CN115687862A - Rotating machinery signal time-frequency analysis method based on time-varying filtering - Google Patents
Rotating machinery signal time-frequency analysis method based on time-varying filtering Download PDFInfo
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Abstract
The invention provides a time-varying filtering-based rotating machinery signal time-frequency analysis method, and belongs to the technical field of state monitoring and fault diagnosis of rotating machinery equipment. The method comprises the following steps: acquiring a time domain signal of a target rotating machine under a non-steady working condition as an original signal; determining a time-frequency curve of each single-component signal in the original signal; extracting single-component signals corresponding to all time-frequency curves in a time domain through time-varying filtering; and calculating the Hilbert time-frequency distribution of each extracted single-component signal, and superposing the Hilbert time-frequency distributions to obtain the time-frequency distribution of the original signal. By adopting the method and the device, the problems of time-frequency fuzziness, cross item interference and mode confusion can be solved, and the time-frequency distribution with higher time-frequency resolution can be obtained.
Description
Technical Field
The invention relates to the technical field of state monitoring and fault diagnosis of rotary mechanical equipment, in particular to a time-varying filtering-based rotary mechanical signal time-frequency analysis method.
Background
The rotary machine is widely applied to the fields of traffic, energy, industry and the like, carries out state monitoring and fault diagnosis on the rotary machine through dynamic operation signals such as vibration, current, stress strain and the like, and is of great importance to equipment operation and maintenance. The characteristic frequency of each rotating component (including shafts, gears, bearings, etc.) in a rotary machine typically varies in proportion to the input rotational frequency. The operating conditions of the rotating machinery often have strong instability, so that each frequency component in the signal has time-varying characteristics and is overlapped in a frequency domain, and at the moment, the signal cannot be simply analyzed and extracted through a time domain or a frequency domain to obtain the characteristics. The time-frequency analysis method can comprehensively reveal the time-varying characteristics of the non-stationary signal in three aspects of time, frequency and amplitude (or power), and has important significance for monitoring the state of the rotating machinery and diagnosing faults.
The traditional time-frequency analysis method (such as short-time Fourier transform, continuous wavelet transform and the like) has the defects of low time-frequency resolution, cross term interference (Wigner-Ville distribution) and the like, and is difficult to accurately display weak transient characteristics when the frequency of signal components is close to or the noise is strong. Hilbert-Huang transform decomposes a multi-component signal into a plurality of single-component signals by an adaptive mode decomposition method, and then constructs the time-frequency distribution of the original signal by respectively calculating the instantaneous frequency and the envelope curve of the single-component signals. The time-frequency distribution has good time-frequency resolution, is not interfered by cross terms, can reflect the transient characteristics of signals, and is suitable for time-frequency analysis of complex multi-component non-stationary signals. Common adaptive mode decomposition methods include Empirical Mode Decomposition (EMD), local Mean Decomposition (LMD), intrinsic time scale decomposition (ITD), variational Mode Decomposition (VMD), and the like. However, when signals with large frequency variation range or frequency interruption are decomposed, the adaptive mode decomposition method has a mode confusion problem, and the same frequency component with the same physical meaning may be decomposed into different single-component signals, so that the decomposed signals cannot further reveal the time-frequency distribution of the original signals. The mode confusion problem causes the time-frequency analysis method based on the self-adaptive mode decomposition to have poor robustness, and the application of the time-frequency analysis method in the engineering problem is limited.
Disclosure of Invention
The embodiment of the invention provides a time-frequency analysis method for a rotating machinery signal based on time-varying filtering, which can overcome the problems of time-frequency blur, cross item interference and mode confusion and obtain time-frequency distribution with higher time-frequency resolution.
