CN113988125A - Torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation - Google Patents

Torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation Download PDF

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CN113988125A
CN113988125A CN202111243696.7A CN202111243696A CN113988125A CN 113988125 A CN113988125 A CN 113988125A CN 202111243696 A CN202111243696 A CN 202111243696A CN 113988125 A CN113988125 A CN 113988125A
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torsional vibration
vibration signal
swarm optimization
particle swarm
synchronous compression
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曹宏瑞
周铖
魏江
史江海
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Xian Jiaotong University
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Abstract

The invention discloses a torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation, which mainly comprises the steps of taking an energy entropy as a fitness function of a particle swarm optimization algorithm, and optimizing parameters of a variational modal decomposition algorithm by adopting the particle swarm optimization algorithm; then substituting the optimized optimal parameter combination into a variational modal decomposition algorithm to realize the decomposition and noise reduction of the torsional vibration signal; then, an intrinsic mode function IMF with a large correlation coefficient is adopted to realize the reconstruction of the torsional vibration signal; then, Fourier-based synchronous compression transformation is adopted for the reconstructed torsional vibration signals to obtain time-frequency distribution with clear resolution; and finally, extracting the instantaneous frequency of the torsional vibration signal from the time-frequency distribution by adopting a Viterbi algorithm. According to the transient frequency extraction method of the torsional vibration signal, parameters K and alpha of the variational modal decomposition algorithm are calculated through the particle swarm optimization algorithm to be the optimal combination, the most effective noise reduction of the torsional vibration signal is realized on the basis, and the more accurate transient frequency can be extracted.

Description

Torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation
Technical Field
The invention belongs to the field of torsional vibration signal processing methods, and particularly relates to a torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation.
Background
Torsional vibration is a special form of vibration, so-called torsional vibration, i.e. periodic vibration caused by rotation of an object about its own axis. Torsional vibration is one of the important dynamic properties affecting the safe operation of rotating machinery such as gas turbines, aircraft engines, air compressors, armored vehicles and propulsion shafting. Torsional vibration, which is a difficult problem to avoid in the above rotating mechanical shafting, is one of the main factors affecting the operational reliability and the service life of the shafting, and the damage caused by the torsional vibration has been widely paid attention for a long time.
The instantaneous frequency is an effective description of the characteristics of the non-stationary signals, the statistical characteristics of the non-stationary signals are related to time, and the key for extracting the characteristics of the torsional vibration fault of the mechanical equipment is to grasp the change rule of the frequency components of the torsional vibration signals along with the time.
The time-frequency analysis method is a signal analysis method under the non-stationary working condition, two variables of time and frequency are comprehensively considered, and the change rule of each component in the signal along with the time can be revealed. The synchronous compression transformation is a time-frequency post-processing method, and the result of the time-frequency transformation is post-processed, the time-frequency energy distribution is rearranged, the energy of each time-frequency point is superposed to an energy center, and the time-frequency distribution with higher time-frequency aggregation than the traditional time-frequency analysis (such as short-time Fourier transformation and wavelet transformation) is obtained, but the defect of poor noise robustness exists. In the time-frequency analysis process by adopting synchronous compression transformation, because the noise is usually accompanied in the time-frequency spectrum of the short-time Fourier transformation, the noise can be compressed in the compression process, the anti-noise effect is poor, and the great interference is caused to the extraction of the instantaneous frequency in the later period.
The variational modal decomposition algorithm has higher noise immunity and better filtering characteristic in the process of signal processing. However, when the variation modal decomposition algorithm is applied to decompose and denoise the torsional vibration signal, corresponding variation modal decomposition parameters [ K, α ] need to be specified in advance, and the parameters corresponding to different signals are different, where K is the decomposition number of the torsional vibration signal into the single-component eigen-modal function IMF, and α is a penalty factor. If the K value is too small, problems of mode aliasing or mode loss and the like can occur, and torsional vibration characteristics cannot be effectively extracted; too large a value of K will result in excessive decomposition and increase in algorithm processing time.
