Complexity

Volume 2018 (2018), Article ID 8740989, 14 pages

https://doi.org/10.1155/2018/8740989

## Fault Diagnosis for Hydraulic Servo System Using Compressed Random Subspace Based ReliefF

Correspondence should be addressed to Wen-jin Zhang

Received 28 October 2017; Revised 5 January 2018; Accepted 14 January 2018; Published 18 February 2018

Academic Editor: Gangbing Song

Copyright © 2018 Yu Ding 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

Playing an important role in electromechanical systems, hydraulic servo system is crucial to mechanical systems like engineering machinery, metallurgical machinery, ships, and other equipment. Fault diagnosis based on monitoring and sensory signals plays an important role in avoiding catastrophic accidents and enormous economic losses. This study presents a fault diagnosis scheme for hydraulic servo system using compressed random subspace based ReliefF (CRSR) method. From the point of view of feature selection, the scheme utilizes CRSR method to determine the most stable feature combination that contains the most adequate information simultaneously. Based on the feature selection structure of ReliefF, CRSR employs feature integration rules in the compressed domain. Meanwhile, CRSR substitutes information entropy and fuzzy membership for traditional distance measurement index. The proposed CRSR method is able to enhance the robustness of the feature information against interference while selecting the feature combination with balanced information expressing ability. To demonstrate the effectiveness of the proposed CRSR method, a hydraulic servo system joint simulation model is constructed by HyPneu and Simulink, and three fault modes are injected to generate the validation data.

#### 1. Introduction

Hydraulic servo system plays a crucial role in electromechanical systems, like engineering machinery, metallurgical machinery, ships, and other equipment. Failures of hydraulic servo system caused by severe and complex conditions may lead to catastrophic accidents and enormous economic losses. Fault diagnosis based on monitoring and sensory signals is able to classify the current state of complex systems, which plays a key role in performance evaluation [1]. Feature set extracted from signals is an important index to reflect the fault mechanism and performance evolution laws. The quality of feature set plays a key role in improving the generalization ability of fault identification [2]. The common feature extraction methods are time-frequency index extraction, wavelet analysis, Hilbert transform, Duffing oscillator, and so on. Despite their respective applicable conditions and limitations, those methods are able to mine the health characteristics of the system from multiaspect [3, 4]. Same as machine learning, features extracted from images, speeches, and other signals often have certain correlations and hidden mutual influences. Information expressed by a single feature is usually inadequate, which can be greatly improved when the single feature is aggregated with others [5]. Similarly, due to the nonlinearity, instability, and nonconformity of complex electromechanical systems, the expression of the information on individual feature is often one-sided. Thus, a new challenge is how to utilize those features more effectively and efficiently, in other words, how to obtain the feature set that expresses the information sufficiently by eliminating the redundant and negatively correlated features [6–9].

To tackle the challenge mentioned above, on the premise of existing feature extraction techniques, feature processing techniques including feature selection and dimension reduction have gradually become an important research focus. Both feature selection and dimension reduction can reduce the scale of feature set by obtaining a set of principal variables. Such techniques often use a variety of feature extraction methods to integrate the features into a comprehensive representation of the signal [10]. For the purpose of enhancing the expressing ability of core information on multiclass feature sets, spatial transformation or importance measurement methods are used [11]. Such methods are able to reduce redundancy existing in features and improve learning efficiency while retaining the performance advantages. The data transformation may be linear, such as principal component analysis (PCA). But many nonlinear dimension reduction techniques also exist. The common feature processing techniques include linear dimensionality reduction methods (FDA, LPP, etc.), kernel function based dimension reduction methods (KPCA, KFDA, etc.), manifold based dimension reduction methods (Isomap, LLE, MDS, etc.), filter method based feature selection methods (Relief, Focus, information gain, CBFS, etc.), wrapper method based feature selection methods (genetic algorithm, distribution estimation, differential algorithm, etc.), and embedded method based feature selection methods (SVN-RFE, RF, etc.) [12–14].

