Mine microseismic signal noise reduction method based on sparse decomposition

Abstract

The invention relates to a mine micro-seismic signal noise reduction method based on sparse decomposition. The method starts with priori knowledge analysis of mine micro-seismic signal characteristic waveforms, and comprises the following steps: firstly, selecting Laplace wavelet parameters which are most matched with the micro-seismic signal characteristic waveforms through a correlation filtering method, and constructing a Laplace wavelet parameter dictionary according to the Laplace wavelet parameters; secondly, sparsely reconstructing a characteristic waveform of the micro-seismic signal by combining an orthogonal matching pursuit (OMP) algorithm; in consideration of large calculation amount and long time of a correlation filtering method, a whale optimization algorithm (WOA) is used to carry out rapid global parameter optimization. The analysis result of the simulated micro-seismic signal and the actually measured signal shows that the characteristic waveform of the micro-seismic signal can be effectively reconstructed by the provided method, the noise reduction of the micro-seismic signal is realized, and the method has certain anti-interference capability on noise; compared with a common ensemble empirical mode decomposition (EEMD) method, the sparse noise reduction method based on the self-adaptive Laplace wavelet dictionary provided by the invention has certain superiority.

Description

Technical Field

[0001] This invention relates to a method for noise reduction of mine microseismic signals based on sparse decomposition, belonging to the field of signal processing technology. Background Technology

[0002] With the rapid development of my country's national economy, the demand for mineral resources is increasing daily. To meet the needs of stable economic development, expanding mining scale and conducting deep mining have become priorities. Deep mining areas have complex and variable environments; once the stability of the rock mass is compromised, it can easily lead to rockfall and collapse. Microseismic signals from underground mines contain rich information about the internal activity and changes of the rock mass. Therefore, microseismic signals can effectively detect the internal activity of the rock mass, providing important reference value for ensuring safe mine production. However, the mining environment is harsh, and microseismic signals contain a large amount of background noise. Therefore, effective microseismic signal noise reduction technology is of great research significance. Mine microseismic signals are a typical nonlinear and non-stationary signal. Commonly used nonlinear signal processing methods include Variational Mode Decomposition (VMD), Empirical Mode Decomposition (EMD), and wavelet transform. Zhang Xingli et al. first used VMD to decompose noisy microseismic signals into multiple variational mode components. By calculating the energy entropy of the components, they determined the boundary between noise and useful signals, and finally successfully achieved denoising of noisy microseismic signals. Jia Ruisheng et al. combined EMD with independent component analysis, using the cross-correlation coefficients between the original signal and the mode components obtained from the EMD boundary to determine the boundary between noise and signal. Then, they used independent component analysis to perform blind source separation on the boundary mode components to extract the useful signals. Xu Hongbin et al. achieved denoising of microseismic signals of large-scale rock mass structures based on wavelet transform. The above methods have achieved significant results in microseismic signal denoising. However, the EMD method and VMD algorithm require setting parameter thresholds, which requires a certain amount of human experience. Wavelet transform requires selecting a suitable wavelet basis and setting appropriate threshold parameters to achieve a good signal denoising effect. Sparse decomposition, as an effective method for processing non-stationary signals, has been applied to many fields such as underwater acoustic signal denoising, mechanical fault signal denoising, and circuit signal denoising, but its application in mine microseismic signal denoising is relatively limited. Summary of the Invention

[0003] To address the noise reduction problem of mine microseismic signals, this invention proposes a noise reduction method for mine microseismic signals based on sparse decomposition.

[0004] Starting from the prior knowledge characteristics of microseismic signals, a periodically arranged Laplace wavelet parameter dictionary is constructed. This dictionary is then combined with an orthogonal matching pursuit algorithm to sparsely reconstruct the original microseismic signal, thereby reducing the influence of noise components. To avoid the impact of manual parameter selection on signal denoising and to reduce computation time and save costs, this invention utilizes the whale optimization algorithm to automatically find the optimal parameters of the Laplace wavelet dictionary.

