Parameter Identification Method and Terminal for Oscillation Signal

Abstract

The present invention provides a method and a terminal for identifying parameters of an oscillating signal. The method includes: performing a measurement signal acquisition step, which includes acquiring a measurement signal; performing low-pass filtering on the acquired measurement signal to obtain a filtered signal; performing modal order estimation on the filtered signal to obtain an estimated signal and a modal order; determining whether the estimated signal contains an oscillating signal. If the estimated signal does not contain an oscillating signal, then go to the measurement signal acquisition step, where the oscillating signal includes a subsynchronous oscillating signal and / or a supersynchronous oscillating signal; if the estimated signal contains an oscillating signal, then perform Hankel structured low-rank approximation on the filtered signal according to the modal order to obtain a reconstructed signal; calculate the parameters of the oscillating signal through a matrix constraint method. The present invention can improve the identification accuracy of subsynchronous and / or supersynchronous oscillating signals in a power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power system signal processing, and in particular, to a method and a terminal for identifying parameters of an oscillation signal. Background Art

[0002] In recent years, the scale of new energy power plants incorporated into the power system has been increasing day by day, and the resulting subsynchronous and supersynchronous oscillation phenomena pose a serious challenge to the normal operation of the power system. Sub-synchronous and super-synchronous oscillations are abnormal phenomena occurring in series-compensated transmission lines and high-voltage direct current (HVDC) transmission systems. Their essence is the sub-synchronous and super-synchronous interaction between the mechanical shaft system of a conventional turbine generator and the series-compensated transmission line or fast control device. With the increasing scale of wind power grid connection, multiple sub / supersynchronous oscillation events have occurred in wind farms, causing serious damage to the units and posing a serious threat to the safe operation of the power system. At the same time, with the emergence of phasor measurement units (PMUs) and wide area measurement systems (WAMS), it has become a reality to monitor sub-synchronous and super-synchronous oscillation events through the data obtained from WAMS. Therefore, in order to establish effective control strategies and mitigate sub / supersynchronous oscillation phenomena, it is of great significance to accurately identify the parameters of sub / supersynchronous oscillation signals in real time.

[0003] Some existing technologies, such as parametric model methods, have advantages such as fast speed and high accuracy, and can meet the requirements for real-time monitoring of sub-synchronous and super-synchronous oscillation signal parameters. However, the noise sensitivity problem of such methods poses a challenge to practical applications. When there is noise, the existing technologies have low accuracy in identifying the parameters of sub-synchronous and super-synchronous oscillation signals. Summary of the Invention

[0004] In view of this, the present invention provides a method and a terminal for identifying parameters of an oscillation signal, which can solve the problem of low accuracy of the existing technologies in identifying the parameters of sub-synchronous and super-synchronous oscillation signals.

[0005] In a first aspect, an embodiment of the present invention provides a method for identifying parameters of an oscillation signal, including:

[0006] Performing a measurement signal acquisition step, where the measurement signal acquisition step includes acquiring a measurement signal;

[0007] Performing low-pass filtering on the acquired measurement signal to obtain a filtered signal;

[0008] Performing modal order estimation on the filtered signal to obtain an estimated signal and a modal order;

[0009] Determine whether the estimated signal contains an oscillatory signal. If the estimated signal does not contain an oscillatory signal, go to the measurement signal acquisition step, where the oscillatory signal includes a subsynchronous oscillation signal and / or a supersynchronous oscillation signal;

[0010] If the estimated signal contains an oscillatory signal, perform Hankel structured low-rank approximation on the filtered signal according to the modal order to obtain a reconstructed signal;

[0011] Calculate the parameters of the oscillatory signal by means of a matrix constraint method for the reconstructed signal.

[0012] In a possible implementation manner, the estimating the modal order of the filtered signal to obtain the estimated signal and the modal order includes:

[0013] Construct an autocorrelation matrix of the filtered signal, and perform eigenvalue decomposition on the autocorrelation matrix to obtain an eigenvalue sequence arranged in descending order;

[0014] For each eigenvalue in the eigenvalue sequence, calculate the relative change rate of the eigenvalue, where the relative change rate of the eigenvalue is used to represent the relative change between the eigenvalue and two adjacent eigenvalues, and sort the obtained relative change rates in descending order to obtain the first Q relative change rates;

[0015] Sequentially judge each eigenvalue corresponding to each relative change rate in the first Q relative change rates until the first eigenvalue that satisfies a preset verification condition is obtained, and calculate the modal order according to the serial number of the relative change rate corresponding to the eigenvalue in the first Q relative change rates.

[0016] In a possible implementation manner, the preset verification condition is to satisfy a first formula, and the first formula is

[0017]

[0018] where λ k is used to represent the eigenvalue corresponding to the kth relative change rate in the first Q relative change rates, β is used to represent a preset sensitivity coefficient, r is used to represent the rank of the autocorrelation matrix, and k is used to represent the serial number of the relative change rate corresponding to λ k in the first Q relative change rates;

[0019] The calculating the modal order according to the serial number of the relative change rate corresponding to the eigenvalue in the first Q relative change rates includes: calculating the modal order according to a second formula, and the second formula is

[0020]

[0021] Among them, M is used to represent the modal order.

[0022] In a possible implementation, if the estimated signal contains an oscillatory signal, then according to the modal order, a Hankel structured low-rank approximation is performed on the filtered signal, and the obtained reconstructed signal includes:

[0023] Execute the first Hankel matrix construction step, and the first Hankel matrix construction step includes constructing a first Hankel matrix, and the first Hankel matrix is the Hankel matrix of the filtered signal;

[0024] Perform a fast singular value decomposition on the first Hankel matrix to obtain a first decomposition result;

[0025] According to the modal order and the first decomposition result, reconstruct a signal Hankel matrix;

[0026] Judge whether the rank of the signal Hankel matrix is equal to the signal modal order. If the rank of the signal Hankel matrix is not equal to the signal modal order, then go to the first Hankel matrix construction step;

[0027] If the rank of the signal Hankel matrix is equal to the signal modal order, then obtain the reconstructed signal according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix.