Disclosure of Invention
In view of the above-mentioned deficiencies in the prior art, the present invention provides a method for extracting the instantaneous frequency of a torsional vibration signal based on improved synchronous compression transformation. The method comprises the steps of solving parameters K and alpha of a variational modal decomposition algorithm through a particle swarm optimization algorithm to be an optimal combination, decomposing torsional vibration signals and carrying out noise reduction reconstruction on the basis of the optimal combination, obtaining time-frequency distribution of the torsional vibration signals by adopting short-time Fourier synchronous compression transformation, and finally extracting more accurate torsional vibration instantaneous frequency by adopting a Viterbi algorithm.
In order to achieve the purpose, the invention is realized by adopting the following technology:
a torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation comprises the following processes:
calculating the optimal combination of the variation modal decomposition parameters by utilizing a particle swarm optimization algorithm;
carrying out modal decomposition on the acquired torsional vibration signals by adopting a variational modal decomposition algorithm and the optimal parameter combination to obtain a single component IMF;
calculating Pearson's correlation coefficient r (Y (t), Y) of the single component IMF and the acquired torsional vibration signalIMFk(t))；
Reconstructing the acquired torsional vibration signal by using a single-component IMF with a large Pearson correlation coefficient to obtain a noise-reduced torsional vibration signal;
carrying out short-time Fourier synchronous compression transformation on the torsional vibration signals subjected to noise reduction to obtain time-frequency distribution of the torsional vibration signals;
and extracting the torsional vibration instantaneous frequency from the time-frequency distribution of the torsional vibration signal by adopting a Viterbi algorithm.
Preferably, when the particle swarm optimization algorithm is used for obtaining the optimal combination of the variational modal decomposition parameters, the particle swarm optimization algorithm is adopted as follows:
Figure BDA0003320169390000021
wherein the content of the first and second substances,
Figure BDA0003320169390000022
i represents the ith particle; c. C1、c2Is a learning factor; r is1、r2A random function that adjusts the relationship between the particles and the optimum value; x is the number ofiIndicating the position of the ith particle;
Figure BDA0003320169390000031
representing the velocity of the ith particle at the nth iteration;
Figure BDA0003320169390000032
representing the position of the ith particle at the nth iteration; n is the number of iterations; p is a radical ofiRepresenting the local optimal solution searched by the ith particle; p is a radical ofgiRepresenting the global optimal solution searched by the ith particle; w is the inertial weight; the output result of the particle swarm optimization algorithm is x, x represents the position of the particle, and x is [ K, alpha ]]K denotes the number of decompositions for decomposing the torsional vibration signal into the single component IMF, and α is a penalty factor.
Preferably, when the particle swarm optimization algorithm is used for solving the optimal combination of the variational modal decomposition parameters, the particle swarm optimization algorithm is initialized, and then the initialized particle swarm optimization algorithm is used for solving the optimal combination of the variational modal decomposition parameters;
the initialization of the particle swarm optimization algorithm comprises the position initialization and the speed initialization of all the particles:
wherein for the position x of the ith particleiThe initialization is as follows:
xi＝round(3rand(1,1))(xmax-xmin)+xmin
velocity v for the ith particleiThe initialization is as follows:
vi＝round(3rand(1,1))+2
in the formula: round () means rounding a number to an integer; rand () represents a random number between 0 and 1; x is the number ofmax、xminEach represents x ═ K, α]Maximum and minimum values of;
the inertial weight w is:
Figure BDA0003320169390000033
wherein: w is amaxIs the maximum inertia weighted value; w is aminIs the minimum inertia weight value; n is the nth iteration; n ismaxIs the maximum number of iterations.
Preferably, the fitness function value L of the particle swarm optimization algorithmpThe following were used:
Figure BDA0003320169390000034
wherein the content of the first and second substances,
Figure BDA0003320169390000035
j represents the sequence number of the single component IMF, E (j) represents the energy of the jth single component IMF, and K represents the number of decompositions for decomposing the torsional vibration signal into the single component IMF.