The rotating machinery signal time-frequency analysis method based on time-varying filtering provided by the embodiment of the invention comprises the following steps:
acquiring a time domain signal of a target rotating machine under a non-steady working condition as an original signal;
determining a time-frequency curve of each single-component signal in the original signal;
extracting single-component signals corresponding to each time-frequency curve in a time domain through time-varying filtering;
and calculating the Hilbert time-frequency distribution of each extracted single-component signal, and superposing the Hilbert time-frequency distributions to obtain the time-frequency distribution of the original signal.
Wherein the time domain signal comprises: vibration, displacement, sound, strain, pressure, or electrical signal.
Wherein, the determining the time-frequency curve of each single-component signal in the original signal comprises:
acquiring input frequency conversion of a target rotating machine;
calculating the characteristic order of each characteristic frequency of the rotating machinery relative to the input frequency;
and multiplying the input frequency conversion by the characteristic order to obtain a time-frequency curve of each single-component signal in the original signal.
Wherein, the determining the time-frequency curve of each single-component signal in the original signal comprises:
carrying out short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
and estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph to obtain the time-frequency curve of each single-component signal in the original signal.
Wherein, the determining the time-frequency curve of each single-component signal in the original signal comprises:
acquiring input frequency conversion of a target rotating machine;
carrying out short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
calculating a characteristic order of a frequency component in direct proportion to the input conversion frequency, and multiplying the input conversion frequency by the characteristic order to estimate a time-frequency curve of the frequency component;
and for other frequency components irrelevant to input frequency conversion, estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph.
Wherein, the extracting the single component signal corresponding to each time-frequency curve in the time domain through the time-varying filtering comprises:
a1, determining the upper cut-off frequency f of time-varying filtering according to the obtained time-frequency curve cu (t) and lower cut-off frequency f cl (t)：
Wherein t represents time, s k (t) represents the time-frequency curve of the kth characteristic order, and b (t) represents the time-varying filtering bandwidth;
a2, according to the upper cut-off frequency f of the obtained time-varying filter cu (t) and lower cut-off frequency f cl (t) determining the local filter length l n ：
Where N =0,1, \8230;, N-1, N is the length of the time domain signal, L denotes the filter length parameter, α denotes the coefficient of variation, ρ (N) denotes the sum of the squared derivatives of the local cut-off frequencies, ρ (N) denotes the sum of the local cut-off frequencies max Represents the maximum value of ρ (n), f cu (n) represents the upper cut-off frequency of the time-varying filtering, f cl (n) represents the lower cut-off frequency of the time-varying filtering, t (n) represents the nth point in time,
represents rounding down;
wherein, L represents a filter length parameter, alpha represents a change coefficient, N =0,1, \8230, and N-1, N is the length of a time domain signal;
a3, according to the obtained upper cut-off frequency f cu (t), lower cut-off frequency f cl (t) and local filter length l n Constructing a filter matrix W;
a4, performing time-varying filtering on the original signal by using a filter matrix to obtain a single-component signal:
Y＝WX
wherein, X is the original signal, Y is the single component signal;
and A5, repeating the steps A1-A4 to obtain single-component signals corresponding to the time-frequency curves.
Wherein the filter matrix W is represented as:
wherein, W (n) Denotes a local filter at t (n), an
Is a local filter W (n) Filter coefficients of (2) with a local filter length equal to n +1。
Wherein, the calculating the Hilbert time-frequency distribution of each extracted single-component signal, and the overlapping the Hilbert time-frequency distribution to obtain the time-frequency distribution of the original signal comprises:
performing Hilbert transform on each single-component signal to convert the real signal into a complex signal;
calculating the amplitude envelope and instantaneous frequency of each single-component signal based on the complex signal;
constructing Hilbert time-frequency distribution of each single-component signal based on the obtained amplitude envelope and instantaneous frequency of each single-component signal;
and overlapping the Hilbert time-frequency distribution of each single-component signal to obtain the time-frequency distribution of the original signal.
