Landslide deep deformation monitoring data noise reduction method based on IHBA-VMD-IWT

Abstract

The invention discloses a landslide deep deformation monitoring data noise reduction method based on IHBA-VMD-IWT. The method comprises the following steps: acquiring a landslide deep deformation original signal; a sample entropy is used as a fitness function, an improved badger algorithm is adopted to optimize VMD decomposition parameters, and optimal combination parameters, namely a decomposition modal number K and a penalty factor alpha, are obtained; substituting the obtained optimal combination parameter into the VMD, and performing VMD decomposition on the landslide deep deformation 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; the obtained effective components are reserved, noise components are abandoned, and noise reduction processing is carried out on the noisy components by using an improved wavelet soft threshold function; and reconstructing the IMF component after noise reduction and the effective IMF component, and finally realizing signal noise reduction. The method significantly improves the precision and reliability of landslide deep deformation monitoring data, and shows a good application prospect.

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 IHBA-VMD-IWT. BACKGROUND

[0002] Landslide deformation monitoring is a core technical means for landslide disaster early warning and risk prevention and control. 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.) to obtain landslide deep deformation data by being embedded in the slope body. However, due to the complex internal structure of the landslide body and 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 landslide deep deformation monitoring signal has non-stationarity and randomness. The commonly used methods for processing landslide deep deformation signals mainly include Fourier transform, Kalman filtering, wavelet transform, empirical mode decomposition (EMD), and variational mode decomposition (VMD). Since Fourier transform lacks time domain positioning function, it can only give the overall effect of the signal, resulting in poor spectral analysis effect of non-stationary signals; Kalman filtering 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 sudden part of signal noise. 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 a modal aliasing problem, and the reconstructed signal will mix a lot of noise. Variational mode decomposition (VMD) is a new time-frequency analysis method proposed in recent years, which can effectively process non-linear and non-stationary signals by decomposing multi-component signals into multiple single amplitude modulation (AM) and frequency modulation (FM) signals at one time. With the unique Wiener filtering characteristics, VMD can effectively compensate for the modal aliasing and boundary effect problems in EMD decomposition.

[0004] However, the current method only uses wavelet threshold denoising or variational mode decomposition single method for landslide deep deformation monitoring signal denoising, and lacks fusion technology of multiple methods. At the same time, the variational mode decomposition method and the traditional wavelet threshold denoising cannot eliminate the influence of artificial experience setting parameters. The specific performance is as follows: (1) The variational mode decomposition needs to manually input two key parameters, i.e., the decomposition mode number K and the penalty factor α, which are both set according to experience. However, due to the lack of prior information and understanding of the original signal, it is difficult to correctly select K and α to ensure the accuracy of signal decomposition. If K is set too small, the signal decomposition will be insufficient, 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 is, and the more noise it contains; and if α is too large, the effective components will be removed incorrectly, which seriously limits the application of the variational mode decomposition method in practical engineering.

[0005] (2) The relationship between the frequency components and the wavelet basis function can be characterized by the approximation coefficients (low-frequency coefficients) and the detail coefficients (high-frequency coefficients) after wavelet decomposition. Noise usually exists in high-frequency components. Wavelet threshold denoising is to remove signal noise by using a threshold function to zero or reduce the detail coefficients while retaining part of the approximation coefficients. However, wavelet threshold denoising is affected by key parameters such as wavelet basis function, decomposition level and threshold function. If not properly selected, users usually select the above parameters based on experience, which may lead to the incorrect removal of useful information in noisy signals, greatly limiting its application range. SUMMARY

[0006] To solve the above technical problems, the present application provides a landslide deep deformation monitoring data denoising method based on IHBA-VMD-IWT. First, Tent chaotic mapping, WOA spiral search mechanism and Levy flight strategy are introduced into the traditional honey bee algorithm (HBA) to avoid the problems of uneven initialization population and premature convergence of the original honey bee algorithm (HBA). The improved honey bee algorithm (HBA) is used to optimize the two key parameters K and α of VMD decomposition to obtain the optimal parameter combination; the wavelet threshold function algorithm is improved, and the high-precision modulus fourth power processing method is set to overcome the defect of constant deviation of the traditional threshold function. Based on the signal-to-noise ratio, the optimal number of wavelet decomposition and the wavelet basis function are determined by adaptively comparing various wavelet basis functions and decomposition levels, and the improved wavelet threshold algorithm is used for denoising processing of the noisy component; finally, the denoised component and the effective component are reconstructed into a denoised signal. This method significantly improves the accuracy and reliability of landslide deep deformation monitoring data and has good application prospects.

