CN115146672A - Dense-frequency modal separation reconstruction method and device - Google Patents
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Abstract
The application relates to a dense-frequency modal separation and reconstruction method and a device, which belong to the technical field of dense-frequency modal, wherein the dense-frequency modal separation and reconstruction method comprises the steps of obtaining an original vibration time sequence signal, and separating the original vibration time sequence signal into a plurality of single-modal time sequence signals; constructing a Hankel matrix corresponding to each monomodal time sequence signal; the method has the advantages that the method can overcome the problem of reconstruction modal distortion of a TSVD method, improve modal reconstruction precision, effectively realize dense-frequency modal separation reconstruction, and lay a foundation for subsequently obtaining more accurate modal parameter identification.
Description
Technical Field
The application belongs to the technical field of dense frequency modes, and particularly relates to a dense frequency mode separation reconstruction method and device.
Background
The vibration detection technology is one of important technologies in safety detection of various large structures, plays an important role in safety production of the large structures, and is widely applied to safety detection of various large equipment and buildings closely related to life of people, such as rotating machinery, bridges, rails and the like. Modal decomposition and parameter identification thereof are core algorithms of the vibration detection technology, and play a key role in the vibration detection process. The vibration modes are inherent characteristics of the elastic structure, and each mode has specific mode parameters which can reflect the health condition of the structure. Dense modes are created if the natural frequencies of the modes are close together and the respective damping ratios are large. In dense modal parameter identification, complex multi-modal signals need to be decomposed into single-modal signals, and then a simple and reliable single-modal parameter identification method is adopted to identify modal parameters. Therefore, the separation and reconstruction of the dense-frequency mode into the single mode is a key technology for mode decomposition and parameter identification. Although the conventional dense-frequency mode separation and reconstruction method such as short-time Fourier transform, wavelet transform, empirical mode decomposition and the like can solve the problem of dense-frequency mode separation, filters are overlapped with each other and adjacent modes interfere with each other during mode reconstruction, so that the mode information is distorted after reconstruction. In the related art, a single-mode signal is obtained by reconstructing a dense-frequency mode signal after hard truncation by a TSVD (Truncated Singular Value Decomposition) method, but this method may cause waveform distortion and loss of mode components, and in practical application, due to noise interference of a working environment, the dense-frequency mode distortion may be more serious, which may affect the subsequent mode parameter identification effect.
Disclosure of Invention
In order to overcome at least a certain extent that the prior art carries out dense frequency mode separation reconstruction by a TSVD method, which causes waveform distortion, when noise interference of a working environment exists, the method and the device for separating and reconstructing the dense-frequency mode solve the problems that the dense-frequency mode distortion is more serious and the subsequent modal parameter identification effect is influenced.
In a first aspect, the present application provides a dense-frequency modal separation reconstruction method, including:
acquiring an original vibration time sequence signal;
separating the original vibration time series signal into a plurality of single-mode time series signals;
constructing an initial Hankel matrix corresponding to each monomodal time sequence signal;
performing iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
and restoring the Hankel matrix after the morphological reconstruction meeting the iteration exit condition into a single-mode time sequence reconstruction signal.
Further, the separating the original vibration time series signal into a plurality of single-mode time series signals includes:
respectively calculating a power spectrum and a Fourier spectrum of an original vibration time series signal;
determining each modal boundary according to the power spectrum;
cutting the Fourier spectrum by using a Meyer wavelet filter bank and using the frequency corresponding to each modal boundary as a filter value to obtain a plurality of Fourier spectrum fragments;
carrying out Fourier inversion on each Fourier spectrum segment to obtain a wavelet coefficient corresponding to each mode;
and performing inverse discrete wavelet transform according to the wavelet coefficient corresponding to each mode to obtain a plurality of single-mode time sequence signals.
Further, the determining each modal boundary according to the power spectrum includes:
acquiring each extreme point on the power spectrum;
and determining a modal boundary corresponding to each modal according to each extreme point, wherein the modal boundary is a trough position at two ends of each extreme point on the power spectrum.
Further, the iterative computation of truncated singular value decomposition and matrix form reconstruction for each initial Hankel matrix includes:
performing singular value decomposition on each initial Hankel matrix, and truncating singular values;
performing matrix form reconstruction on the data after the singular value truncation;
judging whether the Hankel matrix after morphological reconstruction meets an iteration exit condition;
if not, performing singular value decomposition and morphological reconstruction on the reconstructed Hankel matrix again;
and if so, judging that the reconstructed Hankel matrix meets the iteration exit condition.
