UwDAS signal adaptive framing and denoising method based on TVF-EMD and GWO

Abstract

The invention discloses a UwDAS signal adaptive framing denoising method based on TVF-EMD and GWO, and the method comprises the steps: setting a signal detected by a UwDAS as y (n), selecting a Hanning window to carry out the framing of the y (n), obtaining y (t, l), selecting permutation entropy as a fitness function, carrying out the optimization of TVF-EMD decomposition parameters of the y (t, l) through employing a gray wolf optimization algorithm GWO, and obtaining an optimal bandwidth threshold Tbest and an optimal B-spline fitting order Bbest; selecting an optimal bandwidth threshold Tbest and an optimal B spline fitting order Bbest to carry out TVF-EMD decomposition on the y (t, l) to obtain K IMFs; according to the permutation entropy PeEn (k) of each IMF, effective IMF reconstruction is selected according to the permutation entropy threshold th, and a denoised signal x (t, l) of the current frame is obtained; and recovering the denoised complete signal x (n) according to the Hanning window function. The method not only considers the time-varying characteristic of the non-stationary signal, but also considers the balance of noise removal and signal retention, can perform high-performance denoising, and improves the signal quality.

Description

Technical Field

[0001] The present invention relates to the technical field of uwDAS signal processing, and in particular to a uwDAS signal adaptive framing denoising method based on TVF-EMD and GWO. Background Art

[0002] Distributed acoustic sensing (DAS) systems (uwDAS) based on ultra-weak fiber Bragg gratings (uwFBGs) offer significant advantages in sensitivity, immunity to electromagnetic interference, and long-distance continuous monitoring, and have been widely used in industrial equipment monitoring, rail transit, security warning, and other fields. However, due to the ultra-high sensitivity of uwDAS, it is easily affected by various non-target signals such as environmental noise and mechanical vibration in practical applications, resulting in complex noise being mixed into the collected signals, which in turn affects the accuracy of subsequent processing such as state recognition and fault warning. Therefore, how to effectively denoise uwDAS signals has become a key issue in improving system performance and broadening its application areas.

[0003] In recent years, a variety of methods have been proposed for signal denoising, such as those based on wavelet transform, empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and variational mode decomposition (VMD). Wavelet transform-based methods require presetting the wavelet basis and the number of wavelet decomposition layers, making adaptive filtering difficult. EMD is suitable for processing non-stationary signals and does not require presetting basis functions, but suffers from problems such as modal aliasing and endpoint effects, and its decomposition stability is poor. EEMD can effectively alleviate the modal aliasing problem, but the introduction of noise can lead to energy leakage, and it is computationally intensive and slow. VMD has better noise immunity than EMD and EEMD, but requires the number of decomposition modes to be set in advance, is sensitive to parameters, and is limited in its effectiveness when processing complex signals.

[0004] Time-Varying Filter Empirical Mode Decomposition (TVF-EMD) can adaptively decompose non-stationary signals into several narrowband intrinsic mode functions (IMFs), demonstrating excellent denoising capabilities in the presence of non-stationary noise. The selection of the bandwidth threshold and B-spline fitting order has a significant impact on the decomposition effect. The Grey Wolf Optimizer (GWO) algorithm, by simulating the group collaboration and prey search mechanisms of grey wolves, can efficiently search for the optimal bandwidth threshold and B-spline fitting order in a complex parameter space, further improving the accuracy and robustness of signal denoising.

[0005] Defects and shortcomings of existing technology:

[0006] (1) Most existing denoising methods use fixed decomposition parameters for the entire signal, ignoring the significant differences in the statistical and noise characteristics of non-stationary signals over different time periods. Unified parameter decomposition can easily lead to local over-decomposition or under-decomposition, affecting the denoising quality. This is especially true for uwDAS signals with significant time-varying characteristics, where signal details are easily lost or a large amount of noise is not effectively suppressed.

