Landslide deep deformation monitoring data noise reduction method based on HBP-VMD combined improvement wavelet threshold

Abstract

The invention relates to a landslide deep deformation monitoring data noise reduction method based on an HBP-VMD combined improvement wavelet threshold. The method comprises the steps of collecting a landslide deep deformation original signal; the sample entropy is used as a fitness function, a badger optimization algorithm is adopted to optimize VMD decomposition parameters, and an optimal combination parameter combination is obtained; substituting the optimal combination parameter into the VMD, and performing VMD decomposition on the original signal to obtain K intrinsic mode components IMF of different frequencies; calculating a variance contribution rate and a correlation coefficient corresponding to each obtained IMF component, and dividing the IMF components into an effective component, a noisy component and a noise component; retaining the obtained effective component, abandoning the noise component, and carrying out noise reduction processing on the noisy component by using an improved wavelet soft threshold; and reconstructing the IMF component after noise reduction and the effective IMF component, and finally realizing signal noise reduction. According to the method, the deformation monitoring signal of the deep part of the landslide can be efficiently stripped from the noisy signal, and the waveform is clearer than that before noise reduction; the SNR of the signal after noise reduction is the highest, the SMES is the lowest, and the excellent noise reduction effect is achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of landslide deep deformation monitoring signal denoising, and particularly relates to a landslide deep deformation monitoring data denoising method based on HBA-VMD combined improved wavelet threshold. BACKGROUND

[0002] Landslide deformation monitoring is an important means to prevent and control landslide disasters. Landslide deep deformation monitoring is in a closed complex environment underground, and it is difficult to directly measure by external electricity, light, magnetism, etc. It often uses sensors with specific functions (acceleration sensors, gyroscopes, etc.) buried in the slope body to obtain landslide deep deformation data. However, due to the complex internal structure of the landslide body, combined with many external environmental interference factors, the obtained original data often contains a large amount of noise, which seriously affects the reliability of data analysis. Therefore, how to extract the true information of landslide deformation from the noisy monitoring data is a key problem that needs to be solved at present.

[0003] The traditional landslide deep deformation signal denoising method mainly includes Fourier transform, Kalman filter, wavelet transform, empirical mode decomposition (EMD) and the like. Landslide deep deformation monitoring signal is non-stationary. Since Fourier transform lacks time domain positioning function, it can only give the overall effect of the signal, resulting in poor effect of non-stationary signal spectrum analysis; Kalman filter uses matrix operation, which makes the calculation time longer and may cause serious waveform distortion; wavelet transform has the characteristics of multi-resolution analysis, and is more suitable for analyzing and processing non-stationary signals, and can better distinguish the mutation part of signal noise, but it needs to pre-select wavelet basis function and decomposition level, and different wavelet basis functions and decomposition levels will directly affect the denoising effect. Empirical mode decomposition (EMD) can decompose the signal into a finite number of intrinsic mode functions from high frequency to low frequency, but when the modal frequency is close, there will be modal aliasing problem, and the reconstructed signal will mix a lot of noise. Then, many scholars proposed various EMD improvement algorithms, such as EEMD, CEEMD, etc., but the inherent defects of EMD method have not been fundamentally solved.

[0004] Variational mode decomposition (VMD) is a new time-frequency analysis method proposed in recent years, which can effectively process nonlinear and non-stationary signals by decomposing multi-component signals into multiple single amplitude modulation (AM) and frequency modulation (FM) signals at one time. With its unique Wiener filtering characteristics, VMD can effectively compensate for the mode mixing and boundary effect problems in EMD decomposition. However, VMD method requires manual input of two key parameters, namely the number of decomposition modes K and the penalty factor α. If K is set too small, the signal decomposition will not be sufficient, and if K is set too large, it will easily lead to over-decomposition, frequency overlap, and other problems. The smaller α is, the larger the bandwidth of each IMF obtained will be, and the more noise it will contain. If α is too large, it will incorrectly remove effective components. Therefore, if the input parameters can be selected adaptively, the efficiency and application range of the VMD method can be improved.

[0005] To address this issue, many scholars have studied the optimization of VMD parameters using optimization algorithms. For example, in the paper [1]: “Wei Zijun, Yang Shiwu, Li Wentao, et al. Track circuit signal analysis method based on optimized variational mode decomposition [J]. China Railway Science, 2024, 45(05): 198-208.”, the authors used the SSA-VMD algorithm to optimize the parameters of VMD when analyzing track circuit signals. The SSA algorithm has the advantages of high search accuracy and fast convergence speed, and can obtain better parameter combinations. In the paper [2]: “Chen Zhu’an, Xiong Xin, Li Yijia. Deformation signal denoising method based on PSO-DVMD-WT [J]. Surveying and Mapping Science, 2020, 45(08): 41-50.”, the authors proposed a method of optimizing VMD decomposition parameters using PSO and applied it to denoising of dam deformation monitoring data, obtaining good signal-to-noise ratio and mean square error. In the paper [3]: “Zhang Weiping, Fu Min, Zhang Haiyan, et al. Application of improved WOA-VMD algorithm in underwater acoustic signal denoising [J]. Journal of Ocean University of China (Natural Science Edition), 2023, 53(01): 138-146.”, the authors used WOA to select the best parameter combination of VMD for underwater acoustic signals, improving the signal-to-noise ratio of the target signal and achieving good denoising effect.

