A Hilbert-based physics-informed neural network for instantaneous meshing frequency estimation of planetary gear set

The instantaneous meshing frequency (IMF) is core information for monitoring the operation of planetary gear sets. Due to the complex amplitude modulation, estimating the IMF from vibration signal is challenging. Ridge extraction methods based on time–frequency analysis (TFA) are widely used to estimate the IMF in rotating machinery. However, since these methods process vibration signal in batches, they are unsuitable for online status monitoring applications. In this work, based on the vibration signal model of planetary gear set, a Hilbert-based physics-informed neural network (PINN) is designed to estimate IMF online. The proposed PINN mainly contains three modules. A FIR Hilbert filter is used to extract variation features from vibration signal. An encoder module implemented by transformer network is employed to estimate the IMF. A notch filter group decoder based on vibration signal model is designed to calculate the estimated errors. The parameters of transformer encoder module are updated using error signals. Leveraging the filtering capability of the notch filter group decoder, the PINN adaptively tracks IMF variations without requiring labeled datasets and offline model training. Furthermore, the modules in the PINN process data sequentially, making it well-suited for real-time online status monitoring of planetary gear sets. Simulations and experiments demonstrate the effectiveness and robustness of the PINN for IMF estimation in planetary gear sets.