Automobile rolling bearing fault diagnosis method based on variational mode decomposition

Abstract

The invention relates to an automobile rolling bearing fault diagnosis method based on variational mode decomposition, and the method comprises the following steps: 1, decomposing an input bearing fault signal into a plurality of fault frequency domain signal components IMF with a determined number, and converting the fault frequency domain signal components from a frequency domain into fault time domain signals; and step 2, based on the fault time domain signal obtained in the step 1, carrying out marginal spectrum analysis on the bearing fault signal to obtain a real fault characteristic frequency condition. According to the invention, the fault type can be identified more accurately, and a more ideal diagnosis effect can be obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of bearing fault diagnosis, and relates to a method for diagnosing automobile rolling bearing faults, in particular to a method for diagnosing automobile rolling bearing faults based on variational mode decomposition. Background Art

[0002] Bearings are rotating mechanical devices used in many key automotive components. Their normal operation is an important factor in ensuring the safety, efficiency and long-term operation of the entire equipment. By analyzing the bearing vibration signal, especially extracting its time-frequency characteristics, the type of fault can be analyzed and the fault can be accurately located. However, when analyzing the bearing fault signal, due to the special properties of the fault signal such as huge amplitude changes and mixed local sudden extreme values, it is difficult to extract the fault characteristics of the bearing and determine the fault type.

[0003] At present, there are many commonly used signal time-frequency analysis methods, such as the classic wavelet analysis. However, wavelet analysis lacks adaptability due to the fact that its wavelet basis function construction is independent of the signal being analyzed, which limits the accurate extraction of bearing impact fault characteristics. In addition, the Empirical Mode Decomposition (EMD) method is a powerful tool for analyzing signals with huge amplitude fluctuations and mixed local sudden extreme value characteristics. However, in the process of signal decomposition, due to the overall step-by-step separation operation method used, the defects and disadvantages of the EMD method itself are difficult to eliminate through method improvements.

[0004] Therefore, how to improve the accuracy of fault feature extraction and determine the fault type more efficiently is crucial for bearing fault diagnosis.

[0005] Therefore, the present invention proposes a method for diagnosing automobile rolling bearing faults based on variational mode decomposition.

[0006] After searching, no public documents of the prior art identical or similar to the present invention were found. Summary of the invention

[0007] The purpose of the present invention is to overcome the deficiencies of the prior art and to propose a method for diagnosing automobile rolling bearing faults based on variational modal decomposition, which can more accurately identify the fault type and obtain a more ideal diagnostic effect.

[0008] The present invention solves the practical problem by adopting the following technical solutions:

[0009] A method for fault diagnosis of automobile rolling bearings based on variational mode decomposition comprises the following steps:

[0010] Step 1, decomposing the input bearing fault signal into a certain number of fault frequency domain signal components IMF, and transforming the fault frequency domain signal components from the frequency domain into fault time domain signals;

[0011] Step 2: Based on the fault time domain signal obtained in step 1, perform marginal spectrum analysis on the bearing fault signal to obtain the actual fault characteristic frequency.

[0012] Moreover, the specific method of step 1 is:

[0013] (1) Assuming that a bearing fault signal f is to be decomposed into k IMF components, the corresponding variational problem needs to be constructed;

[0014] (2) Solve the constrained variational problem;

[0015] (3) In the process of solving the constrained variational problem, each IMF component directly completes the replacement of the old and new center frequencies and the corresponding bandwidths within the frequency variation range. Then, the frequency bands can be divided according to the special properties of the original signal within the frequency variation range, thereby realizing the gradual decomposition of the signal. Finally, the signal components are transformed from the frequency domain to the time domain through the inverse Fourier transform.

[0016] Moreover, the specific steps of step 1 (1) include:

[0017] ①For each IMF component u k (t), the time domain is converted into the frequency domain through Hilbert transform to obtain its analytical signal, and u k The single-sided spectrum of (t):

[0018]

[0019] Where δ(t) is the pulse function, where {u k}={u 1 ,...,u k} represents the k IMF components obtained by decomposition.

