Reliability‐based design optimization with dependent interval variables

Reliability‐based design optimization (RBDO) ensures design requirements are satisfied at required reliability levels in the presence of uncertainty. The recent RBDO methodologies can accommodate two types of uncertainty – aleatory type, represented by random variables, and epistemic type, represented by interval variables. However, only independent interval variables can be handled. The objective of this research is to introduce dependent interval variables into RBDO. The dependency of interval variables comes from equality and inequality constraints. With the intervals, the reliability is also an interval, and its lower bound is considered to preserve conservativeness. An efficient optimization method is developed to solve RBDO problems. The method is an extension of the existing framework of sequential optimization and reliability analysis with the inclusion of inequality constraints of interval variables. The new method is efficient because it decouples the optimization process from the process of reliability and interval analyses. The new method is applied to the RBDO of a slider mechanism with joint clearances, which are known as dependent interval variables. Copyright © 2012 John Wiley & Sons, Ltd.

[1]  A. M. Hasofer,et al.  Exact and Invariant Second-Moment Code Format , 1974 .

[2]  J. Chakraborty,et al.  Synthesis of mechanical error in linkages , 1975 .

[3]  R. Rackwitz,et al.  Structural reliability under combined random load sequences , 1978 .

[4]  Sanjay G. Dhande,et al.  Analysis and synthesis of mechanical error in path-generating linkages using a stochastic approach , 1987 .

[5]  A. K. Mallik,et al.  Mechanical error of a four-bar linkage coupler curve , 1987 .

[6]  Yan Zhang,et al.  Two Improved Algorithms for Reliability Analysis , 1995 .

[7]  Jaehoon Choi,et al.  Stochastic Linkage Modeling for Mechanical Error Analysis of Planar Mechanisms , 1998 .

[8]  Kyung K. Choi,et al.  A NEW STUDY ON RELIABILITY-BASED DESIGN OPTIMIZATION , 1999 .

[9]  Jianmin Zhu,et al.  Uncertainty analysis of planar and spatial robots with joint clearances , 2000 .

[10]  Y.-T. Wu,et al.  Safety-Factor Based Approach for Probability-Based Design Optimization , 2001 .

[11]  Xiaoping Du,et al.  Sequential Optimization and Reliability Assessment Method for Efficient Probabilistic Design , 2004, DAC 2002.

[12]  Wei Chen,et al.  An integrated framework for optimization under uncertainty using inverse Reliability strategy , 2004 .

[13]  Edward D. Arnheiter,et al.  The integration of lean management and Six Sigma , 2005 .

[14]  A. Sudjianto,et al.  Reliability-Based Design With the Mixture of Random and Interval Variables , 2005, DAC 2003.

[15]  Zissimos P. Mourelatos,et al.  A Single-Loop Approach for System Reliability-Based Design Optimization , 2006, DAC 2006.

[16]  L. Watson,et al.  An inverse-measure-based unilevel architecture for reliability-based design optimization , 2007 .

[17]  Jia Guo,et al.  Sequential optimization and reliability assessment for multidisciplinary systems design , 2008 .

[18]  Xiaoping Du,et al.  Saddlepoint Approximation for Sequential Optimization and Reliability Analysis , 2008 .

[19]  Sankaran Mahadevan,et al.  Design Optimization With System-Level Reliability Constraints , 2008 .

[20]  Jun Zhou,et al.  Design under Uncertainty using a Combination of Evidence Theory and a Bayesian Approach , 2008 .

[21]  Ikjin Lee,et al.  System Reliability-Based Design Optimization Using MPP-Based Dimension Reduction Method , 2008 .

[22]  Ming-June Tsai,et al.  Accuracy analysis of a multi-loop linkage with joint clearances , 2008 .

[23]  Xiaoping Du,et al.  Robust Mechanism synthesis with random and interval variables , 2009 .

[24]  Selçuk Erkaya,et al.  Optimization of transmission angle for slider-crank mechanism with joint clearances , 2009 .

[25]  K. Choi,et al.  System reliability-based design optimization using the MPP-based dimension reduction method , 2010 .

[26]  Christopher A. Mattson,et al.  Optimization of near-constant force springs subject to mating uncertainty , 2010 .

[27]  Xiaoping Du,et al.  Reliability Analysis for Multidisciplinary Systems with Random and Interval Variables , 2010 .

[28]  S. Azarm,et al.  Multi-Objective Robust Optimization Under Interval Uncertainty Using Online Approximation and Constraint Cuts , 2011 .

[29]  Xiaoping Du,et al.  Hybrid dimension reduction for mechanism reliability analysis with random joint clearances , 2011 .

[30]  Kuei-Yuan Chan,et al.  β-Pareto Set Prediction for Bi-Objective Reliability-Based Design Optimization , 2011 .