Wideband signal parameter identification method based on wavelet noise reduction and improved VMD-Prony algorithm

Abstract

The invention discloses a broadband signal parameter identification method based on wavelet noise reduction and an improved VMD-Prony algorithm, and the method comprises the following steps: carrying out the noise reduction preprocessing of a broadband signal based on a soft threshold wavelet noise reduction method, so as to reduce the interference of the noise to a measurement process, and building an evaluation index according to a Pearson's correlation coefficient and a signal-to-noise ratio for evaluating the noise reduction effect; parameters of a mutual information entropy and an energy entropy optimization VMD algorithm are introduced, the noise-reduced signal is decomposed by using the parameter optimization VMD algorithm, a plurality of modes with center frequencies are decomposed, and the complexity of broadband signal processing is reduced; performing parameter estimation on each mode by using a Prony algorithm, selecting a proper model order p according to the characteristics of the modes, performing numerical calculation by constructing a plurality of functions, obtaining frequency, amplitude and phase information of each mode, and realizing parameter identification of the broadband signal; according to the invention, the problems of noise interference and insufficient identification precision of the broadband oscillation signal in the parameter identification process are solved.

Description

Technical Field

[0001] The present invention relates to the technical field of broadband oscillation, and in particular to a method for identifying broadband signal parameters based on wavelet denoising and improved VMD-Prony algorithm. Background Art

[0002] With the rapid development and massive access of "high proportion of renewable energy" and "high proportion of power electronic devices", the power system presents the characteristics of "double high", namely high proportion of renewable energy and high proportion of power electronic devices. This characteristic has led to significant changes in the dynamic characteristics and operation modes of the power system, triggering a series of new broadband oscillation instability phenomena. Different from traditional power system oscillations, the frequency distribution of broadband oscillations is from a few hertz to several kilohertz, and is accompanied by severe noise interference, posing a serious threat to the safe and stable operation of the power system.

[0003] Accurately identifying the parameter information of broadband signals is the basis for analyzing broadband oscillations in the power grid, but the identification process faces challenges of noise interference and insufficient accuracy. Existing denoising methods such as adaptive filters and linear filters have problems such as high computational complexity or poor filtering effects; while methods such as compressive sensing require prior knowledge of the sparsity of the signal and have complex reconstruction algorithms. In addition, existing methods for identifying broadband signal parameters such as Fourier transform, modern spectral estimation methods, and modal decomposition methods also have their own limitations and are difficult to balance the denoising effect and parameter identification accuracy. Therefore, how to effectively denoise broadband oscillation signals and accurately identify them has become an urgent problem to be solved. Summary of the Invention

[0004] The purpose of the present invention is to overcome the above deficiencies and provide a method for identifying broadband signal parameters based on wavelet denoising and improved VMD-Prony algorithm to solve the problems of noise interference and insufficient identification accuracy faced by broadband oscillation signals during the parameter identification process.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a method for identifying broadband signal parameters based on wavelet denoising and improved VMD-Prony algorithm, including the following steps:

[0006] Step 1: Perform denoising preprocessing on the broadband signal based on the soft-threshold wavelet denoising method to reduce the interference of noise on the measurement process, and establish an evaluation index based on the Pearson correlation coefficient and signal-to-noise ratio to evaluate the denoising effect;

[0007] Step 2: Introduce mutual information entropy and energy entropy to optimize the parameters of the VMD algorithm, and use the VMD algorithm with optimized parameters to decompose the denoised signal, decomposing it into multiple modes with center frequencies to reduce the complexity of broadband signal processing;

[0008] Step 3: Use the Prony algorithm to estimate the parameters of each mode respectively. Select an appropriate model order p according to the characteristics of the mode. Through constructing multiple functions for numerical calculation, obtain the frequency, amplitude, and phase information of each mode, and realize the parameter identification of the broadband signal.

