Abstracting Prediction of Surface Roughness in Laser Powder Bed Fusion Using Logical Reasoning and Category Theory

Accurately predicting the surface roughness of laser powder bed fusion parts based on process design is critical for optimisation of process design to reduce excessive surface roughness in laser powder bed fusion. So far, many prediction models have been presented within academia. The key elements of these models, such as the techniques adopted, process variables considered, machines, materials, and surfaces targeted, and roughness parameters used, may all be different. How to put aside these differences and explore the nature of the prediction problem has become a research question to be addressed. In this paper, logical reasoning and category theory are introduced to abstract the prediction of surface roughness in laser powder bed fusion and therefore a unified abstract model is presented. Firstly, existing prediction models are classified into deductive and inductive models from the perspective of logical reasoning. The strengths and inherent limitations of each type of models are discussed and the lack of abductive reasoning in these models is highlighted. Then, a complete framework for surface roughness prediction in laser powder bed fusion is built via combining abductive reasoning with deductive and inductive reasoning. After that, the framework and prediction process are formalised using category theory and thus a topologically and logically stable and interpretable abstract model is obtained. Finally, the application of the abstract model is illustrated through a simple example. This work provides a generalised, formalised, and rigorous framework for all existing prediction models and would facilitate development of new prediction models in the future.