Surrogate Modeling with Sequential Updating: Applications to Bridge Deck–Wave and Bridge Deck–Wind Interactions

Abstract

This paper presents a methodology for sequentially updating surrogate models with augmented data in order to substantially enhance the design of experiments in civil engineering applications and to reach a balance between exploration and exploitation for the approximated surrogate functions with the constraint of limited laboratory and/or computational resources. In this methodology, two surrogate models involving kriging and support vector regression (SVR) are used concurrently in one updating cycle to propose new design samples. The error estimation capability of Gaussian variance (i.e., mean squared error) intrinsically furnished with kriging is successfully imported to SVR. Specifically, the surrogate-based design-updating methodology is introduced first, where two infill criteria, the mean squared error (MSE), and expected improvement (EI), are employed for balancing the exploration and exploitation of surrogate approximations. Three evaluation approaches, the normalized maximum absolute error (NMAE), normalized root mean squared error (NRMSE), and correlation coefficient (CR), are adopted to evaluate the model performance. In one updating cycle, each constructed surrogate model, kriging, or SVR, provides a set of new design points based on the adopted infill criteria, respectively. This sequential updating procedure is constrained with the computational budget and the global tolerance (the requirements of precision) prescribed based on the prior knowledge of the dataset. Then, two benchmark nonlinear functions are demonstrated following the procedure developed. Two typical civil engineering applications (bridge deck–wave interaction and aerodynamics optimization) are carried out for demonstrating the effective performance of both kriging and SVR-based updating strategy. This study provides an effective approach to design experiments in civil engineering to maximize the information gain based on limited computational/experimental effort.