**2. The hybrid intelligent method based on fuzzy inference system**

The hybrid intelligent method is shown in Fig. 1. It includes the following five steps. First, vibration signals are filtered, and at the same time they are decomposed by empirical mode decomposition (EMD) and intrinsic mode functions (IMFs) are produced. The filtered signals and IMFs are further demodulated to calculate their Hilbert envelope spectra. Second, six feature sets are extracted. They are respectively time- and frequency-domain statistical features of both the raw and preprocessed signals. Third, each feature set is evaluated and a few sensitive features are selected from it by applying the improved distance evaluation technique. Correspondingly, six sensitive feature sets are obtained. Forth, each sensitive feature set is input into one classifier based on ANFIS for training and testing. There are altogether six different classifiers corresponding to the six sensitive feature sets. Fifth, the weighted averaging technique based on GAs is employed to combine the outputs of the six ANFISs and come up with the final diagnosis results.

The combination of multiple intelligent techniques has been intensively studied to overcome the limitations of individual intelligent techniques and achieve better performance [11–13]. Multiple intelligent classifiers input different feature sets usually exhibit complementary classification behaviors. Thus, if the classification results of multiple intelligent techniques are combined to yield the final classification result, the final performance may be superior to

Based on the above analysis, a hybrid intelligent fault diagnosis method is presented in this chapter to diagnose incipient and compound faults of complex equipments. The method is developed by combining multiple adaptive neuro-fuzzy inference systems (ANFISs), genetic algorithms (GAs) and vibration signal processing techniques. The method employs signal preprocessing techniques to mine fault information embedded in vibration signals. Statistical features reflecting machinery health conditions from various aspects are synthesized to construct multiple feature sets and to fully reveal fault characteristics. Using an improved distance evaluation technique, the sensitive features are selected from all feature sets. Based on the independency and the complementary in nature of multiple ANFISs with different input feature sets, a hybrid intelligent method is constructed using GAs. The hybrid intelligent method is applied to fault diagnosis of rolling element bearings. The experimental results show the method based on multiple fuzzy inference systems is able to reliably recognize both incipient faults and compound

The rest of this chapter is organized as follows. Section 2 presents the hybrid intelligent method based on fuzzy inference system. Feature extraction and selection, and adaptive neuro-fuzzy inference system are also introduced in this section. Section 3 gives two cases of fault diagnosis for rolling element bearings. The hybrid intelligent method is applied to diagnosing bearing faults and the corresponding results are reported. Section 4 compares the proposed hybrid intelligent method with individual intelligent methods in the light of classification accuracy, and further discusses the causes of the improvement produced by

The hybrid intelligent method is shown in Fig. 1. It includes the following five steps. First, vibration signals are filtered, and at the same time they are decomposed by empirical mode decomposition (EMD) and intrinsic mode functions (IMFs) are produced. The filtered signals and IMFs are further demodulated to calculate their Hilbert envelope spectra. Second, six feature sets are extracted. They are respectively time- and frequency-domain statistical features of both the raw and preprocessed signals. Third, each feature set is evaluated and a few sensitive features are selected from it by applying the improved distance evaluation technique. Correspondingly, six sensitive feature sets are obtained. Forth, each sensitive feature set is input into one classifier based on ANFIS for training and testing. There are altogether six different classifiers corresponding to the six sensitive feature sets. Fifth, the weighted averaging technique based on GAs is employed to combine the outputs of the six ANFISs and come

the best performance of individual classifiers [14–16].

the hybrid method. Finally, conclusions are given in Section 5.

up with the final diagnosis results.

**2. The hybrid intelligent method based on fuzzy inference system** 

faults.

