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Coating maintenance optimization for steel penstocks Siu, Milton 1997

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COATING MAINTENANCE  OPTIMIZATION  FOR STEEL PENSTOCKS by M I L T O N SIU B . A . S C , The U n i v e r s i t y o f B r i t i s h Columbia, 1995  A THESIS 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 DEGREE OF M A S T E R O F A P P L I E D SCEENCE in T H E F A C U L T Y OF G R A D U A T E STUDIES Department o f C i v i l Engineering  W e accept this thesis as c o n f o r m i n g t o the required standard  THE UNIVERSITY OF BRITISH COLUMBIA O C T O B E R , 1997 © M i l t o n Siu, 1997  In  presenting  degree freely  this  at the  thesis  in  partial  fulfilment  of  University  of  British  Columbia,  I agree  available for  copying  of  department publication  this or of  reference  thesis by  this  for  his thesis  and  study.  scholarly  or for  her  I further  purposes  gain  of  f\?PLl  The University of British Vancouver, Canada  Date  DE-6 (2/88)  /3  OCT  Sd Columbia  that  be  It  shall not  permission.  Department  requirements  agree  may  representatives.  financial  the  C/V/L  that  the  by  understood be  allowed  an  advanced  Library shall  permission  granted  is  for  for  the that  without  make  it  extensive  head  of  my  copying  or  my  written  Abstract T w o methods f o r minimizing coating maintenance costs f o r steel penstocks are presented i n this thesis. The first m e t h o d performs a life-cycle cost analysis using equivalent annual costs t o compare the three maintenance strategies: t o u c h - u p , overcoat, and, strip and recoat. T h e strategy w i t h the lowest annual costs is considered t o be optimal. T h e second m e t h o d uses a dynamic p r o g r a m m i n g approach t o obtain the m i n i m u m costs resulting f r o m a sequence o f rehabilitation choices.  A c o m p u t e r application, Penstock Maintenance P r o g r a m ( P M P ) , was developed based o n the t w o o p t i m i z a t i o n procedures. I t was intended f o r this p r o g r a m t o serve as a practical t o o l t o minimize the yearly costs o f penstock coating maintenance. The p r o g r a m was therefore developed o n a p l a t f o r m w h i c h is b o t h accessible and familiar. A n on-line help feature has also been p r o v i d e d t o ease the use o f the p r o g r a m .  I n addition t o p e r f o r m i n g the t w o o p t i m i z a t i o n procedures, P M P allows the user t o enter trial sequences o f rehabilitation strategies t o compare equivalent annual costs. Interval calculations have also been implemented t o handle imprecisely defined cost data.  ii  Contents  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 2.2.1 Touch-Up (or Spot Repair) 2.2.2 Over-Coat 2.2.3 Re-Coat  4 5 5 5  3. Coating Optimization Procedures  7  3.1 Coating Deterioration Simulation  7  3.2 Equivalent Annual Cost Comparison 3.3 Dynamic Programming Approach 3.3.1 Fonnulation . 3.3.2 Illustrative Example  12 13 15  s  3.4 Model Assumptions and Limitations.  4. Penstock Maintenance Program 4.1 Input 4.1.1 4.1.2 4.1.3 4.1.4 4.1.5  9  22  25 28 28 30 32 33 34  General Costs Deterioration Curve Condition Ratings Data Check  4.2 Results 4.2.1 Touch-Up, Over-Coat, and Re-Coat 4.2.2 Combined  36 37 37  4.3 Strategy Calculator 4.3.1 Strategy Input 4.3.2 Results  39 40 41  5. Summary and Conclusions  43 iii  6. F u t u r e D e v e l o p m e n t s  44  Bibliography  45  Appendix 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 like t o thank m y graduate advisor, D r . S. F. Stiemer, f o r all his patience and counsel. F u r t h e r m o r e , t h e expert advice afforded t o me b y D a v e Parry o f B . C . H y d r o is gratefully acknowledged. Financial support t h r o u g h the U.B.C / B . C . H y d r o Professional Partnership P r o g r a m is greatly appreciated. Last b u t n o t least, I w o u l d like t o t h a n k m y f a m i l y f o r their continued support and encouragement t h r o u g h o u t m y education and especially d u r i n g the preparation o f this paper.  