Preferably, the optimal combination of the variational modal decomposition parameters is obtained as follows:
and (3) performing iteration preset times on the particle swarm optimization algorithm, obtaining a fitness function value of the corresponding particle swarm optimization algorithm through each iteration, and taking the combination of the variation modal decomposition parameters corresponding to the maximum fitness function value as an optimal combination.
Preferably, the single component IMF is correlated with the Pearson's correlation coefficient r (Y (t), Y) of the acquired torsional vibration signalIMFk(t)) the following:
Figure BDA0003320169390000041
wherein: r (Y (t), YIMFk(t)) for the original torsional vibration signal Y (t) and each decomposed IMF signal YIMFk(t) a measure of linear dependence; cov (Y (t), Y)IMFk(t)) are Y (t) and YIMFk(t) covariance; var [ y (t)]Is the variance of the original torsional vibration signal y (t); var [ Y ]IMFk(t)]Is decomposed intoIMF signal YIMFk(t) variance.
Preferably, the short-time Fourier synchronous compression transform is:
Figure BDA0003320169390000042
wherein: u is a time variable; xi is a frequency variable; g (t) is a tightly supported window function in the time domain, and the window function is a Gaussian window function
Figure BDA0003320169390000043
Figure BDA0003320169390000044
Expressed as a short-time Fourier transform of the noise-reduced torsional vibration signal;
Figure BDA0003320169390000045
estimating an operator for the instantaneous frequency;
Figure BDA0003320169390000046
to represent
Figure BDA0003320169390000047
The effective support area of (a).
The invention also provides a torsional vibration signal instantaneous frequency extraction system based on improved synchronous compression transformation, which comprises:
an optimal combination calculation module: the method is used for solving the optimal combination of the variation modal decomposition parameters by utilizing a particle swarm optimization algorithm;
a modal decomposition module: the system comprises a parameter combination module, a component modal decomposition algorithm module and a single component IMF module, wherein the parameter combination module is used for carrying out modal decomposition on the acquired torsional vibration signals by adopting a variational modal decomposition algorithm and the optimal parameter combination to obtain a single component IMF;
a correlation coefficient calculation module: for calculating a pearson correlation coefficient of a single component IMF with the acquired torsional vibration signal;
a signal reconstruction module: the torsional vibration signal processing unit is used for reconstructing the acquired torsional vibration signal by using a single-component IMF with a large Pearson correlation coefficient to obtain a torsional vibration signal after noise reduction;
synchronous compression of transform blocks: the short-time Fourier synchronous compression transformation is carried out on the torsional vibration signals after noise reduction to obtain the time-frequency distribution of the torsional vibration signals;
a torsional vibration instantaneous frequency extraction module: and the Viterbi algorithm is adopted for extracting the torsional vibration instantaneous frequency from the time-frequency distribution of the torsional vibration signal.
The present invention also provides an electronic device, comprising:
one or more processors;
a storage device having one or more programs stored thereon;
when executed by the one or more processors, cause the one or more processors to implement the improved synchronous compression transform-based torsional vibration signal instantaneous frequency extraction method of the present invention as described above.
The present invention also provides a storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for extracting instantaneous frequency of a torsional vibration signal based on improved synchronous compression transformation according to the present invention.
