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Research Papers: Design Automation

Model-Based Reliability Analysis With Both Model Uncertainty and Parameter Uncertainty

[+] Author and Article Information
Zhimin Xi

Mem. ASME
Department of Industrial and
Systems Engineering,
Rutgers University—New Brunswick,
96 Frelinghuysen Road,
Piscataway, NJ 08854
e-mail: zhimin.xi@rutgers.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 8, 2018; final manuscript received November 3, 2018; published online January 11, 2019. Assoc. Editor: Nam H. Kim.

J. Mech. Des 141(5), 051404 (Jan 11, 2019) (11 pages) Paper No: MD-18-1618; doi: 10.1115/1.4041946 History: Received August 08, 2018; Revised November 03, 2018

Model-based reliability analysis may not be practically useful if reliability estimation contains uncontrollable errors. This paper addresses potential reliability estimation errors from model bias together with model parameters. Given three representative scenarios, reliability analysis strategies with representative methods are proposed. The pros and cons of these strategies are discussed and demonstrated using a tank storage problem based on the finite element model with different fidelity levels. It is found in this paper that the confidence-based reliability analysis considering epistemic uncertainty modeling for both model bias and model parameters can make reliability estimation errors controllable with less conservativeness compared to the direct reliability modeling using the Bayesian approach.

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Figures

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Fig. 1

Bias model construction and CDF comparison between the high-fidelity model and the low-fidelity model with bias correction: (a) bias model with 30 samples and (b) CDF comparison with known parameter distributions

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Fig. 2

Reliability analysis results for scenario #1 using strategy A: (a) PDF comparison for T, (b) PDF comparison for P, (c) CDF comparison, and (d) reliability prediction errors

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Fig. 3

Reliability analysis results for scenario #1 using strategy B: (a) PDF comparison for T, (b) PDF comparison for P, (c) CDF comparison for maximum stress, and (d) reliability estimation errors

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Fig. 4

Reliability analysis results for scenario #1 using strategy C: (a) reliability distributions versus true reliability and (b) reliability prediction errors

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Fig. 5

Bias model construction and CDF comparison with known parameter distributions for scenario #2: (a) bias model with five samples and (b) CDF comparison with known parameter distributions

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Fig. 6

Reliability analysis results for scenario #2 using strategy A: (a) PDF comparison for T, (b) PDF comparison for P, (c)CDF comparison, and (d) reliability estimation errors

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Fig. 7

Reliability analysis results for scenario #2 using strategy B: (a) PDF comparison for T, (b) PDF comparison for P, (c)CDF comparison for maximum stress, and (d) reliability estimation versus true reliability

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Fig. 8

Reliability analysis results for scenario #2 using strategy C: (a) reliability distributions versus true reliability and (b)reliability estimations with 95% confidence versus true reliability

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Fig. 9

Reliability analysis results for scenario #3 using strategy B: (a) PDF comparison for T, (b) PDF comparison for P, (c) CDF comparison and five random stress responses for bias calibration, and (d) reliability estimation with 95% confidence versus true reliability

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