Natural potential signal denoising method based on ensemble mode decomposition

Abstract

The invention relates to a natural potential signal denoising method based on ensemble modal decomposition, which creates a plurality of IMF column vectors according to natural potential vectors, and comprises the following steps: S1, adding random Gaussian noise to an initial vector of a jth IMF column vector to obtain a vector D1, and subtracting a mean envelope vector of the D1 and a high-order term vector of the D1 from the D1 to obtain an intermediate vector of the jth IMF column vector; s2, if the intermediate vector meets an IMF constraint condition, taking the intermediate vector as a jth IMF column vector, and if the intermediate vector does not meet the IMF constraint condition, updating an initial vector of the jth IMF column vector by using the intermediate vector, returning to the step S1 until the intermediate vector meeting the IMF constraint condition is obtained or the repeated process reaches a preset number of times, and taking an average value of the intermediate vectors of the IMF column vector as IMFj; and performing post-processing based on the natural potential vector S and the obtained IMF column vector to obtain a result after the natural potential signal is denoised.

Description

Technical Field

[0001] The invention relates to the technical field of engineering rock mass damage monitoring, and in particular to a natural potential signal denoising method based on collective mode decomposition. Background Art

[0002] In geological disaster warning, tunnel construction, safety monitoring and assessment, etc., it is crucial to accurately analyze the development and destruction process of microcracks inside the rock mass. The natural potential method is sensitive to the changes in the physical and chemical properties of the rock mass and has been widely used in various monitoring and early warning systems. However, the natural potential signal is easily interfered by various noises during the acquisition process, such as electromagnetic interference, which often appears as high-frequency noise with periodicity; environmental noise, which is often low-frequency and continuous fluctuations. This type of engineering rock mass interference reduces the accuracy of data analysis.

[0003] In order to remove noise from natural potential signals to reduce interference, denoising methods based on frequency domain filtering and wavelet transform denoising are often used. Among them, frequency domain filtering uses a bandpass filter to remove high-frequency noise and low-frequency trend terms, which can effectively remove periodic noise, but it is not effective for nonlinear or sudden noise processing, and may filter out some useful signal features; wavelet transform has multi-resolution characteristics and multi-scale analysis capabilities, but when the mode is complex or the noise intensity is high, the selection of wavelet basis and threshold setting are more difficult, which can easily lead to signal distortion. Therefore, a natural potential denoising method that adapts to the nonlinear and non-stationary characteristics of natural potential signals and does not rely on preset basis functions is needed to improve the signal-to-noise ratio of the signal. Summary of the invention

[0004] In view of the above analysis, an embodiment of the present invention aims to provide a natural potential signal denoising method based on collective mode decomposition, so as to solve the problem in the existing engineering rock damage monitoring that there is a lack of a natural potential denoising method that can adapt to the nonlinear and non-stationary characteristics of the natural potential signal and improve the signal-to-noise ratio.

[0005] The embodiment of the present invention provides a method for denoising a spontaneous potential signal based on collective mode decomposition, which collects spontaneous potential signals for monitoring rock mass damage and performs preprocessing to obtain a spontaneous potential vector; Create multiple IMF column vectors based on the self-potential vector, including: The natural potential vector S is used as the first IMF column vector IMF1; For the remaining IMF column vectors, their initial vectors are set based on the IMF column vector before the IMF column vector, and the remaining IMF column vectors are obtained through the following steps: S1: Add random Gaussian noise to the initial vector of the IMF column vector to obtain vector D1, obtain the mean envelope vector of vector D1, and subtract the mean envelope vector of D1 and the high-order term vector of D1 from vector D1 to obtain the intermediate vector IMFr of the IMF column vector; S2: Determine whether the intermediate vector IMFr satisfies the IMF constraint condition. If the intermediate vector IMFr satisfies the IMF constraint condition, the intermediate vector IMFr is used as the IMF column vector. If the intermediate vector IMFr does not satisfy the IMF constraint condition, the initial vector of the IMF column vector is updated to the intermediate vector IMFr, and the process returns to step S1 until an intermediate vector IMFr that satisfies the IMF constraint condition is obtained or the process is repeated for a preset number of times, and the average value of all the intermediate vectors IMFr of the IMF column vector is used as the IMF column vector. Post-processing is performed based on the natural potential vector S and the obtained IMF column vector to obtain the result of denoising the natural potential signal.