The invention has the following beneficial effects:
in the method for extracting the torsional vibration signal instantaneous frequency based on the improved synchronous compression, the parameters [ K, alpha ] of the variational modal decomposition algorithm can be more accurately extracted by adopting the particle swarm optimization algorithm, so that the torsional vibration signal decomposition effect processed by adopting the variational modal decomposition algorithm reaches the maximum and the most reasonable effect, the noise reduction effect is more obvious, then the torsional vibration signal after noise reduction is processed by adopting short-time Fourier synchronous compression transformation to obtain time-frequency distribution, and finally the Viterbi algorithm is adopted to extract the torsional vibration instantaneous frequency with high precision from the time-frequency distribution.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flow chart of the method for extracting the instantaneous frequency of a torsional vibration signal based on improved synchronous compression transformation according to the present invention;
FIG. 2 is a time domain waveform of an algorithm signal according to an embodiment of the present invention;
FIG. 3 is a graph of theoretical instantaneous frequency of a signal of an algorithm of the present invention as validated by an embodiment of the present invention;
FIG. 4 is a time-frequency distribution diagram of an unoptimized short-time Fourier synchronous compression transform for verifying the superiority of the algorithm of the present invention in an embodiment of the present invention;
FIG. 5 is a graph of the results of the non-optimized instantaneous frequency extraction for verifying the superiority of the algorithm of the present invention in the embodiment of the present invention;
FIG. 6 is a fitness function curve obtained by particle swarm optimization in the embodiment of the present invention;
fig. 7(a) is a graph of a first mode function IMF of a torsional vibration signal subjected to a variable mode decomposition according to an embodiment of the present invention, and fig. 7(b) is a spectrum graph of the first mode function IMF of the torsional vibration signal subjected to the variable mode decomposition according to the embodiment of the present invention; fig. 7(c) is a diagram of a second mode function IMF of a torsional vibration signal decomposed by a variable mode in an embodiment of the present invention, and fig. 7(d) is a spectrum diagram of the second mode function IMF of the torsional vibration signal decomposed by the variable mode in the embodiment of the present invention; fig. 7(e) is a diagram of a third mode function IMF of the torsional vibration signal subjected to the variable mode decomposition in the embodiment of the present invention, and fig. 7(f) is a frequency spectrum diagram of the third mode function IMF of the torsional vibration signal subjected to the variable mode decomposition in the embodiment of the present invention; fig. 7(g) is a graph of a fourth mode function IMF of the torsional vibration signal decomposed by the variable mode in the embodiment of the present invention, and fig. 7(h) is a frequency spectrum graph of the fourth mode function IMF of the torsional vibration signal decomposed by the variable mode in the embodiment of the present invention;
FIG. 8 is a time domain waveform diagram of a reconstructed torsional vibration signal according to an embodiment of the present invention;
FIG. 9 is a time-frequency distribution diagram of a reconstructed signal according to an embodiment of the present invention;
FIG. 10 is a graph of the extracted torsional instantaneous frequency in an embodiment of the present invention;
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The method comprises the main processes of taking the energy entropy as a fitness function of a particle swarm optimization algorithm and adopting the particle swarm optimization algorithm to realize the accurate extraction of parameters of the variational modal decomposition algorithm; and substituting the extracted optimal parameter combination into a variational modal decomposition algorithm to realize noise reduction decomposition on the torsional vibration signal, then adopting an intrinsic mode function IMF with a large Pearson correlation coefficient to realize reconstruction on the torsional vibration signal, then carrying out short-time Fourier synchronous compression transformation on the reconstructed torsional vibration signal to obtain time-frequency distribution of the torsional vibration signal, and finally adopting a Viterbi algorithm to process the time-frequency distribution to realize instantaneous frequency extraction on the torsional vibration signal.
Referring to fig. 1-10, in particular, the method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation of the present invention comprises the following steps:
s1, collecting torsional vibration signals y (t);
s2, initializing relevant parameters of the particle swarm optimization algorithm:
the particle swarm optimization algorithm is as follows:
Figure BDA0003320169390000071
Figure BDA0003320169390000072
wherein: i is the ith particle; c. C1、c2Is a learning factor; r is1、r2To adjust the random function of the relationship between the particle and the optimum, r is often taken1、r2∈[0,1](ii) a The output result of the particle swarm optimization algorithm is x, x ═ K, alpha]K represents the number of the torsional vibration signals decomposed into single-component IMFs (intrinsic mode functions), and alpha is a penalty factor;
Figure BDA0003320169390000073
representing the velocity of the ith particle at the nth iteration;
Figure BDA0003320169390000074
representing the position of the ith particle at the nth iteration; n is the number of iterations, v is the particle velocity, and x is the particle position; p is a radical ofiRepresenting the local optimal solution searched by the ith particle; p is a radical ofgiRepresenting the global optimal solution searched by the ith particle; w is the inertial weight.
