CN111027414B - Hankel matrix structure optimization method, hankel matrix structure optimization device, computing equipment and storage medium - Google Patents
Hankel matrix structure optimization method, hankel matrix structure optimization device, computing equipment and storage medium Download PDFInfo
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Abstract
The invention discloses a Hankel matrix structure optimization method, a Hankel matrix structure optimization device, a computing device and a storage medium, wherein the Hankel matrix structure optimization method comprises the following steps: setting an iteration parameter initial value, and setting the effective order of matrix reconstruction to k=1; constructing a Hankel matrix by taking different values of the matrix parameter L, reconstructing signals through SVD, and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L; detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not; taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1, and setting the row number of the matrix as N-L; n is the signal length, and N is more than L, so that the signal denoising efficiency can be effectively improved.
Description
Technical Field
The present invention relates to the field of signal processing technologies, and in particular, to a method and apparatus for optimizing a Hankel matrix structure, a computing device, and a storage medium.
Background
In the prior art, SVD (singular value decomposition) denoising algorithm has good stability and invariance, and has wide application in the field of signal processing, such as bearing vibration signal feature extraction, biological signal processing and the like. The main characteristic of SVD is that the signal can be decomposed into a plurality of component signals for linear superposition, the denoising signal is reconstructed by selecting useful components, and the denoising effect of SVD is determined by the Hankel matrix structure (including the number of rows and columns) and the effective singular value (or the effective order). At present, a common method for determining the Hankel matrix structure is a maximum dimension method, namely, the difference between the number of rows and the number of columns of the matrix is 1 as much as possible, the constructed matrix is square or very close to square, but in practical application, it is found that if the denoising signal-to-noise ratio is used as a reference index, the denoising effect of the square Hankel matrix is not ideal, the number of singular values required to be calculated is large, the calculation time is long, and therefore the calculation efficiency is low.
Disclosure of Invention
The present invention aims to solve at least one of the technical problems existing in the prior art. Therefore, the invention provides a Hankel matrix structure optimization method which can effectively improve the denoising efficiency of signals.
According to an embodiment of the first aspect of the present invention, a Hankel matrix structure optimization method includes:
setting an iteration parameter initial value, and setting the effective order of matrix reconstruction to k=1;
constructing a Hankel matrix by taking different values of the matrix parameter L, reconstructing signals through SVD, and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L;
detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not;
taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1, and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
The Hankel matrix structure optimization method provided by the embodiment of the invention has at least the following beneficial effects: the obtained signal data are constructed into a Hankel matrix, different values are taken for matrix parameters L, signals are reconstructed through SVD, the signal to noise ratio is calculated, a relation curve between the signal to noise ratio and the matrix parameters L is obtained, a first signal to noise ratio curve which has a symmetrical structure and has symmetrical global maximum peaks and the peaks are positioned at two ends is selected, a characteristic signal to noise ratio curve is obtained, the coordinates of the first peak point of the obtained characteristic signal to noise ratio curve are taken as the values of the matrix parameters L, a new matrix parameters L are obtained, the Hankel matrix is constructed, at the moment, singular values of the Hankel matrix are fewer, the signal denoising efficiency can be effectively improved, and more signal details can be reserved.
According to some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of matrix columns to l+1, and setting the number of matrix rows to N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max Setting the effective order k as k=k+1 if a characteristic signal-to-noise ratio curve is not obtained, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal-to-noise ratio to obtain a relation curve of the signal-to-noise ratio and the matrix parameters L, and detecting whether the relation curve is the characteristic signal-to-noise ratio curve or not until the effective order k is equal to a preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
According to some embodiments of the invention, further comprising: if the relation curve is detected to be not the characteristic signal-to-noise ratio curve, adding 1 to the effective order, taking different values of the matrix parameter L in a preset range to construct a Hankel matrix, reconstructing signals through SVD, and calculating the signal-to-noise ratio to obtain the relation curve of the signal-to-noise ratio and the matrix parameter L until the relation curve is detected to be the characteristic signal-to-noise ratio curve.
