CN114996641A - Variational modal decomposition optimization method based on time-frequency correlation coefficient joint factor - Google Patents
Variational modal decomposition optimization method based on time-frequency correlation coefficient joint factor Download PDFInfo
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Abstract
The invention provides a variational modal decomposition optimization method based on a time-frequency correlation coefficient joint factor, which comprises the following steps: s1, initializing a K value, and enabling K to be 2; s2, performing VMD decomposition on the signal to obtain K IMF components; s3, calculating time domain correlation coefficient rho between each IMF component and original signal K,i And frequency domain correlation coefficient
Calculating time-frequency correlation coefficient joint factor delta K,i (ii) a S4, enabling K to be K +1, and performing VMD decomposition again to obtain K +1 IMF components; s5, calculating time domain correlation coefficient rho between each IMF component and original signal K+1,j And frequency domain correlation coefficient
Calculating time-frequency correlation coefficient joint factor delta K+1,j (ii) a S6, calculating K to be differentTime-frequency correlation coefficient joint factor difference beta between IMF components under the same decomposition times under the value K,r (ii) a S7, when beta K,r Theta is less than or equal to 0.05, and is regarded as an effective factor, otherwise, the theta is regarded as an ineffective factor; and S8, when K is equal to m, the number of the continuous effective factors reaches the maximum value, namely when the number of the continuous effective factors is less than K which is equal to m when K is equal to m +1, the decomposition is considered to be optimal, and finally K which is equal to m is selected as the optimal value. The method is simple and convenient to operate, the extraction of the correlation characteristics is comprehensive and reliable, and the influence of the factors of the signal is small.
Description
Technical Field
The invention relates to the technical field of signal decomposition and processing, in particular to a variational modal decomposition optimization method based on a time-frequency correlation coefficient joint factor.
Background
Signals extracted by common sensors are limited by the influence of factors such as transmission equipment, background environment and the like, and the signals often have the characteristics of nonlinearity and non-stationarity. The Fourier-based signal decomposition method comprises the following steps: fourier transform, fast fourier transform, wavelet transform, and the like are not ideal for the processing of such signals. For such signals, the time-frequency analysis method has better applicability and analysis accuracy, and the empirical mode decomposition method and the overall empirical mode decomposition method are most widely applied. However, the above method generates serious endpoint effect and modal aliasing problem after the decomposition process, which is limited by weak theoretical basis and instability of the signal decomposition process. In 2014, a Variational Modal Decomposition (VMD) method is proposed, which is different from empirical mode decomposition or total empirical mode decomposition, and is a non-recursive signal decomposition method, which is substantially based on a group of adaptive wiener filters that become a problem solving optimal solution, and has a solid theoretical basis, and at the same time, the decomposition process is more reasonable, and effectively avoids the generation of problems such as end effect and modal aliasing.
For the VMD method, the number K of modal decomposition is a very important parameter, and in the K value setting process, if the value is too small, each Intrinsic Modal Function (IMF) in the decomposition result will contain a plurality of components with different frequency characteristics; on the contrary, the components with the same frequency characteristics exist in a plurality of IMF components, so that the problem of mode aliasing occurs, and the decomposition accuracy and the subsequent signal processing effect are influenced.
The research of the selection method aiming at the modal decomposition number K becomes an important direction for the optimization of the VMD method, although a center frequency observation method and an intelligent search algorithm are used for solving the problem, the center frequency observation has certain subjectivity, the intelligent search algorithm needs to consume a large amount of time, and the purpose of high-efficiency signal processing is difficult to realize. Therefore, it is desirable to provide a method for optimizing a variational modal decomposition based on a time-frequency correlation coefficient joint factor, so as to solve the existing problems.
Disclosure of Invention
In view of this, the present invention provides a variation modal decomposition optimization method based on a time-frequency correlation coefficient joint factor, so as to solve the problems existing in the background art.
In order to solve the technical problem, the invention provides a variational modal decomposition optimization method based on a time-frequency correlation coefficient joint factor, which comprises the following steps:
step S1, initializing a K value, and making K equal to 2;
step S2, VMD decomposition is carried out on the signal to obtain K IMF components;
step S3, calculating time domain correlation coefficient rho between each IMF component and the original signal K，i And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta K，i ；
Step S4, making K equal to K +1, and performing VMD decomposition on the signal again to obtain K +1 IMF components;
step S5, calculating time domain correlation coefficient rho between each IMF component and the original signal K+1，j And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta K+1，j ；
Step S6, calculating the difference beta of the time-frequency correlation coefficient joint factors among IMF components when K takes the same decomposition times under different values K，r ；
Step S7, when beta K，r When theta is less than or equal to 0.05, the theta is regarded as an effective factor, otherwise, the theta is regarded as an ineffective factor;
and step S8, assuming that K is m, the number of consecutive effective factors reaches a maximum value, that is, when the number of consecutive effective factors when K is m +1 is less than K, m, the decomposition is considered to be optimal, and finally K is m is selected as an optimal value.
