A variational mode decomposition optimization method based on joint factor of time-frequency correlation coefficients

Abstract

The present invention provides a variational mode decomposition optimization method based on a time-frequency correlation coefficient joint factor, comprising: S1, initializing the K value, setting K=2; S2, performing VMD decomposition on the signal to obtain K IMF components; S3, calculating the time domain correlation coefficient ρ between each IMF component and the original signal K,i and frequency domain correlation coefficient #imgabs0#Calculate the time-frequency correlation coefficient joint factor δ K,i ; S4, let K = K + 1, perform VMD decomposition again, and obtain K + 1 IMF components; S5, calculate the time domain correlation coefficient ρ between each IMF component and the original signal K+1,j and frequency domain correlation coefficient #imgabs1#Calculate the time-frequency correlation coefficient joint factor δ K+1,j ; S6, calculate the time-frequency correlation coefficient joint factor difference β between each IMF component when K takes different values ​​and the same decomposition number K,r ; S7, when β K,r ≤θ(θ=0.05), it is considered as an effective factor, otherwise it is considered as an invalid factor; S8, when K=m, the number of continuous effective factors reaches the maximum value, that is, when K=m+1, the number of continuous effective factors is less than K=m, it is considered that the decomposition is optimal, and K=m is finally selected as the optimal value. The present invention is simple to operate, the correlation feature extraction is comprehensive and reliable, and is less affected by the factors of the signal itself.

Description

Technical Field

[0001] The present invention relates to the technical field of signal decomposition and processing, and in particular to a variational mode decomposition optimization method based on a joint factor of time-frequency correlation coefficients. Background Art

[0002] For the signals extracted by common sensors, due to the influence of factors such as transmission equipment and background environment, such signals often show nonlinear and non-stationary characteristics. Signal decomposition methods based on Fourier such as Fourier transform, fast Fourier transform and wavelet transform are not ideal for processing such signals. For such signals, time-frequency analysis methods have better applicability and analysis accuracy, among which empirical mode decomposition and total empirical mode decomposition methods are the most widely used. However, due to the weak theoretical foundation and the instability of the signal decomposition process, the above methods will produce serious endpoint effects and modal aliasing problems after the decomposition process. In 2014, the variational mode decomposition (VMD) method was proposed. This method is different from empirical mode decomposition or total empirical mode decomposition. It is a non-recursive signal decomposition method. Its essence is a set of adaptive Wiener filters based on the optimal solution of the problem. While having a solid theoretical foundation, the decomposition process is more reasonable, effectively avoiding the problems of endpoint effects and modal aliasing.

[0003] For the VMD method, the number of modal decompositions K is a very important parameter. When setting the K value, if the value is too small, each intrinsic mode function (IMF) in the decomposition result will contain multiple components with different frequency characteristics; conversely, there will be components with the same frequency characteristics in multiple IMF components, resulting in modal aliasing problems, which will affect the decomposition accuracy and subsequent signal processing effects.

[0004] The study of the selection method of the number of modal decompositions K has become an important direction for the optimization of the VMD method. Although the center frequency observation method and the intelligent search algorithm are used to solve this problem, the center frequency observation is subjective, and the intelligent search algorithm takes a lot of time and is difficult to achieve efficient signal processing. Therefore, it is necessary to provide a variational mode decomposition optimization method based on the joint factor of the time-frequency correlation coefficient to solve the above existing problems. Summary of the invention

[0005] In view of this, the present invention provides a variational mode decomposition optimization method based on a joint factor of time-frequency correlation coefficients to solve the problems existing in the background technology.

[0006] In order to solve the above technical problems, the present invention provides a variational mode decomposition optimization method based on a joint factor of time-frequency correlation coefficients, comprising the following steps:

[0007] Step S1, initialize K value, set K=2;

[0008] Step S2, performing VMD decomposition on the signal to obtain K IMF components;

[0009] Step S3: Calculate the time domain correlation coefficient ρ between each IMF component and the original signal K，i and frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor δ K，i ;

[0010] Step S4, let K=K+1, perform VMD decomposition on the signal again to obtain K+1 IMF components;

[0011] Step S5: Calculate the time domain correlation coefficient ρ between each IMF component and the original signal K+1，j and frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor δ K+1，j ;

[0012] Step S6: Calculate the difference β of the joint factor of the time-frequency correlation coefficients between the IMF components when K takes different values ​​and the same number of decompositions K，r ;

[0013] Step S7: When β K，r When ≤θ(θ=0.05), it is considered as a valid factor, otherwise it is considered as an invalid factor;

[0014] Step S8: When K=m, the number of consecutive effective factors reaches the maximum value, that is, when the number of consecutive effective factors when K=m+1 is less than K=m, it is considered that the decomposition is optimal, and K=m is finally selected as the optimal value.

