## 1 Introduction
However, EMD has the problem of mode mixing, that different time scales are contained in a mode function, which blurs the distinction between effective components and random noise. To eliminate the problem, [PERSON] and [PERSON] [32] developed ensemble empirical mode decomposition (EEMD), applying noise-assisted technology to compensate for the absent frequency. As the mean of white noise is zero, the amplitude of the signal has hardly changed after multiple iterations. Based on the promising characteristics, [PERSON] and [PERSON] [33] developed a new seismic denoising method combining EEMD with adaptive thresholding. For less energy leakage caused by the extra noise, [PERSON] et al. [34] proposed a novel noise-supplement method called complete ensemble empirical mode decomposition (CEEMD). By adding a set of positive and negative white noise to the signal, its decomposition result is the average of the added signals. [PERSON] and [PERSON] [20] applied it to acquire a higher spectral-spatial resolution than WT. The problem of mode aliasing has been alleviated in these methods by altering the distribution of extreme points, but is never solved. [PERSON] and [PERSON] [35] developed a new recursive method, called variational mode decomposition (VMD), as an alternative of EMD-based methods. It can achieve adaptive separation between frequency bands of nonstationary time series through iterative optimization. Different from the EMD-based methods, it has a sufficient mathematic foundation, and its mode has a specific physical meaning, which is assumed into a frequency component mostly compacted around a certain center frequency. Besides, there is no modal aliasing existing in its non-linear components. However, MS signals, unlike voice signals or current signals covering the entire time window, usually account for only a part of the monitoring period due to their own uniqueness. Except for the interval where the effective signal exists, the sample points at other locations have little contribution to the post-analysis of MS events. The VMD algorithm, despite its outstanding performance, processes the noisy signal in the entire time window like most of the above algorithms. It can only separate the high-frequency noise from the effective signal by choosing appropriate components. However, it does not play an important role in residual fluctuations at non-signal positions because of their similarity in wave characteristics. To overcome the shortcoming, Akaike information criterion (AIC) is introduced to determine the location of the effective signal in the time window. The quality of MS signal can be further improved by being processed in sections. The purpose of this paper is to develop a new method combining VMD and AIC to suppress random noise in MS signals. In the following section, we first introduce the theoretical background of VMD and AIC, and give the basic criterion of choosing valuable modes. Next, the proposed method is applied to a simple synthetic example and 11 synthetic MS signals with different SNRs to compare its performance with EEMD, CEEMD and VMD. Finally, we denoise 40 noisy signals collected in Shuangjiangkou Hydropower Station by these methods.