CPO-VMD Combined With Multiscale Permutation Entropy for Noise Reduction in GNSS Vertical Time Series in Mining Areas

The vertical time series of deformation monitoring data are often interfered with by multiple noises, which makes it difficult to extract useful information. In order to effectively filter out the noise components in the deformation monitoring data, this paper proposes a time series noise reduction method (CPO-VMD-MPE) that integrates the crested porcupine optimizer (CPO), the variational modal decomposition (VMD), and the multiscale permutation entropy (MPE). The method uses the CPO algorithm to optimize the key parameters of the VMD, determines the high-frequency components with MPE values higher than a set threshold as noise components and removes them, and then reconstructs the remaining components in order to obtain the noise-reduced time series. The results of simulation and example analysis show that compared with wavelet denoising (WD), empirical modal decomposition (EMD), ensemble empirical mode decomposition (EEMD), and improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), this method shows significant advantages in the evaluation indexes of noise reduction effect—Pearson’s correlation coefficient (R), the signal-to-noise ratio (SNR), and the root-mean-square error (RMSE)—and all the indexes are better than the comparative methods. Taken together, the CPO-VMD-MPE method proposed in this paper significantly reduces the noise in the time series and provides a better theoretical and methodological reference for deformation analysis and prediction.