A motor fault detection method based on single-classification tensor hyperdisk

Abstract

The present invention discloses a motor fault detection method based on a single-classification tensor hyperdisk, comprising the following steps: obtaining multi-source signals of the motor in different health states and establishing a sample set of original signals; extracting feature tensors from the multi-source signals based on wavelet packet decomposition; training a single-classification tensor hyperdisk model with the feature tensor of the motor in a normal state to obtain its decision function; testing the sample to be detected using the trained model, and finally outputting the detection result. Comparative analysis of motor fault detection results shows that the single-classification tensor hyperdisk proposed by the present invention is superior to the current mainstream detection method.

Description

Technical Field

[0001] The invention belongs to the field of motor fault detection, and in particular is a novel motor fault detection method based on single classification tensor hyperdisk (OCTHD). Background Art

[0002] Drive motors play a vital role in the machinery manufacturing, transportation, electric power and other industries. The real-time operating status of drive motors will directly affect the safety of their corresponding industrial equipment systems. At the same time, fault detection and diagnosis of drive motors is a key technology for the health management and intelligent operation and maintenance of their equipment. Therefore, it has important engineering practical value for fault detection of motors and their different components.

[0003] In actual engineering fault detection, the health status data of the monitored object is often collected, while there are few fault samples in real-time and historical data. The vector space model can only handle the detection problem of the vector space. However, the feature tensor extracted from the multi-source signal in the tensor space of the drive motor cannot be directly input into the above model for fault detection. Compared with the single-classification vector model, although the single-classification tensor model can use the feature tensor extracted from the multi-source signal to detect the health status of the motor, the model itself still has the following problems. The above model can be geometrically regarded as a tensor convex hull with strict geometric edges. On the one hand, the tensor convex hull is an underestimate of the sample set. On the other hand, due to its strict geometric boundaries, when the number of training samples under normal conditions is small, the model obtained by training is too compact, which will lead to the misjudgment of healthy samples in the test samples. This means that the false alarm rate in motor fault detection will increase. Summary of the invention

[0004] The purpose of the present invention is to provide a motor fault detection method based on single-classification tensor superdisk in order to solve the above problems.

[0005] To achieve the above object, the technical solution adopted by the present invention is: a new motor fault detection method based on single-classification tensor hyperdisk, comprising the following steps:

[0006] Step 1: Obtain multi-source signals of the motor under different health conditions and establish a sample set of original signals;

[0007] Step 2: Extract feature tensors from multi-source signals based on wavelet packet decomposition;

[0008] Step 3: Train the single-classification tensor superdisc model with the feature tensor only in the normal state of the motor to obtain its decision function;

[0009] Step 4: Use the trained single-class tensor hyperdisk to detect the sample to be detected;

[0010] Step 5: Output the detection results.

[0011] Furthermore, in step 2, the steps of extracting the feature tensor of the multi-source signal based on wavelet packet decomposition are as follows:

[0012] For each sample the 7 signals are decomposed as follows:

[0013] X=[x 1 ,x 2 ,…,x M ] T ∈R M×N

[0014] Among them, X is the sample, each signal x i There are N = 2048 points, M is the number of signals;

[0015] By wavelet packet transform, x i Decomposed into P components with different frequency bands as follows:

[0016] p=2 J

[0017] Where, J is the decomposition level;

[0018] For extracting the features of time domain statistical parameters and frequency domain statistical parameters, the statistical parameters are calculated from each component respectively, and there are H = 22 statistical parameters in total. The time domain statistical parameters are: mean value, root mean square, square root amplitude, average amplitude, maximum peak value, standard deviation, skewness, kurtosis, peak factor, margin index, shape factor, which is the pulse factor;

[0019] The frequency domain statistical parameters are: spectrum amplitude mean, spectrum amplitude standard deviation, spectrum gravity frequency, amplitude spectrum kurtosis, spectrum root mean square frequency, spectrum root 4 / 2 moment ratio, spectrum standard deviation frequency, spectrum frequency skewness, and spectrum frequency kurtosis;

