UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Coating maintenance optimization for steel penstocks Siu, Milton 1997

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-ubc_1997-0601.pdf [ 2.85MB ]
Metadata
JSON: 831-1.0050239.json
JSON-LD: 831-1.0050239-ld.json
RDF/XML (Pretty): 831-1.0050239-rdf.xml
RDF/JSON: 831-1.0050239-rdf.json
Turtle: 831-1.0050239-turtle.txt
N-Triples: 831-1.0050239-rdf-ntriples.txt
Original Record: 831-1.0050239-source.json
Full Text
831-1.0050239-fulltext.txt
Citation
831-1.0050239.ris

Full Text

C O A T I N G M A I N T E N A N C E O P T I M I Z A T I O N F O R S T E E L P E N S T O C K S by M I L T O N S I U B . A . S C , The Universi ty o f Br i t ish Columbia, 1995 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F A P P L I E D S C E E N C E in T H E F A C U L T Y OF G R A D U A T E S T U D I E S Department o f C iv i l Engineering W e accept this thesis as conforming to the required standard T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A O C T O B E R , 1997 © M i l t o n Siu, 1997 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of f\?PLl Sd C / V / L The University of British Columbia Vancouver, Canada Date / 3 OCT DE-6 (2/88) Abstract T w o methods for minimizing coating maintenance costs for steel penstocks are presented in this thesis. The first method performs a l i fe-cycle cost analysis using equivalent annual costs to compare the three maintenance strategies: touch-up, overcoat, and, strip and re-coat. The strategy w i t h the lowest annual costs is considered to be opt imal. The second method uses a dynamic programming approach to obtain the min imum costs result ing f r o m a sequence o f rehabil i tation choices. A computer application, Penstock Maintenance Program (PMP) , was developed based on the t w o opt imizat ion procedures. I t was intended fo r this program to serve as a practical too l t o minimize the yearly costs o f penstock coating maintenance. The program was therefore developed on a p la t form wh ich is bo th accessible and familiar. A n on-l ine help feature has also been provided to ease the use o f the program. I n addi t ion to per forming the t w o opt imizat ion procedures, P M P al lows the user to enter tr ial sequences o f rehabil i tation strategies to compare equivalent annual costs. Interval calculations have also been implemented to handle imprecisely defined cost data. i i C o n t e n t s Abstract ii Contents iii Tables v Figures vi Acknowledgments vii 1. Introduction 1 1.1 Objectives. 2 1.2 Literature Review 2 2. Penstock Coating Maintenance 3 2.1 Types of Failure 3 2.2 Maintenance Strategies 4 2.2.1 Touch-Up (or Spot Repair) 5 2.2.2 Over-Coat 5 2.2.3 Re-Coat 5 3. Coating Optimization Procedures 7 3.1 Coating Deterioration Simulation 7 3.2 Equivalent Annual Cost Comparison 9 3.3 Dynamic Programming Approach 12 3.3.1 Fonnulation .s 13 3.3.2 Illustrative Example 15 3.4 Model Assumptions and Limitations. 22 4. Penstock Maintenance Program 25 4.1 Input 28 4.1.1 General 28 4.1.2 Costs 30 4.1.3 Deterioration Curve 32 4.1.4 Condition Ratings 33 4.1.5 Data Check 34 4.2 Results 36 4.2.1 Touch-Up, Over-Coat, and Re-Coat 37 4.2.2 Combined 37 4.3 Strategy Calculator 39 4.3.1 Strategy Input 40 4.3.2 Results 41 5. Summary and Conclusions 43 i i i 6. F u t u r e Deve lopments 44 B i b l i o g r a p h y 45 A p p e n d i x A : P r o g r a m Files 47 iv Tables Table 3-1: Corrosion Performance Rating ASTM D610 8 Table 3-2: Deterioration Functions and Costs for Illustrative Example 17 Table 3-3: Tabulation of Lowest Costs for Feasible Nodes.. 20 Table A-l: Program Files for PMP 47 v Figures Figure 3-1: Coating Deterioration Functions Used in PMP 9 Figure 3-2: Dynamic Programming Framework 13 Figure 3-3: Feasible Region for Illustrative Example 15 Figure 3-4: Deterioration Functions for Illustrative Example. 16 Figure 3-5: Feasible Maintenance Activities to Reach Desired Condition A 18 Figure 3-6: Feasible Maintenance Activities to Reach Desired Condition E 19 Figure 3-7: Evaluation of Cumulative Return Function 21 Figure 3-8: Projection of Present Deterioration Function 22 Figure 4-1: PMP User Interface..... 26 Figure 4-2: Flow Diagram of PMP 27 Figure 4-3: Costs Input Module 30 Figure 4-4: Deterioration Simulation Page 33 Figure 4-5: Condition Ratings and Maintenance Areas.. 34 Figure 4-6: Check Data Page 35 Figure 4-7: Life-Cycle Cost Analysis Results 36 Figure 4-8: Dynamic Programming Results 38 Figure 4-9: Strategy Calculator Input 39 Figure 4-10: Strategy Calculator Results 41 vi Acknowledgments I w o u l d l ike to thank my graduate advisor, Dr . S. F. Stiemer, for all his patience and counsel. Furthermore, the expert advice afforded to me by Dave Parry o f B.C. H y d r o is grateful ly acknowledged. Financial support th rough the U.B.C / B.C. H y d r o Professional Partnership Program is greatly appreciated. Last but not least, I w o u l d l ike to thank my fami ly f o r their continued support and encouragement throughout m y education and especially dur ing the preparation o f this paper. v i i 1. Introduction Disastrous penstock failures are becoming more frequent at hydroelectr ic stations, part icularly i n the past 15 years w i t h older facilities. Histor ical ly, more deaths have occurred due to penstock failures than dam failures [Stutsman, 1996]. I t is therefore necessary to establish cost-effective programs to prevent penstock failure. Penstocks, o f course, are pressurized, closed water conduits used for conduct ing water f r o m the water surface to a power house where electricity is generated. One o f the main reasons for the failure o f steel penstocks is the corrosion o f the base metal, result ing in a loss o f structural integrity. Consequently, the contro l o f ongoing corrosion becomes important in pro longing structure serviceability. A l t h o u g h corrosion cannot be prevented, i t can be control led by preventive maintenance. The application o f rehabil i tat ion activities can extend the service l i fe o f a penstock. Therefore, analysis techniques such as life-cycle cost analysis or dynamic programming can be used to aid decision making in creating rehabil i tat ion strategies. A research project between B.C. H y d r o and the Universi ty o f Br i t i sh Columbia was conducted t o incorporate t w o methods fo r minimiz ing the costs o f a penstock coat ing maintenance program into a computer application. This may aid i n scheduling rehabil i tat ion activities on a t imely, cost-effective basis. 