Semi-Supervised Learning based on Mass Conservation to improve Quality Predictions in a Polymer Pipe Production Process

In polymer pipe production, achieving dimensional accuracy (diameter, wall thickness) is crucial but challenging due to the complexity of the process and its associated fluctuations. Consequently, accurate quality models are required to predict the pipe dimensions in advance to steer the process accordingly. Unfortunately, data scarcity is prevalent in industrial settings hindering the development of purely data-driven models while the integration of physical knowledge is largely neglected by existing work in this domain. Therefore, we propose a semi-supervised method based on mass conservation allowing the usage of synthetically generated data in addition to actual process measurements during the model training. The resulting method of physics-informed machine learning facilitates the training process and improves the generalizability of the resulting model in spite of small data sets. For validation purposes the data from an actual bi-oriented PVC pipe production process is used within a randomized cross-validation. It was shown that the proposed method produces superior results and reduces the mean squared error significantly by 41% to $\mathbf{6 0} \%$ when only 10 to $\mathbf{4 0}$ actual training samples are available. As a result, the prediction accuracy for pipe dimensions is notably increased allowing improved control of the process reducing dimensional fluctuations and material overweight despite data scarcity.