**3.1 Case 1: Fault diagnosis of bearings of CWRU test rig**

Faults were introduced into the tested bearings using the electron discharge machining method. The defect sizes (diameter, depth) of the three faults (outer race fault, inner race fault and ball fault) are the same: 0.007, 0.014 or 0.021 inches. Each bearing was tested under four different loads (0, 1, 2 and 3 hp). The bearing data set was obtained from the experimental system under four different health conditions: (1) normal condition; (2) with outer race fault; (3) with inner race fault; (4) with ball fault. Thus, the vibration data was collected from rolling element bearings under different operating loads and health conditions. More information regarding the experimental test rig and the data can be found in Ref. [21].

We conduct three investigations over three different data subsets (A–C) of the rolling element bearings. The detailed descriptions of the three data subsets are shown in Table 2. Data set A consists of 240 data samples of four health conditions (normal condition, outer race fault, inner race fault and ball fault) with the defect size of 0.007 inches under four various loads (0, 1, 2 and 3 hp). Each of the four health conditions includes 60 data samples. Data set A is split into two sets: 120 samples for training and 120 for testing. It is a four-class classification task corresponding to the four different health conditions.

Data set B also contains 240 data samples. 120 samples with the detect size of 0.021 inches are used as the training set. The remaining 120 samples with the detect size of 0.007 inches are identical with the 120 training samples of data set A and form the testing samples of data set B. The purpose of using this data set is to test the classification performance of the proposed method to incipient faults when it is trained by the serious fault samples.

Data set C comprises 600 data samples covering four health conditions and four different loads. Each fault condition includes three different defect sizes of 0.007, 0.014 and 0.021 inches, respectively. The 600 data samples are divided into 300 training and 300 testing instances. For data set C, in order to identify the severity degrees of faults, we solve the tenclass classification problem.

As mentioned in Section 2, the statistical features are extracted from the raw signal, filtered signal and IMF of each data sample. Three band-pass (BP1–BP3) and one high-pass (HP) filters are adopted for this bearing data. The band-pass frequencies (in kHz) of the BP1–BP3 filters are chosen as: BP1 (2.2–3.8), BP2 (3.0–3.8), and BP3 (3.0–4.5), respectively. The cut-off frequency of the HP filter is chosen as 2.2 kHz. These frequencies are selected to cover the frequency components representing bearing faults.

The Hybrid Intelligent Method Based on

Data set

Data set

individual classifiers

Fuzzy Inference System and Its Application to Fault Diagnosis 163

Fig. 2. Distance evaluation criteria of six feature sets of data set A: (a) feature set 1, (b) feature set 2, (c) feature set 3, (d) feature set 4, (e) feature set 5, and (f) feature set 6.

Classifier 1 Classifier 2 Classifier 3 Classifier 4

Training Testing Training Testing Training Testing Training Testing

Training Testing Training Testing Training Testing Training Testing

classifiers Hybrid method

A 100 100 100 100 100 100 100 100

B 100 62.5 100 79.17 100 74.17 100 80

C 65.67 61 90 87.67 72.67 68 80.33 77

A 100 100 100 100 100 100 100 100

B 100 55.83 100 81.67 100 72.22 100 90.83

C 67.67 67 87.33 81 77.28 73.61 93.67 91.33

Table 3. Diagnosis results of the CWRU bearings using the hybrid intelligent classifier and

Classifier 5 Classifier 6 Average of six


Table 2. Description of three data subsets

In order to demonstrate the enhanced performance of the hybrid intelligent method based on fuzzy inference system, the method is compared with individual classifiers based on ANFIS. Considering the computational burden, in each investigation, only four sensitive features are selected from each of the six feature sets using the improved distance evaluation technique and then input into the corresponding classifier. For data set A, distance evaluation criteria *<sup>j</sup>* of the six feature sets are shown in Fig. 2. The diagnosis results of the four data sets are shown in Table 3 and Fig. 3, respectively.

Observing the results in Table 3 and Fig. 3, we can get the following interesting things.

1. For data set A, since this classification problem is relatively simple, both the six individual classifiers and the hybrid intelligent method achieve the high training and testing accuracy (100%). However, comparing the classification error of the hybrid intelligent method with those of the individual classifiers plotted in Fig. 4, we can see that the classification error of the hybrid intelligent method is the least.

A 30 30 0/0 Normal 1

B 30 30 0/0 Normal 1

C 30 30 0/0 Normal 1

30 30 0.007/0.007 Outer race 2 30 30 0.007/0.007 Inner race 3 30 30 0.007/0.007 Ball 4

30 30 0.021/0.007 Outer race 2 30 30 0.021/0.007 Inner race 3 30 30 0.021/0.007 Ball 4

30 30 0.007/0.007 Outer race 2 30 30 0.007/0.007 Inner race 3 30 30 0.007/0.007 Ball 4 30 30 0.014/0.014 Outer race 5 30 30 0.014/0.014 Inner race 6 30 30 0.014/0.014 Ball 7 30 30 0.021/0.021 Outer race 8 30 30 0.021/0.021 Inner race 9 30 30 0.021/0.021 Ball 10

In order to demonstrate the enhanced performance of the hybrid intelligent method based on fuzzy inference system, the method is compared with individual classifiers based on ANFIS. Considering the computational burden, in each investigation, only four sensitive features are selected from each of the six feature sets using the improved distance evaluation technique and then input into the corresponding classifier. For data set A, distance

Observing the results in Table 3 and Fig. 3, we can get the following interesting things.

