A physics-informed dual-stream convolutional neural network method for in-situ continuous bolt preload monitoring and detection

Accurate perception of bolt preload is crucial for ensuring the reliability and safety of critical equipment such as aero-engines, high-speed trains, and wind turbines. To address the limitations of existing data-driven methods, including poor interpretability, heavy reliance on labeled data, and weak out-of-distribution generalization, this paper proposes a Physics-informed Dual-stream Convolutional Neural Network (PI-CNN) method for bolt preload detection. The core of the method lies in embedding the experimentally verified linear physical relationship between the square of natural frequency of bolt vibration and the preload into the neural network training process in the form of a gradient consistency loss. The model adopts a dual-channel 1D-CNN architecture to extract features from the raw vibration acceleration signals and their frequency spectra separately. It then incorporatesa handcrafted feature, specifically the squared natural frequency, to construct a data-physics dual-driven loss function. This design constrains the model predictions not only to fit the data but also to strictly adhere to the known physical law, thereby significantly enhancing the physical interpretability of the model. Experimental results demonstrate that the proposed method, guided by physical principles, markedly improves model interpretability, reduces dependency on labeled data, and enhances generalization performance under unseen working conditions, offering an efficient data-physics dual-driven solution for bolt preload detection.