CN113283399A - Transient time-frequency feature extraction method based on dynamic response of single-degree-of-freedom system - Google Patents

Transient time-frequency feature extraction method based on dynamic response of single-degree-of-freedom system Download PDF

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CN113283399A
CN113283399A CN202110803596.9A CN202110803596A CN113283399A CN 113283399 A CN113283399 A CN 113283399A CN 202110803596 A CN202110803596 A CN 202110803596A CN 113283399 A CN113283399 A CN 113283399A
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frequency
time
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dynamic response
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CN113283399B (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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    • G06F2218/02—Preprocessing
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Abstract

The invention provides a transient time-frequency feature extraction method based on dynamic response of a single-degree-of-freedom system, and belongs to the technical field of signal time-varying feature extraction. The method comprises the following steps: constructing a series of single-degree-of-freedom systems with different natural frequencies; applying a signal to be analyzed as basic acceleration excitation to each constructed single-degree-of-freedom system to obtain a dynamic response signal of each single-degree-of-freedom system; calculating an envelope square signal of a dynamic response signal of each single-degree-of-freedom system; and endowing each envelope square signal with a corresponding row vector of the time frequency matrix according to the corresponding inherent frequency to obtain the time frequency distribution of the signal to be analyzed, and extracting the transient time frequency characteristics from the time frequency matrix. By adopting the method and the device, the transient time-frequency characteristics in the signal to be analyzed can be accurately extracted.

Description

Transient time-frequency feature extraction method based on dynamic response of single-degree-of-freedom system
Technical Field
The invention relates to the technical field of signal time-varying feature extraction, in particular to a transient time-frequency feature extraction method based on single-degree-of-freedom system dynamic response.
Background
Transient characteristics are often associated with mechanical device signals (e.g., acceleration, displacement, acoustic signals, electrical signals, etc.), and the sources of these characteristics include sudden movements of mechanical structures, sudden changes in dynamic parameters due to faults, etc. In the design, maintenance and other links of mechanical equipment, it is often necessary to accurately extract transient features in signals to reveal the dynamics, operating state and health state of the mechanical equipment. Therefore, the effective and accurate transient characteristic extraction technology has important significance for equipment manufacturing industry and service safety of key equipment.
Specific contents of the transient feature extraction include, but are not limited to, locating the time when the transient feature occurs in the time domain, specifying the oscillation frequency of the transient response in the frequency domain, and the like. However, in a damping environment, the amplitude of the transient feature often decays rapidly, the transient feature has a short maintaining time and is difficult to analyze. The traditional signal analysis methods such as time domain waveform analysis and spectrum analysis are not suitable for extracting transient characteristics.
The time-frequency distribution not only can reveal the frequency structure of the non-stationary signal, but also can reflect the change of frequency and amplitude along with time. Therefore, transient feature extraction based on time-frequency distribution of signals is a feasible scheme. The traditional time frequency distribution can be roughly divided into two types of linear time frequency distribution and bilinear time frequency distribution; wherein the content of the first and second substances,
the linear time-frequency distribution is transformed into a core by the inner product of the basis function, and the measurement of the characteristics is realized by the matching of the basis function and the signal to be analyzed. However, the time and frequency scales of the basis functions are affected by uncertainty, so that time-frequency fuzzy phenomena exist in linear time-frequency distribution, and periodic components and transient characteristics cannot be simultaneously and accurately characterized;
the bilinear time frequency distribution is transformed into a core by an instantaneous autocorrelation function Fourier of a signal, and the energy distribution is constructed only on the basis of the frequency structure characteristics of the signal. However, for a multi-component signal, cross-term interference inevitably exists in bilinear time-frequency distribution of the multi-component signal, which is easy to mislead the correct identification of features, thereby generating false feature information.
At present, most time-frequency analysis methods can be classified into the two types, and part of post-processing methods are also subjected to post-adjustment on the basis of the methods. Chinese patent 201410620570.0 discloses an instantaneous frequency estimation scheme based on synchronous compression transformation. The scheme firstly collects vibration signals of the rotary machine, and further synchronously compresses time-frequency distribution along the frequency direction on the basis of the traditional continuous wavelet transform so as to eliminate the time-frequency fuzzy phenomenon in the frequency direction and improve the time-frequency resolution.