[0007] The technical scheme adopted by the present application is: The landslide deep deformation monitoring data denoising method based on IHBA-VMD-IWT comprises the following steps: Step 1: Collecting the original signal of landslide deep deformation; Step 2: Using the improved honey bee algorithm to optimize the VMD decomposition parameters based on the sample entropy as the fitness function to obtain the best combination of parameters, i.e., the decomposition mode number K and the penalty factor α; Step 3: The optimal combination parameters obtained in step 2 are substituted into VMD to perform VMD decomposition on the original signal of deep deformation of the landslide, so as to obtain K intrinsic modal components (IMFs) of different frequencies; Step 4: The variance contribution rate and correlation coefficient corresponding to each obtained IMF component are calculated, and the IMF components are divided into effective components, noise-containing components and noise components; Step 5: The effective components obtained in step 4 are retained, the noise components are discarded, and the noise-containing components are denoised by using the improved wavelet soft threshold function; Step 6: The denoised IMF components and the effective IMF components are reconstructed, and finally signal denoising is realized.

[0008] 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 transform the signal decomposition into a problem of constructing and solving a variation, and to realize the adaptive decomposition of the signal by searching for the optimal solution of the constraint variation model. In the iteration process, according to the frequency domain characteristics of the signal after decomposition, the signal bandwidth can be decomposed, and a plurality of intrinsic modal components (IMFs) can be obtained. Each intrinsic modal component (IMF) has a corresponding center frequency and a limited bandwidth. Essentially, each intrinsic modal component (IMF) is an amplitude-modulated-frequency-modulated 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; Step 2 includes the following steps: S2.1: Any complex original signal can be decomposed into k modal components, that is, , denotes the kth modal component function; K denotes 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 single side spectrum, and the formula is as follows: (2); In formula (2), is the single side spectrum obtained by Hilbert transform; is the impulse function; j is the imaginary unit; t is time; b: The pre-estimated center frequency Multiplying with equation (2), the spectrum is modulated to the base band matched with it. Then, the square norm of the gradient of the demodulation signal is calculated and the bandwidth of each IMF is estimated, as follows: (3); In equation (3): is the set of center frequencies of IMFs; is the center frequency of the kth IMF; is the set of IMF components; is the kth IMF component; 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 a and a Lagrange multiplier l are introduced to form an extended Lagrange expression as follows: (4); In equation (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 , seeking the saddle point of the extended Lagrange expression as the optimal solution of the above equation (4) constrained variational problem; (5); In equation (5): a is the penalty factor; n is the number of times; is the noise tolerance; , , , , , are the Fourier transforms of , , , , , , respectively; i is the mode number; w is the signal frequency; is the modal component function of the n+1th iteration; and denote the Lagrange functions of the n+1th and nth iterations, respectively.

[0009] The specific iterative updating solution process is as follows: Step 1, initialization Let n=1; k=1; Step 2, let n=n+1, and the VMD algorithm enters a loop; Step 3, let k=1, update according to formula (5) And And loop from 1 to K; Step 4, when k=K, the loop stops, and lambda is updated; Step 5, the convergence condition is given:

[0010] In the above formula: epsilon is the convergence accuracy and epsilon>0.

[0011] When the convergence condition is met, the iteration is stopped, and K IMFs are output, otherwise continue n=n+1 loop.

[0012] S2.4: When the signal is decomposed by VMD, it is difficult to correctly select K and alpha to ensure the accuracy of 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.

[0013] The further improvement of the present application is that the improved honey badger optimization algorithm in S2.4 includes initialization, excavation and honey harvesting three stages: on the basis of traditional HBA algorithm, Tent chaotic mapping is introduced to make the initial population distribution more uniform, in the excavation stage, the spiral search mechanism of WOA is fused to expand the search range of the algorithm near the optimal solution, and in the honey harvesting stage, levy flight strategy is introduced to avoid the algorithm falling into local optimal solution.

