CN113343952A - Transient characteristic time frequency analysis and reconstruction method - Google Patents

Transient characteristic time frequency analysis and reconstruction method Download PDF

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CN113343952A
CN113343952A CN202110894212.9A CN202110894212A CN113343952A CN 113343952 A CN113343952 A CN 113343952A CN 202110894212 A CN202110894212 A CN 202110894212A CN 113343952 A CN113343952 A CN 113343952A
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frequency
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CN113343952B (en
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陈小旺
冯志鹏
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University of Science and Technology Beijing USTB
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Abstract

The invention provides a transient characteristic time-frequency analysis and reconstruction method, and belongs to the technical field of mechanical equipment signal time-varying characteristic extraction. The method comprises the following steps: constructing a series of peak filters with different peak frequencies in an analysis frequency band; respectively acting the signals to be analyzed on each constructed peak filter to obtain peak filtering signals corresponding to each peak filter; wherein the signal to be analyzed is a vibration, displacement, sound or electrical signal of the target mechanical equipment; taking the envelope square signal of the peak filtering signal as a row vector corresponding to the peak frequency in a time frequency matrix, constructing the time frequency matrix of the signal to be analyzed, and extracting transient characteristics from the time frequency matrix; and adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signals by the amplitude correction coefficient to obtain the reconstructed transient characteristic. By adopting the method and the device, the problems of uncertainty limitation and cross term interference of the traditional linear or bilinear time-frequency analysis method can be solved.

Description

Transient characteristic time frequency analysis and reconstruction method
Technical Field
The invention relates to the technical field of extraction of time-varying characteristics of signals of mechanical equipment, in particular to a transient characteristic time-frequency analysis and reconstruction method.
Background
In the operation and maintenance process of mechanical equipment, dynamic signal testing is often required to be performed on a key mechanical structure, and beneficial characteristics are analyzed and extracted from a test signal, so that key information such as the dynamic characteristics and the health state of the mechanical equipment is judged, and targeted regulation and maintenance are guided. If the extracted features are inconsistent with the actual situation, false alarm or missing report of faults can be caused, so that economic loss is caused and even the operation safety is threatened. Therefore, an accurate signal feature extraction technology is very important for the operation and maintenance of mechanical equipment.
Transient characteristics in mechanical equipment signals are short in duration, amplitude changes are fast, accurate extraction is difficult, and the traditional time domain or frequency domain analysis method is difficult to accurately express the transient characteristics. For example, although the conventional time-domain waveform analysis can characterize the change of the amplitude with time, since the actual signal often contains multiple components (periodic frequency components, transient components, etc.), and different signal components may overlap in the time domain or the frequency domain, the time-domain waveform cannot accurately identify the amplitude information of different frequency components. Although traditional spectrum analysis can express different frequency components and corresponding amplitudes, the analyzed signals are required to have the characteristics of stationary or cyclostationarity, and therefore, the traditional spectrum analysis is not suitable for analyzing transient characteristics.
The time-frequency analysis can depict signals in three dimensions of time, frequency and amplitude, and is suitable for expression of transient characteristics. However, the amplitude of the transient feature exhibits rapid change and oscillation characteristics, and in order to accurately extract the transient feature, it is necessary to extract at least the occurrence time of the transient feature and the frequency value of amplitude oscillation. For this reason, the time-frequency analysis is required to have both high time resolution and frequency resolution. The traditional linear time-frequency distribution based on kernel function inner product transformation is restricted by Heisenberg uncertainty, and high time resolution and high frequency resolution cannot be obtained at the same time, so that the time-frequency fuzzy phenomenon is caused. Although the traditional bilinear time-frequency distribution based on the instantaneous autocorrelation function can obtain ideal time and frequency resolution, cross-term interference, namely false time-frequency characteristics, is inevitably generated in the calculation process, and the accurate extraction of transient characteristics is influenced.
