Broadband oscillation signal component analysis method based on non-iterative classification interpolation

Abstract

The invention relates to a broadband oscillation signal component analysis method based on non-iterative classification interpolation. The method comprises the following steps: firstly, carrying out modeling and time domain sampling on a random broadband oscillation signal to obtain a sampling signal; then windowing Fourier transform and twiddle factor correction are carried out on the sampling signals; then, a frequency rough estimation sequence is determined based on the corrected sampling signal; then, oscillation frequency separation is carried out based on the frequency rough estimation sequence, and oscillation frequency and non-oscillation frequency are determined through a classification interpolation formula; and finally, determining a non-oscillation amplitude, an oscillation amplitude and a damping factor by adopting a least square method based on the sampling signal, the oscillation frequency and the non-oscillation frequency. That is to say, signal component analysis and parameter calculation can be quickly carried out under the condition that the number of components in the signal is unknown and component models are different through the non-iterative classification interpolation and the least square method.

Description

Technical Field

[0001] The present application relates to the technical field of signal and data analysis, and in particular to a method for analyzing broadband oscillation signal components based on non-iterative classification interpolation. Background Art

[0002] With the large-scale integration of new energy sources into the power grid, the oscillation characteristics in the power system are no longer limited to low-frequency or subsynchronous oscillations within 100 Hz, but are developing towards a wider frequency. This change results in broadband oscillations and non-oscillating components such as harmonics and interharmonics having similar frequency bands, and the number of different types of components is random, which increases the difficulty of detection. Therefore, when performing signal component analysis, it is necessary not only to deal with fundamental spectrum leakage, but also to consider the energy coupling between oscillations and non-oscillations. In addition, the damping characteristics of the oscillating component make it different from harmonics and interharmonics. It is necessary to model the oscillating component as an exponentially damped sine model and the non-oscillating component as a sine model, and distinguish them when solving the parameters.

[0003] In recent years, researchers at home and abroad have proposed many methods for analyzing oscillation signal components. The main methods include: discrete Fourier transform (DFT), iterative interpolation Fourier transform, and Planny method (PRONY). However, when analyzing broadband oscillation signals with random components, these methods often require additional iterations or matrix operations to obtain prior information such as the number of signal components. At the same time, the detection accuracy of these methods is not ideal.

[0004] Therefore, in the related art, there is an urgent need for a method that can quickly and accurately analyze random broadband oscillation signals. Summary of the invention

[0005] Based on this, it is necessary to provide a broadband oscillation signal component analysis method based on non-iterative classification interpolation that can quickly and accurately analyze random broadband oscillation signals in response to the above technical problems.

[0006] In a first aspect, the present application provides a method for analyzing broadband oscillation signal components based on non-iterative classification interpolation. The method comprises:

[0007] Modeling and time-domain sampling of random broadband oscillation signals are performed to obtain sampling signals;

[0008] Performing windowed Fourier transform and rotation factor correction on the sampled signal;

[0009] Determine a rough frequency estimation sequence based on the corrected sampled signal;

[0010] Separating the oscillation frequency based on the rough frequency estimation sequence, and determining the oscillation frequency and the non-oscillation frequency by a classification interpolation formula;

[0011] The non-oscillation amplitude, the oscillation amplitude and the damping factor are determined by using the least square method based on the sampling signal, the oscillation frequency and the non-oscillation frequency.

[0012] Optionally, in one embodiment of the present application, the sampling signal is as follows:

[0013]

[0014] Among them, A, f, are the amplitude (V), frequency (Hz), initial phase (°), σ v is the damping factor of the oscillation component, which is a constant, n = 0, 1, 2, ..., N-1, N is the total number of sampling points, t s =1 / f s is the sampling period, f s is the sampling frequency, V is the number of oscillating components, and U is the number of non-oscillating components.