[0006] Furthermore, the step of setting the initial vector based on the IMF column vector before the IMF column vector includes: The initial vector of the second IMF column vector is set to the first IMF column vector IMF1; the initial vector of the i-th IMF column vector is set to the difference between the first IMF column vector IMF1 and the i-1-th IMF column vector, where i=3,4,…,N, and N is the total number of IMF column vectors.

[0007] Furthermore, the calculation formula of the intermediate vector IMFr is: , Where D1 is the vector obtained by adding random Gaussian noise to the initial vector of the j-th IMF column vector; is the upper envelope sampling point sequence of D1, is the sampling point sequence of the lower envelope of D1, is the number of iterations, the number of iterations and the IMF column vector IMF j The serial number j is the same, The sum of the maximum and minimum points of the curve fitted to the elements in D1.

[0008] Furthermore, natural potential signals for monitoring rock mass damage are collected and preprocessed to obtain a natural potential vector, including: performing spectrum analysis on the natural potential signals, identifying and obtaining frequency components of engineering rock mass background noise, and constructing a frequency component set; estimating the amplitude of the engineering rock mass background noise component at the frequency point according to the power spectrum density of each frequency point in the frequency component set and the n-th order cumulant of the power spectrum density, estimating the phase of the engineering rock mass background noise component according to the spectrum data of each frequency point in the frequency component set, and then constructing background noise, removing the constructed background noise from the natural potential signal to obtain denoised natural potential data, and standardizing the denoised natural potential data to obtain a natural potential vector.

[0009] Furthermore, the frequency component set is constructed as follows: , in, is the set of frequency components of engineering rock mass background noise, T is the threshold set for identifying the frequency components of background noise, is at frequency The power spectral density of the spontaneous potential signal at .

[0010] Furthermore, the threshold T calculation formula for identifying the frequency component of the background noise is: , Where T0 is the basic threshold, T0 is 10 -5 V 2 / Hz; is the adjustment factor, which is a dimensionless constant and its size is (0.5, 2); is the median of the power spectral density of the collected spontaneous potential signal; is at frequency The power spectral density of the spontaneous potential signal at .

[0011] Further, according to the natural potential data Medium frequency The calculation formula for estimating the amplitude and phase of the background noise component of the engineering rock mass by the spectrum and power spectrum density at is: , in, The natural potential signal is Medium frequency The complex spectrum data at The phase of the complex spectral data, The natural potential signal is Medium frequency The power spectral density at ; is the frequency component set of the natural potential signal Medium frequency The n-order cumulant of the power spectral density at , n=1,2,3; is the weight of the higher-order cumulant, ranging from 0 to 1; is the frequency component set The nth order moment of the power spectrum density of the spontaneous potential signal at each frequency point in, is the frequency component set The nm-order moment of the power spectral density of the natural potential signal at each frequency point in , for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at ; according to Medium frequency The amplitude and phase of the estimated engineering rock mass background noise component at the estimated engineering rock mass background noise.

[0012] Furthermore, the engineering rock mass background noise signal The expression is: , in, is the engineering rock mass background noise signal, is the set of frequency components of engineering rock mass background noise, for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at .

[0013] Furthermore, the constraints include: the sum of the number of maximum and minimum points of the curve fitted by the elements in D1 differs from the number of zero-crossing points of the curve fitted by the elements in D1 by no more than one; the average values ​​of the upper envelope formed by the local maximum points and the lower envelope formed by the local minimum points are zero.

[0014] Furthermore, post-processing is performed based on the natural potential vector S and the obtained IMF column vector to obtain the result of natural potential signal denoising, including: The IMF column vector is subjected to data inverse normalization to obtain the final collective mode decomposition column vector. Based on the natural potential vector S, any one or several of the final collective mode decomposition column vectors are subtracted to obtain the denoised results of the natural potential signals in each dimension.