[0007] (2) In existing TVF-EMD-based signal denoising methods, the selection of key parameters such as bandwidth threshold and B-spline fitting order usually relies on manual experience or simple grid search, lacking a unified theoretical basis. This parameter setting cannot be dynamically adjusted to different signal characteristics, making it difficult to achieve a good balance between decomposition completeness and denoising effect, thus limiting the actual effect of TVF-EMD methods in complex application scenarios.

[0008] (3) In the denoising process based on modal decomposition, empirical rules or simple energy thresholds are usually used to screen and reconstruct IMF components, such as directly discarding high-frequency or low-energy components. This component selection method fails to fully consider the mixing of noise and useful signal components in each IMF component, which can easily lead to noise residue or signal information loss, affecting the final denoising effect and signal reconstruction quality. Summary of the Invention

[0009] In order to solve the above technical problems, the present invention proposes a uwDAS signal adaptive frame denoising method based on TVF-EMD and GWO. This method first performs frame processing on the signal collected by uwDAS, selects permutation entropy as the fitness function, and uses GWO to adaptively optimize the TVF-EMD decomposition parameters for each frame signal. By selecting the optimal decomposition parameters for decomposition, the modal aliasing phenomenon of the decomposition can be effectively avoided, providing a good premise for the subsequent IMF component screening and reconstruction. At the same time, permutation entropy is also an information criterion for the selection of effective IMFs. The non-stationarity and noise content of each component are quantitatively evaluated by permutation entropy to achieve accurate removal of mixed noise. After frame-by-frame denoising, windowing and weighting are used to restore the signal to ensure smooth transition between frames and avoid waveform distortion. This method takes into account the time-varying characteristics of non-stationary signals and the balance between noise removal and signal retention. It can perform denoising with high performance and improve signal quality.

[0010] The technical solution adopted by the present invention is:

[0011] The uwDAS signal adaptive framing denoising method based on TVF-EMD and GWO is characterized by comprising the following steps: Step 1: assuming that the signal detected by the uwDAS is y(n), where n is the sampling point index, 1≤n≤N, and N is the total number of sampling points;

[0012] Step 2: Select the Hanning window to frame y(n) and obtain y(t,l), where l is the frame index, 1≤l≤L, L is the total number of frames, and t is the sampling point index in the frame, 1≤t≤L f , where L f is the frame length;

[0013] Step 3: Select permutation entropy as the fitness function and use the Grey Wolf Optimization Algorithm (GWO) to optimize the TVF-EMD decomposition parameters of y(t,l) to obtain the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best.

[0014] Step 4: Select the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best to perform TVF-EMD decomposition on y(t,l) to obtain K IMFs;

[0015] Step 5: According to the permutation entropy value PeEn(k) of each IMF, the permutation entropy threshold th is used to select the valid IMF for reconstruction to obtain the denoised signal x(t,l) of the current frame, where k is the sequence number of the IMF, 1≤k≤K;

[0016] Step 6: Restore the complete denoised signal x(n) according to the Hanning window function.

[0017] In step 2, selecting a Hanning window to frame y(n) specifically includes:

[0018] 2.1: y(n) according to the frame length L f and frame shift N m Frame to obtain the frame signal y1(t,l) before weighting;

[0019] 2.2: Use Hanning window hanning(t) to weight y1(t,l), and the calculation formula is:

[0020] y(t,l)=y1(t,l)·hanning(t);

[0021] in,

[0022] cos(·) is the cosine function.

[0023] In step 3, using GWO to optimize the TVF-EMD decomposition parameters of y(t,l) includes the following steps:

[0024] S3.1: Initialize the gray wolf population size pop, the maximum number of iterations Max_ite, the bandwidth threshold search range [T_min, T_max], and the B-spline fitting order search range [B_min, B_max],

[0025] Among them, T_min is the lower bound of the bandwidth threshold search, T_max is the upper bound of the bandwidth threshold search, B_min is the lower bound of the B-spline fitting order search, and B_max is the upper bound of the B-spline fitting order search;

[0026] Initialize the current iteration number ite=1, and randomly initialize the wolf pack position within the bandwidth threshold and B-spline fitting order search range The parameter to be optimized Q at the current iteration w (ite)={T w (ite),B w (ite)} as the position coordinates of the w-th wolf; where T w (ite) is the bandwidth threshold of the w-th wolf in the ite-th iteration, B w (ite) is the B-spline fitting order of the w-th wolf in the ite-th iteration, 1≤w≤pop; {T w (ite),B w (ite)} represents the bandwidth threshold and B-spline fitting order set corresponding to the w-th wolf in the ite-th iteration.