1. For data set A, since this classification problem is relatively simple, both the six individual classifiers and the hybrid intelligent method achieve the high training and testing accuracy (100%). However, comparing the classification error of the hybrid intelligent method with those of the individual classifiers plotted in Fig. 4, we can see that the classification error of

*<sup>j</sup>* of the six feature sets are shown in Fig. 2. The diagnosis results of the

Defect size of training/testing samples (inches)

Health conditions Label of classification

The number of testing samples

Data set

The number of training samples

Table 2. Description of three data subsets

the hybrid intelligent method is the least.

four data sets are shown in Table 3 and Fig. 3, respectively.

evaluation criteria

Fig. 2. Distance evaluation criteria of six feature sets of data set A: (a) feature set 1, (b) feature set 2, (c) feature set 3, (d) feature set 4, (e) feature set 5, and (f) feature set 6.


Table 3. Diagnosis results of the CWRU bearings using the hybrid intelligent classifier and individual classifiers

The Hybrid Intelligent Method Based on

experiment are listed in Table 4.

Fig. 5. Test bench of the locomotive rolling bearings.

Fuzzy Inference System and Its Application to Fault Diagnosis 165

2. For data set B, we can see that the training accuracies of all the classifiers are 100%. However, the hybrid intelligent method produces better testing performance (90.83%) than any of the individual classifiers ranging from 55.83% to 81.67% (average 72.22%). This result validates that the hybrid intelligent classifier trained by the serious fault data can diagnose the incipient faults with a higher accuracy in comparison with the individual classifiers.

3. For data set C, the training success rates of all the classifiers decrease and range from 65.67% to 93.67% because it is a ten-class classification problem and therefore relatively difficult. But the highest training accuracy (93.67%) is still generated by the hybrid intelligent method. For testing, the classification success of the six individual classifiers is in the range of 61–87.67% (average 73.61%), whereas the classification success of the hybrid method is much higher (91.33%). These imply that the hybrid method can identify both the

The test bench of locomotive rolling bearings is shown in Fig. 5. The test bench consists of a hydraulic motor, two supporting pillow blocks (mounting with normal bearing), a tested bearing (52732QT) which is loaded on the outer race by a hydraulic cylinder, a hydraulic radial load application system, and a tachometer for shaft speed measurement. The bearing is installed in a hydraulic motor driven mechanical system. 608A11-type ICP accelerometers with a bandwidth up to 5 kHz are mounted on the load module adjacent to the outer race of the tested bearing for measuring its vibrations. The Advanced Data Acquisition and Analysis System by Sony EX is used to capture the vibration data. Parameters in the

A bearing data set containing nine subsets is obtained from the experimental system under the nine different health conditions. The nine conditions of bearings, shown in Table 5, involve not only incipient faults but also compound faults. The incipient faults are actually slight rub of outer races, inner races or rollers. These faulty bearings are shown in Fig. 6. Each data subset corresponds to one of the nine conditions and it consists of 50 samples.

Tachometer

Tested bearing

Load module Accelerometer

Hydraulic cylinder

different fault modes and the different fault severities better.

**3.2 Case 2: Fault diagnosis of locomotive rolling bearings** 

Hydraulic motor Coupling Supporting pillow blocks Shaft

Fig. 3. Diagnosis results of the CWRU bearings: (a) data set A, (b) data set B, and (c) data set C.

Fig. 4. Classification errors: (a) classifier 1, (b) classifier 2, (c) classifier 3, (d) classifier 4, (e) classifier 5, (f) classifier 6, and (g) the hybrid intelligent classifier.

Fig. 3. Diagnosis results of the CWRU bearings: (a) data set A, (b) data set B, and (c) data set C.

Fig. 4. Classification errors: (a) classifier 1, (b) classifier 2, (c) classifier 3, (d) classifier 4, (e)

classifier 5, (f) classifier 6, and (g) the hybrid intelligent classifier.

2. For data set B, we can see that the training accuracies of all the classifiers are 100%. However, the hybrid intelligent method produces better testing performance (90.83%) than any of the individual classifiers ranging from 55.83% to 81.67% (average 72.22%). This result validates that the hybrid intelligent classifier trained by the serious fault data can diagnose the incipient faults with a higher accuracy in comparison with the individual classifiers.

3. For data set C, the training success rates of all the classifiers decrease and range from 65.67% to 93.67% because it is a ten-class classification problem and therefore relatively difficult. But the highest training accuracy (93.67%) is still generated by the hybrid intelligent method. For testing, the classification success of the six individual classifiers is in the range of 61–87.67% (average 73.61%), whereas the classification success of the hybrid method is much higher (91.33%). These imply that the hybrid method can identify both the different fault modes and the different fault severities better.