According to some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of matrix columns to l+1, and setting the number of matrix rows to N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
In a second aspect of the embodiment of the present invention, there is provided a Hankel matrix structure optimization apparatus, including:
the initial value setting module is used for setting an iteration parameter initial value and setting the effective order of matrix reconstruction to k=1;
the relation curve construction module is used for taking different values of the matrix parameter L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L;
the relation curve detection module is used for detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not;
the matrix parameter extraction module is used for taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1 and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
According to some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of matrix columns to l+1, and setting the number of matrix rows to N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max Setting the effective order k as k=k+1 if a characteristic signal-to-noise ratio curve is not obtained, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal-to-noise ratio to obtain a relation curve of the signal-to-noise ratio and the matrix parameters L, and detecting whether the relation curve is the characteristic signal-to-noise ratio curve or not until the effective order k is equal to a preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
According to some embodiments of the invention, further comprising: if the relation curve is detected to be not the characteristic signal-to-noise ratio curve, adding 1 to the effective order, taking different values of the matrix parameter L in a preset range to construct a Hankel matrix, reconstructing signals through SVD, and calculating the signal-to-noise ratio to obtain the relation curve of the signal-to-noise ratio and the matrix parameter L until the relation curve is detected to be the characteristic signal-to-noise ratio curve.
According to some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of matrix columns to l+1, and setting the number of matrix rows to N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
In a third aspect of the embodiments of the present invention, a computing device is provided, including a memory, a processor, and computer instructions stored on the memory and executable on the processor, where the processor implements the steps of the Hankel matrix structure optimization method when executing the instructions.
In a fourth aspect of the embodiments of the present invention, there is provided a computer readable storage medium storing computer instructions, wherein the instructions, when executed by a processor, implement the steps of the Hankel matrix structure optimization method.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
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The foregoing and/or additional aspects and advantages of the invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings in which:
FIG. 1 is a flowchart of a Hankel matrix structure optimization method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a computing device according to an embodiment of the invention;
FIG. 3 is a diagram of polarization branch parameters according to an embodiment of the present invention;
FIG. 4 is a graph showing SNR at different orders according to an embodiment of the present invention;
FIG. 5 is a graph showing SNR at different orders according to another embodiment of the present invention;
FIG. 6 is a Hankel matrix denoising index diagram of various structures according to an embodiment of the present invention;
FIG. 7 is a graph of measured signal versus signal-to-noise characteristic of an embodiment of the present invention;
fig. 8 is a diagram of SVD denoising signals according to an embodiment of the present invention, in which different matrices are selected.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
In the description of the present invention, it should be understood that references to orientation descriptions such as upper, lower, front, rear, left, right, etc. are based on the orientation or positional relationship shown in the drawings, are merely for convenience of description of the present invention and to simplify the description, and do not indicate or imply that the apparatus or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and thus should not be construed as limiting the present invention.
In the description of the present invention, a number means one or more, a number means two or more, and greater than, less than, exceeding, etc. are understood to not include the present number, and above, below, within, etc. are understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, unless explicitly defined otherwise, terms such as arrangement, installation, connection, etc. should be construed broadly and the specific meaning of the terms in the present invention can be reasonably determined by a person skilled in the art in combination with the specific contents of the technical scheme.
Referring to fig. 2, components of the computing device 1000 include, but are not limited to, a memory 1100 and a processor 1200. Processor 1200 is coupled to memory 1100 via bus 1300 and database 1600 is used to store data.
The computing device 1000 also includes an access device 1400, the access device 1400 enabling the computing device 1000 to communicate via one or more networks 1500. Examples of such networks include the Public Switched Telephone Network (PSTN), a Local Area Network (LAN), a Wide Area Network (WAN), a Personal Area Network (PAN), or a combination of communication networks such as the internet. The access device 1400 may include one or more of any type of network interface, wired or wireless (e.g., a Network Interface Card (NIC)), such as an IEEE802.11 Wireless Local Area Network (WLAN) wireless interface, a worldwide interoperability for microwave access (Wi-MAX) interface, an ethernet interface, a Universal Serial Bus (USB) interface, a cellular network interface, a bluetooth interface, a Near Field Communication (NFC) interface, and so forth.
In some embodiments of the invention, the above-described components of computing device 1000, as well as other components not shown in FIG. 3, may be connected to each other, such as by a bus. It should be understood that the block diagram of the computing device illustrated in FIG. 3 is for exemplary purposes only and is not intended to limit the scope of the present invention. Those skilled in the art may add or replace other components as desired.
Wherein the processor 1200 may perform the steps of the adaptive view method shown in fig. 1. Fig. 1 shows a flowchart of a Hankel matrix structure optimization method according to an embodiment of the invention, including steps 100 to 400.