Position x for ith particleiThe initialization is as follows:
xi＝round(3rand(1,1))(xmax-xmin)+xmin (3)
velocity v for the ith particleiThe initialization is as follows:
vi＝round(3rand(1,1))+2 (4)
wherein: round means rounding a number to an integer; rand represents a random number between 0 and 1; x is the number ofmax、xminEach represents an independent variable x ═ K, α]Maximum and minimum values of;
wherein the inertial weight w is:
Figure BDA0003320169390000081
wherein: w is amaxIs the maximum inertia weight value, wmax＝0.9；wminIs the minimum inertia weight value, wmin0.4; n is the nth iteration; n ismaxIs the maximum number of iterations.
S3, performing modal decomposition on the torsional vibration signal y (t) acquired in step S1 by using the variational modal decomposition algorithm as a parameter of the variational modal decomposition algorithm, where x is [ K, α ] obtained after each iteration in step S2 is completed, to obtain K single component IMFs;
s4, constructing a fitness function value of the particle swarm optimization algorithm:
Figure BDA0003320169390000082
Figure BDA0003320169390000083
wherein: l ispAnd E (j) represents the fitness function value of the particle swarm optimization algorithm, and E (j) represents the energy of the jth IMF.
S5, iterating the particle swarm optimization algorithm in the step S2 for N times to obtain fitness function values L of the N particle swarm optimization algorithmspFinding the largest LpThen maximum LpCorresponding [ K ]0,α0]And (4) obtaining the optimal solution of the particle swarm optimization algorithm.
S6, optimizing the obtained K0,α0]As a parameter of the variational modal decomposition algorithm, decomposing the torsional vibration signal y (t) collected in step S1 again to obtain K0Individual single component IMF.
S7, calculating K obtained in step S60Pearson's correlation coefficient r (Y (t), Y) of single component IMF and torsional vibration signal Y (t)IMFk(t))：
Figure BDA0003320169390000084
Wherein: r (Y (t), YIMFk(t)) for the original torsional vibration signal Y (t) and each decomposed IMF signal YIMFk(t) a measure of linear dependence; cov (Y (t), Y)IMFk(t)) are Y (t) and YIMFk(t) covariance; var [ y (t)]Is the variance of the original torsional vibration signal y (t); var [ Y ]IMFk(t)]For each IMF signal Y after decompositionIMFk(t) variance.
S8, taking Pearson correlation coefficient r (Y (t), Y in step S7IMFk(t)) performing noise reduction reconstruction on the torsional vibration signal by using the IMF corresponding to the large correlation number to obtain a noise-reduced torsional vibration signal y' (t).
S9, carrying out short-time Fourier synchronous compression transformation on the torsional vibration signal y' (t) subjected to noise reduction in the step S8:
Figure BDA0003320169390000091
wherein: u is a time variable; xi is a frequency variable; g (t) is a window function of time domain tight support, and the window function adopted by the invention is a Gaussian window function
Figure BDA0003320169390000092
Figure BDA0003320169390000093
Expressed as a short-time Fourier transform of the noise-reduced torsional vibration signal;
Figure BDA0003320169390000094
estimating an operator for the instantaneous frequency;
Figure BDA0003320169390000095
to represent
Figure BDA0003320169390000096
The effective support area of (a).
S10, the time-frequency distribution of the torsional vibration signal y' (t) is obtained in step S9.
And S11, extracting the torsional vibration instantaneous frequency in the time-frequency distribution obtained in the step S10 by adopting a Viterbi algorithm.
