CN111415272B - Dynamic optimization method for preventive replacement time of water supply pipe network - Google Patents
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Abstract
The invention provides a dynamic optimization method for preventive replacement time of a water supply network, which comprises the steps of firstly carrying out failure rate analysis and hydraulic calculation on the water supply network, setting an economic target for maintaining the water supply network and a reliability target for maintaining the water supply network, carrying out decision variable generalization and chromosome gene coding design on the water supply network maintenance to reduce the number of decision variables; then, optimizing and solving the preventive maintenance and replacement time of the pipeline by adopting a non-dominated sorting genetic algorithm with an elite strategy; and finally, comprehensively weighing and identifying the optimal pipe network maintenance scheme. The method can simultaneously give consideration to the dual-target characteristics of the water supply network, faces to a future planning period, dynamically optimizes the preventive replacement time of the water supply pipeline, makes a pipe network maintenance scheme for water supply enterprises, compiles pipe network maintenance planning, has important guiding value, and improves the intelligent level of water supply network construction and management decision.
Description
Technical Field
The invention relates to the technical field of water supply networks, in particular to an economical and reliable dual-target water supply network preventive replacement time dynamic optimization technology. The method can simultaneously give consideration to the dual-target characteristics of the water supply network, faces to a future planning period, dynamically optimizes the preventive replacement time of the water supply pipeline, makes a pipe network maintenance scheme for water supply enterprises, compiles pipe network maintenance planning, has important guiding value, and improves the intelligent level of water supply network construction and management decision.
Background
The water supply network is an important component of a town water supply system as a town life line and directly relates to water supply safety and human health. Along with the evolution of time, the water supply network is aged and loses efficacy, the problems of pipeline leakage and pipe explosion are particularly prominent, the requirements of urban water supply service quality standards cannot be met, and serious social and economic influences are brought. Practice shows that the important way for improving the reliability and the economy of the water supply system is to adopt preventive maintenance measures. Under the condition of limited capital level, large-scale replacement and infrastructure reconstruction of the water supply network are not practical for the complicated urban water supply network. Therefore, it is necessary to determine a certain method for identifying which pipes and when in the water supply pipe system are preventively replaced, so that the water supply system can meet the requirements for reliability while ensuring the indexes of water quantity, pressure and the like, and the economic cost is effective, which becomes a key problem to be urgently solved by decision makers for water supply management. For a long time, water supply decision makers have mainly adopted the following method to determine preventive replacement timing: 1) an empirical method is adopted, such as preventive replacement according to the age of the pipe and the index of the pipe, 2) a comprehensive grading method is adopted to grade and sort the water supply pipeline, the pipeline is selected and replaced under the capital constraint, and the method does not generally consider the influence of the pipeline replacement measure on a pipeline network system; 3) and (4) performing single-target optimization calculation determination by taking the minimum economic cost as a target, and usually not considering the hydraulics constraint. The main disadvantages of these methods are: 1) the economic efficiency and the reliability cannot be considered at the same time, and the scheme with the minimum cost is usually selected, so that the reliability of a water supply network system is damaged; 2) normally, steady-state calculation is implemented, the aging and evolution characteristics of a long-time-scale pipe network system cannot be explained, and dynamic economic analysis cannot be performed. Therefore, the invention provides a technical method considering both economy and reliability, provides an optimal technology for preventive replacement time of a water supply network, has strong operability, and can provide technical support for preventive replacement decision of the water supply enterprise network.