[0028] In a possible implementation, the obtaining of the reconstructed signal according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix includes:

[0029] Obtain the reconstructed signal according to the third formula, and the third formula is

[0030]

[0031] Among them, is the reconstructed signal, is the parallel element of the sub-diagonal of the signal Hankel matrix, and num(n) is the number of parallel elements of the sub-diagonal of the signal Hankel matrix.

[0032] In a possible implementation, the calculation of the parameters of the oscillatory signal by the matrix constraint method includes:

[0033] Construct a second Hankel matrix, and the second Hankel matrix is the Hankel matrix of the reconstructed signal;

[0034] Perform a fast singular value decomposition on the second Hankel matrix to obtain a second decomposition result;

[0035] Reconstruct a third Hankel matrix and a fourth Hankel matrix according to the modal order and the second decomposition result;

[0036] Calculate the signal modal poles based on the generalized eigenvalues of the matrix pencil formed by the third Hankel matrix and the fourth Hankel matrix;

[0037] Calculate the signal modal residues by the least squares method according to the signal modal poles;

[0038] Calculate the parameters of the oscillating signal according to the signal modal poles and the signal modal residues.

[0039] In a possible implementation, the second decomposition result is represented by a fourth formula, and the fourth formula is

[0040]

[0041] where Y is the second Hankel matrix, is an orthonormal matrix of size (N - L)×(N - L), is a diagonal matrix of size (N - L)×(L + 1), is an orthonormal matrix of size (L + 1)×(L + 1), is the conjugate transpose of;

[0042] The reconstructing the third Hankel matrix and the fourth Hankel matrix according to the modal order and the second decomposition result includes:

[0043] According to the first M columns of in the second decomposition result, first M columns of and deleting the last row to reconstruct the third Hankel matrix, and the third Hankel matrix is represented by a fifth formula, and the fifth formula is

[0044]

[0045] where Y1 is the third Hankel matrix, is the first M columns of, is the first M columns of and deleting the last row, M is the modal order, is the conjugate transpose of;

[0046] According to the first M columns of in the second decomposition result, first M columns of and deleting the first row to reconstruct the fourth Hankel matrix, and the fourth Hankel matrix is represented by a sixth formula, and the sixth formula is

[0047]

[0048] wherein, Y2 is the fourth Hankel matrix, is the first M columns of and deleting the first row, is the conjugate transpose of

[0049] In a possible implementation, calculating the signal modal poles according to the generalized eigenvalues of the matrix pencil formed by the third Hankel matrix and the fourth Hankel matrix includes:

[0050] Calculating the signal modal poles according to the seventh formula, and the seventh formula is

[0051]

[0052] wherein, z is the signal modal pole, eig() is the operation of finding the generalized eigenvalues of the matrix, is the pseudo-inverse matrix of the third Hankel matrix Y1.

[0053] In a possible implementation, calculating the parameters of the oscillating signal according to the signal modal poles and the signal modal residues includes:

[0054] Calculating the parameters of the oscillating signal according to the eighth formula, and the eighth formula is

[0055]

[0056] wherein, α l is the damping factor of each component of the oscillating signal, f l is the frequency of each component of the oscillating signal, A l is the amplitude of each component of the oscillating signal, is the phase of each component of the oscillating signal, f s is the sampling frequency of the oscillating signal, M is the modal order, l is the l-th component, b l is the residue of the l-th mode, z l is the signal modal pole of the l-th mode, Re() represents taking the real part, Im() represents taking the imaginary part, abs() represents taking the modulus value, and angle() represents taking the angle.

[0057] In a second aspect, an embodiment of the present invention provides a terminal, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the method described in the first aspect or any possible implementation manner of the first aspect above are implemented.

[0058] The beneficial effects of the embodiments of the present invention compared with the prior art are as follows:

[0059] In the embodiments of the present invention, by filtering the measurement signal and estimating the modal order, it is determined whether the measurement signal contains subsynchronous and / or supersynchronous oscillation signals. If the measurement signal contains subsynchronous and / or supersynchronous oscillation signals, the Hankel structured low-rank approximation is performed on the filtered signal according to the modal order to obtain a reconstructed signal; the parameters of the oscillation signal are calculated by a matrix constraint method for the reconstructed signal. By combining the Hankel structured low-rank approximation and the matrix constraint method, the online identification of the parameters of the subsynchronous and / or supersynchronous oscillation signals is realized, and the noise immunity is improved, thereby improving the accuracy of the identification of the parameters of the subsynchronous / supersynchronous oscillation signals. Description of the Drawings

[0060] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0061] Figure 1 is the implementation flowchart of a method for identifying the parameters of an oscillation signal provided by the embodiments of the present invention;

[0062] Figure 2 is the implementation flowchart of a method for estimating the modal order of a filtered signal provided by the embodiments of the present invention;

[0063] Figure 3 is the schematic flowchart of a method for performing Hankel structured low-rank approximation on a filtered signal provided by the embodiments of the present invention;

[0064] Figure 4 is the implementation flowchart of a method for calculating the component parameters of an oscillation signal from a reconstructed signal by a matrix constraint method provided by the embodiments of the present invention;

[0065] Figure 5 is the schematic structural diagram of a device for identifying the parameters of an oscillation signal provided by the embodiments of the present invention;

[0066] Figure 6 is the schematic diagram of a terminal provided by the embodiments of the present invention. Detailed Embodiments

[0067] In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present invention. However, those skilled in the art should clearly understand that the present invention can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present invention.

[0068] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will be described through specific embodiments in conjunction with the accompanying drawings.

[0069] Currently, extensive research has been conducted on the problem of identifying sub- / supra-synchronous oscillation parameters based on measurement methods. There are mainly two types of methods, namely non-parametric model methods and parametric model methods.

[0070] The non-parametric model methods mainly include time-frequency analysis methods and mode decomposition methods. Among them, the fast Fourier transform (FFT) and continuous wavelet transform (CWT) are applied in low-frequency oscillation monitoring to obtain frequency and damping parameters through time-frequency analysis. However, due to problems such as spectral leakage, signal length limitation, frequency resolution, time resolution, wavelet basis selection, and wavelet decomposition degree, their accuracy is limited. The empirical mode decomposition (EMD) and variational mode decomposition (VMD) decompose the time signal to obtain multi-frequency mode components, and then combine the Hilbert-Huang transform (HHT) to identify the parameters of each subsequence respectively. Although these methods can extract instantaneous information, due to the problem of mode mixing, these methods may identify false modes or miss the main modes, and at the same time, the computational burden is also very large, which is not conducive to online monitoring of sub-synchronous oscillation signals.

