FEM-driven machine learning approach for characterizing stress magnitude, peak temperature and weld zone deformation in ultrasonic welding of metallic multilayers: application to battery cells

Abstract This study investigates the innovative application of machine learning (ML) models to predict critical parameters—stress magnitude (SM), peak temperature (PT), and plastic strain (PS)—in ultrasonic welding of metallic multilayers. Extensive numerical simulations were employed to develop and evaluate three ML models: Radial Basis Function (RBF), Random Forest (RF), and Kernel Ridge Regression (KRR). According to the results, the KRR model demonstrated superior performance, achieving the lowest RMSE and highest R 2 values of 0.068 ( R 2 = 0.941) for SM, 0.075 ( R 2 = 0.929) for PT, and 0.071 ( R 2 = 0.946) for PS, with fewer data samples required. KRR also exhibited low squared bias and variance values, ranging from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>×</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3.2</mml:mn> <mml:mo>×</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> for bias and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mstyle scriptlevel="0"/> <mml:mn>2.2</mml:mn> <mml:mo>×</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> <mml:mo>−</mml:mo> <mml:mn>3.6</mml:mn> <mml:mo>×</mml:mo> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:mrow> </mml:math> for variance, indicating its precision in predicting the output targets. Moreover, the systematic categorization of input features, including material properties, geometrical factors, and welding parameters, highlighted their significant influence on predictive accuracy, particularly the crucial role of welding parameters at higher output values. Finally, a case study on ultrasonic welding of copper multilayers underscores the model’s effectiveness in unraveling complex relationships, providing a robust tool for optimizing and advancing ultrasonic welding processes.