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In order to enhance the performance of bearing fault diagnosis and classification, features extraction and features dimensionality reduction have become more important. The original statistical feature set was calculated from single branch reconstruction vibration signals obtained by using maximal overlap discrete wavelet packet transform (MODWPT). In order to reduce redundancy information of original statistical feature set, features selection by adjusted rand index and sum of within-class mean deviations (FSASD) was proposed to select fault sensitive features. Furthermore, a modified features dimensionality reduction method, supervised neighborhood preserving embedding with label information (SNPEL), was proposed to realize low-dimensional representations for high-dimensional feature space. Finally, vibration signals collected from two experimental test rigs were employed to evaluate the performance of the proposed procedure. The results show that the effectiveness, adaptability, and superiority of the proposed procedure can serve as an intelligent bearing fault diagnosis system.

Bearings are one of the most crucial elements of rotating machinery [

In the phase of signal processing and features extraction, due to the complexity of equipment structure and variety of operation conditions [

In recent years, various intelligent fault diagnosis systems based on EMD [

Generally, the statistical properties of the signal in time, frequency, and time-frequency domain are extracted to represent features information, such as peak value (PV), root mean square (RMS), variance (

For the high-dimensional statistical characteristics data, if these data are used directly in fault classification, it will lead to the very high computational complexity and fault classification accuracy degradation. Therefore, features dimensionality reduction is another crucial stage in the fault diagnosis process [

The contribution of this paper is the development of intelligent fault diagnosis system of rolling bearings based on multidomain features, systematically combining statistical analysis methods with artificial intelligence techniques. FSASD, a novel features extraction method, was proposed to select the fault sensitive statistical characteristics as the basis of subsequent fault analysis. A modified features reduction method, SNPEL, was proposed to excavate abundant and valuable information with low dimensionality. The execution of the proposed bearing fault diagnosis method is divided into four steps: signal processing, features extraction, features reduction, and fault patterns identification. In the first step, vibration signals collected from bearings are decomposed into different terminal nodes by MODWPT, and multidomain features were calculated from the reconstructed signal. In the second step, the adjusted rand index (ARI) criterion of the clustering method and SWD of samples were used to select fault sensitive statistical characteristics, which can represent the fault peculiarity under different working conditions. Furthermore, due to information redundancy and a high-dimensional dataset, in the third step, SNPEL was applied to obtain a new lower-dimensional space in which the new constructed features were obtained by transformations of the original higher-dimensional features such that certain properties were preserved. Finally, vibration signals collected from two test rigs were conducted to validate the effectiveness, adaptability, and superiority of the proposed method for the identification and classification of bearing faults. The first test rig is from Case Western Reserve University; four cases with 12 working conditions were employed to verify the performance of the proposed method. The second test rig is SQI-MFS test rig; two cases with 10 working conditions were employed to verify the performance of the proposed method. The analysis results for the vibration signals of roller bearing under different working conditions show the effectiveness, adaptability, and superiority of the proposed fault diagnosis approach.

The rest of this paper is organized as follows. In Section

For the bearing, the inner race, outer race, ball, and cage which are placed in the space between the rings make rotating possible. However, due to the inappropriate lubrication of the bearing rolling elements, inadequate bearing selection improper mounting, indirect failure and material defects, and manufacturing errors, various defects can occur [

For different bearing components (i.e., outer race, inner race, and ball, as shown in Figure

Structure of a ball bearing.

WT can be treated as a fast-evolving mathematical and signal processing tool in dealing with nonstationary signals [

Although the DWT has been developed to improve the drawback mentioned above of CWT [

Thus, (

In order to avoid downsampling, the MODWT creates appropriate new filters at each stage by inserting

With

However, both the DWT and the MODWT have very poor frequency resolution at low frequencies [

Therefore, with the suitable decomposition scale and disjoint dyadic decomposition, the complicated signal could be decomposed into a number of components whose instantaneous amplitude and instantaneous frequency attain physical meaning [

The LDA was proposed by Fisher [

Let

NPE, which is proposed by He et al. [

Given a dataset of

Constructing an adjacency graph: calculate the Euclidean distance between samples

