A Joint Denoising Method for Rock Fracture Acoustic Emission Signals Based on Improved VMD-ITD

Abstract

The present invention discloses a combined noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD, belonging to the technical field of signal processing. This noise reduction method first performs VMD decomposition on the acoustic emission signals; from the perspective of signal energy, a method for determining the number of VMD modes based on the component energy ratio is proposed to determine the number of modes K for VMD decomposition; calculate the corresponding mutual information between the K IMF components and the original signal, and use it as a weighting coefficient to perform weighted reconstruction on each IMF component; then perform ITD decomposition on the reconstructed signal and reconstruct again to obtain the noise-reduced signal. The present invention can effectively suppress the noise signals generated during the fracture process of rock samples and extract most of the effective information in the original acoustic emission signals.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD. Background Technique

[0002] Rock mass acoustic emission refers to a phenomenon that when a rock mass bears an external load, the stress in its original fracture area is highly concentrated. As the load increases and gradually reaches the point of breaking the original stable stress relationship, macroscopic crack expansion and microscopic internal structure deformation occur in the rock mass, so that the rock mass releases the accumulated stress potential energy to the outside in the form of elastic waves. Since there is a certain non-linear mapping relationship between the internal state of the rock mass and the characteristics of the acoustic emission signal. Therefore, by studying the acoustic emission signal during the rock fracture process, the real-time state of the internal structure change can be better understood.

[0003] During the acquisition of rock fracture acoustic emission signals, due to the test environment, mechanical vibration of the test equipment, and the suddenness of the acoustic emission phenomenon, the acoustic emission signals generated by rock fracture are often mixed with various noises. Moreover, rock mass acoustic emission signals also have the characteristics of non-linearity, non-stationarity, and large samples. If directly analyzed without preprocessing, it is very likely to cause large deviations in the results. Therefore, noise reduction preprocessing is an essential step.

[0004] Patents related to this technology mainly include: a pipeline leakage location method based on VMD component relative entropy analysis (ZL201810436414.7), which performs VMD decomposition on the acoustic emission signal of pipeline leakage, and uses the central frequency observation method to determine the number of VMD decomposition layers K. By observing the central frequencies of each mode corresponding to different K values, when two mode components with similar central frequencies appear, the number of modal layers of the upper layer is determined as the value of K. This method selects the value of K by artificially observing the modal central frequency, which will cause the decomposition and extraction results of effective signals to be inaccurate enough, resulting in a large reconstruction error after VMD decomposition.

[0005] An early fault diagnosis method for planetary gearboxes based on VMD-AMCKD (ZL 201810762387.2), which performs VMD decomposition on the fault vibration signals of planetary gears. Similarly, the central frequency observation method is used to determine the number of decomposition layers K, and there is a lack of theoretical basis when selecting the interpolation of the central frequency, which is easily affected by human subjective factors.

[0006] A noise reduction and filtering method for mine microseismic signals based on VMD (ZL 201710144435.7) performs noise reduction and filtering on the microseismic signals generated during rock fracture. It reads the original noisy microseismic signals for VMD decomposition, calculates the cross-correlation coefficients between the original microseismic signals and each variational mode component, and filters out the variational mode components with cross-correlation coefficients less than the threshold with the original signal. The remaining variational mode components are reconstructed to obtain the denoised and filtered microseismic signals. However, the determination of its threshold has strong subjective factors, and the components removed also contain useful information. Therefore, this method has a greater impact on the noise reduction result. Summary of the Invention

[0007] (1) Technical problems to be solved

[0008] The purpose of the present invention is to overcome the above-mentioned deficiencies of the prior art and propose a joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD to suppress the noise signals generated during the fracture process of rock samples.

[0009] (2) Technical solutions

[0010] To solve the above technical problems, the present invention provides a joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD.

[0011] The specific steps of the invention are as follows:

[0012] Step 1: Perform VMD decomposition on the acoustic emission signals. The method for determining the VMD mode number is to preset the algorithm mode number K = 1, calculate the ratio of the total energy of the first K IMF components to the energy of the original signal , and compare with the set energy threshold . If , stop the decomposition, and at this time the mode number K is 1; if , then update K = K + 1 until , and output the mode number K at this time;

[0013] Step 2: Calculate the corresponding mutual information between the K IMF components and the original signal, and use it as a weighting coefficient to perform weighted reconstruction on each IMF component;

[0014] Step 3: Perform ITD decomposition on the reconstructed signal and reconstruct it again to obtain the noise reduction signal.