[0027] Initialize T_best = T w (1), B_best=B w (1), T w (1) represents the bandwidth threshold randomly initialized by the w-th wolf, B w(1) represents the B-spline fitting order of the w-th wolf randomly initialized, and the initial permutation entropy mean PE avg (1) is an infinite value; S3.2: Use the T corresponding to each wolf w (ite), B w (ite) Perform TVF-EMD decomposition on y(t,l), including the following steps:

[0028] S3.2.1: Compute the Hilbert transform of y(t,l) The calculation formula is:

[0029]

[0030] Where: PV represents the Cauchy principal value, It represents the integration of the integral variable τ from -∞ to +∞.

[0031] S3.2.2: Find the analytical signal z(t,l) of y(t,l), which is calculated as:

[0032]

[0033] Where: A(t,l) is the instantaneous amplitude of z(t,l), is the instantaneous phase of z(t,l), j is the imaginary unit, and e is the base of the natural logarithm;

[0034] A(t,l) and The calculation formula is:

[0035]

[0036] Where: arctan(·) is the inverse tangent function.

[0037] S3.2.3: For the set of local maxima and local minima of A(t,l) {A(t max ,l)} and {A(t min ,l)} to interpolate and obtain β1(t,l) and β2(t,l); respectively and Interpolate to obtain η1(t,l) and η2(t,l);

[0038] Where: t max and t min are the sampling point indices of the local maximum and local minimum of A(t,l), and are the instantaneous frequency of the local minimum value of the lth frame and the instantaneous frequency of the local maximum value of the lth frame respectively.

[0039] S3.2.4: Express the analytical signal z(t,l) as the superposition of two components, which is expressed as:

[0040]

[0041] a1(t,l) and a2(t,l) are the instantaneous amplitudes of the two components, and their calculation formulas are:

[0042]

[0043] and is the instantaneous phase of the two components, and their derivatives correspond to the instantaneous frequencies of the two components and The calculation formula is:

[0044]

[0045] Where: η1(t,l) represents the weighted envelope information based on the local minimum value of A(t,l) and the trend of its derivative change, and η2(t,l) represents the weighted envelope information based on the local maximum value of A(t,l) and the trend of its derivative change.

[0046] S3.2.5: Calculate the local cutoff frequency The calculation formula is:

[0047]

[0048] S3.2.6: Calculate Loughlin instantaneous bandwidth B Lou (t,l) and weighted average instantaneous frequency The calculation formula is:

[0049]

[0050] Where: a'1(t,l) is the derivative of the instantaneous amplitude of the first component a1(t,l), and a'2(t,l) is the derivative of the instantaneous amplitude of the second component a2(t,l);

[0051] S3.2.7: Calculate the current signal bandwidth θ(t,l) using the following formula:

[0052]

[0053] S3.2.8: Determine whether the following narrowband signal conditions are met:

[0054] θ(t,l)≤T w (ite);

[0055] If it satisfies, then y(t,l) is an IMF, denoted as IMFk (ite), represents the kth IMF in the ite-th iteration, and performs S3.3, otherwise calculate B of y(t,l) w (ite) order B-spline fitting result m(t,l), the specific steps are:

[0056] Find the B-spline basis function B q (t), which is calculated as follows:

[0057]

[0058] Where: q is the B-spline basis function B q (t) index number, signal The extreme points are the nodes of the B-spline basis function, t q is the node at the qth position of the B-spline basis function, t q+1 is the node at the q+1th position of the B-spline basis function, is the q+Bth B-spline basis function w (ite)-1 node, is the q+Bth B-spline basis function w The node at the (ite) position; t represents the sampling point index of the current frame. B q-1 (t) is the q-1th B-spline basis function.

