then was to operate the pumps only if the actual storage space was less than that required. Details of membership functions for the input variables and the fuzzy associative memories used in the fuzzy logic program for the polder flood control follow.  5.5.1 Fuzzy Membership Function  In this study, the triangular membership function was chosen because of its simplicity and computational efficiency.  The number of fuzzy values or categories for each decision  variable was minimized as suggested in the experiments in the previous chapter. From the simulated flows and the derived time varying rule curve, it was found that at a time of roughly the 8th hour from the beginning of the storm, the required storage space was mostly close to nil. Most rainstorms in the experiments had already ended, and their discharges were by this time receding. Since the time scale of a storm could often be classified roughly on an hourly basis, the time membership was partitioned every 2 hours between the beginning of the storm and the 8th hour into 5 fuzzy values or categories, as illustrated in Fig. 5.5. The last fuzzy category (T4) included times over 8 hours. Experimenting with the data, it was also found that an average rain intensity greater than 120 mm  was  infrequent. For rain intensities greater than 120 mm hr’, the patterns and magnitudes of required storage were closely similar. During a heavy rainstorm, the required storage space  91  was often large (i.e., FAM cells covering this range of rain intensities would be filled with values close to or greater than the total available system storage). The rain intensity fuzzy membership was then partitioned evely 30 mm hr between 0 (zero) and 120 mm hf’ into 5 fuzzy values or categories, as illustrated in Fig. 5.6. The last fuzzy value (14) included all intensities over 120 mm hr’. For the case where the rainstorm had already ended, the total depth of rainfall was used as a decision fuzzy variable. The total depth over 120 mm was often 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 partitioned every 30 mm between 0 (zero) and 120 mm into 5 fuzzy values, the same way as the average rain intensity, and was shown in Fig. 5.7. Although more detailed membership functions could be constructed, the larger FAM rule base would be more difficult to manage, and it would be more difficult to fill the FAM cells. The fuzzy categories or values defined are all symmetrical around the peak and have uniform widths.  1  I 2 0  2.0  4.0  hr 6.0 8.0 time from the beginning of storm  Fig. 5.5. Membership function of time from the beginning of a storm.  92  1 .  E  0  30  60  120 90 average rain intensity  mm/hr  Fig. 5.6. Membership function of rain intensity. 1  E 0  30  60  120 90 total rain depth  mm  Fig. 5.7. Membership function of rain depth.  5.5.2 Derivation of Fuzzy Associative Memories  The objective of the fuzzy logic programming used here was to give guidance on the empty storage volume required in a flood reservoir system during a flood. The corresponding stormwater (inflow) volume allowed in the system could be translated into a water level of the reservoir by using an established stage-volume curve. Operating instructions were the same as those used in the rule curve operation. A stormwater release was required whenever  93  the remaining empty volume in the reservoir was less than the required volume. The release 3 s_i, 20 m 3s ). Values 1 1 or 60 m 3s or discharge rate was assumed to be constant (i.e., 10 m of the required storage were calculated by the same methodology, described previously in the rule curve construction (Section 5.4). A total of 500 inflows were simulated, and those inflows which had their peaks greater than the maximum release were used as the training data 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 the case before a rainstorm ended, and the other was for the case after the rain ended. Inputs to the first FAM set were the average rain intensities up to the time, and the time from the beginning of storm. Inputs to the second FAM set were the total depth of rainstorm and the time from the beginning of the storm. The entries in the fuzzy associative memory cells were weighted crisp real-numbers of the required storage, as described previously in Section 5.5. A standard-FORTRAN program algorithm (similar to the one used in Section 4.5.2) was written for use in automatically creating the fuzzy rule matrices. For each pair of input output data (e.g., the time from the beginning of the storm, the average rain intensity as the inputs, and required storage as the output), the corresponding fuzzy set membership values were calculated and assigned to input decision variables. The data pair was accepted if each input’s membership value was greater than the threshold value.  The threshold for the  variables was taken as 0.67, which was close to the optimal membership strength of 0.7 found in the experiment in Section 4.5.2.  After a pair of data was accepted, its firing  strength was calculated by multiplying the two input membership values.  This firing  94  strength was multiplied by the crisp output value to give a weighted output.  These  individual weighted outputs were stored for further calculation of a single weighted output for 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 weighted output) were added up. The sum of the weighted outputs was divided by the corresponding sum 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 were done. There were a few empty FAM cells, where none of the training data fell. These missing FAM cells were filled up with values obtained by interpolation. Also, some of the values in the cells were adjusted to give a smoothly changing pattern. Once the FAM’s were established, a simple program was written to “operate” the system one time step at a time, given inflows generated as described previously. Three alternative 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 computed for each time period. If required storage space exceeded the available storage space, the pumps were assumed to operate during the next time interval. If not, pump discharge was set to zero. The available storage space was then computed for the next time period by adding the volume discharge (by pumping) and subtracting the volume of inflow during the time 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 as described previously.  