Reliability-Based Design Optimization Using Confidence-Based Model Validation for Insufficient Experimental Data

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
Min-Yeong Moon ◽  
K. K. Choi ◽  
Hyunkyoo Cho ◽  
Nicholas Gaul ◽  
David Lamb ◽  
...  
Keyword(s):  
Experimental Data ◽  
Simulation Model ◽  
Design Optimization ◽  
Model Validation ◽  
Optimum Design ◽  
Confidence Level ◽  
Optimization Procedure ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

The conventional reliability-based design optimization (RBDO) methods assume that a simulation model is able to represent the real physics accurately. However, this assumption may not always hold as the simulation model could be biased. Accordingly, designed product based on the conventional RBDO optimum may either not satisfy the target reliability or be overly conservative design. Therefore, simulation model validation using output experimental data, which corrects model bias, should be integrated in the RBDO process. With particular focus on RBDO, the model validation needs to account for the uncertainty induced by insufficient experimental data as well as the inherent variability of the products. In this paper, a confidence-based model validation method that captures the variability and the uncertainty, and that corrects model bias at a user-specified target confidence level, has been developed. The developed model validation helps RBDO to obtain a conservative RBDO optimum design at the target confidence level. The RBDO with model validation may have a convergence issue because the feasible domain changes as the design moves (i.e., a moving-target problem). To resolve the issue, a practical optimization procedure is proposed. Furthermore, the efficiency is achieved by carrying out deterministic design optimization (DDO) and RBDO without model validation, followed by RBDO with confidence-based model validation. Finally, we demonstrate that the proposed RBDO approach can achieve a conservative and practical optimum design given a limited number of experimental data.

Reliability-Based Design Optimization Using Confidence-Based Model Validation for Insufficient Experimental Data

2016 ◽  
Author(s):  
Min-Yeong Moon ◽  
K. K. Choi ◽  
Hyunkyoo Cho ◽  
Nicholas Gaul ◽  
David Lamb ◽  
...  
Keyword(s):  
Experimental Data ◽  
Simulation Model ◽  
Design Optimization ◽  
Model Validation ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Validation Process ◽  
Target Problem ◽  
Reliability Based Design ◽  
The Cost

The conventional reliability-based design optimization (RBDO) methods assume that a simulation model is able to represent the real physics accurately. However, the simulation model could be biased. Accordingly, when the conventional RBDO design is manufactured, the product may not satisfy the target reliability. Therefore, model validation, which corrects model bias, should be integrated in the RBDO process by incorporating experimental data. The challenge is that only a limited number of experimental data is usually available due to the cost of actual product testing. Consequently, model validation for RBDO needs to account for the uncertainty induced by insufficient experimental data as well as variability inherently existing in the products. In this paper, a confidence-based model validation process that captures the uncertainty and corrects model bias at user-specified target conservativeness level is developed. Thus, RBDO can be performed using confidence-based model validation to obtain conservative RBDO design. It is found that RBDO with model bias correction becomes a moving-target problem because the feasible domain changes as the design moves. Consequently, the RBDO optimum may not be easily found due to the convergence problem. To resolve the issue, an efficient process is proposed by carrying out deterministic design optimization (DDO) and RBDO without validation, followed by RBDO with confidence-based model validation. Finally, we demonstrate that the proposed RBDO approach can achieve a conservative and practical optimum design given a limited number of experimental data.

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.

Time-Dependent Concurrent Reliability-Based Design Optimization Integrating the Time-Variant B-Distance Index

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Zhonglai Wang ◽  
Zhihua Wang ◽  
Shui Yu ◽  
Xiaowen Cheng
Keyword(s):  
Experimental Data ◽  
Design Optimization ◽  
Confidence Level ◽  
Moment Method ◽  
Extreme Values ◽  
Time Dependent ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Speed Up ◽  
High Computational Efficiency

This paper presents a time-dependent concurrent reliability-based design optimization (TDC-RBDO) method integrating the time-variant B-distance index to improve the confidence level of design results with a small amount of experimental data. The time-variant B-distance index is first constructed using the extreme values of responses. The Hist Loop CDF (HLCDF) algorithm is then presented to calculate the time-variant B-distance index with high computational efficiency. The TDC-RBDO framework is provided by integrating the time-variant B-distance index and time-dependent reliability. The extreme value moment method (EVMM) is implemented to speed up the procedure of the TDC-RBDO. The case of a harmonic reducer is employed to elaborate on the proposed method.

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.

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.

Reliability-based design optimization for vertical vibrations of a modified electric vehicle using fourth-moment polynomial standard transformation method

2020 ◽  
Vol 234 (10-11) ◽  
pp. 2649-2664
Author(s):  
Sheng Wang ◽  
Lin Hua ◽  
Xinghui Han ◽  
Zhuoyu Su
Keyword(s):  
Design Optimization ◽  
Electric Vehicle ◽  
Optimization Problems ◽  
Computing Time ◽  
Optimization Procedure ◽  
Transformation Method ◽  
Vertical Vibration ◽  
Fourth Moment ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

This article presents a new reliability-based design optimization procedure for the vertical vibration issues raised by a modified electric vehicle using fourth-moment polynomial standard transformation method. First, the fourth-moment polynomial standard transformation method with polynomial chaos expansion is used to obtain the reliability index of uncertain constraints in the reliability-based design optimization which is highly precise and saves computing time compared with other common methods. Next, the half-car model with nonlinear suspension parameters for the modified electric vehicle is investigated, and the response surface methodology is adopted to approximate the complex and time-consuming vertical vibration calculation to the polynomial expressions, and the approximation is validated for reliability-based design optimization results within permissible error level. Then, reliability-based design optimization results under both deterministic and uncertain load parameters are shown and analyzed. Unlike the traditional vertical vibration optimization that only considers one or several sets of load parameters, which lacks versatility, this article presents the reliability-based design optimization with uncertain load parameters which is more suitable for engineering. The results show that the proposed reliability-based design optimization procedure is an effective and efficient way to solve vertical vibration optimization problems for the modified electric vehicle, and the optimization statistics, including the maximum probability interval, can provide references for other suspension dynamical optimization.

Reliability-based design optimization of 3D orthogonal woven composite automobile shock tower

2021 ◽  
pp. 002199832110476
Author(s):  
Zhao Liu ◽  
Lei Zhang ◽  
Ping Zhu ◽  
Mushi Li
Keyword(s):  
Design Optimization ◽  
Composite Structures ◽  
Optimization Design ◽  
Optimization Procedure ◽  
Woven Composite ◽  
Reliability Based Design Optimization ◽  
Multi Scale ◽  
Reliability Based Design ◽  
Design Variables ◽  
3D Orthogonal Woven

Three-dimensional orthogonal woven composites are noted for their excellent mechanical properties and delamination resistance, so they are expected to have promising prospects in lightweight applications in the automobile industry. The multi-scale characteristics and inherent uncertainty of design variables pose great challenges to the optimization procedure for 3D orthogonal woven composite structures. This paper aims to propose a reliability-based design optimization method for guidance on the lightweight design of 3D orthogonal woven composite automobile shock tower, which includes design variables from material and structure. An analytical model was firstly set up to accurately predict the elastic and strength properties of composites. After that, a novel optimization procedure was established for the multi-scale reliability optimization design of composite shock tower, based on the combination of Monte Carlo reliability analysis method, Kriging surrogate model, and particle swarm optimization algorithm. According to the results, the optimized shock tower meets the requirements of structural performance and reliability, with a weight reduction of 37.83%.

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