[0005] The purpose of this invention is to provide a noise reduction method for mine microseismic signals based on sparse decomposition, which effectively eliminates noise components in microseismic signals, ensures the effectiveness of microseismic monitoring technology, and improves the accuracy of microseismic monitoring and forecasting.

[0006] A method for denoising mine microseismic signals based on sparse decomposition, comprising the following specific steps:

[0007] 1) First, microseismic signals are collected using a microseismic monitoring system. The parameter values ​​of the whale optimization algorithm are initialized, and the Laplace wavelet parameter optimization range is set. The whale population size is set to 20, the maximum number of iterations is 30, and the Laplace wavelet modal parameters f∈[100, f...]. s / 2], ξ∈[0,0.2], τ∈[0,f s / N], where f is the oscillation frequency, ξ is the damping ratio, τ is the time shift parameter, and f s Where N is the signal sampling frequency, and N = length(y);

[0008] 2) Constructing the Laplace wavelet parameter dictionary: Using the whale optimization algorithm-assisted correlation filtering method, the optimal parameter values ​​(f, ξ, τ) of the Laplace wavelet are quickly found, with the correlation coefficient K... r The maximum value is used as the fitness function of the WOA algorithm. The optimal mode parameters (f,ξ,τ) are substituted into the Laplace wavelet function expression to form the optimal Laplace wavelet. The periodic optimal Laplace wavelet is used as the dictionary atom to construct the Laplace wavelet parameter dictionary.

[0009] 3) Sparse reconstruction of the original microseismic signal: With the help of the orthogonal matching pursuit algorithm, the Laplace wavelet parameter dictionary sparsely reconstructs the original microseismic signal, achieving the purpose of denoising the microseismic signal;

[0010] 4) Optimal result processing and analysis: The rock mass activity state is determined from the characteristic waveforms of the signal after sparse reconstruction by the Laplace wavelet parameter dictionary and the orthogonal matching pursuit algorithm, providing reliable technical support for the microseismic monitoring system.

[0011] Preferably, the specific content of the sparse decomposition is as follows:

[0012] Analysis of relevant references reveals that the original microseismic signal contains multiple periodically occurring impact waveforms and noise components. The principle of noise reduction for mine microseismic signals is to eliminate noise components as much as possible and highlight the periodically occurring impact waveforms. Assuming the periodically occurring impact waveform in the microseismic signal is h(t), and the signal acquired by the microseismic monitoring system is y(t), it can be described as follows:

[0013] y(t) = h(t) + noise

[0014] Sparse decomposition involves decomposing a signal into an overcomplete atomic library, or dictionary D, to select useful components. Therefore, based on the principle of sparse decomposition, the sparse representation formula for the microseismic signal y(t) is:

[0015] y = Dx + noise

[0016] In the formula, D is a dictionary, D = {d} γ} γ∈Γ (Γ={y i ,i=1,2,…},d γ For dictionary atoms; x is the sparse decomposition coefficient, x = {x (1) ,x (2) ,…,x (m)} Γ The goal of sparse representation of a signal is to maximize the number of zero elements in x, i.e., to find the minimum l0 norm of ||x||0.

[0017]

[0018] In the formula, ε represents the reconstruction error. Solving for the l0 norm is an NP-hard problem and cannot be solved directly. Therefore, this invention uses the OMP algorithm to transform the problem of solving the l0 norm into solving the l1 norm problem, as shown in the following formula:

[0019]

[0020] Preferably, the specific content of constructing the Laplace wavelet dictionary is as follows:

[0021] First, microseismic signals were collected using a microseismic monitoring system. The parameter values ​​of the whale optimization algorithm and the optimization range of the Laplace wavelet parameters were initialized. The whale population size was set to 20, the maximum number of iterations was set to 30, and the modal parameters of the Laplace wavelet were set to f∈[100, f...]. s / 2], ξ∈[0,0.2], τ∈[0,f s / N]. The optimal parameter values ​​(f, ξ, τ) of the Laplace wavelet are quickly found using a correlation filtering method assisted by the whale optimization algorithm, with the correlation coefficient K. rThe maximum value is used as the fitness function of the whale optimization algorithm. The optimal mode parameters (f,ξ,τ) are substituted into the Laplace wavelet function expression to form the optimal Laplace wavelet. The periodic optimal Laplace wavelet is used as dictionary atoms to construct the Laplace wavelet parameter dictionary.

