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Comparison of one-class classifiers for Condition Monitoring of rolling bearings in non-stationary operations
Abstract
In most cases Condition Monitoring (CM) classification problems were discussed as two or more class problems. In general this approach is reasonable because a current measurement should be a assigned to one of the predefined classes. The main benefit of using one-class classifiers instead is the absence of a fault class or classes of faults. Samples of this domain are rare because of the limits for artificially damaging a machine or waiting till the damage occurs in order to get fault class samples. A one-class classifier defines a stable reference indicating a healthy state of a machine or process. If the operating conditions are varying, the problem of generalisation of training samples increases. In this paper some discussion will be made about possibilities and problems occurring with the use of single-class classifiers in this context. A set of classifiers will be trained on vibration data samples using some generalised norms and moments. An industrial application dataset will be analysed here and the performance of different classifiers will be discussed in detail.
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Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. Any attempt to detect different types of machine faults reliably at an early stage requires the development of improved signal processing methods. Vibration measurements provide a good basis for condition monitoring. In some cases the simple calculation of root-mean-square and peak values obtained from vibration signals are useful features for detecting various faults. Unbalance, misalignment, bent shaft, mechanical looseness and some electrical faults, for example, can be detected using features of displacement and velocity. Higher order derivatives provide additional possibilities for detecting faults that introduce high-frequency vibrations or impacts. New generalised moments and norms related to lp space have been used for diagnosing faults in a roller contact on a rough surface. This paper extends the field of possible applications from roller bearing fault detection to more complex faults situations where different kinds of fault occur simultaneously. In consequence, feature calculation and signal processing have to be adopted and optimized for each fault type on the basis of one measured signal. The features of x(4) indicate well the intact case and the outer race fault. Velocity x(1) is needed for detecting unbalance. This approach also works for the combined case, outer race fault and unbalance. Derivation reduced the effect of noise by amplifying higher frequency components from bearing faults more than the added noise components.
Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. Rapid changes in acceleration become emphasised upon the derivation of the signal x(2). The aim is to detect faults at an early stage by using the absolute values of the dynamic part of the signals. Generalised norms ‖τMαp‖p can be defined by the order of derivation (α), the order of the norm (p) and sample time (τ), where α and p are real numbers. These norms have the same dimensions as the corresponding signals. A need for maintenance is indicated for lime kilns, which are essential parts of the chemical recovery cycle in a pulp mill. These large machines with very slow rotational speeds must run at different production capacities and speeds. The generalised norms provide an efficient indication of faulty situations in the supporting rolls. Surface damage and alignment problems are clearly detected and in the present system also identified with two norms of different order obtained from the signals x(4). An early indication of friction increase is also achieved. The data set covers the following cases: (1) surface problems, (2) good conditions after grinding, (3) misalignment, (4) stronger misalignment, (5) very good conditions after repair work, and (6) very good conditions one year later. Maintenance was done for one of the supporting rolls. All the rolls can be analysed using the same features throughout the data set. All the faults, friction and minor fluctuations were validated by listening to the recorded acceleration signals and analysing time domain signals and frequency spectra with an oscilloscope and a real time analyser.
Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. Root-mean-square and peak values obtained from vibration signals are useful features for detecting various faults. Unbalance, misalignment, bent shaft, mechanical looseness and some electrical faults, for example, can be detected using features of displacement and velocity. Higher order derivatives provide additional possibilities for detecting faults that introduce highfrequency vibrations or impacts. Real order derivatives increase the number of signal alternatives. New generalised moments and norms related to lp space with short sample times and relatively small requirements for the upper cut-off frequency are feasible approaches for on-line cavitation analysis and power control. In a lime kiln, features were generated from the distribution of the signals x(3) and x(4). Standard deviations of the signal x(4) in three frequency ranges were used in a very fast rotating centrifuge. The nonlinear scaling used in the linguistic equation (LE) approach extends the idea of dimensionless indices to nonlinear systems. In some cases, a single feature provides a good solution, and several features can be combined by means of linear equations. Other measurements, e.g. temperature and pressure, are scaled with similar nonlinear functions as the vibration features. Case-based reasoning (CBR) is used when there are many fault alternatives. Health indices can be formed from condition indices by means of the weighted average. The health index and its inverse, called the measurement index, are good indicators for the need of maintenance.
Advanced signal processing methods combined with automatic fault detection enable reliable condition monitoring for long periods of continuous operation. The signals x(3) and x(4) are very suitable for the condition monitoring of slowly rotating bearings since rapid changes in acceleration become emphasised upon the differentiation of the signal x(2). Real order derivatives x(α) provide additional possibilities, e.g. in a bearing fault case the sensitivities of some features have been found to reach a maximum when α = 4.75. In earlier cavitation indicators, the rms values were combined with either kurtosis or peak values. Generalised moments τMαp can be defined by the order of derivation (α), the order of the moment (p) and sample time (τ). The moment normalised by standard deviation can be used as kurtosis in the model-based analysis.