[0014] Specifically, the following steps are included: S2.4.1: chaotic mapping initialization: The traditional HBA algorithm initializes the honey badger population by random distribution, which leads to uneven distribution in space and affects the search speed and optimization performance of the algorithm. In order to improve this problem, Tent chaotic mapping is introduced to replace random components, so that the initial population is more uniformly distributed in the range of the objective function, reducing the risk of missing the global optimal solution due to random generation of initial individuals, thereby improving the optimization accuracy and search efficiency of the algorithm. The formula of Tent chaotic mapping is: (6); In formula (6): And The i-th and n+1-th chaotic values are respectively.

[0015] According to the Tent chaotic map, the meerkat population position is initialized as: (7); In formula (7), xi represents the position of the i-th meerkat, and E is the dimension; and are the lower limit and the upper limit of the search domain, respectively.

[0016] S2.4.2: Spiral search mechanism of WOA fusion: The spiral search mechanism simulates the spiral movement behavior of whale predation, which can expand the search range and improve the global exploration performance. In the excavation stage, the meerkat movement range is similar to a heart shape, and a spiral search strategy is added to the excavation process to improve the algorithm. The meerkat position is updated twice. The spiral search mechanism formula and position update formula are as follows: (8); In formula (8), xi represents the updated position; is an arbitrary value in the interval [-1, 1]; b is a spiral shape parameter, and the value of the present application is 1; is the current individual position vector; is the current best position vector; D represents the distance vector of the individual to the global best individual.

[0017] (9); In formula (9), xi represents the new position of the meerkat; is the global optimal position of the current prey; β is the ability of the meerkat to prey, and is generally set to 6 by default; I is the odor intensity; is a flag for changing the search direction; F is the distance between the meerkat and the prey; θ is the density factor; , , , is a random number in [0, 1]; F is a flag for changing the search direction. S2.4.3: Introduction of Levy flight strategy: In order to prevent the meerkat optimization algorithm from falling into a local optimal solution in the late iteration stage of the honey collecting stage, the Levy flight strategy is introduced, which effectively avoids local optimal stagnation by expanding the optimization range. The expression of the Levy flight strategy is: (10); In formula (10), β is a random number in [0, 2], and is taken as 1.5; L is the Levy flight function; Г is the gamma function; .

[0018] ​​The position updating formula of the honey collecting stage after introducing the Levy flight strategy is as follows: (11); In formula (11), is the new position of the honey badger; is the global optimal position of the prey; is the Levy flight function; is a random number in [0, 1]; is the distance between the honey badger and the prey; θ is a density factor; and F is a flag for changing the search direction. When the honey badger optimization algorithm is used for optimization, the fitness function is the sample entropy, and the calculation formula thereof is is as follows: (12); In formula (12), is the 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 the sequence standard deviation; represents the probability that two groups of sequences can match m points under the tolerance; represents the probability that two groups of sequences can match m+1 points under the tolerance.

[0019] In the step 3, the optimal combination parameters [K, α] obtained by using the IHBA 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.

[0020] In the step 4, the variance contribution rate of each IMF is calculated to preliminarily screen and 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 under the condition of minimum signal loss; The correlation coefficient represents the closeness between two signals, and 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; The variance contribution rate of the kth IMF is and the correlation coefficient is The calculation formula is as follows: (13); (14); In the above formula, is each modal component obtained by decomposition; is the original signal; , are respectively 、 Mean; T is the length of the signal; 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 as an effective component; If , it is considered as a noisy component; If , it is considered as a noise component.

[0021] In the step 5: The improved wavelet soft threshold value specifically includes: S5.1: In order to overcome the discontinuity of the hard threshold function at , which easily leads to additional oscillation of the reconstructed signal, and the constant deviation problem between the estimated value and the true value of the soft threshold function, the improved soft threshold function method - modulus square processing method is adopted to solve the constant deviation problem of the soft threshold function. A high-precision modulus fourth power processing method is set: (15); In formula (15): is the threshold value, is the original wavelet coefficient, is the quantized wavelet coefficient, is the sign function; The threshold value is , wherein D is the variance, and N is the number of high-frequency coefficients corresponding to the decomposition layer.

