Reliability analysis and reliability-based design optimization using moment methods

2008 ◽  
pp. 57-85
Author(s):  
Sang Hoon Lee
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Reliability Based Design Optimization ◽  
Moment Methods ◽  
Reliability Based Design

scholarly journals A decoupling algorithm with first-order asymptotic integration for reliability-based design optimization

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879333 ◽  
Author(s):  
Zhiliang Huang ◽  
Tongguang Yang ◽  
Fangyi Li
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problems ◽  
Asymptotic Integration ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
First Order Reliability Method ◽  
First Order ◽  
Reliability Based Design ◽  
Reliability Method

Conventional decoupling approaches usually employ first-order reliability method to deal with probabilistic constraints in a reliability-based design optimization problem. In first-order reliability method, constraint functions are transformed into a standard normal space. Extra non-linearity introduced by the non-normal-to-normal transformation may increase the error in reliability analysis and then result in the reliability-based design optimization analysis with insufficient accuracy. In this article, a decoupling approach is proposed to provide an alternative tool for the reliability-based design optimization problems. To improve accuracy, the reliability analysis is performed by first-order asymptotic integration method without any extra non-linearity transformation. To achieve high efficiency, an approximate technique of reliability analysis is given to avoid calculating time-consuming performance function. Two numerical examples and an application of practical laptop structural design are presented to validate the effectiveness of the proposed approach.

Efficient Global Surrogate Modeling for Reliability-Based Design Optimization

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Barron J. Bichon ◽  
Michael S. Eldred ◽  
Sankaran Mahadevan ◽  
John M. McFarland
Keyword(s):  
Global Optimization ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Optimization Problem ◽  
Wide Spectrum ◽  
Surrogate Models ◽  
Efficient Global Optimization ◽  
Test Problems ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

Determining the optimal (lightest, least expensive, etc.) design for an engineered component or system that meets or exceeds a specified level of reliability is a problem of obvious interest across a wide spectrum of engineering fields. Various formulations and methods for solving this reliability-based design optimization problem have been proposed, but they typically involve accepting a tradeoff between accuracy and efficiency in the reliability analysis. This paper investigates the use of the efficient global optimization and efficient global reliability analysis methods to construct surrogate models at both the design optimization and reliability analysis levels to create methods that are more efficient than existing methods without sacrificing accuracy. Several formulations are proposed and compared through a series of test problems.

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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