Fault diagnosis method based on marble intuitionistic fuzzy twin support tensor machine

Abstract

The invention relates to the technical field of rotating machinery fault diagnosis, and provides a marble intuitionistic fuzzy twin support tensor machine-based fault diagnosis method, which comprises the following steps of: firstly, converting an original monitoring signal into a time-frequency diagram through Fourier synchronous compression transformation, and reconstructing the time-frequency diagram of a sensor array signal into a tensor sample; time domain features, frequency domain features and related information in a spatial domain of sensor array monitoring signals are reflected. Intuitive fuzzy scores are distributed for different tensor samples, so that the influence of noise and abnormal values on the optimal hyperplane is reduced. And meanwhile, core information in the sample is reserved by utilizing tensor Tucker decomposition. In addition, a marble loss function is introduced to relieve the problems of noise sensitivity and resampling instability; by converting the solution of the tensor model into the solution of two relatively small quadratic programming problems, the performance and calculation efficiency of fault diagnosis of the rotating machinery are effectively improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of rotating machinery fault diagnosis, and in particular relates to a fault diagnosis method based on a pinball intuitionistic fuzzy twin support tensor machine. Background Art

[0002] Traditional rotating machinery fault diagnosis mainly includes three stages: sensor signal acquisition, feature extraction and selection, and fault classification. Fault diagnosis mainly includes three stages: sensor signal acquisition, feature extraction and selection, and fault classification. Since rotating machinery works in a changing environment, the collected sensor signals not only contain a lot of noise, but also often show nonlinear and non-stationary characteristics. The time-frequency analysis method can simultaneously describe the energy density or intensity of the signal at different times and frequencies through the designed time-frequency joint function, so it can reveal both the frequency component of the signal and the time-varying characteristics of the signal. After feature extraction, diagnostic methods such as extreme learning machines, fuzzy inference systems based on adaptive networks, graph convolutional networks, deep belief networks, and convolutional neural networks are used to distinguish faults. In fact, fault data is difficult to collect, but most methods rely on sufficient data, so there are certain limitations for small samples. However, support vector machines, based on the principle of structural risk minimization and the idea of ​​interval maximization, can not only handle small sample problems, but also have strong generalization performance, and have been widely used in the field of fault diagnosis.

[0003] Although the above fault diagnosis methods have been widely studied, they still have the following problems:

[0004] (1) For example, support vector machine models can only use the original vector signal or the feature vector input of the signal. This type of method is suitable for the case where there is only one state monitoring signal for rotating machinery, that is, directly using a certain state vector signal or extracting the feature vector of a certain state signal as the input of the shallow learning model for intelligent diagnosis. However, for complex rotating machinery systems, their state monitoring signals are often multi-source heterogeneous data such as vibration, sound pressure, speed and torque that are monitored simultaneously. At this time, feature tensors should be used to represent various state signals. Compared with the representation of feature vectors, the feature tensor representation of multi-source heterogeneous data can contain richer data structure information. Although the existing intelligent fault diagnosis methods based on shallow learning models can directly vectorize the feature tensors of multi-source state signals to solve the input problem of the model, the process of vectorizing feature tensors will not only generate high-dimensional vectors, resulting in increased computational complexity and overfitting problems, but also lose the original feature tensor data structure information and the coupling information between different state monitoring signals, thereby affecting the final intelligent fault diagnosis accuracy.

[0005] (2) Although the intelligent diagnosis method based on the deep belief network model can perform high-order tensor operations, the deep neural network method currently used for intelligent fault diagnosis of rotating machinery theoretically requires a large number of samples to train the network model. However, in actual engineering applications, it is difficult to obtain a large number of fault samples of rotating machinery and its key components. Although a deep support vector machine model currently used for intelligent fault diagnosis of rotating machinery can identify faults in small sample situations, it is essentially similar to the support vector machine and cannot directly process feature tensor data. On the other hand, by introducing the transfer learning method, although the requirement for the number of training samples of the deep learning model in the target domain can be reduced, in fact, in the source domain, the deep network model still requires a large number of samples to train the network to obtain the optimal hyperparameters. These limitations all affect the performance of the model in intelligent fault diagnosis, thereby reducing the accuracy of intelligent fault diagnosis of rotating machinery.