[0022] S5.2: The optimal wavelet base function and the decomposition layer number are determined by using the maximum signal-to-noise ratio principle. Specifically as follows: Since the landslide deep deformation monitoring data has discreteness, the wavelet function family excluding the wavelet base function which cannot be discretely transformed is excluded under the support of MATLAB software, and in order to make the reconstructed signal have better smoothing effect and obtain better time-frequency resolution, the wavelet base function of dbN, symN and coifN wavelet system which has regularity and compact support is selected for research, and the decomposition layer number is taken as 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 increasing and then decreasing. The peak value of the signal-to-noise ratio of the signal after denoising with different decomposition layer numbers is taken as the basis to determine the optimal number of wavelet decomposition and the wavelet base function.

[0023] The application provides a landslide deep deformation monitoring data denoising method based on IHBA-VMD-IWT, and the technical effects are as follows: 1) The key parameter selection problem of VMD is introduced into the Tent chaos mapping, WOA spiral search mechanism and Levy flight strategy in the traditional meerkat algorithm to optimize the parameters of the VMD algorithm, improve the optimization ability and convergence speed of the algorithm, and solve the non-optimal problem of selecting VMD parameters by experience; In the optimization process, the sample entropy is used as the fitness function to effectively reduce the computational complexity, quickly find the optimal parameter combination, and improve the running efficiency of the algorithm.

[0024] 2) In the traditional wavelet threshold denoising, the decomposition level and basis function of the wavelet are usually selected based on experience, and the use of fixed decomposition level and wavelet basis function inevitably has limitations. The present application adaptively compares a variety of wavelet basis functions and decomposition levels based on the signal-to-noise ratio as the standard, 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.

[0025] 3) The denoising results of the simulation signal show that the decomposition effect of IHBA-VMD is significantly better than that of EMD and VMD methods when dealing with noisy signals. IHBA-VMD effectively suppresses the modal aliasing phenomenon and significantly improves the accuracy of signal decomposition; Compared with the traditional denoising method, the denoising effect of the present application is superior in terms of intuitive denoising effect and quantitative denoising performance indicators. The present application can retain the original data characteristics while efficiently denoising, ensuring the authenticity and reliability of the signal.

[0026] 4) The signal quality after denoising is further evaluated by combining the smoothness index (RVR), signal energy ratio (SER) and noise mode (NM) three evaluation indexes. The results show that this method greatly improves the smoothness, signal energy ratio and noise mode of the signal compared with other methods, successfully retains the rich deep dynamic characteristic information of the landslide, and can provide reference for future research and application in related fields. BRIEF DESCRIPTION OF DRAWINGS

[0027] The present application will be further described below in conjunction with the drawings and examples: Figure 1 It is the overall flow chart of the landslide deep deformation monitoring data denoising method described in the present application.

[0028] Figure 2 It is the detailed flow chart of the IHBA-VMD described in the present application.

[0029] Figure 3 (a) is the simulation signal waveform graph (original signal) of the present application; Figure 3 (b) is the simulation signal waveform graph (noisy signal) of the present application.

[0030] Figure 4 (a) is the time domain graph of each IMF component obtained by EMD decomposition of the simulation signal; Figure 4(b) is the frequency domain diagram corresponding to the time domain of each IMF component obtained by EMD decomposition of the simulation signal.

[0031] Figure 5(a) is the time domain diagram of each IMF component obtained by VMD decomposition of the simulation signal; Figure 5(b) is the frequency domain diagram corresponding to the time domain of each IMF component obtained by VMD decomposition of the simulation signal.

[0032] Figure 6 It is a comparison diagram of the fitness value convergence curves of different optimization algorithms of the present invention.

[0033] FIG7( a ) is a time domain diagram of each IMF component obtained by IHBA-VMD decomposition of the simulation signal of the present invention; FIG7( b ) is a frequency domain diagram corresponding to the time domain of each IMF component obtained by decomposing the simulation signal IHBA-VMD according to the present invention.

[0034] Figure 8 (a) is a comparison of the signal-to-noise ratio of different wavelet basis functions and decomposition levels of the present invention Figure 1 ; Figure 8 (b) is a comparison of the signal-to-noise ratio of different wavelet basis functions and decomposition levels of the present invention Figure 2 ; FIG8( c ) is a third comparison diagram of the signal-to-noise ratios of different wavelet basis functions and decomposition levels of the present invention.

[0035] Figure 9 It is a waveform diagram of the simulation signal after noise reduction by different algorithms of the present invention.

[0036] Figure 10 It is the waveform diagram of the measured signal of the present invention.

