Design-centred physics-informed modelling: integrating functions, variables, behavioural law discovery, and contradiction resolution

A significant aspect of modern manufacturing involves the selection, modelling, and dynamic control of process parameters. This necessitates the development of advanced modelling methodologies capable of capturing intricate cause-and-effect relationships and interdependencies across systems and subsystems. The Dimensional Analysis and Conceptual Modelling (DACM) framework addresses this need by using directed graphs to represent causal relationships within complex systems. However, while the DACM framework is effective for modelling individual systems, it has limitations when connecting different parts of a system (subsystems) that need to work together. Moreover, the framework requires a mechanism to extract meaningful relationships between variables. To address these limitations, this study introduces new organs derived from bond graph theory, which perform specific functions, enabling effective modelling of interconnected systems. Expert knowledge, combined with the DACM framework, is used to represent systems as collections of functions and to assign appropriate variables to these functions. Relationships between variables are computed as power laws using LASSO and OLS regression algorithms. Unlike previous works, these algorithms rely solely on the fundamental dimensions of variables. In addition to variable assignment, expert knowledge is also used to validate the computed power laws, thus substituting experimental data with expert knowledge. The interaction between the derived dimensionless numbers is represented as a directed graph, capturing the causal relationships between the functions. The approach is demonstrated through a qualitative case study of Gas Metal Arc Welding, illustrating its potential for system modelling, analysis, and using explainable directed graphs for contradiction resolution.