Further, the singular value decomposition and the truncation of the singular value for each initial Hankel matrix include:
decomposing the initial Hankel matrix into a product of a left singular vector, a right singular vector and a diagonal matrix, wherein the diagonal matrix comprises a plurality of singular values;
and reserving a preset number of singular values in the diagonal matrix, and setting other singular values to zero to truncate the singular values.
Further, the preset number is 2, and the iteration exit condition includes:
the rank of the Hankel matrix after morphological reconstruction is equal to 2.
Further, the matrix form reconstruction of the data after truncation of the singular values includes:
performing matrix reconstruction according to the relationship between the reconstructed matrix form and the ideal truth-value matrix, wherein the relationship between the reconstructed matrix form and the ideal truth-value matrix is | | A n+1 -A true || F ≤||A n -A true || F Wherein A is true Is an ideal truth matrix, A n Is Hankel matrix obtained after n-th TSVD and form reconstruction, A n+1 And obtaining a Hankel matrix after n +1 th truncated singular value decomposition and morphological reconstruction.
In a second aspect, the present application provides a dense frequency modal separation reconstruction apparatus, including:
the acquisition module is used for acquiring an original vibration time sequence signal;
a separation module for separating the original vibration time series signal into a plurality of single mode time series signals;
the construction module is used for constructing an initial Hankel matrix corresponding to each monomodal time sequence signal;
the reconstruction module is used for performing iterative calculation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
and the recovery module is used for recovering the Hankel matrix which meets the iteration exit condition and is subjected to form reconstruction into a single-mode time sequence reconstruction signal.
The technical scheme provided by the embodiment of the application can have the following beneficial effects:
the embodiment of the invention provides a dense-frequency modal separation reconstruction method and a device, wherein the dense-frequency modal separation reconstruction method comprises the steps of obtaining an original vibration time sequence signal; separating the original vibration time series signal into a plurality of single-mode time series signals; constructing an initial Hankel matrix corresponding to each monomodal time sequence signal; performing iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix; the reconstructed Hankel matrix meeting the iteration quitting condition is restored into a single-mode time sequence reconstruction signal, so that the reconstructed Hankel matrix can keep the morphological characteristics of the Hankel matrix, the reconstruction precision of the TSVD method is improved, the problem of reconstruction modal distortion can be effectively overcome, and a foundation is laid for the subsequent identification of more accurate modal parameters.
It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the application.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the present application and together with the description, serve to explain the principles of the application.
Fig. 1 is a flowchart of a dense-frequency modal separation reconstruction method according to an embodiment of the present disclosure.
Fig. 2 is a flowchart of a dense-frequency modal separation reconstruction method according to another embodiment of the present application.
Fig. 3 is a schematic filtering diagram of a Meryer filter bank according to an embodiment of the present application.
FIG. 4 is a graph of a detected boundary and Autoregressive (AR) power spectrum provided in accordance with an embodiment of the present application.
Fig. 5 is a diagram illustrating a result of one calculation of the TSVD according to an embodiment of the present application.
Fig. 6 is a diagram illustrating results of an iterative calculation of TSVD according to an embodiment of the present application.
Fig. 7 is a time series diagram of the impulse response provided by an embodiment of the present application.
Fig. 8 is a fourier spectrum diagram of an impulse response provided in an embodiment of the present application.
Fig. 9 is an AR power spectrum obtained from an experiment provided in an embodiment of the present application.
Fig. 10 is a diagram of experimentally detected spectral boundaries provided in an embodiment of the present application.
Fig. 11 is a graph of the first 3 rd order modal spectrum of a signal after one-time TSVD separation reconstruction according to an embodiment of the present application.
Fig. 12 is a graph of the first 3 rd order modal spectrum of a signal after TSVD iterative separation reconstruction according to an embodiment of the present application.
Fig. 13 is a functional block diagram of a dense-frequency mode separation and reconstruction apparatus according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be described in detail below. It is to be understood that the embodiments described are only a few embodiments of the present application and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the examples given herein without making any creative effort, shall fall within the protection scope of the present application.