[0015] (3) Beneficial effects

[0016] The joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD involved in the present invention can effectively solve the influence of subjective factors by determining the decomposition mode number K of VMD from the energy perspective through the component energy ratio, and can eliminate noise signals while retaining the complete information of the signal; the mutual information method is adopted, and the mutual information between each IMF component and the original signal is used as the weighting coefficient for IMF component reconstruction, which can suppress the noise-containing components with small correlation; the ITD decomposition is performed on the reconstructed signal, which can accurately extract the instantaneous characteristics of large-sample and non-stationary signals and achieve the purpose of secondary noise reduction. Using the improved VMD-ITD joint noise reduction algorithm to suppress the noise in non-stationary signals has a smaller root mean square error and a larger signal-to-noise ratio compared with the single VMD and ITD algorithms. This method can effectively suppress the noise signals during the fracture process of rock samples and extract most of the effective information in the original acoustic emission signals. Description of the Drawings

[0017] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. Obviously, the drawings in the following description are only one embodiment of the present invention, and those of ordinary skill in the art can obtain other drawings without creative efforts based on these drawings.

[0018] Figure 1 It is the flowchart of the specific embodiment of the present invention. The flowchart of a joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD of the present invention;

[0019] Figure 2 It is the noisy original signal and its spectrogram in the specific embodiment of the present invention;

[0020] Figure 3 It is the IMF component diagram of the noisy original signal in the specific embodiment of the present invention;

[0021] Figure 4 It is the first reconstructed signal based on weighted components and its spectrogram in the specific embodiment of the present invention;

[0022] Figure 5 It is the second noise-reduced reconstructed signal and its spectrogram in the specific embodiment of the present invention. Specific Embodiments

[0023] To make the technical means, creative features, achieved purposes and effects of the present invention easy to understand, the following clearly and completely describes the technical solutions in the specific embodiments of the present invention to further elaborate the present invention. Obviously, the described specific embodiments are only a part of the embodiments of the present invention, rather than all of them.

[0024] This specific implementation is a joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD. The flow chart of this extraction method is as shown in Figure 1 and the specific steps are as follows:

[0025] Step A. Randomly select a group of acoustic emission signals from the tungsten rock fracture test for noise reduction analysis. The waveforms and spectra of the selected acoustic emission signals are as shown in Figure 2 . Use the improved VMD algorithm to perform preset scale decomposition on the rock fracture acoustic emission signals, and solve the number of modes K according to the VMD number of modes determination method based on the component energy ratio.

[0026] The process of determining the number of modes K of the improved VMD algorithm is as follows:

[0027] (1) Calculate the total energy of the original signal , that is, the square of the 2-norm of

[0028] where represents the 2-norm of the signal .

[0029] (2) Perform VMD decomposition on the original signal , and initialize the number of modes K to 1, then obtain an IMF component . Calculate the energy of

[0030]

[0031] (3) Calculate the component energy ratio according to the formula as follows:

[0032]

[0033] (4) Compare with the set energy threshold . If , stop the decomposition, and the number of modes K is 1 at this time; if , repeat the above steps for the IMF component until , and output the number of modes K at this time.

[0034] The diagrams of each IMF component obtained according to the component energy ratio are as shown in Figure 3 .

[0035] Step B. Calculate the corresponding mutual information between the K IMF components and the original signal, and use it as the weighting coefficient to perform weighted reconstruction on each IMF component. Calculate the mutual information ​Using normal multivariate kernel density estimation, the mutual information The expression is:

[0036]

[0037] where

[0038]

[0039]

[0040] In the above formula, is the number of samples;

[0041] is the kernel function width;

[0042] is the variable dimension;

[0043] is related to When it is the variance, and when it is the covariance matrix, is the matrix determinant.

[0044] Solving gives That is, The mutual information between and the original signal is shown in Table 1.

[0045] Table 1. Mutual information between each IMF and the noisy original signal

[0046] IMF Serial Number 1 2 3 4 5 6 7 8 Mutual Information 0.6200 0.3548 0.2054 0.3084 0.2156 0.2194 0.2252 0.2304

[0047] The reconstructed signal is expressed by the following expression:

[0048]

[0049] In the formula, is the number of modes;

[0050] represents the th component.

[0051] According to the mutual information between each IMF and the noisy original signal, using it as a weighting coefficient to reconstruct each IMF component, the reconstructed signal and its spectrogram are as Figure 4 shown.

