FRF-ASSA-SVM-based RV reducer fault diagnosis method under reciprocating working condition

Abstract

The invention relates to an FRF-ASSA-SVM-based RV reducer fault diagnosis method under a reciprocating working condition, and belongs to the technical field of signal analysis and fault diagnosis. The method comprises the following steps: S1, collecting current signals and vibration signals of an RV speed reducer swing arm system in different fault states; s2, calculating a frequency response function of the swing arm system of the RV speed reducer by using the current signal and the vibration signal; s3, performing spectral analysis on the signal, and determining the maximum current frequency of the input current; s4, determining the analysis bandwidth of the frequency response function through the maximum current frequency; s5, performing ASSA noise reduction on the frequency response function in combination with spectral analysis; and S6, performing fault diagnosis on the RV speed reducer by using the frequency response function after noise reduction and the SVM. According to the method, useful information in the frequency response function can be accurately selected and subjected to noise reduction, the fault characterization capability of the frequency response function is greatly improved, and the fault of the RV speed reducer under the reciprocating working condition can be accurately diagnosed.

Description

Technical Field

[0001] The invention relates to a fault diagnosis method for an RV reducer under reciprocating working conditions based on FRF-ASSA-SVM, and belongs to the technical field of signal analysis and fault diagnosis. Background Art

[0002] RV reducer has the characteristics of large transmission ratio and high precision. It is the core component of industrial robots. Its health directly affects the stability and accuracy of robot operation. It is mainly used in the joints of industrial robots to ensure the precise and efficient operation of robots. With the widespread use of industrial robots in various industries, the status monitoring and fault diagnosis of robots have received more and more attention. As the core component of industrial robots, the RV reducer has become one of the hot issues in the research of its fault diagnosis.

[0003] Signal-based fault diagnosis and analysis is a common method for reducer fault diagnosis, and usually uses vibration signals, current signals, and acoustic emission signals for fault analysis. However, the actual working conditions of the reducer are often complex and changeable, and it is difficult to effectively diagnose the fault of the reducer based on traditional signals. The frequency response function reflects the response of the system to a given frequency. Systems with different faults respond differently to a given input frequency. It is more sensitive to system faults and can accurately reflect the specific faults of the system. At the same time, the frequency response function's ability to characterize faults is not affected by changes in working conditions. It is suitable for complex and changeable non-stationary working conditions and can accurately diagnose reducer faults. Summary of the invention

[0004] In order to solve the above-mentioned problems, the present invention provides an RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM, so as to diagnose the fault of the reducer more accurately.

[0005] The technical solution of the present invention is: a fault diagnosis method for an RV reducer under reciprocating working conditions based on FRF-ASSA-SVM, comprising the following steps:

[0006] S1: Collect the current signal and vibration signal of the RV reducer swing arm system in different fault states;

[0007] S2: Calculate the frequency response function of the RV reducer swing arm system using the current signal and the vibration signal;

[0008] S3: Perform spectrum analysis on the signal to determine the maximum frequency of the input current;

[0009] S4: Determine the analysis bandwidth of the frequency response function by the maximum current frequency;

[0010] S5: Perform ASSA noise reduction on the frequency response function in combination with spectrum analysis;

[0011] S6: Use the noise-reduced frequency response function and SVM to perform fault diagnosis on the RV reducer.

[0012] As a further solution of the present invention, in S1, different fault states include: normal, single tooth crack of sun gear, single tooth crack of planet gear, multiple teeth wear of planet gear, multiple teeth wear of sun gear and single tooth crack of planet gear, multiple teeth wear of sun gear and multiple teeth wear of planet gear.

[0013] As a further solution of the present invention, in S2, the frequency response function of the RV reducer swing arm system is obtained by the current signal and the vibration signal, and the solution process is as follows:

[0014] S2.1. Calculate the power spectrum density of the current signal:

[0015]

[0016] Among them, X i1 (f) is the Fourier transform of the input signal of segment i1, where L is the number of segments;

[0017] S2.2. Calculate the cross power spectrum density of the current signal and the vibration signal:

[0018]

[0019] Among them, Y i1 (f) is the Fourier transform of the input signal of the i1th segment, L is the number of segments, and * represents the complex conjugate;

[0020] S2.3. Calculate the frequency response function:

[0021]

[0022] As a further solution of the present invention, the specific steps of S3 are as follows:

[0023] S3.1. Perform fast Fourier transform on the current signal. The core formula is as follows:

[0024]

[0025] Where X(k) is the current frequency domain signal, x(t) is the current time domain signal, N is the total length of the current signal; k is the independent variable in the frequency domain, and t is time;

[0026] S3.2, the relationship between the maximum current frequency and speed is: Determine the maximum current frequency through the spectrum of the current signal;

[0027] Where N max The maximum speed of the motor, P is the number of pole pairs of the motor, and I is the reduction ratio.