Further, in step S3, a time-domain correlation coefficient ρ between each IMF component and the original signal is calculated according to formula (1) and formula (2) K，i And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta according to a formula (3) K，i ；
Wherein i is 1,2, …, K; u. of k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、G u Are x (t) and u respectively k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean value of power spectrum.
Further, in step S5, a time-domain correlation coefficient ρ between each IMF component and the original signal x (t) is calculated according to formula (4) and formula (5) K+1，j And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta according to a formula (6) K+1，j ；
In the formula u k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、
Are x (t) and u, respectively k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean value of power spectrum.
Further, in step S6, a difference β of time-frequency correlation coefficient joint factors between IMF components when K takes the same decomposition times under different values is calculated according to formula (7) K，r ；
β K，r ＝|δ K+1，r -δ K，r | (7)。
The technical scheme of the invention at least comprises the following beneficial effects:
1. because of the influence of factors such as background noise, an acquisition system and the like, signals acquired by the sensor often contain a large amount of noise and show nonlinear and non-stationary characteristics, and the effectiveness of the VMD method for processing the signals is proved, the invention provides a method based on time-frequency correlation coefficient joint factors for selection aiming at the problem that the modal decomposition number K of the VMD method is difficult to effectively select, fully considers the relation between time domains and frequency domains between IMF components and original signals, has more comprehensive characteristic analysis capability and provides guarantee for the accuracy of signal decomposition;
2. compared with a center frequency observation method which depends on artificial subjective determination and an intelligent search method which consumes a large amount of time and needs to set a plurality of parameters, the method provided by the invention is simple and convenient to operate, has comprehensive and reliable extraction of correlation characteristics, and is slightly influenced by the factors of the signal.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a solid diagram of a ZT-3 rotor vibration simulation experiment table adopted in the embodiment of the invention;
FIG. 3 is a time domain waveform of a rotor vibration signal under an imbalance fault collected in an embodiment of the present invention;
FIG. 4 is a VMD decomposition of a rotor imbalance fault signal and a spectrum of IMF components in an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to fig. 1 to 4 of the embodiments of the present invention. It is to be understood that the embodiments described are only a few embodiments of the present invention, and not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the described embodiments of the invention, are within the scope of the invention.
A variation modal decomposition optimization method based on time-frequency correlation coefficient joint factors comprises the following steps:
step S1, initializing a K value, and making K equal to 2;
step S2, VMD decomposition is carried out on the signal to obtain K IMF components;
step S3, calculating time domain correlation coefficient rho between each IMF component and the original signal according to formula (1) and formula (2) K，i And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta according to a formula (3) K，i ；
Wherein i is 1,2, …, K; u. of k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、G u Are x (t) and u, respectively k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean power spectrum;
step S4, making K equal to K +1, and performing VMD decomposition on the signal again to obtain K +1 IMF components;
step S5, calculating time domain correlation coefficient rho between each IMF component and the original signal x (t) according to formula (4) and formula (5) x+1，j And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta according to a formula (6) K+1，j ；
In the formula u k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、
Are respectively asx (t) and u k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean power spectrum;
step S6, calculating the difference value beta of the time-frequency correlation coefficient joint factors among IMF components when K takes the same decomposition times under different values according to the formula (7) K，r ；
β K，r ＝|δ K+1，r -δ K，r | (7)；
Step S7, when beta K，r When theta is less than or equal to 0.05, the theta is regarded as an effective factor, otherwise, the theta is regarded as an ineffective factor;
and step S8, assuming that K is m, the number of consecutive effective factors reaches a maximum value, that is, when the number of consecutive effective factors when K is m +1 is less than K, m, the decomposition is considered to be optimal, and finally K is m is selected as an optimal value.
In order to verify the effectiveness of the embodiment, fault simulation is carried out on the ZT-3 rotor fault comprehensive simulation test bed, and a rotor unbalance fault signal is obtained. During fault simulation, 2M 2 screws were screwed into the circumferential grooves of the rotor disk. The rotating speed of the experiment table is adjusted through a speed regulator, a direct current shunt motor is adopted for driving, the rated current of the motor is 2.5A, and the output power is 250W; measuring the rotating speed through a photoelectric sensor arranged at the output end; an AI005 type acceleration sensor is used for measuring the acceleration signal of the rotor, and the acceleration signal is processed by an MJ5936 type dynamic signal tester, and the system comprises a signal conditioner, a direct current voltage amplifier, a low-pass filter, an anti-aliasing filter and the like; and a real-time measured rotor acceleration signal is obtained through a computer.
