Battle of Postdisaster Response and Restoration

1 Battle of Postdisaster Response and Restoration 2 Diego Paez1, Yves Filion2, Mario Castro-Gama3, Claudia Quintiliani4, Simone Santopietro5, Chris 3 Sweetapple6, Fanlin Meng7, Raziyeh Farmani8, Guangtao Fu9, David Butler10, Qingzhou Zhang11, Feifei 4 Zheng12, Kegong Diao13, Bogumil Ulanicki14, Yuan Huang15, Jochen Deuerlein16, Denis Gilbert17, Edo 5 Abraham18, Olivier Piller19, Alicja Bałut20, Rafał Brodziak21, Jędrzej Bylka22, Przemysław Zakrzewski23, 6 Yuanzhe Li24, Jinliang Gao25, Cai Jian26, Chenhao Ou27, Shiyuan Hu28, Sophocles Sophocleous29, Eirini 7 Nikoloudi30, Herman Mahmoud31, Kevin Woodward32, Michele Romano33, Giovanni Francesco 8 Santonastaso34, Enrico Creaco35, Armando Di Nardo36, Michele Di Natale37, Attila Bibok38, Camilo 9 Salcedo39, Andrés Aguilar40, Paula Cuero41, Sebastián González42, Sergio Muñoz43, Jorge Pérez44, 10 Alejandra Posada45, Juliana Robles46, Kevin Vargas47, Marco Franchini48, Stefano Galelli49, Joong Hoon 11 Kim50, Pedro Iglesias-Rey51, Zoran Kapelan52, Juan Saldarriaga53, Dragan Savic54, Thomas Walski55 12 1 13 [email protected] 14 2 Queen's University. 58 University Ave., Kingston, Canada. 15 3 KWR Watercycle Research Institute. Groningenhaven 7, 3433 PE Nieuwegein, Netherlands. 16 4 KWR Watercycle Research Institute. Groningenhaven 7, 3433 PE Nieuwegein, Netherlands. 17 5 University of Cassino and Southern Lazio. Via Gaetano Di Biasio 43, 03043 Cassino, Italy. 18 6 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 19 7 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 20 8 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 21 9 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 22 10 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 23 11 College of Civil Engineering and Architecture, Zhejiang University. 866 Yuhangtang Rd, Hangzhou, China. 24 12 College of Civil Engineering and Architecture, Zhejiang University. 866 Yuhangtang Rd, Hangzhou, China. 25 13 De Montfort University. Gateway House, Leicester, UK. 26 14 De Montfort University. Gateway House, Leicester, UK. 27 15 College of Civil Engineering and Architecture, Zhejiang University. 866 Yuhangtang Rd, Hangzhou, China. 28 16 3S Consult GmbH. Albtalstrasse 13, 76137 Karlsruhe, Germany. 29 17 Irstea, UR ETBX, Water Department, Bordeaux regional centre. Cestas F-33612, France. 30 18 Faculty of Civil Engineering and Geosciences, Delft University of Technology. Stevinweg 1, 2628 CN, Delft, 31 Netherlands. 32 19 Irstea, UR ETBX, Water Department, Bordeaux regional centre. Cestas F-33612, France. 33 20 Poznań University of Technology. Berdychowo 4, 60-101 Poznań, Poland. 34 21 Poznań University of Technology. Berdychowo 4, 60-101 Poznań, Poland. 35 22 Poznań University of Technology. Berdychowo 4, 60-101 Poznań, Poland. Queen's University. 58 University Ave., Kingston, Canada (corresponding author). E-mail: 36 23 Poznań University of Technology. Piotrowo 3A, 60-965 Poznań, Poland. 37 24 Harbin Institute of Technology. Harbin, China. 38 25 Harbin Institute of Technology. Harbin, China. 39 26 Harbin Institute of Technology. Harbin, China. 40 27 Harbin Institute of Technology. Harbin, China. 41 28 Harbin Institute of Technology. Harbin, China. 42 29 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 43 30 Centre for Water Systems. University of Exeter. North Park Rd., Exeter, EX4 4QF, UK. 44 31 College of Engineering. University of Duhok. Zakho Street 38, 1006 AJ Duhok, Kurdistan Region-Iraq. 45 32 United Utilities Group PLC. Lingley Green Avenue, Warrington, WA5 3LP, UK. 46 33 United Utilities Group PLC. Lingley Green Avenue, Warrington, WA5 3LP, UK. 47 34 Università della Campania “L. Vanvitelli”. Via Roma, 29, 81031 Aversa, Italy. 48 35 Università di Pavia. Via Ferrata 3, 27100 Pavia, Italy. 49 36 Università della Campania “L. Vanvitelli”. Via Roma, 29, 81031 Aversa, Italy. 50 37 Università della Campania “L. Vanvitelli”. Via Roma, 29, 81031 Aversa, Italy. 51 38 Budapest University of Technology and Economics. Műegyetem rkp. 3 Budapest, Hungary. 52 39 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 53 40 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 54 41 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 55 42 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 56 43 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 57 44 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 58 45 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 59 46 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 60 47 Water Dist. and Sewer Systems Res. Center (CIACUA), Universidad de los Andes. Bogotá, Colombia. 61 48 Università di Ferrara. Via Saragat, 1, 44122 Ferrara, Italy. 62 49 Singapore University of Technology and Design, Pillar of Engineering Systems and Design. 8 Somapah Road, 63 487372, Singapore. 64 50 Korea University. Seoul, South Korea , South Korea. 65 51 Universidad Politécnica de Valencia. Camino de Vera s/n - 46022 (Valencia), Spain. 66 52 Delft University of Technology. Stevinweg 1, 2628CN Delft, Netherlands. 67 53 Universidad de los Andes. Carrera 1 Este No. 19A-40. Bogotá, Colombia. 68 54 KWR Watercycle Research Institute. Groningenhaven 7, 3433 PE Nieuwegein, Netherlands. 69 55 Bentley Systems. 3 Brians Place, Nanticoke, PA, USA. 70 71 Abstract: The paper presents the results of the Battle of Post-Disaster Response and Restoration 72 (BPDRR), presented in a special session at the 1st International WDSA/CCWI Joint Conference, held in 73 Kingston, Ontario, in July 2018. The BPDRR problem focused on how to respond and restore water 74 service after the occurrence of five earthquake scenarios that cause structural damage in a water 75 distribution system. Participants were required to propose a prioritization schedule to fix the damages of 76 each scenario while following restrictions on visibility/non visibility of damages. Each team/approach 77 was evaluated against six performance criteria that included: 1) Time without supply for 78 hospital/firefighting, 2) Rapidity of recovery, 3) Resilience loss, 4) Average time of no user service, 5) 79 Number of users without service for 8 consecutive hours, and 6) Water loss. Three main types of 80 approaches were identified from the submissions: 1) General purpose metaheuristic algorithms, 2) Greedy 81 algorithms, and 3) Ranking-based prioritizations. All three approaches showed potential to solve the 82 challenge efficiently. The results of the participants showed that, for this network, the impact of a large- 83 diameter pipe failure on the network is more significant than several smaller pipes failures. The location 84 of isolation valves and the size of hydraulic segments influenced the resilience of the system during 85 emergencies. On average, the interruptions to water supply (hospitals and firefighting) varied 86 considerably between solutions and emergency scenarios, highlighting the importance of private water 87 storage for emergencies. The effects of damages and repair work were more noticeable during the peak 88 demand periods (morning and noontime) than during the low-flow periods; and tank storage helped to 89 preserve functionality of the network in the first few hours after a simulated event. 90 91 Introduction 92 A water distribution network (WDN) is one of the critical lifeline systems in a city. Its vulnerability to 93 earthquakes, and other natural disasters, not only threatens residential, commercial, and industrial 94 activities, but also can affect the capacity to attend to subsequent emergencies. Two of the most analysed 95 examples in the literature are the 17 January 1994 Northridge earthquake (Los Angeles, California) and 96 the 17 January 1995 Kobe earthquake (Japan). The first case resulted in more than 450,000 people losing 97 water service and at least eight hospitals evacuated due to water and power damages, while for the second 98 case, the earthquake affected the supply to more than 1.5 million people and required more than 30 hours 99 to extinguish the fires due to water unavailability in many hydrants (PAHO, 1998). 