A Machine Learning Approach for Analyzing Residual Stress Distribution in Cold Spray Coatings

Abstract

This study establishes a machine learning (ML) model utilizing the expectation-maximization approach to predict maximum residual stresses, encompassing both tensile and compressive states, in the cold spraying process across various substrates. The main feature of the ML algorithm lies in its two-step iterative process, where the Expectation (E step) refines latent variable estimates, and the Maximization (M step) optimizes the model’s parameters, aligning them with the data. Based on the results, regression analysis highlighted the predictive capabilities of the proposed model for tensile and compressive residual stresses, exhibiting root mean square error values of 8.8 and 3.5%, along with determination coefficient values of 0.915 and 0.968, respectively, indicating higher prediction performance in the compression mode. This suggests higher predictability for residual stress within the depth of material’s body. Moreover, analyzing low residual stress levels underscored the significant impact of substrate and particle mechanical strength on prediction performance, whereas higher residual stress levels highlighted the strong influence of thermal conductivity. This correlation suggests that high stresses during the cold spray process generate more heat, thereby emphasizing the crucial role of thermal conductivity in predicting resultant residual stresses. Furthermore, a notable trend emerges as tensile stress increases, spotlighting the augmented influence of processing parameters in the prediction process. Conversely, at elevated compressive stresses, material properties’ weight factors assume a vital role in predictions. These findings offer insights into the intricate interplay between processing parameters and materials properties in determining resultant residual stresses during cold spraying.