[0015] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects: 1. The present invention adds random Gaussian noise to the initial vector to obtain vector D1, and subtracts the mean envelope vector of D1 and the high-order term vector of D1 from vector D1 to obtain the intermediate vector IMFrj of the j-th IMF column vector; the introduction of the signal high-order term vector enhances the ability to capture the characteristics of the natural potential signal. In each iteration, random Gaussian noise with a mean of 0 and a standard deviation of 0.01-0.2 is added to the signal, and the noise effect is eliminated by averaging the corresponding elements in the final IMF column vector, so as to break the possible modal aliasing phenomenon in each iteration.

[0016] 2. The present invention performs spectrum analysis on the natural potential signal, identifies and obtains the frequency components of the engineering rock background noise, and constructs a frequency component set; estimates the amplitude of the engineering rock background noise component at the frequency point according to the power spectrum density of the frequency point in the frequency component set and the n-order cumulant of the power spectrum density; estimates the phase of the engineering rock background noise component according to the spectrum data of each frequency point in the frequency component set, and then constructs the background noise; removes the constructed background noise from the natural potential signal to obtain the denoised natural potential data; and performs standardization on the denoised natural potential data to obtain the natural potential vector. The above method provides pure natural potential data for subsequent modal decomposition, and provides a strong guarantee for obtaining accurate structure for subsequent modal decomposition.

[0017] In the present invention, the above-mentioned technical solutions can also be combined with each other to achieve more preferred combination solutions. Other features and advantages of the present invention will be described in the subsequent description, and some advantages can become obvious from the description, or can be understood by practicing the present invention. The purpose and other advantages of the present invention can be realized and obtained through the contents particularly pointed out in the description and the drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The accompanying drawings are only used for the purpose of illustrating specific embodiments and are not to be considered as limiting the present invention. In the entire drawings, the same reference symbols represent the same components; Figure 1 This is a flow chart of a method for denoising a spontaneous potential signal based on collective mode decomposition according to the present invention; Figure 2 The original data of engineering rock mass failure spontaneous potential of the spontaneous potential signal denoising method based on collective mode decomposition of the present invention; Figure 3 It is the result of collective modal decomposition of natural potential of engineering rock mass failure according to the natural potential signal denoising method based on collective modal decomposition of the present invention; Figure 4 The present invention provides a natural potential collective modal denoising result of engineering rock mass failure natural potential of a natural potential signal denoising method based on collective modal decomposition. DETAILED DESCRIPTION

[0019] The preferred embodiments of the present invention are described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not used to limit the scope of the present invention.

[0020] A specific embodiment of the present invention discloses a natural potential signal denoising method based on collective mode decomposition, which specifically includes steps 1 to 3.

[0021] Step 1: Collect the natural potential signal of monitoring rock mass damage and pre-process it to obtain the natural potential vector.

[0022] The natural potential signal for monitoring rock mass damage is collected and preprocessed to obtain a natural potential vector, including: performing spectrum analysis on the natural potential signal, identifying and obtaining the frequency components of the engineering rock mass background noise, and constructing a frequency component set; estimating the amplitude of the engineering rock mass background noise component at the frequency point according to the power spectrum density of each frequency point in the frequency component set and the n-order cumulant of the power spectrum density, estimating the phase of the engineering rock mass background noise component according to the spectrum data of each frequency point in the frequency component set, and then constructing the background noise, removing the constructed background noise from the natural potential signal to obtain denoised natural potential data, and performing standardization processing on the denoised natural potential data to obtain the natural potential vector.

[0023] Specifically, the electrodes of the parallel electrical instrument used to monitor engineering rock mass failure are arranged on the target body to collect natural potential data. The data header contains the total number of electrodes and sampling interval information. The collected data are arranged in the format of time and electrode number. Each column of data is the voltage amplitude of the corresponding electrode from the beginning to the end according to the sampling time. Each row of data is the voltage amplitude of each electrode at the same time. The time interval between each row is the sampling interval of the natural potential data.

