A bearing fault diagnosis method based on width incremental learning

Abstract

This invention discloses a bearing fault diagnosis method based on width incremental learning, comprising: acquiring the original time-domain bearing data required for a width-learning fault classification model; preprocessing the original time-domain bearing data and dividing it into new and old datasets; inputting the old dataset into the width-learning fault classification model for training; simultaneously training an SVDD anomaly detection model on the old dataset; secondly, using SVDD anomaly detection to test whether the new dataset is an anomalous type of data; finally, performing width incremental learning (sample increment or class increment) based on the anomaly detection results to achieve model update. This invention utilizes SVDD for preliminary anomaly detection on new data; simultaneously, based on the anomaly detection results, width learning is stacked to achieve the effect of sample increment or class increment of the model, satisfying the model's high real-time performance and high accuracy on new data.

Description

Technical Field

[0001] This invention relates to the field of bearing testing technology, and in particular to a bearing fault diagnosis method based on width incremental learning. Background Technology

[0002] Bearings play a crucial role in modern machinery, being widely used in various rotating machines such as fans, generators, and machine tools. A bearing failure can severely impact the normal operation of these machines, directly affecting their safety and reliability. Therefore, research on bearing fault diagnosis and timely identification of fault types has become a hot research topic.

[0003] To adapt to the intelligent development of mechanical equipment and the characteristics of big data, and to effectively tap the enormous potential value of monitoring data, data-driven intelligent fault diagnosis technology has received increasing attention and research. This technology establishes fault diagnosis models based on a large amount of historical data, automatically extracts fault information hidden in the monitoring data of operating equipment, and completes intelligent identification of equipment health status, achieving more efficient proactive predictive maintenance.

[0004] Width learning combines the advantages of stochastic vector function chain networks and feedforward neural networks, featuring simple and fast model training and low computational resource requirements, thus meeting the requirements of rapid and accurate diagnosis of bearing fault types in practical applications. However, traditional width learning is generally developed based on a one-time learning approach, making it difficult to handle the problem of new fault samples and fault modes appearing in the data stream. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings and improvement needs of the existing technology as described above, and to propose a bearing fault diagnosis method based on width incremental learning. The aim is to use SVDD to perform preliminary anomaly detection on new data; at the same time, based on the anomaly detection results, width learning is stacked to achieve the effect of sample increment or class increment of the model, so as to meet the high real-time performance and high accuracy of the model on new data.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A bearing fault diagnosis method based on width increment learning includes:

[0008] Obtain the original time-domain data of the bearings required for the width-learning fault classification model;

[0009] The original time-domain data of the bearing is preprocessed and divided into an old dataset D1 and a new dataset, wherein the new dataset includes a new dataset D2 and a new dataset D3.

[0010] A width-learning fault classification model was built and trained using an old dataset to obtain an initial width-learning fault classification model. The fault accuracy of the initial width-learning fault classification model was then tested using a new dataset.

[0011] The SVDD model was trained using the old dataset to obtain the initial SVDD anomaly detection model;

[0012] The SVDD anomaly detection model is tested using a new dataset to determine whether the data anomaly rate reaches the anomaly detection threshold. If it is lower than the anomaly detection threshold, wide-sample incremental learning is used; if it is higher than the anomaly detection threshold, wide-class incremental learning is used.

[0013] A width-learning fault classification model based on incremental learning is used to diagnose faults in bearings based on real-time data, and the fault accuracy is obtained.

[0014] Furthermore, the original time-domain data of the bearings is preprocessed and divided into old and new datasets, specifically as follows:

[0015] After performing DC removal, envelope analysis, and downsampling on the original bearing time-domain data, a dataset with a sampling frequency of 800Hz is generated.

[0016] The 800Hz dataset is divided into old and new datasets. The old dataset D1 contains multiple fault types, while the new dataset D2, which is the new sample incremental dataset, contains all fault types belonging to the old dataset. The new dataset D3, which is the new class incremental dataset, contains only one fault type that does not belong to the old dataset.