1 1.1 Objectives One objective o f this research is to provide a br ie f descript ion o f coat ing maintenance fo r steel penstocks. T w o methods o f minimiz ing the annual costs fo r the coating maintenance w i l l be explored. The first method is a l i fe cycle cost analysis using each o f the three maintenance strategies: touch-up, over-coat, and re-coat. The second method involves a dynamic programming approach to minimize costs. The pr imary objective, however, is to create a t o o l t o aid the decision mak ing process fo r coat ing maintenance. This too l , in the f o r m o f a computer model , w i l l incorporate the t w o methods described above in attempting to develop a coating maintenance pol icy. Al ternat ively, it could be used to calculate the costs for a specific maintenance pol icy. 1.2 Literature Review The need f o r developing penstock safety programs have been previously identi f ied [Stustman, 1996]. Maintenance paint ing programs are an important part o f any safety program. I n fact, many researchers are n o w using computer applications as tools fo r developing paint ing maintenance policies [Cunningham, 1994; Smith, 1995], I n addi t ion to serving as in format ion bases, computers have the abil ity to per fo rm high numbers o f calculations quickly. This is useful when per forming l i fe-cycle cost analyses or using dynamic programming approaches to minimiz ing costs. Research has been done using these methodologies to minimize coating maintenance costs fo r bridges [Weyers, 1988; Tarn, 1994]. Some o f the ideas from these previous sources are incorporated into the coating opt imizat ion analysis fo r steel penstocks. 2 2. Penstock Coating Maintenance The pr imary goal o f maintenance coating programs is the visual and physical preservation o f the steel penstocks by preventing metal loss. This is achieved by using quali ty coat ing systems, and per forming coating maintenance on a t imely basis. The coating controls metal loss and corrosion by fo rming a physical barrier and preventing the elements f r o m reaching the steel. The fo l l ow ing sections describe various defects that may occur, and the rehabil i tat ion strategies used to correct these defects. 2.1 Types of Failure Numerous failure modes and defects related to painted structures are possible. Factors that contr ibute to coating failures include the service environment, the type and appl icat ion o f the coating system, age, chemical exposure, and physical impact. Some o f the types o f coating failures are described in the fo l low ing paragraphs. Bl is ter ing is a common defect that can result in early fai lure on the coating system. They can result f r o m a w ide variety o f causes. Of ten, they are f i l led w i t h a l iquid or gas. Bl isters can occur at the metal / coat ing interface or between coat ing layers. Bl isters cont inue t o prov ide corrosion protect ion unt i l they are broken. 3 Undercoat ing refers to corrosion occurr ing beneath the coating system. This type o f fai lure usually occurs at breaks in the coating system. I t is usually caused by poor adhesion. Pinpoint Rust ing refers to rust breakthrough on the coating surface. I t could be caused by inadequate coating thickness or can be caused by aging and the natural degradation o f the coat ing itself. Delaminat ion fai lure is caused by inadequate adhesion o f a coating system. I t can also indicate improper choice o f coat ing materials. Delaminat ion occurs when a coat ing peels o f f o f its substrate. Other defects in coating systems include f laking, scaling, chalking, and checking. These are surface defects result ing f r o m stresses in the coating dur ing cur ing and aging. These failures also contr ibute to the early fai lure o f coat ing systems. 2.2 Maintenance Strategies Three types o f maintenance activities are used to maintain the coat ing systems for steel penstocks. These activities could be compared or combined to provide cost-effective coat ing maintenance programs. The three rehabil i tat ion methods are: Touch-Up , Over-Coat, and Re-Coat. The other alternative to these three maintenance activities is the " d o -noth ing" alternative. O f course, this alternative requires that the penstock be replaced once corrosion has reduced its load carrying capacity be low the min imum acceptable. 4 2.2.1 Touch-Up (or Spot Repair) T o u c h - U p is used where only a few localized failures are occurr ing. The use o f T o u c h - U p maintenance implies that the intact, sound coating is retained. The existing coating where there is localized failure is removed, and a new system is applied. T o u c h - U p maintenance is effective because corrosion is not un i fo rm on the who le penstock, and rehabil i tat ing only the corroded areas w i l l require less effort and reduce the cost o f maintenance. This is t rue when there is only a few areas wh ich require rehabil itation. 2.2.2 Over-Coat Over-Coat ing is used where the existing coat ing system can wi thstand the applicat ion o f addit ional coats. The advantage o f a fu l l coat is that it corrects localized deficiencies that may not be visible dur ing inspection, o r may not be feasible fo r T o u c h - U p maintenance. Over-coat ing involves removing the existing coating where there are defects, cleaning the intact paint, and applying a new coating over the entire structure. The use o f Over-Coat ing delays the eventual complete removal o f the underlying coatings. This may be advantageous due to the high costs associated w i t h the removal, containment, and disposal o f the older coatings. The disadvantage o f Over-Coat maintenance is that the new coat ing may fai l prematurely due to incomplete compat ibi l i ty w i t h the existing coating system. 2.2.3 Re-Coat Re-Coat involves a complete removal o f all existing coatings on the penstock unt i l bare metal is reached. A new coating system is then applied to the entire penstock. The costs associated w i t h Re-Coat may be high due to the costs o f removing, containing and disposing o f the o ld coating systems. Generally, Re-Coat ing is used when Over-Coat ing opt ions are more expensive or are too risky. Re-Coat ing o f the entire structure may also be necessary i f the exist ing coat ing system has deteriorated substantially. Addi t ional ly , Re-Coat ing may be the only opt ion fo r some coating systems that could not be spot-repaired or over-coated. 6 3. C o a t i n g O p t i m i z a t i o n P r o c e d u r e s T w o methods are described for minimiz ing the annual costs related to the coat ing maintenance o f steel penstocks. The first method compares the equivalent annual costs o f using each strategy at regular intervals. The second method al lows the three maintenance strategies to be combined in any order to achieve a minimal equivalent annual cost. B o t h o f the methods are dependent on the simulat ion o f coat ing deterioration. 