[0006] (3) For classifiers in tensor space. Although generalized non-convex tensor robust principal component analysis can perform fault diagnosis on reconstructed tensor samples, it still requires manual identification and is not intelligent. Although the fuzzy support tensor machine model, the pinball loss fuzzy support tensor machine, and the normalized pinball loss intuitionistic fuzzy support tensor machine can process tensor samples, the computational efficiency is reduced because two larger quadratic programming problems are solved based on one classification hyperplane. Although the twin support high-order tensor machine can improve computational efficiency by designing two non-parallel hyperplanes and converting them into solving two smaller quadratic programming problems, it is still sensitive to noise and does not have resampling stability. Summary of the invention

[0007] In view of the problems in the prior art that the correlation information of the sensor array signals is destroyed after the non-stationary monitoring signals collected by the sensor array of the rotating machinery are vectorized and processed, and the sensitivity of the diagnosis model to noise and the instability of resampling lead to low accuracy and computational efficiency of fault diagnosis, a fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine is proposed. The method effectively utilizes the rich sensor array signal information, fully mines the time domain and frequency domain feature information of the signal, retains the relevant information between the sensor array signals, solves the noise sensitivity problem, and improves the computational efficiency and recognition accuracy of the model.

[0008] A fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine, comprising:

[0009] S1: Sensor signal acquisition: Arrange sensors at different parts of the rotating machinery to form a sensor array, and use a multi-channel data acquisition system to collect multiple sensor signals to obtain sensor array monitoring signals under different fault states; the sensor array monitoring signals include: acceleration signal data, speed signal data, temperature signal data, pressure signal data and current signal data;

[0010] S2: Feature extraction and selection: manually determine the time window; divide the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; convert the divided sensor array monitoring signal into a time-frequency diagram through Fourier synchronous compression transformation; reconstruct the time-frequency diagram into a third-order tensor, i.e., a tensor sample;

[0011] S3: Constructing a data set: Repeat step S2 for the sensor array monitoring signals under different fault states to obtain tensor samples under different fault types, and divide the tensor samples into a training set and a test set; the data format in the training set and the test set is [tensor sample, fault type label];

[0012] S4: Calculating the intuitive fuzzy score of the tensor sample: calculating the membership function and the non-membership function of each tensor sample in the training set of step S3; calculating the intuitive fuzzy score of each tensor sample according to the membership function and the non-membership function;

[0013] S5: Tensor Tucker decomposition: Perform tensor Tucker decomposition on the tensor samples in the S3 training set to obtain approximate tensor samples of the tensor samples in the training set;

[0014] S6: Construct and solve the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin-based tensor machine model:

[0015] S61: Construct the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin supporting tensor machine model; the original optimization problem is established through two non-parallel hyperplanes, a positive high-dimensional feature matrix, a negative high-dimensional feature matrix, a pinball loss function and an intuitionistic fuzzy score of S4; the two non-parallel hyperplanes, the positive high-dimensional feature matrix, and the negative high-dimensional feature matrix are constructed through kernel functions and approximate tensor samples of the S5 training set;

[0016] S62: Converting the original optimization problem into a quadratic programming problem: Converting the original optimization problem of S61 into a dual problem through a Lagrangian function; converting the dual problem into two smaller quadratic programming problems;

[0017] S63: Obtaining an optimal solution to the original optimization problem described in S61 by solving the quadratic programming problem in S62;

[0018] S7: Construct a decision function and perform performance evaluation: Construct a decision function based on the optimal solution obtained in S63; the performance evaluation evaluates the performance of the decision function by calculating the accuracy, precision, recall rate, F-score and G-mean of fault judgment.

[0019] Preferably, the specific method of feature and selection in step S2 is:

[0020] S21: Manually determine the time window L; divide the sensor array monitoring signal into one sample every L time windows to obtain the divided sensor array monitoring signal; the sensor array monitoring signal of each sample in the divided sensor array monitoring signal is expressed as Among them, I3 represents the number of sensors;

[0021] S22: convert each sensor monitoring signal in X into a time-frequency graph by Fourier synchronous compression transform; grayscale the time-frequency graph to obtain I3 grayscale graphs; crop each grayscale graph to a size of I1×I2, and perform pixel normalization on the cropped grayscale graph to obtain a normalized I3 pixel matrix;

[0022] S23: Stack the I3 pixel matrices of S22 in a specific order to obtain a third-order tensor, i.e., a tensor sample, of size I1×I2×I3; the third-order tensor includes: the first order corresponds to the time domain information of the sensor array monitoring signal; the second order corresponds to the frequency domain signal of the sensor array monitoring signal; the third order corresponds to the spatial domain related information of the sensor array monitoring signal.

[0023] Preferably, the tensor samples described in step S3 include: positive tensor samples and negative tensor samples; the positive tensor samples are tensor samples whose fault type labels are fault type 1, and the labels of the positive tensor samples are re-labeled as +1; the negative tensor samples are tensor samples whose fault type labels are fault type 2, and the labels of the negative tensor samples are re-labeled as -1.

[0024] Preferably, the membership function and the non-membership function described in S4 are specifically:

[0025] For the i-th tensor sample Its membership function μ i The calculation formula is:

[0026]

[0027] Among them, h>0 is an adjustable parameter to avoid the membership degree being 0; r + represents the positive class radius; r - Indicates negative class radius; M + represents the positive class center; M -Represents the negative class center; m represents the total number of tensor samples; the first l tensor samples are positive class tensor samples, and the last ml are negative class tensor samples;

[0028] For the i-th tensor sample Non-membership function v i The calculation formula is:

[0029]

[0030]

[0031] Among them, s + Represents the maximum distance between the positive class tensor sample and the negative class center; s - Indicates the maximum distance between the negative class tensor samples and the positive class center.