[0024] The constructed frequency component set is: , in, is the set of frequency components of engineering rock mass background noise, T is the threshold set for identifying the frequency components of background noise, is at frequency The power spectrum density of the natural potential signal at . The threshold T calculation formula for identifying the frequency component of the background noise is: , Where T0 is the basic threshold, T0 is 10 -5 V 2 / Hz; is the adjustment factor, which is a dimensionless constant and its size is (0.5, 2); is the median of the power spectral density of the collected spontaneous potential signal; is at frequency The power spectral density of the spontaneous potential signal at .

[0025] The flowchart of the method for denoising the spontaneous potential signal of engineering rock mass failure based on ensemble mode decomposition is as follows: Figure 1 shown.

[0026] The original data of natural potential of engineering rock mass failure is as follows Figure 2 shown.

[0027] In a specific embodiment of the present invention, the data header contains information such as the total number of electrodes 16, the sampling interval 1 minute, the data storage format, etc., and the sampling data is 16 columns×915 rows.

[0028] The spectrum analysis of the sampled data can be performed through the following discrete Fourier transform: , in, The spontaneous potential signal The spectrum of N is the signal length, j is the imaginary unit, is the angular frequency.

[0029] Calculate the power spectral density of the signal and obtain the energy distribution of the signal at different frequencies: , in is at frequency The power spectral density at It's a signal In frequency The engineering rock mass background noise will show higher energy in the low frequency band, so the background noise can be identified by setting the threshold T, and the frequency components with power spectrum density between T and 1.5T will be regarded as noise. In order to make the algorithm adaptable to meet the application requirements of natural potential signals in multiple scenarios, the adjustment factor is used. The median of the power spectral density Co-regulation.

[0030] According to the natural potential data Medium frequency The calculation formula for estimating the amplitude and phase of the background noise component of the engineering rock mass by the spectrum and power spectrum density at is: , in, The natural potential signal is Medium frequency The complex spectrum data at The phase of the complex spectral data, The natural potential signal is Medium frequency The power spectral density at ; is the frequency component set of the natural potential signal Medium frequency The n-order cumulant of the power spectral density at , n=1,2,3; is the weight of the higher-order cumulant, ranging from 0 to 1; is the frequency component set The nth order moment of the power spectrum density of the spontaneous potential signal at each frequency point in, is the frequency component set The nm-order moment of the power spectral density of the natural potential signal at each frequency point in , for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at ; according to Medium frequency The amplitude and phase of the estimated engineering rock mass background noise component at the estimated engineering rock mass background noise.

[0031] Engineering rock mass background noise signal The expression is: , in, is the engineering rock mass background noise signal, is the set of frequency components of engineering rock mass background noise, for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at .

[0032] Specifically, the estimated engineering rock background noise is removed from the original natural potential signal to improve the purity of the natural potential data: , in, In order to remove the natural potential signal after the background noise of the engineering rock mass, is the original natural potential signal, It is the background noise signal of engineering rock mass.

[0033] The denoised natural potential data is standardized to obtain the natural potential vector, including: , , in is the standard deviation of the denoised spontaneous potential data, is the number of sampling points of each electrode's natural potential signal, For the The voltage amplitude of the natural potential data after denoising, is the average value of the voltage amplitude of the column data, After standardization The voltage amplitude of the natural potential data after denoising; is the natural potential vector.

[0034] Specifically, standardization is to facilitate the processing of different electrode signals, eliminate the influence of data scale, and facilitate subsequent analysis and processing.