The Chinese patent 201910602989.6 discloses a method for calculating the instantaneous cable force of a cable-supported bridge based on synchronous compression transformation. The method comprises the steps of firstly calculating short-time Fourier transform time-frequency distribution of the inhaul cable acceleration signal, and then compressing and concentrating the time-frequency distribution in the frequency direction by a synchronous compression method, so that the fuzzy phenomenon in the frequency direction is restrained, and the instantaneous frequency value is identified. The scheme has the advantages that the linear time frequency distribution time frequency fuzzy phenomenon caused by Heisenberg uncertainty is restrained through the time frequency distribution compression in the frequency direction, and the accuracy of instantaneous frequency identification is improved. However, for the time-frequency analysis of transient characteristics, although the compression of the time-frequency distribution in the frequency direction can suppress the frequency domain ambiguity to some extent and help to identify the oscillation frequency, the time-frequency distribution compression cannot suppress the ambiguity phenomenon in the time direction. In addition, the synchronous compression transformation method is a post-processing method, the problems of uncertainty limitation and cross term interference of the traditional linear or bilinear time-frequency analysis method are not completely solved, and the actual effect is still limited.
In addition, time domain reconstruction of transient time-frequency characteristics is also one of the difficult problems. Although some novel time-frequency analysis methods such as time-frequency rearrangement, adaptive iterative generalized demodulation and the like improve the accuracy of feature extraction to a certain extent, due to the fact that complex nonlinear characteristics exist in the calculation process, the time-domain waveform of the transient features cannot be effectively reconstructed from time-frequency distribution, namely the transient features cannot be separated from complex original signals.
Disclosure of Invention
The embodiment of the invention provides a transient characteristic time frequency analysis and reconstruction method, which can overcome the problems of uncertainty limitation and cross term interference of the traditional linear or bilinear time frequency analysis method.
The embodiment of the invention provides a transient characteristic time-frequency analysis and reconstruction method, which comprises the following steps:
constructing a series of peak filters with different peak frequencies in an analysis frequency band;
respectively acting the signals to be analyzed on each constructed peak filter to obtain peak filtering signals corresponding to each peak filter; wherein the signal to be analyzed is a vibration, displacement, sound or electrical signal of the target mechanical equipment;
taking the envelope square signal of the peak filtering signal as a row vector corresponding to the peak frequency in a time frequency matrix, constructing the time frequency matrix of the signal to be analyzed, and extracting transient characteristics from the time frequency matrix;
and adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signals by the amplitude correction coefficient to obtain the reconstructed transient characteristic.
Further, the constructing a series of peak filters with different peak frequencies in the analysis frequency band comprises:
the analysis frequency band is discretized into a series of characteristic frequencies, the discrete frequency is taken as a peak frequency, and a series of peak filters with different peak frequencies are constructed in the analysis frequency band.
Further, the discretizing the analysis frequency band into a series of characteristic frequencies, and taking the discrete frequency as a peak frequency, and constructing a series of peak filters with different peak frequencies in the analysis frequency band comprises:
within the analysis band, the selection being at equal or unequal frequency intervals
Figure 682868DEST_PATH_IMAGE001
A discrete frequency
Figure 858634DEST_PATH_IMAGE002
Wherein, in the step (A),
Figure 65756DEST_PATH_IMAGE003
，
Figure 617960DEST_PATH_IMAGE004
a serial number representing a discrete frequency is used,
Figure 210615DEST_PATH_IMAGE005
represents a discrete frequency sequence length;
at respective discrete frequencies
Figure 576524DEST_PATH_IMAGE002
For peak frequencies, corresponding peak filters are constructed
Figure 989051DEST_PATH_IMAGE006
。
Further, if the constructed peak filter is a second-order peak filter, its transfer function
Figure 830099DEST_PATH_IMAGE007
Comprises the following steps:
Figure 339578DEST_PATH_IMAGE008
wherein the content of the first and second substances,
Figure 60409DEST_PATH_IMAGE009
is composed of
Figure 773282DEST_PATH_IMAGE010
An argument in the transformation;
Figure 667288DEST_PATH_IMAGE011
is the peak frequency of the peak filter
Figure 719689DEST_PATH_IMAGE002
Corresponding angular frequency,;
Figure 673739DEST_PATH_IMAGE012
representing the overall normalized gain.