3.1 Coating Deterioration Simulation Quant i fy ing coating system deteriorat ion and establishing deter iorat ion patterns are di f f icul t tasks to per fo rm accurately. A l t hough guidelines exist fo r evaluating the degree o f deter iorat ion and corrosion, they are di f f icul t t o apply in the assessment o f real structures. Since the evaluation o f corrosion is visual, they are often subjective at best. V isual records such as successive photos f r o m moni tor ing programs are best used w i t h corros ion scales to minimize any discrepancies. Table 3.1 shows a ten point rated scale and descript ion o f rust grades as published in the A S T M D 6 1 0 standard "Standard Test M e t h o d fo r Evaluat ing Degree o f Rust ing on Painted Steel Surfaces". P M P uses this scale to describe the degree o f coating deteriorat ion. 7 Table 3-1: Corrosion Performance Rating A S T M D610 Rust Grade Description 10 no rusting or less than 0.01 % of surface rusted 9 minute rusting, less than 0.03 % of surface rusted 8 few isolated rust spots, less than 0.1 % of surface rusted 7 less than 0.3 % of surface rusted 6 extensive rust spots bust less than 1 % of surface rusted 5 rusting to the extent of 3 % of surface rusted 4 rusting to the extent of 10 % of surface rusted 3 approximately one sixth of the surface rusted 2 approximately one third of the surface rusted 1 approximately one half of the surface rusted 0 approximately 100 % of surface rusted The rate of coating deterioration used in PMP is modeled after deterioration curves published in the Structural Steel Coating Manual from the Ontario Ministry of Transportation. Three different deterioration functions are given, depending on the environment type: marine, industrial, or rural. PMP approximates each of the three deterioration functions with two linear functions. This can be justified since the deterioration functions are already linear beyond the 0.1 - 0.3% rust level. Furthermore, linear functions are easier to model and interpret than high order polynomials. Figure 3.1 shows the deterioration functions used in PMP. PMP also accepts user defined rates of deterioration. 8 % Rust vs. Time 0 10 20 30 40 50 Years Figure 3-1: Coating Deterioration Functions Used in PMP 3.2 Equivalent Annual Cost Comparison Compar ing the equivalent annual cost o f per forming each maintenance strategy at different t ime intervals is a simple approach to minimiz ing coating costs. This method assumes that only one maintenance strategy w i l l be used at equal t ime intervals fo r the design l i fe o f the penstock. The results o f this analysis shows the minimal costs and the opt imal t ime intervals to per form rehabil i tation activities fo r each strategy. A n interval o f a max imum and m in imum annual cost are associated w i t h each t ime interval. The t rue annual cost is bound w i th in the cost interval, the magnitude o f wh ich depends only on the precision o f the cost data. The fo l low ing procedure explains the cost calculation. 9 1. A t t ime j , the degree o f rust ing, %Rj, on the penstock can be calculated f r o m the deter iorat ion curve. This step assumes that at t ime 0, there is no rust ing and the condi t ion rat ing o f the penstock is 10. 2. The percentage o f rusted area, %ARj, is adjusted fo r the type o f maintenance strategy. This is accomplished by mul t ip ly ing %Rj by a curve factor fo r the appropriate strategy. The curve factors are used to account fo r the differences in deter iorat ion rates when different maintenance strategies are used. They are also meant t o offset the assumption that the penstock coating is in a new condi t ion after any maintenance act ivi ty when in fact this is t rue only f o r strip and re-coat operations. 3. The condi t ion at t ime j , Cj, is determined f r o m the A S T M D 6 1 0 standards. I f the condi t ion is not w i th in the condi t ion l imits fo r the strategy as defined by the user, then another t ime interval is tr ied. 4. The percentage o f area fo r wh ich maintenance is required, AMj(%) is entered by the user in the input module o f P M P . This percentage depends on the condi t ion Cj. The actual area fo r wh ich maintenance is required is calculated using the fo l l ow ing formula: AMj = AMj(%) x surface area o f penstock section 5. Costs fo r per forming each strategy include surface preparat ion costs, coating costs, and fixed mobi l izat ion costs. The cost fo r per forming the maintenance at t ime j , Costj, depends on the maintenance strategy. For touch-up, only the rusted areas require surface preparat ion and coating application. The coating is typical ly applied w i t h brush application. Fo r over-coat ing, the who le surface requires coating. Str ip and re-coat activities requires surface preparation and coating o f the entire penstock. Coatings are 10 applied w i t h spray applications for bo th Over-coat and Re-coat strategies. The costs fo r each strategy are calculated using cost intervals. The costs fo r each strategy are as fo l low: For Touch-Up : Costj = AMj x (cost_s + cost_c) + c o s t s m + cost_cm where: cost_s = the unit rate for surface preparation fo r condi t ion Cj c o s t c = the unit rate fo r brush application o f coat ing cost_sm = the mobi l izat ion cost fo r surface preparation fo r condi t ion Cj c o s t c m = the mobi l izat ion cost fo r brush application o f coating For Over-Coat: Costj = AMj x c o s t s + Area x cost_c + c o s t s m + cost_cm where: c o s t s = the unit rate for surface preparation for condi t ion Cj c o s t c = the unit rate fo r spray applicat ion o f coating cost_sm = the mobi l izat ion cost for surface preparation for condi t ion Cj cost_cm = the mobi l izat ion cost fo r spray application o f coat ing Area = the tota l surface area o f penstock For Re-Coat: Costj -- A rea x ( c o s t s + cost_c) + cost_sm + cost_cm where: cost_s = the unit rate for surface preparation for condi t ion Cj c o s t c = the uni t rate fo r spray applicat ion o f coat ing c o s t s m = the mobi l izat ion cost fo r surface preparation fo r condi t ion Cj c o s t c m = the mobi l izat ion cost fo r spray application o f coat ing Area = the tota l surface area o f penstock 11 6. The costs at every year j, Costj, are then discounted to an equivalent annual cost, EACj, using the discount rate r. EACj = Costj x r — ( l + r ) ' - l 3.3 Dynamic Programming Approach Compar ing equivalent annual costs for each strategy separately provides useful in format ion fo r the user. However , it may not provide the most cost-effective sequence o f strategies. Dynamic programming is therefore used to determine the opt imal sequence o f coat ing maintenance activities using any combinat ion o f the three rehabil i tat ion strategies. Dynamic programming is an opt imizat ion technique used to maximize or minimize the sum o f values result ing f r o m a sequence o f decisions, whi le min imiz ing computat ional efforts. I t obtains solutions by w o r k i n g backward f r o m the end o f a problem t o w a r d the beginning, breaking up a large mult i -decision problem into a series o f smaller single decision problems. Formulat ing the rehabil i tation scheduling into a dynamic programming f ramework w i l l b e . discussed, and an example w i l l be used to i l lustrate the concepts. 