Integration method of compressed sensing with variational mode decomposition based on gray wolf optimization and its denoising effect in mud pulse signal

The continuous wave mud pulse transmission holds great promise for the future of downhole data communication. However, significant noise interference during the transmission process poses a formidable challenge for decoding. In particular, effectively eliminating random noise with a substantial amplitude that overlaps with the pulse signal spectrum has long been a complex issue. To address this, an enhanced integration algorithm that merges variational mode decomposition (VMD) and compressed sensing (CS) to suppress high-intensity random noise is proposed in this paper. In response to the inadequacy of manually preset parameters in VMD, which often leads to suboptimal decomposition outcomes, the gray wolf optimization algorithm is designed to obtain the optimal penalty factor and decomposition mode number in VMD. Subsequently, the optimized parameter combination decomposes the signal into a series of intrinsic modes. The mode exhibiting a stronger correlation with the original signal is retained to enhance signal sparsity, thereby fulfilling the prerequisite for compressed sensing. The signal is then observed and reconstructed using the compressed sensing method to yield the final signal. The proposed algorithm has been compared with VMD, CS, and CEEMD; the results demonstrate that the method can enhance the signal–noise ratio by up to ∼20.55 dB. Furthermore, it yields higher correlation coefficients and smaller mean square errors. Moreover, the experimental results using real field data show that the useful pulse waveforms can be recognized effectively, assisting surface workers in acquiring precise downhole information, enhancing drilling efficiency, and significantly reducing the risk of engineering accidents.