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An efficient method for estimating the parameter global reliability sensitivity analysis by innovative single-loop process and embedded Kriging model

Published on Nov 1, 2019in Mechanical Systems and Signal Processing5.005
· DOI :10.1016/j.ymssp.2019.106288
Wanying Yun1
Estimated H-index: 1
(Tongji University),
Zhenzhou Lu21
Estimated H-index: 21
(NPU: Northwestern Polytechnical University)
+ 2 AuthorsXian Jiang8
Estimated H-index: 8
Sources
Abstract
Abstract For evaluating the effect of uncertain distribution parameter on the uncertainty of the failure probability function, the parameter global reliability sensitivity index (PGRSI) is researched and the high efficient estimation algorithm is proposed to approximately estimate the PGRSI. The used definition form of the PGRSI is the expectation of absolute differences between the unconditional expectation of failure probability function and the conditional expectation of failure probability function, which involves a triple-loop evaluation. For efficiently estimating the PGRSI, this paper innovatively inducts the Bayes theorem and the law of total expectation in the successive intervals without overlapping in order to convert the triple-loop evaluation to a single-loop one. The number of actual model evaluations of the single-loop Monte Carlo simulation (MCS) is independent of the dimensionality of uncertain distribution parameters, and the single-loop MCS only needs one set of input-output samples. Besides, the single-loop MCS can be regarded as a classification problem which needs to identify the failure or safety states of samples in the one set. To further enhance the computational efficiency of the proposed single-loop process, the adaptive Kriging (AK) model is embedded in the single-loop MCS, where the Kriging model is used to approximate the actual limit state function to classify the samples. The number of actual model evaluations of the Kriging model nested single-loop process only generates in the process of constructing the AK model. The results of case studies illustrate the accuracy and efficiency of the proposed method.
  • References (49)
  • Citations (1)
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References49
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#1Wanying YunH-Index: 9
#2Zhenzhou LuH-Index: 21
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#1Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
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© 2019 Elsevier Ltd Structural reliability analysis for rare failure events in the presence of hybrid uncertainties is a challenging task drawing increasing attentions in both academic and engineering fields. Based on the new imprecise stochastic simulation framework developed in the companion paper, this work aims at developing efficient methods to estimate the failure probability functions subjected to rare failure events with the hybrid uncertainties being characterized by imprecise probabili...
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#1Wanying Yun (NPU: Northwestern Polytechnical University)H-Index: 9
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Xian JiangH-Index: 8
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Probability density function (PDF)-based and failure probability (FP)-based moment-independent global sensitivity indices can commendably reflect the influence of model input on the whole distribution and partial distribution (or called FP) of model output respectively, yet how to efficiently and accurately estimate these two indices for guiding the engineering practice still remains an essential and challenging problem. In this paper, a novel PDF estimation based method is proposed, which equiv...
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#1Pengfei Wei (NPU: Northwestern Polytechnical University)H-Index: 11
#2Jingwen Song (NPU: Northwestern Polytechnical University)H-Index: 6
Last. Zhufeng Yue (NPU: Northwestern Polytechnical University)H-Index: 4
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Abstract Uncertainty propagation through the simulation models is critical for computational mechanics engineering to provide robust and reliable design in the presence of polymorphic uncertainty. This set of companion papers present a general framework, termed as non-intrusive imprecise stochastic simulation, for uncertainty propagation under the background of imprecise probability. This framework is composed of a set of methods developed for meeting different goals. In this paper, the performa...
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#1Wanying Yun (NPU: Northwestern Polytechnical University)H-Index: 9
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
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Abstract For efficiently estimating the fuzzy failure probability under the probability inputs and fuzzy state assumption (profust model) which generally includes three states, i.e., the absolute safety state, the full failure state and the fuzzy safety-failure transition state, a novel step-wise AK-MCS method is proposed. In the first step, the Kriging model is adaptively updated by U learning function to accurately recognize if the points in the sample pool are in the safety state or in the fa...
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#1Yicheng Zhou (NPU: Northwestern Polytechnical University)H-Index: 6
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Abstract Global sensitivity analysis, such as Sobol’ indices, plays an important role for quantifying the relative importance of random inputs to the response of complex model, and the estimation of Sobol’ indices is a challenging problem. In this paper, Bayesian Monte Carlo method is employed for developing a new technique to estimate the Sobol' indices with low computational cost. In the developing technique, the output response is expanded as the sum of different order components accurately, ...
21 CitationsSource
#1Wanying Yun (NPU: Northwestern Polytechnical University)H-Index: 9
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Xian JiangH-Index: 8
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Due to multiple implicit limit state functions needed to be surrogated, adaptive Kriging model for system reliability analysis with multiple failure modes meets a big challenge in accuracy and efficiency. In order to improve the accuracy of adaptive Kriging meta-model in system reliability analysis, this paper mainly proposes an improved AK-SYS by using a refined U learning function. The improved AK-SYS updates the Kriging meta-model from the most easily identifiable failure mode among the multi...
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#1Iason Papaioannou (TUM: Technische Universität München)H-Index: 10
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Abstract In applications of reliability analysis, the sensitivity of the probability of failure to design parameters is often crucial for decision-making. A common sensitivity measure is the partial derivative of the probability of failure with respect to the design parameter. If the design parameter enters the definition of the reliability problem through the limit-state function, i.e. the function defining the failure event, then the partial derivative is given by a surface integral over the l...
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#1Wanying Yun (NPU: Northwestern Polytechnical University)H-Index: 9
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
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Abstract To efficiently execute the variance-based global sensitivity analysis, the law of total variance in the successive intervals without overlapping is proved at first, on which an efficient space-partition sampling-based approach is subsequently proposed in this paper. Through partitioning the sample points of output into different subsets according to different inputs, the proposed approach can efficiently evaluate all the main effects concurrently by one group of sample points. In additi...
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#1Wanying Yun (NPU: Northwestern Polytechnical University)H-Index: 9
#2Zhenzhou Lu (NPU: Northwestern Polytechnical University)H-Index: 21
Last. Xian JiangH-Index: 8
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The importance sampling method is an extensively used numerical simulation method in reliability analysis. In this paper, a modification to the importance sampling method (ISM) is proposed, and the modified ISM divides the sample set of input variables into different subsets based on the contributive weight of the importance sample defined in this paper and the maximum super-sphere denoted by β-sphere in the safe domain defined by the truncated ISM. By this proposed modification, only samples wi...
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Abstract Current state-of-the-art methods for reliability updating with equality information transform this challenging problem into an inequality one by introducing an auxiliary random variable. However, the joint event of information and failure in the derived conditional probabilities is typically very rare, and therefore, very challenging to estimate. Moreover, updating the reliability as new information arrives requires reevaluation of the probability of the joint event, which involves larg...
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