95  For each set of experiments, 2000 simulated floods were used in comparisons of the pumping control under the rule curve and fuzzy control guidance. A control decision was made every 10 minutes, which was also the time resolution of the storm discharge hydrographs. At each time step, the guidance values were read from both the rule curve and derived from the fuzzy control.  The operation of pump was then set, according to the  general rules of operation, described in the previous paragraph.  The results of the  comparisons are presented and discussed in the following chapter. After some further testing of the derived fuzzy logic program with sets of simulated inflows, it was found that it allowed some flooding in the case of moderate storms, which if operated with optimal (hindsight) information, could have been avoided.  This was  eliminated by making the rule base slightly more conservative. It was also found that the total of the flood volumes from all the simulations was slightly greater with the fuzzy system than with the rule curve. The FAM rule was adjusted to make the total accumulated flood volumes from all simulated flows tested (e.g., 2000 storms) approximately the same magnitude as with the rule curve. This was done to make the comparison of pumping volumes meaningful. The FAM’s used in the Polder #2 are shown in Tables 5.2 and 5.3.  96  TABLE 5.2 First Fuzzy Associative Memory (FAM) for Folder #2—for Use during Rainstorm. (Correlated Rainfall Intensity-Duration Relation) RAIN INTENSITY 14  13  12  Ii  10 TO  265000  410000  379000  368000  330000  T  Ti  259000  256000  365000  444000  414000  I  T2  189000  230000  336000  400000  400000  M  T3  141000  220000  321000  400000  400000  E  T4  113000  210000  309000  400000  400000  TABLE 5.3 Second Fuzzy Associative Memory (FAM) for Folder #2—for Use Following the End of Rainstorm. (Correlated Rainfall Intensity-Duration Relation) TOTAL RAIN DEPTH DO  DI  D2  D3  D4  TO  0  182000  342000  366000  439000  T  Ti  0  88000  297000  348000  438000  I  T2  0  15000  97000  130000  305000  M  T3  0  1000  2000  8000  87000  E  T4  0  0  0  0  6000  97  6 RESULTS AND DISCUSSION  6.1 Introduction  As described in the previous chapter, sets of numerical experiments were conducted with alternative systems for controlling flood releases from a typical polder in Bangkok. The primary purpose of the experiments was to compare the performance of an operating system based on the application of fuzzy logic with the more traditional approach of using a rule curve to decide on whether or not to use the pumps to discharge floodwaters during the next time interval. The rule curve which was used as the basis for comparison shows the amount of 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 the fixed rule system, which is still in general use in Bangkok. Operation with fixed rule curves was also simulated for comparison with the time varying rule curve. To complete the range of alternatives, “optimal operation” was also used. Optimal operation was different from the other alternatives in that it assumed perfect information (i.e., that all the flows were known in advance  -  as could only occur with  hindsight). With the other alternatives, real time operation was simulated (i.e., the system 98  operation at each time interval was determined on the basis of information that would have been available at the time). For each set of experiments, 2000 flood hydrographs were synthetically generated. The results of this main set of experiments, which are presented in the following section, showed that the time varying rule curve system was a considerable improvement over the fixed rule curve system, that the fuzzy system was better than the time varying rule curve approach and that the optimal operation was slightly better again. However, there was not much “room” between the time varying rule curve approach, which represented the base case and the “optimal”, which was the best operation that would be possible even given full advance information on the pattern of flows to come. On examining these results, it was realized that the main difference between the fuzzy system and the base case rule curve approach was with the intermediate storms. With small floods, there was no need for pumping as no flooding occurred. Both systems thus gave similar results, although a small amount of pumping was required by the rule curve operation in this case.  On the other hand, large floods overwhelmed both systems and  caused flooding regardless of the pump operating system.  Thus in this situation, both  systems provided similar operating patterns. However, with intermediate storms, where some pumping was required, there was an opportunity for the application of skill and knowledge in deciding whether and when to pump. In this situation, the fuzzy system did better than the more inflexible rule curve approach. Following on this set of experiments, other sets were conducted in which there was likely to be more room for the fuzzy system to show its merits.  In the first set, the  99  simulation program for generating the flood flows from simulated rainstorms was changed to allow more variability in the flows.  In the original approach, the rain duration was  correlated with the average storm intensity (as is the case in Bangkok) and this results in flood hydrographs which are relatively similar to one another. In this situation, it is not surprising that a rule curve derived from sets of simulated flows would offer an effective approach to controlling floods generated by the same mechanism. It was thought that if the floods were more variable, the fuzzy system could have a greater advantage over the rule curve operation.  Other sets of experiments were conducted in which gravity discharge  controlled by gates was allowed in addition to the pump discharge, and in which tidal effects were simulated. These experiments and their results are also presented in this chapter.  