[0059] Determine the fitting coefficient c q Minimize the overall error:

[0060]

[0061] Where Q = L f +B w (ite), the calculation formula of the fitting result m(t,l) is:

[0062]

[0063] Subtract m(t,l) from y(t,l) and repeat S3.2.1 to S3.2.7.

[0064] S3.3: Calculate IMF k The permutation entropy value of (ite) includes the following steps:

[0065] S3.3.1: Initialize embedding dimension M and time delay T, IMF k (ite) is represented as the following sequence:

[0066]

[0067] Among them: f1, f2, ..., For the IMF k (ite) 1st, 2nd,…, L f The value of the sampling point.

[0068] S3.3.2: By IMF k The sampling point values in (ite) are arbitrarily constructed L f -(M-1)T delayed embedding vector sequences of length M IMF1 k (ite):

[0069] IMF1 k (ite)={f J ,f J+T ,f J+2T ,...,f J+(M-1)T};

[0070] Where: J = 1, 2, ..., L f -(M-1)T;f J ,f J+T ,f J+2T ,...,f J+(M-1)T IMF1 k (ite) The value of the J, J+T, J+2T, …, J+(M-1)T sampling points; T represents the time delay;

[0071] S3.3.3: Calculate IMF k The permutation entropy value PE(k,ite) of (ite) is calculated as follows:

[0072]

[0073] Where: log(·) represents the logarithm operation with base 10; p i1 For each IMF1 k The probability of occurrence of the arrangement pattern of the sample point values in (ite), i1 = 1, 2, ..., M!, where the symbol '!' represents the factorial operation.

[0074] S3.3.4: Calculate the mean PE of PE(k,ite) in the current iteration avg (ite), which is calculated as follows:

[0075]

[0076] Where: K1 is the number of decomposed IMFs, and k is the sequence number of the IMF.

[0077] S3.3.5: Determine whether the mean permutation entropy satisfies the following conditions:

[0078] PE avg (ite) <PE avg(ite-1);

[0079] If satisfied, then T in the current iteration w (ite) and B w (ite) are the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best, respectively. Each decomposed IMF is the optimal decomposition Best_IMF k , the corresponding permutation entropy is the optimal permutation entropy value PeEn(k), and S3.4 is performed; otherwise, T_best, B_best, Best_IMF k and PeEn(k) remain unchanged, and proceed to S3.4.

[0080] S3.4: In the GWO algorithm, wolves are divided into four levels: α, β, δ, and ω according to their permutation entropy values from low to high. The following updates the behavior of wolves surrounding their prey when hunting:

[0081]

[0082] in: denote the distance vectors between the wolf and the prey at the ite-th iteration, α, β, and δ, respectively; is the position vector of wolf ω in the ite-th iteration; Respectively represent the current positions of α, β and δ wolves in the ite-th iteration; They represent the position vectors of ω wolf after being affected by α, β and δ wolves in the ite-th iteration respectively; is a random vector in [0,2]; For regulating parameters and a random vector in [0,1] The joint expression is Three random coefficients are generated.

[0083] S3.5: Update the final position of ω wolf, which is calculated as follows:

[0084]

[0085] S3.6: Update the ranks of α, β, δ, and ω wolves from low to high according to the permutation entropy value. At this time, the position of α wolf is the parameter to be optimized Q w (ite+1)={T w (ite+1),B w (ite+1)}.

[0086] S3.7: Determine whether the following loop conditions are met:

[0087] ite≤Max_ite;

[0088] If satisfied, add 1 to the value of ite and repeat S3.2 to S3.6; otherwise, proceed to step 4.

[0089] In step 4, select T_best and B_best to perform TVF-EMD decomposition on y(t,l) to obtain K IMFs, that is, the optimal decomposition Best_IMF currently determined by S3.3.5 k , and its corresponding permutation entropy is the optimal permutation entropy value PeEn(k).

[0090] In step 5, the effective IMF reconstruction is selected by the permutation entropy threshold th to obtain the denoised signal x(t,l) of the current frame. The reconstruction formula is:

[0091]

[0092] Where: γ is the index of the valid IMF set, k∈γ represents the Best_IMF belonging to the valid IMF set k index.

