A generalised entropy in multifractal time signals analysis of mechanical vibration

Puchalski, Andrzej; Komorska, Iwona

doi:10.21595/jve.2018.18871

Cited by 4 publications

(3 citation statements)

References 16 publications

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“…One of more frequently used nonlinear methods is the study of point regularity of time series, represented by the Holder scaling exponent. The estimation of scaling exponents leads to determination of a multifractal spectrum, which is a statistical model of the monitored signal [2]. This fact was used to determine the diagnostic features of the test gear being tested and to identify assembly errors and wear.…”

Section: Introductionmentioning

confidence: 99%

Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods

Puchalski¹,

Komorska²

2019

MATEC Web Conf.

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Data-driven diagnostic methods allow to obtain a statistical model of time series and to identify deviations of recorded data from the pattern of the monitored system. Statistical analysis of time series of mechanical vibrations creates a new quality in the monitoring of rotating machines. Most real vibration signals exhibit nonlinear properties well described by scaling exponents. Multifractal analysis, which relies mainly on assessing local singularity exponents, has become a popular tool for statistical analysis of empirical data. There are many methods to study time series in terms of their fractality. Comparing computational complexity, a wavelet leaders algorithm was chosen. Using Wavelet Leaders Multifractal Formalism, multifractal parameters were estimated, taking them as diagnostic features in the pattern recognition procedure, using machine learning methods. The classification was performed using neural network, k-nearest neighbours’ algorithm and support vector machine. The article presents the results of vibration acceleration tests in a demonstration transmission system that allows simulations of assembly errors and teeth wear.

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Section: Introductionmentioning

confidence: 99%

Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods

Puchalski¹,

Komorska²

2019

MATEC Web Conf.

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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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“…Fractal dimension (FD) provides a robust computational tool to measure the irregularity of the set and track spike variation in the signal structure (Falconer, 1997; Orbach, 1986). It can directly extract the morphological characteristics of fault components from the original signal (Puchalski and Komorska, 2018), without prefiltering or preprocessing (Raghavendra and Dutt, 2010; Shi and Liang, 2015). We propose a FD means that helps to transform the nonstationary stochastic time series into short quasi-stationary segments (fault components are purely deterministic, and noise interference is stochastic).…”

Section: Introductionmentioning

confidence: 99%

On multi-fault detection of rolling bearing through probabilistic principal component analysis denoising and Higuchi fractal dimension transformation

Yang

Xiang

Jiang

2021

Journal of Vibration and Control

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Bearing multi-fault detection from stochastic vibration signal is still a thorny task to dispose of because of the complex interplay between different fault components under severe noise interference. In such case, conventional techniques such as filter processing and envelope demodulation may cause undesired results. To overcome the limitation, this article explores a filtering-free technique combined probabilistic principal component analysis denoising with the Higuchi fractal dimension transformation to diagnose the bearing multi-faults. Fractal theory is used to optimize the model parameters and stabilize the random vibrational signal for fast Fourier transform spectrum analysis. Noise interference in the Higuchi transformation is capped using a probabilistic principal component analysis model whose parameters are optimized through embedding dimension Cao algorithm and correlation dimension Grassberger and Procaccia algorithm. The fault diagnostic scheme mainly falls into three steps. First, the original vibration signal is truncated into a series of sub-signal segments by moving window whose length is determined as twice the value of maximum time delay that is provided by examining the steady Higuchi fractal dimension value of a raw signal in a process of plotting the fractal dimension over a range of time delay. Then, the Higuchi approach is used to estimate the average fractal dimension for each segment to create a quasi-stationary Higuchi fractal dimension sequence on which, finally, the fault features are straightforwardly extracted by the fast Fourier transform algorithm. The effectiveness of the proposed method is validated using simulated and experimental compound bearing fault vibration signals. Some fault components may be clouded if applied Higuchi fractal dimension alone because of the noise interference, but using the probabilistic principal component analysis–Higuchi fractal dimension method leads to clear diagnostic results. It indicates that the proposed approach can be incorporated into bearing multi-fault extraction from raw vibration signals.

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A generalised entropy in multifractal time signals analysis of mechanical vibration

Cited by 4 publications

References 16 publications

Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods

Data-driven monitoring of the gearbox using multifractal analysis and machine learning methods

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

On multi-fault detection of rolling bearing through probabilistic principal component analysis denoising and Higuchi fractal dimension transformation

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