mfEGRA: Multifidelity Efficient Global Reliability Analysis through Active Learning for Failure Boundary Location

TL;DR

The paper tackles the high cost of reliability analysis by introducing mfEGRA, a multifidelity active-learning framework that extends Efficient Global Reliability Analysis (EGRA) to fuse multiple information sources with different fidelities and costs for locating the failure boundary. It develops a two-stage adaptive sampling strategy: (i) select the next sample location by maximizing the expected feasibility function (EFF) of a multifidelity Gaussian process surrogate, and (ii) select the information source by maximizing a weighted lookahead information gain based on the KL divergence between the current and a hypothetical future surrogate. A closed-form expression for the lookahead information gain in the multifidelity GP enables efficient source selection, with weights to emphasize sampling near the failure boundary. Demonstrations on analytic multimodal and acoustic horn problems show substantial computational savings (approximately 46% in the analytic case, 24–48% in the acoustic horn cases) compared to single-fidelity EGRA, especially when low-fidelity models are inexpensive or a priori Monte Carlo samples are used, highlighting mfEGRA’s practical impact for robust reliability analysis.

Abstract

This paper develops mfEGRA, a multifidelity active learning method using data-driven adaptively refined surrogates for failure boundary location in reliability analysis. This work addresses the issue of prohibitive cost of reliability analysis using Monte Carlo sampling for expensive-to-evaluate high-fidelity models by using cheaper-to-evaluate approximations of the high-fidelity model. The method builds on the Efficient Global Reliability Analysis (EGRA) method, which is a surrogate-based method that uses adaptive sampling for refining Gaussian process surrogates for failure boundary location using a single-fidelity model. Our method introduces a two-stage adaptive sampling criterion that uses a multifidelity Gaussian process surrogate to leverage multiple information sources with different fidelities. The method combines expected feasibility criterion from EGRA with one-step lookahead information gain to refine the surrogate around the failure boundary. The computational savings from mfEGRA depends on the discrepancy between the different models, and the relative cost of evaluating the different models as compared to the high-fidelity model. We show that accurate estimation of reliability using mfEGRA leads to computational savings of $\sim$46% for an analytic multimodal test problem and 24% for a three-dimensional acoustic horn problem, when compared to single-fidelity EGRA. We also show the effect of using a priori drawn Monte Carlo samples in the implementation for the acoustic horn problem, where mfEGRA leads to computational savings of 45% for the three-dimensional case and 48% for a rarer event four-dimensional case as compared to single-fidelity EGRA.

Figures (14)

• Figure 1: Reliability analysis with (a) high-fidelity model, (b) single fidelity adaptive surrogate, and (c) multifidelity adaptive surrogate.
• Figure 2: Flowchart showing the mfEGRA method.
• Figure 3: Contours of $g_l(\boldsymbol{z})$ using the three fidelity models for the analytic test problem. Solid red line represents the zero contour that denotes the failure boundary.
• Figure 4: Effect of different weights for information gain criterion in mfEGRA for analytic test problem in terms of convergence of relative error in $p_\text{F}$ prediction (shown in log-scale) for 100 different initial DOEs. Solid lines represent the median and dashed lines represent the 25 and 75 percentiles.
• Figure 5: Comparison of mfEGRA vs single-fidelity EGRA for analytic test problem in terms of convergence of relative error in $p_\text{F}$ prediction (shown in log-scale) for 100 different initial DOEs.