[0028] As a further solution of the present invention, S4 includes:

[0029] The number of points in the frequency response function analysis band is calculated using the maximum current frequency determined in S3. Where M is the number of sampling points, F S is the sampling rate.

[0030] As a further solution of the present invention, the specific steps of S5 are as follows:

[0031] S5.1. According to the selection of the frequency band in S5, establish the track matrix. Assume that the signal after the frequency band selection is x = [x1, x2, ..., x n1 ], then the orbital matrix is ​​expressed as:

[0032]

[0033] Where m1 is the dimension of the matrix, l is the sliding window length, and 1<m1<l<n1, n1 represents the signal length used to construct the track matrix, which actually represents the number of points in the frequency response function analysis band;

[0034] S5.2, singular value decomposition;

[0035]

[0036] Where d is the number of non-zero singular values ​​of X, λ i1 is a diagonal matrix consisting of singular values, U i1 is the left singular vector matrix, V i1 is the right singular vector matrix;

[0037] S5.3, Reconstruction matrix;

[0038] According to the optimal matrix approximation theorem under the Frobenious norm, the first r singular values ​​are retained and the singular values ​​at other positions are set to zero. The inverse process of singular value decomposition is used to obtain X′, which is the optimal approximation of the orbital matrix X when the rank is r.

[0039] S5.4, diagonal averaging;

[0040]

[0041] Among them: α = max(1, r-m1+1); β = min(m1, r), r represents the number of singular values ​​to be retained.

[0042] As a further solution of the present invention, S6 includes:

[0043] S6.1. Use the frequency response function after noise reduction to build a data set, label the six faults respectively, and divide all the data into a training set and a data set;

[0044] S6.2. Use the training set to train the fault diagnosis model and input the test set data into the model to obtain the RV reducer fault diagnosis results.

[0045] The beneficial effects of the present invention are:

[0046] 1. The frequency response function of the present invention can accurately reflect the changes in the RV reducer system under reciprocating working conditions, thereby effectively diagnosing the specific faults of the RV reducer;

[0047] 2. The present invention solves the frequency response function of the system through the current signal and the vibration signal, selects the appropriate frequency band for analysis in combination with the spectrum analysis, de-noises the frequency response function through the ASSA algorithm, constructs a training data set using the de-noised frequency response function, realizes the fault diagnosis of the RV reducer in combination with the SVM support vector machine, and then trains the de-noised frequency response function based on the support vector machine algorithm to obtain the RV reducer fault diagnosis model, and effectively diagnoses various faults of the RV reducer;

[0048] 3. The present invention can accurately select useful information in the frequency response function and reduce its noise, greatly improving the fault characterization capability of the frequency response function, and can accurately diagnose the fault of the RV reducer under reciprocating conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a flow chart of the present invention;

[0050] Figure 2 This is the frequency response curve before noise reduction;

[0051] Figure 3 It is the frequency response curve after noise reduction;

[0052] Figure 4 is the test set diagnosis result graph;

[0053] Figure 5 It is the confusion matrix diagram of the test set. DETAILED DESCRIPTION

[0054] Example 1: Figure 1-Figure 5 As shown in FIG. 1 , the fault diagnosis method of the RV reducer under reciprocating working condition based on FRF-ASSA-SVM includes the following steps:

[0055] S1: Collect the current signal and vibration signal of the RV reducer swing arm system in different fault states; the current signal collects the current signal of the drive motor input end, and the vibration signal collects the vertical radial vibration signal of the RV reducer. All signals are collected during the reciprocating swing of the RV reducer swing arm. There are 6 fault states of the RV reducer, including: normal, single tooth crack of the sun gear, single tooth crack of the planetary gear, multiple teeth wear of the planetary gear, multiple teeth wear of the sun gear and single tooth crack of the planetary gear, multiple teeth wear of the sun gear and multiple teeth wear of the planetary gear; the signals are collected during the reciprocating swing of the RV reducer swing arm system, and the maximum output speed is 90° / s.