[0006] However, these optimization algorithms have common shortcomings in the iteration process, such as being easily trapped in local optima, poor performance in complex multi-dimensional scenarios, high computational demand, and slow convergence speed. Landslide deep deformation monitoring data requires large amounts of data collection, and the time problem of signal processing needs to be considered. If we only pursue the computational accuracy of the algorithm while ignoring the complexity, iteration times, and computation time, it will directly affect its application value in practical engineering. SUMMARY

[0007] To solve the above technical problems, the application provides a landslide deep deformation monitoring data denoising method based on HBA-VMD combined improved wavelet threshold, which can efficiently strip the landslide deep deformation monitoring signal from the noisy signal, and the waveform is clearer than before denoising; the denoised signal is basically consistent with the original signal in overall characteristics, peak value and the like, and the basic characteristics of the target signal are successfully retained, so that the SNR of the denoised signal is the highest and the SMES is the lowest, and excellent denoising effect is achieved.

[0008] The technical scheme adopted by the application is: The landslide deep deformation monitoring data denoising method based on HBA-VMD combined improved wavelet threshold comprises the following steps: Step 1: collect landslide deep deformation original signal; Step 2: use sample entropy as fitness function, and use Honey Badger Algorithm (HBA) to optimize VMD decomposition parameters to obtain the best combination of parameters, i.e. decomposition modal number K and penalty factor α; Step 3: put the best combination of parameters obtained in step 2 into VMD, and perform VMD decomposition on the landslide deep deformation original signal to obtain K intrinsic modal components (IMF) of different frequencies; Step 4: calculate the variance contribution rate and correlation coefficient corresponding to each IMF component, and divide the IMF components into effective components, noisy components and noise components; Step 5: retain the effective components obtained in step 4, discard the noise components, and use improved wavelet soft threshold to denoise the noisy components; Step 6: reconstruct the denoised IMF components and effective IMF components to finally realize signal denoising.

[0009] In step 2, the variational mode decomposition is a completely non-recursive signal decomposition and time-frequency distribution estimation method. The core idea of the variational mode decomposition is to convert the signal decomposition into a variational problem, and to realize the adaptive decomposition of the signal by searching for the optimal solution of the constrained variational model. In the iteration process, according to the frequency domain characteristics after signal decomposition, the signal bandwidth can be decomposed, and a plurality of intrinsic modal components (IMF) are obtained, each intrinsic modal component (IMF) has a corresponding center frequency and a limited bandwidth. Essentially, each intrinsic modal component (IMF) is an amplitude-frequency modulation signal, which can be expressed as: (1); In formula (1): is the kth modal component function; is the instantaneous amplitude of the IMF; is the phase function of the IMF; The step 2 comprises the following steps: S2.1: any complex raw signal can be decomposed into k modal components, i.e.: , represents the kth modal component function; K represents the total number of decomposed modes. A variational model is constructed to find the optimal modal function, so that the sum of the estimated bandwidths of all modal functions is minimized; The construction of the variational model is as follows: a: for each modal component function , the Hilbert transform is performed on the IMF component to obtain the one-sided spectrum, and the formula is as follows: (2); In formula (2), is the one-sided spectrum obtained by Hilbert transform; is the impact function; j is the imaginary unit; t is time; b: multiply the estimated center frequency with formula (2) to modulate the spectrum to the base frequency band matched therewith, then calculate the squared norm of the demodulation signal gradient and estimate the bandwidth of each IMF, and the formula is as follows: (3); In formula (3), is the set of center frequencies of the IMF; is the center frequency of the kth IMF; is the set of IMF components; is the constraint condition; is the partial derivative with respect to time; k = 1, 2, 3,..., K; S2.2: To solve the constrained variational problem, a penalty factor α and a Lagrange multiplier λ are introduced, and the extended Lagrange expression is as follows: (4); In formula (4), is the extended Lagrange expression; is the Lagrange multiplier; is the Lagrange function; is the square of the 2-norm of the gradient; is the inner product; S2.3: The alternating direction multiplier method is used to iteratively update , and , to seek the saddle point of the extended Lagrange expression as the optimal solution of the above constrained variational problem formula (4); (5); In formula (5), a is a penalty factor; n is the number of times; is the noise tolerance; , , , , , is the Fourier transform of , , , , , i is the modal number; w is the signal frequency; is the modal component function of the n+1th iteration; and respectively represent the Lagrange function of the n+1th and n th iteration.