[0071] The parametric model method mainly uses the mathematical model of the oscillatory signal to perform least squares estimation on the parameters. Its representative methods include the Prony method, the TLS-ESPRIT method, the matrix pencil method (MPM), the stochastic subspace identification (SSI), and the autoregressive moving average method, etc. These methods have been proven to be effective methods for online monitoring of oscillatory signals. Among them, the Prony method is widely used in the parameter identification of oscillatory signals and has the advantages of fast speed and high accuracy, but its performance is poor in the presence of noise; the TLS-ESPRIT method can estimate the frequency and amplitude of low-frequency oscillatory signals with high precision, but its estimation effect on the damping factor is poor in the presence of noise and the computational complexity is large; the matrix pencil method is a non-iterative method with small computational complexity and certain noise immunity, but its parameter identification effect is poor in the presence of high-intensity noise; the stochastic subspace method and the autoregressive moving average method require a large amount of data and are both sensitive to noise, and their performance is not good in practical applications.

[0072] The parametric model method has the advantages of fast speed and high accuracy and can meet the requirements for real-time monitoring of the parameters of sub / supersynchronous oscillatory signals. However, the noise sensitivity problem of this type of method poses a challenge to practical applications. To solve the noise sensitivity problem, it is usually necessary to combine a denoising algorithm with the parametric model method. For example, denoising methods based on an improved extended Kalman filter, empirical mode decomposition, and wavelet soft thresholding, etc. These methods have good noise suppression effects, but there are certain limitations in implementation. For example, it is difficult to find a good model that conforms to the Kalman filter. The EMD calculation time is long and noise may be aliased in the decomposed signal subsequences. Wavelet soft thresholding denoising involves the selection of wavelet bases and thresholds and is empirical.

[0073] To solve the above problems, the embodiments of the present invention provide a method for parameter identification of oscillatory signals. Refer to Figure 1 , which shows the implementation flowchart of the method for parameter identification of oscillatory signals provided by the embodiments of the present invention, and is described in detail as follows:

[0074] In step 101, a measurement signal acquisition step is executed, and the measurement signal acquisition step includes acquiring a measurement signal.

[0075] In the embodiments of the present invention, when the measurement signal contains an oscillatory signal, the mathematical model is represented by formula (1), and formula (1) is:

[0076]

[0077] Among them, A is used to represent the amplitude of the fundamental frequency component, ω = 2πf, and f is used to represent the frequency of the fundamental frequency component; is used to represent the phase of the fundamental frequency component; Asub used to represent the amplitude of the subsynchronous component, ω sub = 2πf sub , f sub used to represent the frequency of the subsynchronous component, used to represent the phase of the subsynchronous component, α sub used to represent the damping factor of the subsynchronous component, e is used to represent the natural constant; A sup used to represent the amplitude of the supersynchronous component, ω sup = 2πf sup , f sup used to represent the frequency of the supersynchronous component, is the phase of the supersynchronous component, α sup is the damping factor of the supersynchronous component; t is the sampling time. f, f sub and f sup satisfy 2f = f sub + f sup .

[0078] Assume the sampling frequency is f s , the number of sampling points is N, then the discrete signal model after sampling based on the mathematical model of formula (1) is represented by formula (2), and formula (2) is:

[0079]

[0080] where, n = 0, 1,..., N - 1.

[0081] Using Euler's formula the discrete signal model is simplified to the sum of a set of conjugate complex exponential signals, which can be represented by formula (3) as:

[0082]

[0083] where, * represents conjugation, and combining them gives the complex exponential sequence represented by formula (4):

[0084]

[0085] where M is the modal order of the signal.

[0086] Since in actual measurement, the signal often contains noise, the measured signal model can be represented by formula (5), and formula (5) is:

[0087]

[0088] where, noise(n) is the measurement noise.

[0089] The method provided by the embodiments of the present invention is used to suppress the measurement noise in the measurement signal, and on this basis, calculate the component parameters of the oscillation signal to improve the identification accuracy.

[0090] In step 102, the acquired measurement signal is low-pass filtered to obtain the filtered signal.

[0091] In the embodiments of the present invention, a 6th-order Butterworth low-pass filter can be used to low-pass filter the measurement signal obtained in step 101 to filter out the high-frequency harmonic components in the power system detection signal. Filtering can also be performed through other filters, and the embodiments of the present invention do not limit this.

[0092] In step 103, the filtered signal is subjected to modal order estimation to obtain the estimated signal and the modal order.

[0093] In the embodiments of the present invention, in order to effectively identify the parameters of the subsynchronous oscillation signal and / or supersynchronous oscillation signal, it is necessary to first correctly estimate the modal order in the signal. The present invention uses the EMO algorithm to accurately estimate the modal order of the filtered signal. The estimated signal contains the fundamental frequency component and the subsynchronous and / or supersynchronous oscillation components, so as to determine whether the signal contains subsynchronous and / or supersynchronous oscillation components. The present invention can accurately estimate the model order without considering the noise content and the nature of the modes existing in the signal.

[0094] In a possible implementation manner, refer to Figure 2 , which shows the implementation flowchart of the modal order estimation of the filtered signal provided by the embodiments of the present invention, and is described in detail as follows:

[0095] In step 1031, the autocorrelation matrix of the filtered signal is constructed, and the autocorrelation matrix is subjected to eigenvalue decomposition to obtain an eigenvalue sequence arranged in descending order.

[0096] In the embodiments of the present invention, the eigenvalue sequence arranged in descending order can be expressed as:

[0097] λ1≥λ2≥λ3...≥λ M ...≥λ r

[0098] where M is the modal order and r is the rank of the autocorrelation matrix.

[0099] In step 1032, for each eigenvalue in the eigenvalue sequence, calculate the relative change rate of the eigenvalue. The relative change rate of the eigenvalue is used to represent the relative change of the eigenvalue with respect to the two adjacent eigenvalues, and the obtained relative change rates are sorted in descending order to obtain the first Q relative change rates.

[0100] For each eigenvalue in the eigenvalue sequence, calculate the relative change rate of each eigenvalue through formula (6), and formula (6) is:

[0101]

[0102] where, is used to represent the relative change rate of the i-th eigenvalue in the eigenvalue sequence, λ i is used to represent the i-th eigenvalue, λ i-1 is used to represent the previous eigenvalue in the eigenvalue sequence, λ i+1 is used to represent the next eigenvalue in the eigenvalue sequence.

[0103] In step 1033, judge the eigenvalues corresponding to each relative change rate among the Q relative change rates in sequence until the first eigenvalue that satisfies the preset verification condition is obtained, and calculate the modal order according to the serial number of the relative change rate corresponding to this eigenvalue among the first Q relative change rates.

[0104] In a possible implementation manner, the preset verification condition is to satisfy the first formula, and the first formula is

[0105]

[0106] where, λ k is used to represent the eigenvalue corresponding to the k-th relative change rate among the first Q relative change rates, β is used to represent the preset sensitivity coefficient, r is used to represent the rank of the autocorrelation matrix, and k is used to represent the serial number of the relative change rate corresponding to λ k among the first Q relative change rates;

[0107] And calculating the modal order according to the serial number of the relative change rate corresponding to this eigenvalue among the first Q relative change rates includes: calculating the modal order according to the second formula, and the second formula is

[0108]

[0109] where, M is used to represent the modal order.

[0110] In step 104, judge whether the estimated signal contains an oscillatory signal. If the estimated signal does not contain an oscillatory signal, then go to the measurement signal acquisition step.

[0111] where, the oscillatory signal includes a subsynchronous oscillatory signal and / or a supersynchronous oscillatory signal.

[0112] If the estimated signal does not contain an oscillatory signal, then go to step 101 to continue acquiring the measurement signal, that is, go to step 101 to continue monitoring the measurement signal.

[0113] In a possible implementation manner, it is possible to determine whether the estimated signal contains an oscillatory signal according to the value of M. For example, when M = 2, only the fundamental frequency signal is included; when M = 4, the fundamental frequency signal and the subsynchronous oscillatory signal are included; when M = 6, the fundamental frequency signal, the subsynchronous oscillatory signal, and the supersynchronous oscillatory signal are included.

[0114] In step 105, if the estimated signal contains an oscillatory signal, then the filtered signal is subjected to Hankel structured low-rank approximation according to the modal order to obtain a reconstructed signal.

[0115] In a possible implementation manner, in combination with Figure 3 , which shows a schematic flowchart of a method for performing Hankel structured low-rank approximation on a filtered signal provided by an embodiment of the present invention. In combination with Figure 3 , this method includes:

[0116] In step 1051, a first Hankel matrix construction step is executed. The first Hankel matrix construction step constructs a first Hankel matrix, and the first Hankel matrix is the Hankel matrix of the filtered signal.

[0117] The filtered signal is also represented by x(n). Its Hankel matrix, that is, the first Hankel matrix X, is represented as:

[0118]

[0119] where x(0),..., x(N - 1) are the filtered signals at sampling points 0 to N - 1. The filtered signal includes a fundamental frequency signal, a subsynchronous and / or supersynchronous oscillatory signal. N is the number of sampling points, and L is the column parameter of the first Hankel matrix, generally taking

[0120] In step 1052, the first Hankel matrix is subjected to fast singular value decomposition to obtain a first decomposition result.

[0121] Performing fast singular value decomposition on the first Hankel matrix X constructed in step 1051, the obtained first decomposition result can be represented by formula (7). Formula (7) is:

[0122] X = U∑V H

[0123] where U is an orthonormal matrix of size (N - L) × (N - L), ∑ is a diagonal matrix of size (N - L) × (L + 1), V is an orthonormal matrix of size (L + 1) × (L + 1), and (·) H represents conjugate transpose, and V H is used to represent the conjugate transpose of V.

[0124] The present invention uses the fast singular value decomposition algorithm to replace the traditional SVD algorithm, greatly reducing the calculation time while ensuring the accuracy of the approximate decomposition.

[0125] In step 1053, according to the modal order and the first decomposition result, a signal Hankel matrix is reconstructed.

[0126] In the embodiment of the present invention, the reconstruction of the signal Hankel matrix can be represented by Furthermore, It can be represented by formula (8), and formula (8) is:

[0127]

[0128] Wherein, Is the first M columns of the diagonal matrix ∑, Is the first M columns of the unitary orthogonal matrix V;

[0129] The signal Hankel matrix Specifically represented as

[0130]

[0131] Wherein, Is the reconstructed subsynchronous and / or supersynchronous oscillation signal at sampling points 0 to N - 1.

[0132] In step 1054, it is judged whether the rank of the signal Hankel matrix is equal to the signal modal order. If the rank of the signal Hankel matrix is not equal to the signal modal order, it is transferred to the first Hankel matrix construction step.

[0133] In the embodiment of the present invention, by performing Hankel structure low-rank approximation on the filtered signal, the rank of the Hankel matrix converges to be equal to the signal modal order, thereby effectively suppressing the influence of noise in the signal.

[0134] In step 1055, if the rank of the signal Hankel matrix is equal to the signal modal order, the reconstructed signal is obtained according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix.

[0135] In the embodiment of the present invention, the elements Parallel to the sub-diagonal of the signal Hankel matrix Are used to determine the reconstructed signal Specifically, the reconstructed signal is obtained according to the third formula, and the third formula is

[0136]

[0137] Wherein, Is the reconstructed signal, is the parallel element of the sub-diagonal of the signal Hankel matrix, num(n) is the number of parallel elements of the sub-diagonal of the signal Hankel matrix, and the value of num(n) is determined by formula (9), and formula (9) is:

[0138]

[0139] Combining formula (8) and formula (9), we can obtain wherein, is the waveform signal of the denoised signal containing sub-synchronous and / or super-synchronous oscillation signals corresponding to sampling point 0, is the waveform signal of the denoised signal containing sub-synchronous and / or super-synchronous oscillation signals corresponding to sampling point 1, is the waveform signal of the denoised signal containing sub-synchronous and / or super-synchronous oscillation signals corresponding to sampling point N - 1, wherein the denoised waveform signal contains a fundamental frequency component and also contains sub-synchronous and / or super-synchronous oscillation signals.

[0140] In step 106, the parameters of the oscillation signal are calculated for the reconstructed signal through the matrix constraint method.

[0141] In a possible implementation manner, Figure 4 shows the implementation flowchart of a method for calculating the component parameters of the oscillation signal for the reconstructed signal through the matrix constraint method provided by the embodiment of the present invention. Refer to Figure 4 and this method includes:

[0142] In step 1061, a second Hankel matrix is constructed, and the second Hankel matrix is the Hankel matrix of the reconstructed signal.

[0143] The reconstructed signal obtained in step 105 is the denoised signal. The Hankel matrix of the reconstructed signal is constructed to obtain the second Hankel matrix Y, which is expressed as

[0144]

[0145] wherein, is the waveform signal of the denoised signal containing sub-synchronous and / or super-synchronous oscillation signals from sampling point 0 to N - 1, wherein the denoised waveform signal contains a fundamental frequency component and also contains sub-synchronous and / or super-synchronous oscillation signals.

[0146] In step 1062, the second Hankel matrix is subjected to fast singular value decomposition to obtain a second decomposition result.

[0147] In the embodiment of the present invention, the second decomposition result is represented by a fourth formula, and the fourth formula is

[0148]

[0149] Among them, Y is the second Hankel matrix, is an orthonormal matrix of size (N - L)×(N - L), is a diagonal matrix of size (N - L)×(L + 1), is an orthonormal matrix of size (L + 1)×(L + 1), is the conjugate transpose of

[0150] In step 1063, according to the modal order and the second decomposition result, the third Hankel matrix and the fourth Hankel matrix are reconstructed.

[0151] In the embodiment of the present invention, according to the first M columns of and the first M columns of

[0152]

[0153] wherein, Y1 is the third Hankel matrix, is the first M columns of is the first M columns of is the conjugate transpose of

[0154] According to the first M columns of and the first M columns of

[0155]

[0156] wherein, Y2 is the fourth Hankel matrix, is the first M columns of is the conjugate transpose of

[0157] In step 1064, according to the generalized eigenvalues of the matrix pencil composed of the third Hankel matrix and the fourth Hankel matrix, the signal modal poles are calculated.

[0158] In the embodiment of the present invention, the signal modal poles are calculated according to the seventh formula, and the seventh formula is

[0159]

[0160] Among them, z is the signal modal pole, and eig() is the operation of finding the generalized eigenvalues of the matrix. is the pseudo-inverse matrix of the third Hankel matrix Y1.

[0161] Through the seventh formula, the modal poles z=(z1, z2,..., z M ) T of each mode are obtained.

[0162] In step 1065, according to the signal modal poles, the signal modal residues are calculated by the least squares method.

[0163] In the embodiment of the present invention, according to the signal modal poles z calculated in step 1064, the signal modal residues b=(b1, b2,..., b M ) T are calculated by the least squares method, that is

[0164]

[0165] where is the (N-1)th power of the modal pole.

[0166] In step 1066, according to the signal modal poles and the signal modal residues, the parameters of the oscillatory signal are calculated.

[0167] In the embodiment of the present invention, the parameters of each component of the oscillatory signal are calculated according to the eighth formula, and the eighth formula is

[0168]

[0169] where α l is the damping factor of each component of the oscillatory signal, f l is the frequency of each component of the oscillatory signal, A l is the amplitude of each component of the oscillatory signal, is the phase of each component of the oscillatory signal, f s is the sampling frequency of the oscillatory signal, M is the modal order, l is the lth component, b l is the residue of the lth mode, z l is the signal modal pole of the lth mode, Re() represents taking the real part, Im() represents taking the imaginary part, abs() represents taking the modulus value, and angle() represents taking the angle.

[0170] Among them, the oscillatory signal includes subsynchronous and / or supersynchronous oscillatory signals.

[0171] has significantly enhanced anti-noise performance compared with the MP method, and the parameter identification accuracy is higher.

[0172] An embodiment of the present invention proposes a method (HSLRA-MP) that combines Hankel structure low-rank approximation with matrix pencil (MP) to online identify the parameters of sub / supersynchronous oscillation signals and improve their noise resistance. The basic idea of the HSLRA-MP method proposed by the present invention is to use singular value decomposition (SVD) and average the elements parallel to the sub-diagonal in the Hankel structure to alternately and rapidly approximate the low-rank Hankel matrix of the ideal sub / supersynchronous oscillation signal to effectively suppress noise, and then use MP to accurately calculate its parameters. At the same time, fast singular value decomposition (Fast-SVD) is used instead of general SVD to accelerate the convergence rate of HSLRA, enabling it to quickly suppress noise.

[0173] The following conducts a comparative analysis of the identification results of the method of the present invention with the MP method and Prony method in the prior art.

[0174] Add Gaussian white noise with [30, 50] dB and an interval of 5 dB to the original signal respectively, and conduct parameter identification tests on the Prony, MP, and the method provided by the embodiment of the present invention to obtain the absolute errors of each component parameter (amplitude, frequency, and damping factor) and retain two decimal places, as shown in Tables 1, 2, and 3.

[0175] Table 1. Absolute errors of the identification results of the Prony method

[0176]

[0177] Table 2. Absolute errors of the identification results of the MP method

[0178]

[0179]

[0180] Table 3. Absolute errors of the identification results of the method provided by the embodiment of the present invention

[0181]

[0182] From the result comparison in Tables 1, 2, and 3, it can be seen that the parameter identification of the Prony method is seriously distorted in the presence of noise and has the worst noise resistance. The MP method has a certain noise resistance and relatively high parameter identification accuracy. The method of the present invention

[0183] In the embodiments of the present invention, by filtering the measurement signal and estimating the modal order, it is determined whether the measurement signal contains subsynchronous and / or supersynchronous oscillation signals. If the measurement signal contains subsynchronous and / or supersynchronous oscillation signals, the filtered signal is subjected to Hankel structured low-rank approximation according to the modal order to obtain a reconstructed signal; the parameters of the oscillation signal are calculated by a matrix constraint method. By combining the Hankel structured low-rank approximation and the matrix constraint method, online identification of the parameters of subsynchronous and / or supersynchronous oscillation signals is realized, and their noise resistance is improved, thereby improving the accuracy of identifying the parameters of subsynchronous / supersynchronous oscillation signals.

[0184] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not imply the order of execution. The order of execution of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present invention.

[0185] The following are device embodiments of the present invention. For details not described in detail, reference may be made to the corresponding method embodiments above.

[0186] Figure 5 The structural schematic diagram of the device for identifying the parameters of the oscillation signal provided by the embodiments of the present invention is shown. For the sake of convenience of description, only the parts related to the embodiments of the present invention are shown and are described in detail as follows:

[0187] As Figure 5 shown, the device 5 for identifying the parameters of the oscillation signal includes: a measurement signal acquisition module 51, a filtering module 52, a modal order estimation module 53, a judgment module 54, a reconstruction module 55, and an oscillation signal parameter acquisition module 56;

[0188] The measurement signal acquisition module 51 is configured to execute the measurement signal acquisition step, and the measurement signal acquisition step includes acquiring a measurement signal;

[0189] The filtering module 52 is configured to perform low-pass filtering on the acquired measurement signal to obtain a filtered signal;

[0190] The modal order estimation module 53 is configured to estimate the modal order of the filtered signal to obtain an estimated signal and the modal order;

[0191] The judgment module 54 is configured to judge whether the estimated signal contains an oscillation signal. If the estimated signal does not contain an oscillation signal, it goes to the measurement signal acquisition step, where the oscillation signal includes a subsynchronous oscillation signal and / or a supersynchronous oscillation signal;

[0192] If the judgment module 54 judges that the estimated signal contains an oscillation signal, the reconstruction module 55 is configured to perform Hankel structured low-rank approximation on the filtered signal according to the modal order to obtain a reconstructed signal;

[0193] The oscillation signal parameter acquisition module 56 is used to calculate the parameters of the oscillation signal by the matrix constraint method for the reconstructed signal.

[0194] In the embodiment of the present invention, by filtering the measurement signal and estimating the modal order, it is determined whether the measurement signal contains sub-synchronous and / or super-synchronous oscillation signals. If it contains sub-synchronous and / or super-synchronous oscillation signals, the Hankel structured low-rank approximation is performed on the filtered signal according to the modal order to obtain the reconstructed signal; the parameters of the oscillation signal are calculated by the matrix constraint method for the reconstructed signal. By combining the Hankel structured low-rank approximation and the matrix constraint method, the online identification of the parameters of the sub-synchronous and / or super-synchronous oscillation signals is realized, and its anti-noise performance is improved, thereby improving the accuracy of the identification of the parameters of the sub-synchronous / super-synchronous oscillation signals.

[0195] In a possible implementation manner, the modal order estimation module 53 is used to:

[0196] Construct the autocorrelation matrix of the filtered signal, and perform eigenvalue decomposition on the autocorrelation matrix to obtain an eigenvalue sequence arranged in descending order;

[0197] For each eigenvalue in the eigenvalue sequence, calculate the relative change rate of the eigenvalue. The relative change rate of the eigenvalue is used to represent the relative change between the eigenvalue and the adjacent two eigenvalues, and the obtained relative change rates are sorted in descending order to obtain the first Q relative change rates;

[0198] Judge the eigenvalues corresponding to each of the first Q relative change rates in sequence until the first eigenvalue that satisfies the preset verification condition is obtained, and calculate the modal order according to the sequence number of the relative change rate corresponding to the eigenvalue among the first Q relative change rates.

[0199] In a possible implementation manner, the preset verification condition is to satisfy the first formula, and the first formula is

[0200]

[0201] where λ k is used to represent the eigenvalue corresponding to the k-th relative change rate among the first Q relative change rates, β is used to represent the preset sensitivity coefficient, r is used to represent the rank of the autocorrelation matrix, and k is used to represent the sequence number of n k corresponding to the relative change rate among the first Q relative change rates;

[0202] The modal order estimation module 53 is further used to:

[0203] Calculate the modal order according to the second formula, and the second formula is

[0204]

[0205] Among them, M is used to represent the modal order.

[0206] In a possible implementation, the reconstruction module 55 is used to:

[0207] Execute the first Hankel matrix construction step, which includes constructing a first Hankel matrix, and the first Hankel matrix is the Hankel matrix of the filtered signal;

[0208] Perform a fast singular value decomposition on the first Hankel matrix to obtain a first decomposition result;

[0209] According to the modal order and the first decomposition result, reconstruct the signal Hankel matrix;

[0210] Judge whether the rank of the signal Hankel matrix is equal to the signal modal order. If the rank of the signal Hankel matrix is not equal to the signal modal order, then go to the first Hankel matrix construction step;

[0211] If the rank of the signal Hankel matrix is equal to the signal modal order, then obtain the reconstructed signal according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix.

[0212] In a possible implementation, the reconstruction module 55 is also used to:

[0213] Obtain the reconstructed signal according to the third formula, and the third formula is

[0214]

[0215] Among them, is the reconstructed signal, is the parallel element of the sub-diagonal of the signal Hankel matrix, and num(n) is the number of parallel elements of the sub-diagonal of the signal Hankel matrix.

[0216] In a possible implementation, the oscillation signal parameter acquisition module 56 is used to:

[0217] Construct a second Hankel matrix, and the second Hankel matrix is the Hankel matrix of the reconstructed signal;

[0218] Perform a fast singular value decomposition on the second Hankel matrix to obtain a second decomposition result;

[0219] According to the modal order and the second decomposition result, reconstruct the third Hankel matrix and the fourth Hankel matrix;

[0220] Calculate the signal modal poles according to the generalized eigenvalues of the matrix pencil composed of the third Hankel matrix and the fourth Hankel matrix;

[0221] Calculate the signal modal residues by the least squares method according to the signal modal poles;

[0222] Calculate the parameters of the oscillation signal based on the signal modal poles and signal modal residues.

