Bearing fault identification method based on adaptive variational mode decomposition

Abstract

The invention provides a bearing fault identification method based on adaptive variational mode decomposition. The bearing fault identification method based on adaptive variational mode decomposition comprises the following steps: S1, loading a vibration signal of a bearing; s2, determining the optimal initial center frequency of the K potential components by using a VMD convergence trend graph; s3, determining K optimal penalty factors by using a bandwidth empirical formula; s4, decomposing the vibration signal again to obtain an intermediate component; s5, carrying out Hilbert envelope analysis on all the intermediate components; s6, respectively calculating the median kurtosis of all the intermediate components, selecting the component with the maximum median kurtosis as the optimal component, and drawing a 1.5-dimensional spectrum of the optimal component; and S7, judging the fault type of the bearing. The bearing fault identification method based on adaptive variational mode decomposition provided by the invention can accurately and efficiently identify the early single fault of the bearing, and has the advantages of high calculation efficiency and strong anti-interference capability.

Description

Technical Field

[0001] The present invention relates to the technical field of bearing fault diagnosis methods, and in particular to a bearing fault identification method based on adaptive variational mode decomposition. Background Art

[0002] Bearings are one of the most widely used key components in modern mechanical equipment. They play an important role in supporting rotating shafts, reducing friction and bearing loads in rotating mechanical systems. Bearings are widely used in various fields such as automobiles, aerospace, wind power generation, etc. The normal operation of bearings is crucial to the reliability and safety of equipment. However, due to long-term operation, harsh working environment, overload and other factors, bearings are prone to failure. Bearing failure will not only lead to a decline in equipment performance, but may also cause serious safety accidents, and even cause huge economic losses and casualties. Therefore, being able to identify weak bearing faults in a timely and accurate manner at an early stage is of great significance to ensure the normal operation of equipment and prevent potential dangers.

[0003] Variational Mode Decomposition (VMD) is a classic signal processing method that can decompose complex signals into multiple components with different center frequencies and limited bandwidths. It is one of the common methods for bearing fault diagnosis. Studies have shown that the setting of some key initial parameters of the VMD method will have a significant impact on the decomposition results and computational efficiency. These initial parameters include the number of components, penalty factor, and initial center frequency.

[0004] Many scholars use different meta-heuristic algorithms to optimize the number of components and penalty factors at the same time. Although such methods can adaptively determine the number of components and penalty factors, they require multiple iterations to update the calculations, which is inefficient and not suitable for engineering applications. In addition, the processing method based on adaptive VMD will produce some redundant components when diagnosing a single fault signal of a bearing, which will not only affect the accuracy of fault identification, but also further reduce the computational efficiency. Summary of the invention

[0005] In view of this, the present invention aims to propose a bearing fault identification method based on adaptive variational mode decomposition to improve the computational efficiency and accuracy of early weak bearing fault identification based on VMD processing method, so that it can be more widely used in the field of mechanical engineering.

[0006] To achieve the above object, the technical solution of the present invention is achieved as follows:

[0007] A bearing fault identification method based on adaptive variational mode decomposition comprises the following steps:

[0008] S1, vibration signal of the loaded bearing;

[0009] S2, analyzing the vibration signal using a VMD convergence trend diagram to obtain K potential components, and determining the optimal initial center frequencies of the K potential components respectively;

[0010] S3, using the bandwidth empirical formula, according to the K optimal initial center frequencies, determining K optimal penalty factors;

[0011] S4, inputting the optimal initial center frequency, the optimal penalty factor and the number K of potential components into a VMD algorithm, re-decomposing the vibration signal to obtain intermediate components;

[0012] S5, performing Hilbert envelope analysis on all the intermediate components;

[0013] S6, respectively calculating the median kurtosis of all the intermediate components, selecting the component with the largest median kurtosis as the optimal component, and drawing its 1.5-dimensional spectrum;

[0014] S7, comparing the protruding spectrum lines of the 1.5-dimensional spectrum with the theoretical fault characteristic frequency to determine the bearing fault type.