[0015] Optionally, in one embodiment of the present application, the frequency domain signal obtained by performing windowed Fourier transform and correction on the sampled signal and the frequency domain signal after rotation factor correction are as follows:

[0016]

[0017] Among them, X w (k) is the frequency domain signal obtained by windowed Fourier transform, is the corrected frequency domain signal, M is the total number of components contained in the signal, W(·) is the spectrum function of the Hanning window, Δf=1 / (t s N) represents the frequency resolution, k = 0, 1, 2, ..., K represents the spectral line corresponding to each frequency in the frequency domain signal, K = ceil (f s / 2), j is an imaginary unit.

[0018] Optionally, in one embodiment of the present application, the step of determining a rough frequency estimation sequence based on the corrected sampling signal includes:

[0019] Based on the damping characteristics of the oscillation, the difference spectrum corresponding to the oscillation component is identified.

[0020] Optionally, in one embodiment of the present application, the oscillation frequency and the non-oscillation frequency are obtained according to the following formula:

[0021]

[0022] Among them, k vi Indicates the oscillation frequency The corresponding peak spectrum, k ui Indicates non-oscillation frequency The corresponding peak spectrum line is introduced to assist in the description. 1i , R 2i As intermediate variables, they correspond to the oscillating component and the non-oscillating component, δ vi is the frequency correction coefficient corresponding to the oscillation component, δ ui is the frequency correction coefficient corresponding to the non-oscillating component.

[0023] Optionally, in one embodiment of the present application, a parameter matrix P = [p(1) p(2) … p(N)] is constructed by least squares method. T and X=[x(1) x(2) … x(N)], solve the matrix U=(P T P) -1 P T X T , the non-oscillating amplitude, oscillating amplitude, and damping factor are obtained according to the following formula:

[0024]

[0025] Among them, p(n) gives the construction method of the nth item in the parameter matrix P, is the non-oscillating amplitude, is the oscillation amplitude, is the damping factor, the auxiliary matrix I i (n) = [sin 2πf i T s n, cos 2πf i T s n], for the oscillating component, take For the non-oscillatory component, take is the number of oscillations, is the number of non-oscillations, U(i) represents the value of the i-th column in the matrix U, and U is Matrix of order.

[0026] The above-mentioned method for analyzing the components of broadband oscillation signals based on non-iterative classification interpolation firstly models and samples the random broadband oscillation signal in the time domain to obtain a sampled signal; then, the sampled signal is subjected to windowed Fourier transform and rotation factor correction; then, a rough frequency estimation sequence is determined based on the corrected sampled signal; then, the oscillation frequency is separated based on the rough frequency estimation sequence, and the oscillation frequency and non-oscillation frequency are determined by the classification interpolation formula; finally, the non-oscillation amplitude, oscillation amplitude, and damping factor are determined by the least squares method based on the sampled signal, the oscillation frequency, and the non-oscillation frequency. That is to say, by non-iterative classification interpolation and the least squares method, signal component analysis and parameter calculation can be quickly performed when the number of components in the signal is unknown and the component models are different. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 It is a flowchart of a method for analyzing components of a broadband oscillation signal based on non-iterative classification interpolation in one embodiment;

[0028] Figure 2 FIG. 4 is a schematic diagram of a broadband oscillation signal component analysis result in an embodiment. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0030] In one embodiment, Figure 1 As shown, a method for analyzing broadband oscillation signal components based on non-iterative classification interpolation is provided, comprising the following steps:

[0031] S1: Model and sample the random broadband oscillation signal in the time domain to obtain a sampled signal.

[0032] In the embodiment of the present application, the random broadband oscillation signal is assumed to be x(t), the total number of components contained in the signal is M, and the frequency of the oscillation component is recorded as f v , the number of oscillating components is denoted as V, and the frequency of the non-oscillating components is denoted as f u , the number of non-oscillating components is recorded as U. In one embodiment of the present application, the sampling signal obtained by sampling x(t) is as follows:

[0033]

[0034] Among them, A, f, are the amplitude (V), frequency (Hz), initial phase (°), σ v is the damping factor of the oscillation component, which is a constant, n=0,1,2,…,N-1, N is the total number of sampling points, t s =1 / f s is the sampling period, f s is the sampling frequency, V is the number of oscillating components, and U is the number of non-oscillating components.