Disclosure of Invention
In order to overcome the technical problems in the prior art, the invention provides a dynamic optimization method for preventive replacement time of a water supply pipe network. The purpose of the invention is realized by the following technical scheme:
a water supply network preventive replacement time dynamic optimization method comprises the following six steps:
step one, failure rate analysis and hydraulic calculation of a water supply pipe network are carried out: according to the historical record data, analyzing the failure rate of the water supply network to obtain a historical data statistical measurement regression equation of the failure rate of the water supply pipeline and pipeline parameter influence factors, wherein the pipeline parameters comprise pipe diameter, pipe length and pipe age; performing hydraulic calculation of the water supply network, including a node continuity equation, an energy equation and a pressure drop equation, and calculating the flow of each water using node under pressure driving to obtain the actual water supply amount of different nodes after the pipeline fails in sequence;
step two, setting an economic target for maintaining the water supply network:
the economic objective minimization is required, including the following objective function:
Obji＝Min(CCTT) (1)
wherein, Obj1Is the 1 st objective function; min () takes the minimum value for the function; CCTT is the net present value of economic cost for water supply network replacement and maintenance in the future planning period; t is time, t is 1,2,3 … … TN, TN is future planning period time, year; j is a pipeline number, J is 1,2,3 … J, and J is the number of pipelines maintained by a water supply network in the water supply network; djThe time for preventive replacement of the jth water supply pipeline, year; r is annual discount rate; percent; CC (challenge collapsar)j,Dj,kFor the kth pipe of the jth water supply pipeline at DjConstruction costs, dollars, of preventive replacement of time; CRj,t,kAnd CR1j,t,kRespectively the maintenance cost and the unit cost of the kth pipe of the jth water supply pipeline in the tth year before and after the replacement of the water supply pipeline; CLj,t,kAnd CL1j,t,kThe jth water supply pipeline of the kth pipe in the t year before and after the replacement of the water supply pipelineWater consumption loss cost caused by water use interruption after failure is low; CIj,t,kAnd CI1j,t,kRespectively leading to loss caused by insufficient water supply of other water using nodes in the water supply network after the jth water supply pipeline of the kth pipe fails before and after the water supply pipeline is replaced; CSj,t,kAnd CS1j,t,kRespectively, indirect influence loss caused by the failure of the jth water supply pipeline of the kth pipe in the t year before and after the replacement of the water supply pipeline;
step three, setting a reliability target of water supply network maintenance:
mainly aiming at hydraulic reliability, the objective function is as follows:
Obj2＝Max(RELt) (3)
wherein, Obj2Is the 2 nd objective function; max () takes the maximum value for the function; RELtReliability of the water supply pipe network system in the t year; j is a pipeline number, J is 1,2,3 … … J, and J is the number of pipelines maintained by the water supply network in the water supply network; REj,tReliability of the jth pipeline in the t year; PRj,tThe failure rate of the jth pipeline in the t year; rn,ttThe water demand at the nth water node for the tth hour, m3H; n is 1,2,3, … … N, wherein N is the number of water consumption nodes in the water supply network; tt is 1,2,3 … … T, T is the hydraulic calculation duration of the water supply network, h; sj,n,ttThe actual water supply quantity m of the pipe network at the nth node tth after the jth pipeline fails3H; u is the maintenance time of the water supply pipeline, h; AGj,tThe age of the pipeline at the tth time of the jth pipeline is year; DIjThe pipe diameter of the jth pipeline is mm; k1,K2The empirical coefficient is determined by statistical analysis according to historical data;
step four, carrying out decision variable generalization and chromosome gene coding design of water supply network maintenance so as to reduce the number of decision variables;
step five, adopting a non-dominated sorting genetic algorithm with an elite strategy to optimize and solve the problem of the preventive maintenance and replacement opportunity of the pipeline, wherein the method comprises the following 4 substeps:
1) setting basic parameters of a genetic algorithm, including population quantity, genetic algebra, cross rate, mutation rate and planning period time;
2) performing population initialization to generate a parent population for each DjA random generation method is adopted;
3) non-dominated ranking and objective function fitness calculation: setting an economic target according to formulas (1) - (2) in the step two, setting a reliability target according to formulas (3) - (7) in the step three, designing and initializing a population according to chromosome gene codes in the step four, calculating the fitness of a population objective function, performing rapid non-dominated sorting, storing decision variable chromosome gene codes with good two objective functions, performing intersection and mutation on poor solutions to generate new filial generations so as to meet an elite strategy, namely performing competition on the parents and the filial generations, and selecting a decision variable chromosome gene code which best meets the objective function from the decision variable chromosome gene codes and reserving the decision variable chromosome gene code;
4) performing mixed cycle calculation on parent population and offspring population, performing crossover, mutation, non-dominated sorting and fitness calculation, and reserving elite individuals until a pareto frontier meeting algebraic conditions is obtained;
step six, comprehensively weighing and identifying an optimal pipe network maintenance scheme:
if the maintenance cost owned by the water supply enterprise is very sufficient, a pipeline network maintenance scheme with the reliability as high as possible can be selected on the pareto frontier; if the maintenance cost owned by a water supply enterprise is very limited, a maintenance scheme which guarantees that water supply is basically reliable can be selected on the front surface of the pareto, and the investment of the maintenance fund of the pipe network is reduced as much as possible on the premise of meeting the requirement of improving the safety level of the water supply network; and selecting an optimal pipe network maintenance scheme according to the actual condition of the pipe network management of the water supply enterprise, and carrying out related planning, design and engineering implementation.