[0020] The extracted statistical features are expressed as a tensor according to the frequency-feature parameter-sensor third-order tensor:

[0021]

[0022] Among them, F is the third-order feature tensor transformed from the feature of multi-source signal, and the components with different frequency bands, statistical characteristics and different sensor channels are used as the modes of the third-order tensor, among which I 1 =P,I 2 =H,I 3 =M;

[0023] Furthermore, the calculation of the decision function in step 3 specifically includes the following steps:

[0024] For a tensor sample set consisting of l tensor samples Define the tensor superdisk geometry boundaries:

[0025]

[0026] Among them, α i is a tensor sample The combination coefficient of

[0027] For the nearest neighbor point between the origin and the tensor hyperdisk, it is transformed into the minimum modulus optimization problem shown in the following formula:

[0028]

[0029] For the center S and radius r in the constraints of solving the optimization problem, it is converted into the following quadratic programming problem:

[0030]

[0031] For the optimization problem shown in the above formula, the non-negative Lagrange multiplier β is introduced i ,i=1,2,…,l construct the corresponding Lagrangian function:

[0032]

[0033] According to the KKT condition, the partial derivatives of r and S in the following formula are obtained and set to zero respectively:

[0034]

[0035]

[0036] The duality of the quadratic programming optimization problem is expressed as:

[0037]

[0038] For the calculation problem of tensor inner product in the dual equation, CP decomposition is used to decompose the original tensor, and the tensor inner product can be expressed as:

[0039]

[0040] The optimization problem is transformed into:

[0041]

[0042] For the above optimization problem, the optimal solution is obtained by using the standard algorithm: The center S and radius r can be expressed as:

[0043]

[0044]

[0045] Replace the obtained center S and radius r with the optimization problem of quadratic programming, and the optimization problem is transformed into:

[0046]

[0047] The constraints in the optimization problem are further expanded to:

[0048]

[0049] For the tensor inner product calculation problem in the above formula, the tensor inner product formula is used instead, and the optimization problem is further transformed into:

[0050]

[0051] Using the optimal solution of the optimization problem, let the optimal solution be The corresponding nearest neighbor point is Calculate the weight tensor of the optimal hyperplane and deviation b * :

[0052]

[0053]

[0054] The decision function of a single-class tensor hyperdisk can be expressed as:

[0055]

[0056] The detection output of a single-class tensor hyperdisk is expressed as:

[0057]

[0058] The present invention proposes a novel motor fault detection scheme based on a single-classification tensor hyperdisk. The feature tensor extracted from the motor multi-source signal by wavelet packet decomposition is used as the input of the single-classification tensor hyperdisk to realize motor fault detection and obtain better detection results. The present invention provides a new idea for motor fault detection. Geometrically, the boundary of the tensor hyperdisk is looser than the tensor convex hull, so its estimation of the tensor sample set is also more accurate. The present invention only needs to solve the corresponding optimal hyperplane once by introducing tensor decomposition, and the calculation is simpler. In fault detection applications, the single-classification tensor hyperdisk is more loose in estimating small sample sets, thereby reducing the false alarm rate during the test process. Therefore, the single-classification tensor hyperdisk is more suitable for small sample fault detection applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] Figure 1 It is a flow chart of motor fault detection in the present invention.

[0060] Figure 2 are the detection accuracy and detection geometric mean (Gmean) error bars of different methods. DETAILED DESCRIPTION

[0061] In order to enable the present invention to extract feature tensors from multi-source signals, the feature tensor is trained with a single-classification tensor superdisc model only under the normal state of the motor to obtain its decision function, and the purpose of using the trained single-classification tensor superdisc to detect the sample to be detected is achieved. The present invention adopts the following embodiments.