[0037] Figure 11 It is a fitness value convergence curve diagram of the measured signal of the present invention.

[0038] FIG12( a ) is a time domain diagram of the IMF components obtained by IHBA-VMD decomposition of the measured signal of the present invention; FIG12( b ) is a frequency domain diagram corresponding to the time domain of each IMF component obtained by IHBA-VMD decomposition of the measured signal of the present invention; Figure 13 (a) is the waveform of the measured signal after noise reduction of the present invention Figure 1 ; Figure 13 (b) is the waveform of the measured signal after noise reduction of the present invention Figure 2 ; FIG13( c ) is a third waveform diagram of the measured signal after noise reduction according to the present invention. DETAILED DESCRIPTION

[0039] like Figure 1 As shown in Figure 1, the noise reduction method for landslide deep deformation monitoring data based on IHBA-VMD-IWT includes the following steps: Step one: the monitoring data collected by the landslide deep deformation micro-electromechanical monitoring system are denoised. The data collected by each monitoring point are transmitted to the monitoring station in real time through a wireless transmission module, the sampling frequency is 2000Hz, and the original signal of landslide deep deformation is collected.

[0040] Step two: the sample entropy is used as the fitness function, and the improved meerkat optimization algorithm is used to optimize the VMD decomposition parameters to obtain the best combination parameters [K, a].

[0041] Step three: the best combination parameters obtained in step two are substituted into VMD, and the original signal of landslide deep deformation is decomposed by VMD to obtain K IMF components of different frequencies.

[0042] Step four: the variance contribution rate and correlation coefficient corresponding to each IMF component are calculated, and the IMF components are divided into effective components, noisy components and noise components.

[0043] Step five: the effective components obtained in step four are retained, the noise components are discarded, and the noisy components are denoised by using the improved wavelet soft threshold.

[0044] Step six: the denoised IMF components and the effective IMF components are reconstructed to finally realize signal denoising.

[0045] In order to verify the effectiveness of the present application, the simulation and experiment are further illustrated as follows: The signal-to-noise ratio SNR and the root mean square error RMSE are used as the evaluation indexes of the simulation signal denoising result.

[0046] 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: (16); 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: (17); Since it is extremely difficult to obtain a signal completely free of noise from the 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 as the evaluation indexes. 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.

[0047] 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: (18); The signal energy ratio SER and the noise module NM can reflect the change of signal energy before and after noise reduction. The greater the SER and NM, the more effective signal energy is retained in the noise reduction process. The calculation formula is as follows: (19); (20); In the above evaluation index formula: L is the number of sampling points, is the original signal, is the signal after noise reduction.

[0048] The landslide deep deformation monitoring signal often contains various types of noise, and the frequency distribution range of these noises is wide. 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: (21); In formula (21): is the original signal, which is composed of 3 signal components with frequency components of 5 Hz, 15 Hz and 100 Hz; is a 15 dB Gaussian white noise, the sampling frequency is set to 2000 Hz, the number of sampling points is 1500, and the original signal and noisy signal waveform diagram can be seen in Figure 3(a), Figure 3(b).

[0049] In order to verify the superiority of the IHBA optimized VMD method, the VMD and EMD decomposition of the simulation signal are compared with the IHBA-VMD method. When VMD and EMD are decomposed, the parameters need to be set in advance. The parameters set are as follows: penalty factor α=2200, decomposition layer number K=7, and the decomposition results are shown in Figure 4(a), Figure 4(b) and Figure 5(a), Figure 5(b). As can be seen from Figure 4(a), Figure 4(b), Figure 5(a), Figure 5(b), EMD decomposes the noisy simulation signal into 8 modal components, and VMD decomposes the noisy simulation signal into 7 modal components. Among them, in the EMD decomposition, the modal component contains a larger noise interference signal, and there is a serious modal aliasing problem in the decomposition process: multiple frequency components may exist in the same component, such as the mixing of the original signal frequency and other frequencies in IMF2, which fails to separate the effective frequency. As can be seen from the VMD decomposition, compared with the modal aliasing problem in EMD decomposition, the problem is improved, and similar frequency signals can be separated out. However, in the time domain graph, it can be found that the degree of coincidence between the components after VMD decomposition and the original signal is not ideal, which may have a greater impact on the subsequent signal reconstruction process.

