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

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 Y100, 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.

Keywords: Machine learning, Surrogate models, Probabilistic modeling, Structural response estimation, Serviceability Limit State (SLS) calculations, Order statistics.