[0093] The step 6 comprises the following steps:

[0094] S6.1: Calculate the superposition signal x sum (n), which is calculated as follows:

[0095]

[0096] Where: x(nn l ,l) is the sampling point index of the lth frame after denoising, which is nn l signal; n l =l·N m ; is an indicator function whose value is:

[0097]

[0098] S6.2: Calculate the window function weight superposition signal w sum (n), which is calculated as follows:

[0099]

[0100] Among them: hanning1(nn l ) is the Hanning window at sampling point nn l The value of .

[0101] S6.3: Normalize and restore the complete signal x(n) after denoising. The calculation formula is:

[0102]

[0103] The present invention provides a uwDAS signal adaptive framing denoising method based on TVF-EMD and GWO, and the technical effects are as follows:

[0104] 1): Compared with the traditional method of using fixed parameters on the entire signal, the present invention uses a window function to frame the signal and performs independent parameter optimization and decomposition based on the local characteristics of the signal in each frame. This method fully considers the temporal statistical characteristics of the non-stationary signal and can effectively improve the accuracy of denoising and the ability to retain details. At the same time, the splicing method of the window function ensures smooth transitions between frames and avoids energy leakage and waveform distortion introduced by edge effects.

[0105] 2): The present invention adopts the Grey Wolf Optimization algorithm (GWO) to adaptively optimize the bandwidth threshold and B-spline fitting order of the key parameters in TVF-EMD decomposition without relying on human selection, thereby realizing global optimal search and dynamic adjustment of parameters, effectively improving the stability of the TVF-EMD decomposition results, avoiding modal aliasing to the greatest extent, improving the balance between decomposition quality and denoising performance, and expanding the scope of application of TVF-EMD in complex environments.

[0106] 3): By introducing permutation entropy as the information criterion, the non-stationary degree of each IMF component is measured, and the useful information and noise components are effectively distinguished, which can more accurately retain the main components of the signal, suppress the mixed noise, and improve the signal reconstruction quality.

[0107] 4): The denoising algorithm proposed in this invention has good versatility and transferability, does not depend on the specific source of the signal, can be extended to a variety of uwDAS and even non-uwDAS scenarios, and shows high robustness under different devices, different acquisition conditions and variable noise backgrounds. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] The present invention will be further described below with reference to the accompanying drawings and examples:

[0109] Figure 1 Flowchart of the present invention.

[0110] Figure 2 The figure shows the 1000 Hz original sinusoidal signal collected by uwDAS in Example 1 and the result of TVF-EMD decomposition.

[0111] Figure 3 The permutation entropy value corresponding to each IMF component of the TVF-EMD decomposition of the sinusoidal signals with frequencies of 200 Hz, 400 Hz, 600 Hz, and 1000 Hz collected by the uwDAS in Example 1.

[0112] Figure 4 The waveform diagrams are of the sound wave signals collected in Example 1 before and after denoising using the present invention. DETAILED DESCRIPTION

[0113] Example 1:

[0114] The present invention denoises the signal collected by uwDAS, with a sampling frequency of 10kHz and a total of 3s of data collected. The parameters are set as follows:

[0115] Hanning window frame length and frame shift settings during framing: Hanning window frame length N f =2048, frame shift N m =512.

[0116] Gray wolf population size setting: pop=3.

[0117] The maximum number of iterations is set to: Max_ite=5.

[0118] Bandwidth threshold search range setting: [0.1, 0.8].

[0119] B-spline fitting order search range setting: [5,30].

[0120] Embedding dimension setting: M=6.

[0121] Time delay setting: T=1.

[0122] Permutation entropy threshold setting: th = 0.51.

[0123] The signal is denoised using the present invention and compared with the original noisy signal:

[0124] The selection of permutation entropy threshold also greatly affects the denoising performance of the algorithm. Therefore, we first use TVF-EMD decomposition on the sinusoidal signals of known frequencies (200Hz, 400Hz, 600Hz, 1000Hz) collected by uwDAS. By observing the waveforms of each decomposed IMF and calculating the corresponding permutation entropy, we can judge the rationality of the selection of permutation entropy threshold. For example, the result of TVF-EMD decomposition of 1000Hz sinusoidal signal is shown in the figure. Figure 2 As shown in Table 1, the permutation entropy corresponding to each IMF is shown in Table 1.

