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The multi-objective design of water distribution networks (WDNs) is a very challenging task and can be addressed with evolutionary algorithms. Especially for large WDNs, such a process is very computationally demanding, and it is difficult to assess if the obtained solutions could be further optimized. In other words, due to the stochastic nature of evolutionary algorithm, it is not straighforward to recognize whether the solutions are optimal or further generations need to be processed. Characteristics of the network graphs could reveal the progress of the optimization process. For optimal WDNs, the primal graph characteristics and network patterns have already been explored. However, literature is missing a dual graph approach to investigate the properties of optimal WDNs in a dual space. Such a dual graph approach is developed in this work. Therewith, the trajectories of the optimization process from random initialization to the (final) optimal generation are described and systematically investigated. With that the answer to the question is successfully addressed: When is an optimal stage at the optimization achieved, and how can that be assessed and predicted?

This is a joint publication in collaboration with Prof. Zheng's water research group at Zhejiang University in China. The study was carried out for participating the competition of "Battle of Post-Disaster Response and Restoration (BPDRR)" organized in the WDSA/ CCWI 2018 conference, and our result was at the top level among all the participated teams. Two journal papers based on this study are under preparation. The Battle of Post-Disaster Response and Restauration (BPDRR) is a challenging optimization problem which requires the restauration of the B-city water distribution network (WDN) after an earthquake. More specifically, the water utility is looking to schedule the available three crews to isolate, repair or replace the damaged pipes to rapidly improve the system’s capacity of restoring the service. A many-objective analysis framework is used to identify the best way to respond to the disaster and restore functionality of the water distribution network for each post-earthquake scenario. The many-objective formulation focuses on a suite of six objectives, as follows: (1) time that the hospitals and the firefighting flows are without supply, (2) rapidity of recovery, (3) resilience loss, (4) average time each consumer (node) is without service, (5) number of consumers (nodes) without service for more than 8 consecutive hours, and (6) volume of water lost during the next 7 days after the event. We proposed a multi-phase optimization methodology in combination with manual intervention, which takes the advantage of evolutionary computation as well as engineering experiences. The method consists of three stages: (1) preliminary analysis; (2) sub-optimization; and (3) global optimization. A pressure-driven model is used to enable the pipe-breaking analysis as it can simulate the outflows and water shortages induced by pipe breaks. Such a strategy is expected to find feasible and optimal solutions in an efficient manner. The improved genetic algorithm is applied to solve the optimization problem. Details of the recovery strategy resulting from the proposed optimization method are provided. The results provide some value insights on how to make considerate optimal recovery plan. For instance, certain broken pipes have to be fixed between particular time stamps to avoid negative affects on the level of services at some critical facilities.

This is a joint publication in collaboration with Centre for Water Systems at University of Exeter. This research is based on my previous work for Prof. Butler's project of "Safe and SuRe: A New Paradigm for Urban Water Management". A comprehensive assessment of resilience requires consideration of system performance under exceptional conditions, including those that are unforeseen, and can be achieved using a previously developed methodology called ‘global resilience analysis’ (GRA). GRA captures the effects of both probable and highly improbable (unknown probability) system failures and requires no knowledge of threats. Here, a simple, user-friendly tool that automates the simulations required for GRA of a water distribution system and assists comprehension of the results is presented. Provided the user can supply an Epanet .inp file for the system and that this contains demand data (an understanding of Epanet and system failure modelling is not necessary), the tool can be used to quantify the resilience of the system to pipe failure, pump failure, demand increase and contaminant intrusion. An interactive results explorer allows the user to easily identify critical system components based on the selected level of service type and failure measure (e.g. pressure, supply or contamination and failure magnitude or duration). A map of the network can be used to either color-code components based on their criticality in a single component failure analysis or to identify specific combinations of components which result in the greatest level of service failure magnitude or duration when failed simultaneously. ‘Stress-strain’ type response curves can also be automatically generated and key findings automatically extracted. Additionally, the tool enables systems to be compared on a like-for-like basis, enabling the effects of proposed interventions on resilience to be quantified and visualized.

