Confidence-Based Method for Reliability-Based Design Optimization

2014 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
David Lamb
Keyword(s):  
Design Optimization ◽  
Confidence Level ◽  
Probabilistic Model ◽  
Input Data ◽  
Mathematical Problem ◽  
Design Sensitivity ◽  
Conditional Probabilities ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

An accurate input probabilistic model is necessary to obtain a trustworthy result in the reliability analysis and the reliability-based design optimization (RBDO). However, the accurate input probabilistic model is not always available. Very often only insufficient input data are available in practical engineering problems. When only the limited input data are provided, uncertainty is induced in the input probabilistic model and this uncertainty propagates to the reliability output which is defined as the probability of failure. Then, the confidence level of the reliability output will decrease. To resolve this problem, the reliability output is considered to have a probability distribution in this paper. The probability of the reliability output is obtained as a combination of consecutive conditional probabilities of input distribution type and parameters using Bayesian approach. The conditional probabilities that are obtained under certain assumptions and Monte Carlo simulation (MCS) method is used to calculate the probability of the reliability output. Using the probability of the reliability output as constraint, a confidence-based RBDO (C-RBDO) problem is formulated. In the new probabilistic constraint of the C-RBDO formulation, two threshold values of the target reliability output and the target confidence level are used. For effective C-RBDO process, the design sensitivity of the new probabilistic constraint is derived. The C-RBDO is performed for a mathematical problem with different numbers of input data and the result shows that C-RBDO optimum designs incorporate appropriate conservativeness according to the given input data.

Stable Evaluation of Probabilistic Constraint in Reliability-Based Design Optimization for Large Deformation Problem

2001 ◽  
Author(s):  
Young H. Park
Keyword(s):  
Design Optimization ◽  
Large Deformation ◽  
Design Sensitivity ◽  
Performance Measure ◽  
Probabilistic Constraint ◽  
Efficient Design ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Deformation Problem ◽  
Large Deformation Problem

Abstract In this paper, Reliability-Based Design Optimization (RBDO) is carried out using two distinct ways, the Reliability Index Approach (RIA) and the Performance Measure Approach (PMA). It has been theoretically explained that RIA shows instability but PMA is stable and efficient in identifying a probabilistic failure mode in the RBDO process. The PMA is compared to RIA with regard to the stable evaluation of a probabilistic constraint in the RBDO using a large deformation problem. In addition, an efficient Design Sensitivity Analysis (DSA) method is developed to support reliability analysis and reliability-based optimization for a hyper-elastic structure with factional contact using a meshfree method. A numerical result is presented to demonstrate the comparative study between RIA and PMA.

Confidence Level Estimation and Design Sensitivity Analysis for Confidence-Based RBDO

2012 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
David Gorsich
Keyword(s):  
Confidence Level ◽  
Input Data ◽  
Surrogate Models ◽  
Design Sensitivity ◽  
Distribution Model ◽  
Conditional Probabilities ◽  
Probabilistic Constraint ◽  
Input Distribution ◽  
Distribution Parameters ◽  
New Formulation

In practical engineering problems, often only limited input data are available to generate the input distribution model. The insufficient input data induces uncertainty on the input distribution model, and this uncertainty will cause us to lose confidence in the optimum design obtained using the reliability-based design optimization (RBDO) method. Uncertainty on the input distribution model requires us to consider the reliability analysis output, which is defined as the probability of failure, to follow a probabilistic distribution. This paper proposes a new formulation for the confidence-based RBDO method and design sensitivity analysis of the confidence level. The probability of the reliability analysis output is obtained with consecutive conditional probabilities of input distribution parameters and input distribution types using a Bayesian approach. The approximate conditional probabilities of input distribution parameters and types are suggested under certain assumptions. The Monte Carlo simulation is applied to practically calculate the output distribution, and the copula is used to describe the correlated input distribution types. A confidence-based RBDO problem is formulated using the derived the distribution of output. In this new formulation, the probabilistic constraint is modified to include both the target reliability and the target confidence level. Finally, the sensitivity of the confidence level, which is a new probabilistic constraint, is derived to support an efficient optimization process. Using accurate surrogate models, the proposed method does not require generation of additional surrogate models during the RBDO iteration; it only requires several evaluations of the same surrogate models. Hence, the efficiency of the method is obtained. For the numerical example, the confidence level is calculated and the accuracy of the derived sensitivity is verified when only limited data are available.