[0056] S2: Calculate the frequency response function of the RV reducer swing arm system using the current signal and the vibration signal;

[0057] In S2, the frequency response function of the RV reducer swing arm system is obtained through the current signal and the vibration signal, and the solution process is as follows:

[0058] S2.1. Calculate the power spectrum density of the current signal:

[0059]

[0060] Among them, X i1 (f) is the Fourier transform of the input signal of segment i1, where L is the number of segments;

[0061] S2.2. Calculate the cross power spectrum density of the current signal and the vibration signal:

[0062]

[0063] Among them, Y i1 (f) is the Fourier transform of the input signal of the i1th segment, L is the number of segments, and * represents the complex conjugate;

[0064] S2.3. Calculate the frequency response function:

[0065]

[0066] Under the test conditions, the calculated frequency response function curve is as follows Figure 2 As shown;

[0067] S3: Perform spectrum analysis on the signal to determine the maximum frequency of the input current;

[0068] As a further solution of the present invention, the specific steps of S3 are as follows:

[0069] S3.1. Perform fast Fourier transform on the current signal. The core formula is as follows:

[0070]

[0071] Where X(k) is the current frequency domain signal, x(t) is the current time domain signal, N is the total length of the current signal; k is the independent variable in the frequency domain, and t is time;

[0072] S3.2, the relationship between the maximum current frequency and speed is: Maximum motor speed under experimental conditions N max is 90° / s, the number of motor pole pairs P is 5, the reduction ratio I is 141, and the maximum current frequency is determined by the spectrum of the current signal

[0073] S4: Determine the analysis bandwidth of the frequency response function by the maximum current frequency;

[0074] As a further solution of the present invention, S4 includes:

[0075] The number of points in the frequency response function analysis band is calculated using the maximum current frequency determined in S3. Where M is the number of sampling points, which is 33800, and F S The sampling rate is 12800.

[0076] S5: Perform ASSA noise reduction on the frequency response function in combination with spectrum analysis;

[0077] As a further solution of the present invention, the specific steps of S5 are as follows:

[0078] S5.1. According to the selection of the frequency band in S5, establish the track matrix. Assume that the signal after the frequency band selection is x = [x1, x2, ..., x n1 ], then the orbital matrix is ​​expressed as:

[0079]

[0080] Where m1 is the dimension of the matrix, l is the sliding window length, and 1<m1<l<n1, n1 represents the signal length used to construct the track matrix, which actually represents the number of points in the frequency response function analysis band;

[0081] S5.2, singular value decomposition;

[0082]

[0083] Where d is the number of non-zero singular values ​​of X, which is 30, that is, the original sequence is decomposed into 30 orders, λ i1 is a diagonal matrix consisting of singular values, U i1 is the left singular vector matrix, V i1 is the right singular vector matrix;

[0084] S5.3, Reconstruction matrix;

[0085] According to the optimal matrix approximation theorem under the Frobenious norm, the first r singular values ​​are retained and the singular values ​​at other positions are set to zero. The inverse process of singular value decomposition is used to obtain X′, which is the optimal approximation of the orbital matrix X when the rank is r.

[0086] S5.4, diagonal averaging;

[0087]

[0088] Among them: α=max(1,r-m1+1); β=min(m1,r), r represents the number of singular values ​​I to be retained.

[0089] S6: Use the de-noised frequency response function and SVM to perform fault diagnosis on the RV reducer. The de-noised signal x′(r) is as follows: Figure 3 shown.

[0090] The dataset is constructed using the denoised data. The sample information contained in the dataset is shown in Table 1:

[0091] Table 1

[0092]

[0093] As a further solution of the present invention, S6 includes:

[0094] S6.1. Use the frequency response function after noise reduction to build a data set, label the six faults respectively, and divide all the data into a training set and a data set; the training set accounts for 75% and the test set accounts for 25%; input the data into the support vector machine for training,

[0095] S6.2. Input the data into the support vector machine for training, and input the test set data into the model to obtain the RV reducer fault diagnosis results.

[0096] The specific process of inputting data into the support vector machine for training is as follows:

[0097] (1) Establish optimization goals:

[0098]

[0099] Among them, y i is the sample category label; ω is the weight coefficient vector of the classification surface; b is the classification domain value; C is the penalty factor, ξ i is the slack variable, n is the number of samples, x i is the input sample, that is, the frequency response function after noise reduction.

[0100] (2) Establish the Lagrangian function:

[0101]

[0102] where α i , μ i is the Lagrange multiplier.

[0103] (3) For w, b, ξ i Taking partial derivatives respectively, we get:

[0104]

[0105] (4) Substitute the result into the Lagrangian function and solve the dual problem:

[0106]

[0107] (5) Introducing the Gaussian kernel function K(y i ,y j )=<Φ(y i ),Φ(y j )>, where <Φ(y i ),Φ(y j )>denotes Φ(y i ) and Φ(y j ) is the inner product of .