The scheme is characterized in that the traditional linear time frequency distribution is compressed in the frequency direction, so that the fuzzy phenomenon in the frequency direction is eliminated. However, this solution is only suitable for signals whose frequency varies slowly with time, i.e. a theoretical instantaneous frequency value can be calculated at each instant. This assumption does not apply to transient components, since the transient features resemble dirac impulses at the moment of occurrence, theoretically covering the full band range, and cannot be characterized by a single frequency value. In recent two years, researchers have also proposed a compression post-processing method in the time direction, which is characterized by calculating an accurate group delay function and concentrating energy to one point in the time direction. This solution can theoretically improve the time resolution, but is in turn no longer suitable for the extraction of frequency features, i.e. the oscillation frequency of transient features and other frequency components present in the signal cannot be accurately characterized. How to effectively extract the transient time-frequency characteristics under the premise of not influencing the periodic frequency characteristic identification is still a difficulty in current research and application.
Disclosure of Invention
The embodiment of the invention provides a transient time-frequency feature extraction method based on dynamic response of a single-degree-of-freedom system, which can accurately extract transient time-frequency features in a signal to be analyzed. The technical scheme is as follows:
the embodiment of the invention provides a transient time-frequency feature extraction method based on dynamic response of a single-degree-of-freedom system, which comprises the following steps:
constructing a series of single-degree-of-freedom systems with different natural frequencies;
applying a signal to be analyzed as basic acceleration excitation to each constructed single-degree-of-freedom system to obtain a dynamic response signal of each single-degree-of-freedom system;
calculating an envelope square signal of a dynamic response signal of each single-degree-of-freedom system;
and endowing each envelope square signal with a corresponding row vector of the time frequency matrix according to the corresponding inherent frequency to obtain the time frequency distribution of the signal to be analyzed, and extracting the transient time frequency characteristics from the time frequency matrix.
Further, before constructing a series of single degree of freedom systems with different natural frequencies, the method further comprises:
to be provided with
Figure 437191DEST_PATH_IMAGE001
For sampling frequency, collecting signals to be analyzed at equal time intervals
Figure 72441DEST_PATH_IMAGE002
，
Figure 321019DEST_PATH_IMAGE003
Represents time;
selecting an analysis band
Figure 388333DEST_PATH_IMAGE004
Discretizing the analysis frequency band, wherein,
Figure 186393DEST_PATH_IMAGE005
,
Figure 477697DEST_PATH_IMAGE006
。
further, the discretizing of the analysis frequency band comprises:
set the frequency interval as
Figure 213572DEST_PATH_IMAGE007
To a length of
Figure 881314DEST_PATH_IMAGE008
Of the discretized frequency series
Figure 471564DEST_PATH_IMAGE009
The first in the sequence
Figure 199349DEST_PATH_IMAGE010
A frequency value expressed as
Figure 156940DEST_PATH_IMAGE011
Wherein, in the step (A),
Figure 612061DEST_PATH_IMAGE010
a frequency number is shown which indicates the number of frequencies,
Figure 604288DEST_PATH_IMAGE010
=1, 2, 3···
Figure 502974DEST_PATH_IMAGE012
。
further, after discretizing the analysis frequency band, the method further comprises:
structure of the device
Figure 213441DEST_PATH_IMAGE008
Go to,
Figure 206674DEST_PATH_IMAGE013
The time-frequency matrix TFR of a column, each element in the time-frequency matrix TFR is initially 0, wherein,
Figure 318986DEST_PATH_IMAGE013
is the length of the signal to be analyzed.
