A new kind of regional importance measure of the input variable and its state dependent parameter solution

Li, Luyi; Lü, Zhenzhou; Hu, JiXiang

doi:10.1016/j.ress.2014.03.008

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…and failure event F = {x|g(x) ≤ 0}. Then, the definition of CFP can be expressed as following (7) by the probability product principle [19], [20].…”

Section: B a Concise And Easily Estimated Form Of The Cfp Plot Transmentioning

confidence: 99%

“…As can be seen in ( 7), only the conditional probability of x i |x i ∈ −∞, F −1 i (q) on the failure domain F = {x|g(x) ≤ 0} is required, which can be easily estimated by the sampling based methods such as MCS and IS method. In the following sections, MCS and IS are organized to estimate the CFP plot shown in (7).…”

Section: B a Concise And Easily Estimated Form Of The Cfp Plot Transmentioning

confidence: 99%

“…Millwater et al [6] presented a localized probabilistic sensitivity method to detect the critical region of an input probability density function (PDF). Li et al [7] proposed two new regional importance measures (RIMs), i.e., ''contribution to variance of conditional mean (CVCM)'' and ''contribution to mean of conditional mean (CMCM)'', these two new RIMs are proved to provide more information and be more stable than the existing RIMs. Wei et al [2] explored the moment-independent regional importance on the delta index proposed by Borgonovo [8].…”

Section: Introductionmentioning

confidence: 99%

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

Lei

Lü

et al. 2019

IEEE Access

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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.

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“…and failure event F = {x|g(x) ≤ 0}. Then, the definition of CFP can be expressed as following (7) by the probability product principle [19], [20].…”

Section: B a Concise And Easily Estimated Form Of The Cfp Plot Transmentioning

confidence: 99%

Section: B a Concise And Easily Estimated Form Of The Cfp Plot Transmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Lei

Lü

et al. 2019

IEEE Access

Self Cite

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show abstract

“…They base their approach on gradients at multiple points in the input space. Li et al (2014) and Wei et al (2014) consider measures of regional importance which evaluate the impact of inputs with respect to reduced ranges of the individual input space while keeping the input space of the remaining variables global. Similar to our method, this results in sensitivity functions over the input space.…”

Section: Introductionmentioning

confidence: 99%

Support indices: Measuring the effect of input variables over their supports

Fruth

Roustant

Kuhnt

2019

Reliability Engineering & System Safety

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Two new sensitivity indices are presented which give an original solution to the question in sensitivity analysis of how to determine regions within the input space for which the model variation is high. The indices, as functions over the input domain, give insight into the local influence of input variables over the whole domain when the other variables lie in the global domain. They can serve as an informative extension to a standard analysis and in addition are especially helpful in the specification of the input domain, a critical, but often vaguely handled issue in sensitivity analysis. In the usual framework of independent continuous input variables, we present theoretical results that show an asymptotic connection between the presented indices and Sobol' indices, valid for general probability distribution functions. Finally, we show how the indices can be successfully applied on analytical examples and on a real application.

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“…This CFP plot not only provides the sensitivity information that the traditional GRS provides, but also measures the contribution of the specific region of model input variable to failure probability, which the traditional GRS cannot provide. That is why there has been growing interest in the CFP recently [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

Zhang

et al. 2018

Energies

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Abstract:The application of reliability sensitivity analysis (RSA) to the high voltage direct current (HVDC) transmission systems is one of the hot topics in the future. A regional RSA method, the contribution to failure probability (CFP) plot, is investigated in this paper. This CFP plot contains both aleatory and epistemic uncertain variables modeled as random variables by probability theory and interval variables by evidence theory, respectively. A surrogate model of second-level limit state function needs to be established for each joint focal element (JFE), which is a time-consuming process. Additionally, an excessive number of Monte Carlo simulations (MCS) and optimizations may exceed the computing power of modern computers. In order to deal with the above problems and further decrease the computational cost, a more effective CFP calculation method under the framework of random-evidence hybrid reliability analysis is proposed. Three important improvements in the proposed method make the calculation of CFP more efficient and easy to implement. Firstly, an active learning kriging (ALK) based on the symbol prediction idea is employed to directly establish a surrogate model rather than a second-level limit state function with fewer function calls, which greatly simplifies construction of the model. Secondly, a random set-based Monte Carlo simulation (RS-MCS) is used to handle the issue of oversized optimization caused by too many JFEs. Thirdly, for further reducing the size of optimizations and improving the efficiency of the CFP calculation, a Karush-Kuhn-Tucker-based optimization (KKTO) method is recommended in the proposed method to solve the extreme value of performance function. A numerical example and an engineering example were studied to verify the accuracy, effectiveness and practicality of the proposed method. It can be seen from the results that regardless of whether it is modeling or computational efficiency, the proposed method is better than the original method.

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A new kind of regional importance measure of the input variable and its state dependent parameter solution

Cited by 6 publications

References 20 publications

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

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

Support indices: Measuring the effect of input variables over their supports

An Efficient Regional Sensitivity Analysis Method Based on Failure Probability with Hybrid Uncertainty

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