[0062] like Figure 1 ,The steps of a motor fault detection method based on single-classification tensor hyperdisk are as follows:

[0063] Step 1: Obtain multi-source signals of the motor under different health conditions and establish a sample set of original signals;

[0064] Step 2: Extract feature tensors from multi-source signals based on wavelet packet decomposition;

[0065] For each sample the 7 signals are decomposed as follows:

[0066] X=[x 1 ,x 2 ,…,x M ] T ∈R M×N

[0067] Among them, X is the sample, each signal x i There are N = 2048 points, M is the number of signals;

[0068] By wavelet packet transform, x i Decomposed into P components with different frequency bands as follows:

[0069] p=2 J

[0070] Where, J is the decomposition level;

[0071] For extracting the features of time domain statistical parameters and frequency domain statistical parameters, H = 21 statistical parameters are calculated from each component respectively. The time domain statistical parameters are: mean value, root mean square, square root amplitude, average amplitude, maximum peak value, standard deviation, skewness, kurtosis, peak factor, margin index, shape factor, pulse factor;

[0072] The frequency domain statistical parameters are: spectrum amplitude mean, spectrum amplitude standard deviation, spectrum gravity frequency, amplitude spectrum kurtosis, spectrum root mean square frequency, spectrum root 4 / 2 moment ratio, spectrum standard deviation frequency, spectrum frequency skewness, and spectrum frequency kurtosis;

[0073] The extracted statistical features are expressed as a tensor according to the frequency-feature parameter-sensor third-order tensor:

[0074]

[0075] Among them, F is the third-order feature tensor transformed from the feature of multi-source signal, and the components with different frequency bands, statistical characteristics and different sensor channels are used as the modes of the third-order tensor, among which I 1 =P,I 2 =H,I 3 =M;

[0076] Step 3: Train the single-classification tensor superdisc model with the feature tensor only in the normal state of the motor to obtain its decision function;

[0077] For a tensor sample set consisting of l tensor samples Define the tensor superdisk geometry boundaries:

[0078]

[0079] Among them, α i is a tensor sample The combination coefficient of

[0080] For the nearest neighbor point between the origin and the tensor hyperdisk, it is transformed into the minimum modulus optimization problem shown in the following formula:

[0081]

[0082] For the center S and radius r in the constraints of solving the optimization problem, it is converted into the following quadratic programming problem:

[0083]

[0084] For the optimization problem shown in the above formula, the non-negative Lagrange multiplier β is introduced i ,i=1,2,…,l construct the corresponding Lagrangian function:

[0085]

[0086] According to the KKT condition, the partial derivatives of r and S in the following formula are obtained and set to zero respectively:

[0087]

[0088]

[0089] The duality of the quadratic programming optimization problem is expressed as:

[0090]

[0091] For the calculation problem of tensor inner product in the dual equation, CP decomposition is used to decompose the original tensor, and the tensor inner product can be expressed as:

[0092]

[0093] The optimization problem is transformed into:

[0094]

[0095] For the above optimization problem, the optimal solution is obtained by using the standard algorithm: The center S and radius r can be expressed as:

[0096]

[0097]

[0098] Replace the obtained center S and radius r with the optimization problem of quadratic programming, and the optimization problem is transformed into:

[0099]

[0100] The constraints in the optimization problem are further expanded to:

[0101]

[0102] For the tensor inner product calculation problem in the above formula, the tensor inner product formula is used instead, and the optimization problem is further transformed into:

[0103]

[0104] Using the optimal solution of the optimization problem, let the optimal solution be The corresponding nearest neighbor point is Calculate the weight tensor of the optimal hyperplane and deviation b * :

[0105]

[0106]

[0107] The decision function of a single-class tensor hyperdisk can be expressed as:

[0108]

[0109] Step 4: Use the trained single-class tensor hyperdisk to detect the sample to be detected;

[0110]

[0111] Step 5: Output the detection results.

[0112] The present invention is verified by the following experiments.

[0113] In order to verify the effectiveness of the method proposed in the present invention, the working conditions and health status of the test samples were pre-set during the experiment, and five different conditions of the motor under test were established for analysis, including the normal state of the motor, three bearing fault conditions (inner ring fault, outer ring fault, outer ring combined fault) and magnet crack fault condition.