vii  1. Introduction Disastrous penstock failures are b e c o m i n g m o r e frequent at hydroelectric stations, particularly i n the past 15 years w i t h older facilities. Historically, m o r e deaths have o c c u r r e d due t o penstock failures than d a m failures [Stutsman, 1996]. I t is therefore necessary t o establish cost-effective programs t o prevent penstock failure. Penstocks, o f course, are pressurized, closed w a t e r conduits used f o r conducting w a t e r f r o m the w a t e r surface t o a p o w e r house where electricity is generated.  One o f the m a i n reasons f o r the failure o f steel penstocks is the c o r r o s i o n o f the base metal, resulting i n a loss o f structural integrity. Consequently, the c o n t r o l o f o n g o i n g c o r r o s i o n becomes important i n p r o l o n g i n g structure serviceability. A l t h o u g h c o r r o s i o n cannot be prevented, i t can be controlled b y preventive maintenance. T h e application o f rehabilitation activities can extend the service life o f a penstock. Therefore, analysis techniques such as life-cycle cost analysis o r dynamic p r o g r a m m i n g can be used t o aid decision m a k i n g i n creating rehabilitation strategies.  A research project between B . C . H y d r o and the 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 was conducted t o incorporate t w o methods f o r m i n i m i z i n g the costs o f a penstock coating maintenance p r o g r a m i n t o a computer application. This may aid i n scheduling rehabilitation activities o n a timely, cost-effective basis.  1  1.1 Objectives One objective o f this research is t o p r o v i d e a b r i e f description o f coating maintenance f o r steel penstocks. T w o methods o f m i n i m i z i n g the annual costs f o r the coating maintenance w i l l be explored. The first m e t h o d is a life cycle cost analysis using each o f the three maintenance strategies: t o u c h - u p , over-coat, and re-coat. The second m e t h o d involves a dynamic p r o g r a m m i n g approach t o minimize costs.  T h e p r i m a r y objective, however, is t o create a t o o l t o aid the decision m a k i n g process f o r coating maintenance. This t o o l , i n the f o r m o f a computer m o d e l , w i l l incorporate the t w o methods described above i n attempting t o develop a coating maintenance policy. Alternatively, it c o u l d be used t o calculate the costs f o r a specific maintenance policy.  1.2 Literature Review T h e need f o r developing penstock safety p r o g r a m s have been previously identified [Stustman, 1996]. Maintenance painting p r o g r a m s are an i m p o r t a n t part o f any safety p r o g r a m . I n fact, many researchers are n o w using c o m p u t e r applications as t o o l s f o r developing painting maintenance policies [ C u n n i n g h a m , 1994; Smith, 1995], I n addition t o serving as i n f o r m a t i o n bases, computers have the ability t o p e r f o r m h i g h numbers o f calculations quickly. This is useful w h e n p e r f o r m i n g life-cycle cost analyses or using dynamic p r o g r a m m i n g approaches t o m i n i m i z i n g costs. Research has been done using these methodologies t o minimize coating maintenance costs f o r bridges [Weyers, 1988; Tarn, 1994]. Some o f the ideas from these previous sources are incorporated into the coating o p t i m i z a t i o n analysis f o r steel penstocks.  2  2. Penstock Coating Maintenance T h e primary goal o f maintenance coating programs is the visual and physical preservation o f the steel penstocks b y preventing metal loss. This is achieved b y using quality coating systems, and p e r f o r m i n g coating maintenance o n a timely basis. T h e coating controls metal loss and c o r r o s i o n b y f o r m i n g a physical barrier and preventing the elements f r o m reaching the steel.  T h e f o l l o w i n g sections describe various defects that may occur, and the rehabilitation strategies used t o correct these defects.  2.1 Types of Failure N u m e r o u s failure modes and defects related t o painted structures are possible. Factors that contribute t o coating failures include the service environment, the type and application o f the coating system, age, chemical exposure, and physical impact. Some o f the types o f coating failures are described i n the f o l l o w i n g paragraphs.  