A fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine

Abstract

The present application relates to the technical field of rotating machinery fault diagnosis, and proposes a fault diagnosis method based on billiard intuitionistic fuzzy twin support tensor machine, which first converts the original monitoring signal into a time-frequency graph through Fourier synchronous compression transformation, and then reconstructs the time-frequency graph of the sensor array signal into a tensor sample, which embodies the time domain characteristics, frequency domain characteristics and spatial domain related information of the sensor array monitoring signal. By assigning intuitionistic fuzzy scores to different tensor samples, the influence of noise and outliers on the optimal hyperplane is reduced. At the same time, the core information in the sample is retained by using tensor Tucker decomposition. In addition, a billiard loss function is introduced to alleviate the noise sensitivity and resampling instability problems; 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.

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 primarily involves three stages: sensor signal acquisition, feature extraction and selection, and fault classification. Because rotating machinery operates in a highly variable environment, the collected sensor signals not only contain significant noise but also often exhibit nonlinear and nonstationary characteristics. Time-frequency analysis methods, however, utilize a designed joint time-frequency function to simultaneously describe the signal's energy density or intensity at different times and frequencies. This reveals both the signal's frequency components and its time-varying characteristics. 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. Fault data is difficult to collect, and most methods rely on sufficient data, resulting in limitations for small sample sizes. However, support vector machines, based on the principles of structural risk minimization and margin maximization, are not only capable of handling small sample sizes but also exhibit strong generalization performance, making them widely used in 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 characteristic vector input of the signal. This type of method is suitable for applications where there is only one state monitoring signal for rotating machinery, that is, directly using a certain state vector signal or extracting the characteristic 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. In this case, 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 the 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 cases, 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 the classifier of tensor space. Although the generalized non-convex tensor robust principal component analysis can perform fault diagnosis on the 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 intuitive 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 existing technology 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 fault diagnosis accuracy and computational efficiency, a fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine is proposed. It 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, including:

[0009] S1: Sensor signal acquisition: Sensors are arranged at different locations on the rotating machinery to form a sensor array. Multiple sensor signals are collected using a multi-channel data acquisition system to obtain sensor array monitoring signals under different fault conditions. 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 determining a time window; dividing the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; converting the divided sensor array monitoring signal into a time-frequency graph through Fourier synchronous compression transform; reconstructing the time-frequency graph 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 of the training set and the test set is [tensor sample, fault type label];

[0012] S4: Calculating the intuitionistic fuzzy score of the tensor sample: Calculating the membership function and non-membership function of each tensor sample in the training set in step S3; calculating the intuitionistic fuzzy score of each tensor sample based on the membership function and 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-supported 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 a kernel function 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 in 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 selection in step S2 is:

[0020] S21: Manually determine the time window L; divide the sensor array monitoring signal into a 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 image through Fourier synchronous compression transform; grayscale the time-frequency image to obtain I3 grayscale images; crop each grayscale image to a size of I1×I2, and perform pixel normalization on the cropped grayscale image 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×l2×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; and 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 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, in order to avoid the membership 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 sample 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 the 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; n=1,2,3 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 order, R3 represents the third-order core tensor The third-order order, t1 represents the third-order core tensor The first-order index, t2 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, The approximate tensor sample set 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 the positive sample 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; The approximate tensor sample set representing all tensor samples;

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

[0051]

[0052] Where u is a real number and τ is a constant greater than 0.

[0053] A3: The original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model is constructed by using 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 of 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 between one class of samples and 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] Where α, β and γ represent Lagrange multipliers;

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

[0066]

[0067] β T ξ2=0 (26)

[0068] Arranging formula (21)-formula (26) further yields:

[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, we can rewrite formula (29) 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] Where 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 j-th 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 to 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, F-score and G-mean evaluation 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 intuitionistic 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, the important core information in the tensor samples is retained. By introducing the pinball loss function, the noise sensitivity and resampling instability problems are alleviated. 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, ensuring the synchronization of signals collected by all sensors and avoiding data errors caused by timing asynchrony.