Fig. 1 is a flowchart of a dense-frequency modal separation and reconstruction method according to an embodiment of the present application, and as shown in fig. 1, the dense-frequency modal separation and reconstruction method includes:
s11: acquiring an original vibration time sequence signal;
s12: separating the original vibration time series signal into a plurality of single-mode time series signals;
s13: constructing an initial Hankel matrix corresponding to each monomodal time sequence signal;
s14: performing iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
s15: and restoring the Hankel matrix which meets the iteration exit condition and is subjected to the morphological reconstruction into a single-mode time sequence reconstruction signal.
Although the conventional dense-frequency modal separation reconstruction method such as short-time Fourier transform, wavelet transform, empirical mode decomposition and the like can solve the problem of dense-frequency modal separation, filters are overlapped with each other and adjacent modes interfere with each other during modal reconstruction, so that the modal information after reconstruction is distorted. In the related art, a single-mode signal is obtained by reconstructing a dense-frequency mode signal after hard truncation by a TSVD (Truncated Singular Value Decomposition) method, but this method may cause waveform distortion and loss of mode components, and in practical application, due to noise interference of a working environment, the dense-frequency mode distortion may be more serious, which may affect the subsequent mode parameter identification effect.
In this embodiment, the dense-frequency modal separation reconstruction method includes acquiring an original vibration time series signal; separating the original vibration time series signal into a plurality of single-mode time series signals; constructing an initial Hankel matrix corresponding to each monomodal time sequence signal; performing iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix; the reconstructed Hankel matrix meeting the iteration quitting condition is restored into a single-mode time sequence reconstruction signal, so that the reconstructed Hankel matrix can keep the morphological characteristics of the Hankel matrix, the reconstruction precision of the TSVD method is improved, the problem of reconstruction modal distortion can be effectively overcome, and a foundation is laid for the subsequent identification of more accurate modal parameters.
Fig. 2 is a flowchart of a method for separating and reconstructing a dense frequency mode according to another embodiment of the present application, and as shown in fig. 2, the method for separating and reconstructing a dense frequency mode includes:
s201: acquiring an original vibration time sequence signal;
s202: respectively calculating a power spectrum and a Fourier spectrum of an original vibration time series signal;
in this embodiment, the power spectrum is an Autoregressive (AR) power spectrum, and a Pburg forward-backward difference prediction algorithm is used to obtain a smooth spectral line.
S203: determining each modal boundary according to the power spectrum;
in this embodiment, determining each modal boundary according to the power spectrum includes:
s2031: acquiring each extreme point on the power spectrum;
s2032: and determining a modal boundary corresponding to each modal according to each extreme point, wherein the modal boundary is a trough position at two ends of each extreme point on the power spectrum.
As shown in fig. 3, ω n Is the modal frequency boundary contained in the spectrum, the dotted line is the transition region of the modal boundary, the filter boundary is at omega n And omega n+1 γ is a transition region parameter obtained from equation (2). Width of transition section 2 tau n Determined by equations (1), (2).
τ n ＝γ×u n (1)
The detected boundary and AR power spectrum are shown in fig. 4.
Confirming each modal boundary through the power spectrum can improve the accuracy of extracting the modal boundary.
S204: cutting the Fourier spectrum by using a Meyer wavelet filter bank and using the frequency corresponding to each modal boundary as a filter value to obtain a plurality of Fourier spectrum fragments;
s205: carrying out Fourier inversion on each Fourier spectrum segment to obtain a wavelet coefficient corresponding to each mode;
s206: performing inverse discrete wavelet transform according to the wavelet coefficient corresponding to each mode to obtain a plurality of single-mode initial signals;
the spectrum is filtered by using a Meyer wavelet filter bank, and the scale function of the filter
And wavelet function
As shown in equations (3) and (4), respectively, the scale function
For constructing wavelet low-pass filters, wavelet functions
Constructing a band-pass filter;
where ω is frequency, ω 1 Is the right boundary frequency of the first filter formed by the scaling function
And constructing, wherein the amplitude of the right boundary transition band is calculated by a cosine function, the amplitude of the position smaller than the frequency of the transition band is 1, and the amplitude of the position larger than the frequency of the transition band is 0. The other band-pass filters consisting of wavelet functions
Construction of omega n Is the n-th modal boundary frequency, ω, found on the spectrum 0 ＝0，ω n And the parameter of the filter transition section is equal to the requirement of the formula (2), and is generally 0.5.β (x) = x 4 (35-84x+70x 2 -20x 3 ) X is [0,1 ]]The band-pass filter has the advantages that the amplitude of the right boundary transition band of the band-pass filter is calculated by a cosine function, the amplitude of the left boundary transition band of the band-pass filter is calculated by a sine function, the amplitude of the middle part of the band-pass filter is 1, and the amplitudes of the rest positions of the band-pass filter are 0.
