System Reliability-Based Design Optimization Under Tradeoff Between Reduction of Sampling Uncertainty and Design Shift

This paper presents a tradeoff between shifting design and controlling sampling uncertainty in system reliability-based design optimization (RBDO) using the Bayesian network. The sampling uncertainty is caused by a finite number of samples used in calculating the reliability of a component, and it propagates to the system reliability. A conservative failure probability is utilized to consider sampling uncertainty. In this paper, the sensitivity of a conservative system failure probability is derived with respect to the design change and the number of samples in a component using Bayesian network along with global sensitivity analysis (GSA). In the sensitivity analysis, GSA is used for local sensitivity calculation. The numerical results show that sampling uncertainty can significantly affect the conservative system reliability and needs to be controlled to achieve the desired level of system reliability. Numerical examples show that both shifting design and reducing sampling uncertainty are crucial in the system RBDO.

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

Journal of Mechanical Design ◽

10.1115/1.4000483 ◽

2009 ◽

Vol 132 (1) ◽

Cited By ~ 50

Author(s):

Tam H. Nguyen ◽

Junho Song ◽

Glaucio H. Paulino

Keyword(s):

Design Optimization ◽

Failure Probability ◽

System Reliability ◽

Loop System ◽

Probabilistic Constraints ◽

System Failure ◽

Reliability Based Design Optimization ◽

Single Loop ◽

Reliability Based Design ◽

Reliability Method

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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