[0032] Preferably, the specific calculation method of the intuitionistic fuzzy score is:

[0033]

[0034] Among them, s i Represents a tensor sample The corresponding intuitionistic fuzzy score.

[0035] Preferably, the specific method of tensor Tucker decomposition is:

[0036]

[0037] in, Represents a tensor sample An approximate tensor sample of , Represents the i-th tensor sample The core tensor of Represented in the third-order core tensor The element at position r1r2r3; Represents the i-th tensor sample The nth factor matrix of Represents the outer product of vectors, symbol × n represents n modular product, R1 represents the third-order core tensor The first order, R2 represents the third order core tensor The second-order rank, R3 represents the third-order core tensor The third-order rank, r1 represents the third-order core tensor The first-order index, r2 represents the third-order core tensor The second-order index, r3 represents the third-order core tensor The third-order index.

[0038] Preferably, the specific method for constructing the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model in step S61 is:

[0039] A1: Defined by kernel techniques and The kernel function between pass Will Map to m-dimensional space;

[0040] The first hyperplane is defined as:

[0041]

[0042] The second hyperplane is defined as:

[0043]

[0044] in, represents the kernel function, A set of approximate tensor samples representing all tensor samples; b1 represents the weight and unknown deviation of the first hyperplane; b2 represents the weight and unknown deviation of the second hyperplane;

[0045] The high-dimensional feature matrix of positive samples is defined as:

[0046]

[0047] The high-dimensional feature matrix of negative samples is defined as:

[0048]

[0049] in, represents the kernel function, A set of approximate tensor samples representing positive class tensor samples; A set of approximate tensor samples representing negative class tensor samples; A set of approximate tensor samples representing all tensor samples;

[0050] A2: Constructing the pinball loss function L τ , expressed as:

[0051]

[0052] Among them, u is represented by a real number, and τ is represented by a constant greater than 0;

[0053] A3: The original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model is constructed through the two non-parallel hyperplanes, positive high-dimensional feature matrix, negative high-dimensional feature matrix described in A1, the pinball loss function and intuitionistic fuzzy score described in A2; the original optimization problem is expressed as:

[0054]

[0055] Among them, c1 represents the penalty factor of the first hyperplane; c2 represents the penalty factor of the second hyperplane; e1 and e2 represent column vectors whose elements are all 1, represents the transpose of the intuitionistic fuzzy score array for the positive class tensor samples, The transpose of the intuitionistic fuzzy score array representing the negative class tensor samples;

[0056] A4: Introduce slack variables ξ1 and ξ2 to minimize the sum of the squares of the distances from one class of samples to its corresponding hyperplane, and ensure that the other class of samples is at least 1 distance away from the hyperplane. After introducing slack variables, formulas (16) and (17) can be rewritten as:

[0057]

[0058] stξ2≥0

[0059]

[0060] stξ1≥0

[0061] Preferably, S62: the specific method of converting the original optimization problem into a quadratic programming problem is:

[0062] B1: First, construct the Lagrangian function of the original optimization problem (18) as follows:

[0063]

[0064] Among them, α, β and γ represent Lagrange multipliers;

[0065] B2: Calculate the partial derivative of the Lagrangian function (20) and set the partial derivative to 0, and obtain the Karush Kuhn Tucker (KKT) condition:

[0066]

[0067] β T ξ2=0 (26)

[0068] By reorganizing formula (21) to formula (26), we can further obtain:

[0069]

[0070] Let α-γ=λ, Formula (27) can be rewritten as:

[0071] H T Hp+G T λ=0,iep=-(H T H) -1 G T λ (28)

[0072] The final dual problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model (18) is obtained as shown in (29):

[0073]

[0074] B3: Convert the dual problem obtained in B2 into the corresponding quadratic programming problem:

[0075] Since β ≥ 0, the first condition is equivalent to By γ=α-λ, formula (29) is rewritten to obtain the quadratic programming problem:

[0076]

[0077] B4: Repeat steps B1-B3 to transform the original optimization problem (19) into the corresponding quadratic programming problem:

[0078]

[0079] Among them, θ and μ represent Lagrange multipliers, and τ represents a constant greater than 0;

[0080] At the same time, the corresponding solution vector can be obtained:

[0081]

[0082] Preferably, the decision function described in S7 can be expressed as:

[0083]

[0084] in, Represents the jth tensor sample Y in the test set j The approximate tensor sample obtained by Tucker decomposition (10) is Represents an approximate tensor sample and The high-dimensional feature vector z is calculated by the kernel function K(·) i and b i Represents the optimal solutions to two smaller quadratic programming problems.