[0015] Furthermore, the step S2 includes the following sub-steps:

[0016] S201, inputting the vibration signal into the VMD algorithm, setting the number of components K=1, the penalty factor to 2500, obtaining the transformation formula of the VMD algorithm, and using the alternating direction multiplier algorithm to solve the transformation formula of the VMD algorithm to obtain the initial component and the initial center frequency;

[0017] S202, iteratively updating the initial component and the initial center frequency, and determining a convergence trend of the initial center frequency;

[0018] S203, taking the initial center frequency as the horizontal coordinate and the vertical coordinate as the difference between the initial center frequency and the new center frequency after one iteration, displaying in the form of a histogram to form a VMD convergence trend graph;

[0019] S204, in the VMD convergence trend diagram, locate the frequency boundary that satisfies the condition that the center frequency difference changes from positive to negative, and this type of boundary is the optimal initial center frequency.

[0020] Furthermore, in step S202:

[0021] The number of iterative update operations has a fixed mapping relationship with the step length and the sampling frequency, and the step length is 100 Hz.

[0022] Furthermore, in step S3:

[0023] The penalty factor has a fixed mapping relationship with the optimal initial center frequency and the sampling frequency, and the penalty factor is determined by solving the fixed mapping relationship.

[0024] Furthermore, in step S6:

[0025] The median kurtosis has a fixed mapping relationship with the signal mean and standard deviation of the vibration signal, and the determination of the median kurtosis is solved by the fixed mapping relationship.

[0026] Furthermore, in step S6:

[0027] The 1.5-dimensional spectrum is a one-dimensional Fourier transform of the third-order accumulation of the vibration signal.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] The present invention discloses a bearing fault identification method based on adaptive variational mode decomposition, which introduces an empirical formula for the penalty factor and quickly determines the corresponding penalty factor based on the initial center frequency, thereby eliminating the time consumed by multiple iterative update calculations when the VMD algorithm is directly applied, thereby achieving the purpose of the invention of improving the calculation efficiency of early weak fault identification of bearings based on the VMD processing method.

[0030] Secondly, after the signal is decomposed by the adaptive VMD method, multiple components will be obtained; by calculating the median kurtosis of each component and selecting the component with the largest median kurtosis as the optimal component, the influence of redundant components on fault identification can be avoided.

[0031] In addition, the 1.5-dimensional spectrum can effectively curb the impact of Gaussian noise, enhance the accuracy of fault feature extraction, and is simple and efficient to calculate. By drawing the 1.5-dimensional spectrum of the envelope signal of the optimal component, the purpose of the invention to improve the accuracy of fault identification is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings constituting a part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the accompanying drawings:

[0033] Figure 1 Schematic diagram of the steps of a bearing fault identification method based on adaptive variational mode decomposition in an embodiment of the present invention;

[0034] Figure 2 Schematic diagram of the step flow of S2 in an embodiment of the present invention;

[0035] Figure 3 is the time domain waveform of the test signal;

[0036] Figure 4is the envelope spectrum of the test signal;

[0037] Figure 5 It is the VMD convergence trend diagram of the test signal;

[0038] Figure 6 is the median kurtosis of the potential component of the test signal;

[0039] Figure 7 is the time domain waveform of the optimal component of the test signal;

[0040] Figure 8 is the 1.5-dimensional spectrum of the optimal component of the test signal. DETAILED DESCRIPTION

[0041] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other. In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the specific implementation methods of the present invention will be described below with reference to the accompanying drawings. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings and other implementation methods can be obtained based on these drawings without creative work.

[0042] In the description of the present invention, it should be noted that if there are terms indicating orientation or positional relationship such as "upper", "lower", "inner", "outer", etc., they are based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention. In addition, if there are terms such as "first", "second", etc., they are only used for descriptive purposes and cannot be understood as indicating or implying relative importance.

[0043] In addition, in the description of the present invention, unless otherwise clearly defined, a person skilled in the art can understand the specific meanings of the above terms in the present invention in combination with specific circumstances. The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0044] The following will refer to the attached Figure 1 To Attachment Figure 8 The present invention is described in detail with reference to embodiments.

[0045] The VMD algorithm can decompose a non-stationary input signal into K components u with specific sparsity. k , (k=1,2,......,K) and can also clearly define the center frequency ω of each component k and bandwidth.

[0046] In the VMD algorithm, by calculating the gradient of the modulation signal L 2 The norm is used to estimate the bandwidth of each component, and the corresponding constrained variational model is as follows:

[0047]

[0048] In formula (1), {u k} represents the component signal, {ω k} represents the corresponding center frequency set, K represents the number of components, δ(t) is the pulse function, is a partial derivative operation, and * represents convolution.