[0015] Further, in step S3, the 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 calculate the time-frequency correlation coefficient joint factor δ according to formula (3): K，i ;

[0016]

[0017]

[0018]

[0019] Where, i = 1, 2, ..., K; u k (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , G u are x(t) and u respectively k The power spectrum of (t), fa To analyze the frequency, are x(t) and u respectively k (t) is the mean power spectrum of

[0020] Further, in step S5, the 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 calculate the time-frequency correlation coefficient joint factor δ according to formula (6): K+1，j ;

[0021]

[0022]

[0023]

[0024] In the formula, u k (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , are x(t) and u respectively k The power spectrum of (t), f a To analyze the frequency, are x(t) and u respectively k (t) is the mean power spectrum of

[0025] Further, in step S6, the difference β of the joint factor of the time-frequency correlation coefficients between the IMF components when K takes different values ​​and the same decomposition times is calculated according to formula (7): K，r ;

[0026] β K，r =|δ K+1，r -δ K，r | (7).

[0027] The above technical solution of the present invention includes at least the following beneficial effects:

[0028] 1. Due to the influence of background noise, acquisition system and other factors, the signals acquired by the sensor often contain a lot of noise and show nonlinear and non-stationary characteristics. The effectiveness of the VMD method in processing such signals has been proven. Aiming at the problem that the number of modal decompositions K of the VMD method is difficult to effectively select, the present invention proposes a method based on the joint factor of the time-frequency correlation coefficient to select, which fully considers the relationship between each IMF component and the original signal in the time domain and frequency domain, has a more comprehensive characteristic analysis capability, and provides a guarantee for the accuracy of signal decomposition;

[0029] 2. Compared with the center frequency observation method that relies on human subjective determination and the intelligent search method that consumes a lot of time and requires setting multiple parameters, the method proposed in the present invention is easy to operate, extracts correlation features comprehensively and reliably, and is less affected by the factors of the signal itself. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flow chart of the method of the present invention;

[0031] Figure 2 A physical diagram of a ZT-3 rotor vibration simulation test bench used in an embodiment of the present invention;

[0032] Figure 3 is a time domain waveform of a rotor vibration signal under an unbalanced fault collected in an embodiment of the present invention;

[0033] Figure 4 1 is the VMD decomposition result of the rotor unbalance fault signal and the frequency spectrum of each IMF component in the embodiment of the present invention. DETAILED DESCRIPTION

[0034] To make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the following will be combined with the appended drawings of the embodiments of the present invention. Figure 1-4 , the technical scheme of the embodiment of the present invention is clearly and completely described. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field belong to the scope of protection of the present invention.

[0035] A variational mode decomposition optimization method based on a joint factor of time-frequency correlation coefficients includes the following steps:

[0036] Step S1, initialize K value, set K=2;

[0037] Step S2, performing VMD decomposition on the signal to obtain K IMF components;

[0038] Step S3: Calculate the time domain correlation coefficient ρ between each IMF component and the original signal according to formula (1) and formula (2): K，i and frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor δ according to formula (3): K，i ;

[0039]

[0040]

[0041]

[0042] Where i = 1, 2, ..., K; uk (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , G u are x(t) and u respectively k The power spectrum of (t), f a To analyze the frequency, are x(t) and u respectively k The mean power spectrum of (t);

[0043] Step S4, let K=K+1, perform VMD decomposition on the signal again to obtain K+1 IMF components;

[0044] Step S5: Calculate the time domain correlation coefficient ρ 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 calculate the time-frequency correlation coefficient joint factor δ according to formula (6): K+1，j ;

[0045]

[0046]

[0047]

[0048] In the formula, u k (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , are x(t) and u respectively k The power spectrum of (t), f a To analyze the frequency, are x(t) and u respectively k The mean power spectrum of (t);

[0049] Step S6: Calculate the difference β of the joint factor of the time-frequency correlation coefficients between the IMF components when K takes different values ​​and the same number of decompositions according to formula (7): K，r ;

[0050] β K，r =|δ K+1，r -δ K，r | (7);

[0051] Step S7: When β K，r When ≤θ(θ=0.05), it is considered as a valid factor, otherwise it is considered as an invalid factor;

[0052] Step S8: When K=m, the number of consecutive effective factors reaches the maximum value, that is, when the number of consecutive effective factors when K=m+1 is less than K=m, it is considered that the decomposition is optimal, and K=m is finally selected as the optimal value.