Wherein, the formula of Hilbert transform is as follows:
wherein, y k (t) is the k characteristic order single component signal extracted by time-varying filtering, H [ y [ k (t)]Denotes y k (t) a hilbert transformed complex signal;
hilbert time-frequency distribution TFR of single-component signal k (t, f) is expressed as:
TFR k (t,f)＝a k (t)δ[f(t)-f k (t)]
wherein, y k (t) is the k characteristic order single component signal extracted by time-varying filtering, TFR k (t, f) represents a one-component signal y k (t) Hilbert time-frequency distribution, a k (t) is the one-component signal y k (t) amplitude envelope, f k (t) is the one-component signal y k (t) instantaneous frequency, delta [. Cndot.)]F (t) represents a frequency independent variable at the moment t, and t and f are respectively a time independent variable and a frequency independent variable;
the time-frequency distribution TFR (t, f) of the original signal is expressed as:
the technical scheme provided by the embodiment of the invention has the beneficial effects that at least:
(1) The time-varying filtering adopted by the embodiment can directly extract the time-varying single-component signal in the time-domain signal under the non-stable working condition in the time domain, thereby retaining the key information of the time-domain signal such as instantaneous phase, frequency, amplitude and the like, simultaneously avoiding the mode confusion problem of the self-adaptive decomposition method, also avoiding the calculation error introduced by the angular domain resampling mode, and improving the accuracy of the subsequent time-frequency distribution;
(2) Compared with the traditional time-frequency analysis method based on integral transformation, the time-frequency distribution with higher time-frequency resolution can be obtained based on the single-component signal and the Hilbert transformation in the embodiment to reveal the transient characteristics of the signal, so that the transient characteristics of the monitored equipment can be extracted, the transient characteristics are not limited by the Heisenberg uncertainty principle, are not interfered by cross terms, have higher time and frequency resolution, and can clearly show the transient characteristics of various densely distributed components.
Drawings
In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the description below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a time-frequency analysis method for a rotating machine signal based on time-varying filtering according to an embodiment of the present invention;
fig. 2 is a schematic flow chart of a time-frequency analysis method for a rotating machine signal based on time-varying filtering according to embodiment 2 of the present invention;
fig. 3 is a schematic diagram of time-frequency distribution based on short-time fourier transform according to embodiment 3 of the present invention;
fig. 4 is a schematic diagram of time-frequency distribution based on empirical mode decomposition according to embodiment 3 of the present invention;
fig. 5 is a schematic time-frequency distribution diagram based on time-varying filtering according to embodiment 3 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.
Example one
As shown in fig. 1, an embodiment of the present invention provides a time-frequency analysis method for a rotating machine signal based on time-varying filtering, including:
s101, acquiring a time domain signal of a target rotating machine under a non-steady working condition as an original signal;
in the embodiment, a time domain signal x (t) of a target rotating machine is obtained, wherein the length of the time domain signal x (t) is N; the time domain signal includes: vibration, displacement, sound, strain, pressure, or electrical signal.
S102, determining a time-frequency curve of each single-component signal in the original signal;
in this embodiment, the single component signal refers to a signal having only one instantaneous frequency component.
In the embodiment, 3 ways are provided to determine the time-frequency curve of each single-component signal in the original signal; the first method comprises the following steps:
acquiring an input conversion frequency s (t) of a target rotating machine;
calculating the characteristic order of each characteristic frequency (specifically: the characteristic frequency of each gear) of the rotary machine relative to the input rotation frequency to obtain a characteristic order sequence p k Wherein K =1,2, \8230, K represents the number of characteristic frequencies theoretically existing;
converting the input frequency s (t) to a characteristic order p k Multiplying to obtain the time-frequency curve s of each single-component signal in the original signal k (t); wherein s is k (t) represents time-frequency curves of k characteristic orders.
The second method comprises the following steps:
performing short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
and estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph to obtain the time-frequency curve of each single-component signal in the original signal.
