A novel estimation method for failure-probability-based-sensitivity by conditional probability theorem
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RESEARCH PAPER
A novel estimation method for failure-probability-based-sensitivity by conditional probability theorem Liangli He 1 & Zhenzhou Lu 1
&
Kaixuan Feng 1
Received: 27 May 2019 / Revised: 24 September 2019 / Accepted: 16 October 2019 # Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract By the average absolute difference between the unconditional failure probability and the conditional one on fixing an input at its realization, the failure-probability-based-sensitivity (FP-S) is defined to quantify the effect of the fixed input on the failure probability, which provides important information for reliability-based design optimization of the structure. Among the estimation methods for FP-S, the Bayes theorem-based methods are competitive, but the conditional probability density function (PDF) should be estimated in this type method. To alleviate the computational complexity of estimating conditional PDF, a novel FP-S estimation method is proposed by use of the conditional probability theorem. In the proposed method, the conditional failure probability on fixing the input at its realization is approximated by the conditional failure probability on fixing the input in a small interval, in which the conditional probability theorem of the random event can be used to transform FP-S as estimations of a series of probabilities, and they can be simultaneously completed by a numerical simulation for estimating the unconditional failure probability. For ensuring the precision of the approximation introduced by replacing the realization with the small interval, a selection strategy for the small interval is proposed. Comparing with the competitive Bayes theorem-based estimation for FP-S, the proposed method replaces the conditional PDF estimation with the conditional probability estimation, which greatly reduces the computational complexity and improves the accuracy of the FP-S estimation. By combining with the adaptive kriging surrogate model, the efficiency of the proposed method can be drastically improved, and the presented examples demonstrate the efficiency and accuracy of the proposed method. Keywords Failure-probability-based-sensitivity . Bayes theorem-based method . Conditional probability density function . Conditional probability theorem . Adaptive kriging
1 Introduction In engineering applications, uncertainties universally exist in the geometries, the material properties, and the applied loads, and they may lead to the disabled risk of designed structure. In
Responsible Editor: Christian Gogu * Zhenzhou Lu [email protected] Liangli He [email protected] Kaixuan Feng [email protected] 1
School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, Shaanxi, China
the case of uncertainty, sensitivity analysis (Saltelli 2002; Saltelli et al. 2008; Wang et al. 2017; Li and Lu 2017; Borgonovo and Plischke 2016), especially the failureprobability-based-sensitivity (FP-S) analysis (Cui et al. 2010; Li et al. 2012; Yun et al. 2016; Yun et al. 2018a), has attracted signific
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