Optimization and predictive modeling of weld nugget size in resistance spot welding of HSLA-65 steel using finite-element simulation and machine learning

Abstract

This study presents a comprehensive computational study of resistance spot welding (RSW) for high-strength low alloy (HSLA-65) steel. The weld nugget size is one of the critical quality characteristics defining the spot joint strength. Traditionally, the nugget diameter is evaluated through destructive testing, which is not only costly and time-consuming but also leads to material wastage and is inadequate for real-time monitoring and evaluation. To mitigate these challenges, this research develops and proposes a computational framework that combines design of experiments, optimization, and machine learning (ML)-based model to predict and optimize weld nugget size nondestructively. In this article, a weldability lobe curve is developed for HSLA-65, identifying the acceptable, nonacceptable, and expulsion regions based on weld nugget size, providing a robust framework for identifying optimal ranges and levels of crucial process parameters: weld current, weld time, and electrode force. A Box–Behnken experimental design was employed to conduct simulation trials and optimized using the Teaching–Learning-based Optimization algorithm. The optimal parameters are 7000 A weld current, 14 cycles of weld time, and 4 kN electrode force produced a weld nugget size of 9.79 mm, reflecting an 8.16% improvement compared to the best simulation output among the initial trials. Analysis of variance was performed, revealing that weld current (P < 0.05) and weld time (P < 0.05) significantly influence nugget formation, whereas electrode force (P = 0.15) was statistically insignificant. The model's overall statistical validity was confirmed by a computing F-value of 116.9, substantially exceeding the critical F-value of 4.77 at a 95% confidence level. Additionally, regression-based ML algorithms were employed to develop a predictive model for weld nugget diameter. The model's performance was evaluated using three measures: root mean square error (RMSE), mean square error (MSE), and R-squared. Among the tested models, Gaussian process regression exhibited the highest predictive accuracy, with an R-squared value of 0.98, MSE of 0.18, and RMSE of 0.42. A strong correlation was observed between the computational study and ML-based predictions, validating the effectiveness of the proposed approach for accurate nugget size estimation and process optimization in RSW of HSLA-65 steel.