Abstract

The reliability-based sensitivity analysis requires to recursively evaluate a multivariate structural model for many failure probability levels. This is in general a computationally intensive task due to irregular integrations used to define the structural failure probability. In this regard, the performance function is first approximated by using the multiplicative dimensional reduction method in this paper, and an approximation for the reliability-based sensitivity index is derived based on the principle of maximum entropy and the fractional moment. Three examples in the literature are presented to examine the performance of this entropy-based approach against the brute-force Monte-Carlo simulation method. Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model.

Highlights

  • In recent years, advanced computational technologies allow to develop detailed simulation models for virtual analysis and design optimization of structural systems

  • Results have shown that the multiplicative dimensional reduction based entropy approach is rather efficient and able to provide reliability estimation results for the reliability-based sensitivity analysis of a multivariate structural model

  • The paper presents an effective approach for the reliability-based sensitivity analysis based on the principle of maximum entropy (MaxEnt) and the fractional moment

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Summary

Introduction

In recent years, advanced computational technologies allow to develop detailed simulation models for virtual analysis and design optimization of structural systems. The reliability-based sensitivity index pays major attention on the relation between distribution parameters and the structural failure probability In this respect, the application of the variance-based sensitivity result will be rather limited, if the response distribution function of a structural model is highly skewed [17]. Since the reliability-based sensitivity analysis is always limited to a predefined level of the structural failure probability, one way to determine the overall sensitivity result is to repeat the whole simulation procedure many times for a various realizations of the structural failure probability value, which is referred to as the distribution-based sensitivity analysis in the literature [21] To this end, the paper presents an effective approach for the reliability-based sensitivity analysis based on the MaxEnt approach.

Measures for the Probabilistic Sensitivity Analysis
The Moment-Based Sensitivity Measure
The Reliability-Based Sensitivity Measure
An Entropy-Based Approach for the Reliability-Based Sensitivity Analysis
A Brief Summary on the Multiplicative Dimensional Reduction Method
Fractional Moments and the MaxEnt Distribution
The Proposed M-DRM Approach for the Moment-Based Sensitivity Index
The Proposed Approach for the Reliability-Based Sensitivity Analysis
Numerical Examples
Reliability-Based Sensitivity Analysis A Cantilever Tube Structure
Reliability-Based Sensitivity Analysis of a Cracked Membrane
Conclusions
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