Fig. 1. Flow chart of the hybrid intelligent fault diagnosis method

#### **2.1 Feature extraction**

## **2.1.1 Statistical features of raw signals**

Twenty-four feature parameters (*p*1–*p*24), presented in Table 1, are extracted [6] in this study. Eleven parameters (*p*1–*p*11) are time-domain statistical features and thirteen parameters (*p*12– *p*24) are frequency-domain ones. Once faults occur in mechanical equipments, the timedomain signal may change. Both its amplitude and distribution will be different from those of signals collected under healthy conditions. In addition, the frequency spectra and its distribution may change as well, which indicates that new frequency components appear and the convergence of frequency spectra varies. Parameter *p*1 and *p*3–*p*5 reflect the vibration amplitude and energy in time domain. Parameter *p*2 and *p*6–*p*11 represent the time series distribution of the signal in time domain. Parameter *p*12 indicates the vibration energy in frequency domain. Parameter *p*13–*p*15, *p*17 and *p*21–*p*24 describe the convergence of the spectrum power. Parameter *p*16 and *p*18–*p*20 show the position change of major frequencies.

The Hybrid Intelligent Method Based on

**set 3**.

**2.1.2 Statistical features of filtered signals** 

features. This feature set is referred as **feature set 4**.

13× *S* frequency-domain features defined as **feature set 6**.

**2.1.3 Statistical features of IMFs** 

found in Ref. [18].

referred as **feature set 5**.

**2.2 Feature selection** 

Fuzzy Inference System and Its Application to Fault Diagnosis 157

extracted here are hereafter referred as **feature set 1** and **feature set 2**, respectively.

The examination of vibration signals indicates the presence of low-frequency interference. The signals are subjected to either high-pass or band-pass filtration to remove the lowfrequency interference components. *F* filters are adopted and the selected filtration frequencies should completely cover the frequency components characterizing faults of mechanical equipments. The eleven time-domain features are extracted from each of the filtered signals. Therefore 11× *F* time-domain features are obtained and defined as **feature** 

In addition, the interference within the selected frequency band can be minimized by demodulation. Demodulation detection makes the diagnosis process a little more independent of a particular machine since it focuses on the low-amplitude high-frequency broadband signals characterizing machine conditions [17]. By performing demodulation and Fourier transform on the *F* filtered signals, we can obtain *F* envelope spectra. The envelope spectra are further processed to extract another set of 13× *F* frequency-domain

To extract more information, each of these raw signals is decomposed using the EMD method. EMD is able to decompose a signal into IMFs with the simple assumption that any signal consists of different simple IMFs [18]. For signal *x t*( ) , we can decompose it into *I* IMFs 1 2 ,,, *<sup>I</sup> cc c* and a residue *Ir* , which is the mean trend of *x t*( ) . The IMFs include different frequency bands ranging from high to low. The frequency components contained in each IMF are different and they change with the variation of signal *x t*( ) , while *Ir* represents the central tendency of signal *x t*( ) . A more detailed explanation of EMD can be

Generally, first *S* IMFs containing valid information are selected to further analysis. Similar to the feature extraction method of the raw signals, the eleven features in time domain are extracted from each IMF. Then, we get an additional set of 11× *S* time-domain features

Each IMF is demodulated and its envelope spectrum is produced. We extract the thirteen frequency-domain features from the envelope spectrum and finally derive another set of

Although the above features may detect faults occurring in mechanical equipments from different aspects, they have different importance degrees to identify different faults. Some features are sensitive and closely related to the faults, but others are not. Thus, before a feature set is fed into a classifier, sensitive features providing mechanical fault-related information need be selected to enhance the classification accuracy and avoid the curse of

Therefore, feature sets 1 and 2 contain 11 and 13 feature values, respectively.


frequency value of the *k*th spectrum line.

Table 1. The feature parameters

of data points.

Each vibration signal is processed to extract eleven time-domain features and thirteen frequency-domain features from its spectrum. The time- and frequency-domain features extracted here are hereafter referred as **feature set 1** and **feature set 2**, respectively. Therefore, feature sets 1 and 2 contain 11 and 13 feature values, respectively.