Further, the constructing a series of single-degree-of-freedom systems with different natural frequencies comprises:
to be provided with
Figure 122994DEST_PATH_IMAGE014
In order to be the natural frequency of the frequency,
Figure 320757DEST_PATH_IMAGE015
for the damping ratio, a series of single degree-of-freedom systems with different natural frequencies are constructed, wherein,
Figure 117681DEST_PATH_IMAGE010
=1, 2, 3···
Figure 84500DEST_PATH_IMAGE012
。
further, the natural frequency is
Figure 324988DEST_PATH_IMAGE014
The dynamic response signal of the single degree of freedom system of time is expressed as:
Figure 541206DEST_PATH_IMAGE017
wherein the content of the first and second substances,
Figure 892553DEST_PATH_IMAGE018
is a natural frequency of
Figure 963146DEST_PATH_IMAGE014
The dynamic response signal of the single degree of freedom system,
Figure 577798DEST_PATH_IMAGE019
Figure 484574DEST_PATH_IMAGE020
are all the parameters of the filter and are,
Figure 623300DEST_PATH_IMAGE021
which represents a discrete time interval of time,
Figure 564712DEST_PATH_IMAGE022
are respectively as
Figure 943740DEST_PATH_IMAGE023
Of time of day
Figure 337812DEST_PATH_IMAGE024
In the form of a discrete signal of (a),
Figure 30962DEST_PATH_IMAGE025
are respectively as
Figure 810568DEST_PATH_IMAGE026
Of time of day
Figure 767023DEST_PATH_IMAGE027
In the form of a discrete signal of (a),
Figure 648391DEST_PATH_IMAGE028
=1, 2, 3···。
further, according to the natural frequency of the single degree of freedom system
Figure 394499DEST_PATH_IMAGE014
Damping ratio
Figure 44923DEST_PATH_IMAGE015
The filter parameters obtained are:
Figure 703438DEST_PATH_IMAGE030
Figure 72102DEST_PATH_IMAGE031
。
further, a dynamic response signal
Figure 356322DEST_PATH_IMAGE032
The envelope squared signal of (a) is expressed as:
Figure 126832DEST_PATH_IMAGE033
wherein the content of the first and second substances,
Figure 221827DEST_PATH_IMAGE034
representing dynamic response signals
Figure 795896DEST_PATH_IMAGE032
The square of the envelope of (a) the signal,
Figure 634539DEST_PATH_IMAGE035
representing the hubert transform.
Further, the assigning each envelope squared signal to a corresponding row vector of the time-frequency matrix according to the corresponding natural frequency to obtain the time-frequency distribution of the signal to be analyzed includes:
squaring the envelope
Figure 462818DEST_PATH_IMAGE036
In the time-frequency matrix TFR
Figure 712403DEST_PATH_IMAGE037
Line, get a frequency of
Figure 790080DEST_PATH_IMAGE038
The time-frequency distribution of (c):
Figure 432414DEST_PATH_IMAGE039
wherein the content of the first and second substances,
Figure 911937DEST_PATH_IMAGE040
indicating a frequency of
Figure 621440DEST_PATH_IMAGE038
Time-frequency distribution of (2).
The technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
the embodiment of the invention jumps out of the traditional frame of linear time frequency distribution or bilinear time frequency distribution, does not depend on the inner product transformation or instantaneous autocorrelation function of the basis function, and adopts a mode of dynamic response based on a single-degree-of-freedom system to construct signal time domain characteristics (namely, dynamic response signals) at different frequencies so as to construct the time frequency distribution, thereby being capable of avoiding the fuzzy phenomenon caused by the limitation of time frequency resolution and the cross term interference in the bilinear time frequency distribution.