[0114] In order to obtain multi-source signals of the motor under test, a total of 7 signals were collected, including 3 vibration signals, 1 sound pressure signal and 3 current signals. The three-axis vibration accelerometer (x, y, z) was installed on the motor housing, and the microphone was placed 30 cm away from the end cover of the test motor. In the experiment, the speed of the motor under test was 2800RPM and the sampling frequency was 48000Hz. In the following analysis, the samples under different conditions included one sound pressure signal, three acceleration vibration signals and three current signals, and each signal of each sample had 2048 continuous data points.

[0115] In order to verify the effectiveness of the proposed method OCTHD in motor fault detection, the tensor model OCSTM and the vector models OCCCH and OCSVM are used for comparative analysis. In the comparative analysis of this experiment, different numbers of normal state samples (n = 20, 30, 40, 50) are randomly selected as training samples, and then 50 samples are randomly selected from each state (normal state, bearing inner ring fault, outer ring fault, magnet fault, and bearing inner and outer ring composite failure) as samples to be tested. This means that there are a total of 250 test samples, including 50 normal state samples and 200 fault samples. The samples are randomly selected 10 times, and the final average results of these 10 times are reported.

[0116] In the application of motor fault detection, the overall accuracy of detection and the recognition rate of normal samples and faulty samples are of great concern. Therefore, the two indicators of Accuracy (overall accuracy) and Gmean (geometric mean) are first used to quantitatively compare the detection effects of different methods. The definitions of these two indicators are:

[0117]

[0118]

[0119] Where TP is the number of normal samples detected as normal samples, FN is the number of normal samples detected as faulty samples, TN is the number of faulty samples detected as faulty samples, and FP is the number of faulty samples detected as normal samples.

[0120] Table 1 shows the detection accuracy of different methods

[0121]

[0122] Table 1

[0123] Table 2 shows the detection Gmean of different methods

[0124]

[0125] Table 2

[0126] The experiment uses single-class support tensor machine (OCSTM) and vector model single-class convex hull (OCCCH) and single-class support vector machine (OCSVM) to compare and analyze with the method proposed in the present invention. Comparing the detection accuracy and Gmean of the four methods in Table 1 and Table 2 for different normal condition training samples, it can be found that the detection results of all methods increase with the increase of training samples. At the same time, the detection results of the two tensor models (OCTCH and OCSTM) are significantly better than the other two vector models OCCCH and OCSVM. In particular, the method proposed in the present invention has an accuracy of 96.88%, 97.84%, 98.56%, and 98.76%, and a Gmean of 93.04%, 95.57%, 97.27%, and 98.47%. This is because OCTCH and OCSTM can directly use the feature tensor obtained from multi-source signals to process motor fault detection, while the vector models OCCCH and OCSVM need to vectorize the feature tensor, thereby destroying the intrinsic structural information of the feature tensor. Meanwhile, compared with OCSTM, the proposed OCTHD is estimated more loosely from the geometric estimation, thus achieving higher accuracy and Gmean under different training samples.

[0127] In order to better analyze the overall detection results of different methods, Figure 2 The detection accuracy and Gmean error bars of different methods are shown. Comparing the accuracy and standard deviation of Gmean of different methods in Tables 1 and 2, for 10 random experiments, the proposed OCTHD method almost achieves the best standard deviation, indicating that the fluctuation of the detection results is small, further indicating that its algorithm model has the best stability.

[0128] In engineering applications of fault detection, in addition to the overall detection results, it is often necessary to pay attention to the detection accuracy of normal samples and fault samples respectively. The detection accuracy of normal samples can also be called recall, which is defined as:

[0129]

[0130] Table 3 shows the detection recall rate of different methods:

[0131]

[0132] Table 3

[0133] The results in Table 3 show that the recall rates of the tensor detection models OCTHD and OCSTM are significantly higher than those of the vector detection models OCCCH and OCSVM. However, in the OCTHD and OCSTM tensor models, when the number of training samples is n=10, 20, the detection recall rate of the proposed OCTHD is 10% to 20% higher than that of the existing OCSTM. This also shows that the recognition rate of the OCTHD method for normal samples in the detection samples is higher than that of the OCSTM method. This is because when the number of training samples is small (normal state), the boundary of the geometric model obtained by OCSTM training is too compact, resulting in misjudgment of normal state samples, that is, identifying them as faulty samples.