Examples
In order to verify the accuracy of the method provided by the invention on the torsional vibration signal, analog simulation is carried out by adopting an analog signal, and the analog simulation is compared and analyzed with an unoptimized synchronous compression transformation algorithm.
S1, assuming the analog simulation signals are:
y(t)＝sin(0.5×2πft+φ(t))+sin(1.5×2πft+φ(t))+sin(2×2πft+φ(t))+N1(t)
where, phi (t) is 0.5sin (20 pi t + pi/2) -pi/6, f is 100Hz, and the noise is white gaussian noise with a signal-to-noise ratio (SNR) of-5 dB.
The theoretical instantaneous frequencies obtained by calculation are respectively:
f1＝0.5f+5cos(20πt+π/2)
f2＝1.5f+5cos(20πt+π/2)
f3＝2f+5cos(20πt+π/2)
the analog simulation signal waveform and the theoretical instantaneous frequency waveform are shown in fig. 2 and 3, respectively.
S2, initializing relevant parameters of the particle swarm optimization algorithm:
in the particle swarm optimization algorithm, a learning factor c1＝c2＝2，r1、r2∈[0,1]The fitness function independent variables of the particle swarm are respectively K and alpha value ranges, K is more than or equal to 2 and less than or equal to 10, alpha is more than or equal to 10 and less than or equal to 5000, the dimension of the particle is set to 10, the speed v range is set to be [ -3,3]The iteration number of the particle swarm is set to 1000, and the maximum inertia weighted value wmax0.9, minimum inertia weight value wmin＝0.4。
S3, adopting [ K, alpha ] obtained after each iteration of the step S2 is completed as a parameter of a variational modal decomposition algorithm, and adopting the variational modal decomposition algorithm to carry out modal decomposition on the analog simulation signal y (t) in the step S1 to obtain K single-component IMFs;
s4, constructing a fitness function value of the particle swarm optimization algorithm:
Figure BDA0003320169390000101
Figure BDA0003320169390000102
wherein: l ispAnd E (j) represents the fitness function value of the particle swarm optimization algorithm, and E (j) represents the energy of the jth IMF.
S5, iterating the particle swarm optimization algorithm in the step S2 for N times to obtain fitness function values L of the N particle swarm optimization algorithmspFinding the largest LpThen maximum LpCorresponding [ K ]0,α0]And (4) obtaining the optimal solution of the particle swarm optimization algorithm.
Fig. 6 shows a fitness function curve obtained by the particle swarm optimization algorithm, and as can be seen from fig. 6, the particle swarm optimization algorithm iterates 100 times, the particle swarm fitness function value finally reaches convergence, the iteration number of the particle swarm when the convergence is completed is 36, and the corresponding [ K, α ] ═ 4,1500.
S6, taking the optimized [ K, α ] ═ 4,1500] as the parameters of the variational modal decomposition algorithm, and decomposing the analog simulation signal y (t) in step S1 again to obtain 4 single-component IMFs, as shown in fig. 7(a) to 7 (h).
S7, calculating Pearson correlation coefficient r (Y (t), Y of 4 single components IMF and torsional vibration signal Y (t) obtained in step S6IMFk(t)), the results are shown in Table 1, wherein IMF1 to IMF4 are correlation coefficients corresponding to the 1 st to 4 th single-component IMFs, respectively.
TABLE 1
Figure BDA0003320169390000103
S8, as can be seen from table 1, since the correlation coefficients of the single components IMF1 to IMF3 are large, the reconstructed torsional vibration signal y' (t) is obtained by performing reconstruction using the IMFs 1 to IMF3, as shown in fig. 8.
S9, performing short-time Fourier synchronous compression transformation on the torsional vibration signal y '(t) subjected to noise reduction in step S8 to obtain a time-frequency distribution of the torsional vibration signal y' (t), as shown in fig. 9. It can be found from fig. 9 that the time-frequency distribution with high time-frequency aggregation can be obtained by the method provided by the invention, and the time-frequency ridge line is very clear. To further illustrate the superiority of the method, fig. 4 is an unoptimized short-time Fourier synchronous compression transform time-frequency distribution diagram, and fig. 4 shows that the time-frequency ridge is almost submerged in noise in the high-frequency band except for the clear time-frequency ridge in the low-frequency band.
