Improved Training Strategies for Physics-Informed Neural Networks using Real Experimental Data in Aluminum Spot Welding

TL;DR

The paper addresses non-invasive quality control in aluminum resistance spot welding by training physics-informed neural networks (PINNs) that fuse governing equations with real experimental data. It introduces two training strategies: (i) progressive, fading-in experimental losses paired with a look-up-based, temperature-dependent material parameter update activated after a loss threshold, and (ii) a rolling-window learning-rate/early-stopping scheme to prevent premature convergence. The authors develop 1D and 2D axisymmetric PINNs to predict dynamic displacement and nugget diameter, demonstrating stable convergence and accurate predictions within experimental confidence intervals, and they show how parameters and welding-stage behavior can transfer from steel to aluminum. The results indicate strong potential for fast, model-based quality control in industrial RSW, with practical impact in predictive welding control and process optimization. The approach leverages temperature-dependent material properties, contact-heat models, and goal-loss penalties to connect internal process states to a single observable metric, $d_n$, enabling non-destructive quality assessment at scale.

Abstract

Resistance spot welding is the dominant joining process for the body-in-white in the automotive industry, where the weld nugget diameter is the key quality metric. Its measurement requires destructive testing, limiting the potential for efficient quality control. Physics-informed neural networks were investigated as a promising tool to reconstruct internal process states from experimental data, enabling model-based and non-invasive quality assessment in aluminum spot welding. A major challenge is the integration of real-world data into the network due to competing optimization objectives. To address this, we introduce two novel training strategies. First, experimental losses for dynamic displacement and nugget diameter are progressively included using a fading-in function to prevent excessive optimization conflicts. We also implement a custom learning rate scheduler and early stopping based on a rolling window to counteract premature reduction due to increased loss magnitudes. Second, we introduce a conditional update of temperature-dependent material parameters via a look-up table, activated only after a loss threshold is reached to ensure physically meaningful temperatures. An axially symmetric two-dimensional model was selected to represent the welding process accurately while maintaining computational efficiency. To reduce computational burden, the training strategies and model components were first systematically evaluated in one dimension, enabling controlled analysis of loss design and contact models. The two-dimensional network predicts dynamic displacement and nugget growth within the experimental confidence interval, supports transferring welding stages from steel to aluminum, and demonstrates strong potential for fast, model-based quality control in industrial applications.

Figures (23)

• Figure 1: The RSW phases encompass the initial setup, squeezing the workpieces together, executing the weld, and holding the electrodes in place until they return to the initial setup.
• Figure 2: Welding schedule for current $I(t)$ and dynamic displacement $u(t)$. The displacement is recorded up to 760 ms.
• Figure 3: Experimentally measured Temperature-dependent material parameters. Thermal diffusivity $\kappa$, coefficient $\xi$, and thermal expansion $\alpha_\text{th}$.
• Figure 4: Simplified system model. Left: Welding gun with the application point of $F$ and the position of the sheets. Right: Simplified 2D system with a spring displacement $u_\text{k}$ and the upper and lower sheet thicknesses $l^1$ and $l^2$, respectively.
• Figure 5: Left: Interplay between the control signal and the actuator. The evident hysteresis band is overlaid. Right: Estimated PID control behavior by fitting the PID constants.