Then, performing inverse Fourier transform on the cut frequency spectrum to obtain wavelet coefficients, wherein the process is shown in formulas (5) and (6), IFFT represents inverse Fourier transform, tau is a convolution window parameter, t is a time parameter of the wavelet coefficients, n represents the serial number of a band-pass filter,<>representing the inner product, f (t) is the signal to be decomposed, f (ω) is the fourier transform of f (t).
Is a wavelet coefficient of a scale function,
wavelet coefficients that are wavelet functions;
and performing wavelet inverse transformation through the wavelet coefficients to obtain each modal initial signal, as shown in formulas (7) and (8), wherein f (t) is the reconstructed single modal initial signal.
Wherein f is 0 For the modal signal obtained by filtering with a scale function, f k The mode signal obtained by filtering the wavelet function represents convolution, k represents the sequence number of the single mode component, andthe bandpass filter order number should be used.
The Meyer wavelet filter bank is used for carrying out the wavelet filtering method, so that each separated mode can be reconstructed more accurately, and more accurate mode information can be obtained.
S207: constructing an initial Hankel matrix corresponding to each monomodal initial signal;
in some embodiments, constructing an initial Hankel matrix corresponding to each single-mode initial signal includes:
s2071: acquiring a single-mode time sequence initial signal x (k) corresponding to each single mode;
s2072: and constructing an initial Hankel matrix A corresponding to each single-mode initial signal according to the single-mode time sequence initial signal corresponding to each single mode.
Wherein 1< -N, m = N-N +1, N is the number of elements in a sequence signal x (k) = [ x (1), x (2), \8230;, x (N) ], and N is the number of matrix columns, determined by formula (10).
S208: decomposing the initial Hankel matrix into a product of a left singular vector, a right singular vector and a diagonal matrix, wherein the diagonal matrix comprises a plurality of singular values; the method comprises the following steps:
A＝UDV T (11)
wherein T represents a matrix transpose, A m×n (m is more than or equal to n) is a decomposed matrix, and the one-dimensional signals can be constructed into the matrix to be decomposed; u is formed by R m×m And V ∈ R n×n Is a left and right singular vector matrix, and the column vector u in the matrix i ，v i Are each AA T And A T The feature vector of A, the form of diagonal matrix D is shown as (12):
wherein the singular value σ 1 ≥σ 2 ≥……≥σ r Not less than 0 is A T The square root of the eigenvalue of a, writing equation (11) into the form of equation (13):
A＝σ 1 u 1 v T 1 +σ 2 u 2 v T 2 +...+σ r u r v T r (13)
s209: and reserving a preset number of singular values in the diagonal matrix, and setting other singular values to zero to truncate the singular values.
In this embodiment, the preset number is 2, and the truncated and reconstructed Hankel matrix includes:
s210: performing morphological optimization reconstruction by using a Hankel matrix subjected to truncation singular value decomposition;
in this embodiment, the matrix after the truncated singular value decomposition is used
Performing morphology optimization reconstruction, comprising:
will be provided with
The reverse diagonal elements are calculated according to (15) to reconstruct a time sequence
Wherein k is
Serial number of middle element(0,1…N-1),a ij Is that
The middle row is an element whose i column is j, and M is the number of elements satisfying i + j = k + 1.
Will be time-series
Reconfiguring a Hankel matrix
S211: for reconstructed Hankel matrix
Repeatedly carrying out truncated singular value decomposition and morphological optimization reconstruction, namely repeating steps 209 and 210
Up to the matrix
The rank is 2.
And multiple iteration singular value decomposition and optimization meet the following requirements:
wherein the content of the first and second substances,
is the n-th TSVD followed by a morphologically optimized Hankel matrix, A n+1 Is a Hankel matrix obtained after n +1 th truncated singular value decomposition and morphological reconstruction, A true Is an ideal truth matrix.
Thus, TSVD and form optimization are performed through continuous iteration, and more accurate matrix estimation can be obtained.