The third method comprises the following steps:
acquiring the input frequency conversion of a target rotating machine;
performing short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
calculating a characteristic order of a frequency component in direct proportion to the input conversion frequency, and multiplying the input conversion frequency by the characteristic order to estimate a time-frequency curve of the frequency component;
and for other frequency components irrelevant to the input frequency conversion, estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph.
S103, extracting single-component signals corresponding to the time-frequency curves in a time domain through time-varying filtering; the method specifically comprises the following steps:
a1, determining the upper cut-off frequency f of time-varying filtering according to the obtained time-frequency curve cu (t) and lower cut-off frequency f cl (t)：
Wherein t represents time, s k (t) represents the time-frequency curve of the kth characteristic order, and b (t) represents the time-varying filtering bandwidth;
a2, according to the upper cut-off frequency f of the obtained time-varying filter cu (t) and lower cut-off frequency f cl (t) determining the local filter length l n ：
Where N =0,1, \ 8230;, N-1, N is the length of the time domain signal, L represents the filter length parameter, α represents the coefficient of variation, α ranges (0, 1), ρ (N) represents the sum of the square of the derivatives of the local cut-off frequencies, ρ max Represents the maximum value of ρ (n), f cu (n) represents the upper cut-off frequency of the time-varying filtering, f cl (n) represents a lower cut-off frequency of the time-varying filtering, t (n) represents an nth time point,
expressing rounding down, this formulaRequested l n The value range of the local filter length is limited to [ L-alpha L, L]And (4) the following steps.
In the embodiment, the essence of N and t represents time, and when the time can be represented as a continuous value, the time is represented by t, and when the time cannot be represented as a continuous value, the time is represented by N, N =0,1, \ 8230;, N-1.
A3, according to the obtained upper cut-off frequency f cu (t), lower cut-off frequency f cl (t) and local filter length l n Constructing a filter matrix W;
in this embodiment, the upper cut-off frequency f is obtained cu (t), lower cut-off frequency f cl (t) and local Filter Length l n Designing a local bandpass filter W using a window function method (n) And generating a filter matrix W:
wherein, W (n) Denotes a local filter at t (n), an
Wherein the content of the first and second substances,
is a local filter W (n) Filter coefficients of (2) with a local filter length equal to n +1。
And A4, performing time-varying filtering on the original signal by using a filter matrix to obtain a single-component signal:
Y＝WX
wherein, X is the original signal, Y is the single component signal;
wherein the content of the first and second substances,
is an input signal X (t), and X and X (t) are different expressions of the input signal;
for one-shot time-varying filteringOutput signal, i.e. extracted characteristic order k-th mono-component signal y k (t), (X, Y are X (t) and Y, respectively k A matrix format of N rows and 1 columns of (t);
and A5, repeating the steps A1-A4 to obtain single-component signals corresponding to the time-frequency curves.
S104, calculating hilbert time-frequency distributions of the extracted single-component signals, and superimposing the hilbert time-frequency distributions to obtain a time-frequency distribution of an original signal, which may specifically include the following steps:
b1, performing Hilbert transform on each single-component signal, and converting a real signal into a complex signal; wherein, the formula of Hilbert transform is as follows:
wherein, y k (t) is the k characteristic order single component signal extracted by time-varying filtering, H [ y [ k (t)]Denotes y k (t) the hilbert transformed complex signal;
b2, calculating the amplitude envelope a of each single-component signal based on the complex signal k (t) and instantaneous frequency f k (t); wherein, a k (t) and f k (t) is represented by:
wherein, y k (t) is the k-th eigenorder single component signal extracted by time-varying filtering, a k (t) represents the amplitude envelope of the single-component signal, f k (t) represents the instantaneous frequency of the single component signal, j represents an imaginary number;
b3, constructing the Hilbert time-frequency distribution TFR of each single-component signal based on the obtained amplitude envelope and instantaneous frequency of each single-component signal k (t,f)：
TFR k (t,f)＝a k (t)δ[f(t)-f k (t)]
Wherein, delta [ ·]Is a Dirac function, TFR k (t, f) denotes a one-component signal y k (t) Hilbert time-frequency distribution, a k (t) represents the one-component signal y k (t) amplitude envelope, f k (t) represents the one-component signal y k (t), f (t) represents the frequency argument at time t, t and f are the time and frequency arguments, respectively;
and B4, overlapping the Hilbert time-frequency distribution of each single-component signal to obtain the time-frequency distribution TFR (t, f) of the original signal:
in this embodiment, the instantaneous frequency and amplitude of each single-component signal are calculated through hilbert variation to obtain hilbert time-frequency distribution of each single-component signal, and the time-frequency distribution matrices of each single-component signal are superimposed to obtain time-frequency distribution of the original signal.
