A bearing compound fault diagnosis method based on second-order chirplet extraction transform

Abstract

The application discloses a bearing composite fault diagnosis method based on a second-order Chirplet extraction transform, and comprises the following steps: S1, collecting a bearing signal and synchronously measuring a rotating speed signal; S2, expanding a first-order speed synchronous fundamental frequency in a speed synchronous linear Chirplet transform into a second-order speed synchronous fundamental frequency; S3, based on the second-order speed synchronous fundamental frequency, constructing a second-order speed synchronous Chirplet transform to process a bearing vibration signal to obtain a corresponding time-frequency energy distribution result; S4, constructing a local maximum extraction operator according to the time-frequency energy distribution result; S5, using the local maximum extraction operator to obtain a time-frequency energy distribution result of the second-order Chirplet extraction transform; and S6, calculating a theoretical fault characteristic frequency according to bearing geometric parameters and a rotating frequency, and then judging a fault category based on the theoretical fault characteristic frequency and the actual fault characteristic frequency. The method improves time-frequency aggregation, accurately extracts a bearing composite fault characteristic and further identifies a fault type, and is suitable for variable rotating speed rolling bearing vibration signal analysis in the field of fault diagnosis.

Description

Technical Field

[0001] This invention belongs to the field of bearing fault diagnosis, specifically relating to a bearing composite fault diagnosis method based on second-order Chirplet extraction transform. Background Technology

[0002] Bearings, as the most common rotating machinery components, are highly susceptible to damage under long-term high-speed operation, posing a significant risk of safety accidents and economic losses. In practical engineering applications, bearings often exhibit complex fault states with multiple faults coexisting. The mutual interference of multiple fault characteristics further increases the difficulty of separating and extracting complex fault features. Therefore, conducting research on bearing complex fault diagnosis is crucial.

[0003] The Chirplet transform, a time-frequency analysis method, is widely used in bearing fault diagnosis. This method adds a frequency modulation term to the short-time Fourier transform, enabling better handling of non-stationary signals. With in-depth research, several improved versions of the Chirplet transform have become popular, such as the general linear Chirplet transform, the Chirplet transform based on a scaling basis, and the speed-synchronized linear Chirplet transform. The general linear Chirplet transform uses linear Chirplet transforms with different modulation frequencies to match the instantaneous frequency ridge, effectively handling nonlinear frequency-modulated signals. However, due to the retention of inappropriate modulation frequencies, frequency aliasing occurs when processing dense multi-component signals. The Chirplet transform based on a scaling basis constructs a new kernel phase function to accurately match the modulation frequency to the instantaneous frequency trajectory. The speed-synchronized linear Chirplet transform constructs a Chirplet basis function synchronized with the shaft speed, effectively mitigating energy ambiguity. However, the time-frequency convergence of these two methods needs further improvement when processing dense multi-component signals.

[0004] In summary, although traditional time-frequency analysis methods have been widely used in bearing fault diagnosis, their time-frequency clustering in characterizing the characteristic frequencies of dense and complex faults needs further improvement. Summary of the Invention

[0005] To address the aforementioned problems, this invention proposes a bearing composite fault diagnosis method based on second-order Chirplet extraction transform, which can significantly improve time-frequency convergence and achieve accurate characterization of bearing composite fault features.

[0006] Specific technical solution:

[0007] A method for diagnosing composite bearing faults based on second-order Chirplet extraction transform includes the following steps:

[0008] S1. Acquire bearing vibration signals based on an accelerometer and synchronously measure rotational speed signals based on an encoder;

[0009] S2. Extend the first-order velocity synchronization fundamental frequency in the linear Chirplet transform of velocity synchronization to the second-order velocity synchronization fundamental frequency.

[0010] S3. Based on the second-order velocity synchronization fundamental frequency obtained in S2, construct the second-order velocity synchronization Chirplet transform to process the bearing vibration signal and obtain the corresponding time-frequency energy distribution results.

[0011] S4. Construct a local maximum extraction operator based on the time-frequency energy distribution results obtained in S3;

[0012] S5. Using the local maximum extraction operator constructed in S4, the time-frequency energy is redistributed to obtain the time-frequency energy distribution result of the second-order Chirplet extraction transform (actual fault characteristic frequency).

[0013] S6. Calculate the theoretical fault characteristic frequency based on the bearing geometric parameters and rotational frequency, and then determine the fault category based on the theoretical fault characteristic frequency and the actual fault characteristic frequency in S5.

