Efficient Long-Term Structural Reliability Estimation with Non-Gaussian Stochastic Models: A Design of Experiments Approach

Extreme response assessment is important in the design and operation of engineering structures, and is a crucial part of structural risk and reliability analyses. Structures should be designed in a way that enables them to withstand the environmental loads they are expected to experience over their lifetime, without designs being unnecessarily conservative and costly. An accurate risk estimate is essential but difficult to obtain because the long-term behaviour of a structure is typically too complex to calculate analytically or with brute force Monte Carlo simulation. Therefore, approximation methods are required to estimate the extreme response using only a limited number of short-term conditional response calculations. Combining surrogate models with Design of Experiments is an approximation approach that has gained popularity due to its ability to account for both long-term environment variability and short-term response variability. In this paper, we propose a method for estimating the extreme response of black-box, stochastic models with heteroscedastic non-Gaussian noise. We present a mathematically founded extreme response estimation process that enables Design of Experiment approaches that are prohibitively expensive with surrogate Monte Carlo. The theory leads us to speculate this method can robustly produce more confident extreme response estimates, and is suitable for a variety of domains. While this needs to be further validated empirically, the method offers a promising tool for reducing the uncertainty decision-makers face, allowing them to make better informed choices and create more optimal structures.