[0022] Preferably, the specific content of the whale optimization algorithm is as follows:

[0023] The Whale Optimization Algorithm, proposed by Mirjalili et al. in 2016, is a global optimization algorithm inspired by the biological mechanisms of humpback whales. It iteratively optimizes the prey-encircling behavior by mimicking three key actions: surrounding prey, spiraling predation, and searching for prey. During each hunt, humpback whales continuously update and shrink their prey-encircling circle in an upward spiral until they catch their prey. In the prey-shrinking phase, since the location of the optimal solution is unknown, the Whale Optimization Algorithm assumes that the optimal whale position in the current population is the target prey's location. Other whales continuously update their positions to move closer to the prey. This predation behavior can be expressed mathematically as follows:

[0024]

[0025] In the formula: X * X(t) represents the position of the whale individual that achieves the global optimal solution in the population at generation t, i.e., the position of the optimal solution; X(t) represents the current position of the whale after t iterations; D represents the distance between the whale individual and its prey; A and C are coefficient vectors used to control the way the whale swims, and their mathematical expressions are:

[0026] A = 2a·ra

[0027] C = 2r

[0028]

[0029] In the formula: r is a random vector between [0,1]; a is the convergence factor, which decreases linearly from 2 to 0 as the number of iterations increases. max This represents the maximum number of iterations. To simulate a whale approaching its prey in a spiral ascent, assume the whale's coordinates in two-dimensional space are (X,Y), and the prey's position is (X...). * ,Y * The position of an individual whale is updated using the following formula:

[0030] D2=|X * (t)-X(t)|

[0031] X(t+1)=D2·e bl ·cos(2πl)+X *(t)

[0032] In the formula: D2 is the distance between the individual whale and its prey; b is a constant defining the shape of the logarithmic spiral; l is a random number between [-1, 1]. When a whale hunts, its contraction and spiral renewal occur simultaneously. Assuming that the probability of a humpback whale performing contraction and spiral renewal is 50% each, the mathematical model can be expressed as:

[0033]

[0034] In the formula: p is a random number between [0,1]. During the whale's prey-hunting phase, the whale no longer updates its position based on the current optimal solution, but instead randomly selects the position of another whale to update its position, aiming to increase the search range and find the optimal solution. The mathematical model at this time is:

[0035] X(t+1)=X rand (t)-A·D rand

[0036] D rand =|C·X rand -X(t)|

[0037] In the formula: X rand D represents the position of an individual randomly selected from the current population; rand This represents the distance between a randomly selected individual whale and its prey.

[0038] Preferably, the specific content of the Laplace wavelet is as follows:

[0039] Considering that the characteristic waveform of microseismic signals exhibits a swallowtail shape, this invention uses the Laplace wavelet ψ γ (t) is used as the atomic basis function of the dictionary. The mathematical expression for the Laplace wavelet is:

[0040]

[0041] In the formula: f is the oscillation frequency; ξ is the damping ratio; τ is the time shift parameter; W s Let f be the wavelet support width. As can be seen from the above equation, the modal parameters (f, ξ, τ) directly control the waveform characteristics of the wavelet. By selecting different parameter values, the matching between the wavelet and the microseismic characteristic waveform can be achieved.

[0042] Preferably, the specific content of the correlation filtering algorithm for finding Laplace wavelet parameters is as follows:

[0043] Step 1: Assume that the Laplace wavelet oscillation frequency f, damping ratio ξ, and time shift parameter τ belong to sets F, Z, and T, respectively:

[0044]

[0045] Step 2: Traverse all parameter sets to obtain the complete set of Laplace wavelets: ψ = {ψ γ (t): γ∈F×Z×T}={ψ(f∈F,τ∈T,ξ∈Z)}, where t represents time.