100 Considering the potential vulnerability and key role played by WDN during seismic events, researchers 101 have focused on three main topics: 1) How to assess the reliability of WDNs and other lifelines after 102 extreme seismic events (e.g., Hwang, et al., 1998; Wang & O'Rourke, 2006; Shi & O'Rourke, 2006, 103 Fragiadakis, et al., 2013; Liu et al., 2015); 2) How to reinforce the systems to minimize the impact of a 104 given event (e.g., Cimellaro et al., 2015; Yoo et al., 2016); or 3) How to quickly restore the systems to 105 normal/acceptable conditions after the event (e.g., Bonneau, & O'Rourke, 2009; Wang et al., 2010; 106 Mahmoud et al., 2018). From these, the restoration problem has been the least studied, leaving the 107 prioritization of resources to recover the functionality of the system to the expertise and criteria of utility 108 operators. Considering that lives of people are at stake due to vitality of the supply for firefighting, or 109 health care purposes, among other considerations, it is imperative to better characterize this problem and 110 evaluate if current knowledge of WDNs can be of use in such circumstances. 111 The Battle of Post-Disaster Response and Restoration (BPDRR) was the eighth call for academic and 112 non-academic professionals to address a common problem in the water distribution field. Dating back to 113 the first "Battle" in 1985, this series of competitions have focused on WDNs optimization (1985 and 114 2012), sensor placement for contaminant intrusion detection in WDNs (2006); WDNs model calibration 115 (2010); leakage assessment in WDNs (2014); district-metered-area sectorization of WDNs (2016); and 116 detection of cyber-attacks on WDNs (2017). For this version, the “Battle competition” focused on the 117 how to respond and restore the service in an existing WDN after the occurrence of five different 118 earthquake scenarios that damaged part of the distribution network. The results of the BPDRR were 119 presented in a special session in the 1st WDSA/CCWI Joint Conference, held in Kingston, Ontario, in July 120 2018. This manuscript summarizes the challenge, the results, and makes recommendations for future 121 research of the topic. 122 123 Problem formulation 124 The challenge addressed in the Battle is the one of identifying the best operational response in terms of 125 restoration interventions to return a water distribution network to fully functioning pre-catastrophic event 126 condition. 127 After an earthquake, damages to a WDN can degrade the water service in a city. There can be different 128 approaches for prioritization of available resources in order to restore the water service. To evaluate the 129 performance of the different approaches, a set of five post-disaster damage scenarios was generated on a 130 model of the B-City water distribution network, and participants were invited to propose responses and 131 restoration methods to return the system to pre-earthquake conditions. These damage scenarios, along 132 with a calibrated EPANET model of the network, and a description of the performance criteria were 133 provided to the participants. All data are included in the supplemental files of this manuscript and can be 134 found with the problem description (Paez et al., 2018a) in the website: https://www.queensu.ca/wdsa- 135 ccwi2018/problem-description-and-files. 136 B-City 137 B-City is a water distribution network model of a real system in an undisclosed location. The network 138 consists of 4,909 junctions, 6,064 pipes, 1 reservoir, 4 pumps divided between two pump stations, and 5 139 district metered areas (DMA), each with one water tank (Figure 1). A total of 5,963 isolation valves are 140 also distributed along the pipes of the network, delimiting 2,451 segments as defined by Walski (1993). 141 The calibrated model also includes 24-hr demand patterns for residential and commercial/industrial 142 consumers. The daily mean consumption on a typical day is 1,023.8 L/s. 143 For pre-catastrophic conditions, the minimum pressure during the day, amongst all demand nodes is 24.5 144 m, which means that the demand is fully supplied (the minimum required pressure is 20.0 m). 145 Additionally, the tanks do not get emptied at any point, and their minimum levels vary from 0.62 m to 146 1.09 m. 147 Damage scenarios 148 One important assumption required to develop the problem was to consider that out of all network 149 elements, only pipes were damaged during the events. In other words, facilities like pump stations, tanks, 150 and the source reservoir were assumed to remain operational at all times. This assumption is consistent 151 with remarks by Tabucchi et al. (2010), and even though PAHO (1998) mentions examples of tanks and 152 pump stations structurally affected by earthquakes or disconnected temporally from the electric grid, they 153 are significantly less common than damages in pipelines (Tabucchi et al., 2010). 154 To stochastically generate pipe damage scenarios, a Poisson process was used (Shi & O'Rourke, 2006). 155 Therefore, the probability that a pipe was damaged during the earthquake was given by Eq. (1). 𝑃 𝑥𝑖 = 1 − 𝑒 −𝜆 𝑖 𝐿𝑖 156 (1) Where 𝑥𝑖 is the event that pipe 𝑖 is damaged 𝑖 ∈ 1, … ,6064 , 𝐿𝑖 is the length of the pipe 𝑖 in m, and 𝜆𝑖 157 is the average number of seismic-induced damages per m for that type of pipe. The values of 𝜆𝑖 were 158 assumed as 0.0003 damages/m for pipes with diameter under 300 mm and as 0.00005 damages/m for 159 larger diameter pipes, which is a simplification within the ranges presented by American Lifelines 160 Alliance (2001). This means that the effect of other factors mentioned in the previous studies, like type of 161 soil, pipe material, pipe age, and type of joints, on the probability of damage was assumed homogeneous 162 for all pipes. 163 According to Ballantyne et al. (1990) and Hwang et al. (1998), the damages in pipes can be classified as 164 leaks, which are minor damages that can be fixed by installing clamps or welding cracks, and breaks, 165 which are more serious damages that require a replacement of entire pipe sections. The conditional 166 probability that a damage was a break was taken as 0.20 for all pipes according to the assumption by 167 HAZUS (NIBS, 1997) for damages generated by propagation of seismic waves: 𝑃 𝑦𝑖 | 𝑥𝑖 = 0.20 (2) 168 where 𝑦𝑖 is the event that pipe 𝑖 is broken. It is worth mentioning that according to HAZUS method, when 169 the damages are caused by a permanent ground displacement, the probability of a break is considerably 170 higher. 171 After an earthquake disaster, fires are also expected and, therefore, firefighting flows must also be 172 supplied. To include them in the model, two nodes per scenario were randomly selected and assigned a 173 fire flow demand of 35 L/s that would only stop until the delivered/supplied water reached 756 000 L 174 (correspondent to a 6 hr-duration fire if the flow was fully supplied). The number of fire flow nodes was 175 arbitrarily chosen, while the flow rate was suggested by members of the committee. 176 Using these assumptions, a set of five deterministic post-disaster damage scenarios was generated and 177 provided to the participants, and a likelihood based on the probability of the state of each pipe was 178 assigned to each scenario as a weight for the performance evaluation (computed as the logarithm of the 179 normalized product of individual probabilities for the pipes). Figure 2 shows one of the five post-disaster 180 damage scenarios as an example. 