Research Papers

A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization

[+] Author and Article Information
Zequn Wang

e-mail: zxwang5@wichita.edu

Pingfeng Wang

e-mail: pingfeng.wang@wichita.edu
Department of Industrial and Manufacturing Engineering,
Wichita State University, Wichita, KS 67260

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received May 12, 2012; final manuscript received October 10, 2012; published online November 15, 2012. Assoc. Editor: Zissimos P. Mourelatos.

J. Mech. Des 134(12), 121007 (Nov 15, 2012) (14 pages) doi:10.1115/1.4007931 History: Received May 12, 2012; Revised October 10, 2012

A primary concern in practical engineering design is ensuring high system reliability throughout a product's lifecycle, which is subject to time-variant operating conditions and component deteriorations. Thus, the capability of dealing with time-dependent probabilistic constraints in reliability-based design optimization (RBDO) is of vital importance in practical engineering design applications. This paper presents a nested extreme response surface (NERS) approach to efficiently carry out time-dependent reliability analysis and determine the optimal designs. This approach employs the kriging model to build a nested response surface of time corresponding to the extreme value of the limit state function. The efficient global optimization (EGO) technique is integrated with the NERS approach to extract the extreme time responses of the limit state function for any given system design. An adaptive response prediction and model maturation (ARPMM) mechanism is developed based on the mean square error (MSE) to concurrently improve the accuracy and computational efficiency of the proposed approach. With the nested response surface of time, the time-dependent reliability analysis can be converted into the time-independent reliability analysis, and existing advanced reliability analysis and design methods can be used. The NERS approach is compared with existing time-dependent reliability analysis approaches and integrated with RBDO for engineered system design with time-dependent probabilistic constraints. Two case studies are used to demonstrate the efficacy of the proposed NERS approach.

Copyright © 2012 by ASME
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Fig. 1

Time-dependent performance function

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Fig. 2

Global extreme response surface of time

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Fig. 3

Flowchart of NERS approach for reliability analysis

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Fig. 4

Time-dependent limit state of mathematical example

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Fig. 5

(a) First EGO iteration for extreme response identification and (b) ninth EGO iteration for extreme response identification

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Fig. 6

Flowchart of ARPMM mechanism

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Fig. 7

Instantaneous limit states for time interval [0, 5]

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Fig. 8

Initial NTPM for mathematical example

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Fig. 9

(a) Mean square error, e(x) for initial NTPM and (b) mean square error, e(x) for updated NTPM

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Fig. 10

Flowchart of time-dependent RBDO with NERS approach

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Fig. 11

Limit state functions

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Fig. 12

Reliabilities of constraints in iterative RBDO process

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Fig. 13

Schematic of roller clutch

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Fig. 14

(a) Cost function during iterative design process and (b) constraints reliabilities during iterative design process




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