Shock and Vibration

Volume 2016 (2016), Article ID 5141564, 10 pages

http://dx.doi.org/10.1155/2016/5141564

## A Fault Diagnosis Model Based on LCD-SVD-ANN-MIV and VPMCD for Rotating Machinery

^{1}Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, Changde 415000, China^{2}College of Mechanical Engineering, Hunan University of Arts and Science, Changde 415000, China^{3}College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China^{4}Cooperative Innovation Center for Wind Power Equipment and Energy Conversion, Hunan Institute of Engineering, Xiangtan 411101, China

Received 12 March 2016; Revised 4 June 2016; Accepted 12 July 2016

Academic Editor: Lorenzo Dozio

Copyright © 2016 Songrong Luo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The fault diagnosis process is essentially a class discrimination problem. However, traditional class discrimination methods such as SVM and ANN fail to capitalize the interactions among the feature variables. Variable predictive model-based class discrimination (VPMCD) can adequately use the interactions. But the feature extraction and selection will greatly affect the accuracy and stability of VPMCD classifier. Aiming at the nonstationary characteristics of vibration signal from rotating machinery with local fault, singular value decomposition (SVD) technique based local characteristic-scale decomposition (LCD) was developed to extract the feature variables. Subsequently, combining artificial neural net (ANN) and mean impact value (MIV), ANN-MIV as a kind of feature selection approach was proposed to select more suitable feature variables as input vector of VPMCD classifier. In the end of this paper, a novel fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD is proposed and proved by an experimental application for roller bearing fault diagnosis. The results show that the proposed method is effective and noise tolerant. And the comparative results demonstrate that the proposed method is superior to the other methods in diagnosis speed, diagnosis success rate, and diagnosis stability.

#### 1. Introduction

Fault diagnosis is essentially considered as a class discrimination problem. Various methods have been applied to build classifiers to fulfill fault diagnosis [1–5]. However, these existing methods have their intrinsic limitation. To overcome these shortcomings, variable predictive model-based class discrimination (VPMCD) as a new multivariate classification approach [6–8] is presented by Raghuraj and Lakshminarayanan. Recently, our team has made a series of research on VPMCD for its application to fault diagnosis and the results show that VPMCD is a superior solution for fault diagnosis of rotating machinery with small sample and multiclassification problems [9–12].

It is known that there are some interactions among feature variables and VPMCD method can adequately use these interactions. However, in the application to fault diagnosis of rotating machinery, we found that the feature extraction and selection have a great influence on the performance of VPMCD classifier. As a new time-frequency signal processing method, local characteristic-scale decomposition (LCD) method can decompose a nonstationary signal into several intrinsic scale components (ISCs). Many applications show that LCD is superior to empirical mode decomposition (EMD) [13–15] in running time, decreasing the end effect and relieving mode mixing [16, 17]. On the other hand, singular value decomposition (SVD) technique based on phase space reconstruction theory has a good analytical ability for nonlinear and nonstationary time series and has been widely used in fault diagnosis for rotating machinery [18, 19]. However, it is difficult to determine the optimal reconstruction parameters for SVD technique [20]. To solve this problem, LCD method is applied to decompose the original vibration signal to a number of ISCs to construct initial matrix [21]; then feature variables can be obtained by SVD technique.

After feature extraction, we need to answer the following questions: which feature variables cause interrelationship that can describe the system’s dynamic characteristics more effectively? How to select more representative feature variables to improve the performance of the VPMCD classifier? In many practical applications, operators often have not a clear professional theory as guidance, so they cannot select better input features to design better VPMCD classifier. In this case, the accuracy of VPMCD classifier will decrease and seriously affect the accuracy for fault diagnosis. In other words, feature selection is fairly critical to design VPMCD classifier with better performance. Mean impact value can sensitively capture the interaction between the independent variable and dependent variable [22]. Combining artificial neural network (ANN) and mean impact value (MIV), we proposed ANN-MIV approach to choose more suitable features for VPMCD input features. At the end of this paper, a novel fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD is proposed and proved by a practical experiment for roller bearing fault diagnosis.

The rest of this paper is organized as follows. VPMCD method is introduced in Section 2. LCD-SVD technique is given in Section 3. Feature selection approach based on ANN-MIV is described in Section 4. A fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD is proposed in Section 5. We applied the proposed model to roller bearing fault diagnosis for experimental validation in Section 6. Some conclusions were made in Section 7.

#### 2. VPMCD

##### 2.1. Variable Predictive Model (VPM)

It is known that different system behaviors are always quantified by measurable features and interactions among them. For mechanical fault diagnosis, there exist linear or nonlinear associations among the features extracted from the vibration signals in different work conditions. In VPMCD, variable predictive models (VPMs) are defined to distinguish linear/nonlinear and direct/indirect quantitative relationships among the features using one of the mathematical equations in the form of the following formulas:

Suppose that there are classes and different variables in each failure class, which can be expressed by a feature vector . After selecting one of the above mathematical equations and the number of other variables used for prediction (referred to as predictor order , for any variable can be modeled using sample measurements of other variables . In other words, defines variable as a function of best set of other variables of the same class . One of the ways to determine the set of “” values is by solving an ordinary least squares problem as , where is the coefficient vector and is the design matrix containing the polynomial values of predictor variable set. It is noted that the number of possible models is and the mathematical equation with minimum prediction errors during validation is selected as best for variable and the collection of these best is regarded as characteristic model for representing the intervariable associations.

