Dimension Reduction Method for Reliability-Based Robust Design Optimization

2008 ◽  
pp. 381-381
Author(s):  
K. K. Choi ◽  
Ikjin Lee ◽  
David Gorsich
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Robust Design ◽  
Reduction Method ◽  
Robust Design Optimization ◽  
Dimension Reduction Method

Dimension reduction method for reliability-based robust design optimization

2008 ◽  
Vol 86 (13-14) ◽  
pp. 1550-1562 ◽  
Author(s):  
Ikjin Lee ◽  
K.K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Robust Design ◽  
Reduction Method ◽  
Robust Design Optimization ◽  
Dimension Reduction Method

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 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.

Most Probable Point-Based Approximated Dimension Reduction Method in Reliability-Based Design Optimization

2018 ◽  
Author(s):  
Yongsu Jung ◽  
Hyunkyoo Cho ◽  
Ikjin Lee
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Reduction Method ◽  
Dimension Reduction Method ◽  
Reliability Based Design Optimization ◽  
Method Performance ◽  
Most Probable Point ◽  
Reliability Based Design ◽  
Function Information

The conventional most probable point (MPP)-based dimension reduction method (DRM) and following researches show high accuracy in reliability analysis and thus have been successfully applied to reliability-based design optimization (RBDO). However, improvement in accuracy usually leads to reduction in efficiency. The MPP-based DRM is certainly better from the perspective of accuracy than first-order reliability methods (FORM). However, it requires additional function evaluations which could require heavy computational cost such as finite element analysis (FEA) to improve accuracy of probability of failure estimation. Therefore, in this paper, we propose MPP-based approximated DRM (ADRM) that performs one more approximation at MPP to maintain accuracy of DRM with efficiency of FORM. In the proposed method, performance functions will be approximated in original X-space with simplified bivariate DRM and linear regression using available function information such as gradients obtained during the previous MPP searches. Therefore, evaluation of quadrature points can be replaced by the proposed approximation. In this manner, we eliminate function evaluations at quadrature points for reliability analysis, so that the proposed method requires function evaluations for MPP search only, which is identical with FORM. In RBDO where sequential reliability analyses in different design points are necessary, ADRM becomes more powerful due to accumulated function information, which will lead to more accurate approximation. To further improve efficiency of the proposed method, several techniques, such as local window and adaptive initial point, are proposed as well. Numerical study verifies that the proposed method is as accurate as DRM and as efficient as FORM by utilizing available function information obtained during MPP searches.

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