Comparison of FDA-based and PCA-based features in fault diagnosis of automobile gearboxes
Introduction
Gears are the most important part of gearboxes used in lots of rotating machineries. Their availability and reliable operation are necessary for machine safety. Condition monitoring (CM) of gearboxes preserve specified requirements in the field of predictive maintenance. In condition monitoring systems some of machine parameters are monitored and true state of machine is evaluated via them. One of the most reliable parameters for the mechanical systems monitoring is its vibrational behavior which all mechanical machines experience. Condition monitoring systems may be designed to recognize healthy and faulty systems only (fault isolation systems) or to detect the type of fault (fault diagnosis systems). In the second type of systems, a fault diagnosis system is designed and trained with possible fault states for this machine.
The overall procedure for a fault diagnosis system can be stated in several steps: data acquisition, signal processing, feature representation, feature selection (feature extraction) and diagnostics (classifiers) [1]. Continuous wavelet transform (CWT) is mainly considered as an effective tool for vibration based signal processing for fault detection. Wavelet analysis could provide local feature in both time and frequency domains and has the feature of multi-scale, which enables wavelet analysis to distinguish the abrupt components of the vibration signal [2]. Therefore, wavelet analysis has been widely applied to rotating machinery fault diagnosis [3], [4], [5], [6]. Also, Rafiee et al. [7] searched the best mother wavelet for fault diagnosis purposes.
In the field of feature extraction methods, principle component analysis (PCA) is the most used method for fault diagnosis purposes. PCA is a technique that is widely used for applications such as dimensionality reduction, lossy data compression, feature extraction, and data visualization [8]. In the field of vibration-based fault diagnosis [9], [10] PCA is used as the dimension reduction method. Zhang et al. [11] implement variant of dimension reduction methods in the field of bearing fault detection. As an alternative, Zamanian and Ohadi [12] conducted a new method for feature extraction that is based on maximization of local Gaussian correlation function of CWC. Fisher discriminant analysis (FDA) is a linear dimensionality reduction technique, which has better performances for classification problems. FDA is rarely used for mechanical systems fault diagnosis purpose [13], [14].
In general, the current fault detection and diagnosis techniques for rotary machineries are predominantly based on intelligent systems, modeling using classical techniques. Artificial neural network (ANN) is one of the mostly used intelligent methods in the CM system [15], but it suffers from several disadvantages like time consuming train step, sensitivity to unbalanced conditions etc. Adaptive ANN [16], support vector machine (SVM) [12], fuzzy-based [17] and neuro-fuzzy-based systems [18] are the other methods which can be found in the literature. Bayesian based classifiers are rarely used in condition monitoring systems. Their capability for mechanical systems fault diagnosis is also discussed [19]. The KNN rule is an intuitively simple and flexible concept. For a given unlabeled sample, the KNN assigns test samples to the class which is frequent in neighborhood of this sample.
In this paper, a different fault diagnosis system is proposed. Signal containments are extracted using Morlet continuous wavelet transform. Gaussian mixture model (GMM) and K-nearest neighbor (KNN) based sorting methods are exploited, which are applied to the FDA subspaces. KNN is chosen because of its simplicity and practicality. On the other hand, GMM is robust to variation and has unbalanced number of involved samples for different classes of defection. To show the efficiency of the FDA-based features, the obtained results are compared to the ones obtained from the formerly introduced method, the PCA.
The rest of this paper is organized as follows: in Section 2, CWT signal processing techniques is briefly introduced, the FDA and PCA based feature extraction are then presented, and the GMM and KNN classifiers are finally introduced. In Section 3, the used gearbox experimental set-up is explained. The experimental results and conclusion are given in 4 Experimental results, 5 Conclusion, respectively.
Section snippets
Preliminaries
This section provides a brief overview of signal processing, feature extraction and classification techniques that are used in this research. In all equations, vectors and matrices are shown by bold lowercase and uppercase alphabets, respectively.