The reconstruction result obtained without iterative computation is shown in fig. 5, and an example obtained by restoring the Hankel matrix into a signal sequence after iterative decomposition and reconstruction is shown in fig. 6, a spectrum peak curve of the Hankel matrix should be an attenuated sine curve, so that the waveform of a front-section spectrum of the reconstruction result obtained without iterative computation is distorted, the attenuation characteristic is not obvious, and the Hankel matrix obtained through iterative decomposition and reconstruction maintains the morphological characteristic of the Hankel matrix.
S212: rank is 2 matrix
And restoring the single-mode time series reconstruction signal.
In some embodiments, experiments are performed by using a pull rod rotor model, wherein three aluminum alloy blocks in the pull rod rotor model are made of soft supporting materials, the obtained impact response time series data are shown in fig. 7, and the frequency spectrum after low-pass filtering is shown in fig. 8. As can be seen from fig. 8, the frequency band from 10KHz to 25KHz has more frequency density, and the AR power spectrum obtained by processing the signals in the frequency band from 10KHz to 25KHz is as shown in fig. 9, and it can be seen that the spectral line of the AR power spectrum is smoother than the fourier spectrum. The boundaries of the spectrum obtained based on the AR power spectrum are shown in fig. 10, and the modes in the spectrum are effectively separated.
The first 3 rd order mode spectrum of the separated reconstruction is as shown in fig. 11, and the first 3 rd order mode exponential attenuation form of the separated single mode is damaged, which may affect the identification of parameters such as damping. The iterative TSVD method is adopted to perform conformal optimization on the former three-order mode, the obtained result is shown in figure 12, the visible exponential attenuation form is well recovered, and accordingly clear parameters such as damping, frequency and the like can be identified.
In practical application, the distortion caused by mutual interference of close frequency modes is more serious because the close frequency modes are close to each other.
In the embodiment, more accurate modal components are obtained through matrix iteration, and each separated mode can be more accurately reconstructed by combining a Meryer wavelet filtering method, so that more accurate modal information is obtained.
An embodiment of the present invention provides a dense frequency modal separation and reconstruction device, which includes, as shown in a functional structure diagram in fig. 13:
an obtaining module 131, configured to obtain an original vibration time series signal;
a separation module 132 for separating the original vibration time series signal into a plurality of single mode time series signals;
a constructing module 133, configured to construct an initial Hankel matrix corresponding to each monomodal time series signal;
the reconstruction module 134 is configured to perform iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
and the recovery module 135 is configured to recover the Hankel matrix after the morphological reconstruction meeting the iteration exit condition into a single-modal time sequence reconstruction signal.
In the embodiment, an original vibration time sequence signal is obtained through an obtaining module; the separation module separates the original vibration time series signal into a plurality of single-mode time series signals; the construction module constructs an initial Hankel matrix corresponding to each monomodal initial signal; the reconstruction module carries out iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix; the recovery module recovers the Hankel matrix which meets the iterative quit condition and is subjected to form reconstruction into a single-mode time sequence reconstruction signal, can improve the reconstruction precision of the TSVD method, can effectively overcome the problem of reconstruction modal distortion, and lays a foundation for obtaining more accurate modal parameter identification in the follow-up process.
It is understood that the same or similar parts in the above embodiments may be mutually referred to, and the same or similar contents in other embodiments may be referred to for the contents which are not described in detail in some embodiments.
It should be noted that, in the description of the present application, the terms "first", "second", etc. are used for descriptive purposes only and are not to be construed as indicating or implying relative importance. Further, in the description of the present application, the meaning of "a plurality" means at least two unless otherwise specified.
Any process or method descriptions in flow charts or otherwise described herein may be understood as representing modules, segments, or portions of code which include one or more executable instructions for implementing specific logical functions or steps of the process, and the scope of the preferred embodiments of the present application includes other implementations in which functions may be executed out of order from that shown or discussed, including substantially concurrently or in reverse order, depending on the functionality involved, as would be understood by those reasonably skilled in the art of the present application.
It should be understood that portions of the present application may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, the various steps or methods may be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application specific integrated circuit having an appropriate combinational logic gate circuit, a Programmable Gate Array (PGA), a Field Programmable Gate Array (FPGA), or the like.
It will be understood by those skilled in the art that all or part of the steps carried out in the method of implementing the above embodiments may be implemented by hardware related to instructions of a program, which may be stored in a computer readable storage medium, and the program, when executed, includes one or a combination of the steps of the method embodiments.
