A Natural Potential Signal Denoising Method Based on Ensemble Modal Decomposition

Abstract

The present invention relates to a natural potential signal denoising method based on ensemble empirical mode decomposition. Multiple IMF column vectors are created according to the natural potential vector, including: S1: adding random Gaussian noise to the initial vector of the j-th IMF column vector to obtain vector D1, and subtracting the mean envelope vector of D1 and the high-order term vector of D1 from D1 to obtain the intermediate vector of the j-th IMF column vector; S2: if the intermediate vector satisfies the IMF constraint condition, then use it as the j-th IMF column vector, if not, then use it to update the initial vector of the j-th IMF column vector, return to step S1 until an intermediate vector that satisfies the IMF constraint condition is obtained or the repetition process reaches a preset number of times, and use the average value of the intermediate vectors of this IMF column vector as IMFj; perform post-processing based on the natural potential vector S and the obtained IMF column vectors to obtain the result of the denoised natural potential signal.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering rock mass failure monitoring, and particularly to a denoising method for spontaneous potential signals based on ensemble empirical mode decomposition. Background Art

[0002] In scenarios such as geological disaster warning, tunnel construction, safety monitoring and assessment, accurately analyzing the development of microcracks and the failure process inside rock masses is crucial. The spontaneous potential method is sensitive to changes in the physical and chemical properties inside rock masses and has been widely applied in various monitoring and warning systems. However, spontaneous potential signals are easily interfered by various noises during the acquisition process. For example, electromagnetic interference, which often appears as high-frequency noise and has periodicity; environmental noise, which is often low-frequency and continuous fluctuations. Such interference in engineering rock masses reduces the accuracy of data analysis.

[0003] To remove the noise in spontaneous potential signals and reduce interference, denoising methods based on frequency domain filtering and wavelet transform are often used. Among them, frequency domain filtering uses a band-pass filter to remove high-frequency noise and low-frequency trend terms, which can effectively remove periodic noise, but has poor processing effects on non-linear or sudden noises 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, it is difficult to select wavelet bases and set thresholds, which easily leads to signal distortion. Therefore, a spontaneous potential denoising method that adapts to the non-linear and non-stationary characteristics of spontaneous potential signals and does not depend 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, the embodiments of the present invention aim to provide a denoising method for spontaneous potential signals based on ensemble empirical mode decomposition to solve the problem that there is a lack of a spontaneous potential denoising method in existing engineering rock mass failure monitoring that adapts to the non-linear and non-stationary characteristics of spontaneous potential signals and can improve the signal-to-noise ratio of the signal.

[0005] The embodiments of the present invention provide a denoising method for spontaneous potential signals based on ensemble empirical mode decomposition, which collects spontaneous potential signals for monitoring rock mass failure and performs preprocessing to obtain a spontaneous potential vector;

[0006] Create a plurality of IMF column vectors according to the spontaneous potential vector, including:

[0007] Take the spontaneous potential vector S as the first IMF column vector IMF 1 ;

[0008] For the remaining IMF column vectors, set their initial vectors based on the IMF column vectors before this IMF column vector, and obtain the remaining IMF column vectors through the following steps:

[0009] S1: Add random Gaussian noise to the initial vector of the IMF column vector to obtain vector D1, acquire the mean envelope vector of vector D1, and subtract the mean envelope vector of D1 and the high-order term vector of D1 from D1 to obtain the intermediate vector IMFr of the IMF column vector;

[0010] S2: Determine whether the intermediate vector IMFr satisfies the IMF constraint condition. If the intermediate vector IMFr satisfies the IMF constraint condition, then use the intermediate vector IMFr as the IMF column vector. If the intermediate vector IMFr does not satisfy the IMF constraint condition, then update the initial vector of the IMF column vector to the intermediate vector IMFr, and return to step S1 until an intermediate vector IMFr that satisfies the IMF constraint condition is obtained or the repetition process reaches a preset number of times, and take the average value of all intermediate vectors IMFr of this IMF column vector as the IMF column vector;

[0011] Perform post-processing based on the natural potential vector S and the obtained IMF column vector to obtain the result of the denoised natural potential signal.