Further, the overall normalized gain
Figure 60858DEST_PATH_IMAGE012
Expressed as:
Figure 506358DEST_PATH_IMAGE013
wherein the content of the first and second substances,
Figure 928112DEST_PATH_IMAGE014
represents a passband bandwidth of
Figure 256325DEST_PATH_IMAGE015
A filter gain of
Figure 147052DEST_PATH_IMAGE016
Coefficients of the transfer function of time.
Further, the constructing a time-frequency matrix of the signal to be analyzed by using the envelope squared signal of the peak filtering signal as a row vector of the time-frequency matrix corresponding to the peak frequency, and the extracting transient characteristics from the time-frequency matrix includes:
calculating respective peak filtered signals
Figure 382861DEST_PATH_IMAGE017
Envelope squared signal of
Figure 659122DEST_PATH_IMAGE018
；
Number of constructional lines
Figure 705706DEST_PATH_IMAGE019
The number of rows is
Figure 67417DEST_PATH_IMAGE020
A null time-frequency matrix of; wherein the content of the first and second substances,
Figure 857650DEST_PATH_IMAGE020
is the length of the signal to be analyzed;
squaring the envelope
Figure 253996DEST_PATH_IMAGE018
And assigning a row vector of the corresponding peak frequency in the time-frequency matrix, namely: first of the time-frequency matrix
Figure 993852DEST_PATH_IMAGE021
A row, constructing a time-frequency matrix of the signal to be analyzed;
and extracting the occurrence time and the oscillation frequency of the transient characteristics from the time-frequency matrix of the signal to be analyzed.
Further, the peak-filtered signal
Figure 905176DEST_PATH_IMAGE017
Envelope squared signal of
Figure 233520DEST_PATH_IMAGE018
Expressed as:
Figure 484373DEST_PATH_IMAGE022
wherein the content of the first and second substances,
Figure 607181DEST_PATH_IMAGE023
representing the hubert transform.
Further, the adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signal by the amplitude correction coefficient to obtain the reconstructed transient characteristic includes:
according to the constructed time-frequency matrix of the signal to be analyzed, positioning the time-frequency range of the transient characteristic;
filtering the peak value in the time-frequency range of the transient characteristic
Figure 740222DEST_PATH_IMAGE017
Adding to obtain a superposed signal
Figure 324787DEST_PATH_IMAGE024
；
Will add the signal
Figure 180879DEST_PATH_IMAGE024
Is divided by the amplitude correction factor
Figure 989435DEST_PATH_IMAGE025
And obtaining the reconstructed transient characteristics.
Further, the amplitude correction coefficient
Figure 78613DEST_PATH_IMAGE025
Expressed as:
Figure 683514DEST_PATH_IMAGE026
wherein the content of the first and second substances,
Figure 971276DEST_PATH_IMAGE027
indicating a frequency of
Figure 153995DEST_PATH_IMAGE028
The magnitude-frequency response characteristic of the peak filter at time,
Figure 950044DEST_PATH_IMAGE029
indicating a frequency of
Figure 407570DEST_PATH_IMAGE030
The phase-frequency response curve value of the peak filter at time,
Figure 300571DEST_PATH_IMAGE031
a serial number representing a discrete frequency is used,
Figure 388613DEST_PATH_IMAGE032
representing the length of the discrete frequency sequence.