6.2 Main Experiments  The experiments discussed in this section used simulated inflows, generated from rainfalls in which the average rainfall intensities was correlated with the durations as described in Section 5.3. In this set of experiments, it was assumed that excess stormwater, above what could be stored, could only be discharged by pumping. However, it was also assumed that the stored floodwaters could be released by gravity after a set period of 15 hours after the storm began. Summaries of the results of the experiments are given in Tables 6.1 and 6.2. Table 6.1 shows the total volume of floodwater (from the 2000 storms investigated), over and above  100  the volume stored in the available flood storage space and the volumes discharged by pumping. This total volume of floodwaters that cannot be contained or pumped out provides a measure of the overall effectiveness of the flood control system in controlling floods. As explained in the previous chapter, the rule base for the fuzzy operating system was adjusted such that the total volume of excess floodwater was approximately the same as that with the base system, the time varying rule curve. Unless those volumes had been closely similar, the comparison of pumping volumes would have been meaningless. As expected, the total flood volumes under optimal operation were lower than with the fuzzy system or the time varying rule curve. It was found convenient to classify the floods into 3 categories in order to better understand the effects of the alternative operating systems being investigated. categories are:  These  Case 1—no floods and no pumping required; Case 2—no floods but  pumping required; and Case 3—floods even with pumping. This classification is similar to that used by field operators after having had a long experience with pumping operations in Bangkok. They classify storms as light, moderate and heaiy (or vely heay), depending on their rainfall intensities. Figs. 6.1, 6.2 and 6.3 illustrate typical operations in Case 1, 2 and 3, respectively. Flood volume for each storm was defined as the volume of excess stormwater that the system could not cope with despite pumping during the storm period. Pump volume for each storm was defined as the accumulated volume of excess water that was pumped out over that storm.  The values of both pump and flood volumes were calculated as total  volumes over all of the storms.  101  TABLE 6.1  Flood Volumes with Alternative Operating Methods ) 3 tOOD VOLUME x 106 m System  Optimum  Fuzzy  Time-Varying  Fixed Rule  Rule Curve  Operation  0•  Casel  0  0  Case 2  0.2  0.1  0.6  0  Case 3  139.0  129.5  129.8  129.3  Total  139.2  129.6  130.4  129.3  Casel  0  0  0  0  Case 2  0.1  0.7  0.6  0  Case 3  160.9  156.1  153.9  151.8  Total  161.0  156.8  154.5  151.8  Casel  0  0  0  0  Case 2  0.0  0.1  0.2  0  Case 3  606.9  606.1  605.4  605.3  Total  606.9  606.2  605.6  605.3  .  .  102  TABLE 6.2 Pumping Volumes with Alternative Operating Methods PUMPING VOLUME (x 1O m 6 System Operation  [  Fixed Rule  Time-Varying  Optimum  Fuzzy  Rule Curve  Case 1  25.2  11.6  4.6  0  Case 2  77.6  77.2  63.6  49.0  Case 3  405.9  384.1  383.6  382.1  Total  508.7  472.9  451.8  431.2  -17.9%t  -9.7%t  -4.7%t  0  Case 1  73.1  20.1  1.9  Case 2  256.8  208.6  180.0  153.3  Case 3  613.2  610.7  610.8  610.0  Total  943.1  839.3  792.7  763.3  -23.5%t  -9.9%f  -3.8%t  0  Case 1  52.3  12.9  0.5  0  Case 2  719.7  627.8  519.5  477.6  Case 3  2632.5  2521.7  2519.6  2412.7  Total  3404.5  3162.4  3039.6  2890.2  -17.8%t  -9.4%t  -5.1%t  0  % improvement  % improvement  % improvement  ‘  0  Note:  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 perfect forecasts of the flows.  103  30  F  25 4  20  —  -  -  O -  -  -Time Varying Rule Curve Fuzzy Optimum lnflow  E 0  2’ D  10 5 0 300  200  100  0  400  600  500  800  700  900  1000  time from the beginning of the storm (mm)  A typical operation under the time varying rule curve requires pumping for a short period as the inflow rises. Operations under fuzzy and optimum alternatives do not require pumping throughout the storm.  Note:  Fig. 6.1. Typical operation in Case 1 (Pump).  60  50  I —  en E  —  -  -  —  I  0  I  2’  I  I.,  •  \  40  Time Varying Rule Curve Fuzzy Optimum Inflow  20  I.  10 ‘ 0 0  100  I’  200  300  400  500  600  700  800  time from the beginning of thestorm (mm)  Note:  Pumping with the time varying rule curve starts earlier than the other two alternatives. Pumping with the fuzzy system starts before the optimum and stops about the same time as the time varying rule curve. Fig. 6.2. Typical operation in Case 2 (Pump). 104  80 •  70  I  -  ‘  +  /  60  I —  I  50 E  -  -  -  -Time Varying Rule Curve Fuzzy Optimum mt low  —  I I 30  I  20 10 0 0  100  200  300  400  500  600  700  800  time from the beginning of the storm (mm)  Note:  The optimum and time varying rule curve alternatives have pumps started and stopped about the same time. Pumping with the fuzzy system starts and stops later than 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 in Section 5.2). The pump was turned on if the available storage within the system was less than the required value. If the system storage were filled up, and the inflow rates were less than the fixed pump rate with no remaining flooding, then the excess inflows would be calculated and added to the total pump volume. As mentioned previously, the fixed rule operating system is generally used in controlling Bangkok’s flood releases. The fixed rule is a pre-determined, constant water level upstream of a gate or pumping station that the operators have to maintain. The current fixed levels (maintenance water levels) used in Bangkok were calculated from unsteady flow simulations for design rainfalls of the 5-year return period. Thus, a comparative fixed level  105  was derived from the simulated data. A total of 500 rainstorms of 5-year return periods were generated. The empty storage spaces were computed as in Section 5.4. The storage required at the beginning of the storms (with 5% probability of exceedance) was then selected as the 3 (i.e., empty storage required fixed rule. For Polder #2, the fixed rule value was 265 000 m throughout the storm).  3 and 3 (365 000 m Two additional fixed rules of ± 100 000 m  165 000 m ) of the computed rule were also tested to see the effects of the fixed rules. 