[0010] The specific iteration update solving process is as follows: step 1, initialization , let n=1; k=1; step 2, let n=n+1, and the VMD algorithm enters a continuous loop; step 3, let k=1, update and according to formula (5), and loop from 1 to K; step 4, when k=K, the loop stops, and λ is updated; step 5, given the convergence condition:

[0011] In the above formula, ε is the convergence accuracy and ε>0.

[0012] When the convergence condition is met, the iteration is stopped, and K IMFs are output, otherwise the loop of n=n+1 is continued.

[0013] S2.4: When the VMD is used to decompose the signal, it is difficult to correctly select K and a to ensure the accuracy of the signal decomposition due to the lack of prior information and understanding of the input signal. In order to obtain accurate VMD parameter combination, the present application introduces a honey badger optimization algorithm to optimize the two parameters. The honey badger optimization algorithm mainly simulates the foraging behavior of honey badgers in the excavation and honey gathering mode in the natural world. In the excavation stage, the honey badger relies on olfaction to locate prey and select the best place for excavation and hunting; in the honey gathering stage, the honey badger directly locates the beehive with the help of the guide of the honey bird; Specifically, the following steps are included: Initialize the population number N of the honey badger and the position of the individual: (6); In formula (6), the following applies: is the position of the i-th honey badger; i is the position of the i-th honey badger; is the position of the i-th honey badger; is a random number in [0, 1]; and are the lower and upper limits of the search domain, respectively; The honey badger moves by tracking the intensity of the prey scent, and as the intensity of the prey scent increases and the distance to the prey decreases, the honey badger is able to more accurately locate the prey, according to the following formula: (7); In formula (7), the following applies: is the intensity of the prey scent; is the intensity of the source of the scent; is a random number in [0, 1]; is the distance between the prey and the i-th honey badger; is the best position of the prey so far; and are the positions of the i-th and i+1-th honey badger, respectively; The density factor θ adjusts the randomness over time, and the density factor θ decreases as the number of iterations increases, in order to reduce randomization; the update formula is as follows: (8); In formula (8), C is a constant and , generally set to 2 by default, t is the current number of iterations; is the maximum number of iterations; In the excavation phase, the ability of the honey badger to locate the prey is highly dependent on the intensity of the scent , the distance between the honey badger and the prey , and the density factor θ; (9); In formula (9), the following applies: is the new position of the honey badger; is the global optimal position of the honey badger; F is a flag to change the search direction; is the intensity of the scent; is the ability of the honey badger to prey, , generally set to 6 by default; , , is a random number in [0, 1]; In the honey gathering phase, the process of the honey badger following the honey bird to the beehive can be simulated by the following formula: (10); In formula (10): is the new position of the meerkat; is the global optimal position of the meerkat; and θ is a density factor; is a flag for changing the search direction; is a random number in [0, 1].

[0014] When the meerkat optimization algorithm is used for optimization, the fitness function is sample entropy, and the calculation formula thereof is is: (11); In formula (11): is a dimension, generally taking a value of 1 or 2, and 2 is preferred; is a similarity tolerance, generally taking 0.1-0.25 times of a sequence standard deviation; represents a probability that two groups of sequences can match m points under a tolerance; represents a probability that two groups of sequences can match m+1 points under a tolerance.

[0015] In the step 3, the optimal combination parameters [K, a] obtained by using the HBA to adaptively optimize the VMD parameters in the step 2 are substituted into the VMD, and the initial signal containing noise is subjected to VMD decomposition to obtain K IMF components with high to low frequencies.

[0016] In the step 4, the variance contribution rate of each IMF is calculated to preliminarily screen and filter out components with small contribution rates. After setting a threshold to filter out IMF components with low variance contribution rates, the remaining IMF components can retain the characteristics of the original signal under the condition of minimum signal loss.

[0017] The correlation coefficient represents the closeness between two signals. The greater the value, the higher the closeness, and the lower the noise content in the corresponding IMF component. By setting a discrimination criterion, the remaining IMF components are further subdivided into effective components, noise-containing components, and noise components.

[0018] The variance contribution rate of the kth IMF and the correlation coefficient The calculation formula is as follows: (12); (13); In the above formula: is each modal component obtained by decomposition; is the original signal; , respectively , are mean values, and T is the signal length.

[0019] In step 4: the set threshold and the criterion are: The threshold is set to 0.1, and The IMF of is filtered out; If , it is considered that the effective component; If , it is considered that the noise component; If , it is considered that the noise component.

