A sustainable hybrid FEA–AI optimization framework for multistage deep drawing of unidirectionally rolled copper micro-cups

Precision micro-cups for electronic and medical applications require stringent control of resultant tool force (RTF) and spring-back (SB) to prevent defects, excessive tool loading, and material waste. However, conventional micro deep-drawing processes remain reliant on costly trial-and-error experimentation and exhibit limited predictive reliability under severe plastic deformation and rolling-induced anisotropy. To address this challenge, a robust and computationally reproducible optimization framework is developed for sustainable, high-volume manufacturing. Multistage deep drawing of unidirectionally rolled copper strips subjected to 200% thickness reduction (true strain − 2.78) is investigated using validated finite element modeling (FEM), with clearance (C), punch nose radius (PNR), and coefficient of friction (µ) systematically varied through a Central Composite Design. The resulting FEM-generated dataset is used to train predictive models based on Response Surface Methodology (RSM), Levenberg–Marquardt artificial neural networks (LM-ANN), and Bayesian Regularized artificial neural networks (BR-ANN). Experimental trials are conducted independently for model validation and performance assessment, ensuring that the ANN models are FEM-trained and experimentally validated rather than experimentally trained. These predictive models are integrated with a Genetic Algorithm (GA) for global optimization of RTF and SB. Model performance is evaluated using R², RMSE, MAPE, MSRE, and Nash–Sutcliffe Efficiency (NSE) for both seen (simulation-based) and unseen (experimental) datasets. The BR-ANN–GA framework demonstrates superior predictive accuracy and robustness, identifying optimal parameters of C = 0.57, PNR = 2, and µ = 0.10, minimizing RTF and SB. Prediction errors are limited to 0.35% (RTF) and 0.41% (SB) for FEM-trained data, while experimental validation trials maintain low errors of 1.7% and 2.68%, respectively, outperforming FEM, RSM, and LM-ANN approaches. Although the study is constrained to axisymmetric geometries and unidirectionally rolled copper, the proposed FEM-trained and experimentally validated BR-ANN–GA framework significantly enhances predictive reliability while reducing energy consumption, material waste, and experimental cost, offering a scalable optimization methodology for precision micro deep drawing.