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.

Reliability-Based Design Optimization With Confidence Level Under Input Model Uncertainty

2009 ◽  
Author(s):  
Yoojeong Noh ◽  
K. K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Standard Deviation ◽  
Confidence Interval ◽  
Design Optimization ◽  
Optimum Design ◽  
Upper Bound ◽  
Confidence Level ◽  
Limited Data ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Input Model

For obtaining correct reliability-based optimum design, an input model needs to be accurately estimated in identification of marginal and joint distribution types and quantification of their parameters. However, in most industrial applications, only limited data on input variables is available due to expensive experimental testing costs. The input model generated from the insufficient data might be inaccurate, which will lead to incorrect optimum design. In this paper, reliability-based design optimization (RBDO) with the confidence level is proposed to offset the inaccurate estimation of the input model due to limited data by using an upper bound of confidence interval of the standard deviation. Using the upper bound of the confidence interval of the standard deviation, the confidence level of the input model can be assessed to obtain the confidence level of the output performance, i.e. a desired probability of failure, through the simulation-based design. For RBDO, the estimated input model with the associated confidence level is integrated with the most probable point (MPP)-based dimension reduction method (DRM), which improves accuracy over the first order reliability method (FORM). A mathematical example and a fatigue problem are used to illustrate how the input model with confidence level yields a reliable optimum design by comparing it with the input model obtained using the estimated parameters.

Reliability-Based Design Optimization With Confidence Level for Non-Gaussian Distributions Using Bootstrap Method

2011 ◽  
Vol 133 (9) ◽  
Author(s):  
Yoojeong Noh ◽  
Kyung K. Choi ◽  
Ikjin Lee ◽  
David Gorsich ◽  
David Lamb
Keyword(s):  
Statistical Model ◽  
Design Optimization ◽  
Confidence Intervals ◽  
Confidence Level ◽  
Bootstrap Method ◽  
Random Variables ◽  
Reliability Based Design Optimization ◽  
Gaussian Distributions ◽  
Reliability Based Design ◽  
Non Gaussian

For reliability-based design optimization (RBDO), generating an input statistical model with confidence level has been recently proposed to offset inaccurate estimation of the input statistical model with Gaussian distributions. For this, the confidence intervals for the mean and standard deviation are calculated using Gaussian distributions of the input random variables. However, if the input random variables are non-Gaussian, use of Gaussian distributions of the input variables will provide inaccurate confidence intervals, and thus yield an undesirable confidence level of the reliability-based optimum design meeting the target reliability βt. In this paper, an RBDO method using a bootstrap method, which accurately calculates the confidence intervals for the input parameters for non-Gaussian distributions, is proposed to obtain a desirable confidence level of the output performance for non-Gaussian distributions. The proposed method is examined by testing a numerical example and M1A1 Abrams tank roadarm problem.

A Sequential Sampling Strategy to Improve Reliability-Based Design Optimization With Implicit Constraint Functions

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Xiaotian Zhuang ◽  
Rong Pan
Keyword(s):  
Computer Simulation ◽  
Design Optimization ◽  
Sequential Sampling ◽  
Sampling Strategy ◽  
Computer Experiment ◽  
Probabilistic Constraint ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Modern Engineering ◽  
Surrogate Function

Reliability-based design optimization (RBDO) has a probabilistic constraint that is used for evaluating the reliability or safety of the system. In modern engineering design, this task is often performed by a computer simulation tool such as finite element method (FEM). This type of computer simulation or computer experiment can be treated a black box, as its analytical function is implicit. This paper presents an efficient sampling strategy on learning the probabilistic constraint function under the design optimization framework. The method is a sequential experimentation around the approximate most probable point (MPP) at each step of optimization process. Our method is compared with the methods of MPP-based sampling, lifted surrogate function, and nonsequential random sampling. We demonstrate it through examples.

Conservative reliability-based design optimization method with insufficient input data

2016 ◽  
Vol 54 (6) ◽  
pp. 1609-1630 ◽  
Author(s):  
Hyunkyoo Cho ◽  
K. K. Choi ◽  
Nicholas J. Gaul ◽  
Ikjin Lee ◽  
David Lamb ◽  
...  
Keyword(s):  
Design Optimization ◽  
Input Data ◽  
Optimization Method ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

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.

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