The further scheme, step four, is generalized as follows: A. selecting part of water supply pipelines with large risks to perform optimal decision analysis; B. designing gene coding of chromosomes of the genetic algorithm into a combination of replacement time of each water supply pipeline by adopting the gene coding design of chromosomes of the genetic algorithm DjFor the generalized decision variable, the value range is an integer between 1- (TN +1), J is 1,2,3 … … J, J is the number of pipelines in the water supply network, when D isjTN +1, indicating that the water supply line j is not replaced during the planning period.
Further, step five, step 1): the population number is set to be 2000, the genetic algebra is 30, the cross rate and the mutation rate are both 0.02, and the planning period time TN is 10 years.
Further, step five, step 2): for each decision variable DjThe initial value adopts a random generation method, and the specific method is as follows:
DRj＝Dmin+(Dmax-Dmin)×rand() (8)
Dj＝Ceil(DRj×(TN+1)) (9)
wherein, DRjThe decision variables are randomly generated and are real numbers with the numerical values between 0 and 1; dj is a decision variable and is an integer with the value between 1- (TN + 1); dminAs the minimum value of the decision variable, DmaxThe rand () is a random generating function between 0 and 1 as the maximum value of the decision variable; dminAnd DmaxThe values are 0 and 1 respectively; ceil () is a function rounded towards plus infinity, J is 1,2,3 … J, J is the number of pipes in the water supply network.
The technical invention is mainly characterized in that: 1) for a water supply network system with large scale and complicated complexity, decision variables are discrete and numerous, and the technical method can efficiently optimize and balance different decision variable effects by utilizing a multi-objective genetic algorithm; 2) the technical method is oriented to the middle and long term in the future, can consider the time value of pipeline maintenance, carries out dynamic evaluation and optimization selection on the hydraulic reliability and the economical efficiency of the water supply pipe network system, and provides technical support for optimization decision of maintenance measures of the water supply system. 3) The technical method aims at two main targets of water supply network maintenance, namely an economical target and a reliability target. Of course, other water supply management targets such as water quality reaching standards are also embodied in the optimization process, and the invention focuses on the detailed description of the two targets; 4) the technical method is simplified, and the water supply pipeline is supposed to be replaced by the same pipe diameter; 5) the technical method sets the age of the pipeline which is changed preventively in the current year to be zero, establishes a connection with the failure rate of the pipeline, improves the construction cost through the preventive change of the pipeline, reduces the cost of repairing the pipeline due to the fact that the failure rate of the pipeline is reduced along with the reduction of the age of the pipeline, reduces the total maintenance cost, enables a preventive change scheme to be feasible, and provides a quantitative analysis technology for a decision maker to take active maintenance measures.
The invention has the beneficial effects that:
the research provides a dual-target-oriented dynamic optimization technology for preventive replacement time of the water supply network, can dynamically and comprehensively balance the reliability of the water supply network and the economical efficiency of pipe network maintenance according to the actual conditions of a water supply enterprise, is oriented to the future planning period, and provides preventive replacement time and scheme through genetic calculation. The technical method has strong practicability and operability, and can provide quantitative support for water supply enterprises to make maintenance strategies and schemes and make pipeline updating decisions in the future period. The application of the technical method in practice reduces the total cost of the optimization maintenance of the water supply enterprise to 30-60% by providing a decision support quantification tool for enterprise management decision makers, improves the reliability and the safety degree of the operation of the water supply enterprise, and is also beneficial to improving the decision informatization and intelligentization level of the water supply enterprise.
Drawings
FIG. 1 is a schematic overall flow diagram of the process of the present invention;
FIG. 2 genomic coding design in pipeline preventative maintenance replacement timing optimization;
FIG. 3 is a two-goal tradeoff process for preventive maintenance of water supply networks (Zhejiang county case, population number 2000, 30 generations); remarking: the plus sign in the figure is seven optimized schemes, wherein the plus sign point of the second dotted circle at the lower left corner is the optimal scheme recommended according to the actual situation.
FIG. 4 evolution of economic and reliability targets with algebra (Zhejiang county case);
FIG. 5 time of replacement of each pipe in the water supply network (Zhejiang county case);
FIG. 6 shows the network age change of water supply pipe (Zhejiang county case).
Detailed Description
A water supply network preventive replacement time dynamic optimization method comprises the following steps:
the specific implementation of the technical method comprises the following six steps:
step one, failure rate analysis and hydraulic calculation of a water supply pipe network are carried out
And analyzing the water supply network failure rate (including leakage and pipe explosion) according to the historical record data to obtain a historical data statistical measurement regression equation of the water supply pipeline failure rate and the influence factors such as pipe diameter, pipe length, pipe age and the like. For a water supply pipe network with complicated pipe composition, the failure rate of the pipeline needs to be identified separately by pipes. And for the pipeline taking preventive updating measures in the current year, the age of the pipeline is set to be zero, and the failure rate and reliability of the pipeline are recalculated. The change in the failure rate of the pipeline further affects various maintenance costs of the pipeline and affects the total cost of pipeline maintenance.
And carrying out calculation on the hydraulics of the water supply network, wherein the calculation mainly comprises a node continuity equation, an energy equation, a pressure drop equation and the like, and calculating the flow of each water using node under pressure driving to obtain the actual water supply amount of different nodes after the pipeline fails in sequence. Because the position and the effect of different water supply pipelines are different, the influence degree on the node water supply amount is also different. Typically, failure of a water main affects the water supply to the water using node more than a branch, and pipes closer to the water source affect the water supply to the node more than pipes further from the water source.
Step two, setting an economic target for maintaining a water supply network
The economy is the cost of the maintenance measures taken by the pipe network, and the economic target is required to be minimized, so that the economic cost of water supply enterprises can be saved to the maximum extent. The main objective function of economy is specifically shown below. In addition to the preventive renewal Construction Costs (CC), the remaining costs (CR, CL, CI and CS) belong to passive maintenance. The cost is greatly influenced by the failure rate of the pipeline and the importance of the structure of the pipeline in the pipe network, the failure times are more, the importance degree of the pipeline close to a water source is high, and the maintenance cost of the failure of the pipe network is higher.
Ohj1＝Min(CCTT) (1)
Wherein, Obj1Is the 1 st objective function; min () takes the minimum value for the function; CCTT is the net present value of economic cost for water supply network replacement and maintenance in the future planning period; t is time, t is 1,2,3 … … TN, TN is future planning period time, year; j is a pipeline number, J is 1,2,3 … J, and J is the number of pipelines maintained by a water supply network in the water supply network; djThe time for preventive replacement of the jth water supply pipeline, year; r is annual discount rate; percent; CC (challenge collapsar)j,Dj,kFor the kth pipe of the jth water supply pipeline at DjConstruction costs, dollars, of preventive replacement of time; CRj,t,kAnd CR1j,t,kRespectively the maintenance cost and the unit cost of the kth pipe of the jth water supply pipeline in the tth year before and after the replacement of the water supply pipeline; CLj,t,kAnd CL1j,t,kRespectively the cost of water loss caused by water interruption after the jth water supply pipeline of the kth pipe fails in the t year before and after the water supply pipeline is replaced; CIj,t,kAnd CI1j,t,kLeads to other uses in the water supply network after jth pipe jth water supply pipeline of the t year is invalid before and after the water supply pipeline is replaced respectivelyLoss caused by insufficient water supply of water nodes; CSj,t,kAnd CS1j,t,kThe indirect influence loss caused by the failure of the jth water supply pipeline of the kth pipe in the t year before and after the replacement of the water supply pipeline is respectively reduced.
Step three, setting a reliability target for maintaining the water supply network
The reliability of the water supply network comprises mechanical reliability and hydraulic reliability, and the hydraulic reliability is usually adopted for optimization analysis in optimized maintenance, namely the water supply network can meet the water demand capacity of a user within a specified time and under a specified use state. In the daily management of water supply network, generally require the reliability target maximize to furthest's performance water supply network effect improves water supply system's security level. The objective function of reliability is as follows:
Obj2＝Max(RELt) (3)
wherein, Obj2Is the 2 nd objective function; max () takes the maximum value for the function; RELtReliability of the water supply pipe network system in the t year; j is a pipeline number, and J is 1,2,3 … … J; REj,tReliability of the jth pipeline in the t year; PRj,tThe failure rate of the jth pipeline in the t year; rn,ttThe water demand at the nth water node for the tth hour, m3H; n is 1,2,3, … … N, N is water supply pipeThe number of water consumption nodes in the network is one; tt is 1,2,3 … … T, T is the hydraulic calculation duration of the water supply network, h; sj,n,ttThe actual water supply quantity m of the pipe network at the nth node tth after the jth pipeline fails3H; u is the maintenance time of the water supply pipeline, h; AGj,tThe age of the pipeline at the tth time of the jth pipeline is year; DIjThe pipe diameter of the jth pipeline is mm; k1,K2The empirical coefficient is determined by statistical analysis according to historical data.
Step four, carrying out decision variable generalization and chromosome gene coding design for water supply network maintenance
The traditional water supply network maintenance decision variables are which pipes in the water supply pipe system are preventively replaced at what time. If the water supply network has J pipes, B measures, TN years, then the decision variables have J.B.TN. For larger-scale water supply networks, the large number of decision variables needs to be generalized, which is usually closely related to the planning and management decision requirements of water supply enterprises. The generalized method is as follows: 1) if the water supply enterprises detect and evaluate the key pipelines, part of pipelines can be excluded according to experience, and part of water supply pipelines with high risk are selected for optimal decision analysis, so that the number of decision variables is reduced; 2) the genetic algorithm is adopted for the coding design of chromosome genes, so that the number of decision variables is reduced. According to the present technique, the genetic code of the genetic algorithm chromosome can be designed as a combination of the replacement times of the individual water supply lines, as shown in FIG. 2. Wherein D isjThe generalized decision variable (J is 1,2,3 … … J, J is the number of pipes in the water supply network) is an integer in the range of 1- (TN + 1). Wherein, when DjTN +1, indicating that the water supply line j is not replaced during the planning period. In the specific case of the implementation of the method of the invention, there are 94 pipelines, 2 maintenance measures (considering replacement and maintenance) and a future planning period of 10 years, and there are 1880 decision variables according to the traditional enumeration method; according to the simplified method of the present invention, the decision variable is reduced to 94 (J94).
Step five, adopting a non-dominated sorting genetic algorithm with an elite strategy to optimize and solve
The problem of preventive maintenance and replacement opportunity of the pipeline is solved by adopting a non-dominated sorting genetic algorithm (NSGA-II) with an elite strategy in an optimization mode, and the following four steps are required:
1) setting basic parameters of the genetic algorithm, including population quantity, genetic algebra, cross rate and mutation rate, planning period time and the like. In this embodiment, the population number is set to 2000, the genetic generation number is 30, the crossover rate and the mutation rate are both 0.02, and the planning period time TN is 10 years.
2) And carrying out population initialization to generate a parent population. For each decision variable DjThe initial value adopts a random generation method, and the specific method is as follows:
DRj＝Dmin+(Dmax-Dmin)×rand() (8)
Dj＝Ceil(DRj×(TN+1)) (9)
wherein, DRjThe decision variables are randomly generated and are real numbers with the numerical values between 0 and 1; djIs a decision variable which is an integer with a value between 1- (TN + 1); dminAs the minimum value of the decision variable, DmaxThe rand () is a random generating function between 0 and 1 as the maximum value of the decision variable; in this embodiment, DminAnd DmaxThe values are 0 and 1 respectively; ceil () is a function rounded in the positive infinity direction, J is 1,2,3 … J.
3) Non-dominated ranking and objective function fitness calculation: setting an economic target according to formulas (1) - (2) in the step two, setting a reliability target according to formulas (3) - (7) in the step three, designing and initializing a population according to the chromosome gene codes in the step four, calculating the fitness of a population objective function, performing rapid non-dominated sorting, storing the decision variable chromosome gene codes with good two objective functions, performing cross and mutation on poor solutions to generate new filial generations so as to meet an elite strategy, namely performing competition on the parents and the filial generations, and selecting the decision variable chromosome gene code which best meets the objective function from the decision variable chromosome gene codes and retaining the decision variable chromosome gene code. By increasing the crowding degree, the diversity of the population is improved, and the optimization efficiency of the algorithm is improved.
4) And performing mixed cycle calculation on parent population and offspring population, performing intersection, mutation, non-dominated sorting and fitness calculation, and reserving elite individuals until a pareto frontier meeting algebraic conditions is obtained.
Step six, comprehensively weighing and identifying the optimal pipe network maintenance scheme
According to the actual situation of water supply enterprise pipe network management, the dual targets of economy and reliability are comprehensively balanced, and an optimal pipe network maintenance scheme is selected according to local conditions to carry out related planning, design and engineering implementation. If the maintenance cost owned by the water supply enterprise is very sufficient, a pipeline network maintenance scheme with the reliability as high as possible can be selected on the pareto frontier; if the maintenance cost owned by the water supply enterprise is very limited, a maintenance scheme which guarantees that water supply is basically reliable can be selected on the pareto front face, and the investment of the maintenance fund of the pipe network is reduced as much as possible on the premise of meeting the requirement of improving the safety level of the water supply pipe network.
The invention is further explained below with reference to the drawings and the examples.
Fig. 1 is a technical route implemented by the technical method of the present invention, which mainly includes six steps of failure rate analysis and hydraulic calculation of a water supply network, setting of an economic target for water supply network maintenance, setting of a reliability target for water supply network maintenance, determination of a decision variable for water supply network maintenance, optimization solution by using a non-dominated sorting genetic algorithm with an elite strategy, and comprehensive weighing identification of an optimal pipe network maintenance scheme. FIG. 2 shows in detail the genomic coding design for the optimization of the replacement timing for preventive maintenance of water supply pipelines.
The technical method of the invention is specifically implemented in Zhejiang county and city cases. The county is a generalized line 94, about 37.5km in total, with 68 water nodes. Fig. 3 shows pareto frontiers (population numbers 2000, 30 generations) obtained by optimizing and solving in step five by using a non-dominated sorting genetic algorithm with elite strategy after setting parameters, targets and variables in steps one to four, wherein the plus sign points provide references for the government to update and reform the water supply enterprise according to seven schemes actually preferred in the county and city in step six. Due to the fact that the county water supply pipeline reconstruction cost is limited and the requirement of reliability improvement is met, the plus sign point of the second dotted line circle at the lower left corner is the optimal scheme recommended according to the actual situation, and the net current total cost of ten years without preventive replacement is 3.02 million yuan. The net current value of the total investment cost after maintenance is 1.37 billion yuan, which is only 45.3 percent of the total economic cost without preventive replacement, and the total maintenance cost can be obviously reduced. Wherein the net current value of the construction cost is 9002 ten thousand yuan, and the net current value of the maintenance cost is 4695 hundred million yuan, which respectively account for 65.7 percent and 34.3 percent. Meanwhile, the overall reliability of the water supply pipe network system is improved from original 0.8196 to 0.9491, which is improved by 15.8%.
The evolution process of two objective functions of economy and reliability along with the difference of algebra in the optimization solution process of the step five is shown in FIG. 4. With the continuous advance of genetic algorithms, the total economic cost shows a trend of convergence and decline, and the reliability shows a trend of convergence and rise.
Fig. 5 shows the replacement time of each pipe in the optimum plan recommended according to the actual situation in county. If the replacement time for the pipe is 11 years, it indicates that the replacement is not required for the next decade, as shown in pipe numbers 3, 63, 66, 67, 89 and 93, and the pipe numbers that need to be replaced for the remaining years are shown in table 1. Fig. 6 shows the distribution of the average tube age of a water supply network, which is reduced by preventive replacement measures, for example, from 16.3 to 5.8 years in the decade.
TABLE 1 numbering of pipes to be replaced each year
Claims (1)
1. A water supply network preventive replacement time dynamic optimization method is characterized by comprising the following six steps:
step one, failure rate analysis and hydraulic calculation of a water supply pipe network are carried out: according to the historical record data, analyzing the failure rate of the water supply network to obtain a historical data statistical measurement regression equation of the failure rate of the water supply pipeline and pipeline parameter influence factors, wherein the pipeline parameters comprise pipe diameter, pipe length and pipe age; performing hydraulic calculation of the water supply network, including a node continuity equation, an energy equation and a pressure drop equation, and calculating the flow of each water using node under pressure driving to obtain the actual water supply amount of different nodes after the pipeline fails in sequence;
step two, setting an economic target for maintaining the water supply network:
the economic objective minimization is required, including the following objective function:
Obj1＝Min(CCTT) (1)
wherein, Obj1Is the 1 st objective function; min () takes the minimum value for the function; CCTT is the net present value of economic cost for water supply network replacement and maintenance in the future planning period; t is time, t is 1,2,3 … … TN, TN is future planning period time, year; j is a pipeline number, J is 1,2,3 … J, and J is the number of pipelines maintained by a water supply network in the water supply network; djThe time for preventive replacement of the jth water supply pipeline, year; r is annual discount rate; percent; CC (challenge collapsar)j,Dj,kFor the kth pipe of the jth water supply pipeline at DjConstruction costs, dollars, of preventive replacement of time; CRj,t,kAnd CR1j,t,kRespectively the maintenance cost and the unit cost of the kth pipe of the jth water supply pipeline in the tth year before and after the replacement of the water supply pipeline; CLj,t,kAnd CL1j,t,kRespectively the cost of water loss caused by water interruption after the jth water supply pipeline of the kth pipe fails in the t year before and after the water supply pipeline is replaced; CIj,t,kAnd CI1j,t,kRespectively leading to loss caused by insufficient water supply of other water using nodes in the water supply network after the jth water supply pipeline of the kth pipe fails before and after the water supply pipeline is replaced; CSj,t,kAnd CS1j,t,kRespectively, indirect influence loss caused by the failure of the jth water supply pipeline of the kth pipe in the t year before and after the replacement of the water supply pipeline;