In addition, functional units in the embodiments of the present application may be integrated into one processing module, or each unit may exist alone physically, or two or more units are integrated into one module. The integrated module can be realized in a hardware mode, and can also be realized in a software functional module mode. The integrated module, if implemented in the form of a software functional module and sold or used as a separate product, may also be stored in a computer-readable storage medium.
The storage medium mentioned above may be a read-only memory, a magnetic or optical disk, etc.
In the description herein, reference to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the application. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
Although embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application, and that variations, modifications, substitutions and alterations may be made to the above embodiments by those of ordinary skill in the art within the scope of the present application.
It should be noted that the present invention is not limited to the above-mentioned preferred embodiments, and those skilled in the art can obtain other products in various forms without departing from the spirit of the present invention, but any changes in shape or structure can be made within the scope of the present invention with the same or similar technical solutions as those of the present invention.
Claims (8)
1. A dense-frequency modal separation reconstruction method is characterized by comprising the following steps:
acquiring an original vibration time sequence signal;
separating the original vibration time series signal into a plurality of single-mode time series signals;
constructing an initial Hankel matrix corresponding to each monomodal time sequence signal;
performing iterative computation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
and restoring the Hankel matrix which meets the iteration exit condition and is subjected to the morphological reconstruction into a single-mode time sequence reconstruction signal.
2. The dense-frequency modal separation reconstruction method according to claim 1, wherein the separating the original vibration time-series signal into a plurality of single-modal time-series signals comprises:
respectively calculating a power spectrum and a Fourier spectrum of an original vibration time series signal;
determining each modal boundary according to the power spectrum;
cutting the Fourier spectrum by using a Meyer wavelet filter bank and using the frequency corresponding to each modal boundary as a filter value to obtain a plurality of Fourier spectrum fragments;
carrying out Fourier inversion on each Fourier spectrum segment to obtain a wavelet coefficient corresponding to each mode;
performing dispersion according to the wavelet coefficient corresponding to each mode and performing wavelet inverse transformation to obtain a plurality of single-mode time sequence signals.
3. The dense-frequency modal separation reconstruction method according to claim 2, wherein the determining respective modal boundaries from the power spectrum comprises:
acquiring each extreme point on the power spectrum;
and determining a modal boundary corresponding to each modal according to each extreme point, wherein the modal boundary is a trough position at two ends of each extreme point on the power spectrum.
4. The method for separating and reconstructing the dense frequency modes according to claim 1, wherein the iterative computation of truncated singular value decomposition and matrix morphology reconstruction for each initial Hankel matrix comprises:
performing singular value decomposition on each initial Hankel matrix, and truncating singular values;
performing matrix form reconstruction on the data after the singular value truncation;
judging whether the Hankel matrix after the morphological reconstruction meets an iteration exit condition;
if not, performing singular value decomposition and morphological reconstruction on the reconstructed Hankel matrix again;
and if so, judging that the reconstructed Hankel matrix meets the iteration exit condition.
5. The method for separating and reconstructing the dense frequency modes according to claim 4, wherein the performing singular value decomposition on each initial Hankel matrix and truncating singular values includes:
decomposing the initial Hankel matrix into a product of a left singular vector, a right singular vector and a diagonal matrix, wherein the diagonal matrix comprises a plurality of singular values;
and reserving a preset number of singular values in the diagonal matrix, and setting other singular values to zero to truncate the singular values.
6. The method according to claim 5, wherein the predetermined number is 2, and the iteration exit condition includes:
the rank of the Hankel matrix after morphological reconstruction is equal to 2.
7. The method for separating and reconstructing dense frequency modes according to claim 4, wherein the matrix reconstruction of the data after truncation of singular values includes:
performing matrix reconstruction according to the relationship between the reconstructed matrix form and the ideal truth-value matrix, wherein the relationship between the reconstructed matrix form and the ideal truth-value matrix is | | A n+1 -A true || F ≤||A n -A true || F Wherein A is true Is an ideal truth matrix, A n Is Hankel matrix obtained after n-th TSVD and form reconstruction, A n+1 And obtaining a Hankel matrix after n +1 th truncated singular value decomposition and morphological reconstruction.