[0017] Furthermore, a width-learning fault classification model was built and trained using an old dataset to obtain an initial width-learning model. The fault accuracy of the initial width-learning fault classification model was then tested using a new dataset. Specifically:

[0018] The initial width learning fault classification model consists of a feature layer, an enhancement layer, and an output layer;

[0019] Using the data from the old dataset as input to the width-learning fault classification model, we obtain mapping features and augmentation features. Then, based on the mapping features and augmentation features, we calculate the output layer. Combining this with the label Y1 from the old dataset D1, we have:

[0020] W=(λI+AA T ) -1 A T Y1

[0021] Wherein, the feature matrix A = [Z|H], W is the weight connecting the feature layer and the enhancement layer to the output layer, and Z and H represent the network's mapping features and enhancement features, respectively. After calculating W, the model training is complete;

[0022] Performing the same operation on D2 = {X2, Y2} and D3 = {X3, Y3} yields feature matrices A2 and A3, and further, predictive labels Y2′ and Y3′ are obtained:

[0023] Y2′=A2W

[0024] Y3′=A3W

[0025] By comparing Y2′ and Y′3 with Y2 and Y3, the fault accuracy of the new dataset D2 and the new dataset D3 can be obtained.

[0026] Furthermore, the process of training the SVDD model using the old dataset to obtain the initial SVDD anomaly detection model is as follows:

[0027] If we construct a hypersphere using the SVDD model that can accommodate all training samples in a minimum volume, then the hypersphere is represented by its center c and radius R.

[0028] The training process specifically involves solving the boundary of the old dataset to obtain the boundary R;

[0029]

[0030] Where, X = {x i Let {i = 1, 2, ..., I} represent the old dataset. i K represents the Lagrange multiplier, and K(·,·) represents the kernel function.

[0031] Furthermore, it also includes

[0032] For samples x in the new dataset D2 and the new dataset D3 new Perform anomaly detection:

[0033]

[0034] If ||x new -a|| 2 ≤R 2 If the new data is positive, it is accepted; otherwise, the new data is considered an outlier.

[0035] Furthermore, if the anomaly rate is below the anomaly detection threshold, wide-sample incremental learning is used; if the anomaly rate is above the anomaly detection threshold, wide-sample-class incremental learning is used, specifically as follows:

[0036] The aforementioned width-based incremental learning involves incrementing the samples in the new dataset D2 = {X2, Y2}.

[0037]

[0038] In the formula,

[0039] UT =A2(A) + ,S T =A2-U T A

[0040]

[0041] At this point, the sample increment model update is complete;

[0042] The aforementioned width-class incremental learning involves performing class increments on the new dataset D3 = {X3, Y3}.

[0043]

[0044] In the formula,

[0045] U = A + A3,S=A3-AU

[0046]

[0047] W t =A + [Y|Φ]=[W|Φ]

[0048] Where Φ is a zero matrix, A + It is the pseudo-inverse transform of input feature A.

[0049] At this point, the incremental model update is complete.

[0050] Furthermore, the number of initial mapping feature nodes and augmentation nodes in the fault classification model based on width learning is adjusted according to the accuracy of the fault classification model on the old dataset.

[0051] Furthermore, the number of nodes generated by the initial mapping feature k is 20, the number of nodes generated by the mapping feature n is 200, and the number of nodes generated by the enhanced feature m is 200.

[0052] Furthermore, we set the regularization parameters of the SVDD model, the corresponding statistical features for two-dimensional visualization, and the anomaly detection threshold.

[0053] Furthermore, a width-learning fault classification model based on incremental learning is used to diagnose faults in bearings based on real-time data, yielding the fault accuracy rate, specifically:

[0054] Acquire real-time vibration signal data of the bearing;

[0055] The SVDD anomaly detection model is input to determine whether it is an outlier. If it is an outlier, the width learning fault classification model is incremented and the incremented width learning fault classification model is used for fault diagnosis.

[0056] Otherwise, a width-learning fault classification model can be used directly for fault diagnosis.

[0057] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0058] (1) The present invention adopts the original data preprocessing operation of DC removal + envelope analysis + downsampling, which can easily remove the influence of additional signal noise and has good feature mining ability for the fault characteristics of bearings with frequent load and speed changes.