[0020] In the step 5: the improved wavelet soft threshold specifically includes: S5.1: the noise-containing mode is applied to an improved wavelet soft threshold method proposed in the literature [4]: Sun Wanlin, Wang Chao. Power signal denoising based on improved soft threshold wavelet packet network [J]. Journal of Naval Engineering University, 2019, 31(04): 79-82. for denoising; (14); In formula (14): is a threshold value, is the original wavelet coefficient, is the quantized wavelet coefficient, is a sign function; In the S5.1, the threshold value is , wherein D is a variance, and N is the number of high-frequency coefficients corresponding to the decomposition layer; S5.2: the optimal wavelet base function and the decomposition layer number are determined by using the maximum signal-to-noise ratio principle. Specifically: Since the landslide deep deformation monitoring data has discreteness, the wavelet function family supported by MATLAB software excludes the wavelet base function that cannot be discretely transformed, and in order to make the reconstructed signal have better smoothing effect and obtain better time-frequency resolution, the dbN system, symN system and coifN wavelet system are selected for research, which have regularity and tight support. The decomposition layer number is 1-10. When the signal-to-noise ratio value is larger, the signal denoising effect is better, but the signal-to-noise ratio will not always increase, and will appear the trend of first rising and then falling. The peak value of the signal-to-noise ratio of the signal denoised by different decomposition layer numbers is taken as the criterion to determine the optimal number of wavelet decomposition and the wavelet base function.

[0021] The landslide deep deformation monitoring data denoising method based on HBA-VMD combined with improved wavelet threshold has the following technical effects: 1) For the selection problem of the key parameters of VMD, the HBA algorithm is introduced to optimize the two key parameters of the mode number K and the penalty factor alpha, so that the problem of difficult parameter selection is solved; in the optimization process, the sample entropy is used as the fitness function, which can effectively reduce the calculation complexity, quickly find the optimal parameter combination, and improve the operation efficiency of the algorithm.

[0022] 2) The variance contribution rate of each IMF is calculated, the threshold is set according to the variance contribution rate, the signal component with a variance contribution rate less than the threshold is discarded, then the correlation coefficient of the remaining IMF is calculated, the remaining component is subdivided into an effective component, a noisy component and a noise component, and the noisy component is denoised by using the improved wavelet threshold algorithm, and the noise component is removed, thereby providing a reliable basis for the next signal accurate reconstruction.

[0023] 3) In the traditional wavelet threshold denoising, the decomposition level and the base function of the wavelet are usually selected based on experience, and the use of fixed decomposition level and wavelet base function inevitably has limitations. The present application adaptively compares a plurality of wavelet base functions and decomposition levels according to the signal-to-noise ratio, greatly shortens the time of wavelet parameter optimization under the condition that the wavelet threshold denoising effect reaches the best, and improves the overall processing efficiency.

[0024] 4) The denoising analysis of the simulation signal, the wavelet threshold algorithm, the EMD-wavelet threshold algorithm and other denoising methods are compared and analyzed, and the denoising effect of the present application is superior; the denoising analysis of the measured signal, the present application successfully retains the rich landslide deep dynamic characteristic information under the premise of realizing excellent denoising effect, and can provide reference for future research and application in related fields. BRIEF DESCRIPTION OF DRAWINGS

[0025] The present application will be further described below in combination with the drawings and examples: Figure 1 It is a flow chart of the landslide deep deformation monitoring data denoising method described in the present application.

[0026] Figure 2 (a) is a simulation signal waveform graph (original signal) of the present application; Figure 2 (b) is a simulation signal waveform graph (containing noise signal) of the present application.

[0027] Figure 3 It is a comparison graph of the fitness value convergence curves of different optimization algorithms of the present application.

[0028] Figure 4 (a) is a time domain graph of each IMF component obtained by HBA-VMD decomposition of the simulation signal of the present application; Figure 4 (b) is a frequency domain graph corresponding to the time domain graph of each IMF component obtained by HBA-VMD decomposition of the simulation signal of the present application.

[0029] Figure 5(a) is a comparison of the signal-to-noise ratio of different wavelet basis functions and decomposition levels of the present application Figure 1 ; Figure 5(b) is a comparison of the signal-to-noise ratio of different wavelet basis functions and decomposition levels of the present application Figure two Figure 5(c) is a comparison of the signal-to-noise ratio of different wavelet basis functions and decomposition levels of the present application Figure 3 .

[0030] Figure 6 is the waveform diagram of the simulated signal of the present application after noise reduction by different algorithms.

[0031] Figure 7 is the waveform diagram of the measured signal of the present application.

[0032] Figure 8 is the fitness value convergence curve diagram of the measured signal of the present application.

[0033] Figure 9(a) is a time domain diagram of each IMF component obtained by HBA-VMD decomposition of the measured signal of the present application; Figure 9(b) is a frequency domain diagram corresponding to the time domain of each IMF component obtained by HBA-VMD decomposition of the measured signal of the present application; Figure 10 is the waveform diagram of the measured signal of the present application after noise reduction. DETAILED DESCRIPTION

[0034] As shown in Figure 1 , the landslide deep deformation monitoring data denoising method based on HBA-VMD combined with improved wavelet threshold value includes the following steps: Step one: denoising the monitoring data collected by the landslide deep deformation micro-electro-mechanical system. Through the wireless transmission module, the data collected by each monitoring point is transmitted to the monitoring station in real time, the sampling frequency is 2000 Hz, and the landslide deep deformation original signal is collected.