Computing the weights: in this step, the weights of the edges are computed. Let

with constraints

A reasonable criterion for choosing an expected map is to minimize that cost function which is presented as follows [

This optimization problem can be converted to the following expression:

where

The key concept of SVM [

Considering that a dataset

When the data are linearly separable, the formulations presented above can work accurately. However, they will be ineffective when the investigated sample is overlapping or nonlinear [

For roller element bearings, the fault detection is a multiclass pattern recognition task, which can be generally solved by decomposing the multiclass problem into several binary class problems [

In this paper, we suggest that the most sensitive statistical characteristics should be selected before the implementation of the fault patterns recognition technique. For this reason, the

In the training samples, there are

Next,

Consider a set of

Computing the projections: in this step, the linear projections can be computed by solving the following generalized eigen-vector problem:

where

ARI can give a measure of the agreement between partitions and in classification problems [

Once clustering analysis is performed for the characteristics sets,

The SWD of characteristic samples of a kind of statistical characteristic in each type of bearings conditions is calculated, that is, the SWD of the elements of the row of the matrix

Next, we can obtain

In this paper, we presume that the SWD can be used to express the cohesion of data. Thus, there is the standard deviation sequence

Obtain a new sequence,

In this paper, we presume that the greater the value of

Although NPE can preserve the local neighborhood structure on the data manifold, it is mostly used as an unsupervised dimensionality reduction method, which does not take label information into account. However, the label information is useful for improving the dimensionality reduction performance and increasing the classification accuracy. Therefore, a novel dimensionality reduction method, SNPEL, was proposed. SNPEL naturally inherits the merits of SNPEL and LDA. The underlying idea of solving the problem mentioned above is that the optimization objective of LDA can be integrated into NPE; that is, the between-class scatter is maximized and the within-class scatter is minimized.

Based on the description of NPE and LDA in Section

According to (

Finally, the dimensionality reduction projection matrix

The detailed procedures of SNPEL are listed as follows.

Compute Euclidean distance between samples

Compute the weights on the edges. Let

Compute the

Compute between-class scatter matrix

Compute the eigenvectors and corresponding eigenvalues for the matrix

Sort the eigenvectors by decreasing eigenvalues and choose

Compute the equation

Finally, with the utility of SNPEL, the low-dimensional feature matrices of the training and testing dataset can be obtained with more sensitive and less redundant information for the bearings fault identification and classification.

The implementation of the proposed method is shown in Figure

Implementation of the proposed fault diagnostic technique.

In the first step, vibration signals collected from bearings are decomposed into different wavelet packet nodes by MODWPT. The single branch reconstruction signals of terminal nodes will be applied to generate statistical characteristics. With the utility of the proposed FSASD, the most sensitive statistical characteristics can be selected to construct feature vectors for the training classifier. The most sensitive statistical characteristics will be directly applied to extracting features for testing samples. Then, for the feature reduction, the low-dimensional training feature space is obtained by the proposed SNPEL, which generates a projection that can be used for dimensionality reduction of the testing feature space. The low-dimensional testing feature space can be obtained. SASD and projection matrix are obtained by processing the training set, which can be directly used by testing set. In the last step, the low-dimensional training feature set is employed as the input of the fault type to train the classifier. The trained classifier will be employed to conduct fault patterns recognition using the low-dimensional testing feature set. The procedure of this proposed method outputs the fault identification and classification accuracy.

The vibration dataset is freely provided by the Bearing Data Center of Case Western Reserve University (CWRU) [

Experimental test rig 1 [

In order to evaluate the effectiveness, adaptability, and robustness of the proposed bearing fault diagnosis method, the vibration signals of different fault types and degrees were employed. The detailed information of the used dataset is presented in Table

The detailed information of the used vibration dataset.