Claims

1. A motor fault detection method based on a single-class tensor hyperdisk, characterized in that, it includes the following steps: Step 1: Obtain multi-source signals of the motor in different health states and establish an original signal sample set; Step 2: Extract feature tensors from the multi-source signals based on wavelet packet decomposition; Step 3: Train the single-class tensor hyperdisk model with the feature tensors in the normal state of the motor to obtain its decision function. The calculation process includes the following steps: For a tensor sample set consisting of l tensor samples Define the tensor superdisk geometry boundaries: Among them, α i is a tensor sample The combination coefficient For the nearest neighbor point between the origin and the tensor hyperdisk, it is transformed into the minimum modulus optimization problem shown in the following formula: For the center S and radius r in the constraint conditions for solving the optimization problem, and it is transformed into the following quadratic programming problem: For the optimization problem shown in the above formula, the non-negative Lagrange multiplier β is introduced i ,i=1,2,…,l construct the corresponding Lagrangian function: According to the KKT conditions, obtain the partial derivatives of r and S in the following formula and set them to zero respectively: The duality of the quadratic programming optimization problem is expressed as: For the tensor inner product calculation problem in the dual equality, use CP decomposition to decompose the original tensor, and the tensor inner product can be expressed as: The optimization problem is transformed into: For the above optimization problem, the optimal solution is obtained by using the standard algorithm: The center S and radius r can be expressed as: Replace the obtained center S and radius r with the optimization problem of quadratic programming, and the optimization problem is transformed into: Further expand the constraint conditions in the optimization problem to: For the tensor inner product calculation problem in the above formula, use the tensor inner product formula to replace it, and the optimization problem is further transformed into: Using the optimal solution of the optimization problem, let the optimal solution be The corresponding nearest neighbor point is Calculate the weight tensor of the optimal hyperplane and deviation b * : The decision function of the single-class tensor hyperdisk can be expressed as: The detection output result of the single-class tensor hyperdisk is expressed as: Step 4: Use the trained single-class tensor hyperdisk to detect the samples to be detected; Step 5: Output the detection result.

2. The motor fault detection method based on a single-class tensor hyperdisk according to claim 1, characterized in that, in the said Step 2, the steps of extracting the feature tensors of the multi-source signals based on wavelet packet decomposition are as follows: For each sample, decompose 7 signals as follows: X=[x 1 ,x 2 ,…,x M ] T ∈R M×N Among them, X is the sample, each signal x i There are N = 2048 points, M is the number of signals; By wavelet packet transform, x i Decomposed into P components with different frequency bands as follows: p＝2 J where J is the decomposition level; For extracting the feature of time-domain statistical parameters and frequency-domain statistical parameters, calculate them from each component respectively. There are a total of H = 21 statistical parameters. The time-domain statistical parameters are: mean value, root mean square, square root amplitude, average amplitude, maximum peak value, standard deviation, skewness, kurtosis, peak factor, margin index, shape factor, impulse factor; The frequency-domain statistical parameters are: spectral amplitude mean value, spectral amplitude standard deviation, spectral gravity frequency, amplitude spectrum kurtosis, spectral root mean square frequency, spectral root 4 / 2 moment ratio, spectral standard deviation frequency, spectral frequency skewness, spectral frequency kurtosis; Perform tensor representation on the extracted statistical features in a three-order tensor of frequency - feature parameter - sensor: Among them, F is the third-order feature tensor transformed from the feature of multi-source signal, and the components with different frequency bands, statistical characteristics and different sensor channels are used as the modes of the third-order tensor, among which I 1 =P,I 2 =H,I 3 =M.

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