[0046] Step 3: Calculate the Laplace wavelet ψ γ The degree of similarity between y(t) and the analyzed signal y(t), i.e., the correlation coefficient K between the two. r :

[0047] Step 4: Find K r Largest value. Maximum K r The Laplace wavelet parameters corresponding to the value are the optimal wavelet parameters.

[0048] Preferably, the specific content of constructing the Laplace wavelet dictionary is as follows:

[0049] Substituting the optimal modal parameters into the mathematical expression of the Laplace wavelet, a Laplace wavelet that best matches the characteristic waveform of the microseismic signal is constructed. Considering the periodic occurrence of the characteristic waveform of the microseismic signal, the optimal Laplace wavelet arranged periodically is used as the atom of the dictionary. The time shift parameter τ of the wavelet atom is changed to form the Laplace wavelet parameter dictionary.

[0050] Preferably, the specific content of the reconstructed microseismic signal is as follows:

[0051] Combining the Orthogonal Matching Pursuit (OMP) algorithm, the original microseismic signal is sparsely reconstructed using the Laplace wavelet parameter dictionary. The optimization steps are as follows:

[0052] Inputs: the raw microseismic signal y acquired by the sensor, dictionary D, and sparse threshold T;

[0053] Initialization: residual r0 = y, iteration count s = 1, support index set Λ0 = φ;

[0054] Step 1: Set the number of iterations s = 1, 2, ..., T;

[0055] Step 2: Find the subscript λ corresponding to the maximum value in the residual r and the dictionary atomic product, i.e., find the support index.

[0056] Step 3: Update index set Λ s =Λ s-1 ∪{λ s}, update the initial dictionary atoms

[0057] Step 4: Obtained by least squares method

[0058] Step 5: Update residuals The number of iterations s = s + 1;

[0059] Step 6: Determine if the required number of iterations has been met. If so, stop the iteration; otherwise, proceed to step 1.

[0060] Output: Sparse decomposition coefficients

[0061] Preferably, the specific content of the sparse reconstruction of the original microseismic signal is as follows:

[0062] The sparse decomposition coefficients are multiplied by the constructed periodic Laplace wavelet parameter dictionary to obtain the sparsely reconstructed, denoised original microseismic signal.

[0063] Preferably, the specific content of the reconstruction result processing and analysis is as follows:

[0064] Observe whether the reconstructed signal shows characteristic waveforms to determine the activity of the rock mass and provide effective technical support for the microseismic prediction and monitoring system.

[0065] Preferably, the specific content of the effectiveness verification and result comparison of the sparse decomposition-based mine microseismic signal denoising method is as follows:

[0066] (a) The method proposed in this invention effectively eliminates the influence of noise and interference components in both simulated and measured microseismic signals, accurately reconstructing the characteristic waveforms of the microseismic fault impulse response. Therefore, it can be concluded that the method proposed in this invention has certain feasibility and practicality. When noise of different amplitudes is added to the simulated signal, the method proposed in this invention accurately reconstructs the characteristic waveforms of the microseismic signal, thus demonstrating that the method proposed in this invention has a certain degree of noise immunity.

[0067] (b) The empirical mode decomposition method was used to compare and analyze the simulated signal and the measured signal in engineering. The results showed that the empirical mode decomposition can reduce the influence of noise to a certain extent, but it is obviously not as advantageous as the method of the present invention. This shows the superiority of the method proposed in the present invention.

[0068] Compared with the prior art, the beneficial effects of the present invention are:

[0069] 1. Starting with the prior knowledge analysis of mine microseismic signals, noise reduction is performed based on the principle of sparse decomposition. By constructing a periodically arranged Laplace wavelet parameter dictionary and combining it with the orthogonal matching pursuit algorithm to sparsely reconstruct the original microseismic signal, the influence of noise components can be effectively eliminated, and the characteristic waveform of the microseismic signal can be accurately reconstructed, ensuring the effectiveness and accuracy of the microseismic monitoring system.

[0070] 2. The periodically arranged Laplace wavelet parameter dictionary takes into account the characteristic waveforms of real microseismic signals and their periodic occurrence, making the constructed wavelet parameter dictionary more compatible with the characteristic waveforms of real microseismic signals. Thus, the method proposed in this invention has a certain degree of robustness and anti-interference ability.