B l i s t e r i n g is a c o m m o n defect that can result i n early failure o n the coating system. T h e y can result f r o m a w i d e variety o f causes. O f t e n , they are filled w i t h a l i q u i d o r gas. Blisters can occur at t h e metal / coating interface o r between coating layers. Blisters continue t o p r o v i d e c o r r o s i o n p r o t e c t i o n u n t i l they are broken.  3  U n d e r c o a t i n g refers t o c o r r o s i o n o c c u r r i n g beneath the coating system. This type o f failure usually occurs at breaks i n the coating system. I t is usually caused by p o o r adhesion.  P i n p o i n t R u s t i n g refers t o rust b r e a k t h r o u g h o n the coating surface. I t c o u l d be caused by inadequate coating thickness or can be caused by aging and the natural degradation o f the coating itself.  D e l a m i n a t i o n failure is caused b y inadequate adhesion o f a coating system. I t can also indicate i m p r o p e r choice o f coating materials. D e l a m i n a t i o n occurs w h e n a c o a t i n g peels o f f o f its substrate.  O t h e r defects in coating systems include flaking, scaling, chalking, and checking. These are surface defects resulting f r o m stresses i n the coating d u r i n g curing and aging. These failures also contribute t o the early failure o f coating systems.  2.2 Maintenance Strategies Three types o f maintenance activities are used t o maintain the c o a t i n g systems f o r steel penstocks. These activities c o u l d be compared or combined t o p r o v i d e cost-effective coating maintenance programs. The three rehabilitation methods are: T o u c h - U p , OverCoat, and Re-Coat. The other alternative t o these three maintenance activities is the " d o n o t h i n g " alternative. O f course, this alternative requires that the penstock be replaced once c o r r o s i o n has reduced its load carrying capacity b e l o w the m i n i m u m acceptable.  4  2.2.1 Touch-Up (or Spot Repair) T o u c h - U p is used w h e r e only a f e w localized failures are occurring. T h e use o f T o u c h - U p maintenance implies that the intact, sound coating is retained. T h e existing coating w h e r e there is localized failure is removed, and a n e w system is applied. T o u c h - U p maintenance is effective because c o r r o s i o n is n o t u n i f o r m o n t h e w h o l e penstock, and rehabilitating only the c o r r o d e d areas w i l l require less effort and reduce the cost o f maintenance. This is t r u e w h e n there is only a f e w areas w h i c h require rehabilitation.  2.2.2 Over-Coat O v e r - C o a t i n g is used where the existing coating system can w i t h s t a n d the application o f additional coats. T h e advantage o f a f u l l coat is that it corrects localized deficiencies that m a y n o t be visible d u r i n g inspection, o r m a y n o t be feasible f o r T o u c h - U p maintenance. O v e r - c o a t i n g involves r e m o v i n g the existing coating w h e r e there are defects, cleaning the intact paint, and applying a n e w coating over the entire structure. T h e use o f OverC o a t i n g delays the eventual complete r e m o v a l o f the underlying coatings. This m a y be advantageous due t o the high costs associated w i t h the removal, containment, and disposal o f the older coatings. T h e disadvantage o f O v e r - C o a t maintenance is that the n e w coating may fail prematurely due t o incomplete compatibility w i t h the existing coating system.  2.2.3 Re-Coat R e - C o a t involves a complete removal o f all existing coatings o n the penstock u n t i l bare metal is reached. A n e w coating system is then applied t o the entire penstock. T h e costs associated w i t h R e - C o a t m a y be high due t o the costs o f r e m o v i n g , containing and  disposing o f the o l d coating systems. Generally, R e - C o a t i n g is used w h e n O v e r - C o a t i n g options are m o r e expensive o r are t o o risky. R e - C o a t i n g o f the entire structure may also be necessary i f the existing coating system has deteriorated substantially.  