3  TABLE 6.3 Fixed Rule Curve Operation with Different Fixed Rules—Folder #2 System Operation  FIXED RULE  RULE CURVE  FUZZY  165000 m 3 69%f  3%t  2%t  12%t  l0%t  4%t  wage Space: 265000i1 • 3 43%t  3%t  2%t  1 6%t  1 0%t  4%t  Lule Storage space: 365000  3 rn  6%t  3%t  2%t  23%t  1 0%t  4%t  Note:  1•  %=  FixedRule, RuleCurve, orFuzzy Value—” Optimum” Value • 100% “Optimum” Value  106  As 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 operation  depended directly on its value. Setting the fixed rule storage space at a higher value would give better over-all flood reduction. However, it requires more pumping volumes than the lower one, as illustrated in Table 6.3. Thus in comparison with the other alternatives as shown in Tables 6.1 and 6.2, the fixed rule with the higher value of storage space, which gives total flood volume closer to those of the other alternatives, was used.  Fixed rule  3 were used for Polder #1, #2 and #3, 3 and 662 000 m , 365 000 m 3 values of 178 000 m respectively.  500000  400000 C,  E 300000 -I  0 ‘C  200000  2Li. 100000  0 CASE1  CASE2  CASE3A  CASE3B  CASE3C  Fig. 6.4. Mean flood volumes for Folder #2 (Pump).  107  Figs. 6.4 and 6.5 show the mean flood and pumping volumes in each case for Polder #2. 3 In Case 3, the flood volumes were further divided into 3 categories: less than 100 000 m 3 (Case 3C). 3 (Case 3B), and over 300 000 m 3 and 300 000 m (Case 3A), between 100 000 m As in Table 6.2, only small fractions of the difference in pumping volume can be seen between the time varying rule curve, fuzzy, and optimum alternatives.  The fixed rule  operating alternative involved much more pumping than all other alternatives.  1000000  800000 C,  E  Lu  z -I  600000  0  >  0  z  400000  0. 0.  200000  0 CASE 1  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.5. Mean pumping volumes for Polder #2 (Pump).  108  6.3 Additional Experiments  Sets of experiments were carried out with Polder #2 to evaluate the performance of the fuzzy system in more variable and flexible environments. The first set of the experiments used the same physical settings as the main experiments, except the rainfalls were generated from the independent rain intensity and rain duration relation. The second set involved the combined use of a pump and a gate in the flood control operations.  The last set of  experiments dealt with tides by allowing a sudden discharge of floodwaters, simulating the opening of a control gate when the tide level fell below the internal water level. Details of each set of experiments are presented in the following sections.  6.3.1 Experiments with Independent Rainfall Intensity-Duration  In this set of the experiments, rainfall simulations were based on independent generation of rain duration and rain intensity.  Rain duration was generated as described previously.  Average rain intensity was generated from an exponential distribution with a mean of 60 mm br, a typical 2-year storm value used in most of Bangkok’s flood studies. Rain depth was then calculated from the rain intensity and duration. Inflows were constructed as described in Section 5.3. Using the same approach as in the main experiment, the rule curve and fuzzy rules were derived. The FAM’s used are shown in Tables 6.4 and 6.5.  109  TABLE 6.4 First Fuzzy Associative Memory (FAM) for Folder #2—for Use during Rainstorm (Independent Rainfall Intensity-Duration Relationship) RAIN INTENSITY 14  13  12  Ii  10 TO  373000  425000  435000  438000  444000  T  Ti  345000  319000  414000  400000  422000  I  T2  154000  243000  400000  400000  400000  M  T3  92000  186000  400000  400000  400000  E  T4  83000  123000  400000  400000  400000  TABLE 6.5 Second Fuzzy Associative Memory (FAM) for Folder #2—for Use Following the End of Rainstorm (Independent Rainfall Intensity-Duration Relationship) TOTAL RAIN DEPTH DO  Dl  D2  D3  D4  TO  0  174000  182000  374000  643000  T  Ti  0  156000  169000  341000  605000  I  T2  0  28000  84000  105000  265000  M  T3  0  1000  12000  6000  43000  E  T4  0  0  0  0  1000  110  Tables 6.6 and 6.7 show summaries of the results for the rule curve and fuzzy operating systems based on correlated and independent rain durations and intensities. As discussed previously, the fuzzy system offered a slight improvement on the rule curve operation when the simulated inflows were based on the correlated rainfalls. The improvement increased as the variability of the inflows increased, with the uncorrelated durations and intensities. However, the time varying rule curve operating policy performed slightly worse than in the correlated rain intensity-duration simulations.  TABLE 6.6 Flood Volumes with Alternative Operating Methods for Different Simulated Rainfalls ) 3 6m FLOOD VOLUME (x10  :zc* pzpER #2  [System ::  Operation  A  L  Optimum  Fuzzy  Rule Curve  TVfl TNTVNTTV A1’JI1 ThTTP  A ‘I’TflJ  -  Casel  0  0  0  Case 2  0.7  0.6  0  Case 3  156.1  153.9  151.8  All  156.8  154.5  151.8  PENDENT INTENSITY AND DURATION Casel  0  0  0  Case 2  0.3  0.5  0  Case 3  168.8  166.3  166.1  All  169.1  166.8  166.1  111  TABLE 6.7 Pumping Volumes with Alternative Operating Methods for Different Simulated Rainfalls  I  ) 3 6 m PUMPING VOLUME (x10  System CC RELATED INTENSITY  AND DURATION -  r.  Case 1  30.1  1.9  0  Case 2  198.6  180.0  153.3  Case3  610.7  610.8  610.0  All  839.3  792.7  763.3  -9.9%t  -3.8%t  0  % Improvement  INDEPENDENT INTENSITY  AND DURAT.  -  0  Case 1  13.0  3.5  Case 2  139.8  101.3  84.6  3  442.7  438.8  434.9  595.6  543.6  519.5  -14.6%t  -4.6%t  0  Case All  % Improvement  —  Note:  t  Compared with “optimum” values; minus sign (-) means worse.  be noted that in practice the “optimum” is not attainable, as it would require perfect forecasts of the flows.  It should  112  Figs 6.6 and 6.7 show the mean values of flood and corresponding pumping volumes for each case.  In  The classification of Case 3 is the same as in the main experiments.  comparing Fig. 6.7 with Fig. 6.5, there is slight improvement by the fuzzy alternative over the rule curve, as could be expected. Fig. 6.6 also shows the flood volumes resulting from inflows from rainstorms simulated from the independent rain intensity-duration relation. More large floods occurred with the independent intensity-duration relation than when they were correlated.  There was also slight improvement of the pumping pattern (Case 3A)  3 (Fig. 6.7). where floods were less than 100 000 m experiments (Fig. 6.5).  This did not show in the main  However, when all the Case 3 floods were summed up, this  difference can not be seen in Table 6.7.  600000 500000 C,  E  400000  UI -I  0  300000  >  0  200000 U.  100000  CASE I  CASE 2  CASE 3A  CASE 3B  CASE 3C  Fig. 6.6. Mean flood volumes for the independent intensity- duration, Folder #2 (Pump).  