International Journal of Rotating Machinery

Volume 2017, Article ID 2384184, 10 pages

https://doi.org/10.1155/2017/2384184

## Adaptive Morphological Feature Extraction and Support Vector Regressive Classification for Bearing Fault Diagnosis

^{1}School of Urban Rail Transportation, Soochow University, Suzhou 215131, China^{2}School of Mechanical and Electric Engineering, Soochow University, Suzhou 215131, China

Correspondence should be addressed to Changqing Shen; nc.ude.adus@nehsqc

Received 2 December 2016; Revised 18 February 2017; Accepted 23 February 2017; Published 13 March 2017

Academic Editor: Pavan K. Kankar

Copyright © 2017 Jun Shuai 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

Numerous studies on fault diagnosis have been conducted in recent years because the timely and correct detection of machine fault effectively minimizes the damage resulting in the unexpected breakdown of machineries. The mathematical morphological analysis has been performed to denoise raw signal. However, the improper choice of the length of the structure element (SE) will substantially influence the effectiveness of fault feature extraction. Moreover, the classification of fault type is a significant step in intelligent fault diagnosis, and many techniques have already been developed, such as support vector machine (SVM). This study proposes an intelligent fault diagnosis strategy that combines the extraction of morphological feature and support vector regression (SVR) classifier. The vibration signal is first processed using various scales of morphological analysis, where the length of SE is determined adaptively. Thereafter, nine statistical features are extracted from the processed signal. Lastly, an SVR classifier is used to identify the health condition of the machinery. The effectiveness of the proposed scheme is validated using the data set from a bearing test rig. Results show the high accuracy of the proposed method despite the influence of noise.

#### 1. Introduction

Given the rapid development of industrial technology, numerous multifunctional machineries have been employed to replace humans, particularly in dangerous environments. High production efficiency considerably relies on the continuous operation of machineries. However, unexpected machine breakdowns often occur due to mechanical faults, thereby resulting in huge economic losses and even threatening human safety. Researchers have determined that most machine failures are caused by faults in key components, such as bearings and gearboxes [1, 2]. Hence, the demand to inspect the health condition of these crucial components is increasing, and an efficient and intelligent machine fault diagnosis method should be developed to improve the reliability, safety, and effectiveness of operating systems [3, 4].

Extensive studies have been conducted in recent years to improve the effectiveness of fault diagnosis methods. Signal processing- and pattern recognition-based methods are the two main categories of data-driven techniques. Fault signal processing refers to the extraction of fault-related features from raw signals, in which faulty impulses are whelmed with noise. Consequently, a few related theories or methods have been developed. Ben Ali et al. [5] conducted a mathematical analysis to select the most significant intrinsic mode functions after an empirical mode decomposition of the bearing fault signal and evaluated the bearing condition and defect severity. Seshadrinath et al. [6] introduced complex wavelets in multiple fault diagnoses and proved the applicability of this scheme for industrial drives under variable frequencies and load conditions. Cong et al. [7] proposed the slip matrix construction method based on singular value decomposition. Given that the bearing runs from normal state to failure, the initial fault signal component can be selected from the entire life vibration data, thereby achieving an excellent performance in fault detection. Tiwari et al. [8] extracted the bearing fault features based on multiscale permutation entropy, which proved to be a reliable and automated fault diagnosis approach. Wang et al. [9] used the kurtosis extracted from the signal processed by short-time Fourier transform to establish the kurtogram; the enhanced kurtogram was effective in detecting various bearing faults. Zhang et al. [10] improved the Hilbert–Huang transform spectrum, which was constructed with the relevant and nearly monochromatic IMFs. A substantially accurate time-frequency distribution was produced for the inspected signal.

Morphological analysis has also been extensively performed to evaluate the satisfactory performance of signal processing in noise reduction. This process is an originally developed nonlinear method that uses structure elements (SEs) to measure and extract the corresponding shape of a given image [11]. Morphological analysis is also effective in many aspects, such as surface chemistry [12]. Moreover, machine fault diagnosis extracts the fault-related impacts with specific shapes, which are obtained using the component mechanism. Therefore, morphological analysis is applicable in extracting or enhancing the fault features. Dong et al. [13] effectively identified the rotating machinery fault by using a morphological filter, which is optimized by the particle swarm optimization algorithm and nonlinear manifold learning algorithm local tangent space alignment. Rajabi et al. [14] proposed a novel approach by combining mathematical morphology and multioutput adaptive neurofuzzy inference system classifier. Li et al. [15] established a multiscale morphological filtering of the vehicle system model, which displays considerable noise reduction performance. The results demonstrated that the proposed method can extract the influential characteristics of axle box vibration signals and effectively diagnose real-time wheel flat faults. Hong et al. [16] designed a gear fault diagnosis method based on the morphological mean wavelet transform, which has a simple structure, easy realization, sensitive local extremum signal, and high denoising ability, to determine the position of the impact signal. Raj and Murali [17] introduced a new method for the selection of SEs that depends on kurtosis, which is effective and robust in bringing out the impulses from bearing fault signals. Li et al. [18] calculated the general mathematical morphology particle from the normal state to failure; the calculated index was proven to be a valuable indicator of the degradation of the bearing performance. Yu et al. [19] applied an improved morphological component analysis to separate the meshing and periodic impulse components. Several case studies validated the effectiveness of diagnosing the compound fault of gearboxes. Bhateja et al. [20] introduced a scheme that combines the wavelet analysis and morphological filtering in the ECG field. The previous study has completed a few accomplishments in processing and extracting the features of machinery fault. However, the selection of the length of SE is crucial to properly measure and extract such features. Most of them are selected based on the experience or complicated indicators, which is time consuming and inapplicable to online processing.

