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.

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.

Robust Design Optimization of Ball Grid Array Packaging

2011 ◽  
Author(s):  
Jae Chang Kim ◽  
Joo-Ho Choi ◽  
Yeong K. Kim
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Strain Energy ◽  
Reduction Method ◽  
Ball Grid Array ◽  
Robust Design Optimization ◽  
Molding Compound ◽  
Materials Modeling ◽  
Solder Balls ◽  
Input Variables

In this paper, comparisons of the design optimization of ball grid array packaging geometry based on the elastic and viscoelastic material properties are made. Six geometric dimensions of the packaging are chosen as input variables. Molding compound and substrate are modeled as elastic and viscoelastic, respectively. Viscoplastic finite element analyses are performed to calculate the strain energy densities (SED) of the eutectic solder balls. Robust design optimizations to minimize SED are carried out, which accounts for the variance of the parameters via Kriging dimension reduction method. Optimum solutions are compared with those by the Taguchi method. It is found that the effects of the packaging geometry on the solder ball reliability are significant, and the optimization results are different depending on the materials modeling.

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.

scholarly journals Reliability-Based Robust Design Optimization of Structures Considering Uncertainty in Design Variables

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Shujuan Wang ◽  
Qiuyang Li ◽  
Gordon J. Savage
Keyword(s):  
Sensitivity Analysis ◽  
Design Optimization ◽  
Robust Design ◽  
Structural Reliability ◽  
Computational Cost ◽  
Optimization Process ◽  
Robust Design Optimization ◽  
Global Approximation ◽  
Design Variables ◽  
Uncertainty In Design

This paper investigates the structural design optimization to cover both the reliability and robustness under uncertainty in design variables. The main objective is to improve the efficiency of the optimization process. To address this problem, a hybrid reliability-based robust design optimization (RRDO) method is proposed. Prior to the design optimization, the Sobol sensitivity analysis is used for selecting key design variables and providing response variance as well, resulting in significantly reduced computational complexity. The single-loop algorithm is employed to guarantee the structural reliability, allowing fast optimization process. In the case of robust design, the weighting factor balances the response performance and variance with respect to the uncertainty in design variables. The main contribution of this paper is that the proposed method applies the RRDO strategy with the usage of global approximation and the Sobol sensitivity analysis, leading to the reduced computational cost. A structural example is given to illustrate the performance of the proposed method.

Multidisciplinary Robust Design Optimization of an Internal Combustion Engine

2003 ◽  
Vol 125 (1) ◽  
pp. 124-130 ◽  
Author(s):  
Charles D. McAllister ◽  
Timothy W. Simpson
Keyword(s):  
Internal Combustion Engine ◽  
Design Optimization ◽  
Robust Design ◽  
Combustion Engine ◽  
Internal Combustion ◽  
Collaborative Optimization ◽  
Robust Design Optimization ◽  
Optimization Framework ◽  
Design Variables ◽  
Multiobjective Approach

In this paper, we introduce a multidisciplinary robust design optimization formulation to evaluate uncertainty encountered in the design process. The formulation is a combination of the bi-level Collaborative Optimization framework and the multiobjective approach of the compromise Decision Support Problem. To demonstrate the proposed framework, the design of a combustion chamber of an internal combustion engine containing two subsystem analyses is presented. The results indicate that the proposed Collaborative Optimization framework for multidisciplinary robust design optimization effectively attains solutions that are robust to variations in design variables and environmental conditions.

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