[0020] ② Estimate a center frequency ω for each analytical signal k , by means of frequency modulation, the spectrum of each analytical signal is transformed to the corresponding baseband:

[0021]

[0022] In the formula {ω k}={ω 1 ,...,ω k} represents the center frequency of each component.

[0023] ③ Using the frequency shift signal H 1The Gaussian smoothing index calculates the L2 norm of the above demodulated signal gradient to estimate the bandwidth of each IMF component. The resulting constrained variational problem is:

[0024]

[0025] The above formula is a variational model with constrained mode decomposition. In order to minimize the bandwidth between the modes obtained by VMD decomposition and make the sum equal to the original signal f(t), for each mode function u k (t), obtain the single-sided spectrum through Hilbert transform, and then compare it with the estimated center frequency Multiply them together to move the unilateral spectrum of each mode to the estimated center frequency. Finally, the square of the gradient L 2 norm, and calculate the bandwidth of each modal signal. is the partial derivative of the function with respect to time t.

[0026] Moreover, the specific steps of step (2) of step 1 include:

[0027] To solve this constrained variational problem, we need to first use the quadratic penalty function term and Lagrange multipliers to convert it into an unconstrained problem of the following form:

[0028]

[0029] Where α is the penalty factor and λ(t) is the Lagrange multiplier.

[0030] Using the Alternate direction method of multipliers (ADMM) to update the λ n+1 Finding the saddle point of the unconstrained variational problem is the final solution of equation (3).

[0031] Moreover, the specific steps of step 2 include:

[0032] (1) Perform VMD decomposition on any signal to obtain k IMF components.

[0033] (2) Apply Hilbert transform to each IMF component in the decomposition to obtain the corresponding time-frequency distribution of VMD:

[0034]

[0035] Where Re represents the real part; a(t) represents the amplitude; and f(t) represents the frequency.

[0036] (3) By integrating the result of formula (5) over time, the marginal spectrum of VMD can be defined as:

[0037]

[0038] The spectrum peak at the fault characteristic frequency is made more obvious, making it easier to obtain the actual fault characteristic frequency.

[0039] Advantages and beneficial effects of the present invention:

[0040] 1. The present invention proposes a method for diagnosing automobile rolling bearing faults based on variational mode decomposition (VMD). The solution of the variational component model is obtained by step-by-step calculation and search, and the center frequency of each component after decomposition and the corresponding spectral bandwidth are obtained, thereby realizing the effective extraction of the composite fault feature information of the signal and the accurate diagnosis of the bearing fault. The method includes the following steps: decomposing the input bearing fault signal f into a certain number of intrinsic mode functions, converting the fault frequency domain signal into a time domain signal; performing marginal spectrum analysis on the bearing fault signal to obtain the real fault characteristic frequency; and synchronously using the VMD method and the empirical mode decomposition (EMD) method to diagnose the bearing fault. Through comparative analysis, it is confirmed that the VMD method has a good processing ability for signals with huge amplitude changes and mixed local burst extreme value characteristics, and realizes the accurate extraction of bearing fault characteristics.

[0041] 2. The present invention performs bearing fault diagnosis based on the VMD method, obtains signal components within the framework of variable modal component theory, adopts a non-recursive processing strategy, and realizes the decomposition of the original signal by constructing and solving constraint problems. On this basis, the VMD method is combined with the marginal spectrum analysis method to conduct actual research on the simulation signal and the actual signal of the bearing, making the results more intuitive and the fault characteristics more obvious. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A schematic diagram of a bearing inner ring fault signal provided by an embodiment of the present invention;

[0043] Figure 2 A schematic diagram of VMD detection components for inner race faults provided by an embodiment of the present invention;

[0044] Figure 3 A schematic diagram of EMD detection components for inner race faults provided by an embodiment of the present invention;

[0045] Figure 4 A marginal spectrum based on VMD components provided by an embodiment of the present invention;

