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<p>Accurate prediction of milling forces is essential for optimizing machining processes and ensuring quality in difficult-to-cut materials like GH4169 superalloy. This paper presents a novel hybrid data‑driven intelligent framework that integrates a high-fidelity Smoothed Particle Galerkin (SPG) simulation with an Improved Dung Beetle Optimizer (IDBO)-enhanced Back-Propagation Neural Network (BP-NN). First, an SPG-finite element (SPG-FE) model is developed to simulate the milling process. Compared with traditional SPH-FE and FE models, the SPG-FE model achieves superior accuracy, with relative errors for the force components <i>F</i><sub><i>x</i></sub> and <i>F</i><sub><i>y</i></sub> consistently below 6%, providing a reliable dataset for subsequent NN modeling. To overcome the BP-NN’s susceptibility to local optima and slow convergence, the IDBO algorithm is introduced, employing a Chebyshev chaotic map for population initialization to optimize the network’s weights and thresholds. Comprehensive evaluation using five-fold cross-validation (5-CV) is conducted against four benchmark models: the BP-NN, the Genetic Algorithm optimized BP-NN (GA-BP-NN), the Particle Swarm Optimization optimized BP-NN (PSO-BP-NN), and the Dung Beetle Optimizer optimized BP-NN (DBO-BP-NN). The proposed IDBO-BP-NN model achieves a Mean Absolute Deviation (MAD) of 8.7, a Mean Relative Error (MRE) of 3.4%, a Mean Squared Error (MSE) of 76.2, and a coefficient of determination (R<sup>2</sup>) of 0.98. Independent experimental validation on previously unseen milling conditions further confirms the model's accuracy, with relative errors for both force components consistently below 3.5%. These results confirm that the SPG-FE model generates high-quality simulation data, and the IDBO effectively addresses the limitations of BP-NNs. The proposed framework offers an accurate and robust solution for milling forces prediction, with significant potential for intelligent process planning in advanced manufacturing.</p>

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A Data-driven IDBO-BP-NN Model for Predicting Milling Forces of GH4169 Superalloy Based on SPG-FE Simulation

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Guangxu Zhu

摘要

Accurate prediction of milling forces is essential for optimizing machining processes and ensuring quality in difficult-to-cut materials like GH4169 superalloy. This paper presents a novel hybrid data‑driven intelligent framework that integrates a high-fidelity Smoothed Particle Galerkin (SPG) simulation with an Improved Dung Beetle Optimizer (IDBO)-enhanced Back-Propagation Neural Network (BP-NN). First, an SPG-finite element (SPG-FE) model is developed to simulate the milling process. Compared with traditional SPH-FE and FE models, the SPG-FE model achieves superior accuracy, with relative errors for the force components Fx and Fy consistently below 6%, providing a reliable dataset for subsequent NN modeling. To overcome the BP-NN’s susceptibility to local optima and slow convergence, the IDBO algorithm is introduced, employing a Chebyshev chaotic map for population initialization to optimize the network’s weights and thresholds. Comprehensive evaluation using five-fold cross-validation (5-CV) is conducted against four benchmark models: the BP-NN, the Genetic Algorithm optimized BP-NN (GA-BP-NN), the Particle Swarm Optimization optimized BP-NN (PSO-BP-NN), and the Dung Beetle Optimizer optimized BP-NN (DBO-BP-NN). The proposed IDBO-BP-NN model achieves a Mean Absolute Deviation (MAD) of 8.7, a Mean Relative Error (MRE) of 3.4%, a Mean Squared Error (MSE) of 76.2, and a coefficient of determination (R2) of 0.98. Independent experimental validation on previously unseen milling conditions further confirms the model's accuracy, with relative errors for both force components consistently below 3.5%. These results confirm that the SPG-FE model generates high-quality simulation data, and the IDBO effectively addresses the limitations of BP-NNs. The proposed framework offers an accurate and robust solution for milling forces prediction, with significant potential for intelligent process planning in advanced manufacturing.