[0014] Furthermore, the specific derivation process of the second-order velocity synchronization fundamental frequency in step S2 is as follows: Assume that the rotational frequency of the shaft in S1 is f. s (τ), using Taylor expansion to express the rotational frequency f of the shaft. s (τ) expands into a second-order equation, expressed as:

[0015]

[0016] Where: t is the time variable, f s '(t) and f s "(t) represents the rotational frequency f of the shaft." s The first and second derivatives of (t);

[0017] To match the frequency of the signal components, the speed synchronization fundamental frequency must be proportional to the shaft's rotational frequency, expressed as:

[0018] f b (τ)=kf s (τ)=f (2)

[0019] Where: k represents the proportionality coefficient, f b (τ) represents the fundamental frequency at time t = τ, and f represents the frequency;

[0020] Therefore, the second-order velocity synchronization fundamental frequency is expressed as:

[0021]

[0022] make The second-order velocity synchronization fundamental frequency can then be rewritten as:

[0023] f b (τ)=f(1+2m1(τ-t)+3m2(τ-t) 2 (4)

[0024] Furthermore, the expression for the second-order velocity synchronization Chirplet transform in step S3 is:

[0025]

[0026] Where: λ(τ)=τ+m1(τ-t) 2 +m2(τ-t) 3 , λ'(τ)=1+2m1(τ-t)+3m2(τ-t) 2 ; g(·) represents the Gaussian window function.

[0027] Using a discretization method, the tangent of the rotation angle is introduced to evaluate parameters m1 and m2, expressed as:

[0028] m1=tanβ1,m2=tanβ1tanβ2 (6)

[0029] Segmenting the rotation angles β1 and β2 along the interval (-π / 2, π / 2), the expressions are as follows:

[0030]

[0031]

[0032] Where M1 and M2 are the number of segments; the optimal rotation angle is selected using kurtosis theory, assuming the frequency range is [0, Q], and the expression is:

[0033]

[0034] Therefore, the expression for the second-order velocity synchronization Chirplet transform is:

[0035]

[0036] Furthermore, the expression for the local maximum extraction operator in step S4 is:

[0037]

[0038] Where: mean represents the average value, V represents a constant and V∈[1,3]; the purpose of the second row is to improve noise resistance and remove unnecessary noise components;

[0039] Furthermore, the expression for the second-order Chirplet extraction transform in step S5 is:

[0040] W(t,f)=H(t,f)·η(t,f) (12)

[0041] Where: η(·) represents the local maximum extraction operator;

[0042] This invention proposes a bearing composite fault diagnosis method based on second-order Chirplet extraction transform, which has the following advantages: First, the first-order speed synchronization fundamental frequency in the speed synchronization linear Chirplet transform is extended to a second-order speed synchronization fundamental frequency. The second-order speed synchronization Chirplet transform is then used to process the bearing vibration signal. Then, a local maximum extraction operator is constructed to redistribute time-frequency energy. Compared with traditional time-frequency analysis methods, this method significantly improves time-frequency aggregation and enhances noise resistance. It can more accurately characterize the bearing fault characteristic frequencies of dense components under variable speed conditions, thereby accurately identifying the composite fault type of the bearing. Attached Figure Description

[0043] Figure 1 This is a flowchart of the present invention;

[0044] Figure 2 The experimental apparatus provided in the embodiments of the present invention; wherein Figure 2 (a) Bearing vibration signal acquisition test bench Figure 2 (b) is a bearing with an outer ring failure. Figure 2 (c) is a bearing with an inner ring failure;

[0045] Figure 3 This is a time-domain waveform diagram of the original vibration signal in the embodiment;

[0046] Figure 4 The motor rotation frequency in the embodiment;

[0047] Figure 5 The time spectrum is obtained by performing time-frequency analysis on the bearing signal using the method of this invention;

[0048] Figure 6 The time-frequency spectrum of the bearing signal obtained by performing time-frequency analysis on the linear Chirplet transform for speed synchronization;

[0049] Figure 7 The time-frequency spectrum is obtained by performing time-frequency analysis on the bearing signal using a general linear Chirplet transform.

[0050] Figure 8 The time spectrum of the bearing signal was obtained by time-frequency analysis to synchronously extract the transformation. Detailed Implementation

[0051] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0052] Reference Figure 1 This invention provides a method for diagnosing composite bearing faults based on second-order Chirplet extraction transform, the specific steps of which are as follows:

[0053] S1. Acquire bearing vibration signals based on an accelerometer and synchronously measure rotational speed signals based on an encoder;

[0054] S2. Extend the first-order velocity synchronization fundamental frequency in the linear Chirplet transform of velocity synchronization to the second-order velocity synchronization fundamental frequency.

