Optimal probabilistic placement of facilities using a surrogate model for 3D tsunami simulations

Abstract. Tsunamis are associated with numerous uncertainties. Therefore, there has been an emphasis on setting the placement of infrastructure facilities based on probabilistic approaches. However, advanced numerical simulations have been often insufficiently utilized due to high computational costs. Therefore, in this study, we developed a framework that could efficiently utilize the information obtained from advanced numerical simulations for probabilistic assessment and investigation of the optimal placement of facilities based on calculated probability. Proper orthogonal decomposition (POD) techniques were employed for utilizing the data from the numerical simulations for probabilistic risk evaluation. We constructed a surrogate model in which POD was efficiently used to extract the spatial modes. The results of the numerical simulation were expressed as a linear combination of the modes, and the POD coefficients were expressed as a function of the uncertainty parameters to represent a result of an arbitrary scenario at a low computational cost. We conducted numerical simulations of the 2011 tsunami off the Pacific Coast caused by Tohoku Earthquake as an example of the method proposed in this study. The tsunami reached the target area, and the fault parameters of “slip” and “rake” were selected as the target uncertainties. We then created several scenarios in which these parameters were changed and conducted further numerical simulations using POD to construct a surrogate model. We selected the maximum inundation depth in the target area and the maximum impact force that acts on the buildings as the target risk indices, and we constructed a surrogate model of the spatial distributions of each indicator. Furthermore, we conducted Monte Carlo simulations using the constructed surrogate model and the information on fluctuations in uncertainties to calculate the spatial distribution of the failure criterion exceedance probabilities. We then used the Monte Carlo simulation results and a genetic algorithm to identify the optimal placement of facilities based on probability. We also discuss how the optimal placement changes according to differences in risk indices and the differences between parallel and series systems. The failure scenarios for each system are also discussed based on the failure probability. We show that the proposed method of efficiently utilizing advanced numerical simulation information was useful for conducting probabilistic hazard assessments and investigating the optimal placement of facilities based on probability theory.