Condition of the bearings | Defect Size (mm) | Number of training samples | Number of testing samples | Class | |
---|---|---|---|---|---|

2 hp | 2 hp (case | 3 hp (case | |||

Healthy ball | 0 | 20 | 40 | 40 | 1 |

| |||||

Ball fault | 0.007 | 20 | 40 | 40 | 2 |

0.014 | 20 | 40 | 40 | 3 | |

0.021 | 20 | 40 | 40 | 4 | |

0.028 | 20 | 40 | 40 | 5 | |

| |||||

Inner race fault | 0.007 | 20 | 40 | 40 | 6 |

0.014 | 20 | 40 | 40 | 7 | |

0.021 | 20 | 40 | 40 | 8 | |

0.028 | 20 | 40 | 40 | 9 | |

| |||||

Outer race fault | 0.007 | 20 | 40 | 40 | 10 |

0.014 | 20 | 40 | 40 | 11 | |

0.021 | 20 | 40 | 40 | 12 | |

| |||||

Number of samples | 240 | 480 | 480 |

According to the system framework shown in Figure

A vibration signal sample and the corresponding single branch reconstruction signals of terminal nodes.

According to the decomposition of vibration signals, 16 terminal nodes and the corresponding coefficients can be obtained. Then, we obtain 16 single branch reconstruction signals of terminal nodes and 16 corresponding Hilbert envelope spectra (HES), which can generate 192 statistical characteristics using 6 statistical parameters shown in Table

Statistical parameters.

Number | Feature | Expression |
---|---|---|

(1) | Range | |

(2) | Mean value | |

(3) | Standard deviation | |

(4) | Kurtosis | |

(5) | Energy | |

(6) | Energy entropy | |

Here

Two time-domain statistical characteristics of the training samples.

Two HES statistical characteristics of the training samples.

The original feature set is composed of 192 statistical characteristics. Then, the FSASD is employed to select the sensitive statistical characteristics as the input feature vectors for the training classifier. The ARI, SSWD, and ASD of 192 statistical characteristics of the training samples are presented in Figures

The ARI of 192 statistical characteristics of the training samples.

The SSWD of 192 statistical characteristics of the training samples.

The ASD of 192 statistical characteristics of the training samples.

In order to verify the effectiveness and adaptability of the proposed bearing fault diagnosis method, a series of comparative experiments are divided into two groups. The detailed descriptions of them are presented below. Furthermore, in order to verify the superiority of MODWPT, WPT is also applied for fault diagnosis, and the results are compared with those of MODWPT.

In the first group, the FSASD is not applied. The original feature set contains 192 statistical characteristics which are directly processed by some dimensionality reduction methods. OFS-SVM is a SVM-based diagnosis model, in which the OFS is the input of SVM. OFS-PCA/NPE/LDA/SNPEL-SVM are SVM-based diagnosis models with the use of PCA, NPE, LDA, and SNPEL, respectively. According to Tables

Bearing fault diagnosis results obtained by OFS-SVM.

MODWPT | WPT | ||
---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |

98.54 | 83.54 | 95.21 | 76.25 |

Bearing fault diagnosis results obtained by OFS-PCA-SVM.

Dimension size | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

5 | 94.79 | 72.08 | 93.54 | 82.92 |

10 | 98.75 | 81.45 | 93.54 | 73.96 |

15 | 98.33 | 84.58 | 93.54 | 77.50 |

20 | | | | |

30 | | | | |

Bearing fault diagnosis results obtained by OFS-NPE-SVM.

Dimension size | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

5 | 69.17 | 68.75 | 44.38 | 34.17 |

10 | 83.54 | 74.17 | 77.71 | 61.25 |

15 | 90.00 | 76.46 | | |

20 | 95.21 | | 78.96 | 66.46 |

30 | | 74.38 | 83.13 | 53.54 |

Bearing fault diagnosis results obtained by OFS-LDA-SVM.

Dimension size | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

5 | 99.79 | 74.91 | 96.67 | 66.04 |

7 | 99.79 | 83.54 | 98.96 | 76.46 |

9 | 99.79 | 83.12 | 99.38 | 77.92 |

11 | | | | |

Bearing fault diagnosis results obtained by OFS-SNPEL-SVM.