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 transient time-frequency feature extraction method based on a single degree of freedom system dynamic response according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a work flow of the transient time-frequency feature extraction system based on the dynamic response of the single degree of freedom system according to the embodiment of the present invention;
FIG. 3 is a time domain waveform of a simulated signal according to an embodiment of the present invention, where the simulated signal includes a periodic component of 120Hz and a transient impulse occurring at 0.5s, and an oscillation frequency of a transient characteristic is 80 Hz;
fig. 4 is a typical linear time-frequency distribution of the conventional short-time Fourier transform time-frequency distribution of the simulation signal according to the embodiment of the present invention;
fig. 5 is a schematic diagram of a Wigner-Ville time-frequency distribution of the simulation signal according to the embodiment of the present invention, which is a typical bilinear time-frequency distribution;
fig. 6 is a time-frequency distribution diagram of the transient time-frequency feature extraction method based on single degree of freedom system dynamic response 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 time-frequency feature extraction method based on a single degree of freedom system dynamic response, including:
s101, constructing a series of single-degree-of-freedom systems with different natural frequencies;
s102, applying a signal to be analyzed as basic acceleration excitation to each constructed single-degree-of-freedom system to obtain a dynamic response signal of each single-degree-of-freedom system;
s103, calculating an envelope square signal of a dynamic response signal of each single-degree-of-freedom system;
and S104, endowing each envelope square signal with a corresponding row vector of a time frequency matrix according to the corresponding inherent frequency to obtain the time frequency distribution of the signal to be analyzed, and extracting the transient time frequency characteristics from the time frequency matrix.
The transient time-frequency feature extraction method based on the dynamic response of the single-degree-of-freedom system disclosed by the embodiment of the invention jumps out of the traditional frame of linear time-frequency distribution or bilinear time-frequency distribution, does not depend on the inner product transformation of a basis function or an instantaneous autocorrelation function, and adopts a single-degree-of-freedom system dynamic response mode to construct signal time-domain features (namely, dynamic response signals) at different frequencies so as to construct time-frequency distribution, so that the fuzzy phenomenon caused by time-frequency resolution limitation and cross term interference in bilinear time-frequency distribution can be avoided.
In this embodiment, the transient time-frequency characteristics specifically refer to the occurrence time and the oscillation frequency of the transient characteristics.
In this embodiment, the single-degree-of-freedom system is specifically a single-degree-of-freedom spring oscillator system.
In this embodiment, the dynamic response of the single-degree-of-freedom system specifically refers to an acceleration response of the single-degree-of-freedom spring oscillator system.
The transient time-frequency feature extraction method based on the dynamic response of the single-degree-of-freedom system is different from a traditional linear or bilinear time-frequency analysis method framework, and the core of the method is to construct a series of single-degree-of-freedom systems with different natural frequencies for extracting dynamic response signals (also called dynamic response time-domain features) of signals to be analyzed in each frequency band, so that the time-frequency distribution of the signals to be analyzed is constructed, the transient time-frequency features in the signals to be analyzed can be accurately extracted on the premise of not influencing frequency feature identification, the dynamic behavior and the characteristics of mechanical equipment are effectively identified, and the method is used for links of design, maintenance and the like of mechanical equipment, and particularly comprises the following steps:
a1, to
Figure 186413DEST_PATH_IMAGE041
For sampling frequency, collecting signals to be analyzed at equal time intervals
Figure 163596DEST_PATH_IMAGE042
And discretizing the analysis frequency band.
