An Investigation of Nonlinearity of Reliability-Based Design Optimization Approaches
- 1 October 2003
- journal article
- Published by ASME International in Journal of Mechanical Design
- Vol. 126 (3), 403-411
- https://doi.org/10.1115/1.1701880
Abstract
Because deterministic optimum designs obtained without taking uncertainty into account could lead to unreliable designs, a reliability-based approach to design optimization is preferable using a Reliability-Based Design Optimization (RBDO) method. A typical RBDO process iteratively carries out a design optimization in an original random space (X-space) and a reliability analysis in an independent and standard normal random space (U-space). This process requires numerous nonlinear mappings between X- and U-spaces for various probability distributions. Therefore, the nonlinearity of the RBDO problem will depend on the type of distribution of random parameters, since a transformation between X- and U-spaces introduces additional nonlinearity into the reliability-based performance measures evaluated during the RBDO process. The evaluation of probabilistic constraints in RBDO can be carried out in two ways: using either the Reliability Index Approach (RIA), or the Performance Measure Approach (PMA). Different reliability analysis approaches employed in RIA and PMA result in different behaviors of nonlinearity for RIA and PMA in the RBDO process. In this paper, it is shown that RIA becomes much more difficult to solve for non-normally distributed random parameters because of the highly nonlinear transformations that are involved. However, PMA is rather independent of probability distributions because it only has a small involvement with a nonlinear transformation.Keywords
This publication has 12 references indexed in Scilit:
- Hybrid Analysis Method for Reliability-Based Design OptimizationJournal of Mechanical Design, 2003
- Reliability-based structural optimization using improved two-point adaptive nonlinear approximationsFinite Elements in Analysis and Design, 1998
- A mixed design approach for probabilistic structural durabilityStructural and Multidisciplinary Optimization, 1997
- Reliability-based optimization in structural engineeringStructural Safety, 1994
- Computational methods for efficient structural reliability and reliability sensitivity analysisAIAA Journal, 1994
- Optimization algorithms for structural reliabilityStructural Safety, 1991
- Advanced probabilistic structural analysis method for implicit performance functionsAIAA Journal, 1990
- Non-Normal Dependent Vectors in Structural SafetyJournal of the Engineering Mechanics Division, 1981
- Structural reliability under combined random load sequencesComputers & Structures, 1978
- Exact and Invariant Second-Moment Code FormatJournal of the Engineering Mechanics Division, 1974