Dimension size | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

5 | 83.75 | 72.92 | 66.67 | 54.17 |

10 | 98.54 | 91.67 | 94.58 | 81.67 |

15 | 98.75 | 94.58 | 98.13 | 89.58 |

| ||||

20 | 98.75 | 94.58 | 98.13 | 89.79 |

30 | | | | |

The detailed results of all models using MODWPT are presented below. For the testing set of case 1, all models can achieve preferable performance. The accuracies of each model can reach over 96%, and the highest accuracy can reach 100%. For the testing set of case 2, compared with OFS-SVM, OFS-PCA-SVM and OFS-NPE-SVM have improvement in diagnosis accuracy. But the performance of OFS-LDA-SVM and OFS-SNPEL-SVM is better than that of OFS-SVM, OFS-PCA-SVM, and OFS-NPE-SVM, and the highest accuracy of OFS-SNPEL-SVM can reach 94.58%. In the experiments mentioned above, two cases are tested in various approaches. According to the experimental results, it is evident that the fault diagnosis model using SNPEL can achieve preferable performance.

In the second group, the FSASD is applied to select the sensitive statistical characteristics before the implementation of features reduction and fault diagnosis. OFS-FSASD-SVM is a SVM-based diagnosis model, in which the sensitive characteristics can be selected from OFS by FSASD. OFS-FSASD-PCA/NPE/LDA/SNPEL-SVM are SVM-based diagnosis models with the use of PCA, NPE, LDA, and SNPEL, respectively. According to Tables

Bearing fault diagnosis results obtained by OFS-FSASD-SVM.

sfn | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

20 | 87.91 | 63.54 | 99.79 | 44.17 |

30 | 99.79 | 45.21 | 98.13 | 75.63 |

40 | 97.79 | 54.38 | 98.13 | 75.63 |

50 | 97.29 | 81.88 | 97.29 | 83.54 |

70 | | | | |

90 | | | | |

120 | 98.96 | 75.21 | 98.54 | 68.13 |

140 | 98.75 | 79.38 | 97.50 | 70.00 |

160 | 98.54 | 79.58 | 98.13 | 73.13 |

180 | 98.95 | 82.71 | 95.83 | 77.08 |

Bearing fault diagnosis results obtained by OFS-FSASD-PCA-SVM (dimension size is 20).

sfn | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

20 | 97.92 | 64.58 | 97.71 | 55.00 |

30 | 99.58 | 56.25 | 98.75 | 73.75 |

40 | 99.58 | 65.00 | 98.75 | 73.75 |

50 | 98.13 | 77.29 | 97.50 | 70.63 |

70 | | | | |

90 | | | | |

120 | 99.38 | 81.67 | 98.75 | 79.79 |

140 | 98.75 | 80.21 | 98.54 | 80.00 |

160 | 99.17 | 81.04 | 98.54 | 76.88 |

180 | 99.17 | 85.42 | 97.29 | 78.54 |

Bearing fault diagnosis results obtained by OFS-FSASD-NPE-SVM (dimension size is 20).

sfn | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

20 | 88.13 | 70.21 | 99.38 | 75.63 |

30 | 98.13 | 87.08 | 99.79 | 87.71 |

40 | | | | |

50 | | | | |

70 | | | | |

90 | 100.00 | 89.17 | 95.00 | 87.08 |

120 | 96.67 | 74.38 | 96.25 | 78.13 |

140 | 98.96 | 80.83 | 93.13 | 73.96 |

160 | 95.63 | 73.33 | 91.67 | 75.00 |

180 | 97.29 | 87.29 | 88.13 | 69.58 |

Bearing fault diagnosis results obtained by OFS-FSASD-LDA-SVM (dimension size is 11).

sfn | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

20 | 95.83 | 65.63 | 100.00 | 66.67 |

30 | 100.00 | 74.38 | 100.00 | 76.88 |

40 | 100.00 | 75.42 | 100.00 | 83.13 |

50 | 100.00 | 77.92 | | |

70 | 100.00 | 85.42 | | |

90 | 100.00 | 88.96 | 100.00 | 86.46 |

120 | | | 100.00 | 86.88 |

140 | | | 99.79 | 86.46 |

160 | 100.00 | 89.58 | 99.79 | 86.46 |

180 | | | 99.79 | 83.75 |

Bearing fault diagnosis results obtained by OFS-FSASD-SNPEL-SVM (dimension size is 20).

sfn | MODWPT | WPT | ||
---|---|---|---|---|

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) | |

20 | 17.08 | 16.46 | 99.79 | 75.00 |

30 | 100.00 | 66.67 | 99.38 | 62.08 |

40 | 99.79 | 69.79 | 100.00 | 74.17 |

50 | 100.00 | 74.38 | 100.00 | 75.00 |

70 | 100.00 | 75.00 | 100.00 | 83.75 |

90 | | | | |

120 | 99.38 | 76.88 | 99.17 | 83.13 |

140 | 98.33 | 84.58 | 99.58 | 89.17 |

160 | 99.79 | 90.83 | 99.17 | 85.21 |

180 | 99.58 | 92.92 | 98.13 | 89.79 |

The diagnosis results of OFS-FSASR-SVM using MODWPT with different sfn.

