Versatile Formulation for Multiobjective Reliability-Based Design Optimization

2005 ◽  
Vol 128 (6) ◽  
pp. 1217-1226 ◽  
Author(s):  
T. Zou ◽  
S. Mahadevan
Keyword(s):  
Multiobjective Optimization ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Pareto Frontier ◽  
System Level ◽  
Reliability Based Design Optimization ◽  
Component Reliability ◽  
Reliability Based Design ◽  
Uncertainty Model ◽  
Optimization Methodology

This paper develops a multiobjective optimization methodology for system design under uncertainty. Model-based reliability analysis methods are used to compute the probabilities of unsatisfactory performance at both component and system levels. Combined with several multiobjective optimization formulations, a versatile reliability-based design optimization (RBDO) approach is used to achieve a tradeoff between two objectives and to generate the Pareto frontier for decision making. The proposed RBDO approach uses direct reliability analysis to decouple the reliability and optimization iterations, instead of inverse first-order reliability analysis as other existing decoupled approaches. This helps to solve a wide variety of RBDO problems with competing objectives, especially when system-level reliability constraints need to be considered. The approach also allows more accurate methods to be used for reliability analysis, and reliability terms to be included in the objective function. Two important automotive quality objectives, related to the door closing effort (evaluated using component reliability analysis) and the wind noise (evaluated using system reliability analysis), are used to illustrate the proposed method.

scholarly journals Time-Dependent Reliability-Based Design Optimization Utilizing Nonintrusive Polynomial Chaos

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Yao Wang ◽  
Shengkui Zeng ◽  
Jianbin Guo
Keyword(s):  
Design Optimization ◽  
Structural Reliability ◽  
Polynomial Chaos ◽  
Time Dependent ◽  
Fe Model ◽  
Reliability Based Design Optimization ◽  
Wear Process ◽  
Reliability Based Design ◽  
Optimization Methodology ◽  
Wear Law

Time-dependent reliability-based design optimization (RBDO) has been acknowledged as an advance optimization methodology since it accounts for time-varying stochastic nature of systems. This paper proposes a time-dependent RBDO method considering both of the time-dependent kinematic reliability and the time-dependent structural reliability as constrains. Polynomial chaos combined with the moving least squares (PCMLS) is presented as a nonintrusive time-dependent surrogate model to conduct uncertainty quantification. Wear is considered to be a critical failure that deteriorates the kinematic reliability and the structural reliability through the changing kinematics. According to Archard’s wear law, a multidiscipline reliability model including the kinematics model and the structural finite element (FE) model is constructed to generate the stochastic processes of system responses. These disciplines are closely coupled and uncertainty impacts are cross-propagated to account for the correlationship between the wear process and loads. The new method is applied to an airborne retractable mechanism. The optimization goal is to minimize the mean and the variance of the total weight under both of the time-dependent and the time-independent reliability constraints.

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.

Reliability Based Design Optimization of MEMS Considering Pull-In

2009 ◽  
Vol 131 (6) ◽  
Author(s):  
Michael Raulli ◽  
Kurt Maute
Keyword(s):  
Design Optimization ◽  
Reliability Based Design Optimization ◽  
Micro Electro Mechanical Systems ◽  
Operational Conditions ◽  
Electrostatically Actuated ◽  
Reliability Based Design ◽  
Reliability Method ◽  
Optimization Methodology ◽  
Novel Devices ◽  
Fully Coupled

The increased use of micro-electro-mechanical systems (MEMS) as key components for actuation and sensing purposes in novel devices and systems emphasizes the need for optimal design methods. Stochastic variations in manufacturing and operational conditions must be considered in order to meet performance goals. This study proposes a reliability based design optimization methodology for the design of geometrically complex electrostatically actuated MEMS. The first order reliability method is used for reliability analysis of fully-coupled electrostatic-mechanical problems. A general methodology for predicting the instability phenomenon of pull-in and incorporating it into an automatic optimization process is proposed and verified with analytical and experimental results. The potential of this methodology is illustrated with the design of an analog micromirror.

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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