Abstract This paper aims to provide new insights into model calibration, which plays an essential role in improving the validity of Modeling and Simulation (M&S) in engineering design and analysis. Various existing model calibration approaches including the direct Bayesian calibration method, the well-known Kennedy and O’Hagan (KOH) framework and its variants, and the optimization-based calibration method, are first investigated. It is observed that the direct Bayesian calibration and optimization-based calibration may be misled by potentially wrong information if the computer model cannot adequately capture the underlying true physics, while the effectiveness of the KOH framework and its variants is significantly affected by the prior distributions of the unknown model parameters. Based on this observation, a sequential model calibration and validation (SeCAV) framework is proposed to improve the efficacy of both model parameter calibration and bias correction for the purpose of uncertainty quantification and reduction. In the proposed method, the model validation and Bayesian calibration are implemented in a sequential manner, where the former serves as a filter to select the best experimental data for the latter, and provides the latter with a confidence probability as a weight factor for updating the uncertain model parameters. The parameter calibration result is then integrated with model bias correction to improve the prediction accuracy of the M&S. A mathematical example and an engineering example are employed to demonstrate the advantages and disadvantages of different approaches. The results show that the SeCAV framework, in general, performs better than the existing methods.

中文翻译：

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用于模型不确定性量化和降低的顺序校准和验证框架

摘要 本文旨在为模型校准提供新的见解，这对于提高工程设计和分析中建模与仿真 (M&S) 的有效性起着至关重要的作用。首先研究了各种现有的模型校准方法，包括直接贝叶斯校准方法、著名的肯尼迪和奥哈根 (KOH) 框架及其变体，以及基于优化的校准方法。据观察，如果计算机模型不能充分捕捉潜在的真实物理，直接贝叶斯校准和基于优化的校准可能会被潜在的错误信息误导，而 KOH 框架及其变体的有效性受先验分布的显着影响未知的模型参数。基于这一观察，提出了一个序列模型校准和验证 (SeCAV) 框架，以提高模型参数校准和偏差校正的功效，以实现不确定性量化和减少。在所提出的方法中，模型验证和贝叶斯校准以顺序方式进行，其中前者作为过滤器为后者选择最佳实验数据，并为后者提供置信概率作为权重因子更新不确定的模型参数。然后将参数校准结果与模型偏差校正相结合，以提高 M&S 的预测精度。一个数学例子和一个工程例子被用来展示不同方法的优点和缺点。结果表明，SeCAV 框架，一般来说，