[0055] The detailed derivation of the second-order velocity synchronization fundamental frequency is as follows:

[0056] Assume the rotational frequency of the central axis in S1 is f. s (τ), using Taylor expansion to express the rotational frequency f of the shaft. s (τ) expands into a second-order equation, expressed as:

[0057]

[0058] Where: t is the time variable, f s '(t) and f s "(t) represents the rotational frequency f of the shaft." s The first and second derivatives of (t);

[0059] To match the frequency of the signal components, the speed synchronization fundamental frequency must be proportional to the shaft's rotational frequency, expressed as:

[0060] f b (τ)=kf s (τ)=f (2)

[0061] Where: k represents the proportionality coefficient, f b (τ) represents the fundamental frequency at time t = τ, and f represents the frequency;

[0062] Therefore, the second-order velocity synchronization fundamental frequency is expressed as:

[0063]

[0064] make The second-order velocity synchronization fundamental frequency can then be rewritten as:

[0065] f b (τ)=f(1+2m1(τ-t)+3m2(τ-t) 2 (4)

[0066] S3. Based on the second-order velocity synchronization fundamental frequency obtained in S2, construct the second-order velocity synchronization Chirplet transform to process the bearing vibration signal and obtain the corresponding time-frequency energy distribution results.

[0067] The expression for the second-order velocity synchronization Chirplet transform is:

[0068]

[0069] Where: λ(τ)=τ+m1(τ-t) 2 +m2(τ-t) 3 , λ'(τ)=1+2m1(τ-t)+3m2(τ-t) 2 ; g(·) represents the Gaussian window function.

[0070] Using a discretization method, the tangent of the rotation angle is introduced to evaluate parameters m1 and m2, expressed as:

[0071] m1=tanβ1,m2=tanβ1tanβ2 (6)

[0072] Segmenting the rotation angles β1 and β2 along the interval (-π / 2, π / 2), the expressions are as follows:

[0073]

[0074]

[0075] Where M1 and M2 are the number of segments; the optimal rotation angle is selected using kurtosis theory, assuming the frequency range is [0, Q], and the expression is:

[0076]

[0077] Therefore, the expression for the second-order velocity synchronization Chirplet transform is:

[0078]

[0079] S4. Construct a local maximum extraction operator based on the time-frequency energy distribution results obtained in S3;

[0080] The expression for the local maximum extraction operator is:

[0081]

[0082] Where: mean represents the average value, V represents a constant and V∈[1,3]; the purpose of the second row is to improve noise resistance and remove unnecessary noise components;

[0083] S5. Based on the local maximum extraction operator constructed in S4, the time-frequency energy is redistributed to obtain the time-frequency energy distribution result of the second-order Chirplet extraction transform (actual fault characteristic frequency).

[0084] The expression for the second-order Chirplet extraction transform is:

[0085] W(t,f)=H(t,f)·η(t,f) (12)

[0086] Where: η(·) represents the local maximum extraction operator;

[0087] S6. Calculate the theoretical fault characteristic frequency based on the bearing geometric parameters and rotational frequency, and then determine the fault category based on the theoretical fault characteristic frequency and the actual fault characteristic frequency in S5.

[0088] Specific examples:

[0089] The bearing signals with outer and inner ring faults used in this invention are acquired from... Figure 2 The bearing test bench shown in (a) consists of a drive motor, an acceleration sensor, an encoder, a speed controller, and other devices. The sensor is used to measure bearing vibration signals, and the encoder is used to measure rotational speed signals. Figure 2 (b) and (c) show the faulty outer and inner rings of the bearing, respectively. The geometric parameters of this rolling bearing are shown in Table 1:

[0090] Table 1 Geometric parameters of rolling bearings

[0091]

[0092] The time-domain waveform of the bearing signal and the motor frequency distribution are as follows: Figure 3 and 4 As shown. The expression for the frequency conversion equation is:

[0093] f r (t)=-1.02t 2 -5.34t+52.84 (13)

[0094] The time-frequency energy distribution results obtained by the method provided by this invention are as follows: Figure 5 As shown in the figure, the time-frequency ridges are continuous and clear, and the time-frequency clustering is high. The theoretical outer ring fault characteristic coefficient, theoretical inner ring fault characteristic coefficient, and theoretical rolling element fault characteristic coefficient calculated based on the rolling bearing geometric parameters are 2.5, 4.4, and 1.7, respectively.

[0095] Then, based on the rotational frequency calculation, the theoretical outer ring fault characteristic frequency, the theoretical inner ring fault characteristic frequency, and the rolling element fault characteristic frequency are obtained as f, respectively. o (t)=-2.55t 2-13.35t+132.09、f i (t)=-4.48t 2 -23.49t+232.49 and f e (t)=-1.734t 2 -9.078t +89.828. Based on the above theoretical fault characteristic frequency and rotational frequency, it can be determined that... Figure 5 The four time-frequency ridges shown are f i (t), 2f i (t), f o (t) and 2f r (t). As can be seen from the above, the characteristic frequency of the inner ring fault and its second harmonic, the characteristic frequency of the outer ring fault and the second harmonic of the rotational frequency were accurately identified. Therefore, it can be determined that the bearing has both inner and outer ring faults, proving that the method of the present invention can effectively diagnose combined faults in variable speed bearings.