Assume that a one-dimensional sampling signal is
y＝[y(1),y(2),…,y(N)] T (1)
Hankel matrix with dimension (N-L) × (l+1) can be constructed based on phase space theory:
wherein N is the length of the signal, L is a matrix parameter, and the selection of L determines the denoising effect, and L < N.
When the sampled signal contains additive noise, the matrix Y can be expressed as y=x+w (3)
X represents a Hankel matrix of (N-L) X (L+1) constructed from the original signal, and W represents a Hankel matrix of (N-L) X (L+1) constructed from noise. The matrix Y is subjected to singular value decomposition to obtain the following form:
in the formula (4), U and V are orthogonal matrices in (N-L) x (N-L) and (L+1) x (L+1), S is a diagonal matrix in (N-L) x (L+1), and the main diagonal element is a singular value of a matrix Y, which can be expressed as:
where q=min { (N-L), (l+1) }, the singular value sequence satisfies σ 1 ≥σ 2 ≥…≥σ q And is more than or equal to 0. From equation (4), the matrix after singular value decomposition can be further represented as a linear superposition of multiple components, where each component can be represented by the product of a singular value and its corresponding left and right singular vectors.
The denoising concept of SVD decomposition is to reconstruct a matrix by selecting the first m larger singular values, but note that the reconstructed matrix is no longer a Hankel matrix. Since most signals exist in vector form rather than in matrix form, in order to obtain denoised signals, it is necessary to convert the reconstructed matrix into vector form, often by arithmetic averaging of the anti-diagonal of the reconstructed matrix.
In addition to selecting effective singular values, the structure of the Hankel matrix is an important factor affecting the quality of SVD denoising. A common method is to make the number of rows and columns of the matrix as close and maximum as possible, i.e., (N-L) - (l+1) =1, and this matrix structure determination method is called a maximum dimension method. The Hankel matrix determined by the maximum dimension method has good denoising effect, but in practical application, a smaller matrix structure is found to be selected, so that better denoising effect can be achieved. The reason for this result may be that the matrix structure is too large, resulting in a dispersion of the energy of the original signal, and a portion of the dispersion of the signal energy into the noise is eliminated, resulting in a lower signal-to-noise ratio after denoising. In order to retain signal energy, the number of columns of the matrix is determined to be 2, the number of rows is N-1, the matrix structure can retain signals to the greatest extent, noise is retained to the greatest extent, and the denoising result is poor.
In order to more clearly illustrate the influence of the matrix structure on the denoising quality of the polarized current signal, a simulation signal is selected, as shown in fig. 3, it is known that the polarized current is formed by overlapping six branch currents, the time constant of the 6 th branch is longest, the current change amplitude of the 5 th and 6 th polarized branches is not large in the previous 1 minute according to the attenuation rule of the polarized current, and the polarized current amplitude of the two branches can be smaller than that of the other 4 branches according to the ohm law. If the noise is severe, the current of the last two branches is easily submerged.
Gaussian noise with the mean value of 0 and the standard deviation of 2.2361 mu V is added, the sampling frequency is 100Hz, and the time is 10s. The length of the obtained signal is 1000, the effective orders of the obtained matrix are 2 and 3, and the matrix parameter L is set to be 4-998. The signal to noise ratio curve of the reconstructed signal is shown in fig. 4. The two signal-to-noise ratio curves are symmetrical, symmetrical wave peaks exist in the curves, the wave peaks are distributed at two ends, and the signal-to-noise ratio curve with the order of 2 is more obvious in characteristics. L tends to stabilize at a signal to noise ratio of 200-800, but at a distance from the maximum. When L is less than or equal to 100 or greater than or equal to 900, the signal to noise ratio of the denoising signal approaches an optimal value. Comparing the signal to noise ratio of the two curves can find that the curve with the order of 2 has a significantly larger amplitude, which indicates that the noise easily floods the branch current with small amplitude. According to the signal-to-noise ratio curve, the Hankel matrix should be rectangular to obtain a better denoising effect.