[0009] Preferably, the specific steps of Step 1 are as follows:

[0010] Step 1.1: Perform multi-scale wavelet decomposition on the broadband signal to obtain a series of wavelet coefficients. Select an appropriate threshold to process the wavelet coefficients. For the actual noise-containing situation of the broadband oscillation signal, select Bior as the wavelet basis function and select the threshold according to Bayes;

[0011]

[0012] where λ j is the determined threshold, and σ and σ j are the standard deviations of the noise and the wavelet coefficients respectively, which can be calculated by the following formula:

[0013]

[0014] where d is the wavelet coefficient obtained by wavelet transform of the original signal; N is the total number of wavelet coefficients; j is the wavelet decomposition level; i is the sampling point;

[0015] Step 1.2: After determining the threshold, perform threshold processing on the wavelet coefficients of each scale. The soft threshold function is expressed as follows;

[0016]

[0017] where sgn(d j ) is the sign function, which is used to keep the sign of d j and adjust the amplitude of the coefficient according to the threshold λ;

[0018] Step 1.3: Perform wavelet inverse transform on the wavelet coefficients after threshold processing to complete the noise reduction processing of the signal, and establish evaluation indexes according to the Pearson correlation coefficient r and the signal-to-noise ratio SNR to evaluate the noise reduction effect.

[0019] More preferably, the calculation formulas related to the Pearson correlation coefficient r and the signal-to-noise ratio SNR in Step 1.3 are as follows:

[0020]

[0021] where: S is the original signal without random noise interference; S n is the signal after adding noise interference, S de is the signal after noise reduction, S n,m , S de,mare the means of the noisy interference signal and the noise-reduced signal respectively, n is the length of the signal, and the value range of the Pearson correlation coefficient is [-1, 1]. A value close to 1 indicates a high correlation between the noise-reduced signal and the original signal, and the better the noise reduction effect; a value close to -1 indicates a complete negative correlation, and 0 indicates no linear correlation.

[0022] Preferably, the specific content of the second step is as follows:

[0023] Step 2.1: For the broadband signal with multiple signal components of different frequencies, decompose the broadband signal into multiple fixed modes through the VMD algorithm, so that each mode is a finite bandwidth with a center frequency;

[0024] Step 2.2: Introduce a correlation coefficient based on mutual information entropy to design the number of modes k of VMD, and calculate the entropy of the broadband signal;

[0025] Step 2.3: Calculate the conditional entropy for each mode after decomposing the broadband signal by the VMD algorithm;

[0026] Step 2.4: Calculate the mutual information entropy for each mode after decomposing the broadband signal by the VMD algorithm. The mutual information entropy evaluates the correlation between the modal signal and the original broadband signal;

[0027] Step 2.5: Select the value corresponding to the maximum mutual information entropy as the optimal number of modes of the VMD algorithm;

[0028] Step 2.6: Introduce a correlation coefficient based on energy entropy to design the penalty factor α of VMD, and calculate the energy for each mode after decomposing the broadband signal by the VMD algorithm;

[0029] E k =∫|u k (ω)| 2 dω

[0030] In the formula, E k is the modal calculation energy, u k is the frequency domain representation of the mode, and ω is the frequency;

[0031] Step 2.7: Calculate the energy entropy for each mode after decomposing the broadband signal by the VMD algorithm. The energy entropy quantifies the distribution of modal energy and reflects the concentration of the mode in the frequency domain;

[0032]

[0033] In the formula, E H is the entropy quantifying modal energy, p i is the proportion of the energy of the i-th frequency component in the total energy, and N is the total number of frequency components in the mode;

[0034] Step 2.8: Select the value corresponding to the minimum energy entropy as the optimal penalty factor of the VMD algorithm.

[0035] More preferably, in step 2.2, the specific formula for calculating the entropy of the broadband signal is as follows:

[0036]

[0037] where p(x i ) is the probability distribution of the i-th value in the original signal x.

[0038] More preferably, in step 2.3, for each mode after decomposing the broadband signal by the VMD algorithm, the specific formula for calculating the conditional entropy is as follows:

[0039]

[0040] where p(x i , x k,j ) is the joint probability distribution of the i-th mode and the j-th frequency component of the k-th mode x k of the original signal x, and p(x k , j) is the probability distribution of the j-th frequency component of the k-th mode x k .

[0041] More preferably, in step 2.4, the calculation formula for the mutual information entropy is as follows:

[0042]

[0043] where MI k is the mutual information entropy of each mode, H is the entropy of the signal, x is the signal, and x k is the mode decomposed into the k-th one.

[0044] Preferably, the specific steps of step three are as follows:

[0045] Step 3.1: For each fixed mode, use the Prony algorithm for parameter identification respectively, select an appropriate model order p according to the characteristics of the mode, and construct a Prony equation based on the data points of the mode;

[0046]

[0047] where p is the order of the model, b i and z i are the amplitude and attenuation coefficient of the i-th mode respectively, N is the number of sampling data points, A i is the signal amplitude; θ i is the phase; f i is the oscillation frequency; α iis the attenuation factor; Δt is the sampling interval;

[0048] Step 3.2: Construct a constant coefficient linear difference equation to solve for the coefficient a i Total least squares estimation of (i = 1, …, p);

[0049]

[0050] In the formula, ε is the error term, is the estimated value of the signal;

[0051] Step 3.3: In order to make the signal estimated value as close as possible to the actual signal x(n), adopt the principle of minimum square error to construct an error objective function;

[0052]

[0053] In the formula, e is the total calculation error between the estimated signal and the actual signal.

[0054] Step 3.4: Through numerical calculation, obtain the coefficient a under the condition of minimizing the error objective function i value, and obtain the coefficient a i After that, construct a characteristic polynomial and find the roots z of the characteristic polynomial i ;

[0055] Step 3.5: According to the obtained z i , calculate the amplitude A i , phase θ i , frequency f i and attenuation factor α i parameter information to achieve parameter identification of broadband signals.

[0056] More preferably, in step 3.4, the constructed characteristic polynomial is as follows:

[0057] z i p + a1z i p-1 + a2z i p-2 + … + a p-1 z i + a p = 0.

[0058] More preferably, in step 3.5, the specific process of calculating the amplitude Ai, phase θ i , frequency f i and attenuation factor α i parameter information is as follows:

[0059]

[0060] Advantages of the present invention:

[0061] 1. The soft-threshold wavelet denoising method of the present invention can effectively remove noise interference, retain the effective information of the signal, improve the signal quality, and perform better in terms of the Pearson correlation coefficient index compared with the hard-threshold method, and can better meet the denoising requirements of broadband signals in a high-noise environment.

[0062] 2. The improved VMD algorithm of the present invention can decompose the broadband signal into multiple modes with central frequencies, reduce the complexity of signal processing, and improve the decomposition accuracy. By optimizing the VMD parameters through mutual information entropy and energy entropy, the mode mixing phenomenon can be effectively avoided, and the accuracy of signal decomposition can be improved.

[0063] 3. The Prony algorithm of the present invention estimates the parameters of each mode after the VMD decomposes the broadband signal, and obtains information such as the frequency, amplitude, and phase of each mode, improving the identification accuracy of the relevant parameters of the broadband signal.

[0064] 4. The present invention solves the problems of noise interference and insufficient identification accuracy faced by broadband oscillation signals during the parameter identification process. Description of the drawings

[0065] Figure 1 is the flowchart of the method of the present invention;

[0066] Figure 2 is the comparison chart of the denoising effects of the denoising methods with different threshold functions in the embodiments of the present invention;

[0067] Figure 3 is the modal amplitude characteristic curve diagram in the embodiments of the present invention;

[0068] Figure 4 is the modal spectrum characteristic curve diagram in the embodiments of the present invention. Detailed implementation manners

[0069] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0070] Embodiment 1: As Figure 1 shown, a broadband signal parameter identification method based on wavelet denoising and improved VMD-Prony algorithm includes the following steps:

[0071] Step 1: Design a preprocessing method for denoising the broadband signal based on the soft-threshold wavelet denoising method to reduce the interference of noise on the measurement process, and establish evaluation indicators based on the Pearson correlation coefficient and signal-to-noise ratio to evaluate the denoising effect;

[0072] Step 2: Introduce mutual information entropy and energy entropy to optimize the parameters of the VMD algorithm. Use the VMD algorithm with optimized parameters to decompose the denoised signal, decompose it into multiple modes with center frequencies, and reduce the complexity of processing broadband signals;

[0073] Step 3: Use the Prony algorithm to perform parameter estimation on each mode respectively. Select a suitable model order p according to the characteristics of the mode, and obtain information such as the frequency, amplitude, and phase of each mode through numerical calculations by constructing multiple functions, so as to realize the parameter identification of broadband signals.