According to the time-frequency analysis method for the rotating machinery signal based on the time-varying filtering, disclosed by the embodiment of the invention, for the time-domain signal of the rotating machinery under the non-stable working condition, each single-component signal is extracted and the time-frequency distribution of the single-component signal is constructed, so that the problems of time-frequency blurring, cross term interference and mode confusion are solved, the time-frequency distribution with higher time-frequency resolution is obtained, and the transient characteristic of the signal is revealed.
In summary, the time-frequency analysis method for a rotating mechanical signal based on time-varying filtering provided by the embodiment of the present invention has at least the following beneficial effects:
(1) The time-varying filtering adopted by the embodiment can directly extract the time-varying single-component signal in the time-domain signal under the non-stable working condition in the time domain, thereby retaining the key information of the time-domain signal such as instantaneous phase, frequency, amplitude and the like, simultaneously avoiding the mode confusion problem of the self-adaptive decomposition method, also avoiding the calculation error introduced by the angular domain resampling mode, and improving the accuracy of the subsequent time-frequency distribution;
(2) Compared with the traditional time-frequency analysis method based on integral transformation, the time-frequency distribution with higher time-frequency resolution can be obtained based on the single-component signal and the Hilbert transformation in the embodiment to reveal the transient characteristics of the signal, so that the transient characteristics of the monitored equipment can be extracted, the transient characteristics are not limited by the Heisenberg uncertainty principle, are not interfered by cross terms, have higher time and frequency resolution, and can clearly show the transient characteristics of various densely distributed components.
Example 2
In this embodiment, as shown in fig. 2, the obtained time-domain signal x (t) is a superposition of four non-linear am frequency-modulated signals, and an analytic expression thereof is:
wherein, x (k) represents kth single component signal, its amplitude modulation component is 0.5sin (2 pi x 0.5 t), frequency modulation component is 2 pi k ^ integral factor (-100 t) 2 +250t + 50) dt, a sampling frequency of 2000Hz, a duration of 1s, and a signal length N of 2000. The simulation signal can simulate various signal types of time-varying multi-component, including but not limited to physical quantities such as vibration, sound, pressure, electric signals and the like.
Performing short-time Fourier transform on the time-domain signal x (t), and estimating a time-frequency curve s of each single-component signal based on a time-frequency ridge line k (t)；
To obtain a time-frequency curve s k (t) is taken as a central frequency, a time-varying filter bandwidth b (t) is set, and an upper cut-off frequency f of the time-varying filter is calculated cu (t) and lower cut-off frequency f cl (t)；
Based on the obtained upper cut-off frequency f cu (t) and lower cut-off frequency f cl (t) generating a filter matrix W and performing time-varying filtering Y = WX to obtain each single-component signal Y k (t)；
Calculating the instantaneous frequency f of each single-component signal by using Hilbert transform k (t) and amplitude envelope a k (t) generating a Hilbert time-frequency distribution TFR of each of the single-component signals k (t,f)；
Overlapping the Hilbert time-frequency distribution of each single-component signal to obtain the time-frequency distribution TFR (t, f) of the original signal;
the meanings of the subgraphs in FIG. 2 are in turn: inputting multi-component signal waveforms, estimating ridge lines based on traditional time-frequency distribution, time-varying cut-off frequency of each component, extracting each single-component signal through time-varying filtering, time-frequency distribution of each single-component signal, and time-frequency distribution of reconstructed original signals.
