The Parameter-Optimized Recursive Sliding Variational Mode Decomposition Algorithm and Its Application in Sensor Signal Processing

In industrial polishing, the sensor on the polishing motor needs to extract accurate signals in real time. Due to the insufficient real-time performance of Variational Mode Decomposition (VMD) for signal extraction, some studies have proposed the Recursive Sliding Variational Mode Decomposition (RSVMD) algorithm to address this limitation. However, RSVMD can exhibit unstable performance in strong-interference scenarios. To suppress this phenomenon, a Parameter-Optimized Recursive Sliding Variational Mode Decomposition (PO-RSVMD) algorithm is proposed. The PO-RSVMD algorithm optimizes RSVMD in the following two ways: First, an iterative termination condition based on modal component error mutation judgment is introduced to prevent over-decomposition. Second, a rate learning factor is introduced to automatically adjust the initial center frequency of the current window to reduce errors. Through simulation experiments with signals with different signal-to-noise ratios (SNR), it is found that as the SNR increases from 0 dB to 17 dB, the PO-RSVMD algorithm accelerates the iteration time by at least 53% compared to VMD and RSVMD; the number of iterations decreases by at least 57%; and the RMSE is reduced by 35% compared to the other two algorithms. Furthermore, when applying the PO-RSVMD algorithm and the RSVMD algorithm to the Inertial Measurement Unit (IMU) for measuring signal extraction performance under strong interference conditions after the polishing motor starts, the average iteration time and number of iterations of PO-RSVMD are significantly lower than those of RSVMD, demonstrating its capability for rapid signal extraction. Moreover, the average RMSE values of the two algorithms are very close, verifying the high real-time performance and stability of PO-RSVMD in practical applications.