[0096] To further verify the superiority of the method of the present invention in the diagnosis of complex faults in variable speed bearings, the bearing signal was processed using speed synchronous linear Chirplet transform, general linear Chirplet transform, and synchronous extraction transform, respectively, and the resulting time spectrum is shown below. Figure 6 , Figure 7 and Figure 8 As shown. From Figure 6 and Figure 7 The magnified view shows that the time-frequency ridges obtained by the velocity-synchronized linear Chirplet transform and the general linear Chirplet transform have low energy concentration and exhibit time-frequency ambiguity. Figure 8 While the time-frequency clustering of the synchronous extraction and transformation method is improved to some extent, it can be seen from the magnified local image that this method cannot provide an accurate instantaneous frequency characterization and contains severe background noise. The above comparison results show that the method of the present invention is more effective in the diagnosis of complex faults in variable speed bearings, with better noise resistance, more accurate identification of instantaneous frequency ridges, and higher time-frequency energy clustering.

Claims

1. A method for diagnosing composite bearing faults based on second-order Chirplet extraction transform, characterized in that, Includes the following steps: S1. Acquire bearing vibration signals based on an accelerometer and synchronously measure rotational speed signals based on an encoder; S2. Extend the first-order velocity synchronization fundamental frequency in the linear Chirplet transform of velocity synchronization to the second-order velocity synchronization fundamental frequency. S3. Based on the second-order velocity synchronization fundamental frequency obtained in S2, construct the second-order velocity synchronization Chirplet transform to process the bearing vibration signal and obtain the corresponding time-frequency energy distribution results. S4. Construct a local maximum extraction operator based on the time-frequency energy distribution results obtained in S3; S5. Using the local maximum extraction operator constructed in S4, the time-frequency energy is redistributed to obtain the time-frequency energy distribution result of the second-order Chirplet extraction transform, which is the actual fault characteristic frequency. S6. Calculate the theoretical fault characteristic frequency based on the bearing geometric parameters and rotational frequency, and then determine the fault category based on the theoretical fault characteristic frequency and the actual fault characteristic frequency in S5.

2. The bearing composite fault diagnosis method based on second-order Chirplet extraction transform according to claim 1, characterized in that, The derivation process of the second-order velocity synchronization fundamental frequency in step S2 is as follows: The rotational frequency of the axis in S1 is f s (τ), using Taylor expansion to express the rotational frequency f of the shaft. s (τ) expands into a second-order equation, expressed as: Where: t is the time center, f s '(t) and f s "(t) represents the rotational frequency f of the shaft." s The first and second derivatives of (t); τ is the time variable; To match the frequency of the signal components, the speed synchronization fundamental frequency must be proportional to the shaft's rotational frequency, expressed as: f b (τ)=kf s (τ)=f (2) Where: k represents the proportionality coefficient, f b (τ) represents the fundamental frequency at time t = τ, and f represents the frequency; Therefore, the second-order velocity synchronization fundamental frequency is expressed as: make m1 and m2 are pre-known parameters that ensure the highest energy concentration is obtained from the second-order velocity synchronization Chirplet transform; therefore, the second-order velocity synchronization fundamental frequency can be rewritten as: f b (τ)=f(1+2m1(τ-t)+3m2(τ-t) 2 ) (4).

3. The bearing composite fault diagnosis method based on second-order Chirplet extraction transform according to claim 1, characterized in that, The expression for the second-order velocity synchronization Chirplet transform in step S3 is: Where: λ(τ)=τ+m1(τ-t) 2 +m2(τ-t) 3 , λ'(τ)=1+2m1(τ-t)+3m2(τ-t) 2 g(·) represents the Gaussian window function; Using a discretization method, the tangent of the rotation angle is introduced to evaluate parameters m1 and m2, expressed as: m1=tanβ1,m2=tanβ1tanβ2 (6) Segmenting the rotation angles β1 and β2 along the interval (-π / 2, π / 2), the expressions are as follows: Where M1 and M2 are the number of segments; the optimal rotation angle is selected using kurtosis theory, assuming the frequency range is [0, Q], and the expression is: Where: Q is the maximum frequency in the time-frequency representation; the expression for the second-order velocity synchronization Chirplet transform is:

4. The bearing composite fault diagnosis method based on second-order Chirplet extraction transform according to claim 1, characterized in that, The expression for the local maximum extraction operator in step S4 is: Where: mean represents the average value, V represents a constant and V∈[1,3]; the purpose of the second row is to improve noise immunity and remove unnecessary noise components.

5. The bearing composite fault diagnosis method based on second-order Chirplet extraction transform according to claim 1, characterized in that, The expression for the second-order Chirplet extraction transform in step S5 is: W(t,f)=H(t,f)·η(t,f) (12) Where: η(·) represents the local maximum extraction operator.

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