Example 3
In the embodiment, the acquired time domain signal x (t) is a radial displacement signal of a certain water turbine rotor;
calculating characteristic order p of water turbine rotor k ，k＝1,2,…,5；
The input frequency s (t) of the water turbine rotor in example 3 is multiplied by the characteristic order to obtain 5 estimated time-frequency curves s k (t)，k＝1,2,…,5；
Calculating short-time Fourier transform of time-domain signal x (t), and estimating time-frequency curves s of other single-component signals except the 5 time-frequency curves based on the time-frequency ridge line k (t)，k＝6,…,K；
To obtain a time-frequency curve s k (t) is the central frequency, a time-varying filtering bandwidth b (t) is set, and the upper cut-off frequency f of the time-varying filtering is calculated cu (t) and lower cut-off frequency f cl (t)；
Based on the obtained upper cut-off frequency f cu (t) and lower cut-off frequency f cl (t) generating a filter matrix W and performing time-varying filtering Y = WX to obtain each single-component signal Y k (t)；
Calculating the instantaneous frequency f of each single-component signal by using Hilbert transform k (t) and amplitude envelope a k (t) generating a Hilbert time-frequency distribution TFR of each of the single-component signals k (t,f)；
And overlapping the Hilbert time-frequency distribution of each single-component signal to obtain the time-frequency distribution TFR (t, f) of the original signal.
In this embodiment, as can be seen from fig. 3 to 5, the time-frequency distribution with higher time-frequency resolution can be obtained by the time-varying filtering-based time-frequency analysis method for the rotating machine signal provided by the embodiment of the present invention.
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 time-frequency analysis method for rotating machinery signals based on time-varying filtering is characterized by comprising the following steps:
acquiring a time domain signal of a target rotating machine under a non-steady working condition as an original signal;
determining a time-frequency curve of each single-component signal in the original signal;
extracting single-component signals corresponding to each time-frequency curve in a time domain through time-varying filtering;
and calculating the Hilbert time-frequency distribution of each extracted single-component signal, and superposing the Hilbert time-frequency distributions to obtain the time-frequency distribution of the original signal.
2. The time-frequency analysis method for rotating machinery signals based on time-varying filtering according to claim 1, wherein the time-domain signal comprises: vibration, displacement, sound, strain, pressure, or electrical signal.
3. The time-frequency analysis method for rotating machinery signals based on time-varying filtering as claimed in claim 1, wherein the determining the time-frequency curve of each single component signal in the original signal comprises:
acquiring input frequency conversion of a target rotating machine;
calculating the characteristic order of each characteristic frequency of the rotating machinery relative to the input frequency;
and multiplying the input frequency conversion by the characteristic order to obtain a time-frequency curve of each single-component signal in the original signal.
4. The time-frequency analysis method for rotating machinery signals based on time-varying filtering as claimed in claim 1, wherein the determining the time-frequency curve of each single component signal in the original signal comprises:
performing short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
and estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph to obtain the time-frequency curve of each single-component signal in the original signal.
5. The time-frequency analysis method for rotating machinery signals based on time-varying filtering as claimed in claim 1, wherein the determining the time-frequency curve of each single component signal in the original signal comprises:
acquiring the input frequency conversion of a target rotating machine;
performing short-time Fourier transform on the original signal to obtain a traditional time-frequency distribution map of the original signal;
calculating a characteristic order of a frequency component in direct proportion to the input conversion frequency, and multiplying the input conversion frequency by the characteristic order to estimate a time-frequency curve of the frequency component;
and for other frequency components irrelevant to the input frequency conversion, estimating a time-frequency curve corresponding to each time-frequency ridge peak value based on the obtained traditional time-frequency distribution graph.
