**3.2. Results and discussion**

The decision-level fusion method for bearing fault diagnosis is also applied to the rotating machinery from the Case Western Reserve University website [3]. In this experiment, vibration signals are collected from accelerometers which attached to the motor at different positions as Figure 4 shows. And dynamometer is used to control the torque load level. In this work, we study four different operating conditions recognition under four different loads (0, 1, 2 and 3 hp) with fault diameters of 7 mils, 14 mils and 21 mils. And these four operating conditions are normal condition, outer race fault, inner race fault and ball fault.

A1 and A2. A1 is composed by the samples from the driven end accelerometer, while A2 from the fan end accelerometer. Table 7 gives the elements description of data set A in detail.

Data Class Sub Sensor The number of The number of set label dataset source training sample testing sample A 1 A1 driven end accelerometer 40 40

In this work, two different classifiers, *k*-NN (*k* = 7) and Parzen classifier, are used for fault diagnosis task. And these two different classifiers identify rotating machinery operating condition using vibration signals collected from driven end and fan end accelerometers respectively. That is to say, each data set has four individual decision system results. And

Table 8 gives individual classifier recognition accuracy on subsets of data set A and B. It is clear that individual classifiers can attain high bearing diagnosis accuracy on data set A, but they can not maintain the same high-performance on data set B whose fault diagnosis task is

> Data set Subset Classifier Training accuracy Testing accuracy A A1 *k*-NN classifier 100% 100%

B B1 *k*-NN classifier 88% 87.5%

Table 9 shows the fault diagnosis performance of the novel decision-level fusion model using multiple classifier system. It is clear that the novel decision-level fusion model can get high recognition accuracy even in the difficult fault diagnosis task. In the testing phase of data set B, fault diagnosis accuracy of the new fusion model is higher than all base classifiers' accuracy

> Data set Training accuracy Testing accuracy A 100% 100% B 100% 93.5%

Parzen classifier 100% 98.75% A2 *k*-NN classifier 100% 100% Parzen classifier 100% 99.38%

Parzen classifier 100% 85.75% B2 *k*-NN classifier 91.75% 88% Parzen classifier 100% 86.75%

**Table 7.** The elements description of data set A

MCS is composed by these four base classifiers.

extended to various grades of different fault conditions.

**Table 8.** Fault diagnosis performance using base classifier

as Table 8 shows. And it increases 6.5 percentage points averagely.

**Table 9.** Fault diagnosis performance using the new fusion model

A2 fan end accelerometer 40 40 2 A1 driven end accelerometer 40 40 A2 fan end accelerometer 40 40 3 A1 driven end accelerometer 40 40 A2 fan end accelerometer 40 40 4 A1 driven end accelerometer 40 40 A2 fan end accelerometer 40 40

Bearing Fault Diagnosis Using Information Fusion and Intelligent Algorithms 125

**Figure 4.** Schematic diagram of the experimental setup

Two data sets are constructed as Table 6 presents for testing the diagnosis performance of new decision-level fusion method. Each data set samples cover four different operating conditions and four different loads. And each class of two data sets has 160 data samples which are divided into two equal halves, one for training and the other for testing. Data set A is a four-class classification task corresponding to the four operating conditions. Data set B is a ten-class classification task corresponding to various grades of different faults.


**Table 6.** Description of two data sets

These data samples are extracted from two different sensor sources. And the number of samples from each sensor source is half of the total. If each sensor source's samples are seen as a subset of data set, each data set has two subsets. For example, data set A has two subsets:


A1 and A2. A1 is composed by the samples from the driven end accelerometer, while A2 from the fan end accelerometer. Table 7 gives the elements description of data set A in detail.

