Sequential optimization and reliability assessment based on dimension reduction method for accurate and efficient reliability-based design optimization

2015 ◽  
Vol 29 (4) ◽  
pp. 1349-1354 ◽  
Author(s):  
Jongmin Lim ◽  
Byungchai Lee ◽  
Ikjin Lee
Keyword(s):  
Dimension Reduction ◽  
Design Optimization ◽  
Reduction Method ◽  
Reliability Assessment ◽  
Sequential Optimization ◽  
Dimension Reduction Method ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

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.

An Efficient Approach for Reliability-Based Design Optimization Combined Sequential Optimization with Approximate Models

2018 ◽  
Vol 15 (04) ◽  
pp. 1850018 ◽  
Author(s):  
Bao Quoc Doan ◽  
Guiping Liu ◽  
Can Xu ◽  
Minh Quang Chau
Keyword(s):  
Design Optimization ◽  
Reliability Assessment ◽  
Latin Hypercube Sampling ◽  
Assessment Method ◽  
Probabilistic Constraints ◽  
Sequential Optimization ◽  
Reliability Based Design Optimization ◽  
Efficient Approach ◽  
Reliability Based Design ◽  
Approximate Models

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints which can be time-consuming in engineering structural design problems. In this paper, an efficient approach combined sequential optimization with approximate models is suggested for RBDO. The radial basis functions and Latin hypercube sampling are used to construct approximate models of the probabilistic constraints. Then, a sequential optimization with approximate models is carried out by the sequential optimization and reliability assessment method which includes a serial of cycles of deterministic optimization and reliability assessment. Three numerical examples are presented to demonstrate the efficiency of the proposed approach.

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