Importance analysis on the failure probability of the fuzzy and random system and its state dependent parameter solution

For the structural systems with both epistemic and aleatory uncertainties, in order to analyze the effects of different regions of epistemic parameters on failure probability, two regional importance measures (RIMs) are firstly proposed, i.e. contribution to mean of failure probability (CMFP) and contribution to variance of failure probability (CVFP), and their properties are analyzed and verified. Then, to analyze the effect of different regions of the epistemic parameters on their corresponding first-order variance (i.e. main effect) in the Sobol’s variance decomposition, another RIM is proposed which is named as contribution to variance of conditional mean of failure probability (CVCFP). The proposed CVCFP is then extended to define another RIM named as contribution to mean of conditional mean of failure probability, i.e. CMCFP, to measure the contribution of regions of epistemic parameters to mean of conditional mean of failure probability. For the problem that the computational cost for calculating the conditional mean of failure probability may be too large to be accepted, the state dependent parameter (SDP) method is introduced to estimate CVCFP and CMCFP. Several examples are used to demonstrate the effectiveness of the proposed RIMs and the efficiency and accuracy of the SDP-based method are also demonstrated by the examples.

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Regional importance effect analysis of the input variables on failure probability and its state dependent parameter estimation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2013.09.001 ◽

2013 ◽

Vol 66 (10) ◽

pp. 2075-2091 ◽

Cited By ~ 5

Author(s):

Luyi Li ◽

Zhenzhou Lu

Keyword(s):

Parameter Estimation ◽

Failure Probability ◽

Effect Analysis ◽

State Dependent ◽

Dependent Parameter ◽

Input Variables

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State dependent parameter method for importance analysis in the presence of epistemic and aleatory uncertainties

Science China Technological Sciences ◽

10.1007/s11431-012-4842-5 ◽

2012 ◽

Vol 55 (6) ◽

pp. 1608-1617 ◽

Cited By ~ 9

Author(s):

LuYi Li ◽

ZhenZhou Lu ◽

Wei Li

Keyword(s):

Parameter Method ◽

State Dependent ◽

Importance Analysis ◽

Dependent Parameter ◽

State Dependent Parameter Method

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A modified variance-based importance measure and its solution by state dependent parameter

Proceedings of the Institution of Mechanical Engineers Part O Journal of Risk and Reliability ◽

10.1177/1748006x12461242 ◽

2012 ◽

Vol 227 (1) ◽

pp. 3-15

Author(s):

Wenbin Ruan ◽

Zhenzhou Lu ◽

Longfei Tian

Keyword(s):

The State ◽

Importance Measure ◽

Parameter Method ◽

Analysis Method ◽

Output Response ◽

State Dependent ◽

Importance Analysis ◽

Dependent Parameter ◽

Input Variables ◽

State Dependent Parameter Method

To overcome the disadvantage of traditional variance-based importance measures, i.e. the effects of different realizations of input variables on output response may mutually counteract each other, a modified variance-based importance measure is presented for importance analysis of the input variables. The proposed measure analyses the importance of the input variables comprehensively in terms of the expectation and variance of the output response. Compared with the traditional variance-based importance analysis method, the modified importance measure indices not only reflect the old one, but also provide a very useful supplement for it. Furthermore, combined with the advantages of the state dependent parameter model, a solution to the proposed measure indices is provided. Several examples are introduced to show that the modified importance measure is more comprehensive and reasonable, and the solution based on the state dependent parameter method can improve computational efficiency considerably with acceptable precision.

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