[0035] S2: Performing windowed Fourier transform and rotation factor correction on the sampled signal.

[0036] In the embodiment of the present application, the signal x(n) is subjected to a windowed Fourier transform to obtain a frequency domain signal X w (k), the window function is selected as Hanning window. X is corrected by rotation factor w (k), we get

[0037] In one embodiment of the present application, the frequency domain signal obtained by performing windowed Fourier transform and correction on the sampled signal and the frequency domain signal after rotation factor correction are as follows:

[0038]

[0039] Among them, X w (k) is the frequency domain signal obtained by windowed Fourier transform, is the corrected frequency domain signal, M is the total number of components contained in the signal, W(·) is the spectrum function of the Hanning window, Δf=1 / (t s N) represents the frequency resolution, k = 0, 1, 2, ..., K represents the spectral line corresponding to each frequency in the frequency domain signal, K = ceil (f s / 2), d is the imaginary unit.

[0040] S3: Determine a rough frequency estimation sequence based on the corrected sampling signal.

[0041] In the embodiment of the present application, the spectrum The number of quasi-peak values ​​is taken as the estimated number of signal components The rough estimate sequence of the frequency of the signal components is Among them, f ri =k ri Δf, which means The spectrum corresponding to each quasi-peak in .

[0042] In one embodiment of the present application, the method of determining a rough frequency estimation sequence based on the corrected sampling signal comprises:

[0043] Based on the damping characteristics of the oscillation, the difference spectrum corresponding to the oscillation component is identified.

[0044] In one embodiment of the present application, the first or last τ points of x(n) are taken as x′(n) or x″(n), and the corresponding corrected spectrum is recorded as Select the difference spectrum The quasi-peak value of the spectrum is used as an alternative to the oscillation spectrum. According to the damping characteristics of the oscillation, the difference spectrum corresponding to the oscillation should satisfy the following conditions: 1) the amplitude ratio of the maximum difference spectrum and the amplitude ratio of other difference spectrums corresponding to the oscillation is within a certain range; 2) the difference spectrum corresponding to the oscillation has opposite monotonicity in the neighborhood on its left and right sides, that is:

[0045]

[0046] Among them, λ represents the proportionality coefficient, k vi represents the difference spectrum corresponding to the oscillation, k v0represents the maximum difference spectrum, and m is 0, 1, or 2. The spectrum that meets the above characteristics among the oscillation spectrum options is denoted as k v , whose number is recorded as

[0047] S4: Separate the oscillation frequency based on the rough frequency estimation sequence, and determine the oscillation frequency and the non-oscillation frequency by a classification interpolation formula.

[0048] In the embodiment of the present application, according to the principle of minimum Euclidean distance, within the search range Find it in and k v Δf is close to the point, and the set of similar points is recorded as at this time, for l 2 Norm and k v The data set with the smallest Δf distance is a set of roughly estimated oscillation frequencies. The principle of minimum Euclidean distance is that for any x, y, let Minimum, Indicates l 2 Norm. Take exist The complement of is a rough estimate of the non-oscillatory frequency, and the corresponding number of non-oscillatory components is denoted by

[0049] Then the oscillation frequency and the non-oscillation frequency are obtained according to the following formula:

[0050]

[0051] Among them, k vi Indicates the oscillation frequency The corresponding peak line, k ui Indicates non-oscillation frequency The corresponding peak line, To assist in the description, R is introduced. 1i , R 2i As intermediate variables, they correspond to the oscillating component and the non-oscillating component, δ vi is the frequency correction coefficient corresponding to the oscillation component, δ ui is the frequency correction coefficient corresponding to the non-oscillating component.

[0052] S5: Determine the non-oscillation amplitude, the oscillation amplitude, and the damping factor using the least square method based on the sampling signal, the oscillation frequency, and the non-oscillation frequency.

[0053] In the embodiment of the present application, the oscillation frequency obtained according to the sampling signal x(n) in S1 and S4 is Non-oscillation frequency By using the least squares method, construct the parameter matrix P = [p(1) p(2) … p(N)] T and X=[x(1) x(2) …x(N)], solve the matrix U=(P T P) -1 P T X T , the parameters corresponding to each component can be obtained.

