Reliability-Based Design Optimization with Model Bias and Data Uncertainty

2013 ◽  
Vol 6 (3) ◽  
pp. 502-516 ◽  
Author(s):  
Zhen Jiang ◽  
Wei Chen ◽  
Yan Fu ◽  
Ren-Jye Yang
Keyword(s):  
Design Optimization ◽  
Data Uncertainty ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design

Model Uncertainty Approximation Using a Copula-Based Approach for Reliability Based Design Optimization

2016 ◽  
Author(s):  
Hao Pan ◽  
Zhimin Xi ◽  
Ren-Jye Yang
Keyword(s):  
Design Optimization ◽  
Model Uncertainty ◽  
Design Space ◽  
Epistemic Uncertainty ◽  
Minimum Cost ◽  
Vehicle Design ◽  
Model Bias ◽  
Reliability Based Design Optimization ◽  
Reliability Based Design ◽  
Model Inadequacy

Reliability-based design optimization (RBDO) has been widely used to design engineering products with minimum cost function while meeting defined reliability constraints. Although uncertainties, such as aleatory uncertainty and epistemic uncertainty, have been well considered in RBDO, they are mainly considered for model input parameters. Model uncertainty, i.e., the uncertainty of model bias which indicates the inherent model inadequacy for representing the real physical system, is typically overlooked in RBDO. This paper addresses model uncertainty characterization in a defined product design space and further integrates the model uncertainty into RBDO. In particular, a copula-based bias correction approach is proposed and results are demonstrated by two vehicle design case studies.

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.

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