181 Damages modelling 182 To model the hydraulic effect of damages in the network, an emitter was located at the midpoint of the 183 damaged pipe to simulate its water losses. In order to avoid reverse flows at the emitter (i.e. inflows) 184 caused by negative pressures, a dummy check valve was also included upstream of the emitter. One 185 additional assumption was that breaks in pipes with diameters under 150 mm were assumed to produce a 186 full disconnection between the two ends of the pipe, and, therefore, the two halves of the pipe were 187 modelled as check valves. 188 The emitters used to simulate water losses followed Eq. (3), with Eqs. (4) and (5) for the emitter 189 coefficients (Shi & O‟Rourke, 2006): 𝑄𝑖 𝑡 = 𝐾𝑖 ⋅ 𝑕𝑖 𝑡 𝐾𝑖 = 0.5𝑚 ⋅ 0.1° ⋅ 𝐷𝑖 ⋅ 2𝑔 𝐾𝑖 = 190 𝜋 ⋅ 0.5° ⋅ 𝐷𝑖2 ⋅ 2𝑔 2 0.5 (3) for leaks (4) for breaks (5) where 𝑄𝑖 𝑡 is the outflow from the emitter 𝑖 at time 𝑡, 𝑕𝑖 𝑡 is the pressure head at the midpoint of pipe 𝑖 191 at time 𝑡, 𝐷𝑖 is the diameter of pipe 𝑖, and 𝐾𝑖 is the emitter coefficient that represents a 0.5 m longitudinal 192 crack with an angle of 0.1° for leaks, and a 0.5° round crack for breaks (Figure 3). 193 To consider that not all damages are immediately detected by the water utilities, some of them were 194 considered non-visible, meaning that they could not be detected, and therefore fixed, only until some time 195 after the event. Leaks in pipes with a diameter under 300 mm, and breaks in pipes with diameter under 196 150 mm were assumed non-visible unless they reached an outflow higher than 2.5 L/s (values based on 197 the experience of some members of the committee). However, 48 hrs after the event it was assumed that 198 some pressure tests and inspections would be carried out, making all damages visible after that time. 199 Visibility of damages was important from the network restoration point of view (see next section). 200 Response and network restoration 201 After the occurrence of an earthquake, the water utility would require some reaction time (assumed 30 202 mins here) before the crews can be dispatched to begin the restoration works. There were assumed to be 203 three crews able to work 24 hours independently of the turns of each worker, and they could perform four 204 basic tasks: Isolate, Repair, Replace, and Reopen. 205 Both leaking and broken pipes could be isolated by sending a crew to the damage location (even though it 206 is strictly necessary for broken pipes only). It was assumed that the water utility knows the location of all 207 isolation valves in the network and, therefore, isolating a pipe consists of closing all the valves in the 208 hydraulic segment that contains it. Isolation of pipes serves two main purposes: to stop water leaking 209 from the network at a certain damage location, and to dry the pipes in the segment so they can be replaced 210 if required. 211 Leaking pipes must be repaired. To repair a leaking pipe, a crew must be sent to the pipe location where 212 they need to locate the leakage, excavate, repair the pipe either with a clamp or by welding, and restore 213 trench conditions. Broken pipes must be replaced. To replace a broken pipe, it must first be isolated, 214 excavated, replaced, and trench conditions must be restored (disinfection and pressure tests are assumed 215 to be omitted in an emergency scenario). Finally, an isolation valve could be reopened to restore supply to 216 the affected area, once damages were fixed. 217 The time each crew was assumed to take to isolate, repair and replace a pipe is shown in Table 1, where 218 some simplified relations have been adjusted to the data presented in Porter (2016). Transportation times 219 and times for reopening of valves are assumed to be included in the figures and expressions shown in 220 Table 1. 221 Participants were required to propose a prioritization schedule for the three crews, for each scenario, 222 indicating in which order to isolate, repair or replace damages in the network while following two 223 restrictions: 1) Only visible damages could be fixed (details on visible/non-visible damages in the 224 previous section), and 2) Only pipes whose hydraulic segment had been previously isolated could be 225 replaced. Table 2 shows an example of the schedules given by participant teams. 226 227 Performance criteria 228 Since the system is working under low pressure conditions, the pressure driven method by Paez et al. 229 (2018b) was used to compute nodal supplied flows 𝑄𝑖 and compare them with demand 𝑄𝐷𝑖 as follows: 0 𝑝𝑖 𝑄𝑖 𝑝𝑖 = 𝑄𝐷𝑖 𝑝𝑟𝑒𝑞 𝑄𝐷𝑖 230 𝑛 𝑖𝑓 𝑝𝑖 ≤ 0 0 < 𝑝𝑖 ≤ 𝑝𝑟𝑒𝑞 𝑝𝑖 > 𝑝𝑟𝑒𝑞 → enforced by a Check Valve → enforced by a Throttle Control Valve → enforced by a Flow Control Valve (6) 231 where 𝑝𝑖 is the actual pressure head at node 𝑖, and 𝑝𝑟𝑒𝑞 is the minimum required pressure head to ensure 232 full supply (assumed 20 m here). 233 The functionality of the system, at a certain time 𝑡, is then defined as the percentage of the total demand 234 that is supplied by the network according to the pressure driven model (based on the serviceability index 235 discussed in Shi & O‟Rourke, 2006): 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙𝑖𝑡𝑦 𝑡 = 100% ⋅ 𝐷𝑒𝑚𝑎𝑛𝑑 𝑛𝑜𝑑𝑒𝑠 𝑄𝑖 𝑡 𝐷𝑒𝑚𝑎𝑛𝑑 𝑛𝑜𝑑𝑒𝑠 𝐷𝑄𝑖 𝑡 (7) 236 Figure 4 shows the expected behaviour of the functionality as the network gets gradually fixed. Since the 237 demand varies in time, it is likely that the system can fulfill a higher percentage of the demand during 238 nights, while during mornings, when demand increases, the supplied percentage decreases, producing 239 these peaks and troughs in the functionality trend. 240 For each scenario, the schedules proposed by the participants were evaluated according to six main 241 criteria: 242 1) Time that the hospitals and the firefighting flows are without supply (Fire & Hosp.), calculated as 243 the time-step of the simulation times the number of time steps in which the supply/demand ratio 244 for the hospitals and firefighting flows was less than 0.5: 𝐹𝑖𝑟𝑒 & 𝐻𝑜𝑠𝑝. = Δ 𝑡 ∙ 245 246 𝐻𝑜𝑠𝑝𝑖𝑡𝑎𝑙𝑠 𝑎𝑛𝑑 𝐹𝑖𝑟𝑒𝑓𝑖𝑔 𝑕𝑡 𝑛𝑜𝑑𝑒𝑠 count 𝑡 | 𝑄𝑖 𝑡 𝐷𝑄𝑖 𝑡 ≤ 0.5 𝑡∈𝑇 [𝑚𝑖𝑛] (8) where 𝑇 is the set of all 15-minute time steps starting on Day 01 at 6:00am and ending at Day 07 at 6:00am and Δ 𝑡 is 15 minutes. 247 2) Time until the system recovers permanently 95% of its functionality (Rapidity of recovery – t95), 248 calculated as the last (maximum) time-step in which the functionality is lower than 95% (see 249 Figure 4): 𝑡95 = max 𝑡 | 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙𝑖𝑡𝑦 𝑡 ≤ 95% 𝑡∈𝑇 [𝑚𝑖𝑛] (9) 250 3) Accumulated loss of functionality from the occurrence of the disaster until full recovery 251 (Resilience Loss), calculated as the area between the 100% line and the functionality time series 252 (see Figure 4) 𝑅𝑒𝑠. 𝐿𝑜𝑠𝑠 = Δ 𝑡 ∙ 𝑡∈𝑇 100% − 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛𝑎𝑙𝑖𝑡𝑦 𝑡 [% ∗ 𝑚𝑖𝑛] (10) 253 4) Average time, across demand nodes, each consumer (network node) is without service (Time no 254 serv.), calculated by multiplying the time-step and the number of time steps in which the 255 supply/demand ratio was less than 0.5 for each node, and then dividing by the total number of 256 demand nodes (𝐷𝑁 = 4201): 𝑇𝑖𝑚𝑒 𝑛𝑜 𝑠𝑒𝑟𝑣. = Δ𝑡 ∙ 𝐷𝑁 𝐷𝑒𝑚𝑎𝑛𝑑 𝑛𝑜𝑑𝑒𝑠 count 𝑡 | 𝑄𝑖 𝑡 𝐷𝑄𝑖 𝑡 ≤ 0.5 𝑡∈𝑇 [𝑚𝑖𝑛] (11) 257 5) Number of consumers (network nodes) without service for more than 8 consecutive hours (Nodes 258 no serv.), calculated by counting the number of nodes with more than one time-step in which the 259 next 8 hours had always a supply/demand ratio lower than 0.5: 𝑁𝑜𝑑𝑒𝑠 𝑛𝑜 𝑠𝑒𝑟𝑣. = count 𝐷𝑒𝑚𝑎𝑛𝑑 𝑛𝑜𝑑𝑒𝑠 260 261 𝑖 | count 𝑡∈𝑇 𝑡| 𝑄𝑖 𝑡 − Δ𝑡 ≤ 0.5 ∀Δ𝑡 ∈ (0 , 8𝑕𝑟𝑠) ≥ 1 𝐷𝑄𝑖 𝑡 − Δ𝑡 [𝑛𝑜𝑑𝑒𝑠] (12) 6) Volume of water lost during the 7 days after the event (Water loss), calculated as the sum of the outflows across all damages in the network times the time-step: 𝑊𝑎𝑡𝑒𝑟 𝑙𝑜𝑠𝑠 = Δ 𝑡 ∙ 𝑖∈𝐷𝑎𝑚𝑎𝑔𝑒𝑠 𝑡∈𝑇 𝑄𝑖 𝑡 [𝐿] (13) 262 Since there were five scenarios, a total of 30 values had to be reported by each team. To assess an 263 approach, each of the six criteria was averaged amongst the five scenarios using the likelihoods 264 previously described in the section Damage Scenarios as weights, giving as a result one average 265 performance per criteria per team. 266 For this version of the Battle, it was a deliberate decision not to provide a unified metric to rank the 267 solutions. Instead, it was left to the participants‟ engineering judgment to prioritize the six criteria as they 268 considered appropriate for the city. This decision was taken by the committee (Franchini, Galelli, Kim, 269 Iglesias-Rey, Kapelan, Saldarriaga, Savic, and Walski) as a way to allow different approaches including 270 non-optimization frameworks in the competition. 