[0071] 3. The method proposed in this invention has achieved significant results in the processing of microseismic simulation signals and engineering measured signals. It can accurately reconstruct the characteristic waveforms of fault microseismic events. A comparative analysis of the proposed method with commonly used empirical mode decomposition methods shows that the method proposed in this invention has obvious advantages. Attached Figure Description

[0072] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0073] Figure 1 This is a diagram illustrating the principle of sparse decomposition.

[0074] Figure 2 These are the time-domain and frequency-domain plots of the Laplace wavelet, where (a) is the time-domain plot of the Laplace wavelet and (b) is the frequency-domain plot of the Laplace wavelet.

[0075] Figure 3 This is a flowchart of a method for denoising mine microseismic signals based on sparse decomposition;

[0076] Figure 4 These are microseismic simulation signal diagrams, where (a) is the original simulated microseismic signal diagram, (b) is the simulated microseismic signal diagram with added noise, and (c) is the spectrum diagram of the simulated microseismic signal with added noise.

[0077] Figure 5 This is a reconstructed signal diagram of the method proposed in this invention in a simulated signal;

[0078] Figure 6 The image shows the reconstructed signal in the simulation signal compared to the empirical mode decomposition method used.

[0079] Figure 7 The above are comparison charts showing the noise immunity of the method proposed in this invention. (a) is a simulated signal diagram with different noise amplitudes, and (b) is a reconstructed signal diagram corresponding to (a) of the method proposed in this invention.

[0080] Figure 8 These are images of the microseismic signals measured by the sensor, where (a) is the time-domain image of the measured signal and (b) is the spectrum of the measured signal.

[0081] Figure 9 This is a diagram showing the processing results of the method proposed in this invention in engineering measured signals;

[0082] Figure 10 This is a graph showing the processing results of the empirical mode decomposition method used in engineering measured signals. Detailed Implementation

[0083] The invention will be further illustrated below with reference to specific implementation examples and accompanying drawings:

[0084] The signal in Implementation Case 1 comes from a simulated microseismic signal. To simulate the influence of external background noise, random noise of a certain amplitude is added to the simulated microseismic signal. The mathematical expression of the simulated microseismic signal is as follows: In the formula, x(t) represents the swallowtail-shaped periodic waveform, n(t) is the background noise, A0 is the noise amplitude, the attenuation coefficient is 600, and the signal frequency is f = 80Hz. The amplitude of the added noise is set to A0 = 0.2, and the sampling frequency is 12kHz.

[0085] Example 1:

[0086] (1) First, construct the microseismic simulation signal. The original time-domain plot of the microseismic simulation signal is as follows: Figure 4 As shown in (a), the time-domain plot of the signal after adding noise is as follows: Figure 4 As shown in (b). Figure 4 (c) is the spectrum of the simulated signal with added noise. From Figure 4 (b) It can be seen that the useful swallowtail waveform in the microseismic simulation signal is contaminated by noise components. Initialize the parameter values ​​of the whale optimization algorithm and set the optimization range of the Laplace wavelet parameters. Set the whale population size to 20, the maximum number of iterations to 30, and the modal parameters of the Laplace wavelet f∈[100,6000], ξ∈[0,0.2], τ∈[0,0.2].

[0087] (2) Constructing the Laplace wavelet parameter dictionary. First, the optimal modal parameters of the Laplace wavelet are obtained using the correlation filtering method assisted by the whale optimization algorithm: f = 4938 Hz, ξ = 0.0667, τ = 0.1718. Substituting the optimal modal parameters into the function expression of the Laplace wavelet, the Laplace wavelet that best matches the microseismic characteristic waveform is constructed. Then, the optimal Laplace wavelet with periodic arrangement is used as the dictionary atom, and the Laplace wavelet parameter dictionary is constructed by changing the time shift parameter v of the wavelet.

[0088] (3) Sparse reconstruction of the original microseismic signal: The sparse decomposition coefficients are solved using the orthogonal matching pursuit algorithm, and then the sparse coefficients are multiplied by the Laplace wavelet dictionary to obtain the reconstructed vibration signal, such as... Figure 5 As shown, the method proposed in this invention accurately reconstructs the characteristic waveform of the microseismic signal and effectively eliminates the influence of noise.