In this embodiment, the signal to be analyzed
Figure 497626DEST_PATH_IMAGE042
May be a target mechanical device signal, such as acceleration, displacement, acoustic signal, electrical signal, etc., wherein,
Figure 105325DEST_PATH_IMAGE003
representing time, signal to be analyzed
Figure 141283DEST_PATH_IMAGE042
Is expressed as
Figure 859840DEST_PATH_IMAGE043
；
In this embodiment, the analysis frequency band may be 0 to 0
Figure 313955DEST_PATH_IMAGE044
And/2, also from 0 to
Figure 92555DEST_PATH_IMAGE044
An arbitrary frequency band in the range of/2, the analysis frequency band being set to
Figure 881388DEST_PATH_IMAGE045
At a frequency interval of
Figure 403637DEST_PATH_IMAGE046
Wherein, in the step (A),
Figure 712258DEST_PATH_IMAGE047
,
Figure 661760DEST_PATH_IMAGE048
;
selecting analysis frequency band according to actual equipment characteristics, if
Figure 219780DEST_PATH_IMAGE049
And is
Figure 794987DEST_PATH_IMAGE050
Then for the analysis frequency band
Figure 958115DEST_PATH_IMAGE051
Discretizing to obtain the length of
Figure 812938DEST_PATH_IMAGE052
Of the discretized frequency series
Figure 327096DEST_PATH_IMAGE053
The first in the sequence
Figure 705994DEST_PATH_IMAGE054
A frequency value expressed as
Figure 926891DEST_PATH_IMAGE055
Wherein, in the step (A),
Figure 483774DEST_PATH_IMAGE056
a frequency number is shown which indicates the number of frequencies,
Figure 468916DEST_PATH_IMAGE056
=1, 2, 3···
Figure 136658DEST_PATH_IMAGE057
(ii) a Otherwise, for the analysis band
Figure 8799DEST_PATH_IMAGE058
Discretizing to obtain the length of
Figure 736584DEST_PATH_IMAGE059
Of the discretized frequency series
Figure 756492DEST_PATH_IMAGE060
The first in the sequence
Figure 211613DEST_PATH_IMAGE056
A frequency value expressed as
Figure 203840DEST_PATH_IMAGE061
。
A2, structure
Figure 836947DEST_PATH_IMAGE062
Go to,
Figure 281835DEST_PATH_IMAGE063
The time frequency matrix TFR of the column, each element in the time frequency matrix TFR is 0 initially, wherein
Figure 540647DEST_PATH_IMAGE063
Is the length of the signal to be analyzed;
a3, initialization
Figure 652959DEST_PATH_IMAGE064
Taking the initial value of the frequency number
Figure 253705DEST_PATH_IMAGE064
=1；
A4, to
Figure 451468DEST_PATH_IMAGE065
In order to be the natural frequency of the frequency,
Figure 999124DEST_PATH_IMAGE066
constructing a single-degree-of-freedom system for the damping ratio;
a5, converting the signal to be analyzed
Figure 215210DEST_PATH_IMAGE067
Applied on the constructed single-degree-of-freedom system as basic acceleration excitation to obtain a dynamic response signal of the single-degree-of-freedom system
Figure 190120DEST_PATH_IMAGE068
；
In this embodiment, the dynamic response signal
Figure 609600DEST_PATH_IMAGE068
Can be quickly realized on a computer by an infinite impulse response filtering method, and at the moment
Figure 960947DEST_PATH_IMAGE067
And
Figure 31540DEST_PATH_IMAGE068
writable in discrete signal form, i.e.
Figure 239667DEST_PATH_IMAGE069
And
Figure 146443DEST_PATH_IMAGE070
，
Figure 35902DEST_PATH_IMAGE071
=1, 2, 3···，
Figure 711734DEST_PATH_IMAGE072
representing discrete time intervals. The specific calculation steps include:
a51, constructing a second-order infinite impulse response filter, the transfer function of which can be written as
Figure 277713DEST_PATH_IMAGE073
Wherein the content of the first and second substances,
Figure 671785DEST_PATH_IMAGE074
are all the parameters of the filter and are,
Figure 630514DEST_PATH_IMAGE075
is composed of
Figure 426432DEST_PATH_IMAGE076
A unit delay factor in the transform;
a52, natural frequency based on single degree of freedom system
Figure 428892DEST_PATH_IMAGE065
Damping ratio
Figure 44681DEST_PATH_IMAGE066
The filter parameters are defined as follows:
Figure 275942DEST_PATH_IMAGE078
Figure 926366DEST_PATH_IMAGE031
。
wherein the content of the first and second substances,
Figure 647198DEST_PATH_IMAGE079
representing discrete time intervals.
A53, substituting the filter parameters into the following formula, calculating the natural frequency as
Figure 265130DEST_PATH_IMAGE065
Dynamic response signal for single degree of freedom system
Figure 300082DEST_PATH_IMAGE068
：
Figure 805012DEST_PATH_IMAGE080
Wherein the content of the first and second substances,
Figure 634428DEST_PATH_IMAGE081
are respectively as
Figure 739656DEST_PATH_IMAGE082
Of time of day
Figure 312720DEST_PATH_IMAGE068
In the form of a discrete signal of (a),
Figure 937736DEST_PATH_IMAGE083
are respectively as
Figure 203633DEST_PATH_IMAGE084
Of time of day
Figure 78048DEST_PATH_IMAGE085
In the form of discrete signals.