12 3.3.1 Formulation The dynamic programming f ramework consists o f stages and states. The stage variable represents nodes in a path where decisions may be made. This concept is used to a l low decisions to be ordered. The state variable describes the condit ions wh ich may exist at every stage. I n P M P , the stages refer to t ime increments representing each year fo r the length o f the analysis, whi le the condi t ion rat ing o f the penstock at each stage is represented by the state variable. Figure 3.2 shows a representation o f the dynamic programming f ramework used by P M P . C o n d i t i o n Ra t ing Initial State 1 0 9 8 7 6 5 3 2 1 0 0 Stages 3 4 Time (Years) - 1 0 • 9 Final . ^ / State 6 5 4 3 2 1 0 Sta tes Figure 3-2: Dynamic Programming Framework 13 At all stage and state combinations which are feasible, a decision dns from a set of possible decisions must be chosen. This decision describes how the state at the current stage is transformed into the state at the next stage. This state transformation function depends only on the current stage n, state s, and decision dns. It is described by the formula: s'=t(dns,s,n). In PMP, the set of possible decisions include Touch-Up, Over-Coat, Re-Coat, and do nothing. The choice of any rehabilitation method returns the condition rating (transforms the state) to a value of ten for the same stage. There is a return or cost corresponding to each decision. The return function is denoted as g(dns,s,n). The solution of the problem is obtained by finding the optimal or lowest cost sequence of decision choices over all stages. The optimal decision at each stage and state is found using the recursive equation: fn(s) = min [g(dns,s,n) + f„+i(s')] This function describes the return or cost for the current period, and the cumulative cost for the state under consideration at the previous state. Note that the recursive function for the following stages, fn+i(s'), must be known before the current function, fn(s), can be quantified. 14 3.3.2 I l l u s t r a t i v e E x a m p l e Using the dynamic programming approach as described previously, the optimal, or lowest average cost sequence of rehabilitation strategies wil l be obtained for a simplified set of conditions. In this example, the required condition rating of the penstock at the end of 9 years is six, and there is a minimum acceptable condition rating of five. To simplify the example, all costs for maintenance activities are fictitious and remain in time zero dollars. In P M P , all maintenance costs are discounted to account for the time value of money. Figure 3.3 shows the layout of the feasible region of the problem in a dynamic programming framework. 0 1 2 3 4 5 6 7 8 9 T ime (Years) F i g u r e 3-3: Feasible Reg ion f o r I l l u s t r a t i v e E x a m p l e 15 The number of decisions at each stage and state are limited by functional constraints. The decrease in condition rating from one stage to the next is governed by the deterioration of the coating system and the previous maintenance activity. A possible set of deterioration functions for the three maintenance strategies is shown in Figure 3.4. 0 1 2 3 4 5 6 7 8 9 10 Years After Maintenance Figure 3-4: Deterioration Functions for Illustrative Example Table 3.2 summarizes the data presented in Figure 3.4. The table shows the condition rating of the penstock for the years after a certain rehabilitation strategy. For example, the penstock will have a condition rating of six, four years following an Over-Coat. The shaded regions indicate the condition rating interval for which each maintenance strategy is acceptable. The costs are the total average costs for performing the rehabilitation activity. This represents the stage return function previously discussed, and are only tabulated for the conditions that fall within the condition limits for each strategy. Note 16 that for this example, it is not necessary to perform maintenance when the penstock has a rating of eight or higher. Table 3-2: Deterioration Functions and Costs for Illustrative Example Condition Touch-Up Over-Coat Re-Coat Rating Years Cost Years Cost Years Cost 10 Q 0 1 0,1,2 0,1,2,3 y 8 i 3 4,5 7 2 6 3,4 llllliBlllllI lIllilllllHllilllllll $100 6 5 $200 $1000 4 infeasible infeasible infeasible infeasible infeasible infeasible 3 infeasible infeasible infeasible infeasible infeasible infeasible 2 infeasible infeasible infeasible infeasible infeasible infeasible 1 infeasible infeasible infeasible infeasible infeasible infeasible 0 infeasible infeasible infeasible infeasible infeasible infeasible Notes 1. Years column represent number of years alter maintenance to reach condition in condition rating column 2. Costs column shows total cost of performing maintenance at the condition rating indicated 3. Shaded regions indicate condition interval where each strategy is allowed The optimization procedure begins at the required condition at the end of the analysis (end of stage nine, state six). This is represented by point A in Figure 3.5. Point A could be achieved if Touch-Up was performed 3 or 4 years previously, Over-Coat was performed 4 years previously, or Re-Coat was performed 6 years previously (see Table 3.2 or Figure 3.4). The deterioration of the coating system is represented by straight lines to simplify the figure, as only the end points are important. 17 10 c c o c o O 8 + 7 - + 6 - f 0 Touch-Up - ' G T ime (Years) Over-Coat Re-Coat 8 Figure 3-5: Feasible Maintenance Activities to Reach Desired Condition A For each year that a possible strategy has been identified (years 3, 5, and 6), the allowable states for each strategy are cross-referenced with Table 3.2. For example, it is possible to over-coat the penstock in year 5 to reach point A. The penstock condition rating must be 4 or 5 in order for over-coating to occur. This is represented by points E and F. Points B to G in Figure 3.5 represent other allowable states for performing each strategy at the feasible stages. 18 This process is continued for points B through G. In this example, only the allowable strategies that reach point E are analyzed. This is shown in Figure 3.6. In PMP, the process of tracing possible paths of the penstock condition is continued for all possible nodes until stage zero is reached. 