Data engineering and machine learning for solving the inverse problem based on CAE simulation results

The use of machine learning in solving direct forecasting problems is becoming an alternative to the use of comprehensive finite element modeling. However, the solutions of inverse problem by means of machine learning is conventionally not considered in the literature. Traditional approaches are based on iterative calculations that require multiple runs of models and do not work in real time, which limits the creation of digital doubles.

The objective of this study is to solve the inverse problem by developing and verifying a Gaussian regression (GPR) model for determining the strain rate sensitivity index of superplastic material from the results of bulge tests based on the results of finite element calculations. The results of finite element modeling of the superplastic forming process in the ANSYS CAE package were used as a data source. 120 finite element simulations were performed, 40 for each of the three pressure modes. Two GPR models have been developed. One is for defining K with the Matern kernel, the second is for m with the RBF kernel. It is shown that replacing the RBF kernel with the Matern kernel (ν = 2,5) reduces the median relative uncertainty of the forecast for parameter K from 50 to 16%. The following quality metrics were obtained on the test sample: R² = 0.91 for K and R² = 0.92 for m, the relative RMS error is 20% for K and 7% for m.

The developed model can be used for non-destructive quality control, integration into digital twins, and optimization of superplastic forming processes.

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