# Application Research of Negative Pressure Wave Signal Denoising Method Based on VMD
###### Abstract  
The quality of pipeline leakage fault feature extractions deteriorates due to the influence of fluid pipeline running state and signal acquisition equipment. The pressure signal is characterized by high complexity, nonlinear and strong correlation. Therefore, traditional denoising methods have difficulty dealing with this kind of signal. In order to realize accurate leakage fault alarm and leak location, a denoising method based on variational mode decomposition (VMD) technology is proposed in this paper. Firstly, the intrinsic mode functions are screened out using the correlation coefficient. Secondly, information entropy is used to optimize the VMD decomposition layers \(k\). Finally, based on the denoising signal, the inflection point of the negative pressure wave is extracted, and the position of the leakage point is calculated according to the time difference between the two inflection points. To verify the effectiveness of the algorithm, both laboratory experiments and real pipeline tests are conducted. Experimental results show that the method proposed by this paper can be used to effectively denoise the pressure signal. Furthermore, from the perspective of positioning accuracy, compared other methods, the proposed method can achieve a better positioning effect, as the positioning accuracy of the laboratory experiment reaches up to 0.9%, and that of the real pipeline test leakage point reaches up to 0.41%.  
negative pressure wave; denoising; variational mode decomposition; correlation coefficient; information entropy; leak location +
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inflection point, which will lead to a large error in the location of water supply pipeline leakage fault points. Therefore, signal noise reduction processing is particularly important. The denoised signal can clearly represent the change in the NPW pressure drop caused by leakage.  
There are many signal denoising methods available: wavelet denoising can be achieved by setting a reasonable threshold [10]. However, if the pressure signal and the noise are both uncertain, the exact selection of a threshold value is very difficult. Empirical mode decomposition (EMD) can be used for adaptive signal decomposition. However, this algorithm lacks sufficient mathematical theory derivation, and there are some problems of mode aliasing and end effect [11]. Although ensemble EMD (EEMD) improves some of the shortcomings of EMD, it still lacks the definition of extreme points, and the robustness of signal decomposition is not good enough [12]. To solve the above problems, [PERSON] [13] proposed VMD. This algorithm has sufficient mathematical theory foundation. It overcomes the problems of EMD and EEMD algorithms [14].  
The decomposition levels \(k\) of VMD determine the degree of signal decomposition. Therefore, researchers have proposed many VMD parameter optimization methods. [PERSON] et al. [15] utilized the maximum weighted kurtosis index. [PERSON] et al. [16] proposed a parameter optimization method based on particle swarm optimization (PSO). In order to determine the number of modes, [PERSON] et al. [17] proposed a frequency-aided method. A common problem of the above methods is that the calculation amount is relatively large and the calculation time is relatively long [18]. In order to solve these problems effectively, we proposed a novel method based on VMD, which uses a minimum information entropy to optimize the number of decomposition layers, and the optimal noise reduction signal is obtained.  
The structure of this paper is as follows. In Section 1 of this paper, mainly introduces the background and some common detection techniques and methods of water supply pipeline leakage. In this section, we also give a brief introduction to our proposed methods. Section 2 introduces the noise reduction principle of the method based on VMD, in detail. Section 3 mainly introduces and analyzes the results of laboratory tests and field tests, in detail. Finally, Section 4 summarizes the research work of this paper.