Expertise is necessary to implement a signal processing-based method to correctly diagnose the machine fault using the resulting signal. However, the acquired signal is often obtained from multiple sources due to the environment where the machine works; the extraction of the machine fault-related component becomes difficult as well. Consequently, after the denoising process and fault characteristic extraction, an appropriate pattern recognition method is selected to map the features of the fault type. In recent years, several machine learning algorithms, such as support vector machine (SVM), deep neural network, and clustering algorithm, have been employed for this objective [21]. Vapnik [22] proposed SVM, which is regarded as a promising tool for classification with well-defined formulation and performs well in a few sample circumstances. SVM is a binary classifier. However, the condition of the bearing often contains the inner race fault, outer race fault, ball fault, and health status. A few strategies, such as the direct acyclic graph, one against all, and one against one, can be applied to solve this problem [23]. The one against one strategy is the recommended and preferred strategy for the actual application because of its rapid training speed and satisfactory accuracy in classification. However, this strategy is a voting approach. Multiple binary classifiers should be constructed and the samples should be fed into these classifiers to obtain the vote for each class. The class with the highest votes is the output class of the related sample, thereby suffering from equal votes problem. These strategies have drawbacks and increase the computational burden. Support vector regression (SVR), which was developed from SVM, can address the problem with continuous output or target value. Hence, SVR is commonly applied for time series analysis. Gu et al. [24] developed an incremental v-SVR based on v-SVC. The case study on benchmark data sets proved that the incremental SVR learning algorithm can avoid the infeasible updating paths by converging to the optimal solution. Kazem et al. [25] proposed a stock market price predicting method based on SVR. The SVR hyperparameters were optimized using the firefly algorithm and chaos theory. The phase space dynamics were reconstructed using a delay coordinate embedding method and eventually reached high prediction accuracy. Kavousi-Fard et al. [26] used SVR to obtain the accurate electrical load estimate, which outperformed the traditional techniques. Wei et al. [27] selected the parameters of SVR that were estimated through particle filtering and applied thereafter in reliability prediction. Chen and Yu [28] used SVR on the basis of an unscented Kalman filter to precisely update the short-term estimation of wind speed sequence.

This study presents a novel intelligent machine fault diagnosis procedure. The signals are first preprocessed using the improved morphology analysis, which selects the SE length adaptively. Thereafter, a feature vector with nine statistical values is calculated from the processed vibration signal for each sample. SVR theory is used as basis to develop a regressive classifier to overcome the SVM problems. Lastly, one case study for bearing is conducted to verify the satisfactory performance of the proposed procedure. Moreover, SVR exhibits an improved accuracy compared with other fault diagnosis schemes.

The rest of this paper is organized as follows. Section 2 provides a brief description of the principal theory of a morphological analysis and SVR. Section 3 introduces the proposed intelligent fault diagnosis procedure. Section 4 discusses the case study that validates the performance of the proposed method. Lastly, Section 5 presents the conclusion.

#### 2. Theoretical Background

##### 2.1. Morphological Analysis

Serra [29] first introduced morphological analysis in 1982 and used SEs to collect information or deform the shape of an image. Morphological analysis has been verified to exhibit an outstanding performance in denoising. This method functions with two basic operators as follows:

*Erosion*

*Dilation*where is the original one-dimensional vibration signal, is the SE, and and are the operators of erosion and dilation, respectively. Erosion calculation is used to suppress and smooth the positive and negative impacts, respectively. By contrast, dilation calculation is used to flatten and suppress the positive and negative impacts, respectively. Another two operators are created on the basis of two basic operators as follows:

*Opening*

*Closing*where and represent the opening and closing functions, respectively. The opening operator suppresses and preserves the positive and negative impacts, respectively. By contrast, the closing operator suppresses and preserves the negative and positive impacts, respectively.

The preceding four operators only calculate the feature information from one aspect and may lose a few geometric characteristics of the signal, which is meaningful in fault diagnosis. To detect the impulsive components, the closing and opening operators are combined to establish the difference operator, which can extract the positive and negative fault impacts.

*Difference*

The performance of morphological analysis depends on the operators and SEs; therefore, selecting an appropriate SE is significant. SEs are mainly determined by the length, height, and shape. SEs with a straight line shape have been determined to perform well [30]; hence, considerable attention should be focused to determine the length of SEs.

##### 2.2. Support Vector Regression

SVR is a type of machine learning algorithm that uses support vector to realize the function of regression [31]. Let denote the training set, where denotes the th input feature vector and denotes the th output pattern (i.e., its label). -insensitive SVR aims to find the function :where is the coefficient vector that is used to represent the place of function in the space and is a constant quantity. The question is to find the proper and . Moreover, is introduced when considering the error-tolerant rate; hence, the question has changed as follows:where denotes the fitting precision. To reduce the influence of the outlier, the slack variables are introduced:where is the penalty factor. and are slack variables that denote the deviation from the functional margin.

The application of the Lagrange multipliers and can change the formula as follows:To efficiently address the nonlinear regression question, the kernel function is introduced and the nonlinear regression function fitting is obtained as follows:

#### 3. Proposed Fault Identification Scheme

The proposed intelligent fault diagnosis procedure (see Figure 1) is based on the extraction of an adaptive morphological feature and support vector regressive classifier. The proposed procedure mainly comprises three steps: varying-scale morphological analysis, feature extraction, and SVR classification. The following subsections depict the details.