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.
Highlights
Regional sensitivity (RS) analysis [1], [2] recognizes the regional importance which is called the intra-importance of the input, i.e. the importance of the left tail, right tail or the center region, and tells the engineers the most efficient way to intensively reduce the uncertainty of the output, by subtly reducing that of the important region of the inputs.Some researches have been done for the RS
The contribution to failure probability (CFP) plot was proposed to measure the importance of the IROI on the failure probability, and it can provide information on how and how much the IROI affects the failure probability
A detailed geometric interpretation for the CFP plots is presented in this work
Summary
Regional sensitivity (RS) analysis [1], [2] recognizes the regional importance which is called the intra-importance of the input, i.e. the importance of the left tail, right tail or the center region, and tells the engineers the most efficient way to intensively reduce the uncertainty of the output, by subtly reducing that of the important region of the inputs. For effectively and efficiently estimating the CFP plot, a concise and estimated form by appling the probability product principle combined with the adaptive Kriging (AK) model is proposed in this paper. The proposed method is proceeded as follows: Firstly and most importantly, the CFP plot is transformed as a concise and estimated form by using the probability product principle, in which only the conditional probability of the IRoI on the failure domain is required. AK model inserted IS (AK-in-IS) method is elaborately established for estimating the conditional probability of the IRoI on the failure domain, which is transformed from the CFP plot. By using the Metropolis-Hasting algorithm, the failure samples following the importance sampling distribution are transformed without extra evaluation of the performance function to the ones following the original distribution, on which the concerned conditional probability of the IRoI on the failure domain can be directly estimated.
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