[0035] Step two: taking sample entropy as the fitness function, using the Honey Badger Algorithm (HBA) to optimize the VMD decomposition parameters to obtain the best combination of parameters [K, a].

[0036] Step three: substitute the best combination of parameters obtained in step two into VMD to decompose the landslide deep deformation original signal and obtain K IMF components of different frequencies.

[0037] Step four: calculate the variance contribution rate and correlation coefficient corresponding to each IMF component, and divide the IMF components into effective components, noisy components and noise components.

[0038] Step five: retain the effective components obtained in step four, discard the noise components, and use the improved wavelet soft threshold to denoise the noisy components.

[0039] Step six: reconstructing the noise-reduced IMF component and the effective IMF component, and finally realizing signal denoising.

[0040] In order to verify the effectiveness of the present application, further simulation and experimental description is given as follows: The signal-to-noise ratio SNR and the root mean square error RMSE are used as the simulation signal denoising result evaluation indexes.

[0041] The signal-to-noise ratio (SNR) is a measure of the ratio of signal to noise, and the larger the value is, the better the denoising effect is, and the calculation formula is as follows: (15); The root mean square error RMSE is a measure of the difference between the predicted value and the actual value. The smaller the RMSE is, the better the noise effect is, and the calculation formula is as follows: (16); Since it is extremely difficult to obtain a signal completely free of noise in actual landslide deep deformation monitoring signal, it is difficult to accurately reflect the denoising effect by only using the signal-to-noise ratio SNR and the root mean square error RMSE. In order to more comprehensively evaluate the denoising quality, the following three kinds of supplementary evaluation indexes: smoothness RVR, signal energy ratio SER and noise module NM.

[0042] The smoothness RVR reflects the smoothness of the denoised signal relative to the original signal, and the smaller the value is, the smoother the signal is, and the calculation formula is as follows: (17); The signal energy ratio SER and the noise module NM can both reflect the change of signal energy before and after denoising, and the larger the SER and NM are, the more effective signal energy is retained in the denoising process, and the calculation formula is as follows: (18); (19); In the above evaluation index formula: L is the number of sampling points, is the original signal, is the denoised signal.

[0043] The landslide deep deformation monitoring signal often contains multiple types of noise, and the frequency distribution range of these noises is extensive. In order to ensure that the simulation experiment is as consistent as possible with the actual situation, the following composite simulation signal is constructed for the experiment: (20); In formula (20): is the original signal, which is composed of three signal components with frequency components of 5 Hz, 15 Hz and 100 Hz; The noise level is 15 dB Gaussian white noise, the sampling frequency is set to 2000 Hz, and the number of sampling points is set to 1500. The waveforms of the original signal and the noisy signal can be seen in Figure 2 (a) and Figure 2 (b).

[0044] Initialize the VMD decomposition parameter range and the HBA algorithm. Based on experimental experience, set the upper and lower limits of the VMD parameter K to [2, 15], the upper and lower limits of the parameter α to [100, 3000], the number of population iterations of the HBA algorithm to 20, and the population size to 30.

[0045] The HBA algorithm is used to optimize the VMD parameters using sample entropy as the fitness function. At the same time, under the same conditions, it is compared with the particle swarm optimization algorithm (PSO) and sparrow optimization algorithm (SSA) to optimize VMD. The iterative optimization curve is shown in Figure 2. Figure 3 As shown. Figure 3 As can be seen from the figure, HBA reaches its minimum fitness value after the second iteration. Compared to the PSO algorithm, which takes five iterations, and the SSA algorithm, which takes six iterations to reach its optimal state, HBA reaches its optimal state in the fewest iterations and achieves the lowest fitness value. The HBA algorithm also has the shortest runtime. This shows that the HBA algorithm has significant advantages over other algorithms in terms of optimization capability, convergence speed, and time efficiency.

[0046] Substitute the best VMD parameter combination [K, α] into VMD and perform VMD decomposition on the simulated signal containing noise to obtain K IMF components. In this example, considering the randomness in the iterative process, the algorithm is repeated 40 times to ensure the reliability of the results. Finally, the average value of the parameters is selected as the optimal parameter combination. , As shown in Figure 4 (a) and Figure 4 (b), it can be seen from Figure 4 (a) and Figure 4 (b) that the HBA-VMD decomposition results have good decomposition performance and higher decomposition efficiency, retain the effective characteristics of the signal, and there is almost no modal aliasing phenomenon in the decomposition results.