In order to more reasonably determine the structure of the Hankel matrix, the embodiment of the invention provides a Hankel matrix structure optimization method based on a signal-to-noise ratio index. The signal-to-noise ratio is calculated by a snr function of Matlab, and the snr function is calculated as follows:
xs＝snr(s) (6)
where s represents the signal denoised using SVD and xs represents the calculated signal to noise ratio. The signal-to-noise ratio is used as a matrix structure selection index, the signal-to-noise ratio of the denoising signals under the same order and different matrix structures is calculated, and the functional relationship between the signal-to-noise ratio and the matrix parameters can be obtained as follows:
snr＝f(L),L∈(10,N-10) (7)
and calculating signal-to-noise ratio curves of different orders to obtain a set phi:
and selecting a first signal-to-noise ratio curve which has a symmetrical structure and has a symmetrical global maximum peak and the peaks are positioned at two ends, namely a characteristic signal-to-noise ratio curve, taking the coordinate corresponding to the first peak point as the value of a matrix parameter L, and then determining a proper singular value reconstruction signal.
Referring to fig. 1, a flowchart of a Hankel matrix structure optimization method according to an embodiment of the present invention is shown, including steps 100 to 400.
Step S100: an iteration parameter initial value is set, and a matrix reconstruction effective order is set to k=1.
Step S200: and constructing a Hankel matrix by taking different values of the matrix parameter L, reconstructing signals through SVD, and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L.
Step S300: and detecting whether the relation curve is a characteristic signal-to-noise ratio curve.
Step S400: taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1, and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
The Hankel matrix structure optimization method provided by the embodiment of the invention has at least the following beneficial effects: the obtained signal data are constructed into a Hankel matrix, different values are taken for matrix parameters L, signals are reconstructed through SVD, the signal to noise ratio is calculated, a relation curve between the signal to noise ratio and the matrix parameters L is obtained, a first signal to noise ratio curve which has a symmetrical structure and has symmetrical global maximum peaks and the peaks are positioned at two ends is selected, a characteristic signal to noise ratio curve is obtained, the coordinates of the first peak point of the obtained characteristic signal to noise ratio curve are taken as the values of the matrix parameters L, a new matrix parameters L are obtained, the Hankel matrix is constructed, at the moment, singular values of the Hankel matrix are fewer, the signal denoising efficiency can be effectively improved, and more signal details can be reserved.
In some specific embodiments, the setting the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, and setting the number of columns of the matrix to l+1, and setting the number of rows of the matrix to N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max If the characteristic signal-to-noise ratio curve is not obtained, setting the effective order k as k=k+1, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal-to-noise ratio to obtain a relation curve of the signal-to-noise ratio and the matrix parameters L, and detecting whether the relation curve is the characteristic signal-to-noise ratio curve or not until the effective order k is equal to the preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
In some specific embodiments, if the relation curve is detected to be not a characteristic signal-to-noise ratio curve, adding 1 to the effective order, taking different values of the matrix parameter L in a preset range to construct a Hankel matrix, reconstructing a signal through SVD and calculating the signal-to-noise ratio to obtain the relation curve of the signal-to-noise ratio and the matrix parameter L until the relation curve is detected to be the characteristic signal-to-noise ratio curve.
In some specific embodiments, the setting the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, and setting the number of columns of the matrix to l+1, and setting the number of rows of the matrix to N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
The method for optimizing the matrix structure of Hankel according to an embodiment of the present invention will be described in detail with reference to a specific embodiment. It is to be understood that the following description is exemplary only and is not intended to limit the invention in any way.
Step 1: setting an iteration parameter initial value, namely, a matrix reconstruction effective order k=1;
step 2: and L takes different values to construct a Hankel matrix, and the signal to noise ratio is calculated by reconstructing the signal through SVD to obtain a relation curve of the signal to noise ratio and L.
Step 3: judging whether the curve is a characteristic signal-to-noise ratio curve, if not, adding 1 to k, and returning to the step 2; if yes, enter step 4;
step 4: taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, wherein the number of matrix columns is (L+1), and the number of matrix rows is (N-L);
step 5: repeating steps 2 and 3 until when k=k max The iteration ends.
Specifically, the denoising effect is represented by a signal-to-noise ratio (SNR), a Root Mean Square Error (RMSE), a waveform Relative Error (RE), and a goodness-of-fit (R). Where x represents the original signal, xd represents the denoised signal,representing the mean.