[0085] Preferably, the method for performing performance evaluation in step S7 is: perform tensor Tucker decomposition on each tensor sample in the S3 test set to obtain an approximate tensor sample of the tensor sample in the test set, substitute the approximate tensor sample into the S7 decision function, and obtain the predicted label corresponding to the tensor sample in the test set; compare the obtained predicted label with the fault type label, calculate the accuracy, precision, recall rate, F-score and G-mean of the fault judgment to evaluate the performance of the decision function.

[0086] Beneficial effects:

[0087] The present invention proposes a fault diagnosis method based on a pinball intuitive fuzzy twin support tensor machine. First, the original monitoring signal is converted into a time-frequency diagram through Fourier synchronous compression transform, which can effectively extract the time domain and frequency domain features of the sensor monitoring signal, and the time-frequency diagram of the sensor array signal is reconstructed into a tensor sample, which reflects the relevant information of the sensor array monitoring signal in the spatial domain. Secondly, by assigning intuitive fuzzy scores to different tensor samples, the contribution of different samples is highlighted, and the influence of noise and outliers on the optimal hyperplane is effectively reduced. In addition, by performing tensor Tucker decomposition on the samples, important core information in the tensor samples is retained. By introducing the pinball loss function, the noise sensitivity and resampling instability problems are alleviated. And the invented method can directly process tensor samples composed of multiple sensor monitoring signals. Since vectorization processing is avoided, the relevant information of the sensor array monitoring signal is greatly retained, and the accuracy of fault diagnosis is significantly improved. By converting the solution of the tensor model into the solution of two relatively small quadratic programming problems, the performance and computational efficiency of rotating machinery fault diagnosis are effectively improved.

[0088] By arranging multiple sensors at different parts of the rotating machinery and using a multi-channel data acquisition system, it is possible to collect signals from multiple sensors, thereby ensuring the synchronization of signals collected by all sensors and avoiding data errors caused by timing asynchrony.

[0089] By using Fourier synchronous compression transform to convert the collected data into time-frequency diagrams, the time domain and frequency domain features of the sensor monitoring signal can be effectively extracted, and in the process of compression and transmission, it has good anti-interference performance against channel noise and interference. It ensures that the signal can maintain high integrity and accuracy in the presence of noise and interference; by reconstructing the time-frequency diagram into tensor samples, it can effectively reflect the relevant information of the sensor array monitoring signal in the spatial domain; by assigning intuitive fuzzy scores to different tensor samples, the contribution of different tensor samples is highlighted, effectively reducing the impact of noise and outliers on the optimal hyperplane.

[0090] By performing tensor Tucker decomposition on the sample tensor, the tensor can be decomposed into a core tensor and multiple factor matrices, thereby achieving an approximate representation of the data. This representation method maintains the recognition accuracy of the judgment model and improves computational efficiency while maintaining the main features of the data. By introducing the pinball loss function, the noise sensitivity and resampling instability problems are alleviated. The pinball loss function makes the model more robust to noise by considering all training data points, reducing the impact of a small amount of noise data on the diagnostic model, thereby improving the stability and accuracy of the model. At the same time, the pinball loss function does not require additional preprocessing time to generate weights, which simplifies the training process of the model and improves computational efficiency. At the same time, the solution of the nonlinear pinball intuitive fuzzy twin support tensor machine model is transformed into solving two relatively small quadratic programming problems, which effectively improves the performance and computational efficiency of rotating machinery fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 This is a flow chart of a fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine.

[0092] Figure 2 The monitoring signals of the two sensors of fault type 1 at the previous 1024 time points.

[0093] Figure 3 It is the time-frequency grayscale image corresponding to the monitoring signals of the two sensors at the first 1024 time points of fault type 1.

[0094] Figure 4 The monitoring signals of the two sensors of fault type 2 at the previous 1024 time points.

[0095] Figure 5 It is the time-frequency grayscale image corresponding to the monitoring signals of the two sensors at the first 1024 time points of fault type 2. DETAILED DESCRIPTION

[0096] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0097] like Figure 1 As shown, the specific steps of a fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine are as follows;

[0098] S1: Sensor signal acquisition: Arrange sensors at different parts of the rotating machinery to form a sensor array. Use a multi-channel data acquisition system to collect multiple sensor signals to obtain sensor array monitoring signals under different fault conditions; the monitoring signals of the sensor array include: acceleration signal data, speed signal data, temperature signal data, pressure signal data and current signal data;

[0099] S2: Feature extraction and selection: manually determine the time window; divide the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; convert the divided sensor array monitoring signal into a time-frequency diagram through Fourier synchronous compression transformation; reconstruct the time-frequency diagram into a third-order tensor, i.e., a tensor sample;

