Kernel PCA in nonlinear visualization of a healthy and a faulty planetary gearbox data

PCA (Principal Component Analysis) is a powerful method for investigating the dimensionality and extracting structure from multi-dimensional data, however it extracts only linear projections. More general projections – accounting for possible non-linearities among the observed variables – can be obtained using kPCA (Kernel PCA), that performs the same task, however working with an extended feature set. We consider planetary gearbox data given as two 15-dimensional data sets, one coming from a healthy and the other from a faulty planetary gearbox. For these data both the PCA (with 15 variables) and the kPCA (using indirectly 500 variables) is carried out. It appears that the investigated PC-s are to some extent similar; however, the first three kernel PC-s show the data structure with more details

Filtering procedure for local damage detection in gearbox using alpha stable modeling

In the paper a procedure for enhancement of noisy vibration signal for local damage detection is presented. The developed method is based on α-stable distribution approach. This distribution belongs to the rich class of heavy tailed family and was used in different applications. The proposed methodology covers decomposition of the signal via time-frequency spectrogram into set of narrowband sub-signals and estimation of stability parameter under the assumption that sub-signals constitute samples from α-stable distribution. As a result of sub-signals modelling, we obtain distribution of α parameter vs. frequencies that is analogy to spectral kurtosis approach well known in the literature. Such characteristic is basis for filter design used for raw signal enhancement. To evaluate efficiency of our method we compare raw and filtered signal in time, time-frequency and frequency (envelope spectrum) domains. The presented methodology we applied to real vibration signal from two stage heavy duty gearbox used in mining industry

Data-driven vibration signal filtering procedure based on the α-stable distribution

A novel procedure for data-driven enhancement of informative signal is presented in this paper. The introduced methodology covers decomposition of the signal via time-frequency spectrogram into set of narrowband sub-signals. Furthermore, each of the sub-signals is considered as a sample of independent identically distributed random variables and we model the distribution of the sample, in contrast to the classical methodology where the simple statistics, for example kurtosis, for each sub-signal was calculated. This approach provides a new perspective in the signal processing techniques for local damage detection. Using our methodology one can eliminate potential risk related to high sensitivity towards single outlier. In the proposed procedure we model each sub-signal in time-frequency representation by α-stable distribution. This distribution is a generalization of standard Gaussian one and allows us for modeling sub-signals related to both informative and non-informative frequencies. As a result, we obtain distribution of stability parameter vs. frequencies that is analogy to spectral kurtosis approach well known in the literature. Such characteristic is basis for filter design used for raw signal enhancement. To evaluate efficiency of our method we compare raw and filtered signal in time, time-frequency and frequency (envelope spectrum) domains. Moreover, we present comparison to the spectral kurtosis approach. The presented methodology we applied to simulated signal and real vibration signal from two stage heavy duty gearbox used in mining industry

Application of alpha-stable distribution approach for local damage detection in rotating machines

In this paper a novel method for informative frequency band selection for local damage detection is presented. Local damage in bearings/gearbox provides specific vibration signature, i.e. train of impulses with cycle related to fault frequency. The proposed approach is based on the α-stable distribution, which is an extension of the Gaussian one. The choice of this distribution is motivated by its superiority towards other distributions when modeling impulsive data. We introduce here the new selector (to select informative frequency band) which is based on the stability parameter α. Moreover we propose also the new time-frequency maps based on the measures of dependence adequate for α-stable distribution, namely autocodifference and autocovariation maps. The introduced methodology is illustrated by analysis of simulated and real vibration signals from heavy-duty rotating machinery. The results prove that proposed approach allows detection of multiple damages in signal and location of informative frequency band related to these damages. Moreover the analyzed examples indicate the α-stable distribution approach for some cases can give better results in contrast to the classical methodology based on the spectral kurtosis

Seismic multiple events – a study on signals’ separation

In this paper we investigate an issue of multiple seismic events. Such events might occur in the case of both natural and mine-induced seismicity. In this paper we investigate an issue whether the distances between two overlapping impulses can be derived from a noisy seismic vibration measurement if the impulses are not equally spaced in time. Such distances might be therefore used for localization of the events or even for detection if more than one event occurred. The methodology is based on minimum entropy deconvolution (MED) and automatic peak finding. Simulated data analysis are performed in order to examine MED with different distances between events. Moreover, comprehensive simulated data analysis provide recommendations regarding MED filter size

Advances in Machine Condition Monitoring and Fault Diagnosis

In the past few decades, with the great progress made in the field of computer technology, non-destructive testing, signal and image processing, and artificial intelligence, machine condition monitoring and fault diagnosis technology have also achieved great technological progress and played an active and important role in various industries to ensure the efficient and reliable operation of machines, lower the operation and maintenance costs, and improve the reliability and availability of large critical equipment [...

Bearings damage detection in presence of heavy non-Gaussian noise via cyclo-stationary analysis

A problem of rolling element bearings diagnostics is discussed in the paper. In the classical approach, time domain detectors (e.g. kurtosis) or frequency domain representation (envelope spectrum analysis) are used to identify a damage in bearings. However, in our case, the machine (copper ore crusher) produces randomly spaced in time heavy impulsive disturbances related to normal operation of the machine. It eliminates completely possibility of detection of damage in time domain or using analysis of the envelope spectrum of the raw vibration signal. It is well known that effectiveness of envelope analysis might be significantly improved if the signal is pre-processed before enveloping. Unfortunately, again, almost all known criteria based on maximization of impulsiveness of signal in time domain fail in this case. In the paper we propose to incorporate cyclostationarity instead of impulsiveness, namely we propose to perform the spectral coherence density analysis

Identification of cyclic components in presence of non-Gaussian noise – application to crusher bearings damage detection

In this paper an issue of local damage detection in a rolling element bearing is discussed. The bearing operates in a hummer crusher, thus the vibration signal acquired on the housing contains a lot of impacts that originate in various sources. In the case of local damage detection it is crucial to find a set of cyclic impulses in the signal. These impulses are informative, in spite of impulses related to the crushing process, which are non-informative. In order to find the damage signature we provide feasibility study on a tool based on cyclostationary approach, namely cyclic spectral coherence. This comprehensive analysis includes study on four different signals from bearings in various condition and operating with or without load applied. This analysis is preceded by motivating preliminary analysis where we examine a few widely-used methods for local damage detection

Informative frequency band identification for automatic extraction of impulsive components in vibration data from rotating machinery

In this paper authors address the issue of local damage detection in rolling element bearings in the presence of non-Gaussian noise. Typically damage detection problems concern the techniques of filtration, decomposition, separation, extraction etc. In such real-life cases, main difficulty lies in non-Gausianity of the noise present in the operational environment, hence popular denoising techniques cannot be used. In presented article, a real-life industrial scenario will be discussed and a new approach to cyclic component extraction will be presented. Classical detection methods are often not sufficient for the task because of high energy of impulsive noise in comparison to spectral structure of the damage. Proposed method utilizes Cyclic Spectral Coherence map as two-dimensional data representation, and Nonnegative Matrix Factorization as analytical tool to extract individual components