A6, calculating dynamic response signal
Figure 969649DEST_PATH_IMAGE068
Envelope squared signal of
Figure 449172DEST_PATH_IMAGE086
：
Figure 620391DEST_PATH_IMAGE087
Wherein the content of the first and second substances,
Figure 185364DEST_PATH_IMAGE088
a Hilbert transform;
a7, squaring the envelope
Figure 349498DEST_PATH_IMAGE086
Is placed in the second time-frequency matrix TFR constructed in the step A2
Figure 949107DEST_PATH_IMAGE089
Line, get a frequency of
Figure 353543DEST_PATH_IMAGE090
The time-frequency distribution of (c):
Figure 405813DEST_PATH_IMAGE091
wherein the content of the first and second substances,
Figure 124370DEST_PATH_IMAGE092
indicating a frequency of
Figure 827753DEST_PATH_IMAGE090
Time-frequency distribution of (2).
A8, order
Figure 606353DEST_PATH_IMAGE093
=
Figure 145919DEST_PATH_IMAGE093
+1, repeat steps A4 through A7 until
Figure 402588DEST_PATH_IMAGE094
=
Figure 960477DEST_PATH_IMAGE095
The time-frequency matrix based on the dynamic response of the single-degree-of-freedom system provided by the invention is obtained
Figure 909978DEST_PATH_IMAGE096
Obtaining the time-frequency distribution of the signal to be analyzed;
a9, from time-frequency matrix
Figure 671261DEST_PATH_IMAGE096
And extracting transient time-frequency characteristics.
The embodiment of the invention also provides a system corresponding to the transient time-frequency feature extraction method based on the dynamic response of the single-degree-of-freedom system, which can simultaneously acquire and analyze signal features, and as shown in fig. 2, the working process of the system is as follows:
1 collecting signals with sensor units and data acquisition units
Figure 997200DEST_PATH_IMAGE097
；
2, constructing a single-degree-of-freedom system by using a hardware filtering unit and calculating a dynamic response signal
Figure 957066DEST_PATH_IMAGE098
；
Figure 326736DEST_PATH_IMAGE089
Is 1;
calculating envelope square signal by calculation processing unit
Figure 840894DEST_PATH_IMAGE099
；
4 using a time-frequency diagram display unit
Figure 704945DEST_PATH_IMAGE099
Given a time-frequency matrix
Figure 722579DEST_PATH_IMAGE100
Go to, if
Figure 263151DEST_PATH_IMAGE094
=
Figure 999026DEST_PATH_IMAGE095
Displaying the obtained matrix as a picture;
the system comprises:
a sensor unit and a data acquisition unit for sensing the actual analog physical quantity, the data acquisition unit converts the analog physical quantity into a digital value with a frequency of
Figure 401188DEST_PATH_IMAGE101
To be analyzed signal
Figure 538909DEST_PATH_IMAGE097
Wherein, the adopted sensors are acceleration sensors, displacement sensors, sound pressure sensors, current sensors and the like;
a hardware filtering unit for constructing a single-degree-of-freedom system to filter the signal to be analyzed and calculating a dynamic response signal
Figure 63431DEST_PATH_IMAGE098
；
A calculation processing unit for calculating the dynamic response signal
Figure 270290DEST_PATH_IMAGE098
Envelope squared signal of
Figure 741723DEST_PATH_IMAGE099
And constructing a time-frequency matrix;
a time-frequency diagram display unit for displaying
Figure 733950DEST_PATH_IMAGE099
Given the constructed time-frequency matrix
Figure 367056DEST_PATH_IMAGE100
And if all the rows of the time-frequency matrix are assigned, the time-frequency matrix is presented in an image mode for analysts to visually identify the characteristics in the signal.
