Voices That Inspire, Ideas That Transform

Speakers titles abstracts​

Meet the brilliant minds behind this year’s conference! Our speakers are industry leaders, visionaries, and innovators, ready to share their expertise and fresh perspectives. Explore their topics, gain valuable insights, and get inspired by the best in the field. Don’t miss the chance to learn from these remarkable professionals!

Jacek Leśkow

American University, Kyiv, Ukraine
Cracow University of Technology, Krakow, Poland

Functional approach for PC time series – theory and applications

Cyclostationary signals are widespread in many areas of research. Radar signals, GPS signals, vibromechanical signals all share the cyclostationary features. The aim of my talk is to show how recent advances in functional data analysis have impacted analysis of cyclostationary signals. The theoretical results will be illustrated with practical examples.

Elżbieta Gajecka

Cracow University of Technology, Poland

Application of periodically correlated time series

Statistical inference based on asymptotic distributions in the case of dependent data is very often ineffective. In the last four decades there was a significant development of the resampling methods. Using these methods, one can efficiently approximate the sampling distributions of statistics and estimators. The consistency of the proposed procedure, gives ability to capture quantiles of the unknown sampling distribution of the statistic at hand. In the talk a time series model with specific feature: a periodic structure will be considered

The talk is motivated by the works of  H. Hurd [1] and P. Doukhan [2].

The subsampling methodology was used to estimate the mean function in the non-stationary real data example.

Dominique Dehay

Univeristé Rennes 2, France

Harmonizable VARMA time series

Harmonizable time series form a wide class of nonstationary time series, which admit a tractable Fourier analysis and have spectral distributions characterized by correlated com- ponents. They are proved to be useful in many fields of application, for example, recently they were successfully applied in the analysis of replicated ElectroEncephaloGram signals for studying the brain connectivity. We present a parametric form for these harmonizable time series, namely Harmonizable Vector AutoRegressive and Moving Average models (HVARMA). In the same spirit as of standard VARMA models, they are derived as a unique solution of a dfference equation based on a properly defined concept of harmo-nizable noise: by definition a harmonizable noise is uncorrelated, but its variance is not constant over time. We exhibit their spectral characteristics and we provide a method-ology for generating realizations of harmonizable time series based on known spectral characteristics. Then we discuss how to estimate the parameters of the HVARMA model on a simple example of an univariate HVARMA (1,0) model. Here we do not assume any model for the harmonizable noise except its heteroskedasticity. Our topic is illustrated by some simulations and numerical studies. This work is the result of a collaborative work with A. Dudek and J-M. Freyermuth.

Serhii Lupenko

Opole University of Technology, Poland
American University, Kyiv, Ukraine

Common Theoretical and Applied Foundations of Rhythm-adaptive and Scale Transformation Technologies for Statistical Processing of Cyclic Stochastic Signals

The work presents the common mathematical foundations of rhythm-adaptive technologies and scale transformation technologies (time warping technologies) in the problems of statistical processing of cyclic signals based on the theory of cyclic functional relations and based on the concept of their isomorphism. The theoretical equivalence of rhythm-adaptive methods and scale transformation methods is shown. The problem of scale transformation for random cyclic functional relations with arbitrary laws of changing their rhythm is formulated. The necessary and sufficient conditions for the correct application of scale transformation methods have been established. The unbiasedness and consistency of estimates of the cyclic random process initial moment functions of arbitrary order, which are based on scale transformation methods, have been proved. An effective (in terms of accuracy and time computational complexity) method of piecewise linear scale transformation method for isomorphic cyclic random processes has been developed. A comparison of rhythm-adaptive technologies and scale transformation technologies in the problems of statistical processing of electrical, mechanical, and optical cardiac signals was made. A method of testing the quality of solving the scale transformation problems based on computer simulation has been developed. A comparative analysis of known time warping methods with each other and with rhythm-adaptive methods has been conducted.

Mohamed El Badaoui

Laboratoire d’Analyse des Signaux et Processus Industriels, Roanne, France.

Advances in Vibration-Based Fault Detection: Cyclostationary Analysis and Comparative Evaluation of Emerging Techniques for Rolling Element Bearings Diagnosis.

The last decade has witnessed spectacular advances in vibration-based fault detection of rotating machines and, in particular, rolling element bearings. Nowadays, the related state of the art can be considered mature thanks to a set of powerful signal processing techniques able to denoise and process the vibration signal to detect fault symptoms. Among these techniques, two emerging approaches have specifically captured the interest of the scientific community thanks to their efficiency and robustness. They have also been recommended in the bearing diagnostic tutorial written by professors R. B. Randall & J. Antoni, published in MSSP in 2011. The first approach consists of pre-processing the random part of the vibration signal (after removal of deterministic components) through the minimum entropy deconvolution (MED) method, followed by the spectral kurtosis (SK), before analyzing the spectrum of the signal envelope. The MED enhances the signal impulsivity by deconvolving the system transfer function through an optimization approach that maximizes the kurtosis of the filter output. Then, the SK is applied to conceive the optimal filter that promotes the most informative spectral band before computing the (squared) envelope spectrum. The second approach is based on a cyclostationary modeling of the bearing signal. It applies a bi-variable map— called the spectral coherence— of (i) the cyclic frequency, which describes the cyclic content of modulations, and (ii) the spectral frequency which describes the spectral content of the carrier. When applied to the random part of the signal, this quantity is able to detail the signal in this plane according to the signal-to-noise ratio, thus allowing weak fault components to appear in the distribution. This paper investigates and compares these two approaches on real bearing vibration datasets including run-to-failure tests. The study also addresses the extension of these approaches to the nonstationary operating regime.

Antonio Napolitano

University of Parthenope, Napoli, Italy

Irregular Almost-Cyclostationary Model for the Sunspot Number Time Series

The time series of Sunspot number is known to exhibit approximate periodicity. In the brief study of this time series provided here, the details of the irregularity in the periodicity are exposed by fitting an irregular almost-cyclostationary model to the data. By two different experiments, it is shown that from the second-order lag product of the Sunspot number time series, two amplitude- and angle modulated additive sine-wave components can be extracted. The periods of the non-modulated sinusoids agree with those already observed. Moreover, the time-warping functions in the model provide a mathematical description of the irregularity of the cyclicities observed in the time series, something not previously attempted.

Agnieszka Wyłomańska

Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center
Wrocław University of Science and Technology, Poland

Robust methods for detecting hidden periodicity in models with additive non-Gaussian noise

We tackle the challenge of identifying hidden periodicity in signals that display periodic correlation while being influenced by non-Gaussian noise with unknown properties. This situation arises frequently across various fields. Traditional methods for detecting periodically correlated (PC) behavior typically rely on analyses in either the time domain or the frequency domain. In our study, we adopt these methods as well but introduce robust alternatives to the classical estimators for the autocovariance function and the discrete Fourier transform, incorporating Huber function-based M estimation rather than conventional algorithms. Building on these techniques, we develop robust versions of widely used statistical methods initially designed to detect hidden periodicity in pure PC models. Our research examines two types of PC models and two types of additive noise, resulting in PC signals disrupted by non-Gaussