Study On Surrogate Reliability Indices Of Water Distribution Systems

Reliable water distribution systems(WDSs)are important material basis to ensure people’s life and economic development.In order to evaluate the reliability of WDSs quickly,a series of surrogate indices which can reflect the reliability of WDSs with simple calculation have been proposed in the past two decades.However,the performance of these surrogate indices may be different.There are only a few literatures focusing on the comparison of surrogate reliability indices of WDSs.Such literature requires a number of two-objective optimization models for comparing those indices one by one.When comparing a number of surrogate indices,it is imperative to establish many optimization models to solve and analyze them respectively,which is a cumbersome process.To solve the problems mentioned above,an analytical framework based on-manyobjective optimization technique for rapidly comparing the performance of surrogate mechanical reliability indices of WDSs is proposed.The analytical framework consists of five steps.The first step is to select representative reliability surrogate indices through literature survey.In the second step,the selected reliability surrogate indices and the construction cost of the water supply network are taken as individual objectives,and a many-objective optimization model is established to maximize each surrogate indicator and minimize the construction cost of the water supply network.In the third step,a many-objective evolutionary algorithm is used to solve the optimization model,and the Pareto-optimal solution set of the optimization model is obtained.The fourth step,based on the Pareto-optimal solution set of the model,a series of single-pipe failure experiments are carried out,and the mechanical reliability of each solution is calculated.In the fifth step,the performance of each surrogate indicator is measured by calculating the consistency coefficient between each surrogate index and the mechanical reliability score(MRS)in the Pareto-optimal solution set.Meanwhile,the consistency among different surrogate indices are also quantified by calculating the consistency coefficient between each two surrogate indices.In this study,seven representative surrogate indices from domestic and foreign literature are selected,which are divided into resilience-based indices,entropy-based indices and other indices.The resilience-based indices include Resilience Index(RI),Network Resilience Index(NRI),Available Power Index(API),and Pipe Hydraulic Resilience Index(PHRI).The entropy-based indices include Flow Entropy(FE)and Diameter Sensitive Flow Entropy(DSFE).The other indicator considered in this study is Redundancy.Verification is based on two non-extended period simulation pipe networks: the Hanoi network(HAN)in Hanoi,the capital of Vietnam,and the Balerma Irrigation Network(BIN),in Balerma,Spain.The Borg algorithm is used to obtain the Pareto-optimal solution set of the optimization model.The pressure-driven analysis method of EPANET 2.2 is used to evaluate the MRS of WDSs under a series of single-pipe failure events.The experimental results show that the consistency coefficients between five surrogate indices(the four resilience-based indices and the Redundancy)and the MRS are about 0.9,while the consistency coefficients between the two entropy-based indices and the MRS are only 0.508 and 0.687 in the HAN network.In the BIN network,the consistency coefficients between five surrogate indicators(the four resilience-based indicators and the Redundancy)and the MRS are about 0.8,while the consistency coefficients between the two entropy-based indicators and the MRS are only0.497 and 0.505.In the two cases,the consistency coefficients between the four resiliencebased indicators and the Redundancy are all higher than 0.887,while the consistency coefficients between the two entropy-based indicators and the other five surrogate indicators(the four resilience-based indicators and the Redundancy)are all lower than 0.683.In addition,the consistency coefficients between the two entropy-based indicators in the two case studies are lower than 0.487.The main conclusions of this dissertation are as follows.(1)The solutions with high construction costs does not necessarily lead to higher MRS values of WDSs.(2)Compared with the two entropy-based indices,the four resilience-based indices and the Redundancy can better reflect the MRS of the WDSs.(3)There is a good consistency between the four resilience-based indices and the Redundancy,which indicates that these indices may be intrinsically correlated.(4)Because the concept of Redundancy is clearer and the calculation is simpler,it is recommended to use the Redundancy in the optimization model to reflect the mechanical reliability of WDSs.