Abstract
To optimize contributions of uncertain input variables on the statistical parameter of given model, e.g., reliability, global reliability sensitivity analysis (GRSA) provides an appropriate tool to quantify the effects. However, it may be difficult to calculate global reliability sensitivity indices compared with the traditional global sensitivity indices of model output, because statistical parameters are more difficult to obtain, Monte Carlo simulation (MCS)-related methods seem to be the only ways for GRSA but they are usually computationally demanding. This paper presents a new non-MCS calculation to evaluate global reliability sensitivity indices. This method proposes: (i) a 2-layer polynomial chaos expansion (PCE) framework to solve the global reliability sensitivity indices; and (ii) an efficient method to build a surrogate model of the statistical parameter using the maximum entropy (ME) method with the moments provided by PCE. This method has a dramatically reduced computational cost compared with traditional approaches. Two examples are introduced to demonstrate the efficiency and accuracy of the proposed method. It also suggests that the important ranking of model output and associated failure probability may be different, which could help improve the understanding of the given model in further optimization design.
Highlights
Sensitivity analysis (SA) is one of the most important methodologies dealing with optimization in engineering practice
SA methodologies can be classified into local sensitivity analysis (LSA) and global sensitivity analysis (GSA) [1,5]
Global reliability sensitivity analysis aims at measuring the importance statistical parameter
Summary
Sensitivity analysis (SA) is one of the most important methodologies dealing with optimization in engineering practice. Borgonovo proposed the moment-independent global sensitivity indices which are derived from conditional probability density function (PDF) [11,12] Lu accepted this idea and further developed the variance-based importance measurement for global reliability sensitivity analysis (GRSA) with associated global reliability sensitivity indices [13,14]. Unlike traditional global sensitivity indices calculation, the global reliability sensitivity indices aim at calculating importance of input variables on reliability that is a statistical parameter These indices are concerned about the variance of conditional expectation of indicator function according to variance decomposition formula. Since the CFP is dependent on a set of conditional variables, each global reliability sensitivity index corresponding to different conditional variables requires a specific surrogate model This may be time consuming when computing several indices.
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