[0050] Initialize the VMD decomposition parameter range and the IHBA algorithm. According to experimental experience, the upper and lower limits of the VMD parameter K are [2, 15], the upper and lower limits of the parameter a are [100, 3000], the population iteration number of the IHBA algorithm is 20, and the population size is 10.

[0051] Taking the sample entropy as the fitness function, the IHBA algorithm is used to optimize the VMD parameters, and at the same time, the particle swarm optimization algorithm (PSO) and the sparrow optimization algorithm (SSA) are used to optimize the VMD under the same conditions. The iteration optimization curve is as shown in Figure 6 The fitness value of IHBA-VMD reaches the minimum after the second iteration. The IHBA optimization VMD curve quickly reaches the minimum fitness value at the beginning of iteration and remains unchanged in the subsequent iterations. Compared with the 7-time iteration of the PSO algorithm, the 4-time iteration of the SSA algorithm and the 4-time iteration of the HBA algorithm, it can be seen that IHBA-VMD performs well in convergence speed, and the fitness function value found is the smallest and is not prone to local optimum phenomenon, fully proving the efficiency and superiority of IHBA-VMD in the optimization process. Compared with other methods, IHBA-VMD not only converges faster, but also can find high-quality solutions in fewer iteration times.

[0052] The optimal VMD parameter combination [K, a] obtained is substituted into VMD to perform VMD decomposition on the simulated signal containing noise to obtain K IMF components. In this example, considering the randomness in the iteration process, 40 repeated experiments are performed to ensure the reliability of the results. Finally, the average value of the parameters is selected as the optimal parameter combination, K=14 and a=2973. As shown in Figs. 7(a) and 7(b), it can be seen from Figs. 7(a) and 7(b) that the waveforms of the components decomposed by IHBA-VMD are regular, the waveforms of the components are independent, there is no obvious repetition, and it can be seen from the frequency domain graph shown in Fig. 7(b) that the multiple frequency components in the simulated signal are well decomposed into different frequency bands, the independence between the components is good, and the decomposition result almost does not exist modal aliasing phenomenon.

[0053] Table 1 Variance contribution rate values of each IMF component

[0054] According to the screening threshold criterion: the threshold value of the present application is set to 0.1, and the calculation results of the variance contribution rate of each IMF component are shown in Table 1. The sum of the variance contribution rates of IMF1-IMF5 remaining is 0.9703, which can be considered that the effective components of the original signal are preserved as much as possible while the noise is filtered out to the maximum extent, and the preliminary noise reduction is completed.

[0055] Table 2 Correlation coefficient values of the remaining IMF components

[0056] 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.

[0057] A fixed threshold and an improved soft threshold function were used to denoise the original noisy signal. The peak signal-to-noise ratio (SNR) of the denoised signal was used as a benchmark to determine the optimal number of wavelet decomposition layers and wavelet basis functions. Figures 8(a) to 8(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 uses the wavelet basis function db7 and the number of decomposition layers to denoise the noisy component.

[0058] In order to verify the effectiveness of the method of the present invention, the present invention uses the IHBA-VMD-IWT denoising method and the wavelet threshold denoising, EMD-wavelet threshold denoising, EEMD-wavelet threshold denoising and improved wavelet threshold denoising to compare the denoising effects on the same noise signal, and compares the denoising effects of the original signal and the denoised signal. Figure 9 As shown. Figure 9 It can be seen 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 have obvious deviations from the original signal without noise, and do not achieve the expected noise reduction effect. Further comparison shows that although improved wavelet threshold denoising, VMD combined with wavelet threshold denoising and HBA-VMD+wavelet threshold denoising can better retain the original signal characteristics, the IHBA-VMD-IWT noise reduction method proposed in the present invention improves the smoothness of the waveform while maintaining signal consistency, so that it can better fit the target signal and has more significant advantages in noise reduction.

[0059] 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.

[0060] Table 3 Comparison of noise reduction effects of different algorithms

[0061] It can be seen from Table 3 that the use of the IHBA-VMD-IWT denoising algorithm can achieve higher SNR and lower RMSE, and the denoising effect is optimal.