[0108] (6) Solve the dual decomposition problem

[0109]

[0110] (7) Solve the above convex optimization problem and obtain the Lagrangian operator The classification hyperplane curve of the support vector machine is obtained as:

[0111] Choose any satisfying Alpha * , calculate the offset get The corresponding vector y j is the support vector, and the decision function for classification is:

[0112]

[0113] Among them, y j represents the training sample label; b is the classification domain value; x j represents the input training sample; m represents the number of training samples; z i represents the Grangian operator of the i-th sample category, K(x i ,x j) represents the kernel function. f(x) represents the classification decision function of the fault diagnosis state, and sgn represents the sign function, whose value represents different fault states.

[0114] The prediction results and confusion matrix of the test set are as follows Figure 4 and Figure 5 As shown in the figure, it can be seen that the prediction accuracy of the test set is 97.4%.

[0115] The specific implementation modes of the present invention are described in detail above in conjunction with the accompanying drawings, but the present invention is not limited to the above implementation modes, and various changes can be made within the knowledge scope of ordinary technicians in this field without departing from the purpose of the present invention.

Claims

1. The fault diagnosis method of RV reducer under reciprocating working condition based on FRF-ASSA-SVM is characterized by: The following steps are involved: S1: Collect the current signal and vibration signal of the RV reducer swing arm system in different fault states; S2: Calculate the frequency response function of the RV reducer swing arm system using the current signal and the vibration signal; S3: Perform spectrum analysis on the signal to determine the maximum frequency of the input current; S4: Determine the analysis bandwidth of the frequency response function by the maximum current frequency; S5: Perform ASSA noise reduction on the frequency response function in combination with spectrum analysis; S6: Use the noise-reduced frequency response function and SVM to perform fault diagnosis on the RV reducer.

2. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 1 is characterized in that: In S1, different fault states include: normal, sun gear single tooth crack, planet gear single tooth crack, planet gear multiple teeth wear, sun gear multiple teeth wear and planet gear single tooth crack, sun gear multiple teeth wear and planet gear multiple teeth wear.

3. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 1 is characterized in that: In S2, the frequency response function of the RV reducer swing arm system is obtained through the current signal and the vibration signal, and the solution process is as follows: S2.

1. Calculate the power spectrum density of the current signal: Among them, X i1 (f) is the Fourier transform of the input signal of segment i1, where L is the number of segments; S2.

2. Calculate the cross power spectrum density of the current signal and the vibration signal: Among them, Y i1 (f) is the Fourier transform of the input signal of the i1th segment, L is the number of segments, and * represents the complex conjugate; S2.

3. Calculate the frequency response function:

4. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 1 is characterized in that: The specific steps of S3 are as follows: S3.

1. Perform fast Fourier transform on the current signal. The core formula is as follows: Where X(k) is the current frequency domain signal, x(t) is the current time domain signal, N is the total length of the current signal; k is the independent variable in the frequency domain, and t is time; S3.2, the relationship between the maximum current frequency and speed is: Determine the maximum current frequency through the spectrum of the current signal; Where N max The maximum speed of the motor, P is the number of pole pairs of the motor, and I is the reduction ratio.

5. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 4 is characterized in that: The S4 includes: The number of points in the frequency response function analysis band is calculated using the maximum current frequency determined in S3. Where M is the number of sampling points, F S is the sampling rate.

6. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 1 is characterized in that: The specific steps of S5 are as follows: S5.

1. According to the selection of the frequency band in S5, establish the track matrix. Assume that the signal after the frequency band selection is x = [x1, x2, ..., x n1 ], then the orbital matrix is ​​expressed as: Where m1 is the dimension of the matrix, l is the sliding window length, and 1<m1<l<n1, n1 represents the signal length used to construct the track matrix, which actually represents the number of points in the frequency response function analysis band; S5.2, singular value decomposition; Where d is the number of non-zero singular values ​​of X, λ i1 is a diagonal matrix consisting of singular values, U i1 is the left singular vector matrix, V i1 is the right singular vector matrix; S5.3, Reconstruction matrix; According to the optimal matrix approximation theorem under the Frobenious norm, the first r singular values ​​are retained and the singular values ​​at other positions are set to zero. X′ is obtained by the inverse process of singular value decomposition. X′ is the optimal approximation of the orbital matrix X when the rank is r. S5.4, diagonal averaging; Among them: α = max(1, r-m1+1); β = min(m1, r), r represents the number of singular values ​​to be retained.

7. The RV reducer fault diagnosis method under reciprocating conditions based on FRF-ASSA-SVM according to claim 1 is characterized in that: The S6 includes: S6.

1. Use the frequency response function after noise reduction to build a data set, label the six faults respectively, and divide all the data into a training set and a data set; S6.

2. Use the training set to train the fault diagnosis model and input the test set data into the model to obtain the RV reducer fault diagnosis results.

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