A New Study on Reliability-Based Design Optimization

1999 ◽  
Vol 121 (4) ◽  
pp. 557-564 ◽  
Author(s):  
J. Tu ◽  
K. K. Choi ◽  
Y. H. Park
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Index Approach ◽  
Special Cases

This paper presents a general approach for probabilistic constraint evaluation in the reliability-based design optimization (RBDO). Different perspectives of the general approach are consistent in prescribing the probabilistic constraint, where the conventional reliability index approach (RIA) and the proposed performance measure approach (PMA) are identified as two special cases. PMA is shown to be inherently robust and more efficient in evaluating inactive probabilistic constraints, while RIA is more efficient for violated probabilistic constraints. Moreover, RBDO often yields a higher rate of convergence by using PMA, while RIA yields singularity in some cases.

A Hybrid Reliability Approach for Reliability-Based Design Optimization

2010 ◽  
Author(s):  
Po Ting Lin ◽  
Yogesh Jaluria ◽  
Hae Chang Gea
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Optimization Problems ◽  
Performance Measure ◽  
Accurate Solution ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Index Approach ◽  
Hybrid Reliability

Reliability-based Design Optimization problems have been solved by two well-known methods: Reliability Index Approach (RIA) and Performance Measure Approach (PMA). RIA generates first-order approximate probabilistic constraints using the measures of reliability indices. For infeasible design points, the traditional RIA method suffers from inaccurate evaluation of the reliability index. To overcome this problem, the Modified Reliability Index Approach (MRIA) has been proposed. The MRIA provides the accurate solution of the reliability index but also inherits some inefficiency characteristics from the Most Probable Failure Point (MPFP) search when nonlinear constraints are involved. In this paper, the benchmark examples have been utilized to examine the efficiency and stability of both PMA and MRIA. In our study, we found that the MRIA is capable of obtaining the correct optimal solutions regardless of the locations of design points but the PMA is much efficient in the inverse reliability analysis. To take advantages of the strengths of both methods, a Hybrid Reliability Approach (HRA) is proposed. The HRA uses a selection factor that can determine which method to use during optimization iterations. Numerical examples from the proposed method are presented and compared with the MRIA and the PMA.

Sensitivity Analyses of FORM-Based and DRM-Based Performance Measure Approach for Reliability-Based Design Optimization

2008 ◽  
Author(s):  
Ikjin Lee ◽  
Kyung K. Choi ◽  
Liu Du ◽  
David Gorsich
Keyword(s):  
Design Optimization ◽  
Performance Measure ◽  
Second Order ◽  
Probabilistic Constraints ◽  
Sensitivity Analyses ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Reliability Method

In a gradient-based design optimization, it is necessary to know sensitivities of the constraint with respect to the design variables. In a reliability-based design optimization (RBDO), the constraint is evaluated at the most probable point (MPP) and called the probabilistic constraint, thus it requires the sensitivities of the probabilistic constraints at MPP. This paper presents the rigorous analytic derivation of the sensitivities of the probabilistic constraint at MPP for both First Order Reliability Method (FORM)-based Performance Measure Approach (PMA) and Dimension Reduction Method (DRM)-based PMA. Numerical examples are used to demonstrate that the analytic sensitivities agree very well with the sensitivities obtained from the finite difference method (FDM). However, since the sensitivity calculation at the true DRM-based MPP requires the second-order derivatives and additional MPP search, the sensitivity derivation at the approximated DRM-based MPP, which does not require the second-order derivatives and additional MPP search to find the DRM-based MPP, is proposed in this paper. A convergence study illustrates that the sensitivity at the approximated DRM-based MPP converges to the sensitivity at the true DRM-based MPP as the design approaches the optimum design. Hence, the sensitivity at the approximated DRM-based MPP is proposed to be used for the DRM-based RBDO to enhance the efficiency of the optimization.

Optimization of Jacket Type Offshore-Tower Under Uncertainties

2009 ◽  
Author(s):  
V. Togan ◽  
H. Karadeniz ◽  
A. T. Daloglu
Keyword(s):  
Performance Measure ◽  
Environmental Data ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Performance Measure Approach ◽  
Reliability Based Design ◽  
Economical Design ◽  
Design Variables ◽  
Index Approach ◽  
And Performance

In this work, economical design implementation of a jacket tower, which is subjected to some uncertainties associated with the loads, the material properties, and environmental data etc., is presented. In order to fulfill the defined task, reliability based design optimization (RBDO) concept combining the reliability analysis and optimization is performed with reliability constraints including stress, buckling, and the lowest natural frequency. The probabilistic constraints are evaluated by using Reliability Index Approach (RIA) and Performance Measure approach (PMA). The mass of the tower is considered as being the objective function; the thickness and diameter of the cross-section of the jacket members are taken as being design variables of the optimization.