[0125] Table 1 IMF permutation entropy of 1000Hz sinusoidal signal by TVF-EMD decomposition

[0126]

[0127] Depend on Figure 2As shown in Table 1, the waveform of IMF5 is closest to the original sinusoidal signal, and the other IMF components are all noise. At this time, the IMF5 with a permutation entropy smaller than the threshold is selected for signal reconstruction. Similarly, the same operation is performed on the 200Hz, 400Hz and 600Hz sinusoidal signals respectively. The permutation entropy values corresponding to each IMF component at each frequency are as follows: Figure 3 As shown. Figure 3 It can be seen that the threshold th is selected as 0.51, which can effectively remove the noise component while retaining the signal component, so it is a reasonable threshold setting.

[0128] The present invention is used to denoise the acoustic wave signal collected by uwDAS. The signal waveforms before and after denoising are as follows: Figure 4 As shown. Figure 4 It can be seen that the present invention can remove most of the system background noise and environmental noise, such as Figure 4 Solid frame part. At the same time, useful signals can be effectively retained, such as Figure 4 The dotted box part can improve the signal quality and thus enhance the signal availability.

Claims

1. The adaptive framing denoising method for uwDAS signals based on TVF-EMD and GWO is characterized by The following steps are involved: Step 1: Let the signal detected by uwDAS be y(n), where n is the sampling point index, 1≤n≤N, and N is the total number of sampling points; Step 2: Select the Hanning window to frame y(n) and obtain y(t,l), where l is the frame index, 1≤l≤L, L is the total number of frames, and t is the sampling point index in the frame, 1≤t≤L f , where L f is the frame length; Step 3: Select permutation entropy as the fitness function and use the Grey Wolf Optimization Algorithm (GWO) to optimize the TVF-EMD decomposition parameters of y(t,l) to obtain the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best; Step 4: Select the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best to perform TVF-EMD decomposition on y(t,l) to obtain K IMFs; Step 5: According to the permutation entropy value PeEn(k) of each IMF, the permutation entropy threshold th is used to select the valid IMF for reconstruction to obtain the denoised signal x(t,l) of the current frame, where k is the sequence number of the IMF, 1≤k≤K; Step 6: Restore the complete denoised signal x(n) according to the Hanning window function.

2. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 1, characterized in that: In step 2, selecting a Hanning window to frame y(n) specifically includes: 2.1: y(n) according to the frame length L f and frame shift N m Frame to obtain the frame signal y1(t,l) before weighting; 2.2: Use Hanning window hanning(t) to weight y1(t,l), and the calculation formula is: y(t,l)=y1(t,l)·hanning(t); in, cos(·) is the cosine function.

3. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 1, characterized in that: In step 3, the TVF-EMD decomposition parameters of y(t, l) are optimized using GWO, including the following steps: S3.1: Initializing the gray wolf population size pop, the maximum number of iterations Max_ite, the bandwidth threshold search range [T_min, T_max], and the B-spline fitting order search range [B_min, B_max], Among them, T_min is the lower bound of the bandwidth threshold search, T_max is the upper bound of the bandwidth threshold search, B_min is the lower bound of the B-spline fitting order search, and B_max is the upper bound of the B-spline fitting order search; S3.2: Use the T corresponding to each wolf w (ite), B w (ite) Perform TVF-EMD decomposition on y(t,l); S3.3: Calculate IMF k The permutation entropy of (ite); S3.4: In the GWO algorithm, wolves are divided into four levels: α, β, δ, and ω according to their permutation entropy values from low to high. The following updates the behavior of wolves surrounding their prey when hunting: in: denote the distance vectors between the wolf and the prey at the ite-th iteration, α, β, and δ, respectively; is the position vector of wolf ω in the ite-th iteration; Respectively represent the current positions of α, β and δ wolves in the ite-th iteration; They represent the position vectors of ω wolf after being affected by α, β and δ wolves in the ite-th iteration respectively; is a random vector in [0,2]; For the control parameters and a random vector in [0,1] The joint expression is The three random coefficients generated; S3.5: Update the final position of ω wolf, which is calculated as follows: S3.6: Update the ranks of α, β, δ, and ω wolves from low to high according to the permutation entropy value. At this time, the position of α wolf is the parameter to be optimized Q w (ite+1)={T w (ite+1),B w (ite+1)}; S3.7: Determine whether the following loop conditions are met: ite≤Max_ite; If satisfied, add 1 to the value of ite and repeat S3.2 to S3.6; otherwise, proceed to step 4.

4. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 3, characterized in that: In S3.1, initialize the current iteration number ite=1, and randomly initialize the wolf pack positions within the bandwidth threshold and B-spline fitting order search range. The parameter to be optimized Q at the current iteration w (ite)={T w (ite),B w (ite)} as the position coordinates of the w-th wolf; Among them, T w (ite) is the bandwidth threshold of the w-th wolf in the ite-th iteration, B w (ite) is the B-spline fitting order of the w-th wolf in the ite-th iteration, 1≤w≤pop; {T w (ite),B w (ite)} represents the bandwidth threshold and B-spline fitting order set corresponding to the w-th wolf in the ite-th iteration; Initialize T_best = T w (1), B_best=B w (1), T w (1) represents the bandwidth threshold randomly initialized by the w-th wolf, B w (1) represents the B-spline fitting order of the w-th wolf randomly initialized, and the initial permutation entropy mean PE avg (1) is an infinite value.

5. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 3, characterized in that: S3.2 includes the following steps: S3.2.1: Compute the Hilbert transform of y(t,l) The calculation formula is: Where: PV represents the Cauchy principal value, It means integrating the integral variable τ from -∞ to +∞; S3.2.2: Find the analytical signal z(t,l) of y(t,l), which is calculated as: Where: A(t,l) is the instantaneous amplitude of z(t,l), is the instantaneous phase of z(t,l), j is the imaginary unit, and e is the base of the natural logarithm; A(t,l) and The calculation formula is: Where: arctan(·) is the inverse tangent function; S3.2.3: For the set of local maxima and local minima of A(t,l) {A(t max ,l)} and {A(t min ,l)} to interpolate and obtain β1(t,l) and β2(t,l); respectively and Interpolate to obtain η1(t,l) and η2(t,l); Where: t max and t min are the sampling point indices of the local maximum and local minimum of A(t,l), and are the instantaneous frequency of the local minimum value of the lth frame and the instantaneous frequency of the local maximum value of the lth frame respectively; S3.2.4: Express the analytical signal z(t,l) as the superposition of two components, which is expressed as: a1(t,l) and a2(t,l) are the instantaneous amplitudes of the two components, and their calculation formulas are: and is the instantaneous phase of the two components, and their derivatives correspond to the instantaneous frequencies of the two components and The calculation formula is: Where: η1(t,l) represents the weighted envelope information based on the local minimum value of A(t,l) and its derivative change trend, η2(t,l) represents the weighted envelope information based on the local maximum value of A(t,l) and its derivative change trend; S3.2.5: Calculate the local cutoff frequency The calculation formula is: S3.2.6: Calculate Loughlin instantaneous bandwidth B Lou (t,l) and weighted average instantaneous frequency The calculation formula is: Where: a'1(t,l) is the derivative of the instantaneous amplitude of the first component a1(t,l), and a'2(t,l) is the derivative of the instantaneous amplitude of the second component a2(t,l); S3.2.7: Calculate the current signal bandwidth θ(t,l) using the following formula: S3.2.8: Determine whether the following narrowband signal conditions are met: θ(t,l)≤T w (ite); If it satisfies, then y(t,l) is an IMF, denoted as IMF k (ite), represents the kth IMF in the ite-th iteration, and performs S3.3, otherwise calculate B of y(t,l) w (ite)th order B-spline fitting result m(t,l), subtract m(t,l) from y(t,l), and repeat S3.2.1 to S3.2.

