A Concise Transformation Combined With Adaptive Kriging Model for Efficiently Estimating Regional Sensitivity on Failure Probability

Abstract

Regional sensitivity on failure probability (RS-FP) can quantify the effect of the input region of interest (IRoI) on the failure probability and provide useful information for reliability based design optimization. Traditional methods for estimating RS-FP require huge computational cost, especially for implicit performance function and rare failure event in engineering applications. In order to alleviate these issues, Adaptive Kriging (AK) model based methods involving AK model inserted Monte Carlo Simulation (AK-in-MCS) and AK model inserted Importance Sampling (AK-in-IS) are carried out for efficiently estimating the RS-FP. Furthermore, the RS-FP can be estimated by the conditional probability of IRoI on failure domain by employing the probability product principle. Based on this transformation, AK-in-MCS and AK-in-IS can be much conveniently organized for identifying the conditional probability just as a byproduct of estimating the failure probability. Since the original complicated estimation process has been alleviated by the concise transformation, and the AK model is efficiently trained to identify the failure samples from the sample pool generated by MCS or IS, the computational cost of estimating RS-FP is greatly reduced. At the same time, the detailed geometric interpretation for the “contribution to failure probability (CFP) plot” is discussed. Several examples containing numerical and engineering examples are introduced to demonstrate the accuracy and efficiency of the proposed methods.

Keywords

• Regional sensitivity
• failure probability
• AK model
• Monte Carlo simulation
• importance sampling
• probability product principle