An Efficient Algorithm for Instantaneous Frequency Estimation of Nonstationary Multicomponent Signals in Low SNR

A method for components instantaneous frequency (IF) estimation of multicomponent signals in low signal-to-noise ratio (SNR) is proposed. The method combines a new proposed modification of a blind source separation (BSS) algorithm for components separation, with the improved adaptive IF estimation procedure based on the modified sliding pairwise intersection of confidence intervals (ICI) rule. The obtained results are compared to the multicomponent signal ICI-based IF estimation method for various window types and SNRs, showing the estimation accuracy improvement in terms of the mean squared error (MSE) by up to 23%. Furthermore, the highest improvement is achieved for low SNRs values, when many of the existing methods fail.Scopu

Multiple multidimensional morse wavelets

This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved

An intelligent compound gear-bearing fault identification approach using Bessel kernel-based time-frequency distribution

The most crucial transmission components utilized in rotating machinery are gears and bearings. In a gearbox, the bearings support the force acting on the gears. Compound Faults in both the gears and bearings may cause heavy vibration and lead to early failure of components. Despite their importance, these compound faults are rarely studied since the vibration signals of the compound fault system are strongly dominated by noise. This work proposes an intelligent approach to fault identification of a compound gear-bearing system using a novel Bessel kernel-based Time-Frequency Distribution (TFD) called the Bessel transform. The Time-frequency images extracted using the Bessel transform are used as an input to the Convolutional Neural Network (CNN), which classifies the faults. The effectiveness of the proposed approach is validated with a case study, and a testing efficiency of 94% is achieved. Further, the proposed method is compared with the other TFDs and found to be effective

Kombinacija vremensko-frekvencijske analize signala i strojnoga učenja uz primjer u detekciji gravitacijskih valova

This paper presents a method for classifying noisy, non-stationary signals in the time-frequency domain using artificial intelligence. The preprocessed time-series signals are transformed into time-frequency representations (TFrs) from Cohen’s class resulting in the TFr images, which are used as input to the machine learning algorithms. We have used three state-of-the-art deep-learning 2d convolutional neural network (Cnn) architectures (ResNet-101, Xception, and EfficientNet). The method was demonstrated on the challenging task of detecting gravitational-wave (gw) signals in intensive real-life, non-stationary, non-gaussian, and non-white noise. The results show excellent classification performance of the proposed approach in terms of classification accuracy, area under the receiver operating characteristic curve (roC auC), recall, precision, F1 score, and area under the precision-recall curve (PR AUC). The novel method outperforms the baseline machine learning model trained on the time-series data in terms of all considered metrics. The study indicates that the proposed technique can also be extended to various other applications dealing with non-stationary data in intensive noise.Ovaj rad predstavlja metodu klasifikacije šumom narušenih nestacionarnih signala u vremensko-frekvencijskoj domeni korištenjem umjetne inteligencije. Naime, signali u obliku vremenskih nizova transformirani su nakon predobrade u vremensko-frekvencijske prikaze (TFR) iz Cohenove klase, rezultirajući TFR slikama korištenim kao ulaz u algoritme strojnoga učenja. Korištene su tri suvremene metode dubokoga učenja u obliku 2D arhitektura konvolucijskih neuronskih mreža (CNN) (ResNet-101, Xception i EfficientNet). Metoda je demonstrirana na zahtjevnom problemu detekcije signala gravitacijskih valova (GW) u intenzivnom stvarnom i nestacionarnom šumu koji nema karakteristike ni Gaussovog ni bijelog šuma. Rezultati pokazuju izvrsne performanse klasifikacije predloženoga pristupa s obzirom na točnost klasifikacije, površinu ispod krivulje značajke djelovanja prijamnika (ROC AUC), odziv, preciznost, F1-mjeru i površinu ispod krivulje preciznost-odziv (PR AUC). Nova metoda nadmašuje osnovni model strojnoga učenja treniran na podatcima u obliku vremenskih nizova s obzirom na razmatrane metrike. Istraživanje pokazuje da se predložena tehnika može proširiti i na različite druge primjene koje uključuju nestacionarne podatke u intenzivnom šumu

Variations in the dynamic properties of structures: the Wigner-Ville distribution

The Wigner-Ville Distribution (WVD) is a promising method for analyzing frequency variations in seismic signals, including those of interest for structural monitoring. Nonlinearities in the force displacement relationship will temporarily decrease the apparent natural frequencies of structures during strong to moderate excitation, and earthquake damage can permanently change building stiffnesses. A Fourier Transform of a building record contains information regarding frequency content, but it can not resolve the exact onset of changes in natural frequency – all temporal resolution is contained in the phase of the transform. The spectrogram is better able to resolve temporal evolution of frequency content, but has a trade-off in time resolution versus frequency resolution in accordance with the uncertainty principle. Time-frequency transformations such as the WVD allow for instantaneous frequency estimation at each data point, for a typical temporal resolution of fractions of a second. We develop a mathematical foundation for analyzing the evolution of frequency content in a signal, and apply these techniques to synthetic records from linear and nonlinear FEM analysis (including plastic rotation and weld fractures). Our analysis techniques are then applied to earthquake records from damaged buildings

Prediction of nonlinear nonstationary time series data using a digital filter and support vector regression

Volatility is a key parameter when measuring the size of the errors made in modelling returns and other nonlinear nonstationary time series data. The Autoregressive Integrated Moving- Average (ARIMA) model is a linear process in time series; whilst in the nonlinear system, the Generalised Autoregressive Conditional Heteroskedasticity (GARCH) and Markov Switching GARCH (MS-GARCH) models have been widely applied. In statistical learning theory, Support Vector Regression (SVR) plays an important role in predicting nonlinear and nonstationary time series data. We propose a new class model comprised of a combination of a novel derivative Empirical Mode Decomposition (EMD), averaging intrinsic mode function (aIMF) and a novel of multiclass SVR using mean reversion and coefficient of variance (CV) to predict financial data i.e. EUR-USD exchange rates. The proposed novel aIMF is capable of smoothing and reducing noise, whereas the novel of multiclass SVR model can predict exchange rates. Our simulation results show that our model significantly outperforms simulations by state-of-art ARIMA, GARCH, Markov Switching generalised Autoregressive conditional Heteroskedasticity (MS-GARCH), Markov Switching Regression (MSR) models and Markov chain Monte Carlo (MCMC) regression.Open Acces

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

Environmental Noise and Nonlinear Relaxation in Biological Systems

We analyse the effects of environmental noise in three different biological systems: (i) mating behaviour of individuals of \emph{Nezara viridula} (L.) (Heteroptera Pentatomidae); (ii) polymer translocation in crowded solution; (iii) an ecosystem described by a Verhulst model with a multiplicative L\'{e}vy noise.Comment: 32 pages; In "Ecological Modeling" by Ed. Wen-Jun Zhang. ISBN: 978-1-61324-567-5. - Nova Science Publishers, New York, 201