From simulation to metamodel to experiment: Evaluating the prediction accuracy of polynomial regression models for clinch joint properties

In modern lightweight design, mechanical joining methods such as clinching are increasingly used due to their efficiency and suitability for joining dissimilar materials. However, variations in process parameters and material properties can lead to significant deviations in the resulting joint geometry. This study investigates the ability of global polynomial regression models to predict such deviations in clinch joint properties, based on finite element (FE) simulation data and evaluates them through variation simulations and experimental testing. A comprehensive dataset was generated using a validated simulation model to train polynomial regression models. These models were then applied to six distinct clinching process configurations. The metamodels show excellent agreement with the variation simulations, achieving coefficients of prognosis (CoP) above 0.95. Experimental validation using z-scores and Empirical Coverage Probability (ECP) indicates high predictive accuracy for bottom thickness (BT), partially accurate results for neck thickness (NE), and a systematic underestimation of interlock (IL). The predicted 95.5 % confidence intervals are overly conservative for bottom thickness, while for neck thickness and interlock, the intervals are often misaligned with the actual measurements, reflecting biased predictions. The results underline both the potential and the limitations of polynomial regression models for predicting variations in clinch joint properties. While the approach shows promise for designing reliable clinch joints, the study highlights challenges in transferring simulation-trained metamodels to experimental conditions due to uncertainties in the metamodels, the numerical simulations and the experiments.