For the nonlinear signals of complex electromechanical systems, although the dimension reduction methods can reduce the scale of input features for fault diagnosis, they change the basic attributes of the feature set. Such situation makes it difficult to give a clear understanding of the obtained feature subset. Meanwhile, existing feature selection methods sort the importance degree of the features according to the independent feature evaluation result. They ignore the interaction among features, which would lead to information loss in processing the data of electromechanical systems [15]. Aiming at the shortcomings of feature selection and dimension reduction techniques, such as low expandability, unclear evaluation indexes, and strong tendency, this study proposes compressed random space based ReliefF (CRSR) method. Based on ReliefF method, CRSR introduces ensemble strategy on feature level based on compressed random space. Furthermore, CRSR optimizes the objective function using information entropy and fuzzy theory. The main contributions are as follows:(i)This study analyzes the feasibility of the ReliefF based feature selection architecture for the fault diagnosis of complex electromechanical system. Meanwhile, the basic mechanism of measuring the contribution of the features based on ReliefF is also demonstrated.(ii)By converting the assessment process of ReliefF, which takes the entire feature set as object, into the construction and ensemble process of feature subspace, CRSR can improve the global optimization ability of ReliefF.(iii)Considering ReliefF based feature selection as a problem of maximizing the distance, CRSR replaces the traditional spatial distance with fuzzy membership degree, which is able to obtain a robust and steady objective function.

This paper is structured as follows: In Section 2, ReliefF method based feature selection structure is introduced. Then feature integration method based on compressed random subspace is described. Objective function optimization method based on information entropy and fuzzy theory is also introduced. Section 3 presents the overall diagnosis procedure for hydraulic servo systems, the details of construction and fault injection of the hydraulic servo system, and analysis and comparison on feature selection results using the proposed CRSR method which are discusses numerically. Section 4 concludes the paper.

#### 2. Related Theories

##### 2.1. ReliefF Method Based Feature Selection Structure

ReliefF is the extension of Relief method by estimating probabilities more reliably, which is able to handle incomplete and multiclass data sets while the complexity remains the same [16–19]. By calculating the distances between the sample distributions, ReliefF can obtain the correlation weight coefficients of the features which is similar to Relief.

For a specific feature from the feature set, if its difference in same class is much smaller than that in different class, it is considered that this feature contributes to class discrimination [20]. Given a sample set with instances, each sample, , has* m*-dimensional features. Meanwhile, the samples in only belong to two classes which are tagged as . The difference between each two samples ( and ) on feature is defined aswhere the attribute of feature is discrete value. If the attribute of feature is continuous value,

Features extracted from condition monitoring data of electromechanical system mostly are continuous data. Meanwhile and represent the maximum value and minimum value of the entire sample, respectively. The closest same-class instance of sample is called “near-hit (NH),” and the closest different-class instance of sample is called “near-miss (NM).” Meanwhile, the weight of feature is denoted as , and is updated bywhere the initial value of is 0, and is the last value of .

For reducing the randomness in feature evaluation, the whole process needs to repeat times to obtain the average value being the final weight. Although Relief method is very efficient in estimating the quality of attributes, it cannot deal with incomplete data and is limited to two-class problem. Thus ReliefF method is utilized in the paper to deal with the multiclass classification and regression problems for continuous data.

For a multiclass classification problem, assuming that the samples in belong to multiple classes and the tags for are , ReliefF updates on sample by taking near hits (NHS) and near misses (NMS) into consideration, which is different from Relief. Similarly, the weight of feature , which is , can be updated throughwhere represents the ratio of the entire samples in class to all the heterogeneous samples in . Furthermore, ReliefF method equalizes the differentiation of NHs and calculates the average differences between and other classes on feature to evaluate the classification ability of the samples nearby.

##### 2.2. Feature Integration Method Based on Compressed Random Subspace

The purpose of CRSR method is finding the balance between the differences and the correlations of features. Specifically, in the premise of fully mining the correlations of features using ReliefF method, CRSR method is applied to make each feature subset keep a certain degree of difference. Based on random subspace and feature sorting strategy, the feature sets with higher contribution can be obtained in various feature combinations [21, 22]. and are denoted as two random subspaces, so the difference, denoted as , can be calculated aswhere symbol denotes the dimension of random subspaces.

The right side of (5) obtains the noncoincident features of and . is plus one when there is an unrepeated feature . The average difference between two random subspaces on all the features is defined aswhere is the dimension after feature ordering compression. It can be simplified as . Concretely, according to sorting strategy, RS12, the probability of the first strongly related features being selected is , and the relatively poorly related features being selected are . The average difference of feature evaluation based on compressed random subspace method, which is , can be denoted as follows:

Equation (7) shows that the ranking result can balance the difference of ReliefF to determine the dominant features that are crucial for classification, which would improve the feature selection efficiency.

