Data-driven optimization of reliability using buffered failure probability

Design and operation of complex engineering systems rely on reliability optimization. Such optimization requires us to account for uncertainties expressed in terms of complicated, high-dimensional probability distributions, for which only samples or data might be available. However, using data or samples often degrades the computational efficiency, particularly as the conventional failure probability is estimated using the indicator function whose gradient is not defined at zero. To address this issue, by leveraging the buffered failure probability, the paper develops the buffered optimization and reliability method (BORM) for efficient, data-driven optimization of reliability. The proposed formulations, algorithms, and strategies greatly improve the computational efficiency of the optimization and thereby address the needs of high-dimensional and nonlinear problems. In addition, an analytical formula is developed to estimate the reliability sensitivity, a subject fraught with difficulty when using the conventional failure probability. The buffered failure probability is thoroughly investigated in the context of many different distributions, leading to a novel measure of tail-heaviness called the buffered tail index. The efficiency and accuracy of the proposed optimization methodology are demonstrated by three numerical examples. Although they might show slight deviations from a target failure probability because of sampling errors and other inaccuracies, the results underline unique advantages and potentials of the buffered failure probability for datadriven reliability analysis.