[0089] By converting the collected data into a time-frequency diagram using Fourier synchronous compression transform, the time and frequency domain features of the sensor monitoring signal can be effectively extracted. During compression and transmission, the system also exhibits excellent immunity to channel noise and interference. This ensures that the signal maintains high integrity and accuracy even in the presence of noise and interference. By reconstructing the time-frequency diagram into tensor samples, the spatial domain information of the sensor array monitoring signal can be effectively reflected. By assigning intuitive fuzzy scores to different tensor samples, the contributions of different tensor samples are highlighted, effectively reducing the impact of noise and outliers on the optimal hyperplane.

[0090] By performing a 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 maintains the main features of the data while maintaining the recognition accuracy of the judgment model and improving computational efficiency. By introducing the pinball loss function, the problems of noise sensitivity and resampling instability are alleviated. By considering all training data points, the pinball loss function makes the model more robust to noise, reducing the impact of small amounts 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, simplifying the model training process and improving computational efficiency. At the same time, the solution of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model is transformed into solving two relatively small quadratic programming problems, ultimately effectively improving the performance and computational efficiency of rotating machinery fault diagnosis. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

[0093] Figure 3 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 for fault type 2 at the first 1024 time points.

[0095] Figure 5 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 with reference to 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: Sensors are arranged at different locations on the rotating machinery to form a sensor array. A multi-channel data acquisition system is used 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 determining a time window; dividing the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; converting the divided sensor array monitoring signal into a time-frequency graph through Fourier synchronous compression transform; reconstructing the time-frequency graph 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 of the training set and the test set is [tensor sample, fault type label];

[0101] S4: Calculating the intuitionistic fuzzy score of the tensor sample: Calculating the membership function and non-membership function of each tensor sample in the training set in step S3; calculating the intuitionistic fuzzy score of each tensor sample based on the membership function and 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-supported 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 a kernel function 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 in 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: This example uses bearing vibration data collected under time-varying speed conditions from the University of Ottawa as experimental data. Each sampled data set contains two channels: sensor 1 is vibration data collected by an ICP accelerometer placed on the experimental bearing seat, and sensor 2 is shaft speed data collected by an incremental encoder. The signal sampling frequency is 20,000 Hz, and the sampling time is 10 seconds. This case verifies the effectiveness of the present invention through binary classification experiments for fault 1 (inner race fault ID-2, obtained when the operating speed decreases from 25.3 Hz to 15.1 Hz and then increases to 19.8 Hz, labeled +1) and fault 2 (outer race fault OD-2, obtained when the operating speed decreases from 25.2 Hz to 14.9 Hz and then increases to 19.5 Hz, labeled -1). Data from the first 133,120 sampling time points for faults 1 and 2 are selected, with a time window L set to 1024. To verify the noise immunity of the present invention, Gaussian white noise with a signal-to-noise ratio (SNR) of 1 is added to each sensor monitoring signal for faults 1 and 2.

[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 Use Fourier synchronous compression transform to convert each column in X into a time-frequency graph, crop it to 64×64 size, normalize the pixels to [0,1], and grayscale it 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) The first and second sensor monitoring signals are composed of 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. 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 of which 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 as follows: Figure 5 (a) and Figure 5 As shown in (b), we finally get 130 tensor samples of fault 2, 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: For training set samples Perform tensor Tucker decomposition to obtain In this embodiment, the 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 evaluation indicators are used: Accuracy, Precision, Recall, F-score, and G-mean:

[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 ​​obtained:

[0118] Table 1 Confusion matrix

[0119]

[0120] The above experiment was repeated 20 times. The Accuracy, Precision, Recall, F-score, G-mean and calculation time (Time) of the 20 experiments are shown in Table 2, and the confusion matrix is ​​shown in Table 3. The optimal parameter values ​​are 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, precision, recall, F-score, and G-mean across 20 repeated experiments in Table 2 were 96.42%, 97.59%, 95.23%, 96.38%, and 96.41%, respectively, demonstrating that the proposed method can accurately identify the inner race fault (ID-1) and outer race fault (OD-1). Furthermore, each evaluation metric achieved a small standard deviation of 1.89%, 2.21%, 2.52%, 1.91%, and 1.89%, respectively, demonstrating the good stability of the proposed method. The average computation time for the proposed method was 0.62 seconds, demonstrating a significant improvement in computational efficiency. As shown in Table 3, the proposed method achieved good prediction results for both positive samples (inner race fault samples) and negative samples (outer race fault samples) across 20 repeated experiments, further verifying that the proposed method can more accurately diagnose rotating machinery faults under these time-varying speed conditions.