Based on compressed random subspace method, this study proposes redundancy analysis method from statistics to reduce the redundancy of feature. The features are checked in pairs using redundancy analysis method [23, 24]. Firstly, two sets of feature vectors, and , are selected randomly from the feature set obtained by ReliefF. Then, the selected feature vectors are regarded as independent variable and dependent variable separately. The covariance matrixes, denoted as and , can be calculated, respectively, aswhere represents mathematical expectation of vector . Then, the correlation coefficient of and , denoted as , can be formulated aswhere denotes the covariance of and . If the correlation coefficient is greater than a presetting threshold, only the one with larger weight from and will be added to the final selected feature set. It is noticed that redundancy analysis based on matrix transformation focuses on the correlation between features instead of the similarity of data. Thus, CRSR can reduce the influence of numerical confusion existing in feature selection. Furthermore, compared with traditional methods based on data similarity, CRSR is able to obtain higher confidence level.

##### 2.3. Objective Function Optimization Method Based on Information Entropy and Fuzzy Theory

From the aspect of maximizing the distance, Relief method can be seen as a distance optimization algorithm using feature weighting method [25]. Under this condition, the optimization objective function, denoted as , can be described as [26]where denotes the distance of the th sample. Based on (4), can be converted as

For complex electromechanical system signals, two problems occur when using (10) as the optimization objective function of CRSR. One problem is that the objective function concentrates the weight on one or some of the features, which leads to the result that assessment value of the remaining features tends to 0. Meanwhile, (10) regards the samples with stochastic volatility and noise similar to the normal sample. Another problem is the lack of consideration on the influence from the quality of samples on the feature selection process.

Aiming at the first problem, the information entropy theory is proposed based on compressed random subspace method, which combines the maximization of entropy together with maximization of distance to reduce the over tendency problem of the existing ReliefF method. After adding a sample estimation factor , the optimization objective function is denoted as

Supposing that and follow probability distribution, Shannon entropy is used to adjust the sample distribution, as shown below:

Aiming at the second problem, the fuzzy membership degree is chosen to replace the traditional nearest neighbor distance. The fuzzy membership degree has the advantage of being insensitive to sample fluctuations and noise and the ability of updating adaptively while changing the feature weights [27]. In a sample space of same class, the fuzzy membership degree of the feature , denoted as , can be calculated as [28, 29]where is the sample set of same class, and is the fuzzy difference between feature and feature , as shown below:

Then the same fuzzy distance, denoted as , is calculated as

Similarly, the fuzzy difference and the fuzzy membership degree of the heterogeneous sample sets of , which are denoted as and separately, can be calculated as follows:

Therefore, the heterogeneous fuzzy distance, denoted as , is calculated as

Based on the fuzzy distances obtained by (16) and (18), updated (11) can be formulated as follows:

Based on the formulas above, the objective function, which is , can be denoted aswhere the first item on the right side is the maximum distance of ReliefF, which is meant to determine the feature set that contributes most to classification. Meanwhile, from the aspect of entropy maximization, the second and the third items denote the sample evaluation operator and Shannon entropy of feature weight, respectively, which are used to avoid the over tendency problem of objective function. and are the balance coefficients for adjusting the differences between features. When the maximum point of objective function is achieved, the constraint condition of the sample evaluation operator is defined below [30]:where denotes the partial derivative of .

In the process of feature selection for mechanical system, the information entropy and fuzzy theory based optimization objective function ensures that the evaluation process of each subspace using ReliefF is adaptive and robust. Such advantage provides a new thought for feature processing of complex monitoring signal, in other words, under the premise of maintaining the high calculating efficiency of ReliefF method, reducing the bias and redundancy caused by methodological defects and external disturbances [31].

#### 3. Method for Hydraulic Servo System Fault Diagnosis Based on CRSR

The CRSR based fault diagnosis method for hydraulic servo system consists of following successive steps: first, the average, standard deviation, skewness, and wavelet singular entropy features are extracted to form a feature matrix as the input of ReliefF model. Second, the initial contribution of the features sampled randomly is measured by calculating the inner-class distance and between-class distance, and the features of high contribution and features of low contribution are determined for fault classification. The th iteration operation is based on the result of the previous iteration, and the iteration stops as long as reaches the preset threshold. Third, based on the sorting result of the second step, the compressed evaluation of the features is realized using supervised sampling method in current iteration. Finally, keeping the iteration running until certain terms is satisfied to acquire the difference value as the criterion of feature selection. The detailed process of feature selection method using CRSR for hydraulic servo pump is shown in Figure 1.