[0046] Figure 5 A marginal spectrum based on EMD components provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The embodiments of the present invention are further described in detail below with reference to the accompanying drawings:

[0048] A method for fault diagnosis of automobile rolling bearings based on variational mode decomposition comprises the following steps:

[0049] Step 1, decomposing the input bearing fault signal into a certain number of fault frequency domain signal components IMF, and transforming the fault frequency domain signal components from the frequency domain into fault time domain signals;

[0050] The specific method of step 1 is:

[0051] Assuming that a bearing fault signal f is to be decomposed into k IMF components, the corresponding variational problem construction process is:

[0052] ①For each IMF component u k (t), the time domain is converted into the frequency domain through Hilbert transform to obtain its analytical signal, and u k The single-sided spectrum of (t):

[0053]

[0054] Where δ(t) is the pulse function, where {u k}={u 1 ,...,u k} represents the k IMF components obtained by decomposition.

[0055] ② Estimate a center frequency ω for each analytical signal k , by means of frequency modulation, the spectrum of each analytical signal is transformed to the corresponding baseband:

[0056]

[0057] In the formula {ω k}={ω 1 ,...,ω k} represents the center frequency of each component.

[0058] ③ Using the frequency shift signal H 1 The Gaussian smoothing index calculates the L2 norm of the above demodulated signal gradient to estimate the bandwidth of each IMF component. The resulting constrained variational problem is:

[0059]

[0060] The above formula is a variational model with constrained mode decomposition. In order to minimize the bandwidth between the modes obtained by VMD decomposition and make the sum equal to the original signal f(t), for each mode function u k(t), obtain the single-sided spectrum through Hilbert transform, and then compare it with the estimated center frequency Multiply them together to move the unilateral spectrum of each mode to the estimated center frequency. Finally, the square of the gradient L 2 norm, and calculate the bandwidth of each modal signal. is the partial derivative of the function with respect to time t.

[0061] To solve this constrained variational problem, we need to first use the quadratic penalty function term and Lagrange multipliers to convert it into an unconstrained problem of the following form:

[0062]

[0063] Where α is the penalty factor and λ(t) is the Lagrange multiplier.

[0064] Using the Alternate direction method of multipliers (ADMM) to update the λ n+1 Finding the saddle point of the unconstrained variational problem is the final solution of equation (3).

[0065] In the process of solving the constrained variational problem, each IMF component directly completes the replacement of the old and new center frequencies and the corresponding bandwidths within the frequency change range, and then the frequency band division can be completed according to the special properties of the original signal within the frequency change range, thereby realizing the gradual decomposition of the signal, and finally transforming the signal components from the frequency domain to the time domain through the inverse Fourier transform.

[0066] Step 2: Based on the fault time domain signal obtained in step 1, perform marginal spectrum analysis on the bearing fault signal to obtain the actual fault characteristic frequency;

[0067] The specific steps of step 2 include:

[0068] (1) Perform VMD decomposition on any signal to obtain k IMF components.

[0069] (2) Apply Hilbert transform to each IMF component in the decomposition to obtain the corresponding time-frequency distribution of VMD:

[0070]

[0071] Where Re represents the real part; a(t) represents the amplitude; and f(t) represents the frequency.

[0072] (3) By integrating the result of formula (5) over time, the marginal spectrum of VMD can be defined as:

[0073]

[0074] The spectrum peak at the fault characteristic frequency is made more obvious, making it easier to obtain the actual fault characteristic frequency.

[0075] According to the above steps, the marginal spectra after VMD decomposition are calculated respectively, as follows: Figure 4 At the same time, the marginal spectrum after EMD decomposition is calculated as follows Figure 5 As shown in the figure, the results are more intuitive and the fault characteristics are more obvious.