[0062] Furthermore, a noise reduction analysis was performed on the monitoring data collected by a micro-electromechanical system for monitoring deep deformation of a landslide. Data collected at each monitoring point was transmitted to the monitoring station in real time via a wireless transmission module, with a sampling frequency of 2000 Hz. A detailed analysis was conducted using monitoring point 1 as an example. To mitigate potential contingencies in the experimental results and confirm the accuracy of the aforementioned analysis, additional experimental data sets were added for verification. Figure 10 Shows the waveform before processing, from Figure 10 It can be observed that the original measured signal is mixed with a lot of noise components.

[0063] Consistent with the simulation process: First, the IHBA algorithm is used to find the optimal parameter combination of VMD, and the sample entropy is used as the fitness function. The obtained fitness value convergence curve is as follows: Figure 11 As shown. Figure 11 It can be seen that after the second iteration, the fitness value reaches its minimum, resulting in the optimal parameter combination [12, 2974]. After VMD decomposition, 12 modal components are obtained. Figure 12(a) shows the time domain plot of the IMF components, and Figure 12(b) shows the spectrum of the IMF components. The time-frequency domain plots obtained by VMD decomposition show that the frequency bands have almost no overlap and the widths of each band are roughly the same.

[0064] The variance contribution rate of each mode is then calculated, and a threshold is set to discard IMFs with a lower variance contribution rate. The correlation coefficient of the retained IMFs is calculated, and the noisy components are processed using the improved wavelet threshold. The processed components and the effective components are reconstructed to obtain the de-noised signals shown in Figures 13(a) to 13(c). As can be clearly seen from Figures 13(a) to 13(c), the proposed method can effectively extract the deformation monitoring signal deep within the landslide from the noisy signal. The waveform is clearer than before denoising, greatly reducing the interference of noise. The de-noised signal is basically consistent with the original signal in terms of overall characteristics and peak values, successfully retaining the basic characteristics of the target signal.

[0065] Because actual deep deformation monitoring signals from landslides are affected by instrument errors, environmental interference, and signal attenuation during data transmission, obtaining a completely noise-free signal is extremely difficult. Therefore, using only the signal-to-noise ratio (SNR) and root mean square error (RMSE) as evaluation metrics cannot accurately reflect the noise reduction effect.

[0066] To more comprehensively evaluate the noise reduction quality, the following three 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, HBA-VMD+wavelet threshold and the method of the application are used for noise reduction processing, and the noise reduction effects of each method are shown in Tables 4-6. As can be seen from Tables 4-6, the SNR of the signal after noise reduction by the method of the application 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 IHBA-VMD-IWT in actual noise reduction application are proved.

[0067] Table 4 Comparison of noise reduction effects of different algorithms for measured signals at monitoring point 1

[0068] Table 5 Comparison of noise reduction effects of different algorithms for measured signals at monitoring point 2

[0069] Table 6 Comparison of noise reduction effects of different algorithms for measured signals at monitoring point 3

[0070] In summary, the present application provides a new method for landslide deep deformation monitoring data noise reduction of IHBA-VMD-IWT: first, on the basis of traditional HBA algorithm, Tent chaos mapping, WOA spiral search mechanism and Levy flight strategy are introduced, which can improve the search ability and convergence speed of HBA algorithm, and can avoid the algorithm falling into local optimal solution, and sample entropy is selected as the fitness function in the parameter selection process of IHBA, and the optimal combination [K, alpha] of VMD parameters is obtained by IHBA. Then, the noisy signal is decomposed by VMD to obtain a series of IMF, and the variance contribution rate of each IMF is calculated, and the components with small variance contribution rate are filtered. After that, the remaining IMF components are further subdivided into effective components, noisy components and invalid components according to the size of correlation coefficient. Finally, the noisy components are denoised by improved wavelet threshold, and the threshold function is optimized in the improved wavelet threshold denoising, a high-precision modulus four power processing method is set, and the optimal wavelet basis and decomposition level combination are determined by the signal-to-noise ratio. In addition, the target signal is analyzed, and the signal-to-noise ratio is used as the standard to adaptively compare various wavelet basis functions and decomposition levels, which greatly shortens the time of wavelet parameter optimization and improves the overall processing efficiency under the condition that the wavelet threshold denoising effect reaches the best. The denoised components and effective components are reconstructed to obtain the final denoised signal. The denoising method proposed in the present application realizes the efficient filtering of random noise, effectively preserves the original signal feature information, has higher signal-to-noise ratio and lower root mean square error, effectively improves the precision and reliability of landslide deep deformation monitoring data, and provides strong support for landslide disaster warning.