[0100] S3: Constructing a data set: Repeat step S2 for the sensor array monitoring signals under different fault states to obtain tensor samples under different fault types, and divide the tensor samples into a training set and a test set; the data format in the training set and the test set is [tensor sample, fault type label];

[0101] S4: Calculating the intuitive fuzzy score of the tensor sample: calculating the membership function and the non-membership function of each tensor sample in the training set of step S3; calculating the intuitive fuzzy score of each tensor sample according to the membership function and the non-membership function;

[0102] S5: Tensor Tucker decomposition: Perform tensor Tucker decomposition on the tensor samples in the S3 training set to obtain approximate tensor samples of the tensor samples in the training set;

[0103] S6: Construct and solve the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin-based tensor machine model:

[0104] S61: Construct the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin supporting tensor machine model; the original optimization problem is established through two non-parallel hyperplanes, a positive high-dimensional feature matrix, a negative high-dimensional feature matrix, a pinball loss function and an intuitionistic fuzzy score of S4; the two non-parallel hyperplanes, the positive high-dimensional feature matrix, and the negative high-dimensional feature matrix are constructed through kernel functions and approximate tensor samples of the S5 training set;

[0105] S62: Converting the original optimization problem into a quadratic programming problem: Converting the original optimization problem of S61 into a dual problem through a Lagrangian function; converting the dual problem into two smaller quadratic programming problems;

[0106] S63: Obtaining an optimal solution to the original optimization problem described in S61 by solving the quadratic programming problem in S62;

[0107] S7: Construct a decision function and perform performance evaluation: Construct a decision function based on the optimal solution obtained in S63; the performance evaluation evaluates the performance of the decision function by calculating the accuracy, precision, recall rate, F-score and G-mean of fault judgment.

[0108] The specific implementation process is:

[0109] A rotating machinery fault diagnosis method based on nonlinear intuitionistic fuzzy twin support tensor machine, the method comprising the following steps:

[0110] Step 1: In this example, the bearing vibration data collected by the University of Ottawa under time-varying speed conditions are used as experimental data. The specific data can be downloaded from http: / / dx.doi.org / 10.17632 / v43hmbwxpm.1. Each sampling data set contains two channels: sensor 1 is the vibration data collected by the ICP accelerometer placed on the experimental bearing seat, and sensor 2 is the shaft speed data collected by the incremental encoder. The sampling frequency of the signal is 20000 Hz, and the sampling time is 10s. This case verifies the effectiveness of the present invention through a binary classification experiment of fault 1 (the inner ring fault ID-2 obtained by the operating speed decreasing from 25.3Hz to 15.1Hz and then increasing to 19.8Hz, the label is +1) and fault 2 (the outer ring fault OD-2 obtained by the operating speed decreasing from 25.2Hz to 14.9Hz and then increasing to 19.5Hz, the label is -1). The data of the first 133120 sampling time points of fault 1 and fault 2 are selected, and the time window L is set to 1024. In order to verify the anti-noise performance of the present invention, Gaussian white noise with a signal-to-noise ratio (SNR) value equal to 1 is added to each sensor monitoring signal of Fault 1 and Fault 2 respectively.

[0111] Step 2: Perform sample division on the first sensor monitoring signal and the second sensor monitoring signal of fault 1 to obtain 130 samples of fault 1, where the sensor array monitoring signal of each sample is expressed as Each column in X is converted into a time-frequency graph using Fourier synchronous compression transform, which is cropped to 64×64 size, pixels are normalized to [0,1], and grayscaled to obtain the corresponding grayscale image. For example, for the first sample of fault 1 (the first 1024 time points), Figure 2 (a) and Figure 2 (b) is composed of the first and second sensor monitoring signals, and the time-frequency grayscale images corresponding to the first and second sensor monitoring signals are shown in 3(a) and Figure 3 (b) shows that the two sensor monitoring signals are converted into two grayscale images of size 64×64, and the pixel matrices corresponding to these grayscale images are stacked along the direction of the forward slice, and the sample X is reconstructed into a third-order tensor sample of size 64×64×2. A total of 130 tensor samples of fault 1 are obtained, 65 samples are randomly selected for training, and the remaining 65 samples are used for testing.

[0112] Step 3: Repeat step 2 for fault 2. For example, for the first sample of fault 2 (the first 1024 time points), Figure 4 (a) and Figure 4(b) shows the first and second sensor monitoring signals. The time-frequency grayscale images corresponding to the first and second sensor monitoring signals are shown in Figure 2. Figure 5 (a) and Figure 5 As shown in (b), 130 tensor samples of fault 2 are finally obtained, from which 65 samples are randomly selected for training and the remaining 65 samples are used for testing.