[0074] Further, the specific content of the said Step 1 is as follows:

[0075] Step 1.1: Perform multi-scale wavelet decomposition on the broadband signal to obtain a series of wavelet coefficients. Select a suitable threshold to process the wavelet coefficients. For the actual noise-containing situation of the broadband oscillation signal, select Bior as the wavelet basis function and select the threshold according to Bayes;

[0076]

[0077] where λ j is the determined threshold, and σ and σ j are the standard deviations of the noise and the wavelet coefficients respectively, and can be calculated by the following formula:

[0078]

[0079] where d is the wavelet coefficient obtained by wavelet transform of the original signal; N is the total number of wavelet coefficients; j is the number of wavelet decomposition layers; i is the sampling point;

[0080] Step 1.2: After determining the threshold, perform threshold processing on the wavelet coefficients of each scale. The soft threshold function is expressed as follows;

[0081]

[0082] where sgn(d j ) is the sign function, which is used to keep the sign of d j and adjust the amplitude of the coefficient according to the threshold λ;

[0083] Step 1.3: Perform wavelet inverse transform on the wavelet coefficients after threshold processing to complete the denoising process of the signal, and establish evaluation indicators based on the Pearson correlation coefficient and the signal-to-noise ratio to evaluate the denoising effect;

[0084]

[0085] where: S is the original signal without random noise interference; S n is the signal after adding noise interference, S deis the signal after noise reduction, S n,m , S de,m are the means of the signal with noise interference and the noise-reduced signal respectively, n is the length of the signal, and the value range of the Pearson correlation coefficient is [-1, 1]. A value close to 1 indicates a high correlation between the noise-reduced signal and the original signal, and the better the noise reduction effect; a value close to -1 indicates a complete negative correlation, and 0 indicates no linear correlation.

[0086] Furthermore, the specific content of step 2 is as follows:

[0087] Step 2.1: For the wideband signal with multiple signal components of different frequencies, the wideband signal is decomposed into multiple fixed modes by the VMD algorithm, so that each mode is a finite bandwidth with a central frequency;

[0088] Step 2.2: Introduce the correlation coefficient based on mutual information entropy to design the number of modes k of VMD, and calculate the entropy of the wideband signal;

[0089]

[0090] In the formula, p(x i ) is the probability distribution of the i-th value in the original signal x;

[0091] Step 2.3: Calculate the conditional entropy for each mode after the wideband signal is decomposed by the VMD algorithm;

[0092]

[0093] In the formula, p(x i , x k,j ) is the joint probability distribution of the i-th mode and the j-th frequency component of the k-th mode x k of the original signal x, and p(x k , j) is the probability distribution of the j-th frequency component of the k-th mode x k ;

[0094] Step 2.4: Calculate the mutual information entropy for each mode after the wideband signal is decomposed by the VMD algorithm, and the mutual information entropy evaluates the correlation between the modal signal and the original wideband signal;

[0095]

[0096] In the formula, MI k is the mutual information entropy of each mode, H is the entropy of the signal, x is the signal, and x k is decomposed into the k

[0097] -th mode.

[0098] Step 2.5: Select the value corresponding to the maximum mutual information entropy as the optimal number of modes of the VMD algorithm;

[0099] Step 2.6: Introduce the correlation coefficient based on energy entropy to design the penalty factor α of VMD, and calculate the energy for each mode after decomposing the broadband signal by the VMD algorithm;

[0100] E k =∫|u k (ω)| 2 dω (11)

[0101] In the formula, E k is the modal calculation energy, u k is the frequency-domain representation of the mode, and ω is the frequency.

[0102] Step 2.7: Calculate the energy entropy for each mode after decomposing the broadband signal by the VMD algorithm. The energy entropy quantifies the distribution of modal energy and reflects the concentration of the mode in the frequency domain;

[0103]

[0104] In the formula, E H is the entropy to quantify modal energy, p i is the proportion of the energy of the i-th frequency component in the total energy, and N is the total number of frequency components in the mode.

[0105] Step 2.8: Select the value corresponding to the minimum energy entropy as the optimal penalty factor of the VMD algorithm.

[0106] Furthermore, the specific content of Step 3 is as follows:

[0107] Step 3.1: For each fixed mode, use the Prony algorithm for parameter identification respectively. Select an appropriate model order p according to the characteristics of the mode, and construct a Prony equation based on the data points of the mode;

[0108]

[0109] In the formula, p is the order of the model, b i and z i are the amplitude and attenuation coefficient of the i-th mode respectively, N is the number of sampling data points, A i is the signal amplitude; θ i is the phase; f i is the oscillation frequency; α i is the attenuation factor; Δt is the sampling interval;

[0110] Step 3.2: Construct a constant coefficient linear difference equation to solve the total least squares estimation of the coefficients a i (i = 1,…,p);

[0111]

[0112] In the formula, ε is the error term, is the estimated value of the signal.