Experimental set-up, data collection AND faults description
A chip or wear gear tooth failure may cause fatal accidents; so, the gear tooth fault recognition is very important for the safety of a gearbox. In a multi-speed gearbox, most of the times, the second or third gear transmits power; therefore, fault diagnosis of these two gears is crucial and is studied in this research. The tested gears are used to study only one kind of failure in the same time: chip or wear on the tooth. Thus four conditions are assumed for gear 2, named as healthy gear,
Experimental results
Each of the vibration data samples is recorded for a few seconds synchronously with the tachometer signal. The tachometer pulses once for every complete revolution of the input shaft. In this manner, the vibration signal could be segmented based on individual revolutions of the input shaft. Each of the obtained segments is called an observation. For each observation, original space with 64 dimensions (means 64 variable for each observation) is constructed from variances of the CWC evaluated at
Conclusion
In this paper, a linear feature extraction approach is presented for fault diagnosis purpose of an automobile gearbox, using the recorded vibration signal. First, CWT is applied over the signal, employing the Morlet mother wavelet. To cover all the physical and meaningful frequencies of the vibration signal of the gearbox, CWC must be calculated in several scales which cause the curse of dimensionality. To solve this problem, the FDA dimension reduction method was used to project the original
Acknowledgment
The authors are grateful to the Magfa ITDC (Information Technology Development Center), an affiliation of the Industrial Development and Renovation Organization of Iran, IDRO, for supporting this research.
Mohammad Hossein Gharavian received both his B.S. and M.S. degrees from Amirkabir University of Technology, Tehran, Iran, in Mechanical Engineering in 2010 and 2013, respectively. His research interests include Fault Detection and Health Monitoring of Rotating and Reciprocating Systems using Applied Signal Processing with considering probabilistic aspect.
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2021, Reliability Engineering and System SafetyCitation Excerpt :In their experiments, their proposed feature reduction was superior in accuracy and training time, compared to classifying the non-reduced feature space. For a similar problem setting, Gharavian et al. [112] classify the vibration data of a gearbox. Their focus is on the comparison of feature extraction methods.
Mohammad Hossein Gharavian received both his B.S. and M.S. degrees from Amirkabir University of Technology, Tehran, Iran, in Mechanical Engineering in 2010 and 2013, respectively. His research interests include Fault Detection and Health Monitoring of Rotating and Reciprocating Systems using Applied Signal Processing with considering probabilistic aspect.
Farshad Almasganj received the M.S. degree in Electrical Engineering from Amirkabir University of Technology, Islamic Republic of Iran, in 1987 and the Ph.D. degree in Biomedical Engineering from Tarbiat Modarress University, Islamic Republic of Iran, in 1998. He is an Associate Professor in the Biomedical Faculty of Amirkabir University of Technology in Tehran. His research interests include Signal Processing, Speech Recognition, Prosody, Language Modeling for ASR Systems and Automatic Detection of Voice Disorders
Abdolreza Ohadi was born in 1967 in Tehran. He is an Associate Professor of the Faculty of Mechanical Engineering at Amirkabir University of Technology (Tehran Polytechnic) in Tehran. Dr. Ohadi is interested in Noise and Vibration, Structural Dynamics, Noise and Vibration Control (AVC, ANC), Rotor Dynamics and Fault Detection. He has published more than 100 conference and journal papers and has more than 20 years professional experience in automotive and other industries. He has done over 20 industrial projects. Dr. Ohadi received his B.Sc. and M.Sc. degrees from Amirkabir University and his Ph.D. from Sharif University, both in Mechanical Engineering. Currently, he is the head of Iranian Society of Acoustics and Vibration (ISAV).
Hojat Heidari Bafroui received his B.S. degree from Isfahan University of Technology, Isfahan, Iran, and the M.S. degree from Amirkabir University of Technology, Tehran, Iran, both in Mechanical Engineering in 2009 and 2012, respectively. His research interests include Dynamic, Vibration and Control of Mechanical Systems, Fault Detection and Health Monitoring of Rotating Systems and Applied Signal Processing.