A model validation framework based on parameter calibration under aleatory and epistemic uncertainty
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RESEARCH PAPER
A model validation framework based on parameter calibration under aleatory and epistemic uncertainty Jiexiang Hu 1,2 & Qi Zhou 1 & Austin McKeand 3 & Tingli Xie 3 & Seung-Kyum Choi 3 Received: 3 January 2020 / Revised: 28 July 2020 / Accepted: 5 August 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Model validation methods have been widely used in engineering design to evaluate the accuracy and reliability of simulation models with uncertain inputs. Most of the existing validation methods for aleatory and epistemic uncertainty are based on the Bayesian theorem, which needs a vast number of data to update the posterior distribution of the model parameter. However, when a single simulation is time-consuming, the required simulation cost for the validation of a simulation model may be unaffordable. To overcome this difficulty, a new model validation framework based on parameter calibration under aleatory and epistemic uncertainty is proposed. In the proposed method, a stochastic kriging model is constructed to predict the validity of the candidate simulation model under different uncertainty input parameters. Then, an optimization problem is defined to calibrate the epistemic uncertainty parameters to minimize the discrepancy between the simulation model and the experimental model. K–S test finally decides whether to accept or reject the calibrated simulation model. The performance of the proposed approach is illustrated through a cantilever beam example and a turbine blade validation problem. Results show that the proposed framework can identify the most appropriate parameters to calibrate the simulation model and provide a correct judgment about the validity of the candidate model, which is useful for the validation of simulation models in practical engineering design. Keywords Model validation . Parameter calibration . Stochastic kriging model . Area metric . Epistemic uncertainty
1 Introduction Simulation modeling has become an important tool to analyze or predict the behavior of physical systems, especially under some specific scenarios where physical experiments cannot be conducted (often due to limited design cost). However, there Responsible Editor: Nam Ho Kim Electronic supplementary material The online version of this article (https://doi.org/10.1007/s00158-020-02715-z) contains supplementary material, which is available to authorized users. * Qi Zhou [email protected] 1
School of Aerospace Engineering, Huazhong University of Science & Technology, Wuhan 430074, People’s Republic of China
2
School of Material Science and Engineering, Huazhong University of Science & Technology, Wuhan 430074, People’s Republic of China
3
George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA
are inevitably some differences between the simulation results and experimental observations (Lü et al. 2018), which are generally caused by the uncertainties that exist in the design, manufacture, and experimental process, such as
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