The Performance Moment Integration Method for Reliability-Based Robust Design Optimization

2004 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi
Keyword(s):  
Design Optimization ◽  
Product Quality ◽  
Robust Design ◽  
Mean Value ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Integration Scheme ◽  
Quality Loss ◽  
Reliability Based Design ◽  
Different Types

Reliability-based robust design optimization deals with two objectives of structural design methodologies subject to various uncertainties: reliability-based design and robust design. A reliability-based design optimization deals with the probability of failure, while a robust design optimization 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 numerical integration scheme for output response to estimate the product quality loss. For the reliability part of the reliability-based robust design optimization, the performance measure approach (PMA) and its numerical method, hybrid-mean value (HMV) method, are used. New formulations of reliability-based robust design optimization are presented for three different types of robust objectives, such as smaller-the-better, larger-the-better, and nominal-the-better types. Examples are used to demonstrate the effectiveness of reliability-based robust design optimization using the proposed PMI method for different types of robust objective.

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

2006 ◽  
Vol 129 (8) ◽  
pp. 876-882 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Product Quality ◽  
Robust Design ◽  
Epistemic Uncertainty ◽  
Performance Measure ◽  
Robust Design Optimization ◽  
Quality Loss ◽  
Different Types ◽  
Practical Engineering ◽  
General Product

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.

Robustness Metrics for Time-Dependent Quality Characteristics

2011 ◽  
Author(s):  
Xiaoping Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Quality Characteristics ◽  
Time Dependent ◽  
Robust Design Optimization ◽  
Time Interval ◽  
Mechanism Analysis ◽  
Quality Loss ◽  
Time Period ◽  
Robustness Metrics

Quality characteristics (QC’s) are often treated static in robust design optimization while many of them are time dependent in reality. It is therefore desirable to define new robustness metrics for time-dependent QC’s. This work shows that using the robustness metrics of static QC’s for those of time-dependent QC’s may lead to erroneous design results. To this end, we propose the criteria of establishing new robustness metrics for time-dependent QC’s and then define new robustness metrics. Instead of using a point expected quality loss over the time period of interest, we use the expectation of the maximal quality loss over the time period to quantify the robustness for time-dependent QC’s. Through a four-bar function generator mechanism analysis, we demonstrate that the new robustness metrics can capture the full information of robustness of a time-dependent QC over a time interval. The new robustness metrics can then be used as objective functions for time-dependent robust design optimization.

Hybrid Analysis Method for Reliability-Based Design Optimization

2003 ◽  
Vol 125 (2) ◽  
pp. 221-232 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi ◽  
Young H. Park
Keyword(s):  
Design Optimization ◽  
Mean Value ◽  
Performance Measure ◽  
Equality Constraint ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Reliability Based Design ◽  
Advanced Mean Value

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the optimization process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the advanced mean value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the conjugate mean value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the hybrid mean value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

Robustness Metric for Robust Design Optimization Under Time- and Space-Dependent Uncertainty Through Metamodeling

2019 ◽  
Vol 142 (3) ◽  
Author(s):  
Xinpeng Wei ◽  
Xiaoping Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Model Building ◽  
Robustness Analysis ◽  
Numerical Procedure ◽  
Quality Characteristics ◽  
Robust Design Optimization ◽  
Quality Loss ◽  
Time And Space ◽  
Spatial Variables

Abstract Product performance varies with respect to time and space in many engineering applications. This paper discusses how to measure and evaluate the robustness of a product or component when its quality characteristics (QCs) are functions of random variables, random fields, temporal variables, and spatial variables. At first, the existing time-dependent robustness metric is extended to the present time- and space-dependent problem. The robustness metric is derived using the extreme value of the quality characteristics with respect to temporal and spatial variables for the nominal-the-better type quality characteristics. Then, a metamodel-based numerical procedure is developed to evaluate the new robustness metric. The procedure employs a Gaussian Process regression method to estimate the expected quality loss that involves the extreme quality characteristics. The expected quality loss is obtained directly during the regression model building process. Four examples are used to demonstrate the robustness analysis method. The proposed method can be used for robustness analysis during robust design optimization (RDO) under time- and space-dependent uncertainty.

Alternative Methods for Reliability-Based Robust Design Optimization Including Dimension Reduction Method

2006 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Reduction Method ◽  
Statistical Moments ◽  
Robust Design Optimization ◽  
Quality Loss ◽  
Dimension Reduction Method ◽  
Quality Loss Function ◽  
Performance Function ◽  
Design Variables

The objective of reliability-based robust design optimization (RBRDO) is to minimize the product quality loss function subject to probabilistic constraints. Since the quality loss function is usually expressed in terms of the first two statistical moments, mean and variance, many methods have been proposed to accurately and efficiently estimate the moments. Among the methods, the univariate dimension reduction method (DRM), performance moment integration (PMI), and percentile difference method (PDM) are recently proposed methods. In this paper, estimation of statistical moments and their sensitivities are carried out using DRM and compared with results obtained using PMI and PDM. In addition, PMI and DRM are also compared in terms of how accurately and efficiently they estimate the statistical moments and their sensitivities of a performance function. In this comparison, PDM is excluded since PDM could not even accurately estimate the statistical moments of the performance function. Also, robust design optimization using DRM is developed and then compared with the results of RBRDO using PMI and PDM. Several numerical examples are used for the two comparisons. The comparisons show that DRM is efficient when the number of design variables is small and PMI is efficient when the number of design variables is relatively large. For the inverse reliability analysis of reliability-based design, the enriched performance measure approach (PMA+) is used.

Robust Design Optimization of Gear Parameters for a Wind Turbine Using Interval Analysis

2010 ◽  
Vol 224 (10) ◽  
pp. 2235-2245 ◽  
Author(s):  
R Dong ◽  
W Sun ◽  
H Xu
Keyword(s):  
Wind Turbine ◽  
Design Optimization ◽  
Robust Design ◽  
Optimization Method ◽  
Mean Value ◽  
Robust Design Optimization ◽  
Upper And Lower Bounds ◽  
Interval Numbers ◽  
Minimum Sensitivity ◽  
The Mean

A robust design optimization method is suggested to optimize the system parameters of a gear transmission for a wind turbine with minimum sensitivity of fatigue strength to variations in uncertain application factor, dynamic load coefficient, material property parameters, and other coefficients representing unknown working condition. Interval numbers are employed to model the uncertainties by which only the upper and lower bounds are needed. Based on interval mathematics, the original real-valued objective and constraint functions are replaced by the interval-valued functions, which directly represent the variation bounds of the new functions under uncertainty. The single-objective function is converted into two-objective functions for minimizing the mean value and the variation, and the constraint functions are reformulated with the acceptable robustness level, resulting in a bi-level mathematical model. The optimization results of gear parameter demonstrate the validity and feasibility of the presented method.

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