Hybrid Analysis Method for Reliability-Based Design Optimization

2003 ◽  
Vol 125 (2) ◽  
pp. 221-232 ◽  
Author(s):  
Byeng D. Youn ◽  
Kyung K. Choi ◽  
Young H. Park
Keyword(s):  
Design Optimization ◽  
Mean Value ◽  
Performance Measure ◽  
Equality Constraint ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Reliability Based Design ◽  
Advanced Mean Value

Reliability-based design optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the reliability index approach (RIA) and the performance measure approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the optimization process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the advanced mean value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the conjugate mean value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the hybrid mean value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

Discussion of Mathematical Models of Probabilistic Constraints Calculation in Reliability-Based Design Optimization

2011 ◽  
Vol 243-249 ◽  
pp. 5717-5726
Author(s):  
Ping Yi
Keyword(s):  
Mathematical Models ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Mean Value ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
The Mean

In a reliability-based design optimization (RBDO) problem, most of the computations are used for probabilistic constraints assessment, i.e., reliability analysis. Therefore, the effectiveness, especially the correctness of the reliability analysis is very important. If the probabilistic constraint is misjudged, the optimization iteration would have convergence problems or arrive at erratic solutions. The probabilistic constraint assessment can be carried out using either the conventional reliability index approach (RIA) or the performance measure approach (PMA). In this paper, the mathematical models to calculate the reliability index in RIA and to calculate the probabilistic performance measure (PPM) in PMA are discussed. In RIA, through estimating whether the mean-value point in safe domain or not, we should use a positive or negative reliability index respectively. In PMA, one should always minimize the performance measure to compute PPM whether the performance measure at the mean-value point is positive or negative, which puts right the wrong mathematical model in some literatures and makes it possible to produce effective and efficient approach for RBDO.

Hybrid Analysis Method for Reliability-Based Design Optimization

2001 ◽  
Author(s):  
Kyung K. Choi ◽  
Byeng D. Youn
Keyword(s):  
Design Optimization ◽  
Mean Value ◽  
Performance Measure ◽  
Equality Constraint ◽  
Probabilistic Constraints ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Performance Function ◽  
Reliability Based Design ◽  
Advanced Mean Value

Abstract Reliability-Based Design Optimization (RBDO) involves evaluation of probabilistic constraints, which can be done in two different ways, the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). It has been reported in the literature that RIA yields instability for some problems but PMA is robust and efficient in identifying a probabilistic failure mode in the RBDO process. However, several examples of numerical tests of PMA have also shown instability and inefficiency in the RBDO process if the Advanced Mean Value (AMV) method, which is a numerical tool for probabilistic constraint evaluation in PMA, is used, since it behaves poorly for a concave performance function, even though it is effective for a convex performance function. To overcome difficulties of the AMV method, the Conjugate Mean Value (CMV) method is proposed in this paper for the concave performance function in PMA. However, since the CMV method exhibits the slow rate of convergence for the convex function, it is selectively used for concave-type constraints. That is, once the type of the performance function is identified, either the AMV method or the CMV method can be adaptively used for PMA during the RBDO iteration to evaluate probabilistic constraints effectively. This is referred to as the Hybrid Mean Value (HMV) method. The enhanced PMA with the HMV method is compared to RIA for effective evaluation of probabilistic constraints in the RBDO process. It is shown that PMA with a spherical equality constraint is easier to solve than RIA with a complicated equality constraint in estimating the probabilistic constraint in the RBDO process.

Reliability-Based Design Optimization in X-Space Using Ensemble of Gaussian Reliability Analyses (EoGRA)

2015 ◽  
Author(s):  
Po Ting Lin ◽  
Shu-Ping Lin
Keyword(s):  
Design Optimization ◽  
Reliability Analysis ◽  
Reliability Index ◽  
Design Space ◽  
Performance Measure ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Design Point ◽  
Reliability Based Design ◽  
Standard Normal

Reliability-Based Design Optimization (RBDO) algorithms have been developed to solve design optimization problems with existence of uncertainties. Traditionally, the original random design space is transformed to the standard normal design space, where the reliability index can be measured in a standardized unit. In the standard normal design space, the Modified Reliability Index Approach (MRIA) measured the minimum distance from the design point to the failure region to represent the reliability index; on the other hand, the Performance Measure Approach (PMA) performed inverse reliability analysis to evaluate the target function performance in a distance of reliability index away from the design point. MRIA was able to provide stable and accurate reliability analysis while PMA showed greater efficiency and was widely used in various engineering applications. However, the existing methods cannot properly perform reliability analysis in the standard normal design space if the transformation to the standard normal space does not exist or is difficult to determine. To this end, a new algorithm, Ensemble of Gaussian Reliability Analyses (EoGRA), was developed to estimate the failure probability using Gaussian-based Kernel Density Estimation (KDE) in the original design space. The probabilistic constraints were formulated based on each kernel reliability analysis for the optimization processes. This paper proposed an efficient way to estimate the constraint gradient and linearly approximate the probabilistic constraints with fewer function evaluations. Some numerical examples with various random distributions are studied to investigate the numerical performances of the proposed method. The results showed EoGRA is capable of finding correct solutions in some problems that cannot be solved by traditional methods.

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