[0053] To verify the effectiveness of this embodiment, a fault simulation is carried out on the ZT-3 rotor fault comprehensive simulation test bench to obtain the rotor imbalance fault signal. During the fault simulation, two M2 screws are screwed into the circumferential groove of the rotor disc. The speed of the test bench is adjusted by the speed regulator, and a DC shunt motor is used for driving. The rated current of the motor is 2.5A and the output power is 250W; the speed is measured by the photoelectric sensor installed at the output end; the rotor acceleration signal is measured using the AI005 acceleration sensor, and the acceleration signal is processed by the MJ5936 dynamic signal tester. The system includes a signal conditioner, a DC voltage amplifier, a low-pass filter, an anti-mixing filter, etc.; and the real-time measured rotor acceleration signal is obtained by a computer.

[0054] During the experiment, the signal sampling frequency was set to 2000 Hz, synchronous sampling, sampling time of 20 s, and analysis time of 1 s. The motor speed was 1640 r / min.

[0055] Figure 3 It is the time domain waveform of a group of rotor vibration signals randomly selected under the measured misalignment fault state.

[0056] 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.

[0057]

[0058] Table 1 Joint factor δ of time-frequency correlation coefficients of each IMF component obtained under the same K value.

[0059] In order to determine the optimal value of the modal decomposition number K, the difference of the joint factor of the time-frequency correlation coefficient between each IMF component when K takes different values ​​and the same decomposition number is calculated according to the method proposed in this paper. The calculation results are shown in Table 2.

[0060]

[0061]

[0062] Table 2 Differences of the joint factors of the time-frequency correlation coefficients of each IMF component.

[0063] According to the algorithm results selected according to relevant parameters, the IMF components and their spectra obtained by VMD decomposition of the rotor unbalance fault signal are as follows: Figure 4 shown.

[0064] Depend on Figure 4It can be seen that the VMD decomposition results are relatively reasonable, and the IMF components are mainly concentrated near the center frequency, without obvious frequency divergence. This shows that the proposed parameter selection method can effectively suppress the endpoint effect, modal aliasing and other problems generated in the decomposition process, reduce the information leakage between the modal components, and provide effective guarantees for the subsequent extraction of signal features, providing favorable guarantees for the application of this method.

[0065] The above are preferred embodiments of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A variational mode decomposition optimization method based on a joint factor of time-frequency correlation coefficients, characterized in that: The following steps are involved: Step S1, initialize K value, set K=2; Step S2, performing VMD decomposition on the signal to obtain K IMF components; Step S3: Calculate the time domain correlation coefficient ρ between each IMF component and the original signal K,i and frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor ρ K,i ; Step S4, let K=K+1, perform VMD decomposition on the signal again to obtain K+1 IMF components; Step S5: Calculate the time domain correlation coefficient ρ between each IMF component and the original signal K+1,j and frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor δ K+1,j ; Step S6: Calculate the difference β of the joint factor of the time-frequency correlation coefficients between the IMF components when K takes different values ​​and the same number of decompositions K,r ; Step S7: When β K,r When ≤θ(θ=0.05), it is considered as a valid factor, otherwise it is considered as an invalid factor; Step S8: When K=m, the number of continuous effective factors reaches the maximum value, that is, when the number of continuous effective factors when K=m+1 is less than ρ=m, it is considered that the decomposition is optimal, and K=m is finally selected as the optimal value; In step S3, the 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 calculate the time-frequency correlation coefficient joint factor δ according to formula (3): K,i ; Where, i = 1, 2, ..., K; u k (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , G u are x(t) and u respectively k The power spectrum of (t), f a To analyze the frequency, are x(t) and u respectively k The mean power spectrum of (t); In step S5, the 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 the frequency domain correlation coefficient And calculate the time-frequency correlation coefficient joint factor δ according to formula (6): K+1,j ; In the formula, u k (t) is the Kth IMF component obtained by VMD decomposition, x(t) is the signal to be decomposed, G x , are x(t) and u respectively k The power spectrum of (t), f a To analyze the frequency, are x(t) and u respectively k The mean power spectrum of (t); In step S6, the difference β of the joint factor of the time-frequency correlation coefficients between the IMF components when K takes different values ​​and the same decomposition times is calculated according to formula (7): K,r ; b K,r =|δ K+1,r -d K,r |(7).

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