[0059] (2) The diagnostic model based on width incremental learning in this invention can effectively handle the problem of new fault samples and fault modes appearing in the data stream. At the same time, width incremental learning for sample increments only needs to store the old model when updating the model, without storing the old data; width incremental learning for class increments only needs to store the label information of the old model and the old data, which greatly reduces the pressure on computer data storage, saves costs, and has practical value. Attached Figure Description

[0060] Figure 1 This is a schematic diagram of the overall process of an embodiment of the method of the present invention.

[0061] Figure 2 This is the dataset distribution used in the method of this invention.

[0062] Figures 3(a)-3(b) This is a network structure diagram of the width learning and width incremental learning methods of the present invention.

[0063] Figures 4(a)-4(c) These are schematic diagrams illustrating the implementation of SVDD anomaly detection using the method of this invention. Detailed Implementation

[0064] The present invention will be further described in detail below with reference to the embodiments, but the implementation of the present invention is not limited thereto.

[0065] Example

[0066] like Figure 1 As shown, a bearing fault diagnosis method based on width incremental learning includes the following:

[0067] To obtain the raw time-domain bearing data required for the width-learning fault classification model,

[0068] This embodiment uses a publicly available laboratory dataset as the source of the raw data, specifically the raw data from the Case Western Reserve University bearing dataset. The dataset must contain bearing vibration data with a complete range of fault types and sufficient data volume, with complete and correct labels and a balanced amount of data across various health states.

[0069] like Figure 2As shown, this embodiment uses vibration signals from a 7mil damaged bearing under four load conditions (0, 1, 2, 3hp) at the motor drive end. The bearing health statuses are: no fault, inner ring fault, outer ring fault, and rolling element fault. The sampling frequency is 12000Hz.

[0070] The original time-domain data of the bearing is preprocessed and divided into an old dataset D1 and a new dataset, wherein the new dataset includes a new dataset D2 and a new dataset D3.

[0071] Specifically:

[0072] DC removal is performed on all raw time-domain data to extract useful AC information from the bearing signals;

[0073] Envelope analysis is performed on the time series obtained after DC operation to achieve noise reduction and obtain the enveloped time domain signal.

[0074] The enveloped time-domain signal is downsampled. The signal is uniformly reduced to a sampling frequency of 800Hz to facilitate rapid model training.

[0075] The 800Hz signal bearing dataset was divided into three parts: the old dataset D1 = {X1, Y1}, the new sample increment dataset D2 = {X2, Y2}, and the new class increment dataset D3 = {X3, Y3}. Dataset D1 contains sufficient data with a large number of labels (fault classifications); D2 contains sufficient data with labels belonging to the D1 class; and D3 contains sufficient data with fault data whose labels do not belong to the D1 class.

[0076] As shown in Figures 3(a) and 3(b), a width learning fault classification model is built, the number of initial mapping feature nodes and augmentation nodes is set, and the model is trained using an old dataset to obtain an initial width learning fault classification model. The fault accuracy of the initial width learning fault classification model is tested using a new dataset.

[0077] The width learning fault classification model consists of a feature layer, an enhancement layer, and an output layer.

[0078] Specifically:

[0079] Construct an auto-encoder-based feature layer Z. Multiple time-domain sequences from the fault dataset D1 are used as input X = {x} to this feature extraction network. i Let i = 1, 2, ..., I}. Assuming that each feature node window of the width learning network has n mapped features, the feature expression of the i-th mapping is as shown in equation (1):

[0080]

[0081] Where: weight and deviation Randomly generated and optimized using a sparse autoencoder. It is usually a linear transformation.

[0082] definition m = 1, 2, ..., k is the number of nodes generated for each mapping feature. The final mapping feature is represented as follows: The mapping feature Z is connected to the enhancement layer through a nonlinear transformation to form the enhancement feature. Assuming that the enhancement layer m of the width learning network has an enhancement node, the expression of the j-th enhancement feature is shown in equation (2):

[0083]

[0084] In the formula: the activation function ξ = relu(x), and Randomly generated.

[0085] The enhancement features of the enhancement layer are represented as follows The mapping feature Z and the enhancement feature H are input together into the output layer of the wide learning network. Given that the label of the input data X is Y, the relationship between the mapping feature Z, the enhancement feature H and the label Y is shown in equation (3):

[0086] Y=[Z∣H]W (3)

[0087] In the formula: W is the weight connecting the feature layer and the enhancement layer to the output layer. The calculation of W is shown in equation (4):

[0088] W = [Z | H] + Y (4)

[0089] In the formula: Let the characteristic matrix A = [Z | H], then W = A + Y, A + Let A represent the pseudo-inverse matrix.

