A parallel Bayesian interval optimization approach for static analysis of structures with interval uncertainties

Abstract

This paper aims at approximating the bounds of the static response of structures with interval uncertainties. Such task is often challenging due to the large number of computationally intensive response evaluations required. To address this challenge, we propose an efficient non-intrusive method, namely, parallel Bayesian interval optimization (PBIO). The PBIO first assumes a Gaussian process (GP) prior over the response function. Such a prior can be updated to a posterior GP given observations arising from evaluating the response function at some locations. The main contribution lies in proposing a two-stage infill sampling strategy to guide the selection of multiple update points at each iteration. Briefly, the first stage is to search for promising points that bring significant improvements to the current minimum and maximum responses, using a new acquisition function called Average expected improvement (AvEI) and an improved multi-modal optimization (MMO) algorithm. The second stage is to find additional points that still have significant improvements to the current minimum or maximum response, based on traditional EI and improved MMO. By using PBIO, multiple response values can be evaluated in parallel, and both lower and upper response bounds can be obtained simultaneously in a single run. A static finite element example is studied to show the effectiveness of PBIO.