6. The time-varying filtering-based time-frequency analysis method for a rotating machine signal according to claim 1, wherein the extracting the single-component signal corresponding to each time-frequency curve in the time domain by the time-varying filtering comprises:
a1, determining the upper cut-off frequency f of time-varying filtering according to the obtained time-frequency curve cu (t) and lower cut-off frequency f cl (t)：
Wherein t represents time, s k (t) represents the time-frequency curve of the kth characteristic order, and b (t) represents the time-varying filtering bandwidth;
a2, according to the upper cut-off frequency f of the obtained time-varying filter cu (t) and lower cut-off frequency f cl (t)，Determining a local filter length l n ：
Where N =0,1, \8230;, N-1, N is the length of the time domain signal, L denotes the filter length parameter, α denotes the coefficient of variation, ρ (N) denotes the sum of the squared derivatives of the local cut-off frequencies, ρ (N) denotes the sum of the local cut-off frequencies max Represents the maximum value of ρ (n), f cu (n) represents the upper cut-off frequency of the time-varying filtering, f cl (n) represents the lower cut-off frequency of the time-varying filtering, t (n) represents the nth point in time,
represents rounding down;
wherein L represents a filter length parameter, α represents a coefficient of variation, N =0,1, \8230, and N-1, N is the length of the time domain signal;
a3, according to the obtained upper cut-off frequency f cu (t), lower cut-off frequency f cl (t) and local filter length l n Constructing a filter matrix W;
a4, performing time-varying filtering on the original signal by using a filter matrix to obtain a single-component signal:
Y＝WX
wherein, X is the original signal, Y is the single component signal;
and A5, repeating the steps A1-A4 to obtain single-component signals corresponding to the time-frequency curves.
7. The time-frequency analysis method for rotating machine signals based on time-varying filtering according to claim 6, wherein the filter matrix W is expressed as:
wherein, W (n) Denotes a local filter at t (n), an
Is a local filter W (n) Filter coefficients of (2) with a local filter length equal to n +1。
8. The time-varying filtering-based time-frequency analysis method for a rotating machine signal according to claim 1, wherein the calculating the extracted hilbert time-frequency distribution of each single-component signal, and the superimposing the hilbert time-frequency distributions to obtain the time-frequency distribution of the original signal comprises:
performing Hilbert transform on each single-component signal to convert the real signal into a complex signal;
calculating the amplitude envelope and instantaneous frequency of each single-component signal based on the complex signal;
constructing Hilbert time-frequency distribution of each single-component signal based on the obtained amplitude envelope and instantaneous frequency of each single-component signal;
and overlapping the Hilbert time-frequency distribution of each single-component signal to obtain the time-frequency distribution of the original signal.
9. The time-frequency analysis method for rotating mechanical signals based on time-varying filtering according to claim 8, wherein the hilbert transform is formulated as:
wherein, y k (t) is the k characteristic order single component signal extracted by time-varying filtering, H [ y [ k (t)]Denotes y k (t) the hilbert transformed complex signal;
hilbert time-frequency distribution TFR of single-component signal k (t, f) is expressed as:
TFR k (t,f)＝a k (t)δ[f(t)-f k (t)]
wherein, y k (t) is the k characteristic order single component signal extracted by time-varying filtering, TFR k (t, f) represents a one-component signal y k (t) Hilbert time-frequency distribution, a k (t) is the one-component signal y k (t) amplitude envelope, f k (t) is the one-component signal y k (t) instantaneous frequency, delta [. Cndot.)]F (t) represents a frequency independent variable at the moment t, and t and f are respectively a time independent variable and a frequency independent variable;
the time-frequency distribution TFR (t, f) of the original signal is expressed as:
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