The diagnosis results of OFS-FSASR-SVM using WPT with different sfn.

The diagnosis results obtained by OFS-FSASD-PCA-SVM using MODWPT with different dimension sizes for PCA. The PC represents the number of dimension sizes.

The diagnosis results obtained by OFS-FSASD-PCA-SVM using WPT with different dimension sizes for PCA. The PC represents the number of dimension sizes.

The diagnosis results obtained by OFS-FSASD-NPE-SVM using MODWPT with different dimension sizes for NPE. The NPE

The diagnosis results obtained by OFS-FSASD-NPE-SVM model using WPT with different dimension sizes for NPE. The NPE

The diagnosis results obtained by OFS-FSASD-LDA-SVM using MODWPT with different dimension sizes for LDA. The LDA

The diagnosis results obtained by OFS-FSASD-LDA-SVM using WPT with different dimension sizes for LDA. The LDA

The diagnosis results obtained by OFS-FSASD-SNPEL-SVM using MODWPT with different dimension sizes for SNPEL. The SNPEL

The diagnosis results obtained by OFS-FSASD-SNPEL-SVM using WPT with different number of dimension sizes for SNPEL. The SNPEL

The diagnosis results of models using MODWPT for the testing sets of two cases with the use of FSASD and different dimensionality reduction methods. The output dimension sizes of PCA, LDA, and SNPEL are 20, 11, and 20, respectively. The “NO” represents the model without using dimensionality reduction method.

The diagnosis results of models using WPT for the testing sets of two cases with the use of FSASD and different dimensionality reduction methods. The output dimension sizes of PCA, LDA, and SNPEL are 20, 11, and 20, respectively. The “NO” represents the model without using dimensionality reduction method.

The sfn is the number of selected characteristics. For the testing set of case 1, all models can achieve preferable performance. For the testing set of case 2, compared with the experimental results of the first group, diagnosis accuracies of all models using FSASD appear to be an improvement. The performance of OFS-FSASD-SNPEL-SVM and OFS-FSASD-LDA-SVM is better than that of OFS-FSASD-SVM, OFS-FSASD-PCA-SVM, and OFS-FSASD-NPE-SVM. For OFS-FSASD-SNPEL-SVM and OFS-FSASD-LDA-SVM, the performance of OFS-FSASD-SNPEL-SVM is better. For the testing set of case 1, both the diagnosis accuracies of OFS-FSASD-SNPEL-SVM and OFS-FSASD-LDA-SVM can reach 100%. For the testing set of case 2, the maximum diagnosis accuracy of OFS-FSASD-SNPEL-SVM can reach 100%, but the maximum diagnosis accuracy of OFS-FSASD-LDA-SVM can only reach 97.92%. According to the experimental results of the second group, when a suitable parameter sfn is selected, it can achieve a desirable improvement on the diagnosis accuracy. According to Figures

In order to validate the adaptability of the proposed bearing fault diagnosis method, we collected vibration signals from SQI-MFS test rig to conduct some experiments. Figure

Experimental test rig 2.

SER205 bearings.

The detailed information of the used vibration dataset is presented in Table

The detailed information of the used vibration dataset.