[0090] The pseudoinverse is a least-squares estimator of a linear equation. Its goal is to solve for the output weights W while minimizing the training error. In particular, when the feature matrix A is not a full-rank matrix, A cannot be solved directly. + Therefore, the ridge regression algorithm is introduced, and equation (5) is used to solve for W.

[0091]

[0092] In equation (5): σ1>0, σ2>0, u, v represent norm regularization. The optimization problem of equation (5) is set as L2 norm regularization by σ1=σ2=u=v=2.

[0093] Equation (5) represents a regularization function that is convex and has good generalization performance. Here, λ is a further constraint on the weights. Theoretically, if λ = 0, equation (5) becomes a least-squares problem; if λ → ∞, the solution to equation (5) is strictly constrained and tends towards 0. Therefore, λ is usually set to 0. Taking the derivative of equation (5) and setting it to 0, we get:

[0094] W=(λI+AA T ) -1 A T Y (6)

[0095] In equation (6): I represents the identity matrix. The process of obtaining W is the training process of the model (including incremental and non-incremental). At this point, the model training is completed.

[0096] Finally, the same operation is performed on D2 = {X2,Y2} and D3 = {X3,Y3} to obtain feature matrices A2 and A3. The predicted labels Y2′ and Y3′ are then calculated, and the fault accuracy of the new data D2 and D3 is calculated using the known Y2 and Y3, which is the model testing process.

[0097] Y2′=A2W (7)

[0098] Y3′=A3W. (8)

[0099] Furthermore, the initial number of mapped feature nodes and the number of augmented nodes are preset. The number of nodes is adjusted according to the model's accuracy on D1. By default, the initial number of mapped feature nodes k is 20, the number of nodes generated by mapped features n is 200, and the number of nodes generated by augmented features m is 200.

[0100] like Figures 4(a)-4(c) As shown, the regularization statement of the SVDD model, the corresponding statistical features and anomaly detection threshold are set in two dimensions. The SVDD model is trained using the old dataset to obtain the initial SVDD anomaly detection model, and then the anomaly rate of the new dataset is obtained.

[0101] As shown in Figure 4(b), the orange batch of data mostly consists of old fault type data. In contrast, the batch of data in Figure 4(c) mostly consists of new fault type data.

[0102] Given a training dataset X = {x i Let i = 1, 2, ..., I. Construct a hypersphere using SVDD that can hold all training samples in the smallest volume. The hypersphere can be represented by its center c and radius R; therefore, the optimization problem of SVDD can be expressed as:

[0103]

[0104] Where, ξ iis a slack variable, which is used to penalize the possible outliers in the training dataset, and the regularization parameter C is used to trade off between quantity and error.

[0105] Using the Lagrange multiplier, the following quadratic optimization problem can be obtained:

[0106]

[0107] α i represents the Lagrange multiplier, K(·,·) represents the kernel function, and the Gaussian kernel is used here. Then the KKT conditions are shown in Equation (11):

[0108]

[0109] The few samples located on the boundary of the hypersphere are called support vectors x sv , and its α i > 0.

[0110] Calculate R 2 , and the specific calculation formula is shown in Equation (12):

[0111]

[0112] where x k ∈x sv＜C , that is, the support vector set where α k < C.

[0113] Furthermore, according to the initial SVDD anomaly detection model, the anomaly rate of the new dataset is further obtained, specifically:

[0114] To test a data x new in the new dataset, the distance to the center of the hypersphere is obtained through the following formula (13):

[0115]

[0116] If ||x new - a|| 2 ≤ R 2 , then the new data is accepted, otherwise, the new data is an outlier.

[0117] When the proportion of new data outliers in dataset D2 or D3 is less than the threshold, the model is updated using width sample incremental learning later. Otherwise, the model is updated using width class incremental learning.

[0118] In this method, judging the relationship between x new and R is the process of SVDD testing.