Additionally,  R e - C o a t i n g may be the only o p t i o n f o r some coating systems that c o u l d not be spotrepaired 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 f o r m i n i m i z i n g the annual costs related t o the coating maintenance o f steel penstocks. T h e first m e t h o d compares the equivalent annual costs o f using each strategy at regular intervals. T h e second m e t h o d allows the three maintenance strategies t o be combined in any order t o achieve a minimal equivalent annual cost.  Both  o f the methods are dependent o n the simulation o f coating deterioration.  3.1 Coating Deterioration Simulation Q u a n t i f y i n g coating system deterioration and establishing deterioration patterns are difficult tasks t o p e r f o r m accurately. A l t h o u g h guidelines exist f o r evaluating t h e degree o f deterioration and corrosion, they are difficult t o apply i n the assessment o f real structures. Since the evaluation o f c o r r o s i o n is visual, they are often subjective at best. V i s u a l records such as successive photos f r o m m o n i t o r i n g programs are best used w i t h c o r r o s i o n scales t o minimize any discrepancies. Table 3.1 shows a t e n p o i n t rated scale and description o f rust grades as published i n the A S T M D 6 1 0 standard "Standard Test M e t h o d f o r E v a l u a t i n g Degree o f R u s t i n g o n Painted Steel Surfaces". P M P uses this scale t o describe the degree o f coating deterioration.  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 C o m p a r i n g the equivalent annual cost o f p e r f o r m i n g each maintenance strategy at different t i m e intervals is a simple approach t o m i n i m i z i n g coating costs. This m e t h o d assumes that only one maintenance strategy w i l l be used at equal time intervals f o r the design life o f the penstock. T h e results o f this analysis shows the minimal costs and the o p t i m a l t i m e intervals t o p e r f o r m rehabilitation activities f o r each strategy. A n interval o f a m a x i m u m and m i n i m u m annual cost are associated w i t h each time interval. T h e t r u e annual cost is b o u n d w i t h i n the cost interval, the magnitude o f w h i c h depends only o n the precision o f the cost data. The f o l l o w i n g procedure explains the cost calculation.  9  1.  A t t i m e j , the degree o f rusting, %Rj, o n the penstock can be calculated f r o m the  deterioration curve. This step assumes that at t i m e 0, there is n o rusting and the c o n d i t i o n rating o f the penstock is 10. 2.  The percentage o f rusted area, %ARj, is adjusted f o r the type o f maintenance  strategy. This is accomplished b y m u l t i p l y i n g %Rj b y a curve factor f o r the appropriate strategy. T h e curve factors are used t o account f o r the differences i n deterioration rates w h e n different maintenance strategies are used. T h e y are also meant t o offset t h e assumption that the penstock coating is i n a n e w c o n d i t i o n after any maintenance activity w h e n i n fact this is t r u e o n l y f o r strip and re-coat operations. 3.  T h e c o n d i t i o n at time j , Cj, is determined f r o m the A S T M D 6 1 0 standards. I f the  c o n d i t i o n is n o t w i t h i n the c o n d i t i o n limits f o r the strategy as defined b y the user, then another t i m e interval is tried. 4.  The percentage o f area f o r w h i c h maintenance is required, AMj(%) is entered b y  the user i n the input module o f P M P . This percentage depends o n the c o n d i t i o n Cj. T h e actual area f o r w h i c h maintenance is required is calculated using the f o l l o w i n g f o r m u l a : AMj 5.  = AMj(%) x surface area o f penstock section  Costs f o r p e r f o r m i n g each strategy include surface preparation costs, coating  costs, and fixed mobilization costs. The cost f o r p e r f o r m i n g the maintenance at t i m e j , Costj, depends o n the maintenance strategy. F o r t o u c h - u p , only the rusted areas require surface preparation and coating application. T h e coating is typically applied w i t h brush application. F o r over-coating, the w h o l e surface requires coating. Strip and re-coat activities requires surface preparation and coating o f the entire penstock. Coatings are  10  applied w i t h spray applications f o r b o t h Over-coat and Re-coat strategies. T h e costs f o r each strategy are calculated using cost intervals. The costs f o r each strategy are as f o l l o w :  For Touch-Up: Costj = AMj x (cost_s + cost_c) + c o s t s m + cost_cm where: cost_s  =  the unit rate f o r surface preparation f o r c o n d i t i o n Cj  costc  =  the unit rate f o r brush application o f coating  cost_sm  =  the mobilization cost f o r surface preparation f o r c o n d i t i o n Cj  costcm  =  the mobilization cost f o r brush application o f coating  For Over-Coat: Costj = AMj x c o s t s + A r e a x cost_c + c o s t s m + cost_cm where: costs  =  the unit rate f o r surface preparation f o r c o n d i t i o n Cj  costc  =  the unit rate f o r spray application o f coating  cost_sm  =  the mobilization cost f o r surface preparation f o r c o n d i t i o n Cj  cost_cm  =  the m o b i l i z a t i o n cost f o r spray application o f c o a t i n g  Area  =  the t o t a l surface area o f penstock  For Re-Coat: Costj -- A r e a x ( c o s t s + cost_c) + cost_sm + cost_cm where: cost_s  =  the unit rate f o r surface preparation f o r c o n d i t i o n Cj  costc  =  the unit rate f o r spray application o f coating  costsm  =  the mobilization cost f o r surface preparation f o r c o n d i t i o n Cj  costcm  =  the m o b i l i z a t i o n cost f o r spray application o f c o a t i n g  Area  =  the t o t a l surface area o f penstock  11  6.  T h e costs at every year j, Costj, are then discounted t o an equivalent annual cost,  EACj, using the discount rate r.  EACj = Costj x  — (l+r)'-l r  3.3 Dynamic Programming Approach C o m p a r i n g equivalent annual costs f o r each strategy separately provides useful i n f o r m a t i o n f o r the user. H o w e v e r , it may n o t provide the most cost-effective sequence o f strategies. D y n a m i c p r o g r a m m i n g is therefore used t o determine the o p t i m a l sequence o f coating maintenance activities using any c o m b i n a t i o n o f the three rehabilitation strategies. D y n a m i c p r o g r a m m i n g is an o p t i m i z a t i o n technique used t o maximize or minimize the sum o f values resulting f r o m a sequence o f decisions, w h i l e m i n i m i z i n g c o m p u t a t i o n a l efforts. I t obtains solutions b y w o r k i n g b a c k w a r d f r o m the end o f a p r o b l e m t o w a r d the beginning, breaking up a large multi-decision p r o b l e m into a series o f smaller single decision problems.  F o r m u l a t i n g the rehabilitation scheduling into a dynamic p r o g r a m m i n g f r a m e w o r k w i l l b e . discussed, and an example w i l l be used t o illustrate the concepts.  12  3.3.1  Formulation  T h e dynamic p r o g r a m m i n g f r a m e w o r k consists o f stages and states. T h e stage variable represents nodes i n a path w h e r e decisions m a y be made. This concept is used t o a l l o w decisions t o be ordered. T h e state variable describes the conditions w h i c h may exist at every stage. I n P M P , the stages refer t o time increments representing each year f o r the length o f the analysis, w h i l e the c o n d i t i o n rating o f the penstock at each stage is represented b y the state variable. Figure 3.2 shows a representation o f the dynamic p r o g r a m m i n g f r a m e w o r k used b y P M P .  Stages 3  4 -  10  10  • 9 . ^ /  9 8  Final State  7  Condition Rating  6  6  5  5 4  Initial  3  3  State  2  2  1  1 0  0 0  Time (Years)  Figure 3-2: Dynamic Programming Framework  13  States  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: f (s) = min [g(dns,s,n) + f„ i(s')] n  +  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, f +i(s'), must be known before the current function, f (s), can be n  n  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 o f rehabilitation strategies will be obtained for a simplified set o f conditions. In this example, the required condition rating o f the penstock at the end o f 9 years is six, and there is a minimum acceptable condition rating o f five. T o 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 o f money. Figure 3.3 shows the layout o f the feasible region o f the problem in a dynamic programming framework.  