Condition of the bearings | Defect size (mm) | Number of training samples | Number of testing samples | Class | |
---|---|---|---|---|---|

1800 tr/min | 1800 tr/min (case 1) | 1200 tr/min (case 2) | |||

Healthy ball | 0 | 20 | 40 | 40 | 1 |

| |||||

Ball fault | 0.05 | 20 | 40 | 40 | 2 |

0.1 | 20 | 40 | 40 | 3 | |

0.2 | 20 | 40 | 40 | 4 | |

| |||||

Inner race fault | 0.05 | 20 | 40 | 40 | 5 |

0.1 | 20 | 40 | 40 | 6 | |

0.2 | 20 | 40 | 40 | 7 | |

| |||||

Outer race fault | 0.05 | 20 | 40 | 40 | 8 |

0.1 | 20 | 40 | 40 | 9 | |

0.2 | 20 | 40 | 40 | 10 | |

| |||||

Number of samples | 240 | 480 | 480 |

The procedure of bearing fault diagnosis for SQI-MFS test rig is the same as that for the test rig 1. In the experiments, MODWPT is applied for vibration signals processing. For 192 statistical characteristics, the class discriminative degree of each characteristic is reflected in Figures

Two time-domain statistical characteristics of training samples.

Two HES statistical characteristics of training samples.

When the original feature set has been obtained, the FSASD is employed to select the sensitive statistical characteristics as the input feature vectors for the bearing fault diagnosis. Then, ARI, SSWD, and ASD of 192 statistical characteristics of training samples can be obtained. They are presented in Figures

The ARI of 192 statistical characteristics of training samples.

The SSWD of 192 statistical characteristics of training samples.

The ASD of 192 statistical characteristics of training samples.

In order to verify the effectiveness and adaptability of the proposed fault diagnosis method for SQI-MFS test rig, a series of comparative experiments are divided into two groups. In the first group, the FSASD is not applied. The fault diagnosis results of OFS-SVM, OFS-PCA-SVM, OFS-NPE-SVM, OFS-LDA-SVM, and OFS-SNPEL-SVM are presented in Tables

Bearing fault diagnosis results obtained by the OFS-SVM.

Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|

98.17 | 77.17 |

Bearing fault diagnosis results obtained by the OFS-PCA-SVM.

Dimension size | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

5 | 89.00 | 68.83 |

10 | 95.17 | 70.83 |

15 | 96.67 | 74.50 |

20 | 97.00 | 74.00 |

30 | | |

Bearing fault diagnosis results obtained by the OFS-NPE-SVM.

Dimension size | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

5 | 67.67 | 57.33 |

10 | 84.00 | |

15 | 93.83 | 53.17 |

20 | 94.50 | 56.33 |

30 | | 25.83 |

Bearing fault diagnosis results obtained by the OFS-LDA-SVM.

Dimension size | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

5 | 91.67 | |

7 | 98.83 | 59.83 |

9 | | 59.17 |

11 | | 59.50 |

Bearing fault diagnosis results obtained by the OFS-SNPEL-SVM.

Dimension size | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

5 | 78.50 | 64.33 |

10 | | 65.33 |

15 | | 65.17 |

20 | | |

30 | | 66.00 |

In OFS, different statistical characteristics have different fault sensitivity; some are beneficial to fault identification and classification, but some are not. The FSASD can evaluate the fault sensitivity of each statistical characteristic and select the sensitive statistical characteristics. For the second group, the FSASD is applied before the implementation of features reduction and fault diagnosis. The fault diagnosis results of OFS-FSASD-SVM, OFS-FSASD-PCA-SVM, OFS-FSASD-NPE-SVM, OFS-FSASD-LDA-SVM, and OFS-FSASD-SNPEL-SVM are presented in Tables

Bearing fault diagnosis results obtained by the OFS-FSASD-SVM.

sfn | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

10 | 60.67 | 54.67 |

20 | 62.50 | 67.67 |

30 | 62.83 | 50.67 |

50 | 64.67 | 57.00 |

70 | 73.00 | 60.17 |

| ||

90 | 96.33 | 75.33 |

110 | 97.00 | |

130 | 97.17 | 76.67 |

150 | 97.33 | 75.00 |

170 | | 74.50 |

190 | 98.00 | 76.50 |

Bearing fault diagnosis results obtained by the OFS-FSASD-PCA-SVM (dimension size is 20).

sfn | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

20 | 70.50 | 71.67 |

30 | 71.50 | 69.00 |

50 | 78.00 | 63.00 |

70 | 82.67 | 64.50 |

90 | 86.50 | 68.83 |

110 | 93.33 | 72.33 |

130 | 93.00 | |

150 | 95.17 | 74.83 |

170 | 96.17 | 73.67 |

190 | | 74.33 |

Bearing fault diagnosis results obtained by the OFS-FSASD-NPE-SVM (dimension size is 20).