[0113] Step 3.3: In order to make the signal estimated value as close as possible to the actual signal x(n), the principle of minimum square error is adopted,

[0114] Construct an error objective function;

[0115]

[0116] In the formula, e is the total calculation error between the estimated signal and the actual signal.

[0117] Step 3.4: Through numerical calculation, obtain the value of coefficient a under the condition that the error objective function is minimized, i value,

[0118] Obtain coefficient a i After that, construct a characteristic polynomial and find the roots z i ;

[0119] z i p + a1z i p-1 + a2z i p-2 + … + a p-1 z i + a p =0 (19)

[0120] Step 3.5: According to the obtained z i , calculate the amplitude A i , phase θ i , frequency f i and attenuation factor α i and other parameter information of the signal through solving the equations, and realize the parameter identification of the broadband signal.

[0121]

[0122] Example 2:

[0123] To verify the correctness and effectiveness of the improved method proposed in this paper, the test signal containing noise is denoised. To verify the denoising effect of the method proposed in this paper, two wavelet denoising methods of hard threshold and soft threshold are used to analyze and compare the test signal.

[0124] A test signal is established, which consists of an original signal without noise and noise. Considering that the wide - frequency oscillation frequency has a wide distribution range and may contain multiple oscillation components, the original signal contains 4 wide - frequency oscillation frequencies of 33Hz, 87Hz, 246Hz, and 1500Hz in addition to the fundamental frequency of 50Hz, and the oscillation amplitudes are randomly generated. The noise contains Gaussian white noise and background noise. The sampling frequency is set to 10kHz, and the time length of the monitored data is set to 1s. The test signal model used is as follows:

[0125]

[0126] where \(x_1(t)\) is the original signal, \(x\) N is the noise, \(N\) G and \(N\) P are Gaussian white noise and impulse noise respectively.

[0127] After denoising with three wavelet denoising methods respectively, the signal - to - noise ratio and Pearson coefficient results of the test signal are as Figure 2 shown. The signal - to - noise ratio and Pearson coefficient of the test signal before denoising are 8.38 and 0.9291 respectively. The signal - to - noise ratio and Pearson coefficient of the test signal after denoising are shown in Table 1.

[0128] Table 1 Comparison of Denoising Effects of Denoising Methods with Different Threshold Functions

[0129] Threshold function Signal-to-noise ratio Pearson correlation coefficient Hard threshold 16.78 0.9901 Soft threshold 17.40 0.9920

[0130] Table 1 gives the results of quantitative comparison of different threshold methods. It can be seen from Table 1 that after using three different threshold wavelet denoising methods, the signal - to - noise ratios of the denoised signals are increased by 8.4 and 9.02 respectively; the signal - to - noise ratios of the denoised signals are increased by 0.061 and 0.0629 respectively. The soft threshold proposed in this paper performs better in the denoising effect evaluation index and is more suitable for application in wide - frequency signals with high noise.

[0131] Example 3:

[0132] To verify the decomposition effect of the VMD algorithm and the accuracy of Prony parameter identification, a test signal is constructed.

[0133] Considering that the wide - frequency oscillation frequency has a wide distribution range and may have multiple oscillation components, 4 wide - frequency oscillation frequencies are generated in addition to the fundamental frequency of 50Hz, and the oscillation amplitudes are randomly generated. A wide - frequency multi - modal original signal composed of a low - frequency constant - amplitude oscillation signal, a subsynchronous constant - amplitude oscillation signal, two wide - frequency constant - amplitude oscillation signals, and a power - frequency signal is constructed. The signal expression

[0134] is as follows:

[0135] x(t) = 220cos(2π×50t) + 50cos(2π×114t) + 20cos(2π×295t) + 10cos(2π×780t) (22)

[0136] The above signal is decomposed by VMD with optimized parameters, and the VMD decomposition results are as Figure 3 , Figure 4

[0137] shown, Figure 3 which are the time-domain decomposition results of each mode, Figure 4 and the frequency-domain decomposition results of each mode. It can be seen that the proposed method can effectively decompose the broadband signal into multiple modes.

