Research Papers: Design Automation

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

[+] Author and Article Information
Sangjune Bae

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: sjune.bae@ufl.edu

Nam H. Kim

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: nkim@ufl.edu

Seung-gyo Jang

Agency for Defense Development,
Daejeon 305-600, South Korea
e-mail: Jsg4580@add.re.kr

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 12, 2018; final manuscript received October 17, 2018; published online January 11, 2019. Assoc. Editor: Ping Zhu.

J. Mech. Des 141(4), 041403 (Jan 11, 2019) (10 pages) Paper No: MD-18-1308; doi: 10.1115/1.4041859 History: Received April 12, 2018; Revised October 17, 2018

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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Cadini, F. , and Gioletta, A. , 2016, “ A Bayesian Monte Carlo-Based Algorithm for the Estimation of Small Failure Probabilities of Systems Affected by Uncertainties,” Reliab. Eng. Syst. Saf., 153, pp. 15–27. [CrossRef]
Howard, R. A. , 1988, “ Uncertainty About Probability: A Decision Analysis Perspective,” Risk Anal., 8(1), pp. 91–98. [CrossRef]
Mosleh, A. , and Bier, V. M. , 1996, “ Uncertainty About Probability: A Reconciliation With the Subjectivist Viewpoint,” IEEE Trans. on Syst., Man, and Cybern. Part A: Syst. and Hum., 26(3), pp. 303–310.
Reneke, J. A. , Wiecek, M. M. , Fadel, G. M. , Samson, S. , and Nowak, D. , 2010, “ Design Under Uncertainty: Balancing Expected Performance and Risk,” ASME J. Mech. Des., 132(11), p. 111009. [CrossRef]
Hofer, E. , Kloos, M. , Krzykacz-Hausmann, B. , Peschke, J. , and Woltereck, M. , 2002, “ An Approximate Epistemic Uncertainty Analysis Approach in the Presence of Epistemic and Aleatory Uncertainties,” Reliab. Eng. Syst. Saf., 77(3), pp. 229–238. [CrossRef]
Choi, J. , An, D. , and Won, J. , 2010, “ Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method,” ASME J. Mech. Des., 132(5), p. 051003. [CrossRef]
Nannapaneni, S. , and Mahadevan, S. , 2016, “ Reliability Analysis Under Epistemic Uncertainty,” Reliab. Eng. Syst. Saf., 155, pp. 9–20. [CrossRef]
Bae, S. , Kim, N. H. , Park, C. , and Kim, Z. , 2017, “ Confidence Interval of Bayesian Network and Global Sensitivity Analysis,” AIAA J., 55(11), pp. 3916–3924. [CrossRef]
Bae, S. , Kim, N. H. , and Jang, S. G. , 2018, “ Reliability-Based Design Optimization Under Sampling Uncertainty: Shifting Design Versus Shaping Uncertainty,” Struct. Multidiscip. Optim., 57(5), pp. 1845–1855. [CrossRef]
Grigoriu, M. , 1982, “ Methods for Approximate Reliability Analysis,” Struct. Saf., 1(2), pp. 155–165. [CrossRef]
Au, S. K. , and Beck, J. L. , 2001, “ Estimation of Small Failure Probabilities in High Dimensions by Subset Simulation,” Probab. Eng. Mech., 16(4), pp. 263–277. [CrossRef]
Sheather, S. J. , and Jones, M. C. , 1991, “ A Reliable Data-Based Bandwidth Selection Method for Kernel Density Estimation,” J. R. Stat. Soc. Ser. B Stat. Methodol., 53(3), pp. 683–690.
Jensen, F. V. , and Nielsen, T. D. , 2007, Bayesian Networks and Decision Graphs, Springer Science & Business Media, New York.
Hu, Z. , and Mahadevan, S. , 2018, “ Bayesian Network Learning for Data-Driven Design,” J. Risk Uncertain. Eng. Syst. Part B Mech. Eng., 4(4), p. 041002.
Liang, C. , and Mahadevan, S. , 2016, “ Multidisciplinary Optimization Under Uncertainty Using Bayesian Network,” SAE Int. J. Mater. Manuf., 9(2), pp. 419–429.
Liang, C. , and Mahadevan, S. , 2017, “ Pareto Surface Construction for Multi-Objective Optimization Under Uncertainty,” Struct. Multidiscip. Optim., 55(5), pp. 1865–1882. [CrossRef]
Jin, R. , Chen, W. , and Sudjianto, A. , 2004, “ Analytical Metamodel-Based Global Sensitivity Analysis and Uncertainty Propagation for Robust Design,” SAE Tech. Paper No. 2004-01–0429.
Fraser, D. A. S. , 1958, Statistics-An Introduction, John Wiley and Sons, New York, pp. 124–125
Picheny, V. , Kim, N. H. , and Haftka, R. T. , 2010, “ Application of Bootstrap Method in Conservative Estimation of Reliability With Limited Samples,” Struct. Multidiscip. Optim., 41(2), pp. 205–217. [CrossRef]
Mahadevan, S. , Zhang, R. , and Smith, N. , 2001, “ Bayesian Networks for System Reliability Reassessment,” Struct. Saf., 23(3), pp. 231–251. [CrossRef]
Bichon, B. J. , McFarland, J. M. , and Mahadevan, S. , 2011, “ Efficient Surrogate Models for Reliability Analysis of Systems With Multiple Failure Modes,” Reliab. Eng. Syst. Saf., 96(10), pp. 1386–1395. [CrossRef]
Saltelli, A. , 2004, “ Global Sensitivity Analysis: An Introduction,” 4th International Conference on Sensitivity Analysis of Model Output (SAMO'™04), Santa Fe, NM, Mar. 8–11. https://library.lanl.gov/cgi-bin/getdoc?event=SAMO2004&document=samo04-proceedings.pdf
Jiang, Z. , Chen, W. , and German, B. J. , 2016, “ Multidisciplinary Statistical Sensitivity Analysis Considering Both Aleatory and Epistemic Uncertainties,” AIAA J., 54(4), pp. 1326–1338. [CrossRef]
Chen, W. , Jin, R. , and Sudjianto, A. , 2005, “ Analytical Variance-Based Global Sensitivity Analysis in Simulation-Based Design Under Uncertainty,” ASME J. Mech. Des., 127(5), pp. 875–886. [CrossRef]
Lee, I. , Choi, K. K. , and Zhao, L. , 2011, “ Sampling-Based RBDO Using the Stochastic Sensitivity Analysis and Dynamic Kriging Method,” Struct. Multidiscip. Optim., 44(3), pp. 299–317. [CrossRef]
Jang, S. G. , Lee, H. N. , and Oh, J. Y. , 2014, “ Performance Modeling of a Pyrotechnically Actuated Pin Puller,” Int. J. Aeronaut. Space Sci., 15(1), pp. 102–111. [CrossRef]


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Fig. 1

Options to satisfy reliability constraint with conservative probability of failure: (a) living with uncertainty and (b) shaping uncertainty

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Fig. 2

Example of three-node Bayesian network

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Fig. 3

Two-node Bayesian network

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Fig. 4

Bayesian network of PMD system

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Fig. 6

Failure modes in Pyrolock

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Fig. 7

Motion of piston in each stage



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