0  1  2  3  4  5  T i m e (Years)  F i g u r e 3-3: Feasible R e g i o n f o r I l l u s t r a t i v e E x a m p l e  15  6  7  8  9  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 Rating 10 Q  y  8 7 6 5 4 3 2 1 0  Touch-Up Years 0  Over-Coat  Cost  Years 0,1,2  Cost  Re-Coat Years 0,1,2,3  Cost  1  i  3  2 3,4  llllliBlllllIlIllilllllHllilllllll  infeasible infeasible infeasible infeasible infeasible Notes  infeasible infeasible infeasible infeasible infeasible  infeasible infeasible infeasible infeasible infeasible  4,5 $100 $200  6  infeasible infeasible infeasible infeasible infeasible  infeasible infeasible infeasible infeasible infeasible  $1000 infeasible infeasible infeasible infeasible infeasible  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  +  -  '  G  0  8  T i m e (Years)  Touch-Up  Over-Coat  Re-Coat  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 oo  -  8  -f-  6  +  0  7  8  T i m e (Years)  Touch-Up  Over-Coat  Re-Coat  F i g u r e 3-6: F e a s i b l e M a i n t e n a n c e A c t i v i t i e s t o R e a c h D e s i r e d 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 F e a s i b l e N o d e s  Year  Cond Rate 0  1  2  3  4  5  6  10 9 8  7 6 5  TS30  T$30  T$40  T$40  O$120 OS220  TS10  TS10  T$20  T$20  O$100 R $1000  O$200  Note: T = Touch-Up, O = Over-Coat, R = Re-Coat  20  7  8  9  Point E:  Point K:  $20 = min  $40 = min  /  "$20" $100 "$20" $100  + $0  + $20  \  •  /  f«(s) - min [ g(dns,s,n) + f i(s') ] n+  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  General j Costs | Deterioration Curve j Condition Ratings j Data Check \ Penstock Geometry  (1606  Condition Limits j  Touch-Up (Bfush Paint)  Slope  Over-Coat (Spray Paint)  Diametei  Re-Coat (Spray Paint) Length of Analysis Years  J60  F~ ir- F~  Optimization Conditions  jib  Age  1  _______  W  ir-  Present Condition  Last Maintenance! Years Aoo  ]G  (25" 3  ~j  :|4Q Mas Allowed  Required End Condition mini Minimum Allowable Condition  Help  F i g u r e 4 - 1 : P M P User Interface  26  £ 1  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 afieldfor naming the project and a pagesensitive 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.  •PenInput  5(rti»|»le.^eh  j Results | Strategy Calculator j Reference Date j Information |  Name of Structure General  Cost* | D e t e c t i o n Curve] C c n f t o n Bating, j Data Check]  Surafce Preparation Description  $/Area Mm  Mobilization  Max  Mm  Man  Condition From  To  Water Blast  [l  J2  |4000  J6000  JG  (lO  Water & Sweep  j1  J3  (9000  J13000  j5  jlfj  Sand  J3  JG  J5000  |7000  |b  ]G  (3  |10  J2000  13500  |5  (4  :jHand Tool  Coating Costs  Discount Rate Mobilization Mm  Max  Min  Max  Rateft) |T™3  Brush Application  (5  |S  (500  J1000  Spray Application  J2  J5  J2000  J5000  Help  Figure 4-3: Costs Input Module  30  1  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  •••±:i?.. Severe Slope C Custom  0036  15  t AM Final Slops  .06  Start  ?  1 06 |2CT  2.5  Curve Factors 100 V, 80 ^  60  s 8  40  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  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  6  a  ?:fe^is^lateij r«st :$rj«*s> less, than DM £ t u g 1  7  less than &3£fust  6  esterrava rus* spots, less thai LOSS rust  8 18  5 fe« than 18& lust  40  3  approxtmatelji 1/6 ef surface lusted  60  2  approxfoately V 3 c f swfaefHWSteri  100  11  apflrosimatftij? 1/2 of surface fustetl  100  0  apptoxaaatelj! l£B&ef surface iMStet*  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» + Input  Sample.pen  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 Water eia*t Water „S weep Sand Hand Tool  4  8  4  9  6 e  12 16  Over-Coat 3i i i i i i i 3 a 6  n  18  Re Coat 3 5  S  ?  *  11 IS  Area Limits for Strategies The Gross Area of the Penstock is 47124 square units. Touch-Up when rusted area ranges trom 5to4?