A probabilistic estimation model for seismic physical portfolio loss of a water supply pipeline system

Abstract

Losses due to hazards are inevitable and numerical simulations for estimations are complex. This study proposes a model for estimating correlated seismic damages and losses of a water supply pipeline system as an alternative for numerical simulations. The common approach in other research shows average damage spots per mesh estimated statistically independent to one another. Spatially distributed lifeline systems, such as water supply pipelines, are interconnected, and seismic spatial variability affects the damages across the region; thus, spatial correlation of damage spots is an important factor in target areas for portfolio loss estimation. Generally, simulations are used to estimate possible losses; however, these assume each damage behaves independently and uncorrelated. This paper assumed that damages per mesh behave in a Poisson distribution to avoid over-dispersion and eliminate negative losses in estimations. The purpose of this study is to obtain a probabilistic portfolio loss model of an extensive water supply area. The proposed model was compared to the numerical simulation data with the correlated Poisson distribution. The application of the Normal To Anything (NORTA) obtained correlations for Poisson Distributions. The proposed probabilistic portfolio loss model, based on the generalized linear model and central limit theory, estimated the possible losses, such as the Probable Maximum Loss (PML, 90% non-exceedance) or Normal Expected Loss (NEL, 50 % non-exceedance). The proposed model can be used in other lifeline systems as well, though additional investigation is needed for confirmation. From the estimations, a seismic physical portfolio loss for the water supply system was presented. The portfolio was made to show possible outcomes for the system. The proposed method was tested and analyzed using an artificial field and a location-based scenario of a water supply pipeline system. This would aid in pre-disaster planning and would require only a few steps and time.

Keywords

Spatial correlation / Probable maximum loss / Risk management / Water supply pipeline / Portfolio loss estimation

References

[1] Liu H, Zhang DL. Analysis and prediction of hazard risks caused by tropical cyclones in southern China with fuzzy mathematical and grey models. Appl Math Model 2012;36(2):626-37. doi: 10.1016/j.apm.2011.07.024.

[2] Deelstra A, Bristow D. Characterizing uncertainty in city-wide disaster recov-ery through geospatial multi-lifeline restoration modeling of earthquake impact in the district of North Vancouver. Int J Disaster Risk Sci 2020;11(6):807-20. doi: 10.1007/s13753-020-00323-5.

[3] Kwong NS, Jaiswal KS, Baker JW, Luco N, Ludwig KA, Stephens VJ. Earthquake risk of gas pipelines in the conterminous United States and its sources of un-certainty. ASCE-ASME J Risk Uncertain Eng Syst Part A Civ Eng 2022;8(1). doi: 10.1061/ajrua6.0001202.

[4] Tang A, Tao X, Ou J, Aihua W. Lifeline systems interaction and their seismic per-formance assessment. In:Proceedings of the 13th world conference on earthquake engineering. B.C., Canada: Vancouver; 2004. p. 13. Retrieved March 212018 from. http://www.iitk.ac.in/nicee/wcee/article/13_3437.pdf.

[5] Cremen G, Galasso C, McCloskey J. Modelling and quantifying tomor-row’s risks from natural hazards. Sci Total Environ 2022;817:152552. doi: 10.1016/j.scitotenv.2021.152552.

[6] Gulati S, George F, Golam Kibria BM, Hamid S, Cocke S, Pinelli JP. Probable max-imum loss for the Florida Public Hurricane loss model: comparison. ASCE-ASME J Risk Uncertain Eng Syst Part A Civ Eng 2017;3(4). doi: 10.1061/ajrua6.0000913.

[7] Jarder SLN, Garciano LEO, Maruyama O. Probable maximum loss of a pipe network due to earthquakes: a case study in Iloilo city, Philippines. Int J Disaster Resil Built Environ 2021;12(2):223-37. doi: 10.1108/IJDRBE-03-2020-0017.

[8] O’Rourke TD, Jeon SS. Factors affecting the earthquake damage of water distribution systems, optimizing post-earthquake lifeline system reliability. In: Elliott WM, Mc-Donough P, editors. Proceedings of the, fifth U.S. conference on lifeline earthquake engineering. Seattle: ASCE; 1999. p. 379-88.

[9] Isoyama R, Ishida E, Yune K, Shirozu T. Seismic damage estimation procedure for water supply pipelines. Water Supply 2000;18(3):63-8.

[10] ALA American Lifeline Alliance Seismic fragility formulation for water systems. Washington, DC: AL; 2001.

[11] O’Rourke M, Deyoe E. Seismic damage to segmented buried pipe. Earthq Spectra 2004;20(4):1167-83. doi: 10.1193/1.1808143.

[12] ASTM E2026- 99 Standard guide for the estimation of building damageability in earthquakes. West Conshohocken, PA: ASTM International; 1999.

[13] Poulos A, Espinoza S, de la Llera JC, Rudnick H. Seismic risk assessment of spatially distributed electric power systems. In: Proceedings of the 16th world conference on earthquake; 2017. 16WCEE 2017. Retrieved January 2022, from https://hrudnick.sitios.ing.uc.cl/paperspdf/Paper3825.pdf.