271 272 Post-disaster response and restoration algorithms 273 Ten teams participated in the BPDRR and submitted their approaches, prioritization schedules, results, 274 and recommendations. This section briefly describes each approach: 275 • Castro-Gama et al. (2018) proposed an implementation based on a preliminary graph theory analysis of 276 the network required to identify neighboring pipes. Second, an ε-MOEA algorithm (Deb et al., 2005) 277 from an optimization library for Python: Platypus was used to obtain the Pareto front for the 6 criteria. 278 Decision variables were set as a permutation of the possible interventions. The procedure took into 279 account a constant time of displacement between locations (30 min), which increased the operation time 280 of each crew from the values in Table 1. From the 6D Pareto front, a single solution per scenario was 281 selected based on a Visual Analytics approach (Castro-Gama et al., 2017). The ε-MOEA solution was 282 also compared with the one obtained using a greedy algorithm. Both methods showed similar outcomes 283 with different prioritization of interventions, although the latter had the advantage of requiring only 30% 284 of the computational time of the former. Finally, four engineering interventions (to increase/decrease the 285 storage capacity or the pump flow) were evaluated for each selected solution and damage scenario. 286 • Sweetapple et al. (2018) developed an approach based upon graph theory and heuristic methodologies. 287 First, graph theory was used to enable identification of hydraulic segments (Meng et al., 2018) and, 288 subsequently, valve operations required to isolate each pipe break. Next, a single performance indicator 289 incorporating all six objectives was developed to enable the problem to be reformulated as a single 290 objective (assuming equal weights). Lastly, actions (i.e., isolations, replacements and repairs) were 291 allocated to each crew using an adaptation of the „nearest neighbour‟ algorithm (Cover and Hart, 1967), a 292 „greedy optimization heuristic. In this approach, performance was evaluated starting with no actions, and 293 adding subsequent actions. Each new action was assigned to the first crew that finished the previously 294 assigned actions. At each stage, the next action selected was the one that provided the greatest 295 performance benefit (represented by the single objective value), given the specified prior actions and not 296 accounting for future actions. 297 • Zhang et al. (2018) proposed a dynamic optimization framework with the objective function consisting 298 of six different metrics summed by introducing weights. To identify an optimal sequencing of recovery 299 actions for each post-earthquake scenario, a tailored Genetic Algorithms-based optimization algorithm 300 was used, where the algorithm operators were modified to identify the optimal sequencing of recovery 301 actions for post-disaster WDNs. The most important feature of the proposed method was that the total 302 number of the decision variables (damaged segments) and the decision variables themselves (e.g., the 303 pipes that need to be repaired) could both vary when the hydraulic status of the WDN was updated. That 304 updating process was carried out at the completion of each intervention to the post-disaster WDN, and the 305 final sequencing of recovery actions for each crew was identified. The results provided some insights on 306 how to propose an optimal recovery plan. For instance, certain broken pipes were fixed between 307 particular time stamps to avoid negative effects on the service level at some critical locations. 308 • Deuerlein et al. (2018) proposed greedy heuristics to schedule isolation, repairs and replacement by 309 minimizing a weighted sum of the objectives. In the disaster response, the trade-off between water loss 310 and the other criteria was explored. The method used graph decomposition techniques to identify the 311 valves that isolated a hydraulic segment for replacement (Deuerlein 2008). The authors also analysed the 312 network hydraulics and how the depletion of tanks affected service levels. Using these and systematic 313 engineering judgement (Gilbert et al., 2017), recommendations were made for improving the capacity of 314 the system and its absorptive and restorative resilience by design. This included the improvement of 315 pumping stations, installation of control valves and some pipe reinforcement. The same greedy task 316 scheduling algorithm was then used under these alternative network improvements, to evaluate the 317 improvements with respect to all criteria. 318 • Balut et al. (2018) proposed a ranking-based approach where water network pipes‟ „importance‟ was 319 prioritized and applied in a pipe repair schedule. Several approaches to define the importance and create 320 the rankings were proposed, based on hydraulic analyzes (using model under normal operating 321 conditions). Expert knowledge was used, collected via conducted surveys, to define the „rankings‟. 322 Authors surveyed 46 managers, consultants, IT specialists and water distribution modellers from utilities, 323 asking them to list the main criteria that influenced the sequence of repair scheduling, in their opinion. 324 For each disaster scenario, all types of „rankings‟ developed (diameter, diameter and distance from the 325 source, diameter and velocity, flow with and without strategic points, impact of pipes‟ closure on 326 network‟s hydraulics) were applied to schedule tasks for all repair teams. Additionally, experts were also 327 asked in the surveys to assign weights to four criteria that addressed the rapidity of recovery, number of 328 nodes without service and volume of water lost. Results from the rankings were evaluated with use of 329 Visual Promethee – a multicriteria decision aid software, and weights based on the recommendation by 330 the experts. Calculation of hydraulic parameters and evaluation of the final solution based on the six 331 predefined criteria were performed using the Epanet-Matlab toolkit (Eliades et al., 2016). 332 • Li et al. (2018) proposed a two-stage WDN restoration method based on Epanet-Matlab toolkit (Eliades 333 et al., 2016). In the first stage, a shortest path algorithm and greedy algorithm were used to gain the top 334 priority recovery action for a quick response to the disaster. Firstly, Dijkstra algorithm was used to 335 calculate the shortest path from water source to hospital and fire point. The flow could be guaranteed to 336 these locations by repairing the damaged point on the path and closing the valves of the damaged pipeline 337 closest to the path. Then the greedy algorithm was used to obtain the restoration order of the remaining 338 pipes. In the second stage, Particle Swarm Optimization algorithm was used to minimize the total amount 339 of water loss during the restoration process. 