113  C,  E  w -I  0  >  0  z 0.  CASE 1  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.7. Mean pumping volumes for the independent intensity-duration, Folder #2 (Pump).  6.3.2 Experiments with Pump and Gate Discharges  In order to make the polder flood control operation more flexible, the operation of a gate was introduced in addition to the pumping operation. The gate was allowed to remain open throughout the storm period. The total discharge capacity of the polder system was kept the same as in the polder using pumping only. For Folder #2, the gate discharge capacity was 8 3 m  3 and pump discharge capacity was 12 m  . 1 s  Therefore, the total discharge capacity  3 s’). In this set of experiments, the time was equal to the pumping only setting (20 m varying 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 independent rainfall intensity-duration cases were used in the experiments.  114  Tables 6.8 and 6.9 show summaries of the results of these experiments. Improvement of the operation by the fuzzy over the rule curve can again be seen as a small percentage of total pumping volumes. The fuzzy system shows a greater improvement (13%) over the rule curve operating system with the independent intensity-duration relation. In this case, the setting of the experiments is more variable and more operationally flexible.  In both  independent and correlated rain simulations, the flood volumes were compatible (Table 6.8).  TABLE 6.8 Flood Volumes with Alternative Operating Methods for Pump/Gate Operations  115  TABLE 6.9 Pumping Volumes with Alternative Operating Methods for Pump/Gate Operations ) 3 6m PUMPING VOLUME (x10  PUMP/GATE System Operation  Optimum  Fuzzy  Rule Curve  CORRELATED INTENSI1Y AND DURATION -  - an...  >*-t:c4  -  -  -  -  -  Case 1  4.5  0.3  0  Case 2  103.2  88.3  83.2  Case 3  349.3  354.1  346.9  All  461.8  437.9  430.1  -7.4%t  -1.8%t  0  % Improvement  :  INDEPENDENT INTENSITY AND DURATION  Case 1  10.4  0.1  0  Case 2  102.3  74.2  71.4  Case 3  260.1  256.6  254.9  All  372.8  330.9  326.3  -14.2%t  -1.4%t  0  % Improvement Note:  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 perfect forecasts of the flows.  116  Figs. 6.8 and 6.9, 6.9 and 6.10 show the mean values of flood and corresponding pumping volumes for correlated and uncorrelated rainfalls, respectively. In both cases, the small 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 the previous section (Section 6.3.1).  C,  E uJ -I  0  ‘C  0  2 LI.  CASE I  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.8. Mean flood volumes for the correlated rainfall intensity-duration Folder #2 (Pump/Gate).  117  700000 600000 500000  uJ -J  400000  0  >  300000 0.  200000 100000  CASE I  CASE 2  CASE 3A  CASE 3B  CASE 3C  Fig. 6.9. Mean pumping volumes the correlated rainfall intensity-duration, Folder #2 (Pump/Gate).  600000  500000 C.,  !  400000  LU  z  300000  >  0 200000 U  100000  0 CASE 1  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.10. Mean flood volume for the independent rainfall intensity-duration, Polder #2 (Pump/Gate).  118  $00000 700000 —  n  600000  E 500000  -J  400000 0 300000  z -  200000 100000 0 CASE1  CASE2  CASE3A  CASE3B  CASE3C  Fig. 6.1l.Mean pumping volumes for the independent rainfall intensity-duration, Polder #2 (Pump/Gate).  6.3.3 Experiments with Tides  Timing of low tides is an important factor in polder flood control operation. At low tide, a large discharge release can be made in a short period of time. Typically, gates have much more discharge capacity than pumps. Including tidal effects increased the complexity of the fuzzy system by adding one more decision variable. Tidal effects were simplified and modeled as a time that the system could suddenly discharge excess stormwater through an opening gate with unlimited capacity. From this point on, the operation of the pumping system is terminated. Initially, the time of low tides was randomly generated from a uniform distribution within the 12 hour period from the time the storm began. It was found that the tides had more effect if the large release occurred at a  119  time around the peak inflow. If low tides occurred early in the storm event, there was no particular advantage of an elaborate release strategy.  If low tides happened late, the  operations 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 of  the time of concentration of the polder. The inflows were simulated as before and required release computed for various times of low tides. At each time interval, the required storage was calculated.  500000 _  400000 Time tide occurs  4 300000 200000 ‘  100000 0 0  100  50  150  200  250  300  350  400  450  time from the beginning of the storm (mm)  Fig. 6.12. Time varying rule curve with tidal effects for Polder #2 with the correlated rainfall intensity-duration. The polder setting used in this set of experiments was PokIer #2, operated with 3 pumping only (20 m  1)•  The rule curve became a set of curves, one for each time of low  tide at 30 minute intervals (Fig. 6.12 and 6.13). The rule curves were derived in the same way as described previously in Section 5.4, except that now a set of rule curves was required. For each fixed time of low-tides, the required storage spaces were calculated only 120  up to such a time. During a simulation run, the operating curve was chosen as the one closest to the next time of low tide (e.g., if a low tide occurred at 3.2 hr, the curve at 3.5 hr would be used). In practice, once the predicted time of low-tides was known, then a specific rule curve would be selected based on the next closest time of low-tide. 700000 cC  6  j , ENDENT INTENSITY) cURV jDEP OU 1 RULE H T h  600000  4 hr 500000 —3 hr  Time tide occurs rom t e eginning of the storm):  D  400000  30mm  C,  300000 200000 °‘  100000 0 10  50  90  130  170  210  250  290  330  370  410  450  time from the beginning of the storm (mm)  Fig. 6.13.Time varying rule curve with tidal effects for Polder #2 with the rainfall intensityduration. The fuzzy programming also required an additional fuzzy variable, the time that a low tide occurred. It was incorporated into FAM’s with 3 dimensions. This required more rigorous 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. Large numbers of cells were filled with 0 (zero) if their time from the beginning storm membership was greater than the time of low-tides. The fuzzy membership function of the time of lowtides is shown in Fig. 6.14. Tables 6.10 and 6.11, 6.12 and 6.13 show examples of FAM’s  121  with tide effects (where the time of low-tide membership is TD3) for the correlated and independent rain intensity-duration relations, respectively.  