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
in the embodiment of the invention, a traditional linear or bilinear time-frequency analysis frame is skipped, and the constructed time-frequency matrix is not influenced by time-frequency fuzzy caused by Heisenberg uncertainty and is not interfered by cross terms, so that the constructed time-frequency matrix can have higher time resolution and higher frequency resolution at the same time, and the occurrence time and the oscillation frequency of transient characteristics can be accurately identified; in the analysis frequency band, a series of peak filters with different peak frequencies are constructed, have uniform and ideal amplitude-frequency and phase-frequency characteristic curves, and support the time domain reconstruction of transient characteristics.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a schematic flow chart of a time-frequency analysis and reconstruction method for transient characteristics according to an embodiment of the present invention;
FIG. 2 is a schematic time-domain waveform of a vibration signal of a gearbox of a wind turbine provided in an embodiment of the present invention;
fig. 3 is a schematic diagram of an amplitude-frequency response characteristic curve of a peak filter according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of a phase-frequency response characteristic of a peak filter according to an embodiment of the present invention;
FIG. 5 is a schematic time-frequency distribution diagram of a vibration signal of a gearbox of a wind turbine constructed by the transient characteristic time-frequency analysis method according to the embodiment of the invention;
fig. 6 is a schematic time-domain waveform of a reconstructed signal constructed by the transient characteristic reconstruction method according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.
As shown in fig. 1, an embodiment of the present invention provides a transient characteristic time-frequency analysis and reconstruction method, including:
s101, constructing a series of peak filters with different peak frequencies in an analysis frequency band;
s102, respectively acting the signals to be analyzed on each constructed peak filter to obtain peak filtering signals corresponding to each peak filter; wherein the signal to be analyzed is a vibration, displacement, sound or electrical signal of the target mechanical equipment;
s103, constructing a time-frequency matrix of the signal to be analyzed by taking the envelope square signal of the peak filtering signal as a row vector corresponding to the peak frequency in the time-frequency matrix, and extracting transient characteristics from the time-frequency matrix;
and S104, adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signals by the amplitude correction coefficient to obtain the reconstructed transient characteristic.
The transient characteristic time-frequency analysis and reconstruction method disclosed by the embodiment of the invention jumps out of the traditional linear or bilinear time-frequency analysis frame, and the constructed time-frequency matrix is not influenced by time-frequency blur caused by Heisenberg uncertainty and is not interfered by cross terms, so that the constructed time-frequency matrix can have higher time resolution and higher frequency resolution at the same time, and the occurrence time and the oscillation frequency of the transient characteristic can be accurately identified; in the analysis frequency band, a series of peak filters with different peak frequencies are constructed, have uniform and ideal amplitude-frequency and phase-frequency characteristic curves, and support the time domain reconstruction of transient characteristics.
In an embodiment of the foregoing transient characteristic time-frequency analysis and reconstruction method, further, constructing a series of peak filters with different peak frequencies within an analysis frequency band includes:
discretizing the analysis frequency band into a series of characteristic frequencies;
a series of peak filters with different peak frequencies are constructed in an analysis frequency band by taking discrete frequencies as peak frequencies.
In an embodiment of the foregoing transient characteristic time-frequency analysis and reconstruction method, further discretizing an analysis frequency band into a series of characteristic frequencies, where a discrete frequency is a peak frequency, and constructing a series of peak filters with different peak frequencies within the analysis frequency band includes:
a1, selecting at equal frequency intervals or at unequal frequency intervals in the analysis frequency band
Figure 186804DEST_PATH_IMAGE033
A discrete frequency
Figure 464333DEST_PATH_IMAGE034
Wherein, in the step (A),
Figure 398791DEST_PATH_IMAGE035
，
Figure 923313DEST_PATH_IMAGE036
a serial number representing a discrete frequency is used,
Figure 759201DEST_PATH_IMAGE033
represents a discrete frequency sequence length;
in this embodiment, the signals to be analyzed are collected at equal time intervals
Figure 27371DEST_PATH_IMAGE037
The signal to be analyzed
Figure 81915DEST_PATH_IMAGE037
Vibration, displacement, sound or electrical signals of the target mechanical equipment; assuming the signal to be analyzed
Figure 324808DEST_PATH_IMAGE037
For a certain wind turbine gearbox vibration signal as shown in FIG. 2, the sampling frequency
Figure 97592DEST_PATH_IMAGE038
At 1000Hz, the length of the signal to be analyzed
Figure 903874DEST_PATH_IMAGE039
Is 10000.