If there are classes and the structure of associations among the same set of variables is different in each class, then can be suitably developed during the supervised training using the known dataset of feature variables, so the distinct VPMs can be used to identify the class of an unknown sample.

##### 2.2. Classification Algorithm

Taking a fault diagnosis problem, for example, VPMCD algorithm includes two steps. The first step is to train VPMs of each class; the second step is to repredict feature variables by mapping on each of these VPMs and then to establish classifier. The detailed procedure is given as follows.

*Step 1 (VPMs training procedure). *(1) Collect samples with different fault classes.

(2) Extract feature vector for each class, respectively.

(3) For any predicted variable in a special class, choose the appropriate model type, predictor variables, and predictor order and establish using the observation samples belonging to this class.

(4) For the classification problem with classes, establish .

*Step 2 (classification procedure). *(1) For unknown sample, extract feature vector .

(2) Repredict each feature variable through VPMs, respectively, to obtain its prediction values.

(3) Calculate the sum of squared prediction errors of all feature variables.

(4) The unknown sample is classified into class which has the sum of minimum squared prediction errors :

#### 3. LCD-SVD Technique

A trajectory matrix can be decomposed into a series of mutually orthogonal, unit-rank, and elementary matrices by using SVD; that is, where and and is a diagonal matrix; let be nonzero diagonal elements arranged in decreasing order; are called singular values of matrix , namely, singular spectrum, where .

It is known that reconstruction parameters, such as lag time and embedding dimension, would have effect on the result of SVD method. It is difficult to determine reconstruction parameters. In order to solve this problem, LCD-SVD technique is presented. We introduced LCD method as follows.

LCD method can decompose a complex multicomponent signal into series of intrinsic scale components (ISCs), in which each ISC is a monocomponent signal whose instantaneous frequency has specific physical meaning.

That is, the original signal is decomposed intowhere is the th ISC component and is the residual component. Since the basic functions in LCD method are obtained by linear transformation of the signal, LCD method has obvious advantages compared to the EMD method and LCD. The details can be described in [16].

#### 4. Feature Selection Approach Based on ANN-MIV

MIV is the evaluation index showing how much the independent variables influence the dependent variable. Its absolute value represents the relative importance degree of the independent variables. In combination with ANN, we use MIV to rank the independent variables to select more representative feature. The ANN-MIV algorithm is described as follows.

To elaborate the algorithm, is used to represent the number of classes; is used to represent the sample number of each class in the training sets. is used to represent a special class and its value equals 1 to .

*Step 1. *-dimensional features are extracted from the training sample sets of different classes.

*Step 2. *For a special class , the feature variable is used as the dependent variable and the remaining feature variables are used as the independent variables in turn. Then we train ANN model with the training sample sets of the th class. It is noted that the input size of ANN is equal to the dimension of the independent variables and the output size is equal to one.

*Step 3. *The th sample from the training sets of the th class is selected and the simulated results are obtained via the trained ANN. Then the value of th feature variable varied by ±10% to constitute a pair of new feature variables and form a pair of new samples.

*Step 4. *The pair of new samples are, respectively, tested, and a pair of simulation outputs, noted as and , is obtained by feeding the corresponding ANN. Then the difference between the pairs of simulation outputs is calculated as follows:where represents how much the th independent feature variable affects the dependent feature variable in special class . Here, the value of the difference is called impact value (IV) of the corresponding dependent variable when considering that the certain independent variable changes.

*Step 5. *For the th class, the process is repeated from the remaining samples. We can calculate impact values and the mean of these impact values, which is called mean impact value (MIV):

*Step 6. *The process from Step 2 to Step 5 is repeated for the other feature variables of th class and the series of corresponding can be calculated. For example, considering the feature as the dependent feature variable, then can be expressed as .

*Step 7. *The value of can determine which feature variables have more distinct interaction with a special . Thus, we rank the value of and select some features with larger MIVs as more suitable variables to form VPM for VPMCD classifier. In the end, the process is repeated for the other classes and the corresponding MIV matrix can be calculated and the VPMCD classifiers for each class can be obtained.

#### 5. Fault Diagnosis Model

A novel fault diagnosis model based on LCD-SVD-ANN-MIV and VPMCD for rotating machinery was proposed in this paper. Firstly, LCD-SVD technique was introduced for the fault feature extraction. Subsequently, more suitable features were selected by ANN-MIV approach to form feature vector. Lastly, VPMCD method was utilized to design the classifier to identify the work condition. The flow chart of the proposed fault diagnosis model is given in Figure 1.