To eliminate the noise from the signals received by MEMS vector hydrophone, a joint algorithm is proposed in this paper based on wavelet threshold (WT) denoising, variational mode decomposition (VMD) optimized by a hybrid algorithm of Multiverse Optimizer (MVO) and Particle Swarm Optimization (PSO), and correlation coefficient (CC) judgment to perform the signal denoising of MEMS vector hydrophone, named as MVO-PSO-VMD-CC-WT, whose fitness function is the root mean square error (RMSE) and whose individual is the parameters of VMD. For every individual, the original signal is decomposed by VMD into pure components, noisy components, and noise components in terms of CC judgment, where the pure components are directly retained, the noisy components are denoised by WT denoising, and the noise components are discarded, and then, the denoised noisy components and the pure components are reconstructed to be the denoised signal of the original signal. Then, the obtained optimal individual is utilized to perform the signal denoising by MVO-PSO-VMD-CC-WT by the use of the above repeated signal processing. Two simulated experimental results show that the MVO-PSO-VMD-CC-WT algorithm which has the highest signal-to-noise ratio and the least RMSE is superior to the other compared algorithms. And the proposed MVO-PSO-VMD-CC-WT algorithm is effectively applied to perform the signal denoising of the actual lake experiments. Therefore, the proposed MVO-PSO-VMD-CC-WT is suitable for the signal denoising and can be applied into the actual experiments in signal processing.

中文翻译：

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基于小波阈值去噪和优化变分模式分解的信号去噪

为了消除MEMS矢量水听器接收信号中的噪声，本文提出了一种基于小波阈值(WT)去噪、变分模式分解(VMD)的联合算法，该算法通过多元宇宙优化器(MVO)和粒子群的混合算法优化。 MEMS矢量水听器信号去噪的优化（PSO）和相关系数（CC）判断，命名为MVO-PSO-VMD-CC-WT，其适应度函数为均方根误差（RMSE），个体为VMD 的参数。对于每个个体，通过VMD将原始信号分解为纯成分、噪声成分和CC判断中的噪声成分，其中纯成分直接保留，噪声成分通过WT去噪，噪声成分被丢弃， 然后，去噪后的噪声分量和纯分量被重构为原始信号的去噪信号。然后，利用获得的最优个体，通过使用上述重复信号处理，通过MVO-PSO-VMD-CC-WT进行信号去噪。两个模拟实验结果表明，具有最高信噪比和最小RMSE的MVO-PSO-VMD-CC-WT算法优于其他比较算法。并且所提出的 MVO-PSO-VMD-CC-WT 算法有效地应用于执行实际湖泊实验的信号去噪。因此，所提出的 MVO-PSO-VMD-CC-WT 适用于信号去噪，可以应用于信号处理的实际实验中。MVO-PSO-VMD-CC-WT利用得到的最优个体，利用上述重复信号处理进行信号去噪。两个模拟实验结果表明，具有最高信噪比和最小RMSE的MVO-PSO-VMD-CC-WT算法优于其他比较算法。并且所提出的 MVO-PSO-VMD-CC-WT 算法有效地应用于执行实际湖泊实验的信号去噪。因此，所提出的 MVO-PSO-VMD-CC-WT 适用于信号去噪，可以应用于信号处理的实际实验中。MVO-PSO-VMD-CC-WT利用得到的最优个体，利用上述重复信号处理进行信号去噪。两个模拟实验结果表明，具有最高信噪比和最小RMSE的MVO-PSO-VMD-CC-WT算法优于其他比较算法。并且所提出的 MVO-PSO-VMD-CC-WT 算法有效地应用于执行实际湖泊实验的信号去噪。因此，所提出的 MVO-PSO-VMD-CC-WT 适用于信号去噪，可以应用于信号处理的实际实验中。两个模拟实验结果表明，具有最高信噪比和最小RMSE的MVO-PSO-VMD-CC-WT算法优于其他比较算法。并且所提出的 MVO-PSO-VMD-CC-WT 算法有效地应用于执行实际湖泊实验的信号去噪。因此，所提出的 MVO-PSO-VMD-CC-WT 适用于信号去噪，可以应用于信号处理的实际实验中。两个模拟实验结果表明，具有最高信噪比和最小RMSE的MVO-PSO-VMD-CC-WT算法优于其他比较算法。并且所提出的 MVO-PSO-VMD-CC-WT 算法有效地应用于执行实际湖泊实验的信号去噪。因此，所提出的 MVO-PSO-VMD-CC-WT 适用于信号去噪，可以应用于信号处理的实际实验中。