Stable Distributions and Fractal Diagnostic Models of Vibration Signals of Rotating Systems

Puchalski, Andrzej; Komorska, Iwona

doi:10.1007/978-3-319-61927-9_9

Cited by 10 publications

(8 citation statements)

References 15 publications

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“…Another approach to the problem of estimating local scaling exponents as a method of studying the regularity of time series and their multifractality is related to the multifractal detrended fluctuation analysis (MF-DFA) method. MF-DFA enables to study the observed signals in terms of their multifractality, provides a more stable approach to multifractal formalism than the WTMM method [31,36,[45][46][47].…”

Section: Multifractal Formalismmentioning

confidence: 99%

Rotating Machinery Diagnosing in Non-Stationary Conditions with Empirical Mode Decomposition-Based Wavelet Leaders Multifractal Spectra

Komorska

Puchalski

2021

Sensors

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Diagnosing the condition of rotating machines by non-invasive methods is based on the analysis of dynamic signals from sensors mounted on the machine—such as vibration, velocity, or acceleration sensors; torque meters; force sensors; pressure sensors; etc. The article presents a new method combining the empirical mode decomposition algorithm with wavelet leader multifractal formalism applied to diagnosing damages of rotating machines in non-stationary conditions. The development of damage causes an increase in the level of multifractality of the signal. The multifractal spectrum obtained as a result of the algorithm changes its shape. Diagnosis is based on the classification of the features of this spectrum. The method is effective in relation to faults causing impulse responses in the dynamic signal registered by the sensors. The method has been illustrated with examples of vibration signals of rotating machines recorded on a laboratory stand, as well as on real objects.

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Section: Multifractal Formalismmentioning

confidence: 99%

Rotating Machinery Diagnosing in Non-Stationary Conditions with Empirical Mode Decomposition-Based Wavelet Leaders Multifractal Spectra

Komorska

Puchalski

2021

Sensors

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“…Other interesting applications include: physics [18][19][20][21][22], and biology [23][24][25][26][27]. The segmentation problems appear also in condition monitoring [28][29][30][31][32].…”

Section: Introductionmentioning

confidence: 99%

“…Interesting approaches used for the problem related to the changing of the location parameter (like mean) can be found in [33][34][35][36][37][38][39][40] while the methods for changing the scale parameter (like variance) are presented, for instance, in [33,[41][42][43][44][45][46][47][48]. A specific case is related to heavy-tailed processes [28][29][30][31] where we expect the impulsive behavior of the corresponding data. In that case, the simple statistics are useless.…”

Section: Introductionmentioning

confidence: 99%

Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

Grzesiek

Gąsior

Wyłomańska

et al. 2021

Sensors

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Many real-world systems change their parameters during the operation. Thus, before the analysis of the data, there is a need to divide the raw signal into parts that can be considered as homogeneous segments. In this paper, we propose a segmentation procedure that can be applied for the signal with time-varying characteristics. Moreover, we assume that the examined signal exhibits impulsive behavior, thus it corresponds to the so-called heavy-tailed class of distributions. Due to the specific behavior of the data, classical algorithms known from the literature cannot be used directly in the segmentation procedure. In the considered case, the transition between parts corresponding to homogeneous segments is smooth and non-linear. This causes that the segmentation algorithm is more complex than in the classical case. We propose to apply the divergence measures that are based on the distance between the probability density functions for the two examined distributions. The novel segmentation algorithm is applied to real acoustic signals acquired during coffee grinding. Justification of the methodology has been performed experimentally and using Monte-Carlo simulations for data from the model with heavy-tailed distribution (here the stable distribution) with time-varying parameters. Although the methodology is demonstrated for a specific case, it can be extended to any process with time-changing characteristics.

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“…As a result, the BCM and feature extraction methods, employing α-SPDF into current-based signals is practically absent in the literature. However, the non-Gaussian parameters for the α-SPDF may fully represent the healthy and the bearing damaged behavior for current-based signals, which have dense and elongated tails (Puchalski and Komorska, 2018).…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, this study fit the α-SPDF into current-based distributions to extract non-Gaussian parameters. Furthermore, this paper introduces a change of coordinates in time domain, creating orbits to extract the fractal dimension (FD), which is a measure for the capacity to cover a multidimensional space (Puchalski and Komorska, 2018).…”

Section: Introductionmentioning

confidence: 99%

A New Approach for Bearing Condition Monitoring and Damage Detection Using Machine Learning Algorithms

Barcelos

Mazzoni

Cardoso

2021

Procedings Do XV Simpósio Brasileiro De Automação Inteligente

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Bearing condition monitoring (BCM) and damage identification are usually performed by vibration-based signals and supervised learning algorithms. However, this approach is impractical in many industrial facilities because some industrial motors are unable to provide access to vibration-based signals or they are prevented from performing their functions under damaged conditions. In this context, this work employs a density-based and fractal approach to extract features from current-based signals. These features create an unlabelled database that feeds a fuzzy c-means algorithm to perform BCM and the support vector machines to classify bearing damages in an unsupervised learning approach. Tests with several bearing damages under various load and speed conditions are reported, presenting promising results.

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Stable Distributions and Fractal Diagnostic Models of Vibration Signals of Rotating Systems

Cited by 10 publications

References 15 publications

Rotating Machinery Diagnosing in Non-Stationary Conditions with Empirical Mode Decomposition-Based Wavelet Leaders Multifractal Spectra

Rotating Machinery Diagnosing in Non-Stationary Conditions with Empirical Mode Decomposition-Based Wavelet Leaders Multifractal Spectra

Divergence-Based Segmentation Algorithm for Heavy-Tailed Acoustic Signals with Time-Varying Characteristics

A New Approach for Bearing Condition Monitoring and Damage Detection Using Machine Learning Algorithms

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