Microseismic signal denoising method based on BWOA optimized VMD combined with wavelet threshold denoising
The VMD-wavelet thresholding denoising method optimized by BWOA solves the problem of the VMD and wavelet thresholding denoising algorithms relying on experience, and achieves more efficient micro-seismic signal denoising, improved signal-to-noise ratio, and enhanced waveform smoothness.
Patent Information
- Application Number
- CN202410309225.9
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-19
- Publication Date
- 2026-01-02
- Estimated Expiration
- 2044-03-19
AI Technical Summary
In existing microseismic signal processing methods, the parameter determination of the VMD algorithm relies on experience, resulting in poor denoising effect. EMD suffers from mode aliasing. The wavelet threshold denoising algorithm relies on experience for parameter selection and has a large workload, making it difficult to effectively filter out high-frequency noise and affecting subsequent analysis.
A VMD-wavelet thresholding denoising method based on BWOA optimization is adopted. The parameters of VMD and wavelet thresholding denoising algorithms are determined by the Black Widow Optimization Algorithm (BWOA), the effective modal components are screened by Pearson correlation coefficient, and the signal is reconstructed by combining VMD and wavelet thresholding denoising algorithms.
It achieves more thorough noise filtering, resulting in a smoother signal waveform and a higher signal-to-noise ratio after noise reduction. The noise reduction effect is superior to traditional methods, lowering the barrier to entry and improving ease of use.
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Figure CN118364226B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of microseismic signal denoising technology, and particularly relates to a microseismic signal denoising method based on BWOA optimization and VMD combined with wavelet threshold denoising. BACKGROUND
[0002] As an efficient ground pressure monitoring method, microseismic monitoring technology has the ability of real-time monitoring, and can effectively monitor the micro-fracture that may develop into macro-instability and damage in the rock mass, and reveal the damage evolution process in the rock mass, thereby playing an important role in ensuring the safe and smooth production activities. Therefore, the microseismic monitoring technology is widely used. Due to the complexity of the underground construction environment and geological conditions, the signals collected by the microseismic monitoring system usually contain various noises, the frequency and amplitude of which are distributed in the entire cycle, which will have a significant impact on the subsequent analysis such as P / S wave arrival picking and calculation of the source parameters. Therefore, denoising of the collected microseismic signals is a prerequisite for subsequent analysis and research.
[0003] The microseismic signal is non-stationary and random, and the commonly used methods for processing such signals include wavelet transform, empirical mode decomposition (EMD) and improved methods based on EMD such as ensemble empirical mode decomposition (EEMD). However, the wavelet threshold denoising algorithm needs to determine multiple parameters such as wavelet basis function and decomposition level, which leads to the mutual influence of harmonic components in each frequency band of the original signal, making it difficult to conduct qualitative research and analysis, and the algorithm cannot filter out high-frequency noise, affecting the denoising effect. EMD lacks a solid mathematical theoretical basis and is prone to modal aliasing; EEMD needs to increase the processing times to achieve the premise that the superposition result of multiple white noises is approximately zero, which leads to an increase in computational complexity.
[0004] Variational mode decomposition (VMD) is an adaptive and completely non-recursive modal variational and signal processing algorithm. In VMD, the number of decomposition modes can be set according to actual conditions, the limited bandwidth and optimal center frequency of the mode can be matched autonomously in the algorithm process, the mode separation is more effective, and it does not have the modal aliasing problem existing in EMD. When applied to complex nonlinear time series, it can effectively reduce the non-stationarity, so it has been widely used in recent years.
[0005] The decomposition effect of the VMD algorithm is affected by the number of modal components and the penalty factor . When the number of modal components When the value of is small, the amount of information filtered out from the original signal will increase, leading to the loss of some information in the original signal after decomposition. When the number of modal components... When the value of is large, the center frequencies of adjacent modes will be closer, and mode aliasing is more likely to occur. Penalty factor The smaller the value, the larger the modal bandwidth, which easily leads to modal aliasing and worsens the denoising effect. Penalty factor The larger the value, the smaller the bandwidth of each mode, which may lead to the loss of some important information in the original signal. Currently, the determination of these two parameters mainly relies on experience, which greatly increases the barrier to entry and severely limits the application of VMD algorithm for noise reduction. In addition, after decomposition using VMD algorithm, low-mid frequency noise is prone to remain. Wavelet thresholding denoising algorithm can be used to remove the residual low-mid frequency noise. The denoising effect of wavelet thresholding denoising is affected by parameters such as wavelet basis function, number of decomposition levels, thresholding algorithm, threshold function, and threshold scale. When using wavelet thresholding denoising, users usually select the above parameters based on experience or through continuous trial and error, which greatly restricts its application.