[0054] In one embodiment of the present application, a parameter matrix P = [p(1) p(2) … p(N)] is constructed by the least squares method. T and X=[x(1) x(2) … x(N)], solve the matrix U=(P T P) -1 P T X T , the non-oscillating amplitude, oscillating amplitude, and damping factor are obtained according to the following formula:

[0055]

[0056] Among them, p(n) gives the construction method of the nth item in the parameter matrix P, is the non-oscillating amplitude, is the oscillation amplitude, is the damping factor, the auxiliary matrix I i (n) = [sin 2πf i T s n, cos2πf i T s n], for the oscillating component, take For the non-oscillatory component, take is the number of oscillations, is the number of non-oscillations, U(i) represents the value of the i-th column in the matrix U, and U is Matrix of order.

[0057] In one embodiment of the present application, discrete Fourier transform (DFT) and Planny algorithm (PRONY) are selected as comparison algorithms. s The sampling window length is 10 power frequency cycles, i.e. 0.2 seconds, and the proportional coefficient λ = 50. Indicates rounding down. Frequency error (Hz) and amplitude error (%) are used as test indicators to evaluate the algorithm performance. The selection of broadband oscillation test signal is as follows:

[0058]

[0059] Among them, t s =1 / fs is the sampling period, n=0, 1, 2, ..., N-1, and N=1000 is the total number of sampling points. The number of oscillating components V=2, the number of non-oscillating components U=4, and the corresponding component parameters are shown in Table 1, where the damping factor is a constant with a unit of 1.

[0060]

[0061] Table 1 Broadband oscillation signal component parameters

[0062] The noise snosie is set to zero, and the analysis accuracy of the broadband oscillation signal components is tested in the absence of noise. The results are shown in Table 2. The frequency estimation accuracy of each component is within 10 -2 The frequency measurement accuracy of the oscillation component can reach 10 -4 The estimation errors of amplitude and damping factor are small. The present invention can realize accurate analysis and estimation of broadband oscillation signal components with unknown component types and unknown component numbers.

[0063]

[0064] Table 2 Analysis results of broadband oscillation signal components of the present invention in the absence of noise

[0065] The noise s nosie The accuracy of broadband oscillation signal component analysis under noise conditions is compared between the proposed algorithm and the comparative algorithm, and the frequency error (Hz) and amplitude error (%) are presented in Figure 2 In. By Figure 2 It can be seen that the present invention has a certain anti-noise ability and has a relatively stable performance when estimating different components; at the same time, compared with the comparative algorithm, the present invention has basically improved the frequency and amplitude estimation accuracy by more than 20 times through a non-iterative method with a smaller computational cost.

[0066] In the above-mentioned method for analyzing the components of broadband oscillation signals based on non-iterative classification interpolation, first, the random broadband oscillation signal is modeled and sampled in the time domain to obtain a sampled signal; then, the sampled signal is subjected to a windowed Fourier transform and a rotation factor correction; then, a rough frequency estimation sequence is determined based on the corrected sampled signal; then, the oscillation frequency is separated based on the rough frequency estimation sequence, and the oscillation frequency and the non-oscillation frequency are determined by the classification interpolation formula; finally, the non-oscillation amplitude, oscillation amplitude, and damping factor are determined by the least squares method based on the sampled signal, the oscillation frequency, and the non-oscillation frequency. In other words, by using the non-iterative classification interpolation and least squares method, signal component analysis and parameter calculation can be performed quickly when the number of components in the signal is unknown and the component models are different.

[0067] It should be understood that, although the various steps in the flowcharts involved in the above-mentioned embodiments are displayed in sequence according to the indication of the arrows, these steps are not necessarily executed in sequence according to the order indicated by the arrows. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be executed in other orders. Moreover, at least a part of the steps in the flowcharts involved in the above-mentioned embodiments can include multiple steps or multiple stages, and these steps or stages are not necessarily executed at the same time, but can be executed at different times, and the execution order of these steps or stages is not necessarily to be carried out in sequence, but can be executed in turn or alternately with other steps or at least a part of the steps or stages in other steps.

