Reliability-Based Design Optimization of Structures Combining Genetic Algorithms and Finite Element Reliability Analysis

2015 ◽  
pp. 143-152 ◽  
Author(s):  
Luis Celorrio
Keyword(s):  
Finite Element ◽  
Genetic Algorithms ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Geng Zhang ◽  
Efstratios Nikolaidis ◽  
Zissimos P. Mourelatos
Keyword(s):  
Finite Element ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Large Scale ◽  
Analysis Method ◽  
Reliability Based Design Optimization ◽  
Large Scale Structures ◽  
Reliability Based Design ◽  
Scale Structures

Probabilistic analysis and design of large-scale structures requires repeated finite-element analyses of large models, and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability-based design optimization of large-scale structures that consists of two re-analysis methods, one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite-element models consisting of tens or hundreds of thousand degrees of freedom and design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for different probability distributions of the random variables by performing a single Monte Carlo simulation of one design. The methodology is demonstrated on probabilistic vibration analysis and reliability-based design optimization of a realistic vehicle model. It is shown that the computational cost of the proposed re-analysis method for a single reliability analysis is about 1/20 of the cost of the same analysis using MSC/NASTRAN. Moreover, the probabilistic re-analysis approach enables a designer to perform reliability-based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic re-analysis approach, it would be impractical to perform reliability-based design optimization of the vehicle.

An Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

2008 ◽  
Author(s):  
Geng Zhang ◽  
Efstratios Nikolaidis ◽  
Zissimos P. Mourelatos
Keyword(s):  
Finite Element ◽  
Design Optimization ◽  
Reliability Analysis ◽  
Probabilistic Analysis ◽  
Large Scale ◽  
Reliability Based Design Optimization ◽  
Large Scale Structures ◽  
Reliability Based Design ◽  
Design Variables ◽  
Scale Structures

It is challenging to perform probabilistic analysis and design of large-scale structures because it requires repeated finite-element analyses of large models and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability-based design optimization of large-scale structures that consists of two re-analysis methods; one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. Deterministic re-analysis can analyze efficiently large-scale finite element models consisting of tens or hundreds of thousand degrees of freedom and large numbers of design variables that vary in a wide range. Probabilistic re-analysis calculates very efficiently the system reliability for different probability distributions of the design variables by performing a single Monte Carlo simulation. The methodology is demonstrated on probabilistic vibration analysis and a reliability-based design optimization of a realistic vehicle model. It is shown that computational cost of the proposed reanalysis method for a single reliability analysis is about 1/20th of the cost of the same analysis using NASTRAN. Moreover, the probabilistic re-analysis approach enables a designer to perform reliability-based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic re-analysis approach, it would be impractical to perform reliability-based design optimization of the vehicle.

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 optimal design software for earthquake engineering applications

2007 ◽  
Vol 34 (7) ◽  
pp. 856-869 ◽  
Author(s):  
Hong Liang ◽  
Terje Haukaas ◽  
Johannes O Royset
Keyword(s):  
Finite Element ◽  
Design Optimization ◽  
Seismic Design ◽  
Earthquake Engineering ◽  
Structural Response ◽  
Object Oriented ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Nonlinear Structural ◽  
Nonlinear Structural Response

This paper describes a functional tool for engineers to make rational design decisions by balancing cost and safety. Focus is on seismic design, in which nonlinear structural response must be considered. For this purpose, we implement and apply a state-of-the-art algorithm for reliability-based design optimization. The work extends the OpenSees software, which is rapidly gaining users in the earthquake engineering community. Consequently, design optimization with sophisticated nonlinear finite element models of real structures is possible. An object-oriented software architecture is employed that focuses on maintainability and extensibility of the software. This approach also offers flexibility in the choice of optimization and reliability methods for each specific problem, supported by the decoupled nature of the optimization algorithm. Our work utilizes and extends the existing tools for structural reliability analysis in OpenSees. In particular, we employ response sensitivities that are computed within the finite element code by direct differentiation. The implementation is tested through case studies with nonlinear structural response. Discontinuous response gradients are overcome by use of fibre cross sections and smoothed material models. The numerical examples include the seismic design optimization of a six-storey, three-bay, reinforced concrete building. Key words: reliability-based design optimization, nonlinear finite elements, earthquake engineering, object-oriented software development, OpenSees.

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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