[0223] In a possible implementation, the oscillation signal parameter acquisition module 56 is further configured to:

[0224] Represent the second decomposition result by a fourth formula, and the fourth formula is

[0225]

[0226] where Y is the second Hankel matrix, is an orthonormal matrix of size (N - L)×(N - L), is a diagonal matrix of size (N - L)×(L + 1), is an orthonormal matrix of size (L + 1)×(L + 1), is the conjugate transpose of;

[0227] Reconstruct the third Hankel matrix and the fourth Hankel matrix according to the modal order and the second decomposition result, including:

[0228] According to the first M columns of in the second decomposition result, the first M columns of and delete the last row to reconstruct the third Hankel matrix, and the third Hankel matrix is represented by a fifth formula, and the fifth formula is

[0229]

[0230] where Y1 is the third Hankel matrix, is the first M columns of, is the first M columns of and delete the last row, M is the modal order, is the conjugate transpose of;

[0231] According to the first M columns of in the second decomposition result, the first M columns of and delete the first row to reconstruct the fourth Hankel matrix, and the fourth Hankel matrix is represented by a sixth formula, and the sixth formula is

[0232]

[0233] where Y2 is the fourth Hankel matrix, is the first M columns of and delete the first row, is the conjugate transpose of.

[0234] In a possible implementation, the oscillation signal parameter acquisition module 56 is further configured to:

[0235] Calculate the signal modal poles according to the seventh formula, where the seventh formula is

[0236]

[0237] where z is the signal modal pole, and eig() is the operation of finding the generalized eigenvalue of the matrix, is the pseudo-inverse matrix of the third Hankel matrix Y1.

[0238] In a possible implementation, the oscillation signal parameter acquisition module 56 is further configured to:

[0239] Calculate the parameters of the oscillation signal according to the eighth formula, where the eighth formula is

[0240]

[0241] where α l is the damping factor of each component of the oscillation signal, f l is the frequency of each component of the oscillation signal, A l is the amplitude of each component of the oscillation signal, is the phase of each component of the oscillation signal, f s is the sampling frequency of the oscillation signal, M is the modal order, l is the l-th component, b l is the residue of the l-th mode, z l is the signal modal pole of the l-th mode, Re() represents taking the real part, Im() represents taking the imaginary part, abs() represents taking the modulus value, and angle() represents taking the angle.

[0242] The oscillation signal parameter identification device provided in this embodiment can be used to execute the steps in the above-mentioned oscillation signal parameter identification method embodiment, and its implementation principle and technical effects are similar, which will not be elaborated here in this embodiment.

[0243] Figure 6 is a schematic diagram of a terminal provided in an embodiment of the present invention. As Figure 6 shown, the terminal 6 in this embodiment includes: a processor 60, a memory 61, and a computer program 62 stored in the memory 61 and executable on the processor 60. When the processor 60 executes the computer program 62, it implements the steps in the above-mentioned oscillation signal parameter identification method embodiments, such as Figure 1 the steps 101 to 106 shown. Alternatively, when the processor 60 executes the computer program 62, it implements the functions of each module / unit in the above-mentioned device embodiments, such as Figure 5 the functions of the modules 51 to 56 shown.

[0244] Exemplarily, the computer program 62 can be divided into one or more modules / units, which are stored in the memory 61 and executed by the processor 60 to implement the present invention. The one or more modules / units can be a series of computer program instruction segments capable of performing specific functions, and these instruction segments are used to describe the execution process of the computer program 62 in the terminal 6.

[0245] The terminal 6 can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The terminal 6 may include, but is not limited to, a processor 60 and a memory 61. Those skilled in the art can understand that Figure 6 merely examples of the terminal 6, which do not constitute a limitation on the terminal 6, and may include more or fewer components than shown in the figure, or combine certain components, or different components. For example, the terminal may further include input / output devices, network access devices, a bus, etc.

[0246] The processor 60 can be a central processing unit (CPU), or can also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0247] The memory 61 can be an internal storage unit of the terminal 6, such as the hard disk or memory of the terminal 6. The memory 61 can also be an external storage device of the terminal 6, such as a plug-in hard disk equipped on the terminal 6, a smart media card (SMC), a secure digital (SD) card, a flash card, etc. Further, the memory 61 can also include both the internal storage unit and the external storage device of the terminal 6. The memory 61 is used to store the computer program and other programs and data required by the terminal. The memory 61 can also be used to temporarily store the data that has been output or is to be output.

[0248] Those skilled in the art can clearly understand that, for the convenience and conciseness of description, only the above division of each functional unit and module is used as an example. In actual applications, the above functions can be allocated to different functional units and modules according to needs, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. Each functional unit and module in the embodiment can be integrated into a processing unit, or each unit can exist physically alone, or two or more units can be integrated into one unit. The above integrated unit can be implemented in the form of hardware or in the form of a software functional unit. In addition, the specific names of each functional unit and module are only for the convenience of mutual distinction and do not limit the protection scope of this application. The specific working process of the units and modules in the above system can refer to the corresponding process in the foregoing method embodiment and will not be elaborated here.

[0249] In the above embodiments, the descriptions of the various embodiments have their own emphases. For the parts not detailed or recorded in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0250] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in combination with the embodiments disclosed herein can be implemented by electronic hardware, or by a combination of computer software and electronic hardware. Whether these functions are executed in the form of hardware or software depends on the specific application and design constraints of the technical solution. Professionals can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present invention.

[0251] In the embodiments provided by the present invention, it should be understood that the disclosed device / terminal and method can be implemented in other ways. For example, the device / terminal embodiments described above are only illustrative. For example, the division of the modules or units is only a logical function division, and there can be other division methods in actual implementation. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections to each other can be through some interfaces, and the indirect couplings or communication connections of the devices or units can be in electrical, mechanical or other forms.

[0252] The units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0253] In addition, in each embodiment of the present invention, each functional unit may be integrated into a processing unit, or each unit may exist physically alone, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of a software functional unit.

