Gaussian Process Surrogate Models for Efficient Estimation of Structural Response Distributions and Order Statistics

Abstract: Engineering disciplines often rely on extensive simulations to ensure that structures are designed to withstand harsh conditions while avoiding over-engineering for unlikely scenarios. Assessments such as Serviceability Limit State (SLS) involve evaluating weather events, including estimating loads not expected to be exceeded more than a specified number of times (e.g., 100) throughout the structure's design lifetime. Although physics-based simulations provide robust and detailed insights, they are computationally expensive, making it challenging to generate statistically valid representations of a wide range of weather conditions. To address these challenges, we propose an approach using Gaussian Process (GP) surrogate models trained on a limited set of simulation outputs to directly generate the structural response distribution. We apply this method to an SLS assessment for estimating the order statistics (Y_{100}), representing the 100th highest response, of a structure exposed to 25 years of historical weather observations. Our results indicate that the GP surrogate models provide comparable results to full simulations but at a fraction of the computational cost.