1.0  I )/43/TD4 2.0  3.0  6.0 hr 4.0 5.0 time from the beginning of storm  Fig. 6.14. Membership function of time of low tides.  TABLE 6.10 First Fuzzy Associative Memory (FAM) with Tides (TD3) for Folder #2— for Use during Rainstorm (Correlated Rainfall Intensity-Duration Relationship) RAIN INTENSITY  TIDE  14  13  12  Ii  TD3 )  290000  264000  229000  235000  141000  237000  387000  486000  400000  I  104000  171000  395000  400000  400000  M  14000  24000  400000  400000  400000  0  0  0  0  0  122  TABLE 6.11 Second Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2—for Use Following the End of Rainstorm (Correlated Rainfall Intensity-Duration Relationship) TOTAL RAIN DEPTH DO D1  TD3  D2  D1  D4  0  137000  181000  334000  396000  0  110000  151000  293000  380000  0  29000  26000  77000  156000  M  0  6000  2000  6000  21000  E  0  0  0  0  0  TO  TABLE 6.12 First Fuzzy Associative Memory (FAM) with Tides (TD3) for Polder #2—for Use during Rainstorm. (Independent Rainfall Intensity-Duration Relationship) RAIN INTENSITY  I  TO....  257000  292000  I 271000 fl  12.  Ii  TD3  289000  ‘ 336000  422000 477000 388000 206000 ___ 195000 T__ I  M E  T4  86000  170000  298000  400000  400000  28000  36000  46000  400000  400000  0  0  0  0  0  123  TABLE 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) TOTAL RAIN DEPTH  TIDE  ‘  Di  D2  155000  177000  337000  462000  0  139000  152000  292000  430000  0  62000  29000  76000  157000  0  14000  2000  6000  20000  0  0  0  0  0  DO  TD3  Vjrr  Yrr”  M  TABLE 6.14 Flood Volumes with Different Operating Alternatives with Tides  I  — ) 3 FLOOD VOLUME (x1O’ m  ,Iuw System Operation  Optimum  Rule Curve  f(1DD1’T ATfl  TT$JTENSTTV AND DURATION  Casel  0  0  0  Case 2  0.2  0.3  0  Case 3  14.2  14.4  14.0  All  14.4  14.7  14.0  Casel  0  0  0  Case 2  0.0  0.0  0.0  Case 3  74.0  74.4  73.9  All  74.0  74.4  73.9 124  Tables 6.14 and 6.15 show summaries of the results of the experiments with tides. The flood volumes were reduced significantly in both rain simulating settings. This resulted from the opportunity to suddenly release all excess waters at the tide change.  The  improvement by the fuzzy alternative was larger than those of the other sets of experiments discussed before. The percentage improvement with both rain simulations was about the same magnitude.  TABLE 6.15 Pumping Volumes with Different Operating Alternatives with Tides ) 3 6m PUMPING VOLUME (x10  z  System Operation  Rule Curve A lED  Optimum  Fuzzy  INTENSifY AND DURATION  Case 1  30.7  15.4  0  Case2  116.2  98.0  79.8  Case 3  58.6  56.1  54.2  205.5  169.5  134.0  -53.3%t  -26.4%t  0  All % Improvement  INI EPENDENT 1NTE SITY.AND DURAT ON Case 1  36.1  12.0  0  Case 2  72.4  53.3  42.4  Case 3  155.6  151.8  149.8  All  264.1  217.1  192.2  -37.4%t  -l2.9%t  0  % Improvement Note:  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 perfect forecasts of the flows. 125  Figs. 6.15 and 6.16, 6.17 and 6.18 show time varying rule curves with tidal effects for the case with the correlated and independent intensity-duration, respectively. As mentioned previously, the flood volumes and pumping volumes were significantly reduced by large low tide 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 the advantages of the fuzzy alternative over the rule curve when compared to the optimum ones.  E LU -l  CASEI  CASE2  CASE3A  CASE3B  CASE3C  Fig. 6.15. Mean flood volumes for the correlated rainfall intensity-duration, Polder #2 (Tide).  126  S 300000 -I  0 C, 0.  200000  a.  CASE I  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.16.Mean pumping volume for the correlated rainfall intensity-duration, Polder #2 (Tide).  500000  400000 S 300000 -  200000  SLI. 100000  0 CASE 1  CASE 2  CASE 3A  CASE 3B  CASE 3C  Fig. 6.17.Mean flood volumes for the independent rainfall intensity-duration, Polder #2 (Tide).  127  CASE 1  CASE 2  CASE3A  CASE3B  CASE3C  Fig. 6.18.Mean pumping volumes for the independent rainfall intensity-duration, Folder #2 (Tide).  6.4 Discussion  Table 6.16 shows a comparison of the total volumes of water pumped from Folder #2 during 2000 simulated floods with alternative operating policies. The simulated flood flows were typical of the flood flow regime in Bangkok. Table 6.14 summaries the main results from the numerical experiments described in Chapter 5 and this chapter. The operating policies and parameters were adjusted such that the total amount of flooding (the total volume of floodwaters that could not be either discharged or stored with the available storage) was approximately the same with all the alternative operating systems considered. Thus the comparison of total pumping volumes shown in Table 6.16 gives a direct comparison of the effectiveness of the alternative flood control operating systems.  128  The 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; and 4. 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), which -  involved pumping only, the time varying rule curve was significantly more effective than the fixed rule curve. The fuzzy system was about 6% more effective than the time varying rule curve, and the optimal system was about 4% more effective still. However, the margin between the time varying rule curve (which was taken as the base case) and the optimal system, which had the most effective possible operation was only about 10%, which did not leave much room for the fuzzy system to demonstrate its merits over the base case, the time varying rule curve. It is also worth noting that the fuzzy operating system offered little advantage over the base case, time varying rule curve approach with small floods, where little pumping was required with any system; and also with very large floods, where continuous pumping was required with all systems. However, with intermediate floods, the fuzzy system did offer a significant improvement over the base case.  129  TABLE 6.16 Summary of Improvement of the Various Operations Using Different Alternatives % IMPROVEMENT OF PUMPING(Polder #2)  System  Fixed Ru1e  f  Time Varyliig  Rule CurvC  PUMP .  -9.9%t  -3.8%t  -14.6%t  -4.6%t  3ATE .  -7.4%t  -1.8%t  -14.2%t TIDES COj*elated  -53.3%t  -26.4%t  independen  -37.4%t  -12.9%t  Note: 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 perfect forecasts of the flows.  130  In the second set of experiments (shown as Row 2  -  “Independent” in Table 6.16), the  rainfall generating algorithm was changed to eliminate the correlation between the rainfall duration and its average intensity, although in Bangkok, the storm durations and average rainfall intensities are in fact correlated. This allowed more variability in the flows and as expected, shows the fuzzy system to be better than the time varying rule curve by about 11%. The fuzzy system is more flexible than the time varying rule curve approach and thus is better able to cope with the more variable flood flow regime. The operation of a flood control system involving both pumping and gravity discharge controlled by gates was simulated with the same operating systems. (Rows 3 and 4, under PUMP/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, but by a similar margin to those with only the pump discharges. Finally a flood control system involving the effect of tidal levels was simulated, again with 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 effect was simulated by assuming that the time between this large increase in discharge and the start of the rainstorm was a random variable. This introduced a third variable into the fuzzy operating rule base and required a family of curves instead of a single time varying rule curve. With the additional variability introduced by the timing of the tide change, there was a much larger margin (37% to 53%) between the time varying rule curve approach and the optimal operation. In this situation, the more flexible fuzzy logic operating system showed a large improvement of about 25% over the base case, time varying operating system.  131  7 CONCLUSIONS  7.1 Summary  Floods 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 and heavy tropical rainfalls all influence floods. For decades, the planning of Bangkok’s flood control has been driven by major flood events. Although many studies and consulting reports on comprehensive flood mitigation and control alternatives have been conducted, in practice incremental flood control measures have been adopted. Presently flood control relies mainly on the polder concept. This is mainly due to the flexibility of the polder concept which allows phased development of the flood control works, which require substantial 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 polder flood-control is the independent drainage-management of floodwater in each of the flood protection units. Polder drainage management mainly deals with the disposal of excess water in polders either through gravity drainage or pumping. Finding the most effective way to manipulate the release of the excess water is very important to the successful flood management. The 132  present 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 of the pumping or gate station. Through many years of experience, the operators recognize that there could be improvements in the operation, but they are reluctant to move away from the comfort and ease of operation with the fixed rule curve. The literature on flood control operating system was reviewed. It was found that most of the technical papers came from academic sources and most dealt with the application of optimization techniques.  However, the papers which described actual flood control  operations, pointed out that almost none of the optimization techniques described in the technical literature had found their way into practice.  The main explanation was that  optimization techniques are too complex to be readily understood by the actual operators and that the operators are reluctant to use tools that they do not fully understand. Rule curves are easy to understand and apply, and if they are followed, they tend to resolve the operators from blame, should flooding actually occur. Fuzzy logic offers a relatively new control technology, that could be useful in flood control. Applications both depend and build on experience with the actual system being controlled.  It was thought that it could be acceptable to flood control operators, as it  represents an extension of the present day rule curve approach.  Fuzzy logic was  investigated, and it was found that although the approach is reasonably straightforward, there are many alternative ways of combining the available information and deciding on what to do in any given situation. Numerical experiments were carried out with simple functions  133  (where the “correct” answer could be easily computed) to find a fuzzy logic control system that could be used for flood control. The most promising fuzzy logic system was adapted to flood control situations for a  polder, typical of those in Bangkok. Ideally, actual data would have been used, but as they were not available, synthetic simulated data had to be utilized. This involved generating rainfall and runoff in a Monte Carlo simulation. The resulting synthetic “floods” were typical of actual floods in Bangkok and were considered sufficiently realistic for developing and testing the fuzzy logic flood control system. Five hundred floods were used as input data for developing the fuzzy logic rule base; and 2000 additional floods were then used in testing the performance of the system. In addition to the fuzzy logic system, three other systems were tested for purposes of the comparison. 