[0126] This is mainly due to the fact that the present invention combines a rich set of sensor array signals for diagnosis, and the tensor samples constructed fully capture the time domain and frequency domain feature information of the sensor signals and the correlation between the sensor array signals. At the same time, the tensor-based model developed can avoid the problem of correlation information being destroyed due to the vectorization of the sensor array signals. By assigning different intuitive fuzzy scores to each tensor sample, the contribution of different samples is highlighted. At the same time, 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 correlation information to a great extent during the mapping process, ultimately significantly improving the accuracy of fault diagnosis. The model is also converted 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 should not be understood as limiting the patent scope of the present invention. It should be pointed out that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention, which all fall within the scope of protection of the present invention.

Claims

1. A fault diagnosis method based on pinball intuitionistic fuzzy twin support tensor machine, characterized by: include: S1: Sensor signal acquisition: Sensors are arranged at different locations on the rotating machinery to form a sensor array. Multiple sensor signals are collected using a multi-channel data acquisition system to obtain sensor array monitoring signals under different fault conditions. The sensor array monitoring signals include: acceleration signal data, speed signal data, temperature signal data, pressure signal data and current signal data; S2: Feature extraction and selection: manually determining a time window; dividing the sensor array monitoring signal according to the time window to obtain the divided sensor array monitoring signal; converting the divided sensor array monitoring signal into a time-frequency graph through Fourier synchronous compression transform; reconstructing the time-frequency graph 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 of the training set and the test set is [tensor sample, fault type label]; S4: Calculating the intuitionistic fuzzy score of the tensor sample: Calculating the membership function and non-membership function of each tensor sample in the training set in step S3; calculating the intuitionistic fuzzy score of each tensor sample based on the membership function and 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-supported 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 a kernel function 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 in 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 a 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 a 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 image through Fourier synchronous compression transform; grayscale the time-frequency image to obtain I3 grayscale images; crop each grayscale image to a size of I1×I2, and perform pixel normalization on the cropped grayscale image 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; and 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 the 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 the 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, in order to avoid the membership being 0; r + represents the positive class radius; r - Indicates the 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; 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 sample 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 a 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 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 order, R3 represents the third-order core tensor The third-order order, 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. The fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1 is characterized in that: The specific method for 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 techniques 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, The approximate tensor sample set 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 the positive sample 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; The approximate tensor sample set representing all tensor samples; A2: Constructing the pinball loss function L τ , expressed as: Where y is a real number and τ is a constant greater than 0. A3: The original optimization problem of the nonlinear pinball intuitionistic fuzzy twin support tensor machine model is constructed by using 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 of 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 the squares of the distances between one class of samples and 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. The fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1 is 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: Where α, β and γ represent Lagrange multipliers; B2: Calculate the partial derivative of the Lagrangian function (20) and set it to 0 to obtain the Karush Kuhn Tucker (KKT) condition: Arranging formula (21)-formula (26) further yields: Let α-γ=λ, Rewritten as: H T Hp+C T λ=0,i.e. p=-(H 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, we can rewrite formula (29) to obtain the quadratic programming problem: B4: Repeat steps B1-B3 to transform the original optimization problem (19) into the corresponding quadratic programming problem: Where 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. The fault diagnosis method based on the pinball intuitionistic fuzzy twin support tensor machine according to claim 1 is characterized in that: The decision function described in S7 can be expressed as: in, Represents the j-th 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 a pinball intuitionistic fuzzy twin support tensor machine according to claim 1, characterized in that: The performance evaluation method 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 to 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.

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