A new model updating strategy with physics-based and data-driven models

Abstract

For engineering simulation models, insufficient experimental data and imperfect understanding of underlying physical principles often make predictive models inaccurate. It is difficult to reduce the model bias effectively with limited information. To improve the predictive performances of the models, this paper proposes a new model updating strategy utilizing a data-driven model to integrate with a physics-based model. One of the main strengths of the proposed method is that it maximizes the utilization of existing limited information by combining physics-based and data-driven models built based on different principles. First, the physics-based model is updated via selecting a suitable updating method and updating formulation. A data-driven model is then constructed using the Gaussian process (GP) regression. Finally, a weight combination is employed to obtain the updated predictive model where the weights of experimental sites and non-experimental sites are determined by the minimum discrepancy of probability distributions of the posterior error and another data-driven model, respectively. The Sandia thermal challenge problem is used to demonstrate the effectiveness of the proposed method.

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Funding

This work was supported by the China Scholarship Council (No. 201808330375), National Natural Science Foundation of China (Grant No. 51475425), and Zhejiang Provincial Natural Science Foundation of China (Grant No. LQ18E050014).

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Correspondence to Baisong Pan.

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The presented results are produced in MATLAB, and the code and data are available from the corresponding author on reasonable request.

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Xiang, Y., Pan, B. & Luo, L. A new model updating strategy with physics-based and data-driven models. Struct Multidisc Optim (2021). https://doi.org/10.1007/s00158-021-02868-5

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Keywords

  • Model updating
  • Physics-based model
  • Data-driven model
  • Gaussian process
  • Maximum likelihood estimation