[14] Toprak S, Taskin F. Estimation of earthquake damage to buried pipelines caused by ground shaking. Nat Hazards 2006;40(1):1-24. doi: 10.1007/s11069-006-0002-1.

[15] Thioulouse J, Chessel D, Champely S. Multivariate analysis of spatial patterns: a unified approach to local and global structures. Environ Ecol Stat 1995;2(1):1-14. doi: 10.1007/bf00452928.

[16] Yahav I, Shmueli G. On generating multivariate poisson data in management science applications. SSRN Electr J 2009. doi: 10.2139/ssrn.1457347.

[17] Nelder JA, Wedderburn RW. Generalized linear models. J R Stat Soc Ser A 1972;135(3):370. doi: 10.2307/2344614.

[18] İŞ Çİ Güneri Ö Durmuş B. An application of the generalized poisson model for over dispersion data on the number of strikes between 1984 and 2017. Alphanumeric J 2020. doi: 10.17093/alphanumeric.670611.

[19] Morris DS, Sellers KF. A flexible mixed model for clustered count data. Stats 2022;5(1):52-69. doi: 10.3390/stats5010004.

[20] Wang S, Gui W. Corrected maximum likelihood estimations of the distribution pa-rameters. Symmetry (Basel) 2020;12(6):968. doi: 10.3390/sym12060968.

[21] Chang KH. Reliability analysis. In: e-Design: computer-aided engineer-ing design. Academic Press; 2015. p. 523-95. essayRetrieved from. doi: 10.1016/B978-0-12-382038-9.00010-7.

[22] Philippine Institute of Seismology and Volcanology (2018), [Iloilo city earthquake data], Unpublished raw data

[23] Youngs RR, Chiou SJ, Silva WJ, Humphrey JR. Strong ground motion attenuation relationships for subduction zone earthquakes. Seismol Res Lett 1997;68(1):58-73. doi: 10.1785/gssrl.68.1.58.

[24] Kramer S.L. (1996). Lateral Spreading. In the encyclopedia of natural hazards

[25] Japan Water Works Association. (1998). Estimation of seismic damage of water sup-ply system, Engineering Report.

[26] Aitchison J, Ho CH. The multivariate poisson-log normal distribution. Biometrika 1989;76(4):643-53. doi: 10.1093/biomet/76.4.643.

[27] Mardia KV. Measures of multivariate skewness and kurtosis with applications. Biometrika 1970;57(3):519-30. doi: 10.1093/biomet/57.3.519.

[28] Wang M, Takada T. Macrospatial correlation model of seismic ground motions. Earthq Spectra 2005;21(4):1137-56. doi: 10.1193/1.2083887.

[29] Pietrucha-Urbanik K, Studzi ń ski A. Qualitative analysis of the failure risk of water pipes in terms of water supply safety. Eng Fail Anal 2019;95:371-8. doi: 10.1016/j.engfailanal.2018.09.008.

[30] Studzi ń ski A, Pietrucha-Urbanik K. Failure risk analysis of water distribu-tions systems using hydraulic models on real field data. Economics and Environment 2019;68(1):14. Retrieved from https://ekonomiaisrodowisko.pl/journal/article/view/106.

[31] Silva V, Crowley H, Pagani M, et al. Development of the OpenQuake engine, the Global Earthquake Model’s open-source software for seismic risk assessment. Nat Hazards 2014;72:1409-27. doi: 10.1007/s11069-013-0618-x.

[32] Zhang Y, Romanelli F, Vaccari F, Peresan A, Jiang C, Wu Z, Gao S, Kos- sobokov VG, Panza GF. Seismic hazard maps based on neo-deterministic Seismic Hazard Assessment for China Seismic Experimental site and adjacent areas. Eng Geol 2021;291:106208. doi: 10.1016/j.enggeo.2021.106208.

[33] Kazantzidou-Firtinidou D, Kyriakides N, Votsis R, Chrysostomou C. Seismic risk assessment as part of the National Risk Assessment for the Republic of Cyprus: from probabilistic to scenario-based approach. Nat Hazards 2022;112(1):665-95. doi: 10.1007/s11069-021-05200-y.

[34] Asad R, Saleem MQ, Habib MS, Mufti NA, Mayo SM. Seismic risk assessment and hotspots prioritization: a developing country perspective. Natural Hazards 2023;117(3):2863-901. doi: 10.1007/s11069-023-05970-7.

[35] Chen W, Zhang L. An automated machine learning approach for earthquake ca-sualty rate and economic loss prediction. Reliab Eng Syst Saf 2022;225:108645. doi: 10.1016/j.ress.2022.108645.

[36] Baker JW, Jayaram N. Correlation of spectral acceleration values from NGA ground motion models. Earthq Spectra 2008;24(1):299-317. doi: 10.1193/1.2857544.