Heteroscedastic Gaussian Process Surrogate Modeling

Summary

Seismic risk analysis is a method of evaluating an infrastructure asset’s expected ability to meet service needs during extreme earthquake events. While this form of risk analysis is traditionally conducted at the level of individual buildings, increasing the scope to a population of buildings is important for quantifying economic risks at the municipality or regional level. However, the state-of-art of seismic response simulation by nonlinear response history analysis (NLRHA) presents a high computational cost which limits the scale and resolution of regional-level earthquake simulations. Moreover, seismic response simulation using recorded ground motions provides a more realistic representation of seismic excitation, but it concurrently introduces a greater amount of aleatory uncertainty in the structural response estimate compared to synthetic ground motion models due to record-to-record variability.

We demonstrate stochastic kriging as a robust surrogate model which is able to estimate heteroscedastic variance in seismic response resulting from variability in ground motion excitation. As a Bayesian technique of surrogate modeling, kriging allows for the propagation of uncertainty in the estimated structural response to decision factors in probabilistic seismic risk analysis. Stochastic kriging is a two-tiered statistical model in which one Gaussian process models the relative variability of estimator variance across the parameter space (the “nugget”) and another Gaussian process models the distribution of seismic response incorporating variance information from the first model. The surrogate model is constructed using a dataset generated by performing NLRHA on a number of building configurations parameterized by structural properties, then replicating simulations for a subset of configurations in order to learn the GP model of heteroscedastic variance. We study the tradeoff in accuracy and cost to determine an appropriate composition of building configurations and replications to query in dataset generation.

Related Papers

J. Zou, D. P. Welch, A. Zsarnoczay, A. Taflanidis, G. Deierlein. “Surrogate Modeling for the Seismic Response Estimation of Residential Wood Frame Structures.” Proceedings of the 17th World Conference in Earthquake Engineering. Sendai, Japan. 2020.