[0049] By introducing the quadratic penalty factor and Lagrange multiplier, equation (1) is transformed into an unconstrained optimization model, which is expressed as follows:

[0050]

[0051] In formula (2), α represents the penalty factor and λ represents the Lagrange multiplier.

[0052] The alternating direction multiplier algorithm is used to solve the optimal solution of equation (2). The iterative update formula for the component and its center frequency is as follows:

[0053]

[0054] In formula (3), Respectively x(t),λ n (t), n represents the number of iterations.

[0055] The iterative termination condition of the above update process is shown in formula (5):

[0056]

[0057] In formula (5), ε is the convergence parameter, ε = 1 × 10 -7 .

[0058] The present embodiment relates to a bearing fault identification method based on adaptive variational mode decomposition, which is based on the basic framework of the VMD algorithm, establishes a VMD convergence trend diagram through simple calculations, determines the optimal initial parameters according to the VMD convergence trend diagram, and finally inputs the optimal initial parameters into the original VMD algorithm to re-decompose the signal to obtain multiple intermediate components and perform envelope analysis on each component, and selects the best component by calculating the median kurtosis of the intermediate components.

[0059] Compared with the method described in the previous article of directly inputting signals into the VMD algorithm and performing multiple iterative calculations and analyses, the overall calculation process has been simplified, the number of iterative update operations has been significantly reduced, and irrelevant noise components have been filtered out before calculation. This achieves the purpose of the invention of improving the calculation efficiency and accuracy of early weak fault identification of bearings based on the VMD processing method, so that it can be more widely used in the field of mechanical engineering.

[0060] Specifically, refer to Figure 1 , a bearing fault identification method based on adaptive variational mode decomposition in this embodiment includes the following steps:

[0061] S1, loads the vibration signal of the bearing.

[0062] In this step, the vibration signal generated by the rotation of the bearing for which fault identification is required is input into the VMD algorithm.

[0063] S2, use the VMD convergence trend diagram to analyze the vibration signal, obtain K potential components, and determine the optimal initial center frequency of the K potential components respectively.

[0064] Reference Figure 2 In this step, step S2 includes the following sub-steps:

[0065] S201, input the vibration signal into the VMD algorithm, set the number of components K=1, the penalty factor is 2500, obtain the transformation formula of the VMD algorithm, and use the alternating direction multiplier algorithm to solve the transformation formula of the VMD algorithm to obtain the initial component and the initial center frequency.

[0066] Based on the original VMD algorithm, let K = 1, and equation (2) can be converted into the following form:

[0067]

[0068] Equation (6) is solved by the alternating direction multiplier algorithm, and the components are continuously updated according to equation (7) and its center frequency

[0069]

[0070] In formula (7), u(ω) and x(ω) are the Fourier transforms of u(t) and x(t), respectively.

[0071] S202, iteratively updating the initial component and the initial center frequency, and determining the convergence trend of the initial center frequency.

[0072] The convergence trend is determined by an iterative update of the center frequency:

[0073]

[0074] In formula (8), represents the initial center frequency; express The new center frequency is obtained after one iteration.

[0075] According to the rule established by equation (8), the vibration signal x(t) is repeatedly operated M times, where M is determined by equation (9). A different initial center frequency is set for each operation, but α is always maintained at 2500. The initial center frequency is between 0 and f s / 2, with a step size of γ=100Hz.

[0076] M=1+floor(f s / 2γ) (9)

[0077] In formula (9), f s Indicates the sampling frequency.

[0078] S203, with the initial center frequency as the horizontal axis and the vertical axis as the difference between the initial center frequency and the new center frequency after one iteration, the results are displayed in the form of a histogram to form a VMD convergence trend graph.

[0079] The data set is obtained by using equations (8) and (9), and then the initial center frequency is used as the horizontal axis and the vertical axis is the corresponding center frequency difference. It is displayed in the form of a histogram to form a VMD convergence trend graph.

[0080] S204, in the VMD convergence trend diagram, locate the frequency boundary that satisfies the condition that the center frequency difference changes from positive to negative, and this type of boundary is the optimal initial center frequency.