[0006] Therefore, it is of great significance to develop a microseismic signal denoising method based on BWOA-optimized VMD combined with wavelet threshold denoising. Summary of the Invention
[0007] The objective of this invention is to overcome the shortcomings of the prior art and provide a method for denoising microseismic signals based on BWOA-optimized VMD combined with wavelet threshold denoising. This method can not only filter out noise more thoroughly and produce a smoother waveform after denoising, but also preserve signal segments more reasonably without excessive amplitude reduction, resulting in the highest signal-to-noise ratio and the best denoising effect after denoising.
[0008] The objective of this invention is achieved through the following technical solution:
[0009] This paper proposes a microseismic signal denoising method based on BWOA-optimized VMD combined with wavelet thresholding. Addressing the shortcomings of both VMD and wavelet thresholding algorithms in practical applications, the method first uses VMD to decompose the signal to be denoised into several modal components. Then, effective modal components are selected based on the Pearson correlation coefficient. Next, wavelet thresholding is used to denoise these effective modal components. Finally, the denoised effective modal components are reconstructed to obtain the denoised signal. The main parameters of the VMD and wavelet thresholding algorithms are optimized using the Black Widow Optimization Algorithm (BWOA). The specific process steps and conditions are as follows:
[0010] Step 1: Let the time series of the microseismic signal to be denoised be... , the Black Widow Optimization Algorithm (BWOA) is used to search for the optimal parameters of the VMD algorithm when decomposing the signal, that is, the optimal parameters of the VMD algorithm are determined by the BWOA and ;
[0011] Step 2: The VMD algorithm is used to decompose the signal to be denoised with the optimal parameters and , and modal components are obtained ;
[0012] Step 3: The Pearson correlation coefficient of each modal component and the signal to be denoised is calculated, and the modal component with a correlation coefficient higher than a threshold value is selected as an effective modal component ~ ;
[0013] Step 4: The BWOA algorithm is used to search for the optimal wavelet threshold denoising parameters when the wavelet threshold denoising algorithm is used to denoise the effective modal component ~ ;
[0014] Step 5: Based on the optimal wavelet threshold denoising parameters obtained in Step 4, the effective modal component is subjected to wavelet threshold denoising, and ~ ;
[0015] Step 6: The effective modal component subjected to wavelet threshold denoising is reconstructed to obtain a denoised signal ~ .
[0016] Compared with the prior art, the present application has the following advantages or effects:
[0017] 1. Because the VMD algorithm is used, the problems of modal aliasing and lack of solid mathematical theoretical basis existing in EMD and improved methods based on EMD can be avoided.
[0018] 2. Since the BWOA is used to determine the optimal VMD parameters, the problems of the number of modal components and the penalty factor mainly relying on experience to determine when the signal is decomposed using the VMD algorithm are solved, so the use threshold of the VMD can be greatly reduced.
[0019] 3. In addition, since the optimal wavelet threshold denoising parameters are determined by using BWOA, the problem of selecting parameters by experience and large workload in using the wavelet threshold denoising algorithm is solved, so that the usability and use efficiency can be greatly improved.
[0020] 4. In addition, since the VMD and wavelet threshold denoising algorithms are combined, and the optimal parameters are used in using the two algorithms, good denoising effects can be achieved for microseismic signals with different noise levels, so that the method has good technical value and application prospect. BRIEF DESCRIPTION OF DRAWINGS
[0021] Figure 1 It is a microseismic signal denoising method based on BWOA optimization VMD combined with wavelet threshold denoising according to the present application.
[0022] Figure 2 It is a waveform diagram of the measured microseismic signal MS1 to be denoised in the example.
[0023] Figure 3 It is a frequency spectrum diagram of the microseismic signal MS1 to be denoised.
[0024] Figure 4 It is a curve of the value of the fitness function Fitness1 varying with the number of iterations when the BWOA algorithm is used for optimization.
[0025] Figure 5 It is the 19 modal components obtained after the signal MS1 to be denoised is decomposed by using the VMD algorithm with the optimal parameters. ~ .