[0052] Step C. Perform ITD decomposition on the reconstructed signal The specific decomposition process is as follows:

[0053] (1) Define is the baseline extraction operator. For the noisy signal to be decomposed it can be expressed as

[0054]

[0055] In the formula, is the baseline signal;

[0056] , is the PRC component.

[0057] (2) Find all the local extreme points of the signal and record the corresponding moments as ( is the number of extreme points), and let . For easy observation, use and to represent and . If is defined on , then the signal is meaningful in the time range of . Define the piecewise linear extraction operator on the interval of consecutive extreme points . The expression of the baseline signal is as follows

[0058]

[0059] where

[0060]

[0061] In the formula, is the linear scaling factor, which is used to control the amplitude of the PRC component, .

[0062] (3) Define the inherent rotation separation operator There is

[0063]

[0064] Each ITD decomposition will obtain a PRC component and a baseline signal, and use the baseline signal as the input signal for the next decomposition. Repeat the ITD decomposition until the iteration termination condition is met, that is, the baseline signal satisfies monotonicity. At this time, a series of PRC components and a residual component will be obtained. The whole process of ITD decomposition can be expressed as:

[0065]

[0066]

[0067]

[0067]

[0068]

[0069]

[0070] In the formula, is the number of decomposition layers, is the residual component.

[0071] For the PRC component obtained by ITD decomposition, the signal is reconstructed again to achieve the purpose of secondary noise reduction. The secondary noise reduction reconstructed signal and its spectrum are as Figure 5 shown. After ITD secondary noise reduction, the spectrum of the original signal is smoother in the high-frequency and low-frequency parts, and the burrs are significantly reduced, indicating that the improved VMD-ITD combined noise reduction algorithm can filter out the high-frequency and low-frequency noises of the signal.

[0072] Step D. To evaluate the noise reduction performance of the improved VMD-ITD, by calculating the signal-to-noise ratio and root mean square error after its noise reduction and comparing with the VMD and ITD algorithms, the results of the signal-to-noise ratio and root mean square error of the three algorithms for the same measured noisy signal after noise reduction are shown in Table 2.

[0073] Table 2. Signal-to-noise ratio and root mean square error of the signals after noise reduction by the three algorithms

[0074] Noise Reduction Algorithm Root Mean Square Error Signal-to-Noise Ratio / dB VMD 13.7352 5.3352 ITD 10.3671 7.5326 Improved VMD-ITD 4.5521 10.0128

[0075] As can be seen from Table 2, the root mean square error of the improved VMD-ITD algorithm is 4.5521, which is the smallest among the three methods, and its signal-to-noise ratio is 10.0128 dB, higher than the other two methods, indicating the feasibility and effectiveness of the improved VMD-ITD method proposed by the present invention in the noise reduction of rock sample fracture acoustic emission signals, and its ability to suppress noise is stronger than that of the VMD and ITD algorithms.

[0076] In this embodiment, the acoustic emission signal of tungsten rock fracture is used for the improved VMD-ITD combined noise reduction processing. The present invention can also be applied to the signal processing of non-linear, non-stationary, and sudden transient characteristics. Various changes and modifications can be made according to the present invention, but these corresponding changes and modifications should fall within the protection scope of the appended claims of the present invention.

Claims

1. A joint noise reduction method for rock fracture acoustic emission signals based on improved VMD-ITD, characterized in that, The specific steps for noise reduction are as follows: Step 1: Perform VMD decomposition on the acoustic emission signal. The method for determining the VMD modal number is that the preset algorithm modal number K = 1, and calculate the ratio of the total energy of the first K IMF components to the energy of the original signal , and compare with the set energy threshold . If , stop the decomposition, and at this time the modal number K is 1; if , then update K = K + 1 until , and output the modal number K at this time; Step 2: Calculate the corresponding mutual information between the K IMF components and the original signal, and use it as a weighting coefficient to perform weighted reconstruction on each IMF component. In Step 2, the corresponding mutual information between each IMF component and the original signal is estimated using normal multivariate kernel density; Step 3: Perform ITD decomposition on the reconstructed signal, and reconstruct again to obtain the noise-reduced signal. In Step 3, performing ITD decomposition on the reconstructed signal yields a PRC component and a baseline signal. The baseline signal is used as the input signal for the next decomposition, and ITD decomposition is repeated until the baseline signal satisfies monotonicity. At this time, a series of PRC components will be obtained, and the noise-reduced signal is reconstructed again.

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