[0138] After the signal is decomposed by VMD, the amplitude-phase, frequency information and relative error percentage of each mode are identified by the Prony algorithm as shown in Table 2.

[0139] Table 2 Theoretical values, identified values and relative error percentages of each mode's parameters

[0140]

[0141] It can be seen from Table 2 that the relative error between the identified frequency value and the theoretical value of each mode is 0, and the frequency identification effect is very good. The relative error percentage between the identified amplitude value and the theoretical value of Mode 1 is 0.271%; the relative error percentage between the identified amplitude value and the theoretical value of Mode 3 is 0.5665%, which is very close to the true value; the relative error percentages between the identified amplitude values and the theoretical values of Mode 2 and Mode 4 are both of the order of 10^-2, and the deviation between the identified value and the theoretical value can be approximately ignored. The error of this identification result is low and the accuracy is high, meeting the requirements of relevant engineering.

[0142] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A wideband signal parameter identification method based on wavelet denoising and improved VMD-Prony algorithm, characterized in that: It includes the following steps: Step 1: Perform noise reduction preprocessing on the broadband signal based on the soft-threshold wavelet denoising method to reduce the interference of noise on the measurement process, and establish evaluation indicators based on the Pearson correlation coefficient and signal-to-noise ratio to evaluate the denoising effect; Step 2: Introduce mutual information entropy and energy entropy to optimize the parameters of the VMD algorithm, and use the VMD algorithm with optimized parameters to decompose the denoised signal, decomposing it into multiple modes with central frequencies to reduce the complexity of broadband signal processing; Step 3: Use the Prony algorithm to perform parameter estimation on each mode respectively, select an appropriate model order p according to the characteristics of the mode, and obtain the frequency, amplitude, and phase information of each mode through numerical calculations of multiple constructed functions to achieve parameter identification of the broadband signal.

2. A method for noise reduction preprocessing of broadband signals based on the soft threshold wavelet denoising method according to claim 1, characterized in that: The specific content of Step 1 is as follows: Step 1.1: Perform multi-scale wavelet decomposition on the broadband signal to obtain a series of wavelet coefficients, select an appropriate threshold to process the wavelet coefficients, and for the actual noise-containing situation of the broadband oscillation signal, select Bior as the wavelet basis function and select the threshold according to Bayes; where λ j is a determined threshold value, and σ and σ j are the standard deviations of noise and wavelet coefficients respectively, which can be calculated by the following formula: In the formula, d is the wavelet coefficient obtained by wavelet transform of the original signal; N is the total number of wavelet coefficients; j is the wavelet decomposition layer number; i is the sampling point; Step 1.2: After determining the threshold, perform threshold processing on the wavelet coefficients of each scale. The soft-threshold function is expressed as follows; where sgn(d j ) is the sign function, which is used to maintain the sign of d j and adjust the amplitude of the coefficient according to the threshold λ; Step 1.3: Perform inverse wavelet transform on the wavelet coefficients after threshold processing to complete the noise reduction processing of the signal, and establish evaluation indicators based on the Pearson correlation coefficient r and signal-to-noise ratio SNR to evaluate the denoising effect.

3. The method for decomposing the denoised signal using the VMD algorithm optimized by parameters according to claim 3, characterized in that: The calculation formulas for the Pearson correlation coefficient r and signal-to-noise ratio SNR involved in Step 1.3 are as follows: Where: S is the original signal without random noise interference; S n is the signal after adding noise interference, S de is the signal after noise reduction, S n,m and S de,m are the means of the signal with noise interference and the signal after noise reduction respectively, n is the length of the signal, and the value range of the Pearson correlation coefficient is [-1, 1]. Being close to 1 indicates a high correlation between the signal after noise reduction and the original signal, and the better the noise reduction effect; being close to -1 indicates a complete negative correlation, and 0 indicates no linear correlation.

