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Research Papers: Design Automation

A High-Dimensional Reliability Analysis Method for Simulation-Based Design Under Uncertainty

[+] Author and Article Information
Mohammad Kazem Sadoughi

Mem. ASME
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: sadoughi@iastate.edu

Meng Li

Mem. ASME
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: meng@iastate.edu

Chao Hu

Mem. ASME
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011;
Department of Electrical and
Computer Engineering,
Iowa State University,
Ames, IA 50011
e-mails: chaohu@iastate.edu; huchaostu@gmail.com

Cameron A. MacKenzie

Department of Industrial and
Manufacturing Systems Engineering,
Iowa State University,
Ames, IA 50011
e-mail: camacken@iastate.edu

Soobum Lee

Mem. ASME
Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
Baltimore, MD 21250
e-mail: sblee@umbc.edu

Amin Toghi Eshghi

Mem. ASME
Department of Mechanical Engineering,
University of Maryland,
Baltimore County,
Baltimore, MD 21250
e-mail: amint1@umbc.edu

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received August 17, 2017; final manuscript received February 13, 2018; published online April 25, 2018. Assoc. Editor: Nam H. Kim.

J. Mech. Des 140(7), 071401 (Apr 25, 2018) (12 pages) Paper No: MD-17-1565; doi: 10.1115/1.4039589 History: Received August 17, 2017; Revised February 13, 2018

Reliability analysis involving high-dimensional, computationally expensive, highly nonlinear performance functions is a notoriously challenging problem in simulation-based design under uncertainty. In this paper, we tackle this problem by proposing a new method, high-dimensional reliability analysis (HDRA), in which a surrogate model is built to approximate a performance function that is high dimensional, computationally expensive, implicit, and unknown to the user. HDRA first employs the adaptive univariate dimension reduction (AUDR) method to construct a global surrogate model by adaptively tracking the important dimensions or regions. Then, the sequential exploration–exploitation with dynamic trade-off (SEEDT) method is utilized to locally refine the surrogate model by identifying additional sample points that are close to the critical region (i.e., the limit-state function (LSF)) with high prediction uncertainty. The HDRA method has three advantages: (i) alleviating the curse of dimensionality and adaptively detecting important dimensions; (ii) capturing the interactive effects among variables on the performance function; and (iii) flexibility in choosing the locations of sample points. The performance of the proposed method is tested through three mathematical examples and a real world problem, the results of which suggest that the method can achieve an accurate and computationally efficient estimation of reliability even when the performance function exhibits high dimensionality, high nonlinearity, and strong interactions among variables.

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Figures

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Fig. 1

A schematic comparison between squared exponential kernel and additive kernel in a 2D space

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Fig. 2

Overall flowchart of the proposed HDRA method

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Fig. 3

A comparison of the sampling strategies in classic UDR (a) and AUDR (b) for the 2D mathematical example in Eq. (16)

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Fig. 4

Reliability errors at different levels of nonlinearity, b, for Example 1

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Fig. 5

Reliability errors by different methods at different reliability levels

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Fig. 6

Reliability error versus number of input variables (or input dimension) for UDR, SEEDT and HDRA in Example 3

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Fig. 7

Components of a piezoelectric energy harvester (cantilever-type) (Reprinted by Permission of SAGE Publications, Ltd. @ 2017 [36]

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Fig. 8

Comparison of reliability levels estimated by HDRA and MCS at different P0 levels. The widths of error bars are ± one standard deviation in reliability estimates. For the ease of visualization, the error bars by UDR and SEEDT are slightly shifted along the x-axis to the left and right, respectively.

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