[0081] The data set ξ=[ξ1,ξ2,......,ξ M ], with the initial center frequency as the horizontal axis and the corresponding ξ value as the vertical axis, it is presented in the form of a histogram, thus forming a VMD convergence trend graph. In the VMD convergence trend graph, determine the condition that satisfies ξ m >0 and ξ m+1 <0(1≤m≤M-1) frequency boundary, this kind of boundary is the optimal initial center frequency. The formula for obtaining the optimal initial center frequency is as follows:

[0082] ICF k =m·γ-50 (10)

[0083] In formula (10), ICF k represents the kth optimal initial center frequency; m represents the mth operation of equation (8).

[0084] S3, using the bandwidth empirical formula, according to the K optimal initial center frequencies, determine K optimal penalty factors.

[0085] In this step, the specific mapping relationship between the number of components K obtained in step S2, and the optimal initial center frequency and penalty factor of each component is as follows:

[0086]

[0087] In formula (11), α k represents the kth component u k The penalty factor α; f kc Indicates u k The center frequency of s Indicates the sampling frequency.

[0088] S4, input the optimal initial center frequency, the optimal penalty factor and the number of potential components K into the VMD algorithm, re-decompose the vibration signal and obtain the intermediate components.

[0089] In this step, the optimal number of components K and the optimal initial center frequency [ICF1, ICF2, ..., ICF K ] and the optimal penalty factor [α1,α2,......,α K ] is input into the VMD algorithm, and the test signal is re-decomposed to obtain K intermediate components.

[0090] S5, perform Hilbert envelope analysis on all intermediate components.

[0091] In this step, Hilbert envelope analysis is performed on each of the K intermediate components obtained in step S4.

[0092] S6, calculate the median kurtosis of all intermediate components respectively, select the component with the largest median kurtosis as the optimal component, and draw its 1.5-dimensional spectrum.

[0093] In this step, the median kurtosis of the K intermediate components obtained in step S4 is calculated respectively. The K intermediate components with the largest median kurtosis are selected as the optimal component. The 1.5-dimensional spectrum of the optimal component is plotted.

[0094] The calculation process of median kurtosis is as follows:

[0095] MK=Median{[K1,K2,......,K i ]} (12)

[0096] In formula (12), MK represents the median kurtosis, i represents the number of sub-signals into which the component is divided, Median{·} is a function for selecting the median of a set of data, K1, K2, ..., K i It represents the kurtosis value of the i-th sub-signal in the component signal. The kurtosis formula is as follows:

[0097]

[0098] In formula (13), μ is the mean of signal x, and δ is the standard deviation of signal x.

[0099] The calculation process of 1.5D spectrum is as follows:

[0100] The third-order cumulative value R of the bearing vibration signal x(t) 3x The diagonal slice of (τ1,τ2) (τ1=τ2=τ) can be expressed as:

[0101] R 3x (τ,τ)=E{x(t)x(t+τ)x(t-τ)} (14)

[0102] In formula (14), E{·} is the mathematical expectation value.

[0103] Then R 3x The one-dimensional Fourier transform of (τ,τ) is the 1.5-dimensional spectrum B(ω) of the signal x(t):

[0104]

[0105] S7, compare the protruding spectrum line of the 1.5-dimensional spectrum with the theoretical fault characteristic frequency to determine the bearing fault type.

[0106] In this step, according to the 1.5-dimensional spectrum drawn in step S6, the protruding spectrum lines are observed and compared with the theoretical fault characteristic frequency to determine the fault type of the bearing.

[0107] The following will further illustrate the bearing fault identification method based on adaptive variational mode decomposition proposed in this application in combination with experiments.

[0108] The test bearing model involved in the experiment is 197726, with a pitch diameter of 176.29 mm, a roller diameter of 24.74 mm, 20 rollers, and a contact angle of 8.83 degrees. Before the experiment, it was known that there were several slight indentations on the outer ring of the test bearing. During the experiment, the speed of the test bearing was 465 r / min, and the sampling frequency was f s =25.6kHz, the theoretical fault characteristic frequency of the outer ring f o =66.75Hz.

[0109] According to step S1, the collected vibration signal of the test bearing is directly input into the VMD algorithm. Figure 3 , Figure 3 This is the time waveform of the test signal. No obvious periodic impact can be seen and there is a lot of background noise. Figure 4 is the envelope spectrum of the test signal. Due to the interference of strong noise, the fault feature information of the outer ring cannot be identified in the envelope spectrum. The conventional VMD algorithm needs to perform up to 300 iterations of update calculations on this basis. The calculation method is shown in equations (1) to (5). The calculation efficiency is low, there are many interference components, the test accuracy is low, and the speed is slow.

