A Physic-Informed Data-Driven Relational Model of Plastic Strain vs. Process Parameters during Integrated Heating and Mechanical Rolling Forming of Hull Plates

Integrated heat and roll forming (IHMRF) is a process that uses thermal and mechanical loads to produce localized plastic strains in plates to form complex curvature hull plates. The magnitude of the resulting plastic strain depends mainly on the following forming parameters: the machining parameters (power of the heat source, speed of the heat source, and the forming depth of the rollers), the thickness of the plate, and the thermo-physical and mechanical properties of the plate. Finding the correspondence between the plastic strain and forming parameters is the key to selecting the appropriate machining parameters for forming. A data-driven approach is ideal for this purpose. However, due to the characteristics of the IHMRF process, the forming process involves a large number of variables, and different materials have different temperature-dependent yield strengths. These high-dimensional input characteristics create a conflict between the required number of samples and the model training requirements. This paper presents a physically informed data-driven (PIDD) approach for modeling the relationship between forming parameters and plastic strains in IHMRF. Based on dimensional analysis and domain knowledge, the proposed method derives the basic thermal and mechanical relationships between the forming parameters, obtaining a much smaller number of physical parameters. These physical parameters are expressions of the physical knowledge of forming in low-dimensional space. Using the physical parameters yields higher accuracy on fewer sample data points than directly using the forming parameters as input features. Furthermore, the models trained on a variety of commonly used materials and plate thicknesses achieved comparable accuracy to the numerical simulation with unseen materials and plate thicknesses. Experimental and numerical simulations further verify the effectiveness of the proposed method by machining plates of various materials to the same shape.