10 -c or c o •B c o o 8 -f-6 + 0 Touch-Up 7 T ime (Years) Over-Coat Re-Coat 8 F i g u r e 3-6: Feasible M a i n t e n a n c e A c t i v i t i e s to Reach Des i red C o n d i t i o n E 19 Until now, only the feasible paths to reach the desired end condition are analyzed. The recursive formula is used at each of the identified nodes to tabulate and rninirnize costs, as well as outline the optimal or lowest cost path. The optimal sequence of rehabilitation strategies could be traced using the recursive formula. Table 3.3 shows a tabulation of the costs calculated using the recursive function for each of the feasible stage/state nodes. Also shown are the possible rehabilitation methods for each node. These are the lowest costs for the rehabilitation methods required to reach point A. For example, the lowest cost to reach point A from Year 1, State 6 is $40. Costs shown italicized represent lowest costs for each stage/state. Figure 3.7 shows details of how the costs are calculated for points E and K. T a b l e 3-3: T a b u l a t i o n o f L o w e s t Costs f o r Feasible Nodes C o n d R a t e Y e a r 0 1 2 3 4 5 6 7 8 9 10 9 8 7 TS30 T$30 TS10 TS10 6 T$40 O$120 T$40 T$20 O$100 T$20 5 OS220 R $1000 O$200 Note: T = Touch-Up, O = Over-Coat, R = Re-Coat 20 Point E: $20 = min "$20" $100 + $0 Point K: $40 / = min "$20" $100 • + $20 \ / f«(s) - min [ g(dns,s,n) + fn+i(s') ] Figure 3-7: Evaluation of Cumulative Return Function The lowest costs from each of the feasible nodes that reach point A are now known. To determine the optimal strategy for this example, the deterioration function of the present coating is projected onto the dynamic programming framework. This is seen in Figure 3.8. Figure 3.8 shows that a maintenance schedule can be implemented in years 1, 2, 3, or 5, or from points J, I, G, or F respectively. From Table 3.3, the cheapest alternative would be to implement a strategy starting year 1 at point J, and the most expensive alternative would be to re-coat at year 5, or point F. The cheapest alternative involves Touch-Up maintenance in year 1 ($10) and Touch-Up maintenance in year 5 ($20). 21 Time (Years) Deterioration of Present System F i g u r e 3-8: P r o j e c t i o n o f Present D e t e r i o r a t i o n F u n c t i o n 3.4 Model Assumptions and Limitations Various assumptions were used in the coating deterioration simulation and the cost minimization modules as described above. Three main types of assumptions are identified: those used for the simulation of coating deterioration, those used in the optimization procedures, and general assumptions regarding the penstock and coating condition. However, some of the assumptions may fit in more than one category. 22 Several assumptions are made in the simulation of coating deterioration. Firstly, quantifying the condition of the existing coating can be very difficult due to the variety of defects. Only visible corrosion defects (percentage of rust) are used to rate the coating condition. The deterioration of the coating itself is assumed to follow fixed paths, and does not take into account the probabilistic behavior due to variability in quality control, environmental conditions, or other factors that affect coating performance. Deterioration functions are also assumed to be similar for each type of strategy, differing only by the use of 'curve factors' or multipliers as explained previously. The use of multipliers are also explained in more detail in the next section. Finally, deterioration is assumed to occur uniformly over the entire surface of the structure. One of the main assumption in modeling of the optimization procedures is that only the same type of coating system, or a coating system with similar deterioration characteristics, is always used. Different combinations of coating systems cannot be accommodated in the current model. Another assumption is that the condition of the penstock is restored to its original condition after any rehabilitation method, although this is only true for strip and re-coat operations. The condition of the penstock itself is assumed not to be an issue, and no structural considerations are incorporated into the model. It is also assumed that there is reasonable adhesion between all coating systems. The thickness of the coating system is also not modeled. Finally, to ensure that coating maintenance is not performed over excessively 23 thick coatings or coatings with poor or degraded adhesion, the maximum age of the underlying substrate is limited before a new complete strip and re-coat is required. 24 4. Penstock Maintenance Program A computer application, PMP, was developed using the ideas from the previous section. PMP is intended to be a tool to aid the engineer in developing a cost-effective coating maintenance program. Ease of use and accessibility are primary objectives for the application, therefore PMP has been developed for use on a PC based computer running Microsoft Windows 95. This operating system sets the application in a familiar working environment. Results from PMP can also be transferred to other Windows applications such as spreadsheets or word processors. A description of the files required to run PMP are listed in Appendix A. Numeric data in PMP are dimensionless. The user is supposed to use a consistent set of units. However, the unit of time is always years. PMP consists of one main set of tabbed pages as shown in Figure 4.1. Specifically, there are five tabbed pages, one page each for: Input, Results, Strategy Calculator, Reference, and General Information. The Input page allows the user to enter values for various calculation parameters. The Results page shows the details of calculations for the two optimization procedures. Trial sequences of rehabilitation methods could be entered for economic comparison in the Strategy Calculator page. The Reference page is used as an information base showing details of past jobs. The General Information page shows some background and usage information. Figure 4.2 shows a schematic representation of the program, its modules, and calculations. 25 Input j Results] Strategy Calculator j Reference Data j Information j Name Structure Slope Diametei Length of Analysis Years J60 Last Maintenance! General j Costs | Deterioration Curve j Condition Ratings j Data Check \ Penstock Geometry Condition Limits (1606 j Touch-Up (Bfush Paint) ]G W Over-Coat (Spray Paint) F~ Re-Coat (Spray Paint) ir- F~ Present Condition ir-Optimization Conditions Years Aoo j i b Age (25 " Required End £ 1 3 Condition 1 _______ ~ j Mas Allowed :|4Q mini M mum Allowable Condition Help F i g u r e 4 - 1 : P M P User I n te r face 26 4.1 Input The Input page is used to enter and change key calculation parameters. The Input page contains a sub-set of five tabbed pages, also shown in Figure 4.1. There is one page each for: General Parameters, Cost Data, Deterioration Curve, Condition Ratings, and Data Check. Other components of the Input page include a field for naming the project and a page-sensitive help function. The name of the structure can be entered to identify the project. The Help button at the bottom of the page opens a window containing variable descriptions and useful comments. The variables and comments correspond to the Input Page that was showing when the Help button is pressed. 