[0113] Step 4: The 65 training samples of fault 1 and the 65 training samples of fault 2 obtained in steps 2 and 3 are combined into a training set. The membership and non-membership of each training set sample are calculated by formula (1) and formula (6), and the intuitive fuzzy score of the training set sample is obtained by formula (9):

[0114] Step 5: Samples of the training set Perform tensor Tucker decomposition to obtain In this embodiment, a Gaussian kernel function is used: Using formula (13) and formula (14), we can get and Combined with the intuitive fuzzy score obtained in step 4 Substitute them into the original optimization problem (18) and (19) of the nonlinear intuitionistic fuzzy twin support tensor machine. Among them, the parameter c1 = c2, and c1, c2, q are all in [2 -7 ,2 -6 ,2 -5 ,2 -4 ,2 -3 ,2 -2 ,2 -1 ,2 0 ,2 1 ,2 2 ,2 3 ,2 4 ,2 5 ,2 6 ,2 7 ] range, and the parameter τ ranges from [0.1, 0.2, 0.3, ..., 1]. The grid search method is used to determine the optimal parameter value. The solution vector of model (18) is obtained by formula (28): The solution vector of model (19) is obtained by formula (32):

[0115] Step 6: 130 test samples in the test set Perform tensor Tucker decomposition to obtain For each j=1,...,130, calculate By decision function To comprehensively evaluate the diagnostic performance of the invented method, the following accuracy, precision, recall, F-score and G-mean are used as evaluation indicators:

[0116]

[0117] Among them, TP represents the number of positive predictions that are actually positive, FN represents the number of negative predictions that are actually positive, FP represents the number of positive predictions that are actually negative, and TN represents the number of negative predictions that are actually negative. The following confusion matrix is ​​further obtained:

[0118] Table 1 Confusion matrix

[0119]

[0120] The above experiment was repeated 20 times, and the Accuracy, Precision, Recall, F-score, G-mean and calculation time (Time) of the 20 experiments were shown in Table 2, and the confusion matrix was shown in Table 3, where the optimal parameter values ​​were c1=1, q=8, and τ=0.1.

[0121] Table 2 Experimental results of 20 repeated experiments

[0122] Accuracy Accuracy Recall F-score G-mean Time (seconds) 1 99.23％ 98.48％ 100.00％ 99.24％ 99.23％ 0.68 2 96.15％ 96.88％ 95.38％ 96.12％ 96.15％ 0.62 3 99.23％ 100.00％ 98.46％ 99.22％ 99.23％ 0.63 4 96.15％ 100.00％ 92.31％ 96.00％ 96.08％ 0.64 5 96.15％ 98.39％ 93.85％ 96.06％ 96.13％ 0.63 6 97.69％ 98.44％ 96.92％ 97.67％ 97.69％ 0.62 7 96.92％ 100.00％ 93.85％ 96.83％ 96.87％ 0.62 8 96.15％ 95.45％ 96.92％ 96.18％ 96.15％ 0.62 9 96.92％ 96.92％ 96.92％ 96.92％ 96.92％ 0.63 10 96.92％ 95.52％ 98.46％ 96.97％ 96.91％ 0.62 11 97.69％ 98.44％ 96.92％ 97.67％ 97.69％ 0.62 12 96.92％ 100.00％ 93.85％ 96.83％ 96.87％ 0.63 13 99.23％ 100.00％ 98.46％ 99.22％ 99.23％ 0.62 14 93.85％ 96.72％ 90.77％ 93.65％ 93.80％ 0.62 15 92.31％ 92.31％ 92.31％ 92.31％ 92.31％ 0.61 16 96.15％ 98.39％ 93.85％ 96.06％ 96.13％ 0.62 17 93.85％ 95.24％ 92.31％ 93.75％ 93.83％ 0.62 18 93.08％ 93.75％ 92.31％ 93.02％ 93.07％ 0.62 19 97.69％ 100.00％ 95.38％ 97.64％ 97.67％ 0.62 20 96.15％ 96.88％ 95.38％ 96.12％ 96.15％ 0.62 average value 96.42％ 97.59％ 95.23％ 96.38％ 96.41％ 0.62 Standard Deviation 1.89％ 2.21％ 2.52％ 1.91％ 1.89％ 0.01％

[0123] Table 3 Confusion matrix of 20 repeated experiments

[0124]

[0125] The average accuracy, average precision, average recall, average F-score and average G-mean of the 20 repeated experiments in Table 2 are 96.42%, 97.59%, 95.23%, 96.38% and 96.41% respectively, indicating that the invented method can accurately identify the inner ring fault (ID-1) and the outer ring fault (OD-1). And each evaluation index has a small standard deviation of 1.89%, 2.21%, 2.52%, 1.91% and 1.89% respectively, indicating that the invented method has good stability. The average calculation time of the invented method is 0.62 seconds, indicating that the calculation efficiency has been significantly improved. It can be seen from Table 3 that the method of the present invention has achieved good prediction effects for both positive samples (inner ring fault samples) and negative samples (outer ring fault samples) in 20 repeated experiments, further verifying that the method of the present invention can more accurately diagnose rotating machinery faults under such time-varying speed conditions.