**Table 7.** The elements description of data set A

10 Will-be-set-by-IN-TECH

The decision-level fusion method for bearing fault diagnosis is also applied to the rotating machinery from the Case Western Reserve University website [3]. In this experiment, vibration signals are collected from accelerometers which attached to the motor at different positions as Figure 4 shows. And dynamometer is used to control the torque load level. In this work, we study four different operating conditions recognition under four different loads (0, 1, 2 and 3 hp) with fault diameters of 7 mils, 14 mils and 21 mils. And these four operating

Two data sets are constructed as Table 6 presents for testing the diagnosis performance of new decision-level fusion method. Each data set samples cover four different operating conditions and four different loads. And each class of two data sets has 160 data samples which are divided into two equal halves, one for training and the other for testing. Data set A is a four-class classification task corresponding to the four operating conditions. Data set B is a

Data The number of The number of Defect size(inches) Operating Class set training sample testing sample (training/testing) condition label A 80 80 0/0 Normal 1

B 80 80 0/0 Normal 1

These data samples are extracted from two different sensor sources. And the number of samples from each sensor source is half of the total. If each sensor source's samples are seen as a subset of data set, each data set has two subsets. For example, data set A has two subsets:

80 80 0.007/0.007 Outer race fault 2 80 80 0.007/0.007 Inner race fault 3 80 80 0.007/0.007 Ball fault 4

 80 0.007/0.007 Outer race fault 2 80 0.007/0.007 Inner race fault 3 80 0.007/0.007 Ball fault 4 80 0.014/0.014 Outer race fault 5 80 0.014/0.014 Inner race fault 6 80 0.014/0.014 Ball fault 7 80 0.021/0.021 Outer race fault 8 80 0.021/0.021 Inner race fault 9 80 0.021/0.021 Ball fault 10

conditions are normal condition, outer race fault, inner race fault and ball fault.

ten-class classification task corresponding to various grades of different faults.

**3.2. Results and discussion**

**Figure 4.** Schematic diagram of the experimental setup

**Table 6.** Description of two data sets

In this work, two different classifiers, *k*-NN (*k* = 7) and Parzen classifier, are used for fault diagnosis task. And these two different classifiers identify rotating machinery operating condition using vibration signals collected from driven end and fan end accelerometers respectively. That is to say, each data set has four individual decision system results. And MCS is composed by these four base classifiers.

Table 8 gives individual classifier recognition accuracy on subsets of data set A and B. It is clear that individual classifiers can attain high bearing diagnosis accuracy on data set A, but they can not maintain the same high-performance on data set B whose fault diagnosis task is extended to various grades of different fault conditions.


**Table 8.** Fault diagnosis performance using base classifier

Table 9 shows the fault diagnosis performance of the novel decision-level fusion model using multiple classifier system. It is clear that the novel decision-level fusion model can get high recognition accuracy even in the difficult fault diagnosis task. In the testing phase of data set B, fault diagnosis accuracy of the new fusion model is higher than all base classifiers' accuracy as Table 8 shows. And it increases 6.5 percentage points averagely.


**Table 9.** Fault diagnosis performance using the new fusion model

To further analyze performance of the new fusion model, a new *k*-NN classifier (*k* = 3) is added to multiple classifier system. The new multiple classifier system is used to test fault diagnosis performance on data set B. And sum rule is used to compare with the new approach. The comparison results are presented in Table 10. From Table 10, it is clear that the new approach attains the highest diagnosis accuracy.

signals is processed to extract some features. In this chapter, machine operating signal features only take into account the time-domain statistical characteristics. These feature parameters of time-domain are presented in Eequations. (13-23), where *x*(*t*) is a signal series and *N* is its

> *N* ∑ *n*=1

*<sup>n</sup>*=1(*x*(*n*) − *<sup>p</sup>*1)<sup>2</sup>

*<sup>n</sup>*=<sup>1</sup> *x*(*n*)<sup>2</sup>

<sup>|</sup>*x*(*n*)<sup>|</sup>

*<sup>n</sup>*=1(*x*(*n*) <sup>−</sup> *<sup>p</sup>*1)<sup>3</sup> (*<sup>N</sup>* <sup>−</sup> <sup>1</sup>)*p*<sup>3</sup> 2

*<sup>n</sup>*=1(*x*(*n*) <sup>−</sup> *<sup>p</sup>*1)<sup>4</sup> (*<sup>N</sup>* <sup>−</sup> <sup>1</sup>)*p*<sup>4</sup> 2

