A Physics-Informed Multimodal Transformer Model for Machining Energy Consumption Prediction

Abstract

Abstract. Machining energy consumption (MEC) prediction plays an important role in energy planning, management, and conservation in the manufacturing industry. Existing MEC prediction techniques are commonly classified into physics-based models (PBMs) and data-driven approaches (DDAs), which rely on physical knowledge and data learning, respectively. While DDAs alleviate limitations associated with PBMs due to assumptions needed to simplify the complexity, most of them ignore the underlying physical knowledge and may struggle with generalization under varying machining conditions. Moreover, machining data is inherently heterogeneous in modalities, such as sensor signals and process parameters, making data fusion another challenge. To address the above issues, this article proposes a physics-informed multimodal transformer (PIMT) model for MEC prediction. First, based on the studies of machining energy nature, a synthetic data augmentation strategy is proposed to incorporate energy-relevant physical principles from PBMs. Second, a structured multimodal network is designed to align and fuse features from diverse data modalities. Then, a transformer with multihead attention is employed to capture complex temporal dependencies and cross-modal interactions within the fused data. Finally, three groups of comparative experiments with different machine tools, materials, cutting tools, and machining parameters are designed to validate and demonstrate the proposed approaches. The results showed that the proposed PIMT model achieves the lowest root mean square error (RMSE) (0.048) and mean absolute percentage error (MAPE) (12.33%), while reducing the training time (at least 152 s, 1.7 s, and 29.9 s) and the number of trainable parameters (at least 49.7%, 51.3%, and 67.6%) compared to state-of-the-art methods. Furthermore, the PIMT model consistently produces smaller errors across nearly all evaluation metrics and accurately forecasts MEC throughout continuous machining conditions.