Fractals have been identified as a common feature of many natural and artificial systems that exhibit similar patterning at different scales. Understanding fractals is a critical aspect of decoding complex systems, as the pattern of such large systems can be revealed by identifying only a small part of the system. Furthermore, identify existing features of such systems can start at the large scale with the fewest details of the system under scrutiny before doing a more detailed analysis at finer scales. Such a process provides an efficient and reliable way of analysing and managing information of big data systems. This study revealed the fractality in water distribution networks (WDNs) based on research on fractals in complex networks. Specifically, we explored the existence of fractal patterns in six real world WDNs of different complexities (e.g. from a network with only 21 pipes to a network with 2465 pipes). The box-covering algorithm has been applied, which is the most widely used method to distinguish between fractal or non-fractal networks. The WDNs are first mapped into undirected graphs. Next, the method partitions the nodes into boxes of size lB, i.e. the maximal distance between nodes within each box is at most lB-1. By varying the box sizes, different minimum numbers of boxes NB required to cover the entire network can be identified. A network is fractal if the regression line for log(NB) and log(lB) is linear. The results demonstrate the existence of fractal patterns in all case study WDNs, as linear regression lines with coefficient of determination over 0.95 (R^2>0.95) are obtained in all analyses. As further verification, the self-similarity on multiscales is revealed, i.e. the similarity in patterns of component criticality. Based on the fractal patterns, a systematic method is also developed for more efficient identification of critical pipes in WDNs, e.g. reducing the computational load by 61% in the case study.

open access article Global threats such as climate change, population growth, and rapid urbanization pose a huge future challenge to water management, and, to ensure the ongoing reliability, resilience and sustainability of service provision, a paradigm shift is required. This paper presents an overarching framework that supports the development of strategies for reliable provision of services while explicitly addressing the need for greater resilience to emerging threats, leading to more sustainable solutions. The framework logically relates global threats, the water system (in its broadest sense), impacts on system performance, and social, economic, and environmental consequences. It identifies multiple opportunities for intervention, illustrating how mitigation, adaptation, coping, and learning each address different elements of the framework. This provides greater clarity to decision makers and will enable better informed choices to be made. The framework facilitates four types of analysis and evaluation to support the development of reliable, resilient, and sustainable solutions: “top-down,” “bottom-up,” “middle based,” and “circular” and provides a clear, visual representation of how/when each may be used. In particular, the potential benefits of a middle-based analysis, which focuses on system failure modes and their impacts and enables the effects of unknown threats to be accounted for, are highlighted. The disparate themes of reliability, resilience and sustainability are also logically integrated and their relationships explored in terms of properties and performance. Although these latter two terms are often conflated in resilience and sustainability metrics, the argument is made in this work that the performance of a reliable, resilient, or sustainable system must be distinguished from the properties that enable this performance to be achieved.