[0126] This is mainly attributed to the fact that the present invention combines rich sensor array signals for diagnosis, and the constructed tensor samples fully capture the time domain and frequency domain feature information of the sensor signals and the related information between the sensor array signals. At the same time, the developed tensor-based model can avoid the problem of related information being destroyed due to the vectorization of sensor array signals; and by assigning different intuitive fuzzy scores to each tensor sample, the contribution of different samples is highlighted, and the pinball loss function is introduced to improve the robustness of the model to noise. On the other hand, by performing Tucker decomposition on the tensor samples, the kernel function can retain the core related information to a great extent during the mapping process, and finally significantly improve the accuracy of fault diagnosis; and the model is transformed into solving two relatively small quadratic programming problems, which improves the computational efficiency of the model.

[0127] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the patent scope of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine, characterized in that: include: S1: Sensor signal acquisition: Arrange sensors at different parts of the rotating machinery to form a sensor array. Use a multi-channel data acquisition system to collect multiple sensor signals to obtain sensor array monitoring signals under different fault conditions; The sensor array monitoring signals include: acceleration signal data, rotation speed signal data, temperature signal data, pressure signal data and current signal data; S2: Feature extraction and selection: manually determine the time window; divide the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; convert the divided sensor array monitoring signal into a time-frequency diagram through Fourier synchronous compression transformation; reconstruct the time-frequency diagram into a third-order tensor, i.e., a tensor sample; S3: Constructing a data set: Repeat step S2 for the sensor array monitoring signals under different fault states to obtain tensor samples under different fault types, and divide the tensor samples into a training set and a test set; the data format in the training set and the test set is [tensor sample, fault type label]; S4: Calculating the intuitive fuzzy score of the tensor sample: calculating the membership function and the non-membership function of each tensor sample in the training set of step S3; calculating the intuitive fuzzy score of each tensor sample according to the membership function and the non-membership function; S5: Tensor Tucker decomposition: Perform tensor Tucker decomposition on the tensor samples in the S3 training set to obtain approximate tensor samples of the tensor samples in the training set; S6: Construct and solve the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin-based tensor machine model: S61: Construct the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin supporting tensor machine model; the original optimization problem is established through two non-parallel hyperplanes, a positive high-dimensional feature matrix, a negative high-dimensional feature matrix, a pinball loss function and an intuitionistic fuzzy score of S4; the two non-parallel hyperplanes, the positive high-dimensional feature matrix, and the negative high-dimensional feature matrix are constructed through kernel functions and approximate tensor samples of the S5 training set; S62: Converting the original optimization problem into a quadratic programming problem: Converting the original optimization problem of S61 into a dual problem through a Lagrangian function; converting the dual problem into two smaller quadratic programming problems; S63: Obtaining an optimal solution to the original optimization problem described in S61 by solving the quadratic programming problem in S62; S7: Construct a decision function and perform performance evaluation: Construct a decision function based on the optimal solution obtained in S63; the performance evaluation evaluates the performance of the decision function by calculating the accuracy, precision, recall rate, F-score and G-mean of fault judgment.

2. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The specific method of feature selection in step S2 is: S21: Manually determine the time window L; divide the sensor array monitoring signal into one sample every L time windows to obtain the divided sensor array monitoring signal; the sensor array monitoring signal of each sample in the divided sensor array monitoring signal is expressed as Among them, I3 represents the number of sensors; S22: convert each sensor monitoring signal in X into a time-frequency graph by Fourier synchronous compression transform; grayscale the time-frequency graph to obtain I3 grayscale graphs; crop each grayscale graph to a size of I1×I2, and perform pixel normalization on the cropped grayscale graph to obtain a normalized I3 pixel matrix; S23: Stack the I3 pixel matrices of S22 in a specific order to obtain a third-order tensor, i.e., a tensor sample, of size I1×I2×I3; the third-order tensor includes: the first order corresponds to the time domain information of the sensor array monitoring signal; the second order corresponds to the frequency domain signal of the sensor array monitoring signal; the third order corresponds to the spatial domain related information of the sensor array monitoring signal.

3. Based on the fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine described in claim 1, the tensor samples described in step S3 include: positive tensor samples and negative tensor samples; the positive tensor samples are tensor samples with a fault type label of fault type 1, and the labels of the positive tensor samples are re-labeled as +1; the negative tensor samples are tensor samples with a fault type label of fault type 2, and the labels of the negative tensor samples are re-labeled as -1.