In the experimental process, the signal sampling frequency is set to 2000Hz, synchronous sampling is carried out, the sampling time is 20s, and the analysis time is 1 s. The rotating speed of the motor is 1640 r/min.
Fig. 3 is a time domain waveform of 1 set of randomly selected rotor vibration signals under a measured misalignment fault condition.
The signal is decomposed according to the method of this embodiment, and the time-frequency correlation coefficient joint factors of each IMF component obtained under different K values are shown in table 1.
Table 1 shows the time-frequency correlation coefficient combination factor δ of each IMF component obtained under the K value.
In order to determine the optimal value of the modal decomposition number K, the difference of the time-frequency correlation coefficient joint factors among IMF components when the K takes the same decomposition times under different values is respectively calculated according to the method provided by the text, and the calculation result is shown in Table 2.
Table 2 difference of time-frequency correlation coefficient joint factors of each IMF component.
The IMF components and frequency spectrums thereof obtained by VMD decomposition of the rotor imbalance fault signal are shown in FIG. 4 according to the result of the algorithm selected by the relevant parameters.
As can be seen from fig. 4, the VMD decomposition result is reasonable, each IMF component is mainly concentrated near the center frequency, and no obvious frequency divergence phenomenon occurs, which indicates that the proposed parameter selection method can effectively suppress the problems of end effect, mode aliasing, and the like generated in the decomposition process, reduce information leakage among the mode components, provide effective guarantee for the extraction of subsequent signal characteristics, and provide favorable guarantee for the application of the method.
The foregoing is a preferred embodiment of the present invention, and it should be noted that it would be apparent to those skilled in the art that various modifications and enhancements can be made without departing from the principles of the invention, and such modifications and enhancements are also considered to be within the scope of the invention.
Claims (4)
1. A variation modal decomposition optimization method based on time-frequency correlation coefficient joint factors is characterized by comprising the following steps:
step S1, initializing a K value, and making K equal to 2;
step S2, VMD decomposition is carried out on the signal to obtain K IMF components;
step S3, calculating time domain correlation coefficient rho between each IMF component and the original signal K,i And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta K,i ；
Step S4, making K equal to K +1, and performing VMD decomposition on the signal again to obtain K +1 IMF components;
step S5, calculating time domain correlation coefficient rho between each IMF component and the original signal K+1,j And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta K+1，j ；
Step S6, calculating the difference value beta of the time-frequency correlation coefficient joint factor between IMF components when K takes the same decomposition times under different values K,r ；
Step S7, when beta K,r When theta is less than or equal to 0.05, the theta is regarded as an effective factor, otherwise, the theta is regarded as an ineffective factor;
and step S8, assuming that K is m, the number of consecutive effective factors reaches a maximum value, that is, when the number of consecutive effective factors when K is m +1 is less than K, m, the decomposition is considered to be optimal, and finally K is m is selected as an optimal value.
2. The method for optimizing the decomposition of the variation mode based on the time-frequency correlation coefficient joint factor as claimed in claim 1, wherein in step S3, the time-domain correlation coefficient ρ between each IMF component and the original signal is calculated according to the formula (1) and the formula (2) K,i And frequency domain correlation coefficient
And according toFormula (3) calculating time-frequency correlation coefficient joint factor delta K,i ；
Wherein i is 1,2, …, K; u. of k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、G u Are x (t) and u, respectively k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean value of power spectrum.
3. The method for optimizing the decomposition of variation modes based on the time-frequency correlation coefficient combination factor as claimed in claim 1, wherein in step S5, the time-domain correlation coefficient ρ between each IMF component and the original signal x (t) is calculated according to the formula (4) and the formula (5) K+1,j And frequency domain correlation coefficient
And calculating a time-frequency correlation coefficient joint factor delta according to a formula (6) K+1，j ；
In the formula u k (t) the Kth IMF component obtained by VMD decomposition, x (t) the signal to be decomposed, G x 、
Are x (t) and u, respectively k (t) power spectrum, f a In order to analyze the frequency of the frequency,
are x (t) and u, respectively k (t) mean value of power spectrum.
4. The method for optimizing the decomposition of variation modal based on the time-frequency correlation coefficient joint factor according to claim 1, wherein in step S6, the difference β of the time-frequency correlation coefficient joint factor between IMF components when K takes the same decomposition times under different values is calculated according to formula (7) K,r ；
β K,r ＝|δ K+1,r -δ K,r | (7)。
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