Determination of the Number of Input Data Through Bi-Objective Confidence-Based Design Optimization

2019 ◽  
Author(s):  
Yongsu Jung ◽  
Hyunkyoo Cho ◽  
Zunyi Duan ◽  
Ikjin Lee
Keyword(s):  
Design Optimization ◽  
Statistical Models ◽  
Input Data ◽  
Operating Cost ◽  
Optimal Number ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Input Model Uncertainty ◽  
Stochastic Sensitivity Analysis

Abstract The confidence of reliability indicates that reliability has randomness induced by any epistemic uncertainties, and these uncertainties can be reduced and manipulated by additional knowledge. In this paper, the uncertainty of input statistical models is mainly treated in the context of confidence-based design optimization (CBDO). Thus, the objective of this paper is to determine the optimal number of data for reliability-based design optimization (RBDO) under input model uncertainty. The uncertainty of input statistical models due to insufficient data is frequent in practical applications since collecting and testing samples of random variables requires engineering efforts. There are two ways to increase the confidence of reliability to be satisfied, which are shifting design vector and supplementing input data. The purpose of this research is to find balanced optimum accounting for a trade-off between two operations since both operations lead to the growth of overall cost. Therefore, it is necessary to optimally distribute the resources to two costs which are denoted as the operating cost of design vector and the development cost of acquiring new data. In this study, two types of costs are integrated as a bi-objective function, satisfying the probabilistic constraint for the confidence of reliability. The number of data is regarded as design variable to be optimized, and stochastic sensitivity analysis of reliability with respect to the number of data is developed. The proposed bi-objective CBDO can determine the optimal number of input data based on the current dataset. Then, the designers decide the additional number of tests for collecting input data according to the optimum of bi-objective CBDO to minimize the overall cost.

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.

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

scholarly journals Reliability-Based Design Optimization for Crane Metallic Structure Using ACO and AFOSM Based on China Standards

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoning Fan ◽  
Xiaoheng Bi
Keyword(s):  
Design Optimization ◽  
Optimal Solution ◽  
Probabilistic Constraints ◽  
Metallic Structure ◽  
Reliability Based Design Optimization ◽  
Metallic Structures ◽  
Practical Applications ◽  
Reliability Indices ◽  
Uncertain Variables ◽  
Reliability Based Design

The design optimization of crane metallic structures is of great significance in reducing their weight and cost. Although it is known that uncertainties in the loads, geometry, dimensions, and materials of crane metallic structures are inherent and inevitable and that deterministic structural optimization can lead to an unreliable structure in practical applications, little amount of research on these factors has been reported. This paper considers a sensitivity analysis of uncertain variables and constructs a reliability-based design optimization model of an overhead traveling crane metallic structure. An advanced first-order second-moment method is used to calculate the reliability indices of probabilistic constraints at each design point. An effective ant colony optimization with a mutation local search is developed to achieve the global optimal solution. By applying our reliability-based design optimization to a realistic crane structure, we demonstrate that, compared with the practical design and the deterministic design optimization, the proposed method could find the lighter structure weight while satisfying the deterministic and probabilistic stress, deflection, and stiffness constraints and is therefore both feasible and effective.

A Sequential Algorithm for Reliability-Based Robust Design Optimization Under Epistemic Uncertainty

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Yuanfu Tang ◽  
Jianqiao Chen ◽  
Junhong Wei
Keyword(s):  
Design Optimization ◽  
Robust Design ◽  
Epistemic Uncertainty ◽  
Robust Design Optimization ◽  
Probabilistic Constraints ◽  
Sequential Algorithm ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Design Variables ◽  
Novel Concept

