Bayesian Reliability-Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method

2007 ◽  
Author(s):  
Pingfeng Wang ◽  
Byeng D. Youn ◽  
Lee J. Wells
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Eigenvector Dimension Reduction

Bayesian Reliability Based Design Optimization Using Eigenvector Dimension Reduction (EDR) Method

2007 ◽  
Author(s):  
Pingfeng Wang ◽  
Byeng D. Youn ◽  
Lee J. Wells
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Engineering Design ◽  
Mean Deviation ◽  
Random Parameters ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Practical Engineering ◽  
Eigenvector Dimension Reduction

In the last decade, considerable advances have been made in Reliability-Based Design Optimization (RBDO). It is assumed in RBDO that statistical information of input uncertainties is completely known (aleatory uncertainty), such as a distribution type and its parameters (e.g., mean, deviation). However, this assumption is not valid in practical engineering applications, since the amount of uncertainty data is restricted mainly due to limited resources (e.g., man-power, expense, time). In practical engineering design, most data sets for system uncertainties are insufficiently sampled from unknown statistical distributions, known as epistemic uncertainty. Existing methods in uncertainty based design optimization have difficulty in handling both aleatory and epistemic uncertainties. To tackle design problems engaging both epistemic and aleatory uncertainties, this paper proposes an integration of RBDO with Bayes Theorem, referred to as Bayesian Reliability-Based Design Optimization (Bayesian RBDO). However, when a design problem involves a large number of epistemic variables, Bayesian RBDO becomes extremely expensive. Thus, this paper presents a more efficient and accurate numerical method for reliability method demanded in the process of Bayesian RBDO. It is found that the Eigenvector Dimension Reduction (EDR) Method is a very efficient and accurate method for reliability analysis, since the method takes a sensitivity-free approach with only 2n+1 analyses, where n is the number of aleatory random parameters. One mathematical example and an engineering design example (vehicle suspension system) are used to demonstrate the feasibility of Bayesian RBDO. In Bayesian RBDO using the EDR method, random parameters associated with manufacturing variability are considered as the aleatory random parameters, whereas random parameters associated with the load variability are regarded as the epistemic random parameters. Moreover, a distributed computing system is used for this study.

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.

Reliability-Based Design Optimization Using Enhanced Dimension Reduction Method With Variable Sampling Points

2009 ◽  
Author(s):  
Sunmin Yook ◽  
Gabseong Lee ◽  
Sang-Joon Yoon ◽  
Jae-Yong Park ◽  
Dong-Hoon Choi
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Random Variable ◽  
Performance Measure ◽  
Reliability Based Design Optimization ◽  
Design Factor ◽  
Random Design ◽  
Reliability Based Design ◽  
Variable Sampling ◽  
Sampling Points

Reliability-Based Design Optimization (RBDO) is an effective method to handle an optimization problem constrained by reliability performance. In spite of its great benefits, one of the most challenging issues for implementing RBDO is associated with very intensive computational demands of Reliability Analysis (RA). Moreover, an accurate and efficient RA method is indispensible to apply RBDO to practical engineering design problems. Among various RA methods, an enhanced Dimension Reduction (eDR) method is the most popular one due to the high computational efficiency. It is very desirable to obtain an accurate and efficient RA result by using the minimum number of sampling points. But, it is difficult to determine it. That is because it depends on the nonlinearity of a constraint from approximating a model and the degree of uncertainty from integrating a design factor. In this research, eDR method with variable sampling points has been studied and proposed to resolve the early mentioned difficulties. The main idea of the suggested method is to employ a different number of axial sampling points for each random design factor. It is according to the nonlinearity of a constraint and the degree of uncertainty of each random design factor. For each random variable, it begins to use three points first and decides to stop or increase the axial sampling points based upon the proposed criteria in this study. In case of increasing sampling points, it is incremented by one sampling point and ended up five sampling points at most. As it shown in the result, the efficiency of eDR method with variable sampling points for each random variable is superior to the one with fixed sampling points without sacrificing any accuracy. Through the three representative RA problems, it is verified that the proposed RA method generates the result 26.5% more efficiently on average than the conventional eDR method with fixed sampling points. Furthermore, the Performance Measure Approach (PMA) was used to evaluate the performance of RBDO using the new RA method. For the comparison, three mathematical and one engineering RBDO problems were solved by both eDR method with variable sampling points and conventional one with fixed sampling points. Finally, the comparison results clearly demonstrate that RBDO using the suggested RA method is superior to the conventional one in terms of accuracy and efficiency.

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