4.1.1 General The General input screen is also shown in Figure 4.1. This page is used to enter miscellaneous data required for the analysis. The variables are described below. The Penstock Geometry box contains three variables for the length, slope, and diameter of the penstock section. The Length of Analysis box sets the number of years to carry out the analysis. 28 The data from the Last Maintenance box is used to calculate a present condition. This is compared with the observed present condition entered in the Condition Limits box. The user is warned of any discrepancies. The number of years since the last strip and re-coat operation is required to determine the age of the underlying substrate. The maximum age of the underlying substrate limits the number of years before another strip and re-coat operation must be performed. The Condition Limits box allows the user to adjust upper and lower condition limits for each of the three maintenance strategies. These bounds are used to constrain the three strategies to the conditions which they are most efficient. Variables for the observed penstock condition are also required. The required condition at the end of the analysis and the minimum acceptable condition specified in the Optimization Conditions box are used in the dynamic programming optimization module. The required condition constrains the condition in the final year of the analysis, while the minimum acceptable condition ensures that the condition remains above an acceptable standard. 29 4.1.2 Costs The Costs page contains variables which provide financial information to perform the optimization analyses. This includes surface preparation costs, coating costs, mobilization costs and the discount rate used. Costs are entered as a maximum and minimum cost interval, thus allowing for imprecisely defined costs data. Figure 4.3 shows the Costs page. •Pen- 5(rti»|»le.^eh Input j Results | Strategy Calculator j Reference Date j Information | Name of Structure General Cost* | D e t e c t i o n Curve] Ccnf ton Bating, j Data Check] Surafce Preparation Description $/Area Mobilization Condition Mm Max Mm Man From To [ l J2 |4000 J6000 JG (lO j1 J3 (9000 J13000 j5 jlfj J3 JG J5000 |7000 |b ]G (3 |10 J2000 13500 |5 (4 Water Blast Water & Sweep Sand :jHand Tool Coating Costs Mm Max Mobilization Min Max Discount Rate Rateft) Brush Application (5 |S (500 J1000 |T™31 Spray Application J2 J5 J2000 J5000 Help Figure 4-3: Costs Input Module 30 The Surface Preparation Costs allow the user to enter up to four different preparation methods, their associated unit rates, and the condition limits to which they are applicable. Mobilization and de-mobilization costs can also be entered for surface preparation operations. Coating system costs are divided into two methods of coating application: brush application and spray application. Typically, brush application is used for touch-up maintenance only, while spray application is used for both over-coat and re-coat maintenance. The unit cost for the coating system includes the cost of the coating system, labour, and any other costs that are necessary in the application of the coating system. Mobilization and de-mobilization of equipment and crew is again entered separately. The discount rate is used to compare the cost of different maintenance strategies in current day dollars. Discounted cash flow analysis is important because it allows for the determination of the time-value of money [Riggs, 1986]. For example, P dollars invested today accumulates interest at rate; and is worth P(l+i)" at the end of n years. Similarly, P dollars spent n years from now must be discounted by 1/(1+/)" to determine the equivalent amount of money today. 31 4.1.3 Deterioration Curve The Deterioration Curve page provides options for simulating the deterioration of the coating system. This is shown in Figure 4.4. Three different deterioration functions are built into the program: moderate, severe, and slow deterioration. The user can choose one of the pre-defined deterioration functions or can input a custom deterioration function for specific projects. The deterioration curves are specified by entering values for the percentage of rust per year. Pressing the Plot button will plot the deterioration curves and highlight the selected one. The curve factors are used as multipliers to the selected deterioration function. These factors account for the differences in deterioration rates when different maintenance strategies are used to apply the same coating system. For example, performing touch-up maintenance on a coating system will not last as long as performing a strip and re-coat maintenance with the same coating system. The curve factor for Touch-Up would therefore be greater than that for Re-Coat. The simulation of rusting on the penstock is accomplished by determining the percentage of rust from the selected deterioration curve and multiplying this by the appropriate curve factor for the maintenance strategy. 32 ,,.,,,N !,,.,. Seneral | Costs OetetteMon Curve | Co^bonfcaftigs j Data Check i Curve "type j r M o d e r a t e : 0056 t AM •••±:i?.. Severe 15 C Custom Slope 0036 Final Slops 1 06 .06 2.5 Start ? |2CT 100 V, 80 ^ 60 s 8 40 Curve Factors Touch Up J3 Over-Coat J2 Re-Coat |i Years Help Figure 4-4: Deterioration Simulation Page 4.1.4 Condition Ratings The Condition Ratings page as shown in Figure 4.5 displays the description of the corrosion performance scale from the A S T M D 6 1 0 standards. The required area for maintenance is related to the condition when maintenance is required. It can be adjusted in the Condition Ratings page. 33 6 a 7 6 5 3 2 11 0 1 Input | Results | Strategy Calculator j Reference Data | Information j Name of Structure General] Costs ] Deterioration Curve Condition Ratings ] Data Check] Description Maintenance Area (%} no rasting or less, than QJQ1& rust f*n>tt*Musi tesstnar»Q.03%fua ?:f e^is^lateij r«st :$rj«*s> less, than DM £ tug less than &3£fust esterrava rus* spots, less thai LOSS rust fe« than 18& lust approxtmatelji 1/6 ef surface lusted approxfoately V 3 c f swfaefHWSteri apflrosimatftij? 