[0035] Step 2: Create multiple IMF column vectors based on the natural potential vector, including: The natural potential vector S is used as the first IMF column vector IMF1; For the remaining IMF column vectors, their initial vectors are set based on the IMF column vector before the IMF column vector, and the remaining IMF column vectors are obtained through the following steps: S1: Add random Gaussian noise to the initial vector of the IMF column vector to obtain vector D1, obtain the mean envelope vector of vector D1, and subtract the mean envelope vector of D1 and the high-order term vector of D1 from vector D1 to obtain the intermediate vector IMFr of the IMF column vector; S2: Determine whether the intermediate vector IMFr satisfies the IMF constraint condition. If the intermediate vector IMFr satisfies the IMF constraint condition, the intermediate vector IMFr is used as the IMF column vector. If the intermediate vector IMFr does not satisfy the IMF constraint condition, the initial vector of the IMF column vector is updated to the intermediate vector IMFr, and the process returns to step S1 until the intermediate vector IMFr that satisfies the IMF constraint condition is obtained or the process is repeated for a preset number of times, and the average value of all the intermediate vectors IMFr of the IMF column vector is used as the IMF column vector.

[0036] The step of setting the initial vector based on the IMF column vector before the IMF column vector comprises: The initial vector of the second IMF column vector is set to the first IMF column vector IMF1; the initial vector of the i-th IMF column vector is set to the difference between the first IMF column vector IMF1 and the i-1-th IMF column vector, where i=3,4,…,N, and N is the total number of IMF column vectors.

[0037] Specifically, compared with the traditional empirical mode decomposition method, in the present embodiment, a certain amount of noise is added to the initial vector in the process of extracting each IMF component to ensure the stability of the algorithm, and the vector obtained by averaging the corresponding elements of the intermediate vector IMFrj in the process of extracting a certain IMF component is used as the j-th IMF column vector, and the interference of the introduced noise is suppressed by averaging.

[0038] Specifically, the preset number of S2 times does not exceed 10 times (applicable to most cases).

[0039] The maximum number of IMFs can be preset manually, exemplarily 5 to 8, which can meet the needs of most engineering scenarios, maintaining a good denoising effect while avoiding unnecessary long-term calculations.

[0040] When the preset maximum number of modes is not reached, the standardized IMF is extracted iteratively. In each iteration, random Gaussian noise (mean 0, standard deviation 0.01~0.2) is added to the signal to generate a new signal D1 to break the possible mode aliasing in each iteration, and the noise effect is eliminated by averaging in the final result; the extreme points of the new signal are calculated, and then the maximum and minimum points are fitted respectively by cubic spline interpolation to obtain the upper and lower envelopes, and the mean envelope and its local high-order terms are subtracted from D1 to obtain the intermediate vector IMFri.

[0041] The calculation formula of the intermediate vector IMFr is: , Where D1 is the vector obtained by adding random Gaussian noise to the initial vector of the j-th IMF column vector; is the upper envelope sampling point sequence of D1, is the sampling point sequence of the lower envelope of D1, is the number of iterations, the number of iterations and the IMF column vector The serial number j is the same, The sum of the maximum and minimum points of the curve fitted to the elements in D1.

[0042] The constraints include: the sum of the number of maximum and minimum points of the curve fitted by the elements in D1 differs from the number of zero-crossing points of the curve fitted by the elements in D1 by no more than one; the average values ​​of the upper envelope formed by the local maximum points and the lower envelope formed by the local minimum points are zero.

[0043] Specifically, the conditions of IMF include: in the entire data segment, the sum of the number of extreme points and the number of zero crossings is either equal or differs by at most one; at any time, the average value of the upper envelope formed by the local maximum points and the lower envelope formed by the local minimum points is zero. The relationship between the extreme points and the zero crossings ensures that the signal is locally smooth and has no mutation points, so that the signal can be decomposed into basic oscillation modes, which can adapt to the nonlinearity and non-stationarity of the signal. The average value is zero, which reflects the equilibrium state of oscillation in the signal. This is easier to visualize in the time domain and helps to intuitively identify different oscillation modes in the signal.

[0044] Step 3: Post-process the natural potential vector S and the obtained IMF column vector to obtain the result of natural potential signal denoising.

[0045] Post-processing is performed based on the natural potential vector S and the obtained IMF column vector to obtain the result of natural potential signal denoising, including: The IMF column vector is subjected to data inverse normalization to obtain the final collective mode decomposition column vector. Based on the natural potential vector S, any one or several of the final collective mode decomposition column vectors are subtracted to obtain the denoised results of the natural potential signals in each dimension.