sfn | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

20 | 91.50 | 39.00 |

30 | 92.50 | 44.83 |

50 | 94.67 | 54.50 |

70 | | 47.67 |

90 | 97.17 | 50.00 |

110 | 97.50 | 48.67 |

130 | 96.50 | 56.50 |

150 | 96.83 | 44.00 |

170 | 97.33 | |

190 | 94.50 | 56.33 |

Bearing fault diagnosis results obtained by the OFS-FSASD-LDA-SVM (dimension size is 11).

sfn | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

20 | 63.83 | 62.33 |

30 | 74.50 | 64.00 |

50 | 81.00 | 54.67 |

70 | 89.00 | 58.17 |

90 | 99.00 | 58.83 |

110 | 98.67 | 59.00 |

130 | 99.17 | |

150 | | 67.33 |

170 | 99.83 | 66.67 |

190 | 99.67 | 56.83 |

Bearing fault diagnosis results obtained by the OFS-FSASD-SNPEL-SVM (dimension size is 20).

sfn | Case 1 testing accuracy (%) | Case 2 testing accuracy (%) |
---|---|---|

20 | 81.50 | 71.83 |

30 | 82.83 | 72.00 |

40 | 84.17 | 75.17 |

50 | 85.67 | 56.67 |

70 | 98.00 | 79.50 |

| | |

| | |

| | |

160 | 99.83 | 80.67 |

180 | 99.33 | 79.17 |

The diagnosis results of the OFS-FSASD-SVM model with different sfn.

The diagnosis results obtained by OFS-FSASD-PCA-SVM with different number of dimension sizes for PCA. The PC represents the number of dimension sizes.

The diagnosis results obtained by OFS-FSASD-NPE-SVM with different number of dimension sizes for NPE. The NPE

The diagnosis results obtained by OFS-FSASD-LDA-SVM with different number of dimension sizes for LDA. The LDA

The diagnosis results obtained by OFS-FSASD-SNPEL-SVM with different number of dimension sizes for SNPEL. The SNPEL

The diagnosis results of the testing set of two cases with the use of FSASD and different dimensionality reduction methods. The output dimension sizes of PCA, LDA, SNPEL, and NPE are 20, 11, 20, and 20, respectively.

This paper proposed a novel procedure in order to identify and classify different bearing fault conditions. The proposed procedure, systematically blending statistical analysis with artificial intelligence, is developed using MODWPT as multidomain features generation approach. Using the proposed FSASD as the most sensitive features extraction method, the modified NPE (SNPEL) as a feature dimensionality reduction technique, and SVM as an automated fault patterns recognition system, the experimental data collected from two experimental test rigs contain different bearing fault conditions such as ball fault, inner race fault, and outer race fault at different defect sizes.

According to the experimental results, the proposed bearing fault diagnosis method has great potential to be an effective and adaptable tool for precise identification and classification of bearing faults for a variety of bearing conditions. For the experimental test rig 1, in the proposed procedure, two cases are employed in experiments. Cases 1 and 2 are a set of comparative cases. They use the testing samples with different motor loads, which are 2 hp and 3 hp, respectively. They use samples with the same motor load (2 hp) as the training samples. Experimental results indicate that the maximum diagnosis accuracy of case 1 can reach 100%. The diagnosis accuracies of case 2 can reach over 99% when the parameter sfn is in a relatively wide range. In order to verify the adaptability of the proposed procedure, vibration datasets collected from the experimental test rig 2 (SQI-MFS) are employed. Cases 1 and 2 use the testing samples with different motor speeds, which are 1200 rmp and 1800 rmp, respectively. They use samples with the same motor speed (1800 rmp) as the training samples. The experimental results can also indicate that the diagnosis model using the proposed methods can achieve preferable performance.

The authors declare that they have no conflicts of interest.

This work is supported by the National Key Research and Development Program of China (no. 2017YFC0804400, no. 2017YFC0804401) and the National Key Basic Research Program of China (973 Program, no. 2014CB046300).