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Research Papers

Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications

[+] Author and Article Information
Tam H. Nguyen

Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801tnguyen3@illinois.edu

Junho Song1

Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801junho@illinois.edu

Glaucio H. Paulino

Department of Civil and Environmental Engineering, University of Illinois, Urbana, IL 61801paulino@illinois.edu

1

Corresponding author.

J. Mech. Des 132(1), 011005 (Dec 17, 2009) (11 pages) doi:10.1115/1.4000483 History: Received January 19, 2009; Revised October 13, 2009; Published December 17, 2009; Online December 17, 2009

This paper proposes a single-loop system reliability-based design optimization (SRBDO) approach using the recently developed matrix-based system reliability (MSR) method. A single-loop method was employed to eliminate the inner-loop of SRBDO that evaluates probabilistic constraints. The MSR method enables us to compute the system failure probability and its parameter sensitivities efficiently and accurately through convenient matrix calculations. The SRBDO/MSR approach proposed in this paper is applicable to general systems including series, parallel, cut-set, and link-set system events. After a brief overview on SRBDO algorithms and the MSR method, the SRBDO/MSR approach is introduced and demonstrated by three numerical examples. The first example deals with the optimal design of a combustion engine, in which the failure is described as a series system event. In the second example, the cross-sectional areas of the members of a statically indeterminate truss structure are determined for minimum total weight with a constraint on the probability of collapse. In the third example, the redistribution of the loads caused by member failures is considered for the truss system in the second example. The results based on different optimization approaches are compared for further investigation. Monte Carlo simulation is performed in each example to confirm the accuracy of the system failure probability computed by the MSR method.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figure 1

Flowchart of the proposed SRBDO/MSR algorithm

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Figure 2

A six-member indeterminate truss example

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Figure 3

Conditional probability importance measures of the truss members

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Figure 4

Component failure events defined for the original system and systems with failed members

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Figure 5

Objective functions versus correlation between member yield strengths

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