Statistical methods for processing, modeling, and time series analysis in application to technical diagnostics

From three years scientists form Faculty of Fundamental Problems at Wroclaw University of Technology (WrUT), Poland, and engineers from Faculty of Geoengineering, Mining and Geology WrUT are cooperating in the area of application of mathematical methods to technical diagnostics.

These studies can be divided into four major groups. The first one is the study of local damage detection of mining machines. The exemplary machine, called copper ore crusher, we present in Fig. 1.


Fig.1. A crusher – general view (note bearings with yellow housing).

This issue has been studied for many years in various contexts and in the literature one can find unconventional methods that allow for damage detection in machines for which the signals are very complex and for which classical methods do not give the expected results. In this research we are trying to prove that using the statistical properties of the analyzed signals we can detect damages in mining machines even in presence of a high level of noise with different nature. Basis is the decomposition and then adaptation of known methods and developing new ones. Novel methods developed for damage detection are based on the fact that for the sub-signals obtained for healthy machines the probability distribution is close to the Gaussian distribution, whereas in the case of damaged machine this property is not satisfied. On the basis of this feature we have proposed several measures of impulsiveness on the basis of which it was possible to detect damages also for such signals, for which the classical method based on kurtosis (in particular spectral) did not give the expected results. The measures we called selectors because they select the informative frequency bands. They are based on the statistics used for testing whether the analyzed data come from the Gaussian distribution. Another property of the sub-signals of analyzed machines is the fact that for the sub-signals in damaged machines we observe so-called local maxima that are related to wideband excitations (corresponding to impulses in the time domain). On the basis of this we have constructed a new selector and an enhanced time-frequency map. On the basis of these selectors it was possible to determine the informative frequency bands of given signals. These selectors also make it possible to signal filtering, after adapting filtration method using spectral kurtosis.

The second group of the studies is based on application of time series methods to modeling of vibration signals in varying operating conditions. In this case the signals are amplitude and frequency modulated and have no constant structure of the spectrum, and therefore classical models (like ARMA) cannot be applied here. In the study we were focused primarily on the ARMA models, for which the coefficients are time-varying. Such systems are an extension of the classical ARMA models (with constant coefficients), which were used to model the vibration of machines working in constant operation conditions. Particular attention is devoted to ARMA models, in which the coefficients are periodic (so-called PARMA models). We have shown that such models reflect the character of the analyzed vibration signals observed, for example, in the driving system for bucket wheels of bucket wheel excavator, see Fig. 2.


Fig.2. Bucket wheel excavator.

In addition, based on the inverse filters of these models it was possible to detect damages on the basis the models’ residuals.

The next area of the  interest is the modeling distributions of diagnostic features for determining the decision thresholds. To describe the distribution of such features it is proposed here to use other than Gaussian distributions. The reason for this is that the mentioned distributions in a better way reflect the nature of the analyzed data. Such distributions are for example Pareto or Weibull. On the basis of estimated parameters of these distributions for the diagnostic features and characteristics of the speed it was possible to determine the decision thresholds that allow to classify the condition of given machine. In this area we have proposed to use also another distribution, the alpha-stable, which perfectly reflects the nature of the different physical phenomena, including those related to diagnostic machines.

The last group of the studies in the context of technical diagnostics is related to the signal segmentation for operating conditions detection of machine. We have proposed here two methods based on statistical properties of the signal, which allow to segmentation of data describing the machines speed. In addition, we have proposed a test for testing if in given signal some statistical properties change. Such behavior with different regimes we observe in fluctuations in relative speed. In addition, we have also analyzed the problem of data description in which there are visible the so-called “traps”, i.e. the intervals at which the signal remains at the same level. Such behavior we observe also for example in speed when the engine is in the idle mode.

The main objectives of the common research in the field of technical diagnosis are:

  1. to show that the statistical and stochastic methods can be applied to adapt the methods previously used in the analysis of vibration signals,
  2. to demonstrate that the proposed frequency band selection criteria have very good properties and can be an alternative to the widely used spectral kurtosis, and in some cases they give better results,
  3. to show that the classical time series models are inadequate to describe the signals for machines working in nonstationary operating conditions therefore it is necessary to propose more advanced models,
  4. to indicate that the commonly used Gaussian distribution is insufficient to describe the data related to the mining machines, therefore it is necessary to use other distributions,
  5. to determine the methods of signal segmentation for detection the state of the machine by using its statistical properties.


  1. Zimroz Radoslaw, Obuchowski Jakub, Wylomanska Agnieszka: Vibration analysis of copper ore crushers used in mineral processing plant – problem of bearings damage detection in presence of heavy impulsive noise , Applied Condition Monitoring. Advances in Condition Monitoring of Machinery in Non-Stationary Operations (Chaari et al. ed.), 57-70, 2015
  2. Wylomanska Agnieszka, Zimroz Radosław, Janczura Joanna: Identification and stochastic modelling of sources in copper ore crusher vibrations, Journal of Physics: Conference Series 628 (2015) 012125, 2015
  3. Obuchowski Jakub, Zimroz Radoslaw, Wylomanska Agnieszka: Identification of cyclic components in presence of non-Gaussian noise – application to crusher bearings damage detection, JVE INTERNATIONAL LTD. JOURNAL OF VIBROENGINEERING 17, 1242-1252, 2015
  4. Wyłomańska Agnieszka, Obuchowski Jakub, Zimroz Radosław, Hurd Harry: Influence of different signal characteristics to PAR model stability, Applied Condition Monitoring. Cyclostationarity: Theory and Methods – II (Chaari et al. ed.), 89-104, 2015
  5. Wyłomańska Agnieszka, Zimroz Radosław: The Analysis of Stochastic Signal from LHD Mining Machine, Stochastic Models, Statistics and Their Applications Springer Proceedings in Mathematics & Statistics Volume 122, 469-478, 2015
  6. Stefaniak Paweł, Wyłomańska Agnieszka, Obuchowski Jakub, Zimroz Radosław: Procedures for decision thresholds finding in maintenance management of belt conveyor system – statistical modeling of diagnostic data, in: Lecture Notes in Production Engineering, Christian Niemann-Delius ed., 391-402, Springer, 2015
  7. Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Two-stage data driven filtering for local damage detection in presence of time varying signal to noise ratio, Vibration Engineering and Technology of Machinery Mechanisms and Machine Science Volume 23, 401-410, 2015
  8. Zak Grzegorz, Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radoslaw: Application of ARMA modelling and alpha-stable distribution for local damage detection in bearings, Diagnostyka 15(3), 3-11, 2014
  9. Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Recent developments in vibration based diagnostics of gear and bearings used in belt conveyors, Applied Mechanics and Materials 683, 171-176, 2014
  10. Obuchowski Jakub, Wyłomańska Agnieszka, Zimroz Radosław: Selection of informative frequency band in local damage detection in rotating machinery, Mechanical Systems and Signal Processing 48, 138–152, 2014

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Contact person:

Agnieszka Wylomanska (Wroclaw University of Technology, Poland)