[0026] Figure 6 It is a frequency spectrum diagram of the 19 modal components. ~
[0027] Figure 7 It is a curve of the value of the fitness function Fitness2 varying with the number of iterations when the BWOA algorithm is used for optimization.
[0028] Figure 8 It is the signal obtained after the effective modal is denoised by using the wavelet threshold denoising algorithm. ~ .
[0029] Figure 9 It is a waveform diagram of the signal DMS1 obtained after the microseismic signal MS1 is denoised by using the method.
[0030] Figure 10 It is a waveform diagram of the signal obtained after the microseismic signal MS1 is denoised by using the VMD algorithm.
[0031] Figure 11 The waveform of the signal obtained after noise reduction of the microseismic signal MS1 using the EMD algorithm is shown.
[0032] Figure 12 The spectrum of signal DMS1 obtained after denoising the microseismic signal MS1 using the method described in this invention.
[0033] Figure 13 The spectrum of the signal obtained after noise reduction of the microseismic signal MS1 using the VMD algorithm.
[0034] Figure 14 The spectrum of the signal obtained after noise reduction of the microseismic signal MS1 using the EMD algorithm.
[0035] The present invention will now be described in further detail with reference to the accompanying drawings. Detailed Implementation
[0036] like Figures 1-12 As shown, a microseismic signal denoising method based on BWOA-optimized VMD combined with wavelet thresholding addresses the shortcomings of both VMD and wavelet thresholding algorithms in practical applications. First, the VMD algorithm is used to decompose the signal to be denoised into several modal components. Then, effective modal components are selected based on the Pearson correlation coefficient. Next, the wavelet thresholding algorithm is used to denoise the effective modal components. Finally, the denoised effective modal components are used to reconstruct the signal, resulting in the denoised signal. The main parameters of the VMD and wavelet thresholding algorithms are optimized using the Black Widow Optimization Algorithm (BWOA). The specific process steps and conditions are as follows:
[0037] Step 1: Let the time series of the microseismic signal to be denoised be... The Black Widow Optimization Algorithm (BWOA) is used to search for the optimal parameters for the VMD algorithm to decompose the signal, i.e. and ;
[0038] Step 2: Use the VMD algorithm with optimal parameters and Treating denoised signals Decompose to obtain Modal components ;
[0039] Step 3: Calculate each modal component With the signal to be denoised The Pearson correlation coefficient was used to filter out modal components with correlation coefficients higher than a threshold. ~ as an effective modal component;
[0040] Step 4: searching for optimal wavelet threshold de-noising parameters for the effective modal component by using the BWOA algorithm ~ optimal wavelet threshold de-noising parameters when de-noising;
[0041] Step 5: performing wavelet threshold de-noising on the effective modal component based on the optimal wavelet threshold de-noising parameters obtained in step 4, to obtain a de-noised signal ~ ;
[0042] Step 6: performing reconstruction on the effective modal component after wavelet threshold de-noising, to obtain the de-noised signal ~ the formula of the de-noised signal.
[0043] The method of the application can further be:
[0044] The parameters of the step 1 VMD algorithm include the number of modal components and a penalty factor , and the optimization ranges of the two are [2, 20] and [100, 10000] respectively.
[0045] When the step 1 uses the BWOA algorithm for optimization, the fitness function is the local minimum envelope entropy, and the calculation formula is
[0046] (1)
[0047] wherein, is a microseismic signal , and the envelope entropy of each modal component obtained after the VMD algorithm is decomposed; the envelope entropy of the modal component can be expressed as
[0048] (2)
[0049] wherein, is the envelope signal obtained after the Hilbert transform of the modal component ; and is the normalized form of .
[0050] The calculation formula of the threshold of the step 3 is
[0051] (3)
[0052] wherein, is the Pearson correlation coefficient of the i-th modal component and the original signal .
[0053] The wavelet thresholding denoising parameters in step 4 include wavelet basis functions, decomposition levels, threshold functions, threshold algorithms, and threshold scales. The optimization range for wavelet basis functions is sym2~8, db2~8, coif1~5, bior1.1, bior1.1, bior2.2, bior3.1, and bior4.4. The optimization range for the decomposition levels is 3~8. The optimization range for threshold functions is hard threshold functions and soft threshold functions. The optimization range for threshold algorithms is sqtwolog, heursure, minimax, and rigrsure. The optimization range for threshold scales is one, sln, and mln.