[0047] Table 1 Variance contribution rate of each IMF component

[0048] According to the screening threshold criterion: the threshold is set to 0.1 in this paper, and the variance contribution rate calculation results of each IMF component are shown in Table 1. The sum of the variance contribution rates of the retained IMF1 to IMF5 is 0.9619. It can be considered that while retaining the effective components of the original signal as much as possible, the noise is filtered out to the greatest extent, completing the initial noise reduction.

[0049] Table 2 Correlation coefficients of the remaining IMF components

[0050] According to the correlation coefficient judgment criterion, the present invention sets a threshold to further screen out the effective components ( ), noisy component ( ), noise component ( The correlation coefficients of IMF1 to IMF5 were calculated, and the results are shown in Table 2. The correlation coefficients of IMF1 and IMF3 were both greater than 0.5, and they were identified as valid components and retained. The correlation coefficient of IMF2 was between 0.1 and 0.5, indicating that it was a noise component and required wavelet threshold denoising. The correlation coefficients of IMF4-IMF5 were all less than 0.1, and they were discarded.

[0051] A fixed threshold and an improved soft threshold function are used to denoise the original noisy signal. The peak signal-to-noise ratio (SNR) of the denoised signal is used as a benchmark to determine the optimal number of wavelet decomposition layers and wavelet basis functions. Figures 5(a) to 5(c) show the SNR peaks for different wavelet bases and decomposition layers. The SNR peaks when the wavelet basis function is db7 and the number of decomposition layers is 3. Therefore, this invention selects the wavelet basis function db7 and the number of decomposition layers to denoise the noisy component.

[0052] In order to verify the effectiveness of the method of the present invention, the HBA-VMD combined with improved wavelet threshold denoising method is used to compare the denoising effects on the same noise signal with wavelet threshold denoising, EMD-wavelet threshold denoising, EEMD-wavelet threshold denoising and improved wavelet threshold denoising. The denoising effects of the original signal and the denoised signal are also compared. Figure 6 As shown. Figure 6 Comparison shows that the noise reduction signal obtained by the method of the present invention is basically consistent with the original signal, although there are still slight deviations in some peak positions. In contrast, the signals processed by wavelet threshold denoising, EMD combined with wavelet threshold denoising and EEMD combined with wavelet threshold denoising methods have a significant deviation from the original signal without noise, and do not achieve the expected noise reduction effect. Further comparison shows that although the improved wavelet threshold denoising and VMD combined with wavelet threshold denoising can better preserve the original signal characteristics, the HBA-VMD-improved wavelet threshold denoising method proposed in the present invention improves the smoothness of the waveform while maintaining signal consistency, thereby better fitting the target signal and having a significant advantage in noise reduction.

[0053] In order to further evaluate the noise reduction effect, the signal-to-noise ratio (SNR) and root mean square error (RMSE) are used to evaluate the final noise reduction effect. The results are shown in Table 3.

[0054] Table 3 Comparison of noise reduction effects of different algorithms

[0055] It can be seen from Table 3 that the HBA-VMD combined improved wavelet threshold algorithm can obtain higher SNR and lower RMSE, and the denoising effect is optimal.

[0056] Further, the monitoring data collected by the micro-electro-mechanical system for monitoring the deep deformation of a landslide is analyzed. The data collected by each monitoring point is transmitted to the monitoring station in real time through a wireless transmission module, and the sampling frequency is 2000 Hz. Monitoring point 1 is taken as an example for analysis. Figure 7 The waveform before processing is shown, and Figure 7 It can be observed that a large amount of noise components are mixed in the original measured signal.

[0057] Consistent with the simulation and processing flow: First, the K optimization range is set as [2, 30], and the alpha optimization range is set as [100, 3000]. The optimal parameter combination of VMD is found by using the HBA algorithm, and the fitness value convergence curve is as shown in Figure 8 It can be seen from Figure 8 that when the iteration number is the 4th time, the fitness value reaches the minimum, and the optimal parameter combination [11, 2812] is obtained; 11 order modal components are obtained after VMD decomposition, Fig. 9 (a) is an IMF component time domain graph, and Fig. 9 (b) is an IMF component frequency spectrum. It can be seen from the time-frequency domain graph obtained by VMD decomposition that each frequency band is almost not overlapped, and each frequency band width is approximately the same.

[0058] The modal variance contribution rate is calculated, the IMFs below the variance contribution rate are discarded by setting a threshold, the relevant coefficients of the remaining IMFs are calculated, the noisy components are processed by using the improved wavelet threshold, and the denoised signal is reconstructed by the processed components and the effective components, as shown in Figure 10 It can be clearly observed from Figure 10 that the method proposed in the application can efficiently strip the deformation monitoring signal of the deep part of the landslide from the noisy signal, the waveform is clearer than before denoising, and the noise interference is greatly reduced; the signal after denoising is basically consistent with the original signal in overall characteristics, peak value and the like, the basic characteristics of the target signal are successfully retained, and excellent denoising effect is achieved.

