**1. Introduction**

Rotating machinery is very common in industrial systems, and it plays an important role in industrial development and economic development. With the rapid advancement in industry, rotating machinery is becoming more and more complex and require constant attention. Although the reliability and robustness of rotating machinery also have been improving, some occasional failure events of components often lead to unexpected downtime while resulting in huge losses. And rolling element bearing is often at the heart of these rotating machinery which suffers from fault more frequently. These faults may cause the machine to break down and decrease its level of performance [6]. So, it is urgent to diagnose the incipient errors exactly in these bearings.

In traditional fault diagnosis, a single sensor is always used to get the operation conditions of several machine components. The collected signal involves many correlated features [33]. During operating process, the machine set can generate many kinds of signals. And those approaches based on the vibration signal analysis are advantageous because of their visual feature, easy measurability, high accuracy and reliability [34]. Fault diagnosis using raw vibration signals, a wide variety of techniques have been introduced in recent years. There are mainly including signal processing methods and intelligent systems application. Signal processing methods are traditional methods which are still common used, such as wavelet and wavelet packet methods [23–25], empirical mode decomposition [15, 35], time-frequency distributions [7], blind source separation [29]. While intelligent system approaches for fault diagnosis are including artificial neural networks (ANNs) [36], support vector machines (SVMs) [33], adaptive neuro-fuzzy inference system (ANFIS) [19] and fuzzy technique [28], etc.. These approaches are based on one data source or individual decision system, and many researchers have realized and shown that an individual decision system with a single data source can only acquire a limited classification capability which may not be enough for a particular application [22]. So, it is necessary to combine multiple decision systems to carry on failure diagnosis.

©2012 Huang, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ©2012 Huang, licensee InTech. This is a paper distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### 2 Will-be-set-by-IN-TECH 116 Performance Evaluation of Bearings Bearing Fault Diagnosis Using Information Fusion and Intelligent Algorithms <sup>3</sup>

Multi-sensor information fusion is an emerging interdisciplinary beginning in the military field, and it has already been successfully applied in many different areas. In the field of industrial equipment fault diagnosis, multi-source information fusion technology application is still in its early stage. Multi-sensor information fusion is divided into three levels: sensor level, feature level and decision level. And multiple classifier ensemble approach belongs to decision level information fusion. In the recent years, the use of multiple classifiers has gained a lot of attention and researches have continuously showed the benefits of using multiple classifiers to solve complex problems [4]. In contrast, the feature-level fusion has not probably received the amount of attention it deserves [32].

the period [0, *T*]. Then, calculating the fractal dimension *D* of *f*(*t*) by using the known values of *f*(*t*) at *tj* = *jT*/2*M*. To achieve this aim, Liaw and Chiu first defined *Lk*(*f*), the piecewise linear interpolation of level *k*(*k* = 0, 1, 2, ..., *M*), to *f*(*t*) as the union of the line segments connecting the points [*tj*, *f*(*tj*)] and [*tj*+1, *f*(*tj*<sup>+</sup>1)], where *tj* = *jT*/2*k*, *j* = 0, 1, 2, ..., 2*<sup>k</sup>* (see Figure 1). And then they checked out how poor the interpolation function *Lk*(*f*) is relative to the next level of interpolation *Lk*<sup>+</sup>1(*f*). The error of *Lk*(*f*) is defined as the sum of the absolute

> 2*k*+<sup>1</sup> ∑ *j*=*odd*

L2(f) <sup>Δ</sup><sup>1</sup> <sup>Δ</sup><sup>0</sup>

**Figure 1.** Piecewise interpolation *Lk* (*f*) to a function *f*(*t*) (grey) at level 0 (dotted), 1 (dashed), and 2 (solid). Δ*<sup>k</sup>* (thick solid) denotes the error of the *k*th level interpolation with respect to the *k* + 1 level [20] Thus, the fractal dimension *D* of *f*(*t*) can be obtained from the slope *s* of the log-plot of Δ*<sup>k</sup>*

In this bearing fault diagnosis method, raw vibration signal will be seen as a time sequences of data. Raw vibration signal is often heavily clouded by various noises due to the compounded effect of other machine elements' interferences and background noises presenting in the measuring device [2]. So, EMD is used to analysis raw vibration signal to filter noise before extracting its fractal feature. As discussed by Huang et al. [10], the EMD method is designated to deal with non-stationary and nonlinear signals. This method is based on the simple assumption that any data consists of different simple intrinsic modes of oscillations. Using the EMD method, complicated signals can be decomposed in a finite set of intrinsic mode functions (IMFs). Each IMF should meet the following two conditions: (1) in the whole data set of a signal, the number of extreme and the number of zero crossings must either equal or differ at most by one, and (2) at any time point, the mean value of the envelope defined by the

Assume *x*(*t*) is a vibration signal, and its empirical mode decomposition process can be

Liaw and Chiu [20] found that the value Δ*<sup>k</sup>* is proportional to (*εk*)1−*<sup>D</sup>* when *k* is large enough.

<sup>|</sup> *<sup>f</sup>*(*tj*) <sup>−</sup> *<sup>f</sup>*(*tj* <sup>−</sup> *<sup>ε</sup>k*) + *<sup>f</sup>*(*tj* <sup>+</sup> *<sup>ε</sup>k*)

Bearing Fault Diagnosis Using Information Fusion and Intelligent Algorithms 117

<sup>2</sup> <sup>|</sup>, *tj* <sup>=</sup> *<sup>j</sup>ε<sup>k</sup>* (1)

value of the differences of *Lk*(*f*) and *Lk*<sup>+</sup>1(*f*) at all *tj* <sup>=</sup> *jT*/2*k*+<sup>1</sup> <sup>≡</sup> *<sup>j</sup>εk*:

Δ1

L0(f)

with respect to the level *k* by *D* = 1 + *s*/*log*2 for large enough *k* values.

local maxima and the envelope defined by the local minima is zero.

Step 2. Extract the *i*-th intrinsic mode function (IMF) *ci*(*t*): Step 2.1. Initialize: *<sup>h</sup>*0(*t*) = *ri*−1(*t*), *<sup>j</sup>* = 1.

described by following steps:

Step 1. Initialize: *r*0(*t*) = *x*(*t*), *i* = 1.


L1(f)

Δ*<sup>k</sup>* ≡

2*k*+<sup>1</sup> ∑ *j*=0

By using information fusion theory, this chapter will introduce some bearing fault diagnosis approaches. And these methods can divide into two categories: fault diagnosis based on feature-level fusion [11] and fault diagnosis based on decision-level fusion [14]. In the proposed fusion methods for bearing fault diagnosis, some intelligent algorithms are used for feature dimension reduction or pattern recognition. The feature-level fusion approach for bearing fault diagnosis is using gene expression programming (GEP), while the decision-level fusion approach using multiple classifier ensemble method. And the decision-level fusion approach is based on the new bearing fault diagnosis method [12] which uses empirical mode decomposition (EMD) and fractal feature parameter classification.