Claims

1. Based on the IHBA-VMD-IWT-based landslide deep deformation monitoring data denoising method, it is 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 improved honey badger algorithm is used to optimize the VMD decomposition parameters to obtain the optimal combination 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 component obtained in step 4 and discard the noise component, and perform noise reduction on the noisy component using the improved wavelet soft threshold function; 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 IHBA-VMD-IWT 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, according to the frequency domain characteristics of the signal after decomposition, the signal bandwidth can be decomposed and multiple intrinsic mode components (IMFs) are obtained. 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 IHBA-VMD-IWT according to claim 1, characterized in that: The step 2 comprises the following steps: S2.1: Original signal can be 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 to the constrained variational problem of equation (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 is the mode number; 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: The improved honey badger optimization algorithm includes three stages: initialization, mining and honey collection. Based on the traditional HBA algorithm, the Tent chaos map is introduced to make the initial population distribution more uniform. The WOA spiral search mechanism is integrated in the mining stage to expand the search range of the algorithm near the optimal solution. The levy flight strategy is introduced in the honey collection stage to prevent the algorithm from falling into the local optimal solution.

4. The method for denoising landslide deep deformation monitoring data based on IHBA-VMD-IWT 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. Then, calculate the square norm of the demodulated signal gradient and estimate 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 the kth IMF component; 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 IHBA-VMD-IWT according to claim 3 is characterized by: In S2.1, 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 IHBA-VMD-IWT according to claim 3 is characterized by: Said S2.4 specifically includes: S2.4.1: Chaotic map initialization: The Tent chaos mapping formula is: （6）； In formula (6): and The first and second are the chaotic values ​​of the i-th and n+1-th times respectively; According to the Tent chaos map, the initial position of the honey badger population is: （7）； In formula (7): It is represented as the position of the i-th honey badger, and E is the dimension; and are the lower and upper bounds of the search domain respectively; S2.4.2: Spiral search mechanism integrated with WOA: During the excavation phase, the honey badger's movement range is similar to a heart shape. A spiral search strategy is added to the excavation process to improve the algorithm and perform a secondary update of the honey badger's position. The spiral search mechanism formula and position update formula are as follows: （8）； In formula (8): is the updated position; is any value in the interval [-1, 1]; b is the spiral shape parameter; is the current individual position vector; is the current best position vector; D represents the distance vector from the individual to the global best individual; （9）； In formula (9): A new location for the honey badger; is the global optimal position of the current prey; β is the predation ability of the honey badger; I is the odor intensity; F A flag to change the search direction; is the distance between the honey badger and the prey; θ is the density factor; 、 、 is a random number in [0, 1]; F is a flag for changing the search direction; S2.4.3: Introducing Levy flight strategy: The Levy flight strategy is introduced to effectively avoid local optimal stagnation by expanding the optimization range; the expression of the Levy flight strategy is: （10）； In formula (10), β is a random number in [0, 2]; L is the Levy flight function; Г is the gamma function; ; The position update formula in the honey collection phase after the Levy flight strategy is introduced is as follows: （11）； In formula (11): A new location for the honey badger; is the current global optimal position of the prey; is the Levy flight function; is a random number in [0, 1]; is the distance between the honey badger and the prey; θ is the density factor; F is the flag for changing the search direction; 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: （12）； In formula (12): 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 IHBA-VMD-IWT according to claim 1, characterized in that: In step 3, the VMD parameters are adaptively optimized using IHBA 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 IHBA-VMD-IWT according to claim 1, characterized in that: 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: （13）； （14）； In the above formula: are the modal components obtained by decomposition; is the original signal; 、 They are 、 mean; T is the signal length.

9. The method for denoising landslide deep deformation monitoring data based on IHBA-VMD-IWT 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 IHBA-VMD-IWT according to claim 8, characterized in that: In step 5, improving the wavelet soft threshold specifically includes: Set up a high-precision modular fourth power processing method: （15）； In formula (15): is the threshold, is the original wavelet coefficient, is the quantized wavelet coefficient, is the sign function; the threshold is , where D is the variance and N is the number of high-frequency coefficients corresponding to the number of decomposition layers; The optimal wavelet basis function and the number of decomposition layers are determined by using the maximum signal-to-noise ratio principle.

Images