340 • Sophocleous et al. (2018) developed a simulation-based response and restoration framework divided 341 into three stages: 1) Pre-Processing, where the possible interventions for each crew were defined together 342 with the time required to complete each intervention, 2) Optimisation, where an optimised schedule for 343 fixing each damage was established using NSGA-II algorithm and a simplified version of weighting 344 objectives, and 3) Restoration Planning, where an action plan (i.e., table of interventions ranked by 345 priority) for each crew was identified using the optimum solution from stage 2. The proposed framework 346 developed a methodology to identify the minimum number of links required to isolate a damaged pipe 347 and enabled simplifying the complexity of the optimisation problem by: 1) solving two sub-problems in 348 sequence (i.e., two-day and seven-day sub-problems, based on the visibility of the damages); and 2) 349 allocating to each crew a particular part of the WDN and a specific number of interventions. This was 350 done through the use of a K-means clustering-based approach (MacQueen, 1967) and engineering 351 judgement (allowing the assumption that in real-life a crew would not be asked to deal with damages 352 spread across the whole network). Simulations were run using the EPANET Programmer‟s Toolkit linked 353 with the MATLAB optimisation tool. 354 • Santonastaso et al. (2018) adopted a strategy to restore the water service after an earthquake following 355 two phases: 1) identification of hydraulic segments, that provided which valves had to be closed to isolate 356 the pipe that needed to be repaired (Creaco et al., 2010); 2) prioritization of the broken pipes according to 357 a topological metric, based on the idea of primary network (Di Nardo et al., 2017) in order to organize the 358 maintenance interventions after the earthquake. The proposed procedure to rank the pipes to be 359 maintained was stated as follows: 1) compute the betweenness for all pipes in the network; 2) repair or 360 replace leaking or broken pipes with high values of edge betweenness; 3) repeat step 2 until no pipes 361 remain to be replaced or repaired. 362 • Bibok (2018) proposed a two-stage approach to the problem. A criticality analysis of network segments 363 was carried out using Bentley System‟s WaterGEMS. It highlighted critical segments, of which size could 364 be reduced by installing additional isolation valves. The visible leaks were determined by an initial 365 hydraulic simulation considering the first 30 minutes. In the second stage, the optimization problem was 366 reduced to a sorting task, which was carried out by a sorting genetic algorithm. The algorithm‟s genome 367 was the ordered list of sequentially executed repair events. A swapping operator during mutation was 368 utilized to preserve the consistency of the visible and non-visible leaks' list. 369 • Salcedo et al. (2018) proposed a decision support model based upon a prioritization methodology 370 described as follows. Initially, a diagnosis of the network was done, including the assessment of the 371 impact of each pipe within the network based on its reliability (Luong & Nagarur, 2005). Then, a 372 prioritization list was developed considering the weighted sum of seven alternative criteria to assign the 373 maintenance activities to each crew. These alternative criteria included the pressure head at hospitals and 374 fire flow nodes, the functionality of the network after rehabilitating a pipe, water losses, and the time 375 needed to rehabilitate each damaged pipe. The weighted list was evaluated at the end of each time step of 376 the simulation using MATLAB and EPANET Programmer‟s toolkit. Finally, the final weights of the 377 decision model were determined using a sensitivity analysis. 378 379 Results and discussion 380 Algorithm performance 381 Three main types of approaches can be identified from the submissions. The first type of approach was 382 based on using general-purpose optimization methods, like Multi Objective Evolutionary Algorithm 383 (MOEA), Non-Dominated Sorting Genetic Algorithms (NSGA-II) and Genetic Algorithms (Castro-Gama 384 et al., 2018; Zhang et al., 2018; Sophocleous et al., 2018; Bibok, 2018). In these approaches, the problem 385 was expressed as an optimal sorting task in which the decision variables were the order in which each 386 damage on the network was fixed. The solution space was all possible permutations of the damages, and 387 the objective functions were either the six criteria from Eqs.(8) to (13), a normalized sum of the six 388 criteria (i.e., a single-objective optimization problem), or a combination of normalization and weighting 389 of the six criteria. The normalization references were the computed range of each criterion (defined by the 390 maximum and minimum values found), or a reference value based on an initial solution. The weights, on 391 the other hand, were mostly based on engineering judgment and sense of importance of each criterion 392 after a natural disaster. 393 The second type of approaches was ranking-based prioritizations, in which different metrics were used to 394 define which pipes should be fixed first according to their “importance” (Balut et al., 2018; Santonastaso 395 et al., 2018; Salcedo et al., 2018). In these approaches, one or various metrics to measure how important 396 is a pipe with respect to the criteria were proposed and tested (the number of metrics tested is shown 397 between square brackets in the second column of Table 3). The nature of proposed metrics included 398 hydraulic properties of the pipes, hydraulic consequences of individual damages, and graph theory 399 metrics. The objective functions used to evaluate a metric were: weighted and normalized sum of the six 400 criteria for Balut et al. (2018); a weighted and normalized sum of scores, developed to simplify 401 computation of the six criteria, for Salcedo et al. (2018); and the six given criteria for Santonastaso et al. 402 (2018). 403 Finally, the third type of approaches was based on algorithms that made local optimum choices aiming to 404 find near-optimal solutions (Sweetapple et al., 2018; Deuerlein et al., 2018; Li et al., 2018). In these 405 approaches, that could be viewed as greedy algorithms, an objective function was defined either as a 406 weighted and normalized sum of the six criteria, or as one of the six criteria depending on the stage of the 407 optimization. Then, starting at the initial time of the simulation, all possible actions (damage fixing) were 408 evaluated, and the one(s) that produced the highest marginal gain in the objective function were selected 409 to be carried out. That process was repeated every time an action was completed until no more actions 410 remained. It is worth noting that Li et al. (2018) used this third type of approach in a first stage of their 411 optimization, followed by an application of a metaheuristic (Particle Swarm Optimization - PSO). 412 Table 3 summarizes the reported results for the six criteria, averaged amongst the five damage scenarios 413 (using the likelihoods as weights), for each team. The top three performance values for each criterion are 414 underlined, with the best performance highlighted with a double underline. 415 Figure 5 presents graphically the results of each team in each criterion compared with the average 416 amongst all teams. Values outside the black dotted line (average), outperformed the average of the ten 417 teams. It is important to note that three teams (Zhang et al., 2018; Deuerlein et al., 2018; Salcedo et al., 418 2018), one from each type of approach, had all six criteria outperforming against the average (all their 419 areas are outside the average circle), showing that all three approaches have potential in solving the 420 response and restoration challenge. 