[0089] (4) Optimal result processing and analysis: Based on Figure 5 The reconstructed microseismic signal shown demonstrates that the method proposed in this invention effectively reduces the influence of background noise, providing a certain technical guarantee for microseismic monitoring systems. Simulation signals indicate that the method proposed in this invention has certain feasibility and effectiveness.

[0090] (5) Comparative analysis of methods:

[0091] To verify the superiority of the method of this invention, the empirical mode decomposition algorithm was used to analyze the original microseismic signal. Figure 4 (b) Decomposition is performed, and the multiple modal components obtained from empirical mode decomposition are as follows: Figure 6 As shown, the maximum kurtosis value was used as the criterion for selecting the optimal mode component. Calculations showed that IMF2 had the largest kurtosis value, 5.2320. The time-domain plot of the IMF2 components was then compared with... Figure 5 The comparison of the processing results of the method proposed in this invention shows that the method proposed in this invention significantly eliminates the influence of noise components and clearly reconstructs the swallowtail waveform. Although the optimal IMF2 component of empirical mode decomposition reduces the influence of noise components to a certain extent, it is still not as advantageous as the method proposed in this invention.

[0092] (6) Analysis of the noise immunity of the method proposed in this invention:

[0093] To verify the anti-interference capability of the method of the present invention, Figure 4 (a) The noise amplitude is set to A0 = 0.4, 0.6, 0.8, 1.0 in sequence, as follows: Figure 7 As shown in (a). Next, using the method proposed in this invention, a Laplace wavelet dictionary is constructed, and sparse reconstruction is performed on it using the OMP algorithm, resulting in the reconstructed signal as shown in (a). Figure 7 As shown in (b). From Figure 7 As shown in (b), a clear characteristic waveform appears in the figure, and the method proposed in this invention still has a good noise reduction effect as the noise amplitude increases. Therefore, it can be concluded that the method proposed in this invention has a certain noise anti-interference capability.

[0094] Example 2:

[0095] To verify the engineering practical value of the method proposed in this invention, the method was applied to the analysis and verification of measured data from an open-pit mine. This open-pit mine is primarily composed of granite, and the mining blasting method is rock drilling and blasting separation. Based on the site topography, six sensors were evenly distributed in a circular pattern around the mine to collect microseismic signals at a sampling frequency of 1000 Hz.

[0096] (1) First, the engineering signal was acquired using a sensor. The time-domain waveform of the micro-vibration signal measured by the sensor is shown in the figure below. Figure 8 As shown in (a). Figure 8 (b) is its spectrum. It can be seen from the time-domain plot of the microseismic signal that the periodic characteristic waveform is disturbed by noise components. The parameter values ​​of the whale optimization algorithm are initialized, and the optimization range of the Laplace wavelet parameters is set. The whale population size is set to 20, the maximum number of iterations is 30, and the modal parameters of the Laplace wavelet are f∈[100,500], ξ∈[0,0.2], and τ∈[0,2].

[0097] (2) Constructing the Laplace wavelet parameter dictionary. First, the optimal modal parameters of the Laplace wavelet are obtained using the correlation filtering method assisted by the whale optimization algorithm: f = 126, ξ = 0.0634, τ = 1. Substituting the optimal modal parameters into the function expression of the Laplace wavelet, the Laplace wavelet that best matches the microseismic characteristic waveform is constructed. Then, the optimal Laplace wavelet with periodic arrangement is used as the dictionary atom, and the Laplace wavelet parameter dictionary is constructed by changing the time shift parameter τ of the wavelet.

[0098] (3) Reconstructing the vibration signal: The micro-vibration signal sparsely reconstructed using the OMP algorithm, such as... Figure 9 As shown in (a), it can be seen from the figure that the periodic impact of the microseismic signal is clearly reconstructed, the noise component is effectively reduced, and the position and period of the reconstructed characteristic waveform are basically consistent with the original microseismic signal.