[0110] According to step S2, draw the VMD convergence trend diagram of the vibration signal of the test bearing, such as Figure 5 As shown in the figure, the vibration signal of the test bearing is analyzed through the VMD convergence trend diagram, and it can be found that there are three potential components.

[0111] According to step S3, the obtained initial center frequency is input into the bandwidth empirical formula to obtain three optimal penalty factors.

[0112] According to step S4, in the VMD algorithm, the number of components is set to 3, and the corresponding optimal initial center frequency and optimal penalty factor are input to decompose the vibration signal of the test bearing to obtain three intermediate components.

[0113] According to step S5, Hilbert envelope analysis is performed on the three intermediate components.

[0114] According to step S6, the median kurtosis of the three components is calculated respectively. Figure 6 After calculation, it is found that the median kurtosis of component 3 is the largest, so component 3 is the optimal component. The corresponding time domain waveform is as follows Figure 7 As shown, we can clearly observe the obvious periodic shock. Plot the 1.5D spectrum of the optimal component, as shown in Figure 8 As shown, three prominent spectral lines can be accurately identified.

[0115] According to step S7, refer to Figure 8 , from which three protruding spectral lines can be accurately identified, which are the first three frequency multiples of the characteristic frequency of the outer race fault, and the experiment ends. The entire calculation process takes only 0.276 seconds. This result shows that the method proposed in this application can accurately and efficiently identify early bearing faults in a strong noise environment.

[0116] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A bearing fault identification method based on adaptive variational mode decomposition, characterized in that: The following steps are involved: S1, vibration signal of the loaded bearing; S2, analyzing the vibration signal using a VMD convergence trend diagram to obtain K potential components, and determining the optimal initial center frequencies of the K potential components respectively; S3, using the bandwidth empirical formula, according to the K optimal initial center frequencies, determining K optimal penalty factors; S4, inputting the optimal initial center frequency, the optimal penalty factor and the number K of potential components into a VMD algorithm, re-decomposing the vibration signal to obtain intermediate components; S5, performing Hilbert envelope analysis on all the intermediate components; S6, respectively calculating the median kurtosis of all the intermediate components, selecting the component with the largest median kurtosis as the optimal component, and drawing its 1.5-dimensional spectrum; S7, comparing the protruding spectrum lines of the 1.5-dimensional spectrum with the theoretical fault characteristic frequency to determine the bearing fault type.

2. A bearing fault identification method based on adaptive variational mode decomposition according to claim 1, characterized in that: The step S2 comprises the following sub-steps: S201, inputting the vibration signal into the VMD algorithm, setting the number of components K=1, the penalty factor to 2500, obtaining the transformation formula of the VMD algorithm, and using the alternating direction multiplier algorithm to solve the transformation formula of the VMD algorithm to obtain the initial component and the initial center frequency; S202, iteratively updating the initial component and the initial center frequency, and determining a convergence trend of the initial center frequency; S203, taking the initial center frequency as the horizontal coordinate and the vertical coordinate as the difference between the initial center frequency and the new center frequency after one iteration, displaying in the form of a histogram to form a VMD convergence trend graph; S204, in the VMD convergence trend diagram, locate the frequency boundary that satisfies the condition that the center frequency difference changes from positive to negative, and this type of boundary is the optimal initial center frequency.

3. The bearing fault identification method based on adaptive variational mode decomposition according to claim 2 is characterized in that: In step S202: The number of iterative update operations has a fixed mapping relationship with the step length and the sampling frequency, and the step length is 100 Hz.

4. The bearing fault identification method based on adaptive variational mode decomposition according to claim 1 is characterized in that: In step S3: The penalty factor has a fixed mapping relationship with the optimal initial center frequency and the sampling frequency, and the penalty factor is determined by solving the fixed mapping relationship.

5. The bearing fault identification method based on adaptive variational mode decomposition according to claim 1 is characterized in that: In step S6: The median kurtosis has a fixed mapping relationship with the signal mean and standard deviation of the vibration signal, and the determination of the median kurtosis is solved by the fixed mapping relationship.

6. The bearing fault identification method based on adaptive variational mode decomposition according to claim 1 is characterized in that: In step S6: The 1.5-dimensional spectrum is a one-dimensional Fourier transform of the third-order accumulation of the vibration signal.

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