421 Participants’ remarks 422 Participants were also encouraged to suggest some mitigation measures that the city could take in order to 423 improve the response and restoration process for other possible scenarios. One factor that almost all 424 participants seemed to agree, was that installing more isolation valves would reduce the size of the 425 hydraulic segments, and therefore reduce the impact on the supply of the isolations required to replace a 426 broken pipe. 427 Castro-Gama et al. (2018) also evaluated the effect of increasing or decreasing the storage and pumping 428 capacity in the network, and found that increasing the storage and pumping capacity reduces the initial 429 impact of the event (before the interventions), but once the fixing schedule is optimized, there is little 430 improvement in the performance criteria. Sweetapple et al. (2018) evaluated the effect of the 431 disconnection of all hydraulic segments in the network and suggested the separation of the most upstream 432 segment to avoid having both the tank T1 and the reservoir isolated simultaneously in case pipe damage 433 or a contaminant intrusion occurred in that segment. Li et al. (2018) used pipe damage statistics of the real 434 Wenchuan earthquake in 2008 to suggest pipeline renewals to avoid concrete and gray iron pipes which 435 seemed to be more vulnerable to this kind of events, while increasing the pipe burial depths to reduce pipe 436 displacement. Finally, Bibok (2018) suggested running in advance combinations of simultaneous 437 hydraulic segments isolation to reduce in advance search space and ease the computation of 438 recommended schedules once the event occurs. 439 General observations 440 After analysing the results and recommendations of all participants, the main insights are summarized as 441 follows: 442 • All six criteria used to evaluate performance of solutions (Eqs.(8) to (13)) were defined as desirable 443 objectives of a response and restoration method, and as metrics that would contribute to better understand 444 the consequences of extreme seismic events. However, the fact that only one out of ten teams used a 445 multi-objective optimization approach using the six criteria, would suggest that it is necessary to prioritize 446 some of them, with engineering judgment, according to the perspective and policies of the city, in order to 447 make it a mathematically tractable problem that actually provides suitable solutions. 448 • Different types of approaches presented in this Battle have all potential to find satisfactory solutions to 449 the problem. The use of metaheuristics requires in general more computational effort and, therefore, are 450 useful to develop, in advance, plans to react in the moment a disaster occurs. Greedy algorithms are, in 451 general, fast enough to be run at the moment a disaster occurs, making use of that reaction time 452 mentioned before and adapting to new information on damages easily. Finally, ranking-based approaches 453 are straightforward and quick to use, allowing an almost immediate reaction and an instantaneous 454 reordering when given updated information but, unlike optimization-based approaches, rely on subjective, 455 expert generated list of intervention options to consider. 456 •The run times for the participants‟ solutions were not reported as it was not a requirement for the 457 submission (in order to allow the use of any available resource and technique), but the computational 458 requirements of metaheuristic algorithms were mentioned by some participants as a drawback for this 459 type of approach. As explained by Castro-Gama et al. (2018), the use of alternatives like greedy 460 algorithms can reduce the computational time to a 30% of the time required by metaheuristics. However, 461 the potential use of parallelization is expected to make the use of this type of optimization algorithms 462 more suited and faster in future. 463 • Figure 6 shows the average Res. Loss among all participants versus the range of diameters of broken 464 pipes in each scenario. It also shows how, for this particular network, the WDN gets more affected in its 465 functionality by the size of the largest broken pipe, rather than by the number of breaks in the scenario. 466 For example, Scenario 05 has ten more pipe breaks than Scenario 03, but since Scenario 03 has a 250mm 467 pipe broken, it has on average higher resilience loss than Scenario 05 which has all its breaks in pipes 468 with diameters under 200mm. 469 • One important factor that drives the resilience of the WDN to these emergency scenarios is the location 470 of isolation valves and the size of hydraulic segments relative to affected areas. All participants agree that 471 having more isolation valves would reduce the impact of repairs and replacement works in the supply. 472 • On average, the interruptions in the supply to emergencies (hospitals and firefighters) was 17.5 hrs, 473 although considerable variability was seen between participants and scenarios (in some scenarios, some 474 participants were able to maintain continuous water supply to the emergency nodes, while in other cases 475 the interruption accumulated nearly 72 hrs). Since most of that demand occurred in hospitals, this 476 suggests the need to install or increase their private storage to autonomously cope with their demand for 477 longer periods of time. 478 • The Functionality time series follows a peaks-and- troughs shape driven by the highs and lows of 479 diurnal water demand in the system. Figure 7 shows an example of a functionality time series (Scenario 480 01 by Zhang et al., 2018) as well as the demand time series. During evenings, the supplied water was 481 more closely matched to the demands, while during mornings and noontime, the effects of the damages 482 and the ongoing repair work were more noticeable. Additionally, water stored in the tanks offered an 483 initial cushion on the functionality, which allowed full supply of the demand during the first few hours 484 after the event. 485 • Regarding the criteria used to evaluate the performance of each team, a correlation analysis allowed to 486 identify that only the pair t95 – Res. Loss has a strong positive correlation (0.92), suggesting that 487 algorithms that minimize one, would indirectly minimize the other. This was difficult to know in advance, 488 but it would indicate that in an optimization framework, only five objective functions were necessary to 489 solve the challenge. All other computed correlations were below 0.55, with negative values for the four 490 pairs between Nodes no serv. or Water Loss, and t95 or Res. Loss. 491 • A Pareto ranking of the ten teams showed that six solutions were non-dominated (Castro-Gama et al., 492 2018; Zhang et al., 2018; Deuerlein et al., 2018; Li et al., 2018; Bibok, 2018; and Salcedo et al., 2018), 493 with Salcedo et al. (2018) dominating three of the four other solutions, followed by Zheng et al. (2018) 494 dominating two, and Deuerlein et al. (2018) and Castro-Gama et al. (2018) dominating one. 495 • To evaluate the robustness of the approaches, the standard deviation across the five scenarios was 496 computed for each criterion and each team. Figure 8 compares the standard deviations with the averages 497 (an ideal approach would be closer to the bottom-left corner indicating good average performance and 498 low variability in its results). It can be seen that generally, teams with good performance in a criterion 499 (small average value) also had a small standard deviation in that criterion, indicating that their approaches 500 are also robust (with consistently good results for all five scenarios). Exceptions to this remark are mostly 501 in the Resilience Loss criteria, where teams a), f) and c) (Castro-Gama et al., 2018; Li et al., 2018; and 502 Zhang et al., 2018), in that order, had comparatively good average performances, but with high variation 503 between scenarios. 504 • The coefficients of variation for the six criteria were computed (across the ten teams). The Nodes no 505 serv., the Fire & Hosp., and the Time no serv. were, in that order, the criteria with highest variability, 506 which would suggest that these might be criteria more difficult to attain. 