[0046] Specifically, inverse normalization is performed to obtain a natural potential signal after noise removal.

[0047] Multiply the IMF result by the standard deviation of the original signal to restore the scale of the original signal and obtain the final ensemble mode decomposition result as follows: Figure 3 shown.

[0048] By eliminating Figure 3 The denoising results of the natural potential signal of engineering rock mass failure by collective mode decomposition are shown in Figure 4 As shown, Figure 4 Remove the natural potential vector S as follows Figure 3 IMF2 and IMF5 are data obtained by periodic interference, and the final data retains the natural potential response of engineering rock mass failure within 15.5h~16.5h.

[0049] Compared with the prior art, the set modal decomposition initial vector provided in this embodiment adds random Gaussian noise to obtain vector D1, and the intermediate vector IMFrj of the jth IMF column vector is obtained by subtracting the mean envelope vector of D1 and the high-order term vector of D1 from vector D1; the introduction of the signal high-order term vector enhances the ability to capture the characteristics of the natural potential signal. In each iteration, random Gaussian noise with a mean of 0 and a standard deviation of 0.01-0.2 is added to the signal, and the noise effect is eliminated by averaging the corresponding elements in the final IMF column vector, so as to break the possible modal aliasing phenomenon in each iteration. This embodiment performs spectrum analysis on the natural potential signal, identifies and obtains the frequency components of the engineering rock background noise, and constructs a frequency component set; estimates the amplitude of the engineering rock background noise component at the frequency point according to the power spectrum density of the frequency point in the frequency component set and the n-order cumulant of the power spectrum density; estimates the phase of the engineering rock background noise component according to the spectrum data of each frequency point in the frequency component set, and then constructs the background noise, removes the constructed background noise from the natural potential signal to obtain the denoised natural potential data, and performs standardization on the denoised natural potential data to obtain the natural potential vector. The above method provides pure natural potential data for subsequent modal decomposition, which provides a strong guarantee for obtaining accurate structure for subsequent modal decomposition.

[0050] Those skilled in the art will appreciate that all or part of the processes of the above-mentioned embodiments can be implemented by instructing related hardware through a computer program, and the program can be stored in a computer-readable storage medium, wherein the computer-readable storage medium is a disk, an optical disk, a read-only storage memory, or a random access memory, etc.

[0051] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for denoising a natural potential signal based on collective mode decomposition, characterized in that: Collect the natural potential signal of monitoring rock mass failure and pre-process it to obtain the natural potential vector; Create multiple IMF column vectors based on the self-potential vector, including: The natural potential vector S is used as the first IMF column vector IMF1; For the remaining IMF column vectors, their initial vectors are set based on the IMF column vector before the IMF column vector, and the remaining IMF column vectors are obtained through the following steps: S1: Add random Gaussian noise to the initial vector of the IMF column vector to obtain vector D1, obtain the mean envelope vector of vector D1, and subtract the mean envelope vector of D1 and the high-order term vector of D1 from vector D1 to obtain the intermediate vector IMFr of the IMF column vector; S2: Determine whether the intermediate vector IMFr satisfies the IMF constraint condition. If the intermediate vector IMFr satisfies the IMF constraint condition, the intermediate vector IMFr is used as the IMF column vector. If the intermediate vector IMFr does not satisfy the IMF constraint condition, the initial vector of the IMF column vector is updated to the intermediate vector IMFr, and the process returns to step S1 until an intermediate vector IMFr that satisfies the IMF constraint condition is obtained or the process is repeated for a preset number of times, and the average value of all the intermediate vectors IMFr of the IMF column vector is used as the IMF column vector. Post-processing is performed based on the natural potential vector S and the obtained IMF column vector to obtain the result of denoising the natural potential signal.

2. The signal denoising method according to claim 1, characterized in that: The step of setting the initial vector based on the IMF column vector before the IMF column vector comprises: The initial vector of the second IMF column vector is set to the first IMF column vector IMF1; the initial vector of the i-th IMF column vector is set to the difference between the first IMF column vector IMF1 and the i-1-th IMF column vector, where i=3,4,…,N, and N is the total number of IMF column vectors.