1/2 of surface fustetl apptoxaaatelj! l£B&ef surface iMStet* 8 18 40 60 100 100 fibT Hdp Figure 4-5: Condition Ratings and Maintenance Areas 4.1.5 Data Check Figure 4.6 shows the Data Check page. This page is used to check the input values for errors, and to check whether the input values make sense. Data checking occurs after the Check Data button is depressed. PMP first checks that data has been entered into all numeric and text boxes, and that the data is correctly formatted. To check if the input 34 values makes sense, PMP calculates a unit cost table for the three maintenance strategies and for the different surface preparation methods. Area limits for each strategy are also calculated. It is up to the user to verify that these numbers make sense before continuing. Whenever any of the input parameters are changed, the Check Data button must be used to ensure that the changes go through the checking procedures. Depressing the Calculate key starts the cost optimization procedures. * Per» + Sample.pen Input j Result j Strategy Calculate! j Reference Data j Information] Name or Structure General] Costs ] Deterioration Curve j Condition Ratings Data Check ] Unit Costs (VArea} Touch-Up Over-Coat Re Coat Water eia*t 4 8 3 i i i i i i i 3 ? Water „S weep 4 9 3 a * Sand 6 12 n 5 11 Hand Tool e 16 6 18 S IS Area Limits for Strategies The Gross Area of the Penstock is 47124 square units. Touch-Up when rusted area ranges trom 5 to 4?1 square units Over-Coat when rusted area ranges from 141 to 1414 square units. Re-Coat when rusted area ranges from 471 to 47124 square units Check Date Calculate Help Figure 4-6: Check Data Page 3 5 4.2 Results The Results page shows the results of the life-cycle cost analysis and for the dynamic programming optimization analysis. The Results page contains a sub-set of four tabbed pages. This is shown in Figure 4.7. There is one page each for Touch-Up, Over-Coat, Re-Coat, and Combined. * f*<?r»- Oamplc.pen ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ Input Results j Strategy Calculator ] Reference Data ] Information ] Touch-Up • &jf*£jrf j Re-Coat j Combined J 2.6E44 2.0&4-I 8l.5Ew4 _1.0E»4 5000 13 7 -° 6 EAC vs Time Interval — i — 10 11 —i— 12 —i— 13 Years Condition vs Time Interval 10 11 Years 12 — i — 13 14 14 Figure 4-7: Life-Cycle Cost Analysis Results 36 4.2.1 Touch-Up, Over-Coat, and Re-Coat Results from the life-cycle cost analysis for the three maintenance strategies could be seen in the Touch-Up, Over-Coat, and Re-Coat pages. The Over-Coat page is shown in Figure 4.7. Each page contains two graphs. The first graph shows the E A C of the strategy plotted for different time intervals. There are two points for each time interval, representing a maximum and a minimum annual cost for performing the maintenance at that particular time interval. The true annual cost is bounded by the minimum and maximum cost interval. Equivalent annual costs are only calculated for the time intervals in which the calculated condition of the penstock falls within the condition limits defined for each strategy. The calculated conditions for each time interval are shown in the second graph. 4.2.2 Combined The Combined page shows the results of the dynamic programming analysis which minimizes the annual costs for a sequence of rehabilitation strategies. Any of the three maintenance strategies can be combined in any order to produce a cost-effective schedule of maintenance activities. There are three sections in the Combined page: Strategy Cost, Condition Rating, and Activity Schedule. This is shown if Figure 4.8. 37 The strategy cost is shown in the Cost of Strategy box. Two dollar amounts represent the minimum and maximum equivalent annual cost interval for the sequence of maintenance activities shown in the Activity Schedule box. The Activity Schedule box shows the optimal sequence of rehabilitation activities and the year the maintenance activity is to be performed. The condition of the penstock as a result of performing the sequence of maintenance activities is plotted for the length of the analysis. Condition Rating 0 10 20 30 40 Time (Years) SO 60 70 19 27 35 43 Touch-Up Re-Coat Touch-Up Touch-Up Figure 4-8: Dynamic Programming Results 3 8 4.3 Strategy Calculator The Strategy Calculator page allows the user to enter trial sequences of rehabilitation strategies. The equivalent annual cost of the sequence of maintenance activities is calculated, as well as the resulting penstock condition for the length of the analysis. There is a sub-set of two tabbed pages in the Strategy Calculator. Figure 4.9 shows the Strategy Input page of the Strategy Calculator. A Results page is the other page contained in the Strategy Calculator. Input | Results Strategy Calculator j Reference Data} Information ] Strategylnput |Results] Input Strategy 3 Clear AH Activity 8 20 40 55 60 Re-Coat •vet-Coat Over-Coat Touch-Up Over-Coat 11111 Calculate #etp Figure 4-9: Strategy Calculator Input 3 9 4.3.1 Strategy Input The Strategy Input page is used to enter a sequence of rehabilitation activities. The page is divided into two sections, an Input box and an Activity Schedule box. The Input box is used to enter single maintenance activities. A year and a maintenance strategy are required. When the Add button is pressed, the strategy is automatically entered into the Activity Schedule box. Similarly, pressing the Delete button when a year and a maintenance strategy are entered deletes the activity from the Activity Schedule box. Pressing the Clear All button deletes all the scheduled maintenance activities. The Input box checks the data for erroneous entries such as input errors or duplicate entries before the maintenance activity is echoed in the Activity Schedule box. The user is notified of any errors. When a trial sequence of maintenance activities has been entered, the Calculate button must be pressed. PMP will then check the sequence of activities for errors. The calculated condition of the penstock must be between the upper and lower condition limits for the scheduled strategy. If the penstock condition is not within the upper and lower condition limits of the scheduled activity, then PMP will choose another strategy with conditions limits that encompass the calculated condition. The number of years since the last strip and re-coat activity is also checked. The user is notified of any errors. 