507 508 Conclusions 509 The paper summarizes the competition challenge and the results of the Battle of Post-Disaster Response 510 and Restoration (BPDRR) held in Kingston, Ontario in July 2018, as part of the 1st International 511 WDSA/CCWI Joint Conference. Participants in the BPDRR were tasked with identifying the best 512 strategies to respond and restore water service following five hypothetical earthquake scenarios. A total of 513 ten teams developed approaches that fell into three broad categories of metaheuristic methods, ranking- 514 based prioritization methods, and near-optimal optimization methods. Six performance criteria were used 515 to evaluate the solutions of the ten teams and they included: 1) Time without supply for 516 hospital/firefighting, 2) Rapidity of recovery, 3) Resilience loss, 4) Average time of no user service, 5) 517 Number of users without service for 8 consecutive hours, and 6) Water loss. 518 The key findings from the Battle are summarized as follows: 519 • Even though, the six performance measures taken together were used to characterize the appropriateness 520 of the response and restoration solutions, the positive correlation found between some of the criteria 521 suggests that in an optimization framework it might not be necessary to include all of them. 522 • All three categories of approaches proved to be appropriate to find satisfactory response and restoration 523 solutions despite important differences in 524 Metaheuristics, on one hand, seem to be suitable to develop plans beforehand the occurrence of the event, 525 as their computational cost limits their application during reaction times. Greedy algorithms, on the other 526 hand, are faster to compute and can also adapt easily to new available information, making them more 527 applicable in the case of an emergency. Finally, ranking-based approaches condense expert knowledge 528 and intuitive criteria to suggest swiftly the recommended interventions to follow. 529 • The location of isolation valves and the size of hydraulic segments relative to areas affected was found 530 to drive the operational resilience of the system. This highlights the importance of having an adequate 531 location and mapping of isolation valves, as well as a regular maintenance to keep them operational in 532 this disaster scenarios. 533 • The average period of interruption to water supply for hospitals and firefighting flows was 17.5 hrs and 534 varied considerably between participants and emergency scenarios. This highlights the importance of 535 private water storage for emergency response entities. computational requirements between approaches. 536 • Tank storage helped to preserve functionality in the network but only in the first few hours after an 537 emergency event. This may be specific for the system analysed, i.e. other WDN may be able to provide 538 water for longer periods of time. 539 One important point to mention is that extending the results and conclusions of this Battle to practise 540 requires that the list of assumptions remains valid in the specific systems. This implies that utilities need 541 to have updated models of their networks, with good mapping of their isolation valves, and with trained 542 crews that can perform the required tasks in periods close to the assumed. Moreover, they need to keep 543 sufficient resources and parts to fix the damages and communicate efficiently with their crews. Only then, 544 a risk assessment and evaluation of alternatives based on the methods presented in this competition 545 should be performed. 546 547 Future research 548 • One aspect that was not explored further was the demand variation that can occur after an earthquake. 549 Depending on the magnitude of the event, commercial and industrial demands can be affected since some 550 businesses would close temporarily while normal conditions are re-established. 551 • Similarly to the previous point, other important simplification for the problem was not to consider 552 damages to other network elements (e.g., pumps, tanks). Power grids energizing the pumping stations and 553 generators may also be damaged during an earthquake. Communication networks that might be used for 554 monitoring and control operations can also be affected in such scenarios. The effect of this type of 555 damages, as well as their probability of occurrence, and the times to fix them, are worth further 556 investigation. 557 • The relationship between demand and functionality (Figure 7) suggests that there can be better and 558 worst times to fix damages, specially breaks that require isolation, and therefore might be good to explore 559 idle times for crews where they do not fix anything and wait until a low demand time, as noted by Bibok 560 (2018). 561 • The impact of catastrophic events such as an earthquake may have a more profound impact on the water 562 quality which needs to be explored further. If this is the case, then partial water supply during the 563 restoration may be of use for specific water uses only (e.g. toilet flushing) and additional measures may 564 have to be considered (e.g. supply of bottled water). 565 • Usually, important earthquakes produce collapse of buildings and roads, making some streets unfit due 566 to rubbles. These aspects affect mobility and possibility of working of the crews activated for repairing 567 water pipes. These aspects were not considered in the current Battle but might have a significant impact 568 on actual restoring and repairing actions. 569 • The simplification of transportation times in Table 1 can not apply in many real cases, specially large 570 cities, as fixing two close damages can be less time consuming than fixing two very separate damages. 571 Future studies could attempt to discard this simplification. 572 • Other practical assumptions made in the competition included the full availability of spare parts and 573 resources to conduct the interventions to all damages. However, this might not be the case in many cities, 574 and therefore, the impact of limited/unavailable resources on the problem could be explored in future. 575 • Smart water technologies, such as pressure sensors, hydrophones and flow meters (Hill et al., 2014), 576 provide a large amount of information on the state of a WDN. Going forward, it would be interesting to 577 understand how these data could aid water utilities in the design of response solutions to earthquakes as 578 well as other catastrophic events. 579 • Recent Battles have focussed on various events that strongly threaten the performance of a WDN, such 580 as contamination events (Ostfeld et al., 2008), cyber-physical attacks (Taormina et al., 2018), or 581 earthquakes (BPDRR). While these Battles provide enhanced understanding on the performance of 582 engineering solutions to specific events, there seems to be a lack of knowledge on how these solutions 583 should be merged and implemented into joint contingency plans. 584 • Due to organizational limitations, this Battle used a disclosed/open set of five scenarios used by the 585 participant teams to develop, adjust and evaluate their approaches, instead of a bigger, concealed set of 586 predefined scenarios to be tested after the submission of their methods/algorithms. This implies that some 587 methodologies might not have been oriented to a generic solution of the problem, but to the specific 588 solution of these five scenarios. Future research in the topic could benefit from using training scenarios to 589 feedback and adjust the approaches, and test scenarios to evaluate the approaches‟ actual performance. 