[0012] Furthermore, setting its initial vector based on the previous IMF column vectors of this IMF column vector includes:

[0013] Set the initial vector of the second IMF column vector as the first IMF column vector IMF 1 ; Set the initial vector of the i-th IMF column vector as the difference between the first IMF column vector IMF 1 and the (i - 1)-th IMF column vector, where i = 3, 4, ……, N, and N is the total number of IMF column vectors.

[0014] Furthermore, the calculation formula of the intermediate vector IMFr is:

[0015] ,

[0016] where D1 is the vector obtained by adding random Gaussian noise to the initial vector of the j-th IMF column vector; is the sampling point sequence of the upper envelope line of D1, is the sampling point sequence of the lower envelope line of D1, is the number of iterations, and the number of iterations is the same as the serial number j of the IMF column vector IMF j ; is the sum of the number of maximum and minimum points obtained from the curve fitted by the elements in D1.

[0017] Furthermore, collect the spontaneous potential signals for monitoring rock mass failure and perform preprocessing to obtain the spontaneous potential vector, including: performing spectral analysis on the spontaneous potential signals, identifying and obtaining the frequency components of the background noise of the engineering rock mass, and constructing a frequency component set; estimating the amplitude of the background noise component of the engineering rock mass at each frequency point in the frequency component set according to the power spectral density and the nth-order cumulant of the power spectral density, estimating the phase of the background noise component of the engineering rock mass according to the spectral data at each frequency point in the frequency component set, and then constructing the background noise, removing the constructed background noise from the spontaneous potential signals to obtain the denoised spontaneous potential data, and performing normalization processing on the denoised spontaneous potential data to obtain the spontaneous potential vector.

[0018] Furthermore, the construction of the frequency component set is as follows:

[0019] ,

[0020] wherein, is the set of frequency components of the background noise of the engineering rock mass, T is the threshold set for identifying the frequency components of the background noise, is at the frequency the power spectral density of the spontaneous potential signal.

[0021] Furthermore, the calculation formula for the threshold T set for identifying the frequency components of the background noise is:

[0022] ,

[0023] where T 0 is the basic threshold, T 0 is 10 -5 V 2 / Hz; is the adjustment factor, a dimensionless constant with a magnitude of (0.5, 2); is the median of the power spectral density of the collected spontaneous potential signal; is at the frequency the power spectral density of the spontaneous potential signal.

[0024] Furthermore, according to the spectral and power spectral density of the spontaneous potential data at the frequency in the calculation formulas for estimating the amplitude and phase of the background noise component of the engineering rock mass are:

[0025] ,

[0026] wherein, is the complex spectral data of the spontaneous potential signal at the frequency in , ∠ is for obtaining the phase of the complex spectral data, is the power spectral density of the spontaneous potential signal at in the frequency; is the n-th order cumulant of the power spectral density of the spontaneous potential signal at the frequency in the frequency component set , where n = 1, 2, 3; is the weight of the high-order cumulant, with a range of 0 - 1; is the n-th order moment of the power spectral density of the spontaneous potential signal at each frequency point in the frequency component set ; is the (n - m)-th order moment of the power spectral density of the spontaneous potential signal at each frequency point in the frequency component set ; is the amplitude of the estimated engineering rock mass background noise component at the frequency in ; is the phase of the estimated engineering rock mass background noise component at the frequency

[0027] The estimated engineering rock mass background noise is estimated according to the amplitude and phase of the estimated engineering rock mass background noise component at the frequency in .

[0028] Furthermore, the expression of the engineering rock mass background noise signal is:

[0029] ,

[0030] where is the engineering rock mass background noise signal, is the set of frequency components of the engineering rock mass background noise, is the amplitude of the estimated engineering rock mass background noise component at the frequency in ; is the phase of the estimated engineering rock mass background noise component at the frequency

[0031] Furthermore, the constraint conditions include: the sum of the number of maximum and minimum points obtained from 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 at most one; 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.