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  Calculate  Check Date  Help  Figure 4-6: Check Data Page  35  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 EAC vs Time Interval  2.6E44 2.0&4-I  8l.5Ew4 _1.0E»4 5000 —i—  —i—  11  10  12  —i— 13  14  Years  Condition vs Time Interval  13  -°  7  6  10  11  12  Years  Figure 4-7: Life-Cycle Cost Analysis Results  36  —i—  13  14  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  SO  Time (Years)  19 27 35 43  Touch-Up Re-Coat Touch-Up Touch-Up  Figure 4-8: Dynamic Programming Results  38  60  70  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  11111  Re-Coat •vet-Coat Over-Coat Touch-Up Over-Coat  20 40 55 60  Calculate  #etp  Figure 4-9: Strategy Calculator Input  39  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  Results  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 Strategylnput  Strategy Calculator j Reference Data | Information) Results]  Cost of Strategy The EAC of the strategy shown below is from  $13,453to$39,564  Condition Rating  uH 0  i 10  i 20  i 30  i 40  j 50  Time (Years)  AcMy  8  20 40 55  Re-Coat Over-Coat Re-Coat Re-Coat  F i g u r e 4-10: Strategy C a l c u l a t o r Results  41  i60  70  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 deterioration has been modeled i n a computer p r o g r a m ( P M P ) w h i c h can be used as a t o o l f o r decision m a k i n g o n coating maintenance policies. This m o d e l uses t w o routines t o determine the optimal t i m i n g and m e t h o d o f penstock coating rehabilitation. T h e first routine uses a life-cycle cost analysis t o compare the equivalent annual costs f o r each o f the three maintenance strategies: t o u c h - u p , over-coat, and r e coat. T h e second routine determines the lowest cost combination o f rehabilitation strategies and ensures that the coating reaches a specified c o n d i t i o n at the end o f the analysis. This m e t h o d uses a dynamic p r o g r a m m i n g approach t o find the o p t i m a l solution. Alternatively, the computer m o d e l can be used t o calculate the annual costs f o r a specific maintenance policy.  Based o n preliminary results using P M P , T o u c h - U p maintenance seems t o have the lowest annual costs, and R e - C o a t maintenance seems t o have the highest annual costs. T h e lowest cost maintenance may be t o p e r f o r m T o u c h - U p maintenance at short intervals. These conclusions must be validated b y developing deterioration functions specific t o each penstock, as w e l l as refining financial data. Preliminary analyses w e r e p e r f o r m e d 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 New York: Academic Press Inc., 1977.  Programming.  Fancutt F. and Hudson, J. C. Protective Painting of Structural Steel. London: Chapman and Hall Ltd., 1968. Guidelines for Evaluating Aging Penstocks. Engineers, 1995.  New York: American Society of Civil  Hansen, Eldon. Global Optimization using Interval Analysis. Dekker Inc., 1992. Hare, Clive H . Painting of Steel Bridges and Other Structures. Nostrand Reinhold, 1990.  New York: Marcel  New York: Van  Hare, Clive H . Protective Coatings for Bridge Steel. Washington: National Research Council, 1987. Keane, JohnD., ed. Steel Structures Painting Manual: Good Painting Pittsburgh: Steel Structures Painting Council, 1982.  Practice.  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. Academic Press Inc., 1978. Riggs, James L. et al. Engineering Economics: McGraw-Hill Ryerson Limited, 1986. 45  New York:  First Canadian Edition.  Toronto:  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,  Tarn, Chun Kwok. A Study of Bridge Coating Maintenance. University of British Columbia, 1994.  1992.  Vancouver: The  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 Algorithms. Boston: PWS-Kent Publishing Company, 1991.  and  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.  Description  File Name pen.exe trial, pen delphi / pen.dpr delphi / pen. res delphi / penstock, dcu delphi / penstock, dfm delphi / penstock, pas  Executable program application file Sample data file Delphi project file Windows resource file Delphi compiled unit Delphi form unit Delphi pascal unit, source code  Table A - l : Program Files for P M P  All the files listed in Table A. 1 are saved on a disk labeled "Penstock Maintenance Program".  47  

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