PEER has published Report No. 2024/10: The 21st Working Conference of the IFIP Working Group 7.5 on Reliability and Optimization of Structural Systems (IFIP WG7.5 2024). It was authored by Ziqi Wang and Jungho Kim, Department of Civil and Environmental Engineering, University of California, Berkeley.
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Abstract
Stochastic emulation techniques are used to surrogate forward simulations involving non-deterministic input-output relationships. Their objective is to address the stochastic uncertainty sources by directly predicting the output distribution for a given parametric input. An example of such application, and the focus of this contribution, is the estimation of structural response (engineering demand parameter) distribution in seismic risk assessment. In this case, the stochastic uncertainty originates from the aleatoric variability in the seismic hazard description. The key challenge in stochastic emulation pertains to addressing heteroscedasticity in the output variability. Relevant approaches to-date for addressing this challenge have focused on scalar outputs. In contrast, this paper focuses on the multi-output stochastic emulation problem and presents a methodology for predicting the output correlation matrix, while fully addressing heteroscedastic characteristics. This is achieved by introducing a Gaussian Process (GP) regression model for approximating the components of the correlation matrix, and coupling this approximation with a correction step to guarantee positive definite properties for the resultant predictions. For obtaining the observation data to inform the GP calibration, different approaches are examined, relying-or-not on the existence of replicated samples for the response output. When available, replicated samples can be readily used to obtain observation for the response statistics (correlation or covariance) to inform the GP development. An alternative approach is to obtain noisy observations of covariance using the sample deviations from a primitive mean approximation. These different observation variants lead to different GP variants that are compared within a comprehensive case study. A computational framework for integrating the correlation matrix approximation within the stochastic emulation for the marginal distribution approximation of each output component is also discussed, to provide the joint response distribution approximation.