In this embodiment, according to the sampling theorem, the maximum analysis frequency band is selected from 0 to 500Hz, and actually, the analysis frequency band may also be any frequency band within the range of 0 to 500Hz
Figure 360395DEST_PATH_IMAGE040
. Within the selected analysis band, it is assumed that the discrete frequencies are constructed with a frequency separation of 1Hz
Figure 492299DEST_PATH_IMAGE041
I.e. length of frequency series
Figure 221220DEST_PATH_IMAGE033
=499。
A2 at respective discrete frequencies
Figure 644243DEST_PATH_IMAGE042
For peak frequencies, corresponding peak filters are constructed
Figure 407799DEST_PATH_IMAGE043
。
In this embodiment, the order of the constructed peak filter can be determined according to the actual requirement (Calculated amount and accuracy) setting, if the constructed peak filter is a second order peak filter, its transfer function
Figure 445025DEST_PATH_IMAGE044
Comprises the following steps:
Figure 471363DEST_PATH_IMAGE045
wherein the content of the first and second substances,
Figure 619447DEST_PATH_IMAGE046
is composed of
Figure 299827DEST_PATH_IMAGE047
An argument in the transformation;
Figure 258687DEST_PATH_IMAGE048
is the peak frequency of the peak filter
Figure 227780DEST_PATH_IMAGE049
Corresponding angular frequency,;
Figure 241873DEST_PATH_IMAGE050
represents the overall normalized gain, expressed as:
Figure 465175DEST_PATH_IMAGE051
wherein the content of the first and second substances,
Figure 906520DEST_PATH_IMAGE052
represents a passband bandwidth of
Figure 362909DEST_PATH_IMAGE053
A filter gain of
Figure 603529DEST_PATH_IMAGE054
Coefficients of the transfer function of time.
In this embodiment, the following are respectively
Figure 258501DEST_PATH_IMAGE055
Taking the passband bandwidth for the peak frequency of the peak filter
Figure 808431DEST_PATH_IMAGE056
Is composed of
Figure 251918DEST_PATH_IMAGE057
Filter gain
Figure 607813DEST_PATH_IMAGE054
Is composed of
Figure 54975DEST_PATH_IMAGE058
And constructing a corresponding peak filter.
In this embodiment, the following
Figure 792118DEST_PATH_IMAGE059
For example, a corresponding peak filter is constructed, and the amplitude-frequency response characteristic curve of the peak filter is
Figure 754258DEST_PATH_IMAGE060
As shown in FIG. 3, the peak filter has a phase-frequency (abbreviated as "phase-frequency") response curve
Figure 585948DEST_PATH_IMAGE061
As shown in fig. 4. As can be seen from fig. 3, the peak filter has a narrow passband region, and thus even the peak frequency of the peak filter is only spaced apart
Figure 966244DEST_PATH_IMAGE062
And the overlapping range of the frequency domain can be ensured to be smaller. As can be seen from fig. 4, the peak filter has a phase offset at the peak frequency of
Figure 857977DEST_PATH_IMAGE063
I.e. the phase before and after filtering of the signal is unchanged, the time domain characteristics are better preserved.