[0054] In step 4, when using the BWOA algorithm for optimization, the fitness function is Fitness2, and its calculation formula is:
[0055] (4)
[0056] in, The denoised signal is obtained by reconstructing the signal after wavelet threshold denoising of each effective modal component. and the original signal Pearson correlation coefficient, Calculate according to formula (6); The signal-to-noise ratio of the denoised signal is defined as follows:
[0057] (5)
[0058] in, and These are the root mean square amplitudes of the signal and noise, respectively. In actual calculations, the first 500 sampling points after the initial arrival of the P-wave are used for calculation. and ,Right now and .
[0059] Step 6 utilizes ~ Reconstructing the denoised signal The formula for the method is:
[0060] (6)
[0061] Example
[0062] This invention provides a method for denoising microseismic signals based on BWOA-optimized VMD combined with wavelet thresholding, see [link to relevant documentation]. Figure 1 The specific process steps and conditions are as follows:
[0063] Step 1: Set the time sequence of the measured microseismic signal to be denoised as MS1, the waveform diagram is shown in Figure 2 , and the frequency spectrum is shown in Figure 3 . After calculation, the signal-to-noise ratio of signal MS1 is 12.80 dB. The optimal parameters for decomposing the signal using VMD algorithm are searched using BWOA algorithm, i.e. and , and the optimization range of the two is [2, 20] and [100, 10000] respectively. In the optimization process, the value curve of fitness function Fitness1 with iteration number is shown in Figure 4 . As can be seen from Figure 4 , the optimal parameters are found at the 6th iteration, and the optimization results are = 19, = 9700.
[0064] Step 2: The optimal parameters = 19, = 9700 are used to decompose the signal to be denoised MS1 using VMD algorithm, and 19 modal components are obtained, as shown in Figure 5 , Figure 6 .
[0065] Step 3: The Pearson correlation coefficients of the 19 modal components obtained in step 2 and the signal to be denoised MS1 are calculated, as shown in Table 1. The threshold value is calculated according to formula (3) as = 0.1514. According to Table 1, it can be found that the modal components with correlation coefficients higher than the threshold value are ~ , so the effective modal components are ~ .
[0066] Table 1 Pearson correlation coefficients of each modal component and the signal to be denoised MS1
[0067] Modal component Pearson correlation coefficient with MS1 Modal component Pearson correlation coefficient with MS1 Modal component Pearson correlation coefficient with MS1 blimf1 0.7773 blimf8 0.0902 blimf 15 ]]> 0.0460 blimf2 0.8836 blimf9 0.0765 blimf 16 ]]> 0.0444 blimf3 0.3930 blimf 10 ]]> 0.0637 blimf 17 ]]> 0.0410 blimf4 0.2470 blimf 11 ]]> 0.0585 blimf 18 ]]> 0.0382 blimf5 0.1589 blimf 12 ]]> 0.0526 blimf 19 ]]> 0.0331 blimf6 0.1240 blimf 13 ]]> 0.0511 blimf7 0.0953 blimf 14 ]]> 0.0470
[0068] Step 4: The optimal wavelet parameters for denoising the effective modal components using wavelet threshold denoising algorithm are searched using BWOA algorithm. In the optimization process, the value curve of fitness function Fitness2 with iteration number is shown in Figure 7 . As can be seen from the figure, the optimal parameters are found at the 8th iteration, and the optimization results are as follows: the wavelet basis function takes bior4.4, the decomposition level takes 8, the threshold function takes the hard threshold function, the threshold algorithm takes minimax, and the threshold scale takes mln.
[0069] Step 5: Based on the optimal wavelet threshold denoising parameters obtained in step 4, the effective modal components ~ are denoised using wavelet threshold denoising, and the denoised signal is obtained As shown in Figure 8 .
[0070] Step 6: effective modal component after wavelet threshold denoising Reconstruction is carried out to obtain the denoised signal DMS1, the waveform of which is shown in Figure 9 , and the spectrum is shown in Figure 12 . After calculation, the signal-to-noise ratio of the denoised signal is 25.01dB.
[0071] As a comparison, the VMD and EMD algorithms are used to denoise the signal MS1, and the denoised waveform and spectrum are shown in Figure 10 、 Figure 11 、 Figure 13 、 Figure 14 . After calculation, the signal-to-noise ratios of the signals denoised by the VMD and EMD algorithms are 14.00dB and 13.380dB, respectively.