*<sup>p</sup>*<sup>8</sup> <sup>=</sup> *<sup>p</sup>*<sup>5</sup> *p*3

*<sup>p</sup>*<sup>9</sup> <sup>=</sup> *<sup>p</sup>*<sup>5</sup> *p*4

In the pattern recognition process of bearing fault diagnosis, we assume that there are *M*

belonging to *m*-th condition (1 ≤ *m* ≤ *M*) from the *i*-th sensor source. Feature-level fusion model is seek a way to fuse these features from different sensor sources. The new feature-level fusion model using GEP fuses these features by looking for a feature recognition function *ϕ* which maps the feature space to another space where samples in the same class are similarity and samples dissimilarity otherwise. And then, the feature recognition function *ϕ* will direct

Functions +, −, ×, /, *sqrt*, *exp* are selected as input functions of GEP. The generation is set

*<sup>i</sup>*=<sup>1</sup> ∑*k*∈*Si*

∑*k*∈*Si*


where *σ<sup>m</sup>* is the mean of all *m*-th condition samples function mapping values, its formula is:

*I* ∑ *i*=1 *<sup>m</sup>*�=*m*+1(*σ<sup>m</sup>* <sup>−</sup> *<sup>σ</sup>m*�)<sup>2</sup>

*<sup>m</sup>* (*ϕ*(*P<sup>i</sup>*

*<sup>m</sup> <sup>ϕ</sup>*(*P<sup>i</sup> k*)

*<sup>p</sup>*<sup>10</sup> <sup>=</sup> *<sup>p</sup>*<sup>3</sup> 1 *<sup>N</sup>* <sup>∑</sup>*<sup>N</sup>*

*<sup>p</sup>*<sup>11</sup> <sup>=</sup> *<sup>p</sup>*<sup>5</sup> 1 *<sup>N</sup>* <sup>∑</sup>*<sup>N</sup>*

the building of a multi-source feature fusion model in reverse direction.

*Fitness* <sup>=</sup> <sup>∑</sup>*M*−<sup>1</sup> *<sup>m</sup>*=<sup>1</sup> <sup>∑</sup>*<sup>M</sup>*

∑*<sup>M</sup> <sup>m</sup>*=<sup>1</sup> <sup>∑</sup>*<sup>I</sup>*

*<sup>σ</sup><sup>m</sup>* <sup>=</sup> <sup>1</sup> *I*

conditions including normal condition. Let *S<sup>i</sup>*

5000, and fitness function is defined as:

*x*(*n*) (13)

*<sup>N</sup>* <sup>−</sup> <sup>1</sup> (14)

*<sup>N</sup>* (15)

*<sup>N</sup>* )<sup>2</sup> (16)

*<sup>n</sup>*=<sup>1</sup> <sup>|</sup>*x*(*n*)<sup>|</sup> (22)

*<sup>n</sup>*=<sup>1</sup> <sup>|</sup>*x*(*n*)<sup>|</sup> (23)

*<sup>m</sup>* represents the set of all training samples

*<sup>k</sup>*) <sup>−</sup> *<sup>σ</sup>m*)<sup>2</sup> (24)

*<sup>m</sup>*<sup>|</sup> (25)

(18)

(19)

(20)

(21)

*p*<sup>5</sup> = max |*x*(*t*)| (17)

Bearing Fault Diagnosis Using Information Fusion and Intelligent Algorithms 127

*<sup>p</sup>*<sup>1</sup> <sup>=</sup> <sup>1</sup> *N*

> ∑*<sup>N</sup>*

> > *n*=1

 ∑*<sup>N</sup>*

*p*<sup>3</sup> =

*<sup>p</sup>*<sup>4</sup> = ( <sup>∑</sup>*<sup>N</sup>*

*<sup>p</sup>*<sup>6</sup> <sup>=</sup> <sup>∑</sup>*<sup>N</sup>*

*<sup>p</sup>*<sup>7</sup> <sup>=</sup> <sup>∑</sup>*<sup>N</sup>*

*p*<sup>2</sup> =

number of data points.


**Table 10.** Further comparison results of fault diagnosis performance
