Enriched Performance Measure Approach Research Articles

Enriched Performance Measure Approach for Efficient Reliability-Based Electromagnetic Designs

This paper proposes an enriched performance measure approach to significantly improve computational efficiency of reliability-based design optimization when applied to electromagnetic products. To achieve the goal, three improvements are made over the original performance measure approach: 1) as a way to launch reliability-based design optimization at a deterministic optimum; 2) as a probabilistic feasibility check; and 3) as a fast reliability analysis under the condition of design closeness. Each of the improvements makes a unique contribution to improving numerical efficiency while maintaining stability in the design optimization process. Finally, the proposed method is tested with a mathematical model and the TEAM Workshop Problem 22, and three improvement effects on the reliability-based optimization process are investigated from a numerical efficiency and accuracy point of view.

Inverse analysis method using MPP-based dimension reduction for reliability-based design optimization of nonlinear and multi-dimensional systems

There are two commonly used analytical reliability analysis methods: linear approximation – first-order reliability method (FORM), and quadratic approximation – second-order reliability method (SORM), of the performance function. The reliability analysis using FORM could be acceptable in accuracy for mildly nonlinear performance functions, whereas the reliability analysis using SORM may be necessary for accuracy of nonlinear and multi-dimensional performance functions. Even though the reliability analysis using SORM may be accurate, it is not as much used for probability of failure calculation since SORM requires the second-order sensitivities. Moreover, the SORM-based inverse reliability analysis is rather difficult to develop. This paper proposes an inverse reliability analysis method that can be used to obtain accurate probability of failure calculation without requiring the second-order sensitivities for reliability-based design optimization (RBDO) of nonlinear and multi-dimensional systems. For the inverse reliability analysis, the most probable point (MPP)-based dimension reduction method (DRM) is developed. Since the FORM-based reliability index ( β) is inaccurate for the MPP search of the nonlinear performance function, a three-step computational procedure is proposed to improve accuracy of the inverse reliability analysis: probability of failure calculation using constraint shift, reliability index update, and MPP update. Using the three steps, a new DRM-based MPP is obtained, which estimates the probability of failure of the performance function more accurately than FORM and more efficiently than SORM. The DRM-based MPP is then used for the next design iteration of RBDO to obtain an accurate optimum design even for nonlinear and/or multi-dimensional system. Since the DRM-based RBDO requires more function evaluations, the enriched performance measure approach (PMA+) with new tolerances for constraint activeness and reduced rotation matrix is used to reduce the number of function evaluations.

Integration of Possibility-Based Optimization and Robust Design for Epistemic Uncertainty

In practical engineering applications, there exist two different types of uncertainties: aleatory and epistemic uncertainties. This study attempts to develop a robust design optimization with epistemic uncertainty. For epistemic uncertainties, a possibility-based design optimization improves the failure rate, while a robust design optimization minimizes the product quality loss. In general, product quality loss is described using the first two statistical moments for aleatory uncertainty: mean and standard deviation. However, there is no metric for product quality loss defined when having epistemic uncertainty. This paper first proposes a new metric for product quality loss with epistemic uncertainty, and then a possibility-based robust design optimization. For numerical efficiency and stability, an enriched performance measure approach is employed for possibility-based robust design optimization, and the maximal possibility search is used for a possibility analysis. Three different types of robust objectives are considered for possibility-based robust design optimization: smaller-the-better type (S-Type), larger-the-better type (L-Type), and nominal-the-better type (N-Type). Examples are used to demonstrate the effectiveness of possibility-based robust design optimization using the proposed metric for product quality loss with epistemic uncertainty.

Enriched Performance Measure Approach for Reliability-Based Design Optimization.

An enriched performance measure approach is presented for reliability-based design optimization to substantially improve computational efficiency when applied to large-scale applications. In the enriched performance measure approach, four improvements are made over the original performance measure approach: as a way to launch reliability-based design optimization at a deterministic optimum design, as a new enhanced hybrid-mean value method, as an efficient probabilistic feasibility check, and as a fast reliability analysis under the condition of design closeness. It is found that deterministic design optimization helps improve numerical efficiency by reducing some reliability-based design optimization iterations. In reliability-based design optimization, a computational burden on the feasibility check of constraints can be significantly reduced by using a mean value first-order method and by carrying out the refined reliability analysis using the enhanced hybrid-mean value method for e-active and violated constraints. The enhanced hybrid-mean value method is developed to handle nonlinear and/or nonmonotonic constraints in reliability analysis. The fast reliability analysis method is proposed to efficiently evaluate probabilistic constraints under the condition of design closeness. Moreover, two numerical examples are provided to compare the enriched performance measure approach to existing reliability-based design optimization methods from a numerical efficiency and stability point of view.

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.