8. A dense-frequency modal separation/reconstruction apparatus, comprising:
the acquisition module is used for acquiring an original vibration time sequence signal;
a separation module for separating the original vibration time series signal into a plurality of single mode time series signals;
the construction module is used for constructing an initial Hankel matrix corresponding to each monomodal time sequence signal;
the reconstruction module is used for performing iterative calculation of truncated singular value decomposition and matrix form reconstruction on each initial Hankel matrix;
and the recovery module is used for recovering the Hankel matrix which meets the iteration exit condition and is subjected to form reconstruction into a single-mode time sequence reconstruction signal.
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Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103246890A (en) * | 2013-05-15 | 2013-08-14 | 中国石油大学(华东) | Modal parameter recognizing method based on multi-input multi-output signal noise reduction |
| CN104360393A (en) * | 2014-10-20 | 2015-02-18 | 李闯 | Seismic data reconstruction method |
| CN109948286A (en) * | 2019-03-29 | 2019-06-28 | 华北理工大学 | Based on the signal decomposition method for improving experience wavelet decomposition |
| CN110967599A (en) * | 2019-12-11 | 2020-04-07 | 贵州电网有限责任公司 | Electric energy quality disturbance detection and positioning algorithm |
| CN112067116A (en) * | 2020-07-13 | 2020-12-11 | 东南大学 | Method for testing and analyzing impact vibration of medium and small bridges with noise resistance |
| CN112101089A (en) * | 2020-07-27 | 2020-12-18 | 北京建筑大学 | Signal noise reduction method and device, electronic equipment and storage medium |
| CN112904197A (en) * | 2021-01-25 | 2021-06-04 | 国网安徽省电力有限公司电力科学研究院 | Parameter identification-based mechanical vibration signal feature extraction method for high-voltage circuit breaker |
| US20210243054A1 (en) * | 2020-01-31 | 2021-08-05 | Kabushiki Kaisha Tokai Rika Denki Seisakusho | Communication device, information processing method, and storage medium |
| CN114021074A (en) * | 2021-11-01 | 2022-02-08 | 国网山西省电力公司临汾供电公司 | Information singular value decomposition reconstruction and semantic information error matrix verification system |
| CN114259240A (en) * | 2021-09-28 | 2022-04-01 | 大连大学 | Electroencephalogram signal dictionary learning method based on improved experience wavelet transformation |
-
2022
- 2022-06-20 CN CN202210698188.6A patent/CN115146672A/en active Pending
Patent Citations (10)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103246890A (en) * | 2013-05-15 | 2013-08-14 | 中国石油大学(华东) | Modal parameter recognizing method based on multi-input multi-output signal noise reduction |
| CN104360393A (en) * | 2014-10-20 | 2015-02-18 | 李闯 | Seismic data reconstruction method |
| CN109948286A (en) * | 2019-03-29 | 2019-06-28 | 华北理工大学 | Based on the signal decomposition method for improving experience wavelet decomposition |
| CN110967599A (en) * | 2019-12-11 | 2020-04-07 | 贵州电网有限责任公司 | Electric energy quality disturbance detection and positioning algorithm |
| US20210243054A1 (en) * | 2020-01-31 | 2021-08-05 | Kabushiki Kaisha Tokai Rika Denki Seisakusho | Communication device, information processing method, and storage medium |
| CN112067116A (en) * | 2020-07-13 | 2020-12-11 | 东南大学 | Method for testing and analyzing impact vibration of medium and small bridges with noise resistance |
| CN112101089A (en) * | 2020-07-27 | 2020-12-18 | 北京建筑大学 | Signal noise reduction method and device, electronic equipment and storage medium |
| CN112904197A (en) * | 2021-01-25 | 2021-06-04 | 国网安徽省电力有限公司电力科学研究院 | Parameter identification-based mechanical vibration signal feature extraction method for high-voltage circuit breaker |
| CN114259240A (en) * | 2021-09-28 | 2022-04-01 | 大连大学 | Electroencephalogram signal dictionary learning method based on improved experience wavelet transformation |
| CN114021074A (en) * | 2021-11-01 | 2022-02-08 | 国网山西省电力公司临汾供电公司 | Information singular value decomposition reconstruction and semantic information error matrix verification system |
Non-Patent Citations (2)
| Title |
|---|
| LI H,ET AL.: "Modal parameter estimation for jacket-type platforms using noisy free-vibration data: Sea test study", 《APPLIED OCEAN RESEARCH》 * |
| 罗治军,等: "一种改进型AR-EWT算法及其在振动模态分解中的应用研究", 《机械设计》 * |
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