[0099] (4) Optimal Result Processing and Analysis: Analysis Figure 9 (a) The time-domain plot of the reconstructed signal shows that it exhibits characteristic waveforms unique to microseismic signals. Therefore, it can be concluded that the microseismic signal noise reduction method proposed in this invention has certain practical engineering value.

[0100] (5) Comparative analysis of methods:

[0101] To verify the superiority of the method of the present invention, empirical mode decomposition was used to... Figure 8 (a) The signal is analyzed and processed; the empirical mode decomposition results are as follows: Figure 10As shown, using kurtosis as the criterion for selecting the optimal modal component, calculations show that the IMF4 modal component has the highest kurtosis value of 20.45, therefore IMF4 is the optimal modal component. Compared with the results obtained by the method of this invention, it can be seen that the optimal modal component IMF4 obtained by empirical mode decomposition reduces the influence of noise to a certain extent, but compared with... Figure 9 (a) The method proposed in this invention is clearly not superior.

[0102] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for denoising mine microseismic signals based on sparse decomposition, characterized in that, The specific steps are as follows: 1) First, collect the microseismic signal using the microseismic monitoring system, initialize the parameter value of the whale optimization algorithm and set the optimization range of the Laplace wavelet parameter, set the whale population number to 20, the maximum iteration number to 30, the modal parameter of the Laplace wavelet f∈[100, f s / 2], ξ∈[0, 0.2], τ∈[0, f s / N], wherein f is the oscillation frequency, ξ is the damping ratio, τ is the time shift parameter, f s is the signal sampling frequency, and N=length(y); 2) Constructing Laplace wavelet parameter dictionary: using the whale optimization algorithm assisted correlation filtering method to quickly find the optimal parameter value (f, ξ, τ) of Laplace wavelet, taking the maximum value of correlation coefficient K r as the fitness function of WOA algorithm, substituting the optimal modal parameter (f, ξ, τ) into the expression of Laplace wavelet function to form the optimal Laplace wavelet, using the periodic optimal Laplace wavelet as the dictionary atom, and constructing the Laplace wavelet parameter dictionary; 3) Sparse reconstruction of the original microseismic signal: With the help of the orthogonal matching pursuit algorithm, the Laplace wavelet parameter dictionary sparsely reconstructs the original microseismic signal, achieving the purpose of denoising the microseismic signal; 4) Optimal result processing and analysis: The rock mass activity state is determined from the characteristic waveforms of the signal after sparse reconstruction by the Laplace wavelet parameter dictionary and the orthogonal matching pursuit algorithm, providing reliable technical support for the microseismic monitoring system.

2. The method for denoising mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the sparse decomposition is as follows: Assuming the periodically occurring impact waveform in the microseismic signal is h(t), and the signal acquired by the microseismic monitoring system is y(t), it can be described as follows: y(t) = h(t) + noise Sparse decomposition involves decomposing a signal into an overcomplete atomic library, or dictionary D, to select useful components. Therefore, according to the principle of sparse decomposition, the sparse representation formula for the microseismic signal y(t) is: y = Dx + noise where D is a dictionary, D = {d γ} γ∈Γ (Γ = {y i , i = 1, 2,...}), d γ is a dictionary atom; x is a sparse decomposition coefficient, x = {x (1) , x (2) ,..., x (m)} r The goal of sparse signal representation is to have as many zero elements in x as possible, i.e., to solve the l0 norm minimization problem: In the formula, ε represents the reconstruction error. Solving for the l0 norm is an NP-hard problem that cannot be solved directly. Therefore, the OMP algorithm is used to transform the problem of solving for the l0 norm into solving for the l1 norm, as shown in the following formula:

3. The method for denoising mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the whale optimization algorithm is as follows: Assuming the optimal whale position in the current population is the target prey position, other whales move closer to the prey by continuously updating their own positions. This predation behavior can be expressed by the following mathematical expression: wherein: X * (t) is the position of the whale individual that obtains the global optimal solution in the population at the tth iteration, i.e., the position of the best solution; X(t) represents the position of the current whale after t iterations; D represents the distance between the whale individual and the prey; and A and C are coefficient vectors for controlling the manner in which the whale swims, and the mathematical expression is: A = 2a·ra C＝2r In the formula: r is a random vector between [0, 1]; a is the convergence factor, which decreases linearly from 2 to 0 with the increase of the number of iterations, T max To maximize the number of iterations, and to simulate the whale's spiral ascent towards its prey, we assume the whale's coordinates in two-dimensional space are (X, Y), and the prey's position is (X, Y). * Y * The position of an individual whale is updated using the following formula: D2=|X * (t)-X(t)| X(t+1)=D2·e bl ·cos(2πl)+X * (t) In the formula: D2 is the distance between the individual whale and its prey; b is a constant defining the shape of the logarithmic spiral; l is a random number between [-1, 1]. When a whale hunts, its contraction and spiral renewal occur simultaneously. Assuming that the probability of a humpback whale contracting and renewing its spiral is 50% each, the mathematical model can be expressed as: In the formula: p is a random number between [0, 1]. During the whale's prey-hunting phase, the whale no longer updates its position based on the current optimal solution, but instead randomly selects the position of another whale to update its position. The purpose is to increase the search range and find the optimal solution. The mathematical model at this time is: X(t+1)=X rand (t)-A·D rand D rand =|C·X rand -X(t)| In the formula: X rand D represents the position of an individual randomly selected from the current population; rand This represents the distance between a randomly selected individual whale and its prey.

4. The method for noise reduction of mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the Laplace wavelet is as follows: Using Laplace wavelet ψ γ (t) is used as the atomic basis function of the dictionary. The mathematical expression for the Laplace wavelet is: In the formula: f is the oscillation frequency; ξ is the damping ratio; τ is the time shift parameter; W s The above formula shows that the modal parameters (f, ξ, τ) directly control the waveform characteristics of the wavelet. By selecting different parameter values, the matching between the wavelet and the microseismic characteristic waveform can be achieved.

5. The method for noise reduction of mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific steps of the correlation filtering algorithm for finding Laplace wavelet parameters are as follows: Step 1: Assume that the Laplace wavelet oscillation frequency f, damping ratio ξ, and time shift parameter τ belong to sets F, Z, and T, respectively: Step 2: Traverse all parameter sets to obtain the complete set of Laplace wavelets: ψ = {ψ γ (t): γ∈F×Z×T}={ψ(f∈F,τ∈T,ξ∈Z)}, where t represents time; Step 3: Calculate the Laplace wavelet ψ γ The degree of similarity between y(t) and the analyzed signal y(t), i.e., the correlation coefficient K between the two. r : Step 4: Find K r Largest value, maximum K r The Laplace wavelet parameters corresponding to the value are the optimal wavelet parameters.

6. The method for noise reduction of mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the orthogonal matching pursuit algorithm is as follows: Inputs: the raw microseismic signal y acquired by the sensor, dictionary D, and sparse threshold T; Initialization: residual r0 = y, iteration count s = 1, support index set Λ0 = φ; Step 1: Set the number of iterations s = 1, 2, ..., T; Step 2: Find the subscript λ corresponding to the maximum value in the residual r and the dictionary atomic product, i.e., find the support index. Step 3: Update index set Λ s =Λ s-1 ∪{λ s }, update the initial dictionary atoms Step 4: Obtained by least squares method Step 5: Update residuals The number of iterations s = s + 1; Step 6: Determine if the required number of iterations has been met. If so, stop the iteration; otherwise, proceed to step 1. Output: Sparse decomposition coefficients 7. The method for noise reduction of mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the sparse reconstruction of the original microseismic signal is as follows: The sparse decomposition coefficients are multiplied by the constructed periodic Laplace wavelet parameter dictionary to obtain the sparsely reconstructed, denoised original microseismic signal.

8. The method for denoising mine microseismic signals based on sparse decomposition as described in claim 1, characterized in that, The specific content of the reconstruction result processing and analysis is as follows: Observe whether the reconstructed signal shows characteristic waveforms to determine the activity of the rock mass and provide effective technical support for the microseismic prediction and monitoring system.

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