590 591 Data Availability Statement 592 Some or all data, models, or code generated or used during the study, including the EPANET models and 593 the 594 ([email protected]). Additionally, requests regarding code used by the participants to solve the 595 problem will be directed by the corresponding author to the developers of the code. results for each team, are available from the corresponding author by request 596 597 References 598 American Lifelines Alliance. (2001). Seismic Fragility Formulations for Water Systems: Guideline. 599 American Lifelines Alliance. 600 Ballantyne, D. B., Berg, E., Kennedy, J., Reneau, R., and Wu, D. (1990). Earthquake loss estimation 601 modeling of the Seattle water system. Tech. 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A Heuristic Approach to Water 688 Network Post-Disaster Response and Restoration. 1st International WDSA / CCWI 2018 Joint Conference, 689 23/07/2018 - 25/07/2018, Kingston, CAN, 14. 690 Tabucchi, T., Davidson, R., & Brink, S. (2010). Simulation of post-earthquake water supply system 691 restoration. Civil Engineering and Environmental Systems, 27(4), 263-279. 692 Taormina et al. (2018) The battle of the attack detection algorithms: disclosing cyber attacks on water 693 distribution networks. Journal of Water Resources Planning and Management, 144(8), 04018048. 694 Walski, T. M. (1993). Water distribution valve topology for reliability analysis. Reliability engineering & 695 system safety, 42(1), 21-27. 696 Wang, Y., Au, S. K., & Fu, Q. (2010). Seismic risk assessment and mitigation of water supply systems. 697 Earthquake Spectra, 26(1), 257-274. 698 Wang, Y., & O'Rourke, T. D. (2006). Seismic performance evaluation of water supply systems. Mceer 699 Yoo, D. G., Kang, D., & Kim, J. H. (2016). Optimal design of water supply networks for enhancing 700 seismic reliability. Reliability Engineering & System Safety, 146, 79-88. 701 Zhang, Q., Zheng, F., Diao, K., Ulanicki, B., Huang, Y. (2018). Solving the battle of post-disaster 702 response and restauration (BPDRR) problem with the aid of multi-phase optimization framework. 1st 703 International WDSA / CCWI 2018 Joint Conference, 23/07/2018 - 25/07/2018, Kingston, CAN, 14. 1 2 Table 1. Tasks duration times per pipe Task Duration time per pipe Isolate 15 min/valve Repair* 0.223 ⋅ 𝐷𝑖0.577 Replace* 0.156 ⋅ 𝐷𝑖0.719 *𝐷𝑖 in mm and resulting times in hours (rounded to the lowest hour) 3 4 5 6 Table 2. Example of prioritization schedule Crew Crew 01 Crew 02 Crew 03 7 8 List of tasks (ordered chronologically) Isolate P136 Isolate P283 Repair P206 Replace P152 Repair P242 ⋮ Isolate P367 Isolate P152 Replace P367 Replace P136 Repair P154 ⋮ Isolate P105 Replace P105 Repair P254 Repair P221 Isolate P133 ⋮ 9 10 Table 3. Performance of participant teams in the six defined criteria Team Algorithm Optimization / Ranking criteria Castro-Gama et al. (2018) Sweetapple et al. (2018) Platypus ε-MOEA 6 (Original criteria) Nearest Neighbor Search Zhang et al. (2018) Improved Genetic Algorithm Deuerlein et al. (2018) Greedy Alg. Balut et al. (2018) Pipe/Damage rankings [x 6] + Expert survey Greedy Alg. + PSO 1 (Weighted and normalized original criteria) 1 (Weighted and normalized original criteria) 1 (Weighted relative increase of 5 original criteria) 1 (Weighted and normalized original criteria) 1 (Fire & Hosp. for stage 1 and Res. Loss for stage 2) 1 (Normalized original criteria) 6 (Original criteria) Li et al. (2018) Sophocleous et al. (2018) Santonastaso et al. (2018) Bibok (2018) NSGA-II Pipe/Damage ranking [x 1] Genetic Algorithm Salcedo et al. (2018) Pipe/Damage rankings [x 5+] AVERAGE 1 (Normalized original criteria) 1 (Weighted and normalized modified criteria) Fire & Hosp. (min) t95 (min) Res. Loss (%*min) Time no serv. (min) Nodes no serv. (nodes) Water Loss. (ML) 1411 4094 13271 38.8 17.9 67 760 365 5154 15472 49.6 90.0 79 982 147 3106 10195 64.1 28.6 60 380 301 3918 13250 54.4 140.3 57 278 3396 5184 25988 79.4 212.1 66 580 1532 3902 13574 364.7 818.0 56 624 2528 9510 42129 86.5 37.6 94 116 315 4845 16958 50.0 104.9 77 881 234 4638 15944 216.6 8.4 73 923 270 4471 14235 46.0 35.6 66 799 1050 4882 18102 105.0 149.3 70 132 Note: Entries underlined represent the top three values for each criterion. MOEA: Multi Objective Evolutionary Algorithm. PSO: Particle Swarm Optimization. NSGA-II: Non-Sorted Genetic Algorithm. 11 12 13 14 15 Figure 1. B-City water distribution network. Dotted lines delimit DMAs and “H” represents the hospitals. Figure 2. Damage scenario 01. Breaks highlighted in red, leaks highlighted in yellow, and fire-flows marked with an “F”. Figure 3. Schematic representation of breaks and leaks. Figure 4. Time variation of Functionality as the system is gradually fixed. Figure 5. Performance comparison of each team with respect to the average (black dotted line). Better performance indicated by larger green areas. a) Results from Castro-Gama et al. (2018); b) Results from Sweetapple et al. (2018); c) Results from Zhang et al. (2018); d) Results from Deuerlein et al. (2018); e) Results from Balut et al. (2018); f) Results from Li et al. (2018); g) Results from Sophocleous et al. (2018); h) Results from Santonastaso et al. (2018); i) Results from Bibok (2018); j) Results from Salcedo et al. (2018). Figure 6. Average Resilience Loss vs. Pipe breaks range per damage scenario Figure 7. Functionality time series for Scenario 01 by Zhang et al. (2018) Figure 8. Average and Standard Deviation per criteria per team. 3 pumps T1 𝐷 ≤ 150𝑚𝑚 Break (Serious, requires replacement) 0.5° 𝐷 > 150𝑚𝑚 0.5° Full disconnection EPANET: EPANET: 0.1° Leak (Small, fixed with clamps or welding) 0.5m EPANET: Cross section 0% Occurrence time Functionality (Water supply rate) 100% 95% Resilience Loss t0 Reaction time t95 t100 a) Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. e) Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. i) Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. Fire & Hosp. b) t_95 Water Loss Nodes no serv. Res. Loss Fire & Hosp. Time no serv. f) t_95 Water Loss Nodes no serv. Res. Loss Fire & Hosp. Res. Loss 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. j) t_95 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. Fire & Hosp. c) t_95 Water Loss Nodes no serv. Res. Loss Fire & Hosp. Time no serv. g) t_95 Res. Loss Fire & Hosp. t_95 Res. Loss 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. Fire & Hosp. d) Water Loss t_95 Nodes no serv. Res. Loss Fire & Hosp. Time no serv. h) t_95 Res. Loss 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Water Loss Nodes no serv. 0.2x 0.4x 0.8x 1.6x 3.2x 6.4x Time no serv. Fire & Hosp. t_95 Res. Loss Fire & Hosp. t_95 Res. Loss Average Res. Loss (%*min) 35000 Scenario 01 30000 Scenario 04 25000 Scenario 03 20000 15000 Scenario 05 10000 Scenario 02 5000 0 100 No. of breaks 30 25 20 200 300 400 500 Broken pipes diameter (mm) 600 Demand (L/s) 2,000 Demand 1,500 Firefight demand 1,000 500 0 105% Functionality 100% 95% 90% 85% 80% 75% 0 24 48 72 96 Time (hr) 120 144 168 2000 1000 0 iii ix 0 x viii 100 0 ii Time no serv. ix iii iv x i 0 vi 4000 iii 2000 0 vii v viii ii 100 200 300 Standard Deviation (min) v ix x 6000 0 viii ii i iv Nodes no serv. 600 ix 400 200 0 0 i x vii iii iv v viii ii v 30000 20000 x 10000 iv 0 200 400 Standard Deviation (nodes) ix viii ii vi i iii 5000 10000 Standard Deviation (%*min) Water loss 100000 vi 800 vii 40000 0 1000 2000 3000 Standard Deviation (min) 1000 vi 300 200 iv 500 1000 1500 Standard Deviation (min) 400 Average (min) i vii 8000 Res. Loss 50000 Average (%*min) vi Average (min) vii Average (nodes) Average (min) v 3000 t95 10000 Average (ML) Fire & Hosp. 4000 80000 v 60000 iv 40000 vii i vi viii ii ix x iii 20000 0 0 10000 20000 30000 Standard Deviation (ML) i. Castro-Gama et al. (2018) ii. Sweetapple et al. (2018) iii. Zhang et al. (2018) iv. Deuerlein et al. (2018) v. Balut et al. (2018) vi. Li et al. (2018) vii. Sophocleous et al. (2018) viii. Santonastaso et al. (2018) ix. Bibok (2018) x. Salcedo et al. (2018).