[0032] Furthermore, post-processing is performed based on the spontaneous potential vector S and the obtained IMF column vectors to obtain the result of denoising the spontaneous potential signal, including:

[0033] 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.

[0034] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0035] 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.

[0036] 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.

[0037] 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

[0038] 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;

[0039] 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;

[0040] Figure 2The original natural potential data of engineering rock mass failure for a natural potential signal denoising method based on ensemble empirical mode decomposition according to the present invention;

[0041] Figure 3 The ensemble empirical mode decomposition result of the natural potential of engineering rock mass failure for a natural potential signal denoising method based on ensemble empirical mode decomposition according to the present invention;

[0042] Figure 4 The ensemble empirical mode denoising result of the natural potential of engineering rock mass failure for a natural potential signal denoising method based on ensemble empirical mode decomposition according to the present invention. Specific embodiments

[0043] The following will specifically describe the preferred embodiments of the present invention with reference to the accompanying drawings. The accompanying drawings form a part of this application and are used together with the embodiments of the present invention to explain the principle of the present invention, rather than to limit the scope of the present invention.

[0044] A specific embodiment of the present invention discloses a natural potential signal denoising method based on ensemble empirical mode decomposition, which specifically includes steps 1 to 3.

[0045] Step 1: Collect the natural potential signals for monitoring rock mass failure and perform preprocessing to obtain a natural potential vector.

[0046] Collecting the natural potential signals for monitoring rock mass failure and performing preprocessing to obtain a natural potential vector includes: performing spectral analysis on the natural potential signals, identifying and obtaining the frequency components of the background noise of the engineering rock mass, constructing a frequency component set; estimating the amplitude of the background noise component of the engineering rock mass at each frequency point according to the power spectral density and the nth-order cumulant of the power spectral density in the frequency component set, estimating the phase of the background noise component of the engineering rock mass according to the spectral data at each frequency point in the frequency component set, and then constructing the background noise, removing the constructed background noise from the natural potential signals to obtain the denoised natural potential data, and performing normalization processing on the denoised natural potential data to obtain a natural potential vector.

[0047] Specifically, the electrodes of a parallel electrical resistivity instrument for monitoring engineering rock mass failure are arranged on the target body to collect natural potential data, and the data header contains information such as the total number of electrodes and the sampling interval. The collected data is arranged in the format of time and electrode number. Each column of data is the voltage amplitude of the corresponding electrode from front to back according to the sampling time, each row of data is the voltage amplitude of each electrode at the same moment, and the time interval between each row is the sampling interval of the natural potential data.

[0048] The construction of the frequency component set is as follows:

[0049] ,

[0050] Among them, is the set of frequency components of the background noise of the engineering rock mass, and T is the threshold set for identifying the frequency components of the background noise. is the power spectral density of the spontaneous potential signal at the frequency . The calculation formula for the threshold T set for identifying the frequency components of the background noise is:

[0051] ,

[0052] where T 0 is the basic threshold, and T 0 is 10 -5 V 2 / Hz; is the adjustment factor, which is a dimensionless constant with a magnitude of (0.5, 2); is the median of the power spectral density of the collected spontaneous potential signal; is the power spectral density of the spontaneous potential signal at the frequency .

[0053] The flowchart of the denoising method for the spontaneous potential signal of engineering rock mass failure based on ensemble empirical mode decomposition is as shown in Figure 1 .

[0054] The original data of the spontaneous potential of engineering rock mass failure is as shown in Figure 2 .

[0055] In a specific embodiment of the present invention, the data trace header contains information such as the total number of electrodes 16, the sampling interval of 1 minute, and the data storage format, and the sampled data is 16 columns × 915 rows.