This exampleIn the analysis of the signal
Figure 58145DEST_PATH_IMAGE064
Acting on each peak filter constructed separately
Figure 693526DEST_PATH_IMAGE065
To obtain the signal to be analyzed corresponding to each peak filter
Figure 177597DEST_PATH_IMAGE066
Peak filtered signal of
Figure 988034DEST_PATH_IMAGE067
。
In a specific implementation manner of the foregoing method for analyzing and reconstructing a transient characteristic, further, the constructing a time-frequency matrix of a signal to be analyzed by using an envelope squared signal of a peak filtering signal as a row vector of a corresponding peak frequency in the time-frequency matrix, and the extracting a transient characteristic from the time-frequency matrix includes:
b1, calculating each peak value filtering signal
Figure 924766DEST_PATH_IMAGE067
Envelope squared signal of
Figure 363837DEST_PATH_IMAGE068
：
Figure 390830DEST_PATH_IMAGE069
Wherein the content of the first and second substances,
Figure 686682DEST_PATH_IMAGE070
representing the hubert transform.
B2, number of constructed rows
Figure 313973DEST_PATH_IMAGE071
The number of rows is
Figure 41888DEST_PATH_IMAGE072
A null time-frequency matrix of; wherein the content of the first and second substances,
Figure 234972DEST_PATH_IMAGE072
is the length of the signal to be analyzed;
in this embodiment, a null time-frequency matrix with 499 rows and 10000 columns is constructed.
B3, envelope square signal
Figure 639409DEST_PATH_IMAGE068
And assigning a row vector of the corresponding peak frequency in the time-frequency matrix, namely: first of the time-frequency matrix
Figure 504728DEST_PATH_IMAGE073
Constructing a time-frequency matrix of the signal to be analyzed to obtain time-frequency distribution of the signal to be analyzed;
in this embodiment, the following components are respectively
Figure 347919DEST_PATH_IMAGE068
Assigning corresponding peak frequencies in a time-frequency matrix
Figure 598772DEST_PATH_IMAGE074
The row vector of (i.e. the first
Figure 927772DEST_PATH_IMAGE073
A row; when in use
Figure 326392DEST_PATH_IMAGE075
The corresponding envelope square signals are all assigned to the corresponding peak frequency in the time frequency matrix
Figure 645378DEST_PATH_IMAGE076
And (4) completing the construction of the time-frequency matrix of the signal to be analyzed to obtain the time-frequency distribution of the signal to be analyzed.
And B4, extracting the occurrence time and the oscillation frequency of the transient characteristics from the time-frequency matrix of the signal to be analyzed.
In this embodiment, information such as the occurrence time and the oscillation frequency of the transient characteristics can be accurately identified from the time-frequency matrix of the signal to be analyzed, so as to extract the transient characteristics of the signal to be analyzed at different peak frequencies. Fig. 5 is a schematic diagram of a two-dimensional image of a time-frequency matrix constructed by the time-frequency analysis method for transient characteristics according to this embodiment, and it can be clearly identified from time-frequency distribution that a series of periodic transient characteristics (marked with capital letters a to J, respectively) appear in the frequency range of 355 to 400Hz, and the occurrence time (vertical line trajectory) and the oscillation frequency (horizontal line trajectory) of these transient characteristics can be accurately identified.
In a specific implementation manner of the foregoing transient characteristic time-frequency analysis and reconstruction method, further, the adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signal by the amplitude correction coefficient to obtain the reconstructed transient characteristic includes:
c1, positioning the time-frequency range of the transient characteristics according to the constructed time-frequency matrix of the signal to be analyzed;
c2, filtering the peak value in the time frequency range of the transient characteristic
Figure 94945DEST_PATH_IMAGE077
Adding to obtain a superposed signal
Figure 841184DEST_PATH_IMAGE078
；
In this embodiment, the transient characteristics time-frequency range identified from the constructed time-frequency matrix of the signal to be analyzed is used as the basis for determining the transient characteristics of the signal to be analyzed
Figure 681095DEST_PATH_IMAGE079
Corresponding peak value filtering signal
Figure 600510DEST_PATH_IMAGE077
Adding to obtain a superposed signal
Figure 560375DEST_PATH_IMAGE078
。
C3, adding the signals
Figure 556144DEST_PATH_IMAGE078
Is divided by the amplitude correction factor
Figure 867040DEST_PATH_IMAGE080
Obtaining reconstructed transient characteristics; wherein the amplitude correction factor
Figure 527828DEST_PATH_IMAGE080
Expressed as:
Figure 152320DEST_PATH_IMAGE081
wherein the content of the first and second substances,
Figure 302679DEST_PATH_IMAGE082
indicating a frequency of
Figure 851603DEST_PATH_IMAGE083
The magnitude-frequency response characteristic of the peak filter at time,
Figure 112820DEST_PATH_IMAGE084
indicating a frequency of
Figure 312857DEST_PATH_IMAGE083
The phase-frequency response curve value of the peak filter at time,
Figure 322533DEST_PATH_IMAGE085
a serial number representing a discrete frequency is used,
Figure 608021DEST_PATH_IMAGE086
representing the length of the discrete frequency sequence.
