Abstract
A part's surface layer quality is dictated by several factors, including surface roughness, the microstructure of the metal surface layer, and the part's mechanical and physical state. The operating characteristics of machine components, such as wear resistance, vibration resistance, contact strength, connection strength, part strength under cyclic loads, etc., are influenced by surface layer conditions. The part's surface roughness is just one of the primary geometric attributes of a part's quality, which is its accuracy in terms of size and shape. The current work models the roughness surface of 3D selective laser melting of metal materials using genetic programming and multiple regression. It then explains how to measure surface roughness using this method. A novel approach to pattern recognition for analyzing the roughness of metal materials melted using a 3D selective laser is introduced. Fractal geometry determines the complexity of 3D selective laser melting of metal materials.

Key words
3D selective melting, graph theory, pattern recognition, genetic programming, multiple regression

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