The transient time-frequency feature extraction method and system based on the dynamic response of the single-degree-of-freedom system, provided by the embodiment of the invention, can serve the field of signal analysis in mechanical dynamics and fault diagnosis, and have important theoretical significance and application value. Compared with the existing linear time-frequency distribution or bilinear time-frequency distribution, the time-frequency distribution constructed by the embodiment is not limited by the size of a window function, does not have cross term interference, can simultaneously extract periodic components and transient time-frequency characteristics, and can effectively represent horizontal and vertical tracks in a time-frequency graph. In addition, the method only relates to basic multiplication and division and convolution operation, the calculation amount is small, the required hardware system is simple, and the requirement of real-time signal acquisition and analysis can be met.
In order to further verify the effectiveness of the invention, the traditional linear time-frequency distribution and bilinear time-frequency distribution and the transient time-frequency feature extraction method based on the dynamic response of the single-degree-of-freedom system are adopted to process the simulation signal shown in fig. 3 to obtain the corresponding time-frequency distribution, as shown in fig. 4-6, as can be seen from fig. 4, the linear time-frequency distribution has a time-frequency fuzzy phenomenon and cannot simultaneously and accurately represent the periodic frequency features; as can be seen from fig. 5, cross-term interference exists in bilinear time-frequency distribution, which generates false characteristic information; as can be seen from fig. 6, the transient time-frequency feature extraction method based on the dynamic response of the single-degree-of-freedom system provided by the invention can accurately reveal the occurrence time and the oscillation frequency of the transient feature without affecting the expression of the periodic frequency feature.
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 time-frequency feature extraction method based on single-degree-of-freedom system dynamic response is characterized by comprising the following steps:
constructing a series of single-degree-of-freedom systems with different natural frequencies; the single-degree-of-freedom system is a single-degree-of-freedom spring oscillator system;
applying a signal to be analyzed as basic acceleration excitation to each constructed single-degree-of-freedom system to obtain a dynamic response signal of each single-degree-of-freedom system; wherein the signal to be analyzed is an acceleration, displacement, sound or electrical signal of the target mechanical equipment;
calculating an envelope square signal of a dynamic response signal of each single-degree-of-freedom system;
and endowing each envelope square signal with a corresponding row vector of the time frequency matrix according to the corresponding inherent frequency to obtain the time frequency distribution of the signal to be analyzed, and extracting the transient time frequency characteristics from the time frequency matrix.
2. The method for extracting transient time-frequency characteristics based on dynamic response of single-degree-of-freedom system according to claim 1, wherein before constructing a series of single-degree-of-freedom systems with different natural frequencies, the method further comprises:
to be provided with
Figure 861306DEST_PATH_IMAGE001
For sampling frequency, collecting signals to be analyzed at equal time intervals
Figure 870851DEST_PATH_IMAGE002
，
Figure 717584DEST_PATH_IMAGE003
Represents time; selecting an analysis band
Figure 36439DEST_PATH_IMAGE004
To analysis frequencyThe strip is discretized, wherein,
Figure 968623DEST_PATH_IMAGE005
。
3. the method for extracting transient time-frequency features based on single degree of freedom system dynamic response according to claim 2, wherein the discretizing the analysis frequency band comprises:
set the frequency interval as
Figure 781858DEST_PATH_IMAGE006
To a length of
Figure 14256DEST_PATH_IMAGE007
Of the discretized frequency series
Figure 989165DEST_PATH_IMAGE009
The first in the sequence
Figure 923492DEST_PATH_IMAGE010
A frequency value expressed as
Figure 9260DEST_PATH_IMAGE011
Wherein, in the step (A),
Figure 565006DEST_PATH_IMAGE010
a frequency number is shown which indicates the number of frequencies,
Figure 960084DEST_PATH_IMAGE010
=1, 2, 3···
Figure 866860DEST_PATH_IMAGE012
。
4. the method for extracting transient time-frequency characteristics based on dynamic response of single degree of freedom system according to claim 2, wherein after discretizing the analysis frequency band, the method further comprises:
structure of the device
Figure 21898DEST_PATH_IMAGE012
Go to,
Figure 697730DEST_PATH_IMAGE013
The time-frequency matrix TFR of a column, each element in the time-frequency matrix TFR is initially 0, wherein,
Figure 529289DEST_PATH_IMAGE013
is the length of the signal to be analyzed.
