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Technical Briefs

A Modified Reliability Index Approach for Reliability-Based Design Optimization

[+] Author and Article Information
Po Ting Lin

 Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854potinglin223@gmail.com

Hae Chang Gea

 Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854gea@rci.rutgers.edu

Yogesh Jaluria

 Department of Mechanical and Aerospace Engineering, Rutgers, The State University of New Jersey, Piscataway, NJ 08854jaluria@jove.rutgers.edu

J. Mech. Des 133(4), 044501 (May 02, 2011) (7 pages) doi:10.1115/1.4003842 History: Received November 17, 2010; Revised March 14, 2011; Accepted March 16, 2011; Published May 02, 2011; Online May 02, 2011

Reliability-based design optimization (RBDO) problems have been intensively studied for many decades. Since Hasofer and Lind [1974, “Exact and Invariant Second-Moment Code Format,” J. Engrg. Mech. Div., 100 (EM1), pp. 111–121] defined a measure of the second-moment reliability index, many RBDO methods utilizing the concept of reliability index have been introduced as the reliability index approach (RIA). In the RIA, reliability analysis problems are formulated to find the reliability indices for each performance constraint and the solutions are used to evaluate the failure probability. However, the traditional RIA suffers from inefficiency and convergence problems. In this paper, we revisited the definition of the reliability index and revealed the convergence problem in the traditional RIA. Furthermore, a new definition of the reliability index is proposed to correct this problem and a modified reliability index approach is developed based on this definition. The strategies to solve RBDO problems with non-normally distributed design variables by the modified RIA are also investigated. Numerical examples using both the traditional and modified RIAs are compared and discussed.

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Figures

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Figure 1

PDF of normal distribution X(d, σ); xa is the active point

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Figure 2

PDF of standard normal distribution U with feasible mean

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Figure 3

PDF of standard normal distribution U with infeasible mean

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Figure 4

Iteration process of example 1 using MRIA; d (0)  = (5,5)

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Figure 5

Iteration process of example 1 using TRIA; d (0)  = (2,2)

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Figure 6

Iteration process of example 1 using MRIA; d (0)  = (2,2)

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Figure 7

Iteration process of example 2; d (0)  = (5,5)

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Figure 8

Iteration process of example 3; d (0)  = (5,5)

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