An integrated framework for reliability analysis and design optimization using input, simulation, and experimental data: Confidence-based design optimization under aleatory and epistemic uncertainty

초록

Engineering systems are inherently influenced by aleatory variability, and quantifying this uncertainty from data and understanding how it propagates to system responses remain significant challenges in reliability analysis and design optimization. In simulation-based reliability analysis, three types of interrelated epistemic uncertainty may arise when only limited data are available: (i) input model uncertainty in the statistical characterization of observable random parameters, (ii) surrogate model uncertainty in Gaussian process (GP) emulators of simulations, and (iii) calibration uncertainty introduced when inversely inferring unobservable random parameters and model discrepancy from experimental data. Although each type of uncertainty has been widely studied, no research has combined all three in a single framework and propagated their effects to the uncertainty in reliability. We propose an integrated framework that quantifies both aleatory and epistemic uncertainty from three complementary data sources - observations for the input model, simulation data for surrogate modeling, and experimental data for model calibration - and propagates their effects through reliability analysis, thereby enabling estimation of the resulting confidence level given limited data. Furthermore, it supports confidence-based design optimization (CBDO) to minimize the objective while achieving a reliable and conservative optimum under epistemic uncertainty. The framework's effectiveness is demonstrated through mathematical examples and an application to a thermoelectric generator (TEG) system.

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