40 4.3.2 Resul ts Figure 4.10 shows the Results page of the Strategy Calculator. The Results page of the Strategy Calculator is very similar in appearance to the Combined Results page. The Results page of the Strategy Calculator is also divided into three sections: a strategy cost, the calculated conditions, and an activity schedule. Be Input ] Results Strategy Calculator j Reference Data | Information) Strategylnput Results] Cost of Strategy The EAC of the strategy shown below is from $13,453 to $39,564 Condition Rating u H i i i i j i-0 10 20 30 40 50 60 Time (Years) 70 A c M y 8 20 40 55 Re-Coat Over-Coat Re-Coat Re-Coat F i g u r e 4-10: S t ra tegy C a l c u l a t o r Resul ts 41 The strategy cost is shown in the Cost of Strategy box. The dollar amounts represent the minimum and maximum equivalent annual costs for the sequence of maintenance activities shown in the Activity Schedule box. The Activity Schedule box contains the trial sequence of maintenance activities, with any changes that may have occurred during error checking. The condition of the penstock as a result of performing the sequence of maintenance activities is plotted for the length of the analysis. 42 5. Summary and Conclusions Penstock coating deteriorat ion has been modeled in a computer program ( P M P ) wh ich can be used as a too l for decision making on coat ing maintenance policies. This model uses t w o routines to determine the opt imal t im ing and method o f penstock coating rehabil i tation. The first rout ine uses a l i fe-cycle cost analysis t o compare the equivalent annual costs fo r each o f the three maintenance strategies: touch-up, over-coat, and re-coat. The second rout ine determines the lowest cost combinat ion o f rehabil i tat ion strategies and ensures that the coating reaches a specified condi t ion at the end o f the analysis. This method uses a dynamic programming approach to find the opt imal solut ion. Al ternat ively, the computer model can be used to calculate the annual costs fo r a specific maintenance pol icy. Based on prel iminary results using P M P , T o u c h - U p maintenance seems to have the lowest annual costs, and Re-Coat maintenance seems to have the highest annual costs. The lowest cost maintenance may be to per form Touch-Up maintenance at short intervals. These conclusions must be validated by developing deteriorat ion funct ions specific t o each penstock, as we l l as ref ining financial data. Prel iminary analyses were per formed using only data f r o m expert estimates. 43 6. Future Developments This thesis represents the preliminary steps towards the cost optimization of coating maintenance scheduling for steel penstocks. The two techniques used to estimate annual costs should be investigated for further refinement to more accurately model the behavior of penstock coatings. Two major assumptions in the optimization techniques should be examined. The first is that for the same coating type, the deterioration rate for the different application methods differ only by the deterioration curve factors. The second assumption is that after any rehabilitation method, the condition of the penstock returns to a 'new' condition. As well as refining the optimization techniques, better information is needed to improve on the estimates. This can be accomplished by collecting, monitoring, and analyzing field data, and setting up an information base which may be tied into the computer model. Specifically, information bases are required to refine cost data and coating deterioration functions. The effects of each rehabilitation strategy on coating deterioration should be investigated. Additionally, the effects of adhesion on coating performance, and the change in adhesion with time must also be considered. The use of different coatings and coating compatibility may also be incorporated into the model. 44 Bibliography Codner, G. P. A Dynamic Programming Approach to the Optimisation of a Complex Urban Water Supply Scheme. Australia: Department of National Development, 1979. Condition Based Maintenance: Material Condition, Structure Performance and Maintenance Scheduling Guidelines. Vancouver: B. C. Hydro and Power Authority, 1994. Cunningham, Tony. "Computer-Aided Control of Maintenance Painting Programs", Journal of Protective Coatings and Linings, Vol. 8, No. 12, 1991, pp. 60-67. Dreyfus, Stuart E. and Law, Averill M. The Art and Theory of Dynamic Programming. New York: Academic Press Inc., 1977. Fancutt F. and Hudson, J. C. Protective Painting of Structural Steel. London: Chapman and Hall Ltd., 1968. Guidelines for Evaluating Aging Penstocks. New York: American Society of Civil Engineers, 1995. Hansen, Eldon. Global Optimization using Interval Analysis. New York: Marcel Dekker Inc., 1992. Hare, Clive H. Painting of Steel Bridges and Other Structures. New York: Van Nostrand Reinhold, 1990. Hare, Clive H. Protective Coatings for Bridge Steel. Washington: National Research Council, 1987. Keane, JohnD., ed. Steel Structures Painting Manual: Good Painting Practice. Pittsburgh: Steel Structures Painting Council, 1982. Larson, Robert E. Principles of Dynamic Programming: Basic Analytic and Computational Methods. New York: Marcel Dekker Inc., 1978. Puterman, Martin L. Dynamic Programming and its Applications. New York: Academic Press Inc., 1978. Riggs, James L. et al. Engineering Economics: First Canadian Edition. Toronto: McGraw-Hill Ryerson Limited, 1986. 45 Smith, Brett S. "Developing Maintenance Painting Programs for Pulp and Paper Mills", Journal of Protective Coatings and Linings, Vol. 13, No. 7, 1996, pp. 70-78. Stutsman, Richard D. "Developing a Cost-Effective Penstock Safety Program", Hydro Review, May 1996, pp. 16-23. Steel Penstocks. New York: American Society of Civil Engineers, 1993. Structural Steel Coating Manual. Ontario: Ministry of Transportation, 1992. Tarn, Chun Kwok. A Study of Bridge Coating Maintenance. Vancouver: The University of British Columbia, 1994. Whitehead, Judy A. Empirical Production Analysis and Optimal Technological Choice for Economists: A Dynamic Programming Approach. Brookfield: Gower House, 1990. Winston, Wayne L. Introduction to Mathematical Programming: Applications and Algorithms. Boston: PWS-Kent Publishing Company, 1991. 1994 Annual Book of ASTM Standards, Volume 06.02: Paints, Related Coatings, and Aromatics. Philadelphia: American Society for Testing and Materials, 1994. 46 Appendix A: Program Files PMP was developed using Borland Delphi version 2.0 for Windows 95. Table A. 1 shows the files required for running and maintaining PMP. Delphi version 2.0 or higher would be required to make any changes to PMP. File Name Description pen.exe Executable program application file trial, pen Sample data file delphi / pen.dpr Delphi project file delphi / pen. res Windows resource file delphi / penstock, dcu Delphi compiled unit delphi / penstock, dfm Delphi form unit delphi / penstock, pas Delphi pascal unit, source code Table A - l : Program Files for PMP All the files listed in Table A. 1 are saved on a disk labeled "Penstock Maintenance Program". 47 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0050239/manifest

Comment

Related Items