A Single-Loop Method for Time-Variant Reliability Sensitivity Analysis of Motion Mechanisms Using Bayes’ Theorem

Abstract

Time-variant reliability sensitivity (TRS) analysis can measure the effect of input factors on the structure/mechanism failure. The traditional method for TRS analysis employs a nested sampling procedure, with computational cost depending on the number of input factors. To address the above weaknesses, a single-loop method is developed for TRS analysis. Based on Bayes’ theorem, the sensitivity measure is derived and expressed by the difference between the probability density function (PDF) and the failure-conditional PDF. This derivation allows for TRS analysis to be performed with just one set of samples, where the computational complexity does not depend on the number of inputs. Then, the procedures for Monte Carlo simulation (MCS) are listed based on the innovative estimation of the sensitivity index. Three examples involving numerical and engineering problems are employed to validate the proposed strategy, with the direct MCS introduced for comparison. The results reveal that the proposed strategy provides satisfactory TRS analysis while significantly saving computational resources.