[0076] The working principle of the present invention is:

[0077] The present invention uses the bearing database data of Case Western Reserve University (CWRU) in the United States, and takes the drive end bearing (model: SKF6205) as an example to simulate the inner ring fault of the bearing for analysis. The inner ring fault bearing data collected when the motor load is 0kW and the speed is 1797rpm is selected, and the sampling frequency is 12kHz. The basic parameters of the bearing are shown in Tables 1 and 2.

[0078] The speed can be obtained from the rotational speed r =29.95Hz, so the theoretical inner ring fault frequency f can be calculated inner =162.1Hz.

[0079] Table 1 Main parameters of bearings

[0080]

[0081] Table 2 Fault characteristic frequency

[0082]

[0083] S1. VMD decomposition of bearing fault signal

[0084] The present invention first needs to decompose the input bearing fault signal f into a certain number of intrinsic mode functions (IMF), and then use a "variational" method to first estimate the center frequency of each mode function, and then solve the bandwidth of each mode according to the constraints to minimize the sum, and finally the sum of all the modal components is the original signal.

[0085] Assuming that a bearing fault signal f is to be decomposed into k IMF components, the corresponding variational problem construction process is summarized as follows:

[0086] ①For each IMF component u k (t), the time domain is converted into the frequency domain through Hilbert transform to obtain its analytical signal, and u kThe single-sided spectrum of (t):

[0087]

[0088] ② Estimate a center frequency ω for each analytical signal k , by means of frequency modulation, the spectrum of each analytical signal is transformed to the corresponding baseband:

[0089]

[0090] ③ Using the frequency shift signal H 1 The Gaussian smoothing index calculates the L2 norm of the above demodulated signal gradient to estimate the bandwidth of each IMF component. The resulting constrained variational problem is:

[0091]

[0092] In the formula {u k}={u 1 ,...,u k} represents the k IMF components obtained by decomposition {ω k}={ω 1 ,...,ω k} represents the frequency center of each component.

[0093] To solve this constrained variational problem, we need to first use the quadratic penalty function term and Lagrange multipliers to convert it into an unconstrained problem of the following form:

[0094]

[0095] Where α is the penalty factor and λ(t) is the Lagrange multiplier.

[0096] Using the Alternate direction method of multipliers (ADMM) to update the λ n+1 The saddle point of the unconstrained variational problem is obtained, which is the final solution of equation (3). In the process of solving the constrained variational problem, each IMF component directly completes the replacement of the new and old center frequencies and the corresponding bandwidths within the frequency variation range, and then the frequency bands can be divided according to the special properties of the original signal within the frequency variation range, realizing the gradual decomposition of the signal, and finally transforming the signal components from the frequency domain to the time domain through the inverse Fourier transform.

[0097] The method of the present invention is Figure 1 The bearing inner ring fault signal shown is decomposed to obtain the result Figure 2 As shown, and compared with the decomposition results of the EMD method, as shown in Figure 3 shown.

[0098] S2. Extract VMD marginal spectrum

[0099] In the frequency domain analysis of general vibration signals, the amplitude of the spectrum can only reflect the actual existence of the fault characteristic frequency in the signal, but cannot accurately reflect whether the frequency actually exists. When the amplitude of a certain frequency appears in the marginal spectrum, it means that the frequency wave must exist locally on the time axis. Therefore, after completing the VMD decomposition of the bearing fault signal, the marginal spectrum analysis is further performed to more accurately reflect the actual fault characteristic frequency of the signal.

[0100] The calculation steps of the VMD-based marginal spectrum algorithm are as follows:

[0101] ① Perform VMD decomposition on any signal to obtain k IMF components.

[0102] ② Apply Hilbert transform to each IMF component in the decomposition formula to obtain the corresponding time-frequency distribution of VMD:

[0103]

[0104] Where Re represents the real part; a(t) represents the amplitude; and f(t) represents the frequency.

[0105] ③ By integrating the result of formula (5) over time, the marginal spectrum of VMD can be defined as:

[0106]

[0107] According to the above steps, the marginal spectra after VMD decomposition are calculated respectively, as follows: Figure 4 At the same time, the marginal spectrum after EMD decomposition is calculated as follows Figure 5 shown.

