Reliability-based Robust Design Optimization Research Articles

Reliability based robust design optimization of steel structures

In this work the uncertainty of a structural system is taken into account in the framework of a structural Reliability based Robust Design Optimization (RRDO) formulation where probabilistic constraints are incorporated into the robust design optimization formulation. A robust design optimization problem is formulated as a multi-criteria optimization problem. The Pareto front representing the solution of the RRDO problem is composed by designs with a state of robustness, since their performance is the least sensitive to the variability of the uncertain variables. The cross section dimensions together with other structural parameters, such as the modulus of elasticity, the yield stress and the applied loading, are considered as random variables. For the solution of the RRDO problem, the non-dominant Cascade Evolutionary Algorithm is employed combined with a weighted Tchebycheff metric.

Dimension reduction method for reliability-based robust design optimization

In reliability-based robust design optimization (RBRDO) formulation, the product quality loss function is minimized subject to probabilistic constraints. Since the quality loss function is expressed in terms of the first two statistical moments, mean and variance, three methods have been recently proposed to accurately and efficiently estimate the moments: the univariate dimension reduction method (DRM), performance moment integration (PMI) method, and percentile difference method (PDM). In this paper, a reliability-based robust design optimization method is developed using DRM and compared to PMI and PDM for accuracy and efficiency. The numerical results show that DRM is effective when the number of random variables is small, whereas PMI is more effective when the number of random variables is relatively large.

Performance Moment Integration (PMI) Method for Quality Assessment in Reliability-Based Robust Design Optimization#

ABSTRACT The reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability and robustness. The reliability constraints deal with the probability of failures, while the robustness minimizes the product quality loss. In general, the product quality loss is described by using the first two statistical moments: mean and standard deviation. In this paper, a performance moment integration (PMI) method is proposed by using a three-level numerical integration on the output range to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the enriched performance measure approach (PMA+) and its numerical method, enhanced hybrid-mean value (HMV+) method, are used. New formulations of reliability-based robust design optimization are presented for three different types of robustness objectives, such as smaller-the-better, larger-the-better, and nominal-the-best types. Examples that include an engine rubber gasket are used to demonstrate the effectiveness of reliability-based robust design optimization using the proposed PMI method for different types of robust objective.