4. A fault diagnosis method based on a pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The membership function and non-membership function described in S4 are specifically: For the i-th tensor sample Its membership function μ i The calculation formula is: Among them, h>0 is an adjustable parameter to avoid the membership degree being 0; r + represents the positive class radius; r - Indicates negative class radius; M + represents the positive class center; M - represents the negative class center; m represents the total number of tensor samples; the first k tensor samples are positive class tensor samples, and the last ml are negative class tensor samples; For the i-th tensor sample Non-membership function v i The calculation formula is: Among them, s + Represents the maximum distance between the positive class tensor sample and the negative class center; s - Indicates the maximum distance between the negative class tensor samples and the positive class center.

5. A fault diagnosis method based on a pinball intuitionistic fuzzy twin support tensor machine according to claim 1 or 4, characterized in that: The specific calculation method of the intuitionistic fuzzy score is: Among them, s i Represents a tensor sample The corresponding intuitionistic fuzzy score.

6. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The specific method of tensor Tucker decomposition is: in, Represents a tensor sample An approximate tensor sample of , Represents the i-th tensor sample The core tensor of Represented in the third-order core tensor The element at position r1r2r3; Represents the i-th tensor sample The nth factor matrix of ; the symbol ° represents the outer product of the vector, and the symbol × n represents n modular product, R1 represents the third-order core tensor The first order, R2 represents the third order core tensor The second-order rank, R3 represents the third-order core tensor The third-order rank, r1 represents the third-order core tensor The first-order index, r2 represents the third-order core tensor The second-order index, r3 represents the third-order core tensor The third-order index.

7. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The specific method of constructing the original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model described in step S61 is: A1: Defined by kernel technique and The kernel function between pass Will Map to m-dimensional space; The first hyperplane is defined as: The second hyperplane is defined as: in, represents the kernel function, A set of approximate tensor samples representing all tensor samples; b1 represents the weight and unknown deviation of the first hyperplane; b2 represents the weight and unknown deviation of the second hyperplane; The high-dimensional feature matrix of positive samples is defined as: The high-dimensional feature matrix of negative samples is defined as: in, represents the kernel function, A set of approximate tensor samples representing positive class tensor samples; A set of approximate tensor samples representing negative class tensor samples; A set of approximate tensor samples representing all tensor samples; A2: Constructing the pinball loss function L τ , expressed as: Among them, u is represented by a real number, and τ is represented by a constant greater than 0; A3: The original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model is constructed through the two non-parallel hyperplanes, positive high-dimensional feature matrix, negative high-dimensional feature matrix described in A1, the pinball loss function and intuitionistic fuzzy score described in A2; the original optimization problem is expressed as: Among them, c1 represents the penalty factor of the first hyperplane; c2 represents the penalty factor of the second hyperplane; e1 and e2 represent column vectors whose elements are all 1, represents the transpose of the intuitionistic fuzzy score array for the positive class tensor samples, The transpose of the intuitionistic fuzzy score array representing the negative class tensor samples; A4: Introduce slack variables ξ1 and ξ2 to minimize the sum of squares of the distances from one class of samples to its corresponding hyperplane, and ensure that the other class of samples is at least 1 distance away from the hyperplane. After introducing slack variables, formulas (16) and (17) can be rewritten as:

8. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: S62: The specific method of converting the original optimization problem into a quadratic programming problem is: B1: First, construct the Lagrangian function of the original optimization problem (18) as follows: Among them, α, β and γ represent Lagrange multipliers; B2: Calculate the partial derivative of the Lagrangian function (20) and set the partial derivative to 0, and obtain the Karush Kuhn Tucker (KKT) condition: b T ξ2=0 (26) By reorganizing formula (21) to formula (26), we can further obtain: Let α-γ=λ, Formula (27) can be rewritten as: H T Hp+G T λ=0,i.e.p=-(G T H) -1 G T λ (28) The final dual problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model (18) is obtained as shown in (29): B3: Convert the dual problem obtained in B2 into the corresponding quadratic programming problem: Since β ≥ 0, the first condition is equivalent to By γ=α-λ, formula (29) is rewritten to obtain the quadratic programming problem: B4: Repeat steps B1-B3 to transform the original optimization problem (19) into the corresponding quadratic programming problem: Among them, θ and μ represent Lagrange multipliers, and τ represents a constant greater than 0; At the same time, the corresponding solution vector can be obtained:

9. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The decision function described in S7 can be expressed as: in, Represents the jth tensor sample Y in the test set j The approximate tensor sample obtained by Tucker decomposition (10) is Represents an approximate tensor sample and The high-dimensional feature vector z is calculated by the kernel function K(·) i and b i Represents the optimal solutions to two smaller quadratic programming problems.

10. A fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The method for performance evaluation in step S7 is as follows: perform tensor Tucker decomposition on each tensor sample in the S3 test set to obtain an approximate tensor sample of the tensor sample in the test set, substitute the approximate tensor sample into the S7 decision function, and obtain the prediction label corresponding to the tensor sample in the test set; compare the obtained prediction label with the fault type label, calculate the accuracy, precision, recall rate of the fault judgment, and evaluate the performance of the decision function by F-score and G-mean.

Images