[0119] As shown in Figure 3(b), the SVDD anomaly detection model is tested using a new dataset to determine whether the data anomaly rate reaches the anomaly detection threshold. If it is lower than the anomaly detection threshold, the threshold is set to 85% in this experiment, and then wide-sample incremental learning is used; if it is higher than the anomaly detection threshold, then wide-class incremental learning is used.

[0120] Specifically:

[0121] X new Perform SVDD outlier detection. If the outlier rate of this batch of data is greater than 85%, then X is considered... new Most of the data represents a different type of fault than the old data, so incremental learning is performed. If the percentage is less than or equal to 85%, then X is considered... new Most of the fault types in the data fall within the fault types of the old data, so incremental learning is performed on the samples. During the incremental learning process, the weight matrix W and features A of the old samples in the fault classification model are introduced into the training width for subsequent calculations.

[0122] During the sample increment process, the model weight parameters W are adjusted. D2 Update:

[0123] X r+1 X represents new Z r+1 and H r+1 They represent X respectively r+1 The linear mapping features and nonlinear enhancement features are used, where r is the fault sample and r+1 represents the sample increment. Therefore, the new feature set A is learned through width learning. r+1 It can be written as:

[0124]

[0125] a r+1 The feature set representing the new fault samples, i.e., a r+1 =[Z r+1 |H r+1 New feature set A r+1 The pseudo-inverse value can be obtained in the following way:

[0126] (A r+1 ) + =[(A) + -VU T |V] (15)

[0127] In the formula,

[0128] U T =a r+1 (A) + ,S T =a r+1 -U T A (16)

[0129]

[0130] Finally, the new weight matrix W can be updated using the following method. r+1 .

[0131] W r+1 =W+(y r+1 -a r+1 W)V (18)

[0132] Among them, y r+1 It is a fault label for a new sample.

[0133] In incremental learning, assume the old dataset contains m failure modes. The new data X... new A new type of failure mode data has emerged, where m represents the failure class and m+1 represents the class increment. To accommodate all these failure modes, the dimension of Y should be expanded from N×m to N×(m+1). Where Φ is a zero matrix with dimension N×1. Based on the obtained... The weight W can be amplified to W t As shown below:

[0134]

[0135] Among them, A + It is a pseudo-inverse transform of input feature A. Let h be the input feature of the newly emerging fault category. m+1 It includes convolutional features and additional features. Then, the input features of the width increment learning model can be represented as... Similar to (14), The calculation method is as follows:

[0136]

[0137] In the formula,

[0138] U = A + h m+1 S = h m+1 -AU (21)

[0139]

[0140] According to the obtained The weights of a fully connected layer can be updated as follows:

[0141]

[0142] Among them, y m+1 These are amplified labels for newly emerging anomalous samples, with a dimension of N. new×(m+1), N new It is new data X new The number of samples in the sample.

[0143] Using the diagnostic method of this invention, the predicted labels of X2 and X3 in the new dataset were calculated and the accuracy was obtained. The results are shown in the following tables. Table 1(a) shows the accuracy of the width learning model on D1 and D2 before and after sample increment, and Table 1(b) shows the accuracy of the width learning model on D1 and D3 before and after class increment.

[0144] Table 1(a) Accuracy of Incremental Model

[0145]

[0146] Table 1(b) Accuracy of the incremental model

[0147]

[0148] The application of this method in a real production environment is as follows:

[0149] Acquire real-time vibration signal data of the bearing;

[0150] The SVDD anomaly detection model is input to determine whether it is an outlier. If it is an outlier, the width learning fault classification model is incremented and the incremented width learning fault classification model is used for fault diagnosis.

[0151] Otherwise, a width-learning fault classification model can be used directly for fault diagnosis.