3. The signal denoising method according to claim 1, characterized in that: The calculation formula of the intermediate vector IMFr is: , Where D1 is the vector obtained by adding random Gaussian noise to the initial vector of the j-th IMF column vector; is the upper envelope sampling point sequence of D1, is the lower envelope sampling point sequence of D1, is the number of iterations, the number of iterations and the IMF column vector IMF j The serial number j is the same, The sum of the maximum and minimum points of the curve fitted to the elements in D1.

4. The signal denoising method according to claim 1, characterized in that: The natural potential signal for monitoring rock mass damage is collected and preprocessed to obtain a natural potential vector, including: performing spectrum analysis on the natural potential signal, identifying and obtaining the frequency components of the engineering rock mass background noise, and constructing a frequency component set; estimating the amplitude of the engineering rock mass background noise component at the frequency point according to the power spectrum density of each frequency point in the frequency component set and the n-order cumulant of the power spectrum density, estimating the phase of the engineering rock mass background noise component according to the spectrum data of each frequency point in the frequency component set, and then constructing the background noise, removing the constructed background noise from the natural potential signal to obtain denoised natural potential data, and performing standardization processing on the denoised natural potential data to obtain the natural potential vector.

5. The signal denoising method according to claim 4, characterized in that: The constructed frequency component set is: ， in, is the set of frequency components of engineering rock mass background noise, T is the threshold set for identifying the frequency components of background noise, is at frequency The power spectral density of the spontaneous potential signal at .

6. The signal denoising method according to claim 5, characterized in that: The calculation formula for the threshold T set to identify the frequency component of background noise is: ， Where T0 is the basic threshold, T0 is 10 -5 V 2 / Hz; is the adjustment factor, which is a dimensionless constant and its size is (0.5, 2); is the median of the power spectral density of the collected spontaneous potential signal; is at frequency The power spectral density of the spontaneous potential signal at .

7. The signal denoising method according to claim 5, characterized in that: According to the natural potential data Medium frequency The calculation formula for estimating the amplitude and phase of the background noise component of the engineering rock mass by the spectrum and power spectrum density at is: ， in, The natural potential signal is Medium frequency The complex spectrum data at The phase of the complex spectral data, The natural potential signal is Medium frequency The power spectral density at ; is the frequency component set of the natural potential signal Medium frequency The n-order cumulant of the power spectral density at , n=1,2,3; is the weight of the higher-order cumulant, ranging from 0 to 1; is the frequency component set The nth order moment of the power spectrum density of the spontaneous potential signal at each frequency point in, is the frequency component set The nm-order moment of the power spectral density of the natural potential signal at each frequency point in , for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at ; according to Medium frequency The amplitude and phase of the estimated engineering rock mass background noise component at the estimated engineering rock mass background noise.

8. The signal denoising method according to claim 7, characterized in that: Engineering rock mass background noise signal The expression is: ， in, is the engineering rock mass background noise signal, is the set of frequency components of engineering rock mass background noise, for Medium frequency The estimated amplitude of the engineering rock mass background noise component at frequency The phase of the estimated engineering rock mass background noise component at .

9. The signal denoising method according to claim 3, characterized in that: The constraints include: the sum of the number of maximum and minimum points of the curve fitted by the elements in D1 differs from the number of zero-crossing points of the curve fitted by the elements in D1 by no more than one; the average values ​​of the upper envelope formed by the local maximum points and the lower envelope formed by the local minimum points are zero.

10. The signal denoising method according to claim 1, characterized in that: Post-processing is performed based on the natural potential vector S and the obtained IMF column vector to obtain the result of natural potential signal denoising, including: The IMF column vector is subjected to data inverse normalization to obtain the final collective mode decomposition column vector. Based on the natural potential vector S, any one or several of the final collective mode decomposition column vectors are subtracted to obtain the denoised results of the natural potential signals in each dimension.

Images