In this embodiment, the amplitude correction coefficient is based on the above
Figure 672929DEST_PATH_IMAGE080
Calculating formula to obtain amplitude correction coefficient
Figure 212625DEST_PATH_IMAGE080
6.282, the superposed signals
Figure 970366DEST_PATH_IMAGE087
Is divided by the amplitude correction factor
Figure 743150DEST_PATH_IMAGE080
And a reconstructed signal is obtained as shown in fig. 6. From fig. 6, the reconstructed series of transient features, labeled with capital letters a through J, respectively, can be clearly identified.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (9)

1. A transient characteristic time frequency analysis and reconstruction method is characterized by comprising the following steps:
constructing a series of peak filters with different peak frequencies in an analysis frequency band;
respectively acting the signals to be analyzed on each constructed peak filter to obtain peak filtering signals corresponding to each peak filter; wherein the signal to be analyzed is a vibration, displacement, sound or electrical signal of the target mechanical equipment;
taking the envelope square signal of the peak filtering signal as a row vector corresponding to the peak frequency in a time frequency matrix, constructing the time frequency matrix of the signal to be analyzed, and extracting transient characteristics from the time frequency matrix;
and adding the peak filtering signals corresponding to the transient characteristic time-frequency range, and dividing the added signals by the amplitude correction coefficient to obtain the reconstructed transient characteristic.
2. The transient feature time-frequency analysis and reconstruction method of claim 1, wherein constructing a series of peak filters with different peak frequencies within the analysis frequency band comprises:
the analysis frequency band is discretized into a series of characteristic frequencies, the discrete frequency is taken as a peak frequency, and a series of peak filters with different peak frequencies are constructed in the analysis frequency band.
3. The transient feature time-frequency analysis and reconstruction method of claim 2, wherein the discretizing of the analysis frequency band into a series of feature frequencies, the discrete frequencies being peak frequencies, and the constructing of a series of peak filters with different peak frequencies within the analysis frequency band comprises:
within the analysis band, the selection being at equal or unequal frequency intervals
Figure 231835DEST_PATH_IMAGE001
A discrete frequency
Figure 140886DEST_PATH_IMAGE002
Wherein, in the step (A),
Figure 551751DEST_PATH_IMAGE003
，
Figure 342989DEST_PATH_IMAGE004
a serial number representing a discrete frequency is used,
Figure 952962DEST_PATH_IMAGE001
represents a discrete frequency sequence length;
at respective discrete frequencies
Figure 263989DEST_PATH_IMAGE002
For peak frequencies, corresponding peak filters are constructed
Figure 301215DEST_PATH_IMAGE005
。
4. The temporal frequency analysis and reconstruction method of transient characteristics of claim 2, wherein if the constructed peak filter is a second order peak filter, its transfer function is
Figure 783012DEST_PATH_IMAGE006
Comprises the following steps:
Figure 478567DEST_PATH_IMAGE007
wherein the content of the first and second substances,
Figure 893367DEST_PATH_IMAGE008
is composed of
Figure 914544DEST_PATH_IMAGE009
An argument in the transformation;
Figure 618058DEST_PATH_IMAGE010
is the peak frequency of the peak filter
Figure 120233DEST_PATH_IMAGE011
A corresponding angular frequency;
Figure 858382DEST_PATH_IMAGE012
representing the overall normalized gain.