[0254] If the above-mentioned integrated module / unit is implemented in the form of a software functional unit and sold or used as an independent product, it may be stored in a computer-readable storage medium. Based on such an understanding, to implement all or part of the processes in the above-mentioned embodiment methods of the present invention, it may also be completed by instructing relevant hardware through a computer program. The computer program may be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-mentioned parameter identification methods of each oscillation signal embodiment may be implemented. Among them, the computer program includes computer program code, and the computer program code may be in the form of source code, object code, executable file or some intermediate form, etc. The computer-readable medium may include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard disk, magnetic disk, optical disc, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal, and software distribution medium, etc. It should be noted that the content included in the computer-readable medium may be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0255] The above-mentioned embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of each embodiment of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A parameter identification method for an oscillation signal, characterized in that, Including: Performing a measurement signal acquisition step, the measurement signal acquisition step including acquiring a measurement signal; Performing low-pass filtering on the acquired measurement signal to obtain a filtered signal; Performing modal order estimation on the filtered signal to obtain an estimated signal and a modal order; Judging whether an oscillation signal is included in the estimated signal. If the oscillation signal is not included in the estimated signal, then turning to the measurement signal acquisition step, where the oscillation signal includes a subsynchronous oscillation signal and / or a supersynchronous oscillation signal; If the oscillation signal is included in the estimated signal, then performing a first Hankel matrix construction step, the first Hankel matrix construction step including constructing a first Hankel matrix, the first Hankel matrix being the Hankel matrix of the filtered signal; Performing fast singular value decomposition on the first Hankel matrix to obtain a first decomposition result; Reconstructing a signal Hankel matrix according to the modal order and the first decomposition result; Judging whether the rank of the signal Hankel matrix is equal to the signal modal order. If the rank of the signal Hankel matrix is not equal to the signal modal order, then turning to the first Hankel matrix construction step; If the rank of the signal Hankel matrix is equal to the signal modal order, then obtaining a reconstructed signal according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix; Calculating the parameters of the oscillation signal by performing matrix constraint method on the reconstructed signal; The performing modal order estimation on the filtered signal to obtain an estimated signal and a modal order includes: Constructing an autocorrelation matrix of the filtered signal, and performing eigenvalue decomposition on the autocorrelation matrix to obtain an eigenvalue sequence arranged in descending order; For each eigenvalue in the eigenvalue sequence, calculating the relative change rate of the eigenvalue, the relative change rate of the eigenvalue being used to represent the relative change between the eigenvalue and two adjacent eigenvalues, and sorting the obtained relative change rates in descending order to obtain the first Q relative change rates; Sequentially judging each eigenvalue corresponding to each relative change rate in the first Q relative change rates until obtaining the first eigenvalue that satisfies a preset verification condition, and calculating the modal order according to the serial number of the relative change rate corresponding to the eigenvalue in the first Q relative change rates; The preset verification condition is to satisfy a first formula, and the first formula is Among them, λ k is used to represent the eigenvalue corresponding to the k-th relative change rate among the first Q relative change rates, β is used to represent a preset sensitivity coefficient, r is used to represent the rank of the autocorrelation matrix, and k is used to represent the sequence number of the relative change rate corresponding to λ k among the first Q relative change rates; The calculating the modal order according to the serial number of the relative change rate corresponding to the eigenvalue in the first Q relative change rates includes: calculating the modal order according to a second formula, and the second formula is Where M is used to represent the modal order.

2. The method according to claim 1, characterized in that The obtaining a reconstructed signal according to the mean value of the parallel elements of the sub-diagonal of the signal Hankel matrix includes: Obtaining a reconstructed signal according to a third formula, and the third formula is Among them, is the reconstructed signal, are the elements parallel to the sub-diagonal of the signal Hankel matrix, and num(n) is the number of elements parallel to the sub-diagonal of the signal Hankel matrix.

3. The method according to claim 1, characterized in that, The calculating the parameters of the oscillation signal by performing matrix constraint method on the reconstructed signal includes: Constructing a second Hankel matrix, the second Hankel matrix being the Hankel matrix of the reconstructed signal; Performing fast singular value decomposition on the second Hankel matrix to obtain a second decomposition result; Reconstruct a third Hankel matrix and a fourth Hankel matrix according to the modal order and the second decomposition result; Calculate the signal modal poles according to the generalized eigenvalues of the matrix pencil formed by the third Hankel matrix and the fourth Hankel matrix; Calculate the signal modal residues by the least squares method according to the signal modal poles; Calculate the parameters of the oscillating signal according to the signal modal poles and the signal modal residues.

4. The method according to claim 3, wherein Represent the second decomposition result by a fourth formula, and the fourth formula is where Y is the second Hankel matrix, is an orthonormal matrix of size (N - L)×(N - L), is a diagonal matrix of size (N - L)×(L + 1), is an orthonormal matrix of size (L + 1)×(L + 1), is the conjugate transpose of; The reconstructing the third Hankel matrix and the fourth Hankel matrix according to the modal order and the second decomposition result includes: According to the first \(M\) columns in the second decomposition result, the first \(M\) columns of, the first \(M\) columns of and deleting the last row to reconstruct the third Hankel matrix, the third Hankel matrix is represented by the fifth formula, and the fifth formula is wherein, Y1 is the third Hankel matrix, is the first M columns of, is the first M columns of and deleting the last row, M is the modal order, is the conjugate transpose of; According to the first M columns in the second decomposition result , the first M columns of and deleting the first row to reconstruct the fourth Hankel matrix, the fourth Hankel matrix is represented by the sixth formula, and the sixth formula is where Y2 is the fourth Hankel matrix, is the first M columns of and deleting the first row, is the conjugate transpose of 5. The method according to claim 4, wherein The calculating the signal modal poles according to the generalized eigenvalues of the matrix pencil formed by the third Hankel matrix and the fourth Hankel matrix includes: Calculate the signal modal poles according to a seventh formula, and the seventh formula is where z is the signal mode pole, and eig() is an operation for finding the generalized eigenvalues of a matrix. is the pseudo-inverse matrix of the third Hankel matrix Y1.

6. The method according to claim 5, wherein The calculating the parameters of the oscillating signal according to the signal modal poles and the signal modal residues includes: Calculate the parameters of the oscillating signal according to an eighth formula, and the eighth formula is where α l is the damping factor of each component of the oscillation signal, f l is the frequency of each component of the oscillation signal, A l is the amplitude of each component of the oscillation signal, is the phase of each component of the oscillation signal, f s is the sampling frequency of the oscillation signal, M is the modal order, l is the l-th component, b l is the residue of the l-th mode, z l is the signal modal pole of the l-th mode, Re() represents taking the real part, Im() represents taking the imaginary part, abs() represents taking the modulus value, and angle() represents taking the angle.

7. A terminal, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1 to 6 above.

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