[0068] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to the memory, database or other medium used in the embodiments provided in the present application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetoresistive random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. As an illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM). The database involved in each embodiment provided in this application may include at least one of a relational database and a non-relational database. Non-relational databases may include distributed databases based on blockchains, etc., but are not limited to this. The processor involved in each embodiment provided in this application may be a general-purpose processor, a central processing unit, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, etc., but are not limited to this.

[0069] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0070] The above-described embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the present application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the present application shall be subject to the attached claims.

Claims

1. A method for analyzing broadband oscillation signal components based on non-iterative classification interpolation, characterized in that: The method comprises: Modeling and time-domain sampling of random broadband oscillation signals are performed to obtain sampling signals; Performing windowed Fourier transform and rotation factor correction on the sampled signal; Determine a rough frequency estimation sequence based on the corrected sampled signal; Separating the oscillation frequency based on the rough frequency estimation sequence, and determining the oscillation frequency and the non-oscillation frequency by a classification interpolation formula; The non-oscillation amplitude, the oscillation amplitude and the damping factor are determined by using the least square method based on the sampled signal, the oscillation frequency and the non-oscillation frequency.

2. The method for analyzing broadband oscillation signal components based on non-iterative classification interpolation according to claim 1, characterized in that: The sampling signal is as follows: Among them, A, f, are the amplitude (V), frequency (Hz), initial phase (°), σ v is the damping factor of the oscillation component, which is a constant, n=0,1,2,…,N-1, N is the total number of sampling points, t s =1 / f s is the sampling period, f s is the sampling frequency, V is the number of oscillating components, and U is the number of non-oscillating components.

3. The method for analyzing broadband oscillation signal components based on non-iterative classification interpolation according to claim 1, characterized in that: The frequency domain signal obtained by performing windowed Fourier transform and correction on the sampled signal and the frequency domain signal after rotation factor correction are as follows: Among them, X w (k) is the frequency domain signal obtained by windowed Fourier transform, is the corrected frequency domain signal, M is the total number of components contained in the signal, W(·) is the spectrum function of the Hanning window, Δf=1 / (t s N) represents the frequency resolution, k = 0, 1, 2, ..., K represents the spectral lines corresponding to each frequency in the frequency domain signal, K = ceil (f s / 2), j is an imaginary unit.

4. The method for analyzing broadband oscillation signal components based on non-iterative classification interpolation according to claim 1, characterized in that: The method of determining a rough frequency estimation sequence based on the corrected sampling signal comprises: Based on the damping characteristics of the oscillation, the difference spectrum corresponding to the oscillation component is identified.

5. The method for analyzing broadband oscillation signal components based on non-iterative classification interpolation according to claim 1, characterized in that: The oscillation frequency and the non-oscillation frequency are obtained according to the following formula: Among them, k vi Indicates the oscillation frequency The corresponding peak spectrum, k ui Indicates non-oscillation frequency The corresponding peak spectrum line is introduced to assist in the description. 1i , R 2i As intermediate variables, they correspond to the oscillating component and the non-oscillating component, δ vi is the frequency correction coefficient corresponding to the oscillation component, δ ui is the frequency correction coefficient corresponding to the non-oscillating component.

6. The method for analyzing broadband oscillation signal components based on non-iterative classification interpolation according to claim 1, characterized in that: By using the least squares method, construct the parameter matrix P = [p(1)p(2)…p(N)] T and X=[x(1)x(2)…x(n)], solve the matrix U=(P T P) -1 P T X T , the non-oscillating amplitude, oscillating amplitude, and damping factor are obtained according to the following formula: Among them, p(n) gives the construction method of the nth item in the parameter matrix P, is the non-oscillating amplitude, is the oscillation amplitude, is the damping factor, the auxiliary matrix I i (n) = [sin2πf i T s n,cos2πf i T s n], for the oscillating component, take For the non-oscillatory component, take is the number of oscillations, is the number of non-oscillations, U(i) represents the value of the i-th column in the matrix U, and U is Matrix of order.

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