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 was  specified. When the floodwaters encroached upon this space, the pumps were started and kept on until the available space increased to the specific level. With the time varying rule curve, the amount of storage space was allowed to vary with the time from the beginning of the storm. These rule curves were derived from analysis of optimal operation during the 500 floods in the data base. The fuzzy logic system was also developed from the same 500 floods. For testing the perfonnance of the alternative flood control systems, 2000 floods were generated, using the same probability distributions for the parameters as in the 500 floods in the “design” data base. The alternative operating systems were adjusted so that they all  134  resulted in the same total volumes of floodwater, that is, surplus water that could not be either discharged or stored in the available storage space. Comparisons of performance were then made on the basis of total pumping volumes. These tests showed the time varying rule curve system to be much better than the fixed rule approach (14% smaller total flood volume pumped); the fuzzy control system to be better than the time varying rule curve (6% smaller flood 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, the fuzzy logic system next and the time varying rule curve third, the differences in performance between these three alternatives were relatively small. Other sets of experiments were then conducted with more variable inflows and more complex systems, one with both pump and gravity discharge controlled, and one that also included tidal effects. These offered more “room” for the more flexible fuzzy operating system to demonstrate better performance than the less flexible time varying rule curve. It is worth repeating that the “optimum” system is not a practical possibility, as it would require perfect flow forecasts.  7.2 Conclusions  Bangkok, one of the largest and fastest growing cities in East Asia faces very serious flood problems. Although many comprehensive flood control schemes have been put forward, the city has in effect settled for an incremental polder based approach in which the city is  135  divided into a number of independent polders, each protected with surrounding dikes and with its own canal and flood discharge. Due to the low elevation of much of the city and possibility of high tides during the rainy season, large pumping stations are needed for discharging water from the polders into the canal or river system. Operating the pumps in an optimal or near optimal way to minimize flooding yet also minimize the volume of the water which has to be pumped is important. Traditionally, in Bangkok the operating system has been the fixed rule curve. A logical extension to the fixed rule curve is the time varying rule curve in which the water level, above which the pumps and/or gates are opened, varies with the time since the beginning of the storm. In this study, a procedure was developed for deriving such a rule curve, on the basis of past flow records or, lacking such records, on the basis of synthesized flows. Operation with these curves showed reductions in the volumes of floodwaters which had 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 provides additional 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 the  Direct method of output inference; 2. in setting up the fuzzy rule base, it was best to only use data sets where input variables had membership values greater than 0.6; 3. the fuzzy logic system is very robust in that rules can be left out or can contain errors without seriously impairing performance;  136  4. it is important to keep the number of fuzzy variables and the number of categories into 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 in  polders typical of those in Bangkok. From simulation studies of the operation of the flood control systems, it was found that: 1. in the simplest flood control situation, where all floodwaters had to be discharged by pumping, 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 fuzzy system. The difference between the various operating systems showed mainly with moderate floods.  With small floods there was no need for pumping, and large  floods overwhelmed all operating systems. 2. in more complex situations, where the flow patterns were more variable and where gate operation and tidal effects were considered as well as pumping, the fuzzy system had a greater advantage over the time varying rule curve operating system (627% better).  In summary the main conclusions are: 1. time varying rule curves are much more effective for flood control in polder situations than the traditional fixed rule curve approach; 2. an effective approach to develop such rule curves has been demonstrated;  137  3. fuzzy logic control systems are more flexible and slightly more effective for flood control than the time varying rule curves; 4. the more variability in the system components and the flows, the better the fuzzy system performs relative to other less flexible systems;  5. in setting up a fuzzy logic control system, it is important to structure the problem with as few input variables as possible.  7.3 Implementation Considerations  Pumping 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. As described above, the logical extension to the present system would be to use time varying rule curves. This would involve the operator in keeping track of the time since the storm began and then reading off a curve the rule curve level for that time. If the water level were above 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 computer and get the operators to keep track of the time since the storm began; and also measure the accumulated rainfall in a simple rain gage. These values would have to be entered into the computer, 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 them on or off). Since portable computers are becoming relatively cheap and since inputting the  138  required information would impose little more burden on the operators than reading a time varying rule curve, it would seem worth going to the fuzzy operating system almost right away. Other advantages of using a computer and fuzzy logic operating system are that it could be set up to record the input information and the actual operations. With these data, it should be possible to fine tune the fuzzy logic rule base and operating system, in effect setting up an adaptive system that would learn from experience.  7.4 Further Research  The results of the numerical experiments with flood control operations with the fuzzy logic control system are promising and suggest that further exploration of the technique is warranted. The fuzzy logic system should be tested in more realistic situations where the simplified methods, such as the time varying rule curve can not well represent the diverse pattern of the storms. It is also noted that a flood control system is a system under stress.  Further  improvement will definitely involve a trade-off between flood damage and pumping energy savings, which has not been included in this study. 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