A Meta-Optimization Framework Based on Hybrid Neuro-Regression for Quality-Oriented Laser Transmission Welding of PMMA–Metal Joints

This study presents an integrated modeling and optimization framework for laser transmission welding (LTW) of transparent polymethyl methacrylate (PMMA) joints using single- and multi-core copper wires as energy absorbers. The highly nonlinear relationships between laser power, welding speed, and spot diameter and the resulting shear force and weld width were modeled using a hybrid neuro-regression strategy combining data-driven learning with physically interpretable analytical formulations. A wide range of candidate mathematical models were systematically evaluated based on training and testing performance, residual behavior, and physical consistency. The results demonstrate that models exhibiting near-perfect training accuracy frequently suffered from severe overfitting and poor generalization, whereas intermediate-complexity formulations provided a more reliable balance between accuracy and robustness. Comparative analysis further showed that multi-core absorbers consistently produced higher shear strength and more uniform weld seams than single-core configurations. The selected robust models were subsequently integrated into a two-level ensemble meta-optimization framework employing Differential Evolution, Nelder–Mead, Random Search, and Simulated Annealing algorithms under multiple design scenarios. The meta-optimization process successfully eliminated model- and algorithm-dependent extreme solutions and identified stable consensus parameter regions. For the multi-core system, an optimal combination of 30 W laser power, 20 mm/s welding speed, and 0.7 mm spot diameter was obtained, achieving improved mechanical performance while remaining within experimentally validated limits. The proposed framework provides a physically grounded and reliable strategy for surrogate-based optimization of nonlinear welding processes.