[0108] It should be emphasized that the embodiments of the present invention are illustrative rather than restrictive. Therefore, the present invention includes but is not limited to the embodiments described in the specific implementation modes. Any other implementation modes derived by those skilled in the art based on the technical solutions of the present invention also fall within the scope of protection of the present invention.

Claims

1. A method for automobile rolling bearing fault diagnosis based on variational modal decomposition, characterized in that: The following steps are involved: Step 1, decomposing the input bearing fault signal into a certain number of fault frequency domain signal components IMF, and transforming the fault frequency domain signal components from the frequency domain into fault time domain signals; Step 2: Based on the fault time domain signal obtained in step 1, perform marginal spectrum analysis on the bearing fault signal to obtain the actual fault characteristic frequency.

2. The method for diagnosing automobile rolling bearing faults based on variational modal decomposition according to claim 1, characterized in that: The specific method of step 1 is: (1) Assuming that a bearing fault signal f is to be decomposed into k IMF components, the corresponding variational problem needs to be constructed; (2) Solve the constrained variational problem; (3) In the process of solving the constrained variational problem, each IMF component directly completes the replacement of the old and new center frequencies and the corresponding bandwidths within the frequency variation range. Then, the frequency bands can be divided according to the special properties of the original signal within the frequency variation range, thereby realizing the gradual decomposition of the signal. Finally, the signal components are transformed from the frequency domain to the time domain through the inverse Fourier transform.

3. The method for diagnosing automobile rolling bearing faults based on variational modal decomposition according to claim 2, characterized in that: The specific steps of step (1) of step 1 include: ①For each IMF component u k (t), the time domain is converted into the frequency domain through Hilbert transform to obtain its analytical signal, and u k The single-sided spectrum of (t): Where δ(t) is the pulse function, where {u k }={u1,...,u k } represents the k IMF components obtained by decomposition; ② Estimate a center frequency ω for each analytical signal k , by means of frequency modulation, the spectrum of each analytical signal is transformed to the corresponding baseband: In the formula {ω k }={ω1,...,ω k } represents the center frequency of each component; ③ Using the frequency shift signal H 1 The Gaussian smoothing index calculates the L2 norm of the above demodulated signal gradient to estimate the bandwidth of each IMF component. The resulting constrained variational problem is: The above formula is a variational model with constrained mode decomposition of variational modes. In order to minimize the bandwidth between modes obtained by VMD decomposition and make the sum equal to the original signal f(t), for each mode function u k (t), obtain the single-sided spectrum through Hilbert transform, and then compare it with the estimated center frequency Multiply them together to move the unilateral spectrum of each mode to the estimated center frequency. Finally, the square of the gradient L 2 norm, calculate the bandwidth of each modal signal; where, is the partial derivative of the function with respect to time t.

4. The method for diagnosing automobile rolling bearing faults based on variational modal decomposition according to claim 2, characterized in that: The specific steps of step (2) of step 1 include: To solve this constrained variational problem, we need to first use the quadratic penalty function term and Lagrange multipliers to convert it into an unconstrained problem of the following form: Where α is the penalty factor, λ(t) is the Lagrange multiplier; Using the Alternate direction method of multipliers (ADMM) to update the λ n+1 Finding the saddle point of the unconstrained variational problem is the final solution of equation (3).

5. The method for automobile rolling bearing fault diagnosis based on variational mode decomposition according to claim 1, characterized in that: The specific steps of step 2 include: (1) Perform VMD decomposition on any signal to obtain k IMF components; (2) Apply Hilbert transform to each IMF component in the decomposition to obtain the corresponding time-frequency distribution of VMD: Where Re represents the real part; a(t) represents the amplitude; f(t) represents the frequency; (3) By integrating the result of formula (5) over time, the marginal spectrum of VMD can be defined as: The spectrum peak at the fault characteristic frequency is made more obvious, making it easier to obtain the actual fault characteristic frequency.

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