Gaussian Process Regression for Product Geometry Prediction in CAE Modeling

Superplastic forming is an advanced technology used in the aerospace and automotive industries, as well as in the medical sector, for fabricating complex seamless components. However, its application is limited by high costs and the extended duration of the process. While finite element analysis in CAE systems such as ANSYS provides accurate results, it is computationally expensive. While finite element analysis performed in CAE systems such as ANSYS provides high-fidelity results, its computational expense creates a need for fast and accurate predictive models capable of supplementing or replacing this approach in multi-criteria analysis tasks. Despite the increasing adoption of machine learning across various disciplines, the development of reliable predictive models for specific geometric characteristics of superplastically formed components remains an understudied research area. The purpose of this study is to develop and verify a Gaussian process based model for predicting key geometric parameters of a hemisphere during the superplastic forming. An additional objective was to create an initial dataset using data generated from numerical simulations. The Latin Hypercube Sampling method was employed to design the experiment and generate the initial dataset, enabling efficient variation of material parameters K, m and pressure regime within ranges typical for aluminum alloys. Based on data from 50 numerical simulations, a predictive model for the hemisphere’s geometric characteristics was developed with Gaussian Process Regression with a composite kernel. Model hyperparameter optimization was performed using RandomizedSearchCV. The developed Gaussian Process Regression model demonstrated high accuracy, achieving a coefficient of determination greater than 0.90 on the validation set for all target variables: thickness at the pole, average height, and height difference. Analysis of the Mean Squared Error confirmed the models generalization capability and absence of overfitting. This research is aimed at integrating the model into a digital twin system for real-time optimization of process parameters. The main challenge in scaling this approach is the computational cost associated with generating the required training data.

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