5. The temporal frequency analysis and reconstruction method according to claim 4, wherein the overall normalized gain
Figure 299728DEST_PATH_IMAGE013
Expressed as:
Figure 506849DEST_PATH_IMAGE014
wherein the content of the first and second substances,
Figure 996737DEST_PATH_IMAGE015
represents a passband bandwidth of
Figure 386130DEST_PATH_IMAGE016
A filter gain of
Figure 686792DEST_PATH_IMAGE017
Coefficients of the transfer function of time.
6. The method for time-frequency analysis and reconstruction of transient characteristics according to claim 1, wherein the step of constructing the time-frequency matrix of the signal to be analyzed by using the envelope squared signal of the peak filtering signal as the row vector of the corresponding peak frequency in the time-frequency matrix, and the step of extracting the transient characteristics from the time-frequency matrix comprises:
calculating respective peak filtered signals
Figure 427215DEST_PATH_IMAGE018
Envelope squared signal of
Figure 720793DEST_PATH_IMAGE019
；
Number of constructional lines
Figure 981004DEST_PATH_IMAGE020
The number of rows is
Figure 436256DEST_PATH_IMAGE021
A null time-frequency matrix of; wherein the content of the first and second substances,
Figure 411778DEST_PATH_IMAGE021
is the length of the signal to be analyzed;
squaring the envelope
Figure 243468DEST_PATH_IMAGE019
And assigning a row vector of the corresponding peak frequency in the time-frequency matrix, namely: first of the time-frequency matrix
Figure 607453DEST_PATH_IMAGE022
A row, constructing a time-frequency matrix of the signal to be analyzed;
and extracting the occurrence time and the oscillation frequency of the transient characteristics from the time-frequency matrix of the signal to be analyzed.
7. According to the rightThe method of claim 6, wherein the peak filtered signal is a peak filtered signal
Figure 46656DEST_PATH_IMAGE023
Envelope squared signal of
Figure 699354DEST_PATH_IMAGE019
Expressed as:
Figure 147784DEST_PATH_IMAGE024
wherein the content of the first and second substances,
Figure 569538DEST_PATH_IMAGE025
representing the hubert transform.
8. The transient feature time-frequency analysis and reconstruction method of claim 1, wherein the adding the peak filtered signals corresponding to the transient feature time-frequency range and dividing the added signals by the amplitude correction factor to obtain the reconstructed transient feature comprises:
according to the constructed time-frequency matrix of the signal to be analyzed, positioning the time-frequency range of the transient characteristic;
filtering the peak value in the time-frequency range of the transient characteristic
Figure 632172DEST_PATH_IMAGE023
Adding to obtain a superposed signal
Figure 319636DEST_PATH_IMAGE026
；
Will add the signal
Figure 758708DEST_PATH_IMAGE026
Is divided by the amplitude correction factor
Figure 97285DEST_PATH_IMAGE027
And obtaining the reconstructed transient characteristics.
9. The temporal frequency analysis and reconstruction method according to claim 8, wherein the amplitude correction factor
Figure 72764DEST_PATH_IMAGE027
Expressed as:
Figure 700054DEST_PATH_IMAGE028
wherein the content of the first and second substances,
Figure 739555DEST_PATH_IMAGE029
indicating a frequency of
Figure 621054DEST_PATH_IMAGE030
The magnitude-frequency response characteristic of the peak filter at time,
Figure 291070DEST_PATH_IMAGE031
indicating a frequency of
Figure 202394DEST_PATH_IMAGE032
The phase-frequency response curve value of the peak filter at time,
Figure 265159DEST_PATH_IMAGE033
a serial number representing a discrete frequency is used,
Figure 781591DEST_PATH_IMAGE034
representing the length of the discrete frequency sequence.
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