5. The method for extracting transient time-frequency characteristics based on dynamic response of single-degree-of-freedom system according to claim 2, wherein the constructing a series of single-degree-of-freedom systems with different natural frequencies comprises:
to be provided with
Figure 657782DEST_PATH_IMAGE014
In order to be the natural frequency of the frequency,
Figure 350931DEST_PATH_IMAGE015
for the damping ratio, a series of single degree-of-freedom systems with different natural frequencies are constructed, wherein,
Figure 396116DEST_PATH_IMAGE016
=1, 2, 3···
Figure 149309DEST_PATH_IMAGE017
。
6. the method of claim 3, wherein the natural frequency is
Figure 30677DEST_PATH_IMAGE014
The dynamic response signal of the single degree of freedom system of time is expressed as:
Figure 527518DEST_PATH_IMAGE019
wherein the content of the first and second substances,
Figure 177942DEST_PATH_IMAGE020
is a natural frequency of
Figure 351303DEST_PATH_IMAGE014
The dynamic response signal of the single degree of freedom system,
Figure 985547DEST_PATH_IMAGE021
Figure 20499DEST_PATH_IMAGE022
are all the parameters of the filter and are,
Figure 525429DEST_PATH_IMAGE023
which represents a discrete time interval of time,
Figure 869692DEST_PATH_IMAGE024
、
Figure 460073DEST_PATH_IMAGE025
、
Figure 564296DEST_PATH_IMAGE026
are respectively as
Figure 189312DEST_PATH_IMAGE027
Of time of day
Figure 455208DEST_PATH_IMAGE020
In the form of a discrete signal of (a),
Figure 782153DEST_PATH_IMAGE028
、
Figure 424487DEST_PATH_IMAGE029
are respectively as
Figure 904010DEST_PATH_IMAGE030
Of time of day
Figure 340808DEST_PATH_IMAGE031
In the form of a discrete signal of (a),
Figure 178486DEST_PATH_IMAGE032
=1, 2, 3···。
7. the method of claim 6, wherein the method comprises extracting the transient time-frequency characteristics according to the natural frequency of the single-degree-of-freedom system
Figure 358932DEST_PATH_IMAGE014
Damping ratio
Figure 224120DEST_PATH_IMAGE015
The filter parameters obtained are:
Figure 831818DEST_PATH_IMAGE034
Figure 618509DEST_PATH_IMAGE035
。
8. the method of claim 7, wherein the dynamic response signal is a dynamic response signal
Figure 851913DEST_PATH_IMAGE020
The envelope squared signal of (a) is expressed as:
Figure 571607DEST_PATH_IMAGE036
wherein the content of the first and second substances,
Figure 350207DEST_PATH_IMAGE037
representing dynamic response signals
Figure 624194DEST_PATH_IMAGE020
The square of the envelope of (a) the signal,
Figure 395710DEST_PATH_IMAGE038
representing the hubert transform.
9. The method for extracting transient time-frequency characteristics based on single-degree-of-freedom system dynamic response according to claim 8, wherein the step of giving each envelope square signal to a corresponding row vector of a time-frequency matrix according to a corresponding natural frequency to obtain the time-frequency distribution of the signal to be analyzed comprises the steps of:
squaring the envelope
Figure 704331DEST_PATH_IMAGE037
Arranged in a time-frequency matrix
Figure 919412DEST_PATH_IMAGE039
To (1) a
Figure 946274DEST_PATH_IMAGE016
Line, get a frequency of
Figure 6634DEST_PATH_IMAGE014
The time-frequency distribution of (c):
Figure 684609DEST_PATH_IMAGE040
wherein the content of the first and second substances,
Figure 70591DEST_PATH_IMAGE041
indicating a frequency of
Figure 319169DEST_PATH_IMAGE014
Time-frequency distribution of (2).
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