Physically Interpretable Soft Sensor for Deformation Diagnostics in Extrusion-Based Shaping: A Case Study on Ceramic Roof Tiles

This study examines the longitudinal shortening of clay blanks during extrusion and introduces a hybrid soft sensor framework for early prediction of ceramic roof tile performance. Targeted properties include shrinkage, water absorption, and saturation. The models integrate real-time process data collected after vacuum extrusion and pressing with clay-specific descriptors such as carbonate content and granulometry, alongside additional variables including moisture, firing temperature, and length reduction. Partial Least Squares (PLS) regression was adopted as the core method due to robustness against multicollinearity and ease of industrial integration. In contrast to complex machine learning pipelines, PLS-based soft sensors enable lightweight edge deployment without reliance on IoT infrastructure. Complementary regression and machine learning models were used to benchmark predictive accuracy and explore nonlinear effects. The results confirm reliable prediction of key performance indicators and reveal mechanistic links between extrusion-induced deformation and downstream behavior. Although developed for clay systems, the framework is generalizable and can be adapted to other traditional ceramic processes or industries seeking interpretable, locally deployable solutions for process control.