S10, extracting the torsional vibration instantaneous frequency in the time-frequency distribution obtained in the step S9 by using a Viterbi algorithm, as shown in FIG. 10. As can be seen from fig. 10, the transient frequency of the torsional vibration signal extracted by the method of the present invention substantially coincides with the theoretical transient frequency. Meanwhile, in order to further illustrate the superiority of the method of the present invention, fig. 5 is a comparison of torsional instantaneous frequencies extracted by the non-optimized Viterbi algorithm, and it can be clearly seen from the figure that the extracted instantaneous frequencies have better overlap ratio with theoretical instantaneous frequency components in the low frequency band, and aliasing occurs in the high frequency band.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.

Claims (10)

1. A torsional vibration signal instantaneous frequency extraction method based on improved synchronous compression transformation is characterized by comprising the following processes:
calculating the optimal combination of the variation modal decomposition parameters by utilizing a particle swarm optimization algorithm;
carrying out modal decomposition on the acquired torsional vibration signals by adopting a variational modal decomposition algorithm and the optimal parameter combination to obtain a single component IMF;
calculating a Pearson correlation coefficient of the single-component IMF and the acquired torsional vibration signal;
reconstructing the acquired torsional vibration signal by using a single-component IMF with a large Pearson correlation coefficient to obtain a noise-reduced torsional vibration signal;
carrying out short-time Fourier synchronous compression transformation on the torsional vibration signals subjected to noise reduction to obtain time-frequency distribution of the torsional vibration signals;
and extracting the torsional vibration instantaneous frequency from the time-frequency distribution of the torsional vibration signal by adopting a Viterbi algorithm.
2. The method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation as claimed in claim 1, wherein when the particle swarm optimization algorithm is used to find the optimal combination of the variable modal decomposition parameters, the particle swarm optimization algorithm is adopted as follows:
Figure FDA0003320169380000011
wherein the content of the first and second substances,
Figure FDA0003320169380000012
i represents the ith particle; c. C1、c2Is a learning factor; r is1、r2A random function that adjusts the relationship between the particles and the optimum value; x is the number ofiIndicating the position of the ith particle;
Figure FDA0003320169380000014
representing the velocity of the ith particle at the nth iteration;
Figure FDA0003320169380000013
representing the position of the ith particle at the nth iteration; n is the number of iterations; p is a radical ofiRepresenting the local optimal solution searched by the ith particle; p is a radical ofgiRepresenting the global optimal solution searched by the ith particle; w is the inertial weight; the output result of the particle swarm optimization algorithm is x, x represents the position of the particle, and x is [ K, alpha ]]K denotes the number of decompositions for decomposing the torsional vibration signal into the single component IMF, and α is a penalty factor.
3. The method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation as claimed in claim 2, wherein when the particle swarm optimization algorithm is used for solving the optimal combination of the variable modal decomposition parameters, the particle swarm optimization algorithm is initialized, and then the initialized particle swarm optimization algorithm is used for solving the optimal combination of the variable modal decomposition parameters;
the initialization of the particle swarm optimization algorithm comprises the position initialization and the speed initialization of all the particles:
wherein for the position x of the ith particleiThe initialization is as follows:
xi＝round(3rand(1,1))(xmax-xmin)+xmin
velocity v for the ith particleiThe initialization is as follows:
vi＝round(3rand(1,1))+2
in the formula: round () means rounding a number to an integer; rand () represents a random number between 0 and 1; x is the number ofmax、xminEach represents x ═ K, α]Maximum and minimum values of;
the inertial weight w is:
Figure FDA0003320169380000021
wherein: w is amaxIs the maximum inertia weighted value; w is aminIs the minimum inertia weight value; n is the nth iteration; n ismaxIs the maximum number of iterations.
