A hybrid IDBO-BP-NN model considering work-hardening for surface roughness prediction in two-step milling of GH4169 superalloy

Purpose The purpose of this study is to accurately predict surface roughness in two-step milling (roughing followed by finishing) of GH4169 superalloy by considering the work-hardening effect induced by the roughing operations. Design/methodology/approach A hybrid improved dung beetle optimizer-back-propagation neural network (IDBO-BP-NN) model is proposed. The IDBO integrates a chaotic circle map into population initialization to enhance diversity and global search capability. Predictive performance is evaluated against the BP-NN, genetic algorithm (GA)-BP-NN, particle swarm optimization (PSO)-BP-NN and DBO-BP-NN models using mean absolute deviation (MAD), mean relative error (MRE), mean squared error (MSE) and coefficient of determination (R²). Findings The IDBO-BP-NN model achieves superior predictive performance, with a MAD of 0.051 µm, MRE of 5.0%, MSE of 0.004 µm2 and R2 of 0.969, along with faster and more stable convergence than all benchmarks. Independent validation on six untested conditions yields a maximum relative error of 9.59%, confirming strong generalization performance. Sensitivity analysis reveals that finishing cutting speed (v2) is the most influential factor (24.7%), followed by roughing cutting speed (v1, 19.2%), finishing feed per tooth (fz2, 15.8%) and roughing axial depth of cut (ap1, 12.5%). The remaining parameters (ap2, ae2, fz1, ae1) contribute between 5.9% and 8.6%, providing a detailed hierarchy for process planning. Originality/value This study integrates a chaotic circle map into DBO to optimize BP-NN model initialization, explicitly considering roughing-induced work-hardening. The IDBO-BP-NN model provides an accurate and generalizable approach for surface roughness prediction in two-step milling of GH4169 superalloy.