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

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

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

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

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

A new segmentation method of roadheader signal based on the statistical analysis of waiting times

Non-stationarity in time series data is one of the most important challenges in signal processing nowadays. One of the most often cases occurs when signal is a mixture of different processes that reveal different statistical properties. Common way to deal with is the data segmentation. In the following paper we propose an automatic segmentation procedure based on gamma distribution approach. In the algorithm we estimate the parameters of gamma distribution for subsequent batches of distance values between consecutive impulses (waiting times). Then we use Expectation-Maximization algorithm to classify estimated parameters. Obtained classes refer to particular signal segments. Procedure has been applied to real vibration signal from roadheader working in underground mining industry

Measures of Dependence for α

Local damage detection in rotating machinery is simply searching for cyclic impulsive signal in noisy observation. Such raw signal is mixture of various components with specific properties (deterministic, random, cyclic, impulsive, etc.). The problem appears when the investigated process is based on one of the heavy-tailed distributions. In this case the classical measure can not be considered. Therefore, alternative measures of dependence adequate for such processes should be considered. In this paper we examine the structure of dependence of alpha-stable based systems expressed by means of two measures, namely, codifference and covariation. The reason for using alpha-stable distribution is simple and intuitive: signal of interest is impulsive so its distribution is heavy-tailed. The main goal is to introduce a new technique for estimation of covariation. Due to the complex nature of such vibration signals applying novel methods instead of classical ones is recommended. Classical algorithms usually are based on the assumption that theoretical second moment is finite, which is not true in case of the data acquired on the faulty components. Main advantage of our proposed algorithm is independence from second moment assumption

Time-varying group delay as a basis for clustering and segmentation of seismic signals

In this paper the applications of group delay in seismic vibration signals analysis are discussed. A method which bases on the autoregressive model with sliding-window is used to track volatility of signal’s properties in time. The analysis of time-frequency maps of group delay can be used in a process of distinguishing signals of different characteristics. Moreover, the method is robust for the different parameters of the sliding-window AR model. In the article applications of the time-frequency maps of group delay in a signal segmentation and clustering are also discussed. In seismic analysis an ability to distinguish signals with different seismic nature is very important, especially in case of safety in copper-ore underground mines. Creation of tools for revealing the origin of vibration will have positive impact on evaluation of hazard level

Assessment of background noise properties in time and time-frequency domains in the context of vibration-based local damage detection in real environment

Any measurement in condition monitoring applications is associated with disturbing noise. Till now, most of the diagnostic procedures have assumed the Gaussian distribution for the noise. This paper shares a novel perspective to the problem of local damage detection. The acquired vector of observations is considered as an additive mixture of signal of interest (SOI) and noise with strongly non-Gaussian, heavy-tailed properties, that masks the SOI. The distribution properties of the background noise influence the selection of tools used for the signal analysis, particularly for local damage detection. Thus, it is extremely important to recognize and identify possible non-Gaussian behavior of the noise. The problem considered here is more general than the classical goodness-of-fit testing. The paper highlights the important role of variance, as most of the methods for signal analysis are based on the assumption of the finite-variance distribution of the underlying signal. The finite variance assumption is crucial but implicit to most indicators used in condition monitoring, (such as the root-mean-square value, the power spectral density, the kurtosis, the spectral correlation, etc.), in view that infinite variance implies moments higher than 2 are also infinite. The problem is demonstrated based on three popular types of non-Gaussian distributions observed for real vibration signals. We demonstrate how the properties of noise distribution in the time domain may change by its transformations to the time-frequency domain (spectrogram). Additionally, we propose a procedure to check the presence of the infinite-variance of the background noise. Our investigations are illustrated using simulation studies and real vibration signals from various machines