[0056] Performing spectral analysis on the sampled data can be carried out through the following discrete Fourier transform:

[0057] ,

[0058] where is the spectrum of the spontaneous potential signal , N is the signal length, j is the imaginary unit, and is the angular frequency.

[0059] Calculating the power spectral density of the signal to obtain the energy distribution of the signal at different frequencies:

[0060] ,

[0061] where is the power spectral density at the frequency , is the signal at the frequency The spectrum at [specific location]. The background noise of engineering rock mass will exhibit higher energy in the low-frequency band. Therefore, by setting a threshold T, the background noise can be identified, and the frequency components with power spectral density in the range of T to 1.5T will be regarded as noise. To make the algorithm have a certain adaptability to meet the application requirements of spontaneous potential signals in multiple scenarios, the adjustment factor and the median of the power spectral density are jointly adjusted.

[0062] According to the spectrum and power spectral density of the spontaneous potential data at in the [specific frequency range] the calculation formulas for estimating the amplitude and phase of the background noise components of the engineering rock mass are as follows:

[0063] ,

[0064] where is the complex spectrum data of the spontaneous potential signal at in the [specific frequency range] at the [specific frequency], ∠ is to obtain the phase of the complex spectrum data, is the power spectral density of the spontaneous potential signal at in the [specific frequency range] at the [specific frequency]; is the nth-order cumulant of the power spectral density of the spontaneous potential signal at the frequency component set in the [specific frequency range] at the [specific frequency], n = 1, 2, 3; is the weight of the higher-order cumulant, ranging from 0 to 1; is the nth-order moment of the power spectral density of the spontaneous potential signal at each frequency point in the frequency component set , is the (n - m)th-order moment of the power spectral density of the spontaneous potential signal at each frequency point in the frequency component set , is in the [specific frequency range] at the [specific frequency] the estimated amplitude of the background noise component of the engineering rock mass, the [specific frequency] at the estimated phase of the background noise component of the engineering rock mass;

[0065] According to in the [specific frequency range] at the estimated amplitude and phase of the background noise component of the engineering rock mass, estimate the background noise of the engineering rock mass.

[0066] The background noise signal of the engineering rock mass The expression is:

[0067] ,

[0068] Among them, is the background noise signal of the engineering rock mass, is the set of frequency components of the background noise of the engineering rock mass, is the frequency at which the amplitude of the estimated background noise component of the engineering rock mass is located, the frequency at which the phase of the estimated background noise component of the engineering rock mass is located.

[0069] Specifically, the estimated background noise of the engineering rock mass is removed from the original spontaneous potential signal to improve the purity of the spontaneous potential data:

[0070] ,

[0071] Among them, is the spontaneous potential signal after removing the background noise of the engineering rock mass, is the original spontaneous potential signal, is the background noise signal of the engineering rock mass.

[0072] The denoised spontaneous potential data is standardized to obtain a spontaneous potential vector, including:

[0073] ,

[0074] ,

[0075] Among them is the standard deviation of the denoised spontaneous potential data, is the number of sampling points of the spontaneous potential signal of each electrode, is the th voltage amplitude of the denoised spontaneous potential data, is the average value of the voltage amplitudes of this column of data, is the voltage amplitude of the th denoised spontaneous potential data after standardization; is the spontaneous potential vector.

[0076] Specifically, standardization is to facilitate the processing of signals from different electrodes. Eliminate the influence of data scale and facilitate subsequent analysis and processing.

[0077] Step 2: Create multiple IMF column vectors based on the spontaneous potential vector, including:

[0078] Take the spontaneous potential vector S as the first IMF column vector IMF 1 ;

[0079] For the remaining IMF column vectors, set their initial vectors based on the previous IMF column vectors of the IMF column vector, and obtain the remaining IMF column vectors through the following steps:

[0080] 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;

[0081] S2: Determine whether the intermediate vector IMFr satisfies the IMF constraint condition. If the intermediate vector IMFr satisfies the IMF constraint condition, then use the intermediate vector IMFr as the IMF column vector. If the intermediate vector IMFr does not satisfy the IMF constraint condition, then update the initial vector of the IMF column vector to the intermediate vector IMFr, and return to step S1 until an intermediate vector IMFr that satisfies the IMF constraint condition is obtained or the repetition process reaches the preset number of times. Take the average of all intermediate vectors IMFr of the IMF column vector as the IMF column vector.