In practical applications, there may exist a disparity between real values and optimal results due to uncertainties. This kind of disparity may cause violations of some probabilistic constraints in a reliability based design optimization (RBDO) problem. It is important to ensure that the probabilistic constraints at the optimum in a RBDO problem are insensitive to the variations of design variables. In this paper, we propose a novel concept and procedure for reliability based robust design in the context of random uncertainty and epistemic uncertainty. The epistemic uncertainty of design variables is first described by an info gap model, and then the reliability-based robust design optimization (RBRDO) is formulated. To reduce the computational burden in solving RBRDO problems, a sequential algorithm using shifting factors is developed. The algorithm consists of a sequence of cycles and each cycle contains a deterministic optimization followed by an inverse robustness and reliability evaluation. The optimal result based on the proposed model satisfies certain reliability requirement and has the feasible robustness to the epistemic uncertainty of design variables. Two examples are presented to demonstrate the feasibility and efficiency of the proposed method.

Confidence-Based Design Optimization for a More Conservative Optimum Under Surrogate Model Uncertainty Caused by Gaussian Process

2021 ◽  
Vol 143 (9) ◽  
Author(s):  
Yongsu Jung ◽  
Kyeonghwan Kang ◽  
Hyunkyoo Cho ◽  
Ikjin Lee
Keyword(s):  
Gaussian Process ◽  
Design Optimization ◽  
Model Uncertainty ◽  
Surrogate Model ◽  
Confidence Estimation ◽  
Mathematical Functions ◽  
Element Analysis ◽  
Computational Burden ◽  
Reliability Based Design ◽  
Stochastic Sensitivity Analysis

Abstract Even though many efforts have been devoted to effective strategies to build accurate surrogate models, surrogate model uncertainty is inevitable due to a limited number of available simulation samples. Therefore, the surrogate model uncertainty, one of the epistemic uncertainties in reliability-based design optimization (RBDO), has to be considered during the design process to prevent unexpected failure of a system that stems from an inaccurate surrogate model. However, there have been limited attempts to obtain a reliable optimum taking into account the surrogate model uncertainty due to its complexity and computational burden. Thus, this paper proposes a confidence-based design optimization (CBDO) under surrogate model uncertainty to find a conservative optimum despite an insufficient number of simulation samples. To compensate the surrogate model uncertainty in reliability analysis, the confidence of reliability is brought to describe the uncertainty of reliability. The proposed method employs the Gaussian process modeling to explicitly quantify the uncertainty of a surrogate model. Thus, metamodel-based importance sampling and expansion optimal linear estimation are exploited to reduce the computational burden on confidence estimation. In addition, stochastic sensitivity analysis of the confidence is developed for CBDO, which is formulated to find a conservative optimum than an RBDO optimum at a specific confidence level. Numerical examples using mathematical functions and finite element analysis show that the proposed confidence analysis and CBDO can prevent overestimation of reliability caused by an inaccurate surrogate model.

A Reliability Index Based Decoupling Method for Reliability-Based Design Optimization

2012 ◽  
Vol 544 ◽  
pp. 223-228 ◽  
Author(s):  
Zhen Zhong Chen ◽  
Hao Bo Qiu ◽  
Hong Yan Hao ◽  
Hua Di Xiong
Keyword(s):  
Design Optimization ◽  
Reliability Index ◽  
Computational Cost ◽  
Probabilistic Constraints ◽  
Reliability Based Design Optimization ◽  
Decoupling Method ◽  
Practical Applications ◽  
Reliability Based Design ◽  
Structure Reliability ◽  
Comparison Results

Reliability-based design optimization (RBDO) evaluates variation of output induced by uncertainties of design variables and results in an optimal design while satisfying the reliability requirements. However, its use in practical applications is hindered by the huge computational cost during the evaluation of structure reliability. In this paper, the reliability index based decoupling method is developed to improve the efficiency of probabilistic optimization. The reliability index is used to calculate the shifting vector in the decoupling process, due to its efficiency in evaluating violated probabilistic constraints. The computation capability of the proposed method is demonstrated using two examples, which are widely used to test RBDO methods. The comparison results show that the proposed method has the same accuracy as the existing methods, and it is also very efficient.

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