This paper introduces a new norm ‖τMαp‖p = (τMαp)1/p = [1/NΣi=1N|xi(α)|p]1/p, where the orders α and p are real numbers. The number of signal values s N =τ N where Ns is the number of samples per second. The new norm has the same dimensions as the corresponding signals x(α ) . The cavitation of a Kaplan water turbine was analysed in the power range 1.5…59.4 MW based on measurements collected with sampling frequency 12800 Hz. The order p was compared in the range from 0.25 to 8 with a step 0.25, and a total of 11 sample times were used: τ = 1, 2,…, 6, 8, 10, 20, 30, and 40 seconds. An optimum order p was detected for each sample time τ. The relative max(‖3^M_4^2.75‖) compared to a cavitation-free case is alone a good indicator for cavitation: strong cavitation and cavitation-free cases are clearly detected, and the power ranges for shortterm cavitation are only slightly wider than in the previously developed knowledge-based cavitation index. Short sample times and relatively small requirements for the frequency ranges make this approach feasible for on-line analysis and power control. The weighted sums of features on a different order of derivation form fault-specific measurement indices MIT, and several indices MIT define the health index SOL. The sensitivity increases with the order of derivation to some limit of α. For faults causing impacts, high MIT values for lower orders of derivation indicate an increase in the severity of the fault.
Data domain description concerns the characterization of a data set. A good description covers all target data but includes no superfluous space. The boundary of a dataset can be used to detect novel data or outliers. We will present the Support Vector Data Description (SVDD) which is inspired by the Support Vector Classifier. It obtains a spherically shaped boundary around a dataset and analogous to the Support Vector Classifier it can be made flexible by using other kernel functions. The method is made robust against outliers in the training set and is capable of tightening the description by using negative examples. We show characteristics of the Support Vector Data Descriptions using artificial and real data.
In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a feature subset selection method should consider how the algorithm and the training set interact. We explore the relation between optimal feature subset selection and relevance. Our wrapper method searches for an optimal feature subset tailored to a particular algorithm and a domain. We study the strengths and weaknesses of the wrapper approach and show a series of improved designs. We compare the wrapper approach to induction without feature subset selection and to Relief, a filter approach to feature subset selection. Significant improvement in accuracy is achieved for some datasets for the two families of induction algorithms used: decision trees and Naive-Bayes.
If a simple and fast solution for one-class classification is required, the most common approach is to assume a Gaussian distribution
for the patterns of the single class. Bayesian classification then leads to a simple template matching. In this paper we show
for two very different applications that the classification performance can be improved significantly if a more uniform subgaussian
instead of a Gaussian class distribution is assumed. One application is face detection, the other is the detection of transcription
factor binding sites on a genome. As for the Gaussian, the distance from a template, i.e., the distribution center, determines
a pattern’s class assignment. However, depending on the distribution assumed, maximum likelihood learning leads to different
templates from the training data. These new templates lead to significant improvements of the classification performance.
Feature selection is applied to reduce the number of features in many applications where data has hundreds or thousands of features. Existing feature selection methods mainly focus on finding relevant features. In this paper, we show that feature relevance alone is insufficient for efficient feature selection of high-dimensional data. We define feature redundancy and propose to perform explicit redundancy analysis in feature selection. A new framework is introduced that decouples relevance analysis and redundancy analysis. We develop a correlation-based method for relevance and redundancy analysis, and conduct an empirical study of its efficiency and effectiveness comparing with representative methods.
The main focus of this paper is given to the detection of different fault types in the inner or outer race of roller bearing. The first group covers faults with an extension beyond the spacing between two rolling elements. In these cases some of the classical methods like envelop techniques could fail. We show that the vibration structure generated by a rough surface differs from a normal state even if the signal energy is eliminated by normalisation of the data. Suitable time domain features are a mathematical description of the shape of selected time domain peaks, which could easily be calculated by the higher derivatives of the time acceleration signal and some parameters characterizing the randomness of the peak positions. After the step of extracting 30 features from the time signal a feature selection process is executed automatically. This enables the selection of a feature subset which is best suited to the present fault situation. As a second group we start investigations for the early detection of very small bearing damages like false brinelling faults, which occur in the presence of a small relative motion between the rollers and raceways during non-rotation times. This leads to a damage which is characterized by elliptical wear marks in the axial direction at each roller position. Some test rig results indicate the high potential of the new time domain features for both fault types.
We study an interesting and challenging problem, online streaming feature selection, in which the size of the feature set is unknown, and not all features are available for learning while leaving the number of observations constant. In this problem, the candidate features arrive one at a time, and the learner's task is to select a “best so far ” set of features from streaming features. Standard feature selection methods cannot perform well in this scenario. Thus, we present a novel framework based on feature relevance. Under this framework, a promising alternative method, Online Streaming Feature Selection (OSFS), is presented to online select strongly relevant and non-redundant features. In addition to OSFS, a faster Fast-OSFS algorithm is proposed to further improve the selection efficiency. Experimental results show that our algorithms achieve more compactness and better accuracy than existing streaming feature selection algorithms on various datasets. 1.
DDtools, the Data Description Toolbox for Matlab
- D M J Tax
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Feature selection methods -an application oriented overview
- J Strackeljan
J Strackeljan, 'Feature selection methods -an application oriented overview',
TOOLMET'01 Symposium, Oulu, Finland, pp 29-49, 2001.
Evolutionäre Algorithmen -Verfahren, Operatoren, Hinweise aus der Praxis
- H Pohlheim
H Pohlheim, 'Evolutionäre Algorithmen -Verfahren, Operatoren, Hinweise aus der
Praxis', Berlin, Heidelberg, New York: Springer-Verlag, 1999.