Integrating dimensional and scaling analyses with functional modelling and graphs: An approach to comprehend mass transfer in welding

Significant efforts have been made to understand the intricacies of the welding process using numerical methods, machine learning, dimensional, and scaling analyses. Dimensional analysis (DA) is used for qualitative studies of weld pool spreading, heat transfer in welding, welding parameters, and detachment-droplet formation in welding. Nevertheless, DA have been used often in a rather conventional manner. This article proposes to combine DA principles with causally oriented
graphical representations and functional analysis to augment the separate capabilities of those methods. The approach uses a physics-based functional model to decompose the welding phenomena into functions, with dimensionless numbers (π)
representing aspects of those functions in form of mathematical relationships between the variables. These mathematical relationships are illustrated as a causally oriented graph. This graph is transformed into a system dynamic counterpart. The
values of π numbers are estimated using a single example with the developed methodology. The π values in the model are the analogous of biases in Artificial Neural Networks (ANN). The current modelling approach has the advantage of exploiting supplementary sources of knowledge and consequently requires limited data in comparison to supervised machine learning (ML) algorithms used in the field. The proposed methodology is demonstrated with a case study of gas metal arc welding (GMAW) for mild steel. The developed model predicts the droplet formation in GMAW with high accuracy and offer multiple possibilities for extension and generalization to other welding and additive manufacturing processes.