[0082] The setting of the initial vector based on the previous IMF column vectors of the IMF column vector includes:

[0083] Set the initial vector of the second IMF column vector as the first IMF column vector IMF 1 ; Set the initial vector of the i-th IMF column vector as the difference between the first IMF column vector IMF 1 and the (i - 1)-th IMF column vector, where i = 3, 4, ……, N, and N is the total number of IMF column vectors.

[0084] Specifically, compared with the traditional empirical mode decomposition method in this embodiment, a certain amount of noise is added to the initial vector during the extraction process of each IMF component to ensure the stability of the algorithm. The vector obtained by averaging the corresponding elements of the intermediate vector IMFrj during the extraction process of a certain IMF component is used as the j-th IMF column vector, and the interference of the introduced noise is suppressed by averaging.

[0085] Specifically, the preset number of times in S2 does not exceed 10 times (suitable for most cases).

[0086] The maximum number of IMFs can be preset artificially. Exemplarily, it is 5 - 8. This number can meet the requirements of most engineering scenarios, maintain a good denoising effect while avoiding unnecessary long-time calculations.

[0087] When the preset maximum number of modes is not reached, iteratively extract the standardized IMF. Each iteration, add random Gaussian noise (mean is 0, standard deviation is 0.01 - 0.2) to the signal to generate a new signal D 1, to break possible modal aliasing in each iteration and eliminate the influence of noise by averaging in the final result; calculate the extreme points of the new signal, and then respectively fit the maximum points and minimum points by cubic spline interpolation to obtain the upper envelope and the lower envelope. Subtract the mean envelope and its local high-order terms from D1 to obtain the intermediate vector IMFri.

[0088] The calculation formula of the intermediate vector IMFr is as follows:

[0089] ,

[0090] where D1 is a vector obtained by adding random Gaussian noise to the initial vector of the j-th IMF column vector; is the sampling point sequence of the upper envelope of D1, is the sampling point sequence of the lower envelope of D1, is the number of iterations, and the number of iterations is the same as the serial number j of the IMF column vector , is the sum of the maximum and minimum point numbers obtained from the curve fitted by the elements in D1.

[0091] The constraint conditions include: the sum of the numbers of maximum and minimum points obtained from 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 at most one; the average value of the upper envelope formed by local maximum points and the lower envelope formed by local minimum points is zero.

[0092] Specifically, the conditions of IMF include: within the entire data segment, the sum of the numbers of extreme points is either equal to or differs from the number of zero-crossing points by at most one; at any time, the average value of the upper envelope formed by local maximum points and the lower envelope formed by local minimum points is zero. The relationship between extreme points and zero-crossing points ensures that the signal is locally smooth without mutation points, so that the signal can be decomposed into basic oscillation modes and can adapt to the nonlinearity and non-stationarity of the signal. The average value of zero reflects the balanced 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.

[0093] Step 3: Perform post-processing based on the spontaneous potential vector S and the obtained IMF column vectors to obtain the result of the denoised spontaneous potential signal.

[0094] Performing post-processing based on the spontaneous potential vector S and the obtained IMF column vectors to obtain the result of the denoised spontaneous potential signal includes:

[0095] 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.

[0096] Specifically, inverse normalization is performed to obtain a natural potential signal after noise removal.

[0097] 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.

[0098] 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.

[0099] 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.

[0100] Those skilled in the art can understand that all or part of the processes of implementing the methods in the above embodiments can be completed by instructing relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. Among them, the computer-readable storage medium is a disk, an optical disc, a read-only memory or a random access memory, etc.

[0101] As mentioned above, the above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art 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