step three, setting a reliability target of water supply network maintenance:
for hydraulic reliability, the objective function is as follows:
Obj2＝Max(RELt) (3)
wherein, Obj2Is the 2 nd objective function; max () takes the maximum value for the function; RELtReliability of the water supply pipe network system in the t year; j is a pipeline number, J is 1,2,3 … … J, and J is the number of pipelines maintained by the water supply network in the water supply network; REj,tReliability of the jth pipeline in the t year; PRj,tThe failure rate of the jth pipeline in the t year; rn,ttThe water demand at the nth water node for the tth hour, m3H; n is 1,2,3, … … N, wherein N is the number of water consumption nodes in the water supply network; tt is 1,2,3 … … T, T is the hydraulic calculation duration of the water supply network, h; sj,n,ttThe actual water supply quantity m of the pipe network at the nth node tth after the jth pipeline fails3H; u is the maintenance time of the water supply pipeline, h; AGj,tThe age of the pipeline at the tth time of the jth pipeline is year; DIjThe pipe diameter of the jth pipeline is mm; k1,K2The empirical coefficient is determined by statistical analysis according to historical data;
step four, carrying out decision variable generalization and chromosome gene coding design of water supply network maintenance so as to reduce the number of decision variables;
step five, adopting a non-dominated sorting genetic algorithm with an elite strategy to optimize and solve the problem of the preventive maintenance and replacement opportunity of the pipeline, wherein the method comprises the following 4 substeps:
1) setting basic parameters of a genetic algorithm, including population quantity, genetic algebra, cross rate, mutation rate and planning period time;
2) performing population initialization to generate a parent population for each DjA random generation method is adopted;
3) non-dominated ranking and objective function fitness calculation: setting an economic target according to formulas (1) to (2) in the step two, setting a reliability target according to formulas (3) to (7) in the step three, calculating the fitness of a population target function according to the population after the chromosome gene coding design and initialization in the step four, performing rapid non-dominated sorting, storing the decision variable chromosome gene codes meeting the fitness requirement, performing cross and mutation on decision variables not meeting the fitness requirement to generate new filial generations, competing the parent generations and the filial generations, and selecting the decision variable chromosome gene codes meeting the fitness requirement from the new filial generations to be reserved;
4) performing mixed cycle calculation on parent population and offspring population, performing crossover, mutation, non-dominated sorting and fitness calculation, and reserving elite individuals until a pareto frontier meeting algebraic conditions is obtained;
step six, comprehensively weighing and identifying an optimal pipe network maintenance scheme:
if the maintenance cost owned by the water supply enterprise is larger than a certain threshold value, selecting a pipeline network maintenance scheme with the highest reliability on the pareto frontier plane; if the maintenance cost owned by the water supply enterprise is less than a certain threshold, selecting a maintenance scheme with the water supply reliability greater than a certain threshold on the pareto frontier, and carrying out related planning, design and engineering implementation;
step four, the generalized method is as follows: A. selecting part of water supply pipelines with large risks to perform optimal decision analysis; B. designing gene codes of chromosomes of genetic algorithm into different supplyCombination of water pipeline replacement time, design DjFor the generalized decision variable, the value range is an integer between 1- (TN +1), J is 1,2,3 … … J, J is the number of pipelines in the water supply network, when D isjTN +1, indicating that the water supply line j is not replaced during the planning period;
step five, step 1): the population quantity is set to be 2000, the genetic algebra is 30, the cross rate and the mutation rate are both 0.02, and the planning period time TN is 10 years;
step five, step 2): for each decision variable DjThe initial value adopts a random generation method, and the specific method is as follows:
DRj＝Dmin+(Dmax-Dmin)×tand(） (8)
Dj＝Ceil(DRj×(TN+1)) (9)
wherein, DRjThe decision variables are randomly generated and are real numbers with the numerical values between 0 and 1; djIs a decision variable which is an integer with a value between 1- (TN + 1); dminAs the minimum value of the decision variable, DmaxThe rand () is a random generating function between 0 and 1 as the maximum value of the decision variable; dminAnd DmaxThe values are 0 and 1 respectively; ceil () is a function rounded towards plus infinity, J is 1,2,3 … J, J is the number of pipes in the water supply network.
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