[0152] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the embodiments described above. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A bearing fault diagnosis method based on width incremental learning, characterized in that, include: Obtain the original time-domain data of the bearings required for the width-learning fault classification model; The original time-domain data of the bearing is preprocessed and divided into an old dataset D1 and a new dataset, wherein the new dataset includes a new dataset D2 and a new dataset D3. A width-learning fault classification model was built and trained using an old dataset to obtain an initial width-learning fault classification model. The fault accuracy of the initial width-learning fault classification model was then tested using a new dataset. The SVDD model was trained using the old dataset to obtain the initial SVDD anomaly detection model; The SVDD anomaly detection model is tested using a new dataset to determine whether the data anomaly rate reaches the anomaly detection threshold. If it is lower than the anomaly detection threshold, wide sample incremental learning is used. If the value exceeds the anomaly detection threshold, then use width-based incremental learning. A width-learning fault classification model based on incremental learning is used to diagnose faults in bearings based on real-time data, and the fault accuracy is obtained. A width-learning fault classification model was built and trained using an old dataset to obtain an initial width-learning model. The fault accuracy of the initial width-learning fault classification model was then tested using a new dataset. Specifically: The initial width learning fault classification model consists of a feature layer, an enhancement layer, and an output layer; Using the data from the old dataset as input to the width-learning fault classification model, we obtain mapping features and augmentation features. Then, based on the mapping features and augmentation features, we calculate the output layer. Combining this with the label Y1 from the old dataset D1, we have: W=(λI+AA T ) -1 A T Y1 in If the feature matrix A = [Z | H] and W is the weight connecting the feature layer and the enhancement layer to the output layer, then the model training is complete. Performing the same operation on D2 = {X2,Y2} and D3 = {X3,Y3} yields feature matrices A2 and A3, and further, predictive labels Y′2 and Y′3 are obtained: Y′2=A2W Y′3=A3W By comparing Y′2 and Y′3 with Y2 and Y3, the fault accuracy of the new dataset D2 and the new dataset D3 can be obtained. The initial SVDD anomaly detection model is obtained by training the old dataset. If we construct a hypersphere using the SVDD model that can contain all training samples in the smallest volume, then the hypersphere is represented by the center c and the radius R. The training process specifically involves solving the boundary conditions of the old dataset to obtain R; This also includes samples x from the new datasets D2 and D3. new Perform anomaly detection: If ||x new -a|| 2 ≤R 2 If the new data is positive, then accept it; otherwise, the new data is considered an outlier. If the anomaly rate is below the anomaly detection threshold, then wide sample incremental learning is used; If the anomaly rate is higher than the anomaly detection threshold, then wide-sample-class incremental learning is used, specifically: The aforementioned width-based incremental learning involves incrementing the samples in the new dataset D2 = {X2, Y2}. In the formula, U T =A2(A) + ,S T =A2-U T A At this point, the sample increment model update is complete; The aforementioned width-class incremental learning involves performing class increments on the new dataset D3 = {X3, Y3}. In the formula, U=A + A3,S=A3-AU W t =A + [Y|Φ]=[W|Φ] At this point, the incremental model update is complete.

2. The bearing fault diagnosis method according to claim 1, characterized in that, The raw time-domain data of the bearings is preprocessed and divided into old and new datasets, as follows: After performing DC removal, envelope analysis, and downsampling on the original bearing time-domain data, a dataset with a sampling frequency of 800Hz is generated. The 800Hz dataset is divided into old and new datasets. The old dataset D1 contains multiple fault types, while the new dataset D2, which is the new sample incremental dataset, contains all fault types belonging to the old dataset. The new dataset D3, which is the new class incremental dataset, contains only one fault type that does not belong to the old dataset.

3. The bearing fault diagnosis method according to claim 1, characterized in that, The width-learning fault classification predetermines the initial number of mapped feature nodes and augmentation nodes, and adjusts them based on the accuracy of the width-learning fault classification model on the old dataset.

4. The bearing fault diagnosis method according to claim 3, characterized in that, The initial mapping feature generates 20 nodes, the mapping feature generates 200 nodes, and the augmentation feature generates 200 nodes.

5. The bearing fault diagnosis method according to claim 1, characterized in that, Both wide sample incremental learning and wide sample class incremental learning involve stacking widths on the feature layers of a wide learning fault classification model.

6. The bearing fault diagnosis method according to any one of claims 1-5, characterized in that, A width-learning fault classification model based on incremental learning is used to diagnose faults in bearings based on real-time data, yielding the fault accuracy rate, specifically: Acquire real-time vibration signal data of the bearing; Input the SVDD anomaly detection model to determine whether it is an outlier. If it is an outlier, increment the width learning fault classification model and use the incremented width learning fault classification model for fault diagnosis. Otherwise, a width-learning fault classification model can be used directly for fault diagnosis.

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