[0059] Due to the influence of instrument error, environmental factors, signal attenuation in the data transmission process and other factors, it is extremely difficult to obtain a signal completely free of noise. Therefore, it is difficult to accurately reflect the denoising effect by using only two evaluation indexes of signal-to-noise ratio (SNR) and root mean square error (RMSE).

[0060] In order to more comprehensively evaluate the noise reduction quality, the following three kinds of supplementary evaluation indexes are introduced: smoothness index (RVR), signal energy ratio (SER) and noise module (NM). The wavelet threshold, EMD+wavelet threshold, EEMD+wavelet threshold, improved wavelet threshold, VMD+wavelet threshold noise reduction algorithm and the method are used for noise reduction processing, and the noise reduction effect of each method is shown in Table 4. As shown in Table 4, the SNR of the signal after noise reduction is the highest, the RMSE and RVR are the smallest, the noise reduction signal is smoother, the energy ratio is more than 99%, the noise reduction effect is the best under the premise of retaining the details of the measured signal as much as possible, and the feasibility and effectiveness of HBA optimized VMD combined with improved wavelet noise reduction in actual noise reduction application are proved.

[0061] Table 4 Comparison of noise reduction effects of different algorithms for measured signals

[0062] The method can effectively realize adaptive noise reduction of landslide deep deformation monitoring data, the noise filtering effect is more significant, the precision and reliability of landslide deep deformation monitoring data are effectively improved, and good application prospect is shown.

Claims

1. A method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold, characterized by The following steps are involved: Step 1: Collect the original signal of deep deformation of landslide; Step 2: Using sample entropy as the fitness function, the Honey Badger Optimization Algorithm (HBA) is used to optimize the VMD decomposition parameters to obtain the best combination of parameters, namely the decomposition mode number K and the penalty factor α; Step 3: Substitute the optimal combination parameters obtained in step 2 into VMD, perform VMD decomposition on the original signal of deep deformation of the landslide, and obtain K intrinsic mode components (IMFs) of different frequencies; Step 4: Calculate the variance contribution rate and correlation coefficient corresponding to each IMF component, and divide the IMF component into effective component, noisy component, and noise component; Step 5: retain the effective components obtained in step 4 and discard the noise components, and perform noise reduction on the noisy components using the improved wavelet soft threshold; Step 6: Reconstruct the denoised IMF components and the effective IMF components to achieve signal denoising.

2. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 1 is characterized by: In step 2, variational mode decomposition converts signal decomposition into a problem of constructing and solving variations, and realizes adaptive decomposition of the signal by searching for the optimal solution of the constrained variational model. In the iterative process, the signal bandwidth can be decomposed according to the frequency domain characteristics after the signal decomposition, and multiple intrinsic mode components (IMFs) are obtained. Each intrinsic mode component (IMF) has a corresponding center frequency and a finite bandwidth. Each intrinsic mode component (IMF) is an amplitude-frequency modulation signal, which is expressed as: （1）； In formula (1): is the kth modal component function; is the instantaneous amplitude of IMF; is the phase function of the IMF.

3. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 2 is characterized by: The step 2 comprises the following steps: S2.1: Original signal Decomposed into k modal components, namely: , represents the kth modal component function; K represents the total number of decomposed modes; a variational model is constructed to find the optimal modal function so that the sum of the estimated bandwidths of all modal functions is minimized; S2.2: To solve the constrained variational problem, we introduce the penalty factor α and the Lagrangian multiplier λ to form the extended Lagrangian expression as follows: （4）； In formula (4): To form the extended Lagrangian expression; is the Lagrange multiplier; is the Lagrangian function; is the square of the 2-norm of the gradient; To find the inner product; S2.3: Iterative update using alternating direction multiplier method 、 and , seek the saddle point of the extended Lagrangian expression as the optimal solution of the above constrained variational problem (4); （5）； In formula (5): α is the penalty factor; n is the number of times; is the noise tolerance; 、 、 、 、 、 They are 、 、 、 、 、 Fourier transform of i Number the mode; w is the signal frequency; is the modal component function of the n+1th iteration; and denote the Lagrangian functions of the n+1th and nth iterations respectively; S2.4: In order to obtain an accurate VMD parameter combination, the honey badger optimization algorithm is introduced to optimize these two parameters. The honey badger optimization algorithm optimizes by simulating the foraging behavior of honey badgers in the digging and honey-gathering modes in nature. In the digging stage, honey badgers rely on their sense of smell to locate prey and choose the best location for digging and hunting. In the honey-gathering stage, honey badgers use the guidance of honey birds to directly locate the hive.

4. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 3 is characterized by: In S2.1, the variational model is constructed as follows: a: For each modal component function , perform Hilbert transform on the IMF component to obtain the unilateral spectrum, the formula is as follows: （2）； In formula (2), is the one-sided spectrum obtained by Hilbert transform; is the impact function; j is the imaginary unit; t is the time; b: Estimated center frequency Multiplying with formula (2) modulates the spectrum to the baseband that matches it, and then calculates the square norm of the demodulated signal gradient and estimates the bandwidth of each IMF. The formula is as follows: （3）； In formula (3): is the central frequency set of IMF; is the center frequency of the kth IMF; is the set of IMF components; is a constraint condition; is the partial derivative with respect to time; k=1,2,3,…,K.

5. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 3 is characterized by: In S2.3, the specific iterative update solution process is as follows: Step 1, Initialization , let n=1; k=1; Step 2: Set n=n+1, and the VMD algorithm enters a continuous loop; Step 3: Let k = 1 and update according to formula (5) and , and it loops from 1 to K; Step 4: When k=K, the loop stops and λ is updated; Step 5. Given the convergence conditions: ; In the above formula: ε is the convergence accuracy and ε > 0; When the convergence condition is met, the iteration stops and K IMFs are output, otherwise the n=n+1 cycle continues.

6. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 3 is characterized by: S2.4 specifically includes: Initialize the population size N of honey badgers and the location of individuals: （6）； In formula (6): For the i The location of the honey badger; are the locations of each honey badger; is a random number in [0,1]; and are the lower and upper bounds of the search domain respectively; Honey badgers move by tracking the intensity of their prey's scent. As the intensity of the prey's scent increases and the distance to the honey badger decreases, the honey badger is able to locate the prey more accurately. The specific formula is as follows: （7）； In formula (7): for the intensity of the prey's scent; is the source intensity of the odor; is a random number in [0,1]; is the distance between the prey and the i-th honey badger; The best position for prey so far; and Respectively represent the positions of the i-th and i+1-th honey badger; The density factor θ adjusts the randomness over time. The density factor θ decreases as the number of iterations increases to reduce randomization. The update formula is as follows: （8）； In formula (8): C is a constant and ; t is the current iteration number; is the maximum number of iterations; During the digging phase, the honey badger's ability to locate prey is highly dependent on odor intensity. , the distance between the prey and the and the density factor θ; （9）； In formula (9): A new location for the honey badger; is the global optimal position of the honey badger; F is the flag for changing the search direction; is the odor intensity; The honey badger's ability to hunt, ; 、 、 is a random number in [0, 1]; In the honey-gathering stage, the process of the honey badger following the honey bird to the hive can be simulated by the following formula: （10）； In formula (10): A new location for the honey badger; is the global optimal position of the honey badger; θ is the density factor; A flag to change the search direction; is a random number in [0, 1]; When using the Honey Badger optimization algorithm to find the best solution, the fitness function is the sample entropy, and its calculation formula is for: （11）； In formula (11): is the dimension; is similarity tolerance; It is expressed as the probability that two sets of sequences can match m points under the tolerance; It is expressed as the probability that two sets of sequences can match m+1 points under the tolerance.

7. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 1, characterized in that: In step 3, the VMD parameters are adaptively optimized using HBA in step 2, and the obtained optimal combination parameters [K, α] are substituted into VMD, and the initial signal containing noise is decomposed by VMD to obtain K IMF components with frequencies from high to low.

8. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 1 is characterized by: In step 4: the variance contribution rate of each IMF is calculated to preliminarily filter out components with small contribution rates, and after setting a threshold to filter out IMF components with low variance contribution rates, the remaining IMF components can retain the characteristics of the original signal with minimal signal loss; The correlation coefficient indicates the closeness between two signals. The larger the value, the higher the closeness, and the lower the noise content in the corresponding IMF component. By setting the discrimination criteria, the remaining IMF components are further subdivided into effective components, noisy components, and noise components. Variance contribution rate of the kth IMF and correlation coefficient The calculation formula is as follows: （12）； （13）； In the above formula: are the modal components obtained by decomposition; is the original signal; 、 respectively 、 mean, T is the signal length.

9. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 8, characterized in that: In step 4: the threshold and discrimination criteria are set as follows: The threshold is set to 0.1, IMF filtering; like , then it is considered to be effective; like , it is considered to contain noise components; like ; it is considered as the noise component.

10. The method for denoising landslide deep deformation monitoring data based on HBA-VMD combined with improved wavelet threshold according to claim 9, characterized in that: In step 5, improving the wavelet soft threshold specifically includes: S5.1: Apply the improved wavelet soft thresholding method to denoise the noisy mode; （14）； In formula (14): is the threshold, is the original wavelet coefficient, is the quantized wavelet coefficient, is a symbolic function; The threshold is taken as , where D is the variance and N is the number of high-frequency coefficients corresponding to the number of decomposition layers; S5.2: Use the maximum signal-to-noise ratio principle to determine the optimal wavelet basis function and number of decomposition levels.

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