Porous metals have recently attracted much attention in both academia and industry. They have many potential applications ranging from light weight structure, thermal management and sound absorption, because of their unique structural, mechanical, thermal and acoustic properties. Open-cell porous metal can be an ideal material for electrochemical applications due to its high surface area, permeability and electric conductivity. The electro-active surface area of porous electrodes is the most important factor in electrochemical applications, such as fuel cells, because it largely determines the current density in the electrode. However, most research to date on the surface area of porous metals has been focused on the geometric and real surface areas. Very little research has been conducted to study the electro-active surface area. The mass transfer coefficient of a solid electrode is a very important factor in flow cell applications, such as flow battery and wastewater treatment, because high mass transfer coefficient means high reaction performance. However, very little research has been carried out on the mass transfer coefficient of open-cell porous metal manufactured by the space-holder method. The main objective of this study is to investigate the electrochemically relevant structural properties of porous Cu and Ni fabricated by the Lost Carbonate Sintering (LCS) process, which is a cost-effective process for manufacturing open-cell porous metals with controlled porosity, pore size and pore shape. In this project, the geometric, electro-active and real surface areas of porous Cu and Ni have been measured by quantitative stereology, cyclic voltammetry (peak current) and cyclic voltammetry (double layer capacitance) methods, respectively. The mass transfer coefficient of porous Ni has been measured by linear sweep voltammetry, using a purpose-built flow cell. The tortuosity of porous Cu has been measured by a diffusion method, using a purpose-built diaphragm cell. The geometric, electro-active and real surface areas of porous metal are due to the contributions from the primary porosity, the primary and secondary porosities, and the surfaces of metal particles, respectively. The geometric, electro-active and real surface areas of porous Cu and Ni samples with pore sizes 75-1500 µm and porosities 0.53-0.81 were in the ranges of 18-110 cm-1, 24-369 cm-1 and 700-1200 cm-1, respectively. Both the geometric and electro-active surface area increased with porosity and decreased with pore size. The real surface area decreased with porosity but the effect of pore size was not pronounced. The values of electro-active surface area of LCS porous metal can be similar to and often greater than those of the existing porous metals, e.g. incofoam Ni. The mass transfer coefficient of porous Ni with pore sizes 250-1500 µm and porosities 0.63-0.81 at different flow rates from 0.24 ml/s to 2.8 ml/s was in the range of 0.0035-0.0727 cm/s. Both the limiting current and mass transfer coefficient increased with flow rate and had the maximum values at a porosity of around 0.65-0.70. The maximum limiting current decreased and the maximum mass transfer coefficient increased with pore size. Compared with a smooth Ni plate at the same flow velocity, the mass transfer coefficient of the LCS porous Ni was increased by up to 9 times. The enhancement is due to the Ni particles providing a rough surface for the cell walls and the tortuous pore structure resulting in a high level of fluid turbulence. The tortuosity of the porous Cu samples, with pore sizes 250-1500 µm and porosities 0.56-0.84, was in the range of 1.33-1.78. It increased with pore size and decreased with porosity, agreeing with an empirical formula for porous media. This research has successfully applied cyclic voltammetry to the measurement of electro-active surface area of porous metals for the first time. It is the first systematic study of the structural properties of relevance to electrochemical applications of porous metals manufactured by LCS process.

Vulnerability assessment is a promising approach to identifying critical components of complex systems. In such systems, critical components could be crucial links and strategic locations for management and control. Managing those components better could, in turn, improve or reinforce a system’s resilience to shock events. However, fully comprehensive vulnerability assessments cannot be guaranteed as enumerating all possible shock events in complex systems is computationally intensive and almost infeasible. Consequently, the important role of some components might be neglected. This paper explores the feasibility of using a dual approach vulnerability assessment for water distribution systems (WDSs). Specifically, complex network analysis (e.g. community detection) and control-theory-based analysis (e.g. controllability analysis) is utilized to identify critical components within WDSs. A real-world benchmark water distribution system is mapped into either undirected or directed graphs by identifying critical pipes and nodes respectively. Here, critical links refer to pipes linking all the subsystems of a WDS together. Critical nodes are defined as actuators based on analogy with control theory. Controlling a suitable set of actuators by different signals can offer full control over a dynamical system. The results from the two different methods are discussed with respect to the criticality of the identified components to water supply during failure, and the correlations among the alternative approaches. It is concluded that, although there is a much larger number of actuators, about 77% of critical links are also identified as actuator pipes (pipes with either of its end points as actuators) and therefore they have the same criticality. For the remaining 23%, the location of critical links is rather close to that of actuators despite differences in criticality. Further study is ongoing to confirm whether any other actuators unexplored in this study could be more critical than the studied actuators and critical links or not. Further, a variety of failures will be compared using the two methods.

This paper introduces a method for automated pipe-sizing of storm sewer or combined sewer systems based on hydrodynamic modelling. The methodology includes three steps. Initially, Graph theoretical description of network topology (e.g. “Sewer branch order”) is utilized for classification of the studied sewer network’s topology. Then, the network is decomposed hierarchically into a number of subsystems based on the network topology. Finally, the pipe sizing is carried out subsystem by subsystem with no flooding in the whole system as the objective. To verify the results of the method, the algorithm is tested on a real world sewer network, and then the solution is compared with the global optimal solution. As proved by the case study, the author-designed method could guarantee a near-optimal solution that is very close to the global optimal solution, while requires dramatically less computational effort than global optimization method. Compared with evolutionary methods, the method has its own advantages, since it does not require any parameter for configuration and execution control, and could produce unique solutions as long as the design principles are fixed.