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

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

Seismic signal segmentation procedure using time-frequency decomposition and statistical modelling

In the paper a novel automatic seismic signal segmentation procedure is proposed. This procedure is motivated by analysis of real seismic vibration signals acquired in an underground mine. During regular mining activities in the underground mine one can expect some seismic events which appear just after the mining activity, e.g. blasting procedures, provoked relaxation of rock and some events that are unexpected, like natural rock burst. It often happens that, during one signal realization, several shocks (events) appear. Apart from two main sources of events (i.e. rock burst and blasting), other activities in the mine might also initiate seismic signal recording procedure (for example machine moving nearby the sensor). Obviously, significance of each type of recorded signal is very different, its shape in time domain, energy and frequency structure (i.e. spectrum of the signal) are different. In order to recognize these events automatically, recorded observation should be pre-processed in order to isolate a single event. The problem of signal segmentation is investigated in literature, several application domains might be found. Although, there are just a few works on seismic signal segmentation. In this paper we propose to use a time-frequency decomposition of the signal and model each sub-signal at every frequency bin using statistical methods. Narrowband components are much easier to search for so called structural breakpoint, i.e. time instance when properties of signal significantly change. It is obvious that simple energy-based methods applied to raw signal fail when one event begins before the previous one relaxed. In order to find beginning and end of a single event we propose to use measures based on empirical quantiles estimated for each sub-signal and, finally, aggregate 2D array into 1D probability vector which indicates location where statistical features has switched from one regime to another one. The proposed procedure can be applied in order to improve time domain isolation of single event for the case, when duration of signal acquisition is longer than duration of the event or to isolate single event from sequence of events (recorded for example during blasting)

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

Segmentation algorithm of roadheader vibration signal based on the stable distribution parameters

In the real signal analysis the main problem is the non-stationarity of given data. The non-stationarity can be manifested in different ways. One of the possibility is the assumption that the signal is a mixture of different processes that exhibit different statistical properties. Thus before the further analysis the observed data should be segmented. In this paper we propose an automatic segmentation method which is based on α-stable distribution approach. In the proposed procedure we estimate the parameters of stable distribution for consecutive sub-signals of given length and then by using expectation-maximization algorithm we classify the parameters. The obtained classes correspond to different segments of the signal. The proposed procedure we apply to the real vibration signal from roadheader working in mining industry. As a final result we obtained segments of real signal which constitute samples of different behaviors and are related to different modes of operation of the machine

Combination of ICA and time-frequency representations of multichannel vibration data for gearbox fault detection

In the paper a multichannel vibration data processing method is presented in the context of local damage detection in gearboxes. The purpose of the approach is to obtain more reliable information about local damage when using several channels in comparison to results obtained for single channel vibration. The method is a combination of time-frequency representation and Independent Component Analysis (ICA) but applied not to raw time series but to each slice (along to time) from spectrogram. Finally we create new time-frequency map, that after aggregation clearly indicates presence of damage. In the paper we will present details of the method and benefits of using our procedure. We will refer to autocorrelation function of mentioned aggregated new time frequency map (1D signal) or simple spectrum (that might be somehow linked to classical envelope analysis). We believe that results are very convincing – detection of cyclic impulses associated to local damage are clearly identifiable. To validate our method we use real vibration data from heavy duty gearbox used in mining industry

Seismic signals discrimination based on instantaneous frequency

In this paper a problem of seismic vibration signals discrimination and clustering is investigated. We propose two criteria based on instantaneous frequency (IF) of the seismic signal. IF of a raw multicomponent signal is meaningless and a decomposition must be performed in order to obtain a monocomponent signal. One of the possible solutions incorporates the Hilbert-Huang transform. It is based on Empirical Mode Decomposition (EMD) algorithm. It is a data-driven procedure which calculates so called Intrinsic Mode Functions (IMFs) and a Residuum, which added all together give the raw signal. One of the proposed criteria quantifies distribution of the IF through the signal and provide limited information about volatility of IF throughout the entire signal (for a given monocomponent). The second criterion gives information about the most frequently occurring instantaneous frequency in the considered monocomponent. Usefulness of IF in discrimination of seismic vibration signals is validated by using considered criteria for clustering of seismic signals

Informative frequency band identification method using bi-frequency map clustering for fault detection in rotating machines

In presented work the problem of local damage detection in rolling element bearings is addressed. Usually such issues require the usage of the techniques of decomposition, separation etc. In such real industrial cases main difficulty lies in relatively low signal-to-noise ratio as well as unpredictable distribution of damage-related information in the frequency domain, hence the typical methods cannot be used. In this paper such industrial scenario is addressed and a simple yet effective approach to underlying component extraction will be discussed. Proposed method analyzes Cyclic Spectral Coherence map as starting data representation, and Expectation-Maximization is used as analytical tool to determine the informative frequency band (IFB) for impulsive component localization in the carrier frequency spectrum. Finally, based on identified IFB, the bandpass filter is constructed to extract the impulsive component from the input signal