4. The method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation as claimed in claim 2, wherein the fitness function value L of the particle swarm optimization algorithmpThe following were used:
Figure FDA0003320169380000022
wherein the content of the first and second substances,
Figure FDA0003320169380000023
j represents the sequence number of the single component IMF, E (j) represents the energy of the jth single component IMF, and K represents the number of decompositions for decomposing the torsional vibration signal into the single component IMF.
5. The method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation as claimed in claim 4, wherein the optimal combination of the parameters of the variational modal decomposition is obtained as follows:
and (3) performing iteration preset times on the particle swarm optimization algorithm, obtaining a fitness function value of the corresponding particle swarm optimization algorithm through each iteration, and taking the combination of the variation modal decomposition parameters corresponding to the maximum fitness function value as an optimal combination.
6. The method as claimed in claim 4, wherein the IMF of the single component and the Pearson correlation coefficient r (Y (t), Y) of the collected torsional vibration signal are derived from the instantaneous frequency extraction method of the torsional vibration signal based on the improved synchronous compression transformIMFk(t)) the following:
Figure FDA0003320169380000031
wherein: r (Y (t), YIMFk(t)) for the original torsional vibration signal Y (t) and each decomposed IMF signal YIMFk(t) a measure of linear dependence; cov (Y (t), Y)IMFk(t)) are Y (t) and YIMFk(t) covariance; var [ y (t)]Is the variance of the original torsional vibration signal y (t); var [ Y ]IMFk(t)]For each IMF signal Y after decompositionIMFk(t) variance.
7. The method for extracting the instantaneous frequency of the torsional vibration signal based on the improved synchronous compression transformation as claimed in claim 1, wherein the short-time Fourier synchronous compression transformation is:
Figure FDA0003320169380000032
wherein: u is a time variable; xi is a frequency variable; g (t) is a tightly supported window function in the time domain, and the window function is a Gaussian window function
Figure FDA0003320169380000033
Figure FDA0003320169380000034
Expressed as a short-time Fourier transform of the noise-reduced torsional vibration signal;
Figure FDA0003320169380000035
estimating an operator for the instantaneous frequency;
Figure FDA0003320169380000036
to represent
Figure FDA0003320169380000037
The effective support area of (a).
8. A system for extracting an instantaneous frequency of a torsional vibration signal based on an improved synchronous compression transformation, comprising:
an optimal combination calculation module: the method is used for solving the optimal combination of the variation modal decomposition parameters by utilizing a particle swarm optimization algorithm;
a modal decomposition module: the system comprises a parameter combination module, a component modal decomposition algorithm module and a single component IMF module, wherein the parameter combination module is used for carrying out modal decomposition on the acquired torsional vibration signals by adopting a variational modal decomposition algorithm and the optimal parameter combination to obtain a single component IMF;
a correlation coefficient calculation module: for calculating a pearson correlation coefficient of a single component IMF with the acquired torsional vibration signal;
a signal reconstruction module: the torsional vibration signal processing unit is used for reconstructing the acquired torsional vibration signal by using a single-component IMF with a large Pearson correlation coefficient to obtain a torsional vibration signal after noise reduction;
synchronous compression of transform blocks: the short-time Fourier synchronous compression transformation is carried out on the torsional vibration signals after noise reduction to obtain the time-frequency distribution of the torsional vibration signals;
a torsional vibration instantaneous frequency extraction module: and the Viterbi algorithm is adopted for extracting the torsional vibration instantaneous frequency from the time-frequency distribution of the torsional vibration signal.
9. An electronic device, comprising:
one or more processors;
a storage device having one or more programs stored thereon;
the one or more programs, when executed by the one or more processors, cause the one or more processors to implement the method for improved synchronous compression transform based transient frequency extraction of a torsional vibration signal as recited in any of claims 1 to 7.
10. A storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the method for transient frequency extraction of a torsional vibration signal based on modified synchronous compression transformation as claimed in any one of claims 1 to 7.
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