4. The method for decomposing the denoised signal using the VMD algorithm optimized by parameters according to claim 1, characterized in that: The specific content of Step 2 is as follows: Step 2.1: For the broadband signal with multiple signal components of different frequencies, decompose the broadband signal into multiple fixed modes through the VMD algorithm, so that each mode is a finite bandwidth with a central frequency; Step 2.2: Introduce the correlation coefficient based on mutual information entropy to design the number of modes k of VMD and calculate the entropy of the broadband signal; Step 2.3: Calculate the conditional entropy for each mode after decomposing the broadband signal by the VMD algorithm; Step 2.4: Calculate the mutual information entropy for each mode after decomposing the broadband signal by the VMD algorithm. The mutual information entropy evaluates the correlation between the modal signal and the original broadband signal; Step 2.5: Select the value corresponding to the maximum mutual information entropy as the optimal number of modes of the VMD algorithm; Step 2.6: Introduce the correlation coefficient based on energy entropy to design the penalty factor α of VMD, and calculate the energy for each mode after decomposing the broadband signal by the VMD algorithm; E k = ∫|u k (ω)| 2 dω where E k is the modal calculation energy, u k is the frequency-domain representation of the mode, and ω is the frequency; Step 2.7: Calculate the energy entropy for each mode after decomposing the broadband signal by the VMD algorithm. The energy entropy quantifies the distribution of modal energy and reflects the concentration of the mode in the frequency domain; where E H is the entropy quantization modal energy, p i is the proportion of the energy of the i-th frequency component in the total energy, and N is the total number of frequency components in the mode; Step 2.8: Select the value corresponding to the minimum energy entropy as the optimal penalty factor of the VMD algorithm.

5. A method for separately estimating parameters of each mode using the Prony algorithm according to claim 4, characterized in that: In Step 2.2, the specific formula for calculating the entropy of the broadband signal is as follows: where p(x i ) is the probability distribution of the i-th value in the original signal x.

6. A method for separately estimating parameters of each mode using the Prony algorithm according to claim 4, characterized in that: In Step 2.3, the specific formula for calculating the conditional entropy for each mode after decomposing the broadband signal by the VMD algorithm is as follows: where p(x i , x k,j ) is the joint probability distribution of the i-th mode and the j-th frequency component of the k-th mode x k of the original signal x, and p(x k , j) is the probability distribution of the j-th frequency component of the k-th mode x k .

7. A method for separately estimating parameters of each mode using the Prony algorithm according to claim 4, characterized in that: In Step 2.4, the calculation formula for the mutual information entropy is as follows: where MI k is the mutual information entropy of each mode, H is the entropy of the signal, x is the signal, and x k is decomposed into the k-th mode.

8. A method for separately performing parameter estimation on each mode by using the Prony algorithm according to claim 1, characterized in that: The specific steps of Step 3 are as follows: Step 3.1: For each fixed mode, use the Prony algorithm for parameter identification respectively. Select an appropriate model order p according to the characteristics of the mode, and construct a Prony equation based on the data points of the mode. where p is the order of the model, b i and z i are the amplitude and decay coefficient of the i-th mode respectively, N is the number of sampled data points, A i is the signal amplitude; θ i is the phase; f i is the oscillation frequency; α i is the decay factor; Δt is the sampling interval; Step 3.2: Construct a constant coefficient linear difference equation to solve for coefficient a i The total least squares estimation of (i = 1, …, p); where ε is the error term, is the estimated value of the signal; Step 3.3: In order to make the signal estimated value as close as possible to the actual signal x(n), adopt the principle of minimum square error to construct an error objective function. In the formula, e is the total calculation error between the estimated signal and the actual signal. Step 3.4: Through numerical calculation, obtain the coefficient a under the condition of minimizing the error objective function i value, and obtain the coefficient a i After that, construct the characteristic polynomial and find the roots z of the characteristic polynomial i ; Step 3.5: According to the obtained z i , calculate the amplitude A of the signal by solving the system of equations i , phase θ i , frequency f i and attenuation factor α i parameter information to achieve parameter identification of broadband signals.

9. A method for separately estimating parameters of each mode using the Prony algorithm according to claim 8, characterized in that: In Step 3.4, the constructed characteristic polynomial is as follows: z i p + a1z i p-1 + a2z i p-2 + … + a p-1 z i + a p = 0。 10. A method for separately estimating parameters of each mode using the Prony algorithm according to claim 8, characterized in that: In step 3.5, the amplitude Ai, phase θ i , frequency f i and attenuation factor α i of the signal are calculated by solving the system of equations. The specific process of the parameter information is as follows:

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