[0072] According to Figure 2 、 Figure 3 , it can be known that the noise frequency of the measured microseismic signal MS1 is mainly in the range of 0~300Hz. It can be known from Figures 9-14 that the denoising method provided by the present application filters out noise more thoroughly than VMD and EMD, and the denoised waveform is smoother, while the signal segment is more reasonably retained and the amplitude does not decrease too much, so that the signal-to-noise ratio after denoising is the highest and the denoising effect is the best.
[0073] As described above, the present application can be better implemented. The above embodiments are only the best implementation of the present application, but the implementation of the present application is not limited by the above embodiments, and other changes, modifications, replacements, combinations and simplifications made without departing from the spirit and principles of the present application should be equivalent replacement methods, and all are included in the protection scope of the present application.
Claims
1. A method for denoising microseismic signals based on BWOA-optimized VMD combined with wavelet thresholding, characterized in that... First, the VMD algorithm is used to decompose the signal to be denoised into several modal components. Then, the effective modal components are selected based on the Pearson correlation coefficient. Next, the wavelet thresholding denoising algorithm is used to denoise the effective modal components. Finally, the denoised effective modal components are used to reconstruct the signal to obtain the denoised signal. The main parameters of the VMD algorithm and the wavelet thresholding denoising algorithm are optimized and determined using the Black Widow Optimization Algorithm (BWOA). The specific process steps and conditions are as follows: Step 1: Let the time series of the microseismic signal to be denoised be... Using the Black Widow Optimization Algorithm (BWOA), the optimal parameters for the VMD algorithm to decompose the signal are searched. and ; Step 2: Use the VMD algorithm with optimal parameters and Treating denoised signals Decompose to obtain Modal components ; Step 3: Calculate each modal component With the signal to be denoised The Pearson correlation coefficient was used to filter out modal components with correlation coefficients higher than a threshold. ~ As an effective modal component; Step 4: Use the BWOA algorithm to search for effective modal components and use the wavelet thresholding denoising algorithm. ~ The optimal wavelet threshold denoising parameters are determined during denoising; when using the BWOA algorithm for optimization, the fitness function is Fitness2, and its calculation formula is... (4) in, The denoised signal is obtained by reconstructing the signal after wavelet threshold denoising of each effective modal component. and the original signal Pearson correlation coefficient, Calculate according to formula (6); The signal-to-noise ratio of the denoised signal is defined as follows: (5) in, and These are the root mean square amplitudes of the signal and noise, respectively. In actual calculations, the first 500 sampling points after the initial arrival of the P-wave are used for calculation. and ,Right now and ; Step 5: Perform wavelet threshold denoising on the effective modal components based on the optimal wavelet threshold denoising parameters obtained in Step 4, to obtain... ~ ; Step 6: Utilize the effective modal components after wavelet thresholding ~ Reconstruct the signal to obtain the denoised signal. The formula.
2. The method according to claim 1, characterized in that: The parameters of the VMD algorithm in step 1 include the number of modal components. and penalty factor The optimization ranges for the two are [2,20] and [100,10000], respectively.
3. The method according to claim 1, characterized in that: In step 1, when using the BWOA algorithm for optimization, the fitness function is the local minimum envelope entropy, and its calculation formula is as follows: (1) in, It is a microseismic signal Envelope entropy of each modal component obtained after decomposition by the VMD algorithm; modal components Envelope entropy It can be represented as (2) in, Modal components The envelope signal obtained after Hilbert transform; yes The normalized form.
4. The method according to claim 1, characterized in that: The formula for calculating the threshold in step 3 is as follows: (3) in, It is the i-th modal component and the original signal The Pearson correlation coefficient.
5. The method according to claim 1, characterized in that: The wavelet thresholding denoising parameters in step 4 include wavelet basis functions, decomposition levels, threshold functions, threshold algorithms, and threshold scales. The optimization range for wavelet basis functions is sym2~8, db2~8, coif1~5, bior1.1, bior2.2, bior3.1, and bior4.
4. The optimization range for the decomposition levels is 3~8. The optimization range for threshold functions is hard threshold functions and soft threshold functions. The optimization range for threshold algorithms is sqtwolog, heursure, minimax, and rigrsure. The optimization range for threshold scales is one, sln, and mln.
6. The method according to claim 1, characterized in that: Step 6 utilizes ~ Reconstructing the denoised signal The formula for the method is: (6)。