The signal length is taken to be 1000, the range of the reconstruction order of the selected matrix is 1-10, the range of the L value is 10-990, and the calculation result of the signal-to-noise ratio curve is shown in figure 5 (the signal-to-noise ratio curves with the orders of 6 and 7). The figure shows that a characteristic signal-to-noise ratio curve appears when the reconstruction order is 6, and the coordinate corresponding to the first peak value is 99, so that the matrix parameter L can be determined to be 99, the matrix structure after optimization is 901×100, the effective order is 2, the denoising index is shown in fig. 6, and the denoising index of the Hankel matrix (namely L=500) determined by the maximum dimension method is also shown in the table. In contrast, when l=99, the signal-to-noise ratio of the denoising signal is improved by about 19%, the root mean square error and the waveform relative error are smaller, and the fitting goodness is closer to 1, which indicates that the denoising signal is effectively reserved in the aspects of waveform and signal amplitude. The Hankel matrix structure determined by the maximum dimension method is 500 multiplied by 501, singular value decomposition is carried out on the matrix, 500 singular values are required to be decomposed, the optimized matrix only needs to decompose 100 singular values, and the calculated amount of the optimized matrix is 20% of the calculated amount of the maximum dimension matrix in terms of the calculated amount required by singular value decomposition.
In order to illustrate that the Hankel matrix after the structure optimization has excellent denoising performance, the denoising result of the singular value decomposition iteration method with the matrix structure of (N-1) x 2 is compared, the effective iteration number is 24, the signal to noise ratio calculation result is shown in fig. 6, and compared with the singular value decomposition iteration, the signal to noise ratio index of the denoising signal after the matrix structure optimization is improved by 70%, the waveform relative error is improved by 60%, the root mean square error is reduced by 69%, and the fitting goodness is improved by about 9%. Comparing the three matrix structures, wherein the matrix constructed by L is too large, and the effective components of the denoised signals are removed too much along with noise, so that the denoising method can be regarded as overdose; l is taken to be too small, so that the constructed matrix of 1 is small in noise removal degree and can be regarded as undernoise reduction; the denoising index of the matrix denoising signal constructed by L-taking 99 is the best of the three, and the matrix structure is proper, so that the useful signal is not removed, and too much noise is not reserved. This is equivalent to a compromise between over-noise reduction and under-noise reduction, where the de-noise signal is brought as close to the ideal signal as possible.
In some specific applications, the transformer polarized current field sampling signal is shown in fig. 7 (a), the collection meter is agilent 34461a, and the sampling period is 0.413s. The signal length is 613, the signal is vertical reduced in the initial stage, the amplitude attenuation is extremely fast, the signal attenuation speed is obviously reduced in the middle and later stages, and the amplitude change slow part is covered by noise. The signals are constructed into Hankel matrixes, singular value decomposition is carried out on the Hankel matrixes, characteristic signal-to-noise ratio curves are obtained according to the method, the curves are completely symmetrical and have two symmetrical peaks distributed at two ends, L can be determined to be 23 by taking the peak coordinates of the first peak, the corresponding matrix structure is 590 multiplied by 24, the number of effective singular values is 3, the obtained denoising signals are shown in fig. 8 (a), compared with the sampled signals, the denoised signals basically completely retain signal trend, noise contained in signals at the middle and later stages is removed, and the attenuation degree of the signals at the initial stage is smaller. The matrix structure determined by the maximum dimension method is 307×307, the number of effective singular values is 6, and the denoising signal is shown in fig. 8 (b). Compared with the noise-containing signal, the signal trend is kept, but the amplitude of the noise-removing signal in the initial stage is obviously much smaller, and the noise-removed signal is too smooth, and part of detail information is removed. From the calculation amount analysis, the optimized matrix only needs to decompose 24 singular values, the matrix with the largest dimension needs to decompose 307 singular values, the calculation time is obviously increased, and the calculation efficiency is far lower than that of the matrix after optimization.
The denoising results of the SVD denoising method and the SVD iteration method after matrix structure optimization are shown in fig. 8 (a) and (c). The SVD iteration number is set to be 10, the matrix structure is 612 multiplied by 2, the denoising signal change trend of the two methods is almost the same when seen from a curve, but the SVD iteration method is not as fine as SVD after Hankel matrix optimization in terms of signal details. An excessive number of SVD iterations removes the useful signal, while a too small number of iterations does not remove the noise effectively. Therefore, selecting the number of iterations in processing the actual data is a cumbersome problem. The same problem exists in the SVD iterative method and the maximum dimension method denoising result, namely the amplitude attenuation degree of the initial stage of the denoising signal is very large, and as can be clearly seen from fig. 8 (c), the amplitude of the initial stage of the denoising signal of the SVD iterative method is obviously smaller than that of the matrix denoising signal after optimization. It is obvious that the SVD iterative denoising method removes part of signals in the initial stage as noise, and the Hankel matrix denoising signals after structure optimization not only well reserve effective signal components, but also realize effective denoising of signals in the middle and rear stages.