7.

6. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 5, characterized in that: Calculate B of y(t,l) w The (ite)-order B-spline fitting result m(t,l) is as follows: Find the B-spline basis function B q (t), which is calculated as follows: Where: q is the B-spline basis function B q (t) index number, signal The extreme points are the nodes of the B-spline basis function, t q is the node at the qth position of the B-spline basis function, t q+1 is the node at the q+1th position of the B-spline basis function, is the q+Bth B-spline basis function w (ite)-1 node, is the q+Bth B-spline basis function w (ite) nodes at the position; t represents the sampling point index of the current frame; B q-1 (t) is the q-1th B-spline basis function; Determine the fitting coefficient c q Minimize the overall error: Where Q = L f +B w (ite), the calculation formula of the fitting result m(t,l) is:

7. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 3, characterized in that: S3.3: Calculate IMF k The permutation entropy value of (ite) includes the following steps: S3.3.1: Initialize embedding dimension M and time delay T, IMF k (ite) is represented as the following sequence: in: For the IMF k (ite) 1st, 2nd,…, L f The value of each sampling point; S3.3.2: By IMF k The sampling point values in (ite) are arbitrarily constructed L f -(M-1)T delayed embedding vector sequences of length M IMF1 k (ite): IMF1 k (ite)={f J ,f J+T ,f J+2T ,...,f J+(M-1)T }; Where: J = 1, 2, ..., L f -(M-1)T;f J ,f J+T ,f J+2T ,...,f J+(M-1)T IMF1 k (ite) The value of the J, J+T, J+2T, …, J+(M-1)T sampling points; T represents the time delay; S3.3.3: Calculate IMF k The permutation entropy value PE(k,ite) of (ite) is calculated as follows: Where: log(·) represents the logarithm operation with base 10; p i1 For each IMF1 k The probability of occurrence of the permutation pattern of the sample point values in (ite), i1 = 1, 2, ..., M!, where the symbol '!' represents the factorial operation; S3.3.4: Calculate the mean PE of PE(k,ite) in the current iteration avg (ite), which is calculated as follows: Where: K1 is the number of decomposed IMFs, k is the sequence number of the IMF; S3.3.5: Determine whether the mean permutation entropy satisfies the following conditions: ON avg (here) <PE avg (ite-1); If satisfied, then T in the current iteration w (ite) and B w (ite) are the optimal bandwidth threshold T_best and the optimal B-spline fitting order B_best, respectively. Each decomposed IMF is the optimal decomposition Best_IMF k , the corresponding permutation entropy is the optimal permutation entropy value PeEn(k), and S3.4 is performed; otherwise, T_best, B_best, Best_IMF k and PeEn(k) remain unchanged, and proceed to S3.

4.

8. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 1, characterized in that: In step 4, select T_best and B_best to perform TVF-EMD decomposition on y(t,l) to obtain K IMFs, that is, the optimal decomposition Best_IMF currently determined by S3.3.5 k , and its corresponding permutation entropy is the optimal permutation entropy value PeEn(k).

9. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 1, characterized in that: In step 5, the effective IMF reconstruction is selected by the permutation entropy threshold th to obtain the denoised signal x(t,l) of the current frame. The reconstruction formula is: Where: γ is the index of the valid IMF set, k∈γ represents the Best_IMF belonging to the valid IMF set k index.

10. The method for adaptive framing denoising of uwDAS signals based on TVF-EMD and GWO according to claim 1, characterized in that: The step 6 comprises the following steps: S6.1: Calculate the superposition signal x sum (n), which is calculated as follows: Where: x(nn l ,l) is the sampling point index of the lth frame after denoising, which is nn l signal; n l =l·N m ; is an indicator function whose value is: S6.2: Calculate the window function weight superposition signal w sum (n), which is calculated as follows: Among them: hanning1(nn l ) is the Hanning window at sampling point nn l The value of S6.3: Normalize and restore the complete signal x(n) after denoising. The calculation formula is:

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