In the embodiment of the invention, in the process of denoising the polarized current of the transformer by using singular value decomposition, the difference of the Hankel matrix structure has great influence on denoising quality. In order to obtain a denoising signal with higher quality, an iterative matrix structure optimization method is provided. Calculating the signal to noise ratio of different matrix structures with different reconstruction orders to obtain a characteristic signal to noise ratio curve, and selecting the peak value coordinates of the curve to determine the number of rows and columns of the matrix. The denoising result of the actually measured polarized current signal shows that the dimension of the optimized matrix structure is small, and the signal-to-noise ratio of the denoising signal is higher than that of the maximum dimension matrix and the matrix with the column number of 2. Experimental results show that a larger matrix structure disperses the effective information contained in the singular values, and that a matrix structure that is too small retains too much more noise information, so that it is important to select an appropriate matrix structure.
Corresponding to the method embodiment, the embodiment of the invention also provides a Hankel matrix structure optimization device. The device comprises:
the initial value setting module is used for setting an iteration parameter initial value and setting the effective order of matrix reconstruction to k=1;
the relation curve construction module is used for taking different values of the matrix parameter L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L;
the relation curve detection module is used for detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not;
the matrix parameter extraction module is used for taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1 and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
In some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of columns of the matrix to l+1, and setting the number of rows of the matrix to N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max Setting the effective order k to k=k+1 if the characteristic signal-to-noise ratio curve is not obtained, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD, and calculating the signal-to-noise ratio to obtain the signal-to-noise ratioDetecting whether the relation curve is a characteristic signal-to-noise ratio curve or not according to the relation curve of the matrix parameter L until the effective order k is equal to the preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
In some embodiments of the invention, the method further comprises: if the relation curve is detected to be not the characteristic signal-to-noise ratio curve, adding 1 to the effective order, taking different values of the matrix parameter L in a preset range to construct a Hankel matrix, reconstructing signals through SVD, calculating the signal-to-noise ratio, and obtaining the relation curve of the signal-to-noise ratio and the matrix parameter L until the relation curve is detected to be the characteristic signal-to-noise ratio curve.
In some embodiments of the present invention, the taking the first peak point coordinate of the characteristic snr curve as the value of the matrix parameter L, setting the number of columns of the matrix to l+1, and setting the number of rows of the matrix to N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
The embodiment of the invention also provides a computing device which comprises a memory, a processor and computer instructions stored on the memory and capable of running on the processor, wherein the processor executes the instructions to realize the steps of the Hankel matrix structure optimization method.
The present invention also provides an exemplary embodiment of a computer-readable storage medium. It should be noted that, the technical solution of the storage medium and the technical solution of the above-mentioned Hankel matrix structure optimization method belong to the same concept, and details of the technical solution of the storage medium which are not described in detail can be referred to the description of the technical solution of the above-mentioned Hankel matrix structure optimization.
The foregoing describes specific embodiments of the present disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.
The computer instructions include computer program code that may be in source code form, object code form, executable file form, or some intermediate form, etc. The computer readable medium includes: any entity or device capable of carrying the computer program code, a recording medium, a computer memory, a Read Only Memory (ROM), a Random Access Memory (RAM), an electrical carrier signal, a telecommunication signal, a software distribution medium, and so forth. It should be noted that the computer readable medium contains content that can be appropriately scaled according to the requirements of jurisdictions in which such content is subject to legislation and patent practice, such as in certain jurisdictions in which such content is subject to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.
It should be noted that, for the sake of simplicity of description, the foregoing method embodiments are all expressed as a series of combinations of actions, but it should be understood by those skilled in the art that the present application is not limited by the order of actions described, as some steps may be performed in other order or simultaneously according to the present application. Further, those skilled in the art will also appreciate that the embodiments described in the specification are all preferred embodiments, and that the acts and modules referred to are not necessarily required in the present application.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and for parts of one embodiment that are not described in detail, reference may be made to related descriptions of other embodiments.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of one of ordinary skill in the art without departing from the spirit of the present invention.
Claims (8)
1. The Hankel matrix structure optimization method is characterized by comprising the following steps:
setting an iteration parameter initial value, and setting the effective order of matrix reconstruction to k=1;
constructing a Hankel matrix by taking different values of the matrix parameter L, reconstructing signals through SVD, and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L;
detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not, wherein the characteristic signal-to-noise ratio curve is a curve which has a symmetrical structure, has symmetrical global maximum peaks and has peaks at two ends;
if the relation curve is detected to be not the characteristic signal-to-noise ratio curve, adding 1 to the effective order, taking different values of a matrix parameter L in a preset range to construct a Hankel matrix, reconstructing a signal through SVD and calculating the signal-to-noise ratio to obtain the relation curve of the signal-to-noise ratio and the matrix parameter L until the relation curve is detected to be the characteristic signal-to-noise ratio curve;
taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1, and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
2. The method for optimizing a Hankel matrix structure according to claim 1, wherein the taking the coordinate of the first peak point of the characteristic signal-to-noise ratio curve as the value of the matrix parameter L, the number of matrix columns is l+1, and the number of matrix rows is N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max Setting the effective order k as k=k+1 if a characteristic signal-to-noise ratio curve is not obtained, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal-to-noise ratio to obtain a relation curve of the signal-to-noise ratio and the matrix parameters L, and detecting whether the relation curve is the characteristic signal-to-noise ratio curve or not until the effective order k is equal to a preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
3. The method for optimizing a Hankel matrix structure according to claim 1, wherein the taking the coordinate of the first peak point of the characteristic signal-to-noise ratio curve as the value of the matrix parameter L, the number of matrix columns is l+1, and the number of matrix rows is N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
4. An optimization device for a Hankel matrix structure, which is characterized by comprising:
the initial value setting module is used for setting an iteration parameter initial value and setting the effective order of matrix reconstruction to k=1;
the relation curve construction module is used for taking different values of the matrix parameter L to construct a Hankel matrix, reconstructing signals through SVD and calculating the signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameter L;
the relation curve detection module is used for detecting whether the relation curve is a characteristic signal-to-noise ratio curve or not, wherein the characteristic signal-to-noise ratio curve is a curve which has a symmetrical structure and has a symmetrical global maximum peak and the peaks are positioned at two ends, if the relation curve is detected to be not the characteristic signal-to-noise ratio curve, the effective order is added with 1, a Hankel matrix is constructed by taking different values of a matrix parameter L in a preset range, a signal is reconstructed through SVD, the signal-to-noise ratio is calculated, and the relation curve of the signal-to-noise ratio and the matrix parameter L is obtained until the relation curve is detected to be the characteristic signal-to-noise ratio curve;
the matrix parameter extraction module is used for taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of a matrix parameter L, setting the column number of the matrix as L+1 and setting the row number of the matrix as N-L;
wherein N is the signal length, and N > L.
5. The Hankel matrix structure optimization device according to claim 4, wherein the taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of the matrix parameter L, the number of matrix columns is l+1, and the number of matrix rows is N-L further includes: if the value of the effective order k is smaller than the preset maximum effective order k max And the characteristic signal-to-noise ratio curve is not obtained, thenSetting the effective order k as k=k+1, then taking different values of matrix parameters L to construct a Hankel matrix, reconstructing signals through SVD and calculating signal to noise ratio to obtain a relation curve of the signal to noise ratio and the matrix parameters L, and detecting whether the relation curve is a characteristic signal to noise ratio curve or not until the effective order k is equal to a preset maximum effective order k max Obtaining a plurality of characteristic signal-to-noise ratio curves, wherein a maximum effective order k is preset max Taking the minimum value of N-L and L+1.
6. The Hankel matrix structure optimization device according to claim 4, wherein the taking the first peak point coordinate of the characteristic signal-to-noise ratio curve as the value of the matrix parameter L, setting the number of matrix columns to l+1 and setting the number of matrix rows to N-L further includes: and re-determining SVD singular values based on the matrix according to the matrix obtained by the matrix parameter L.
7. A computing device comprising a memory, a processor, and computer instructions stored on the memory and executable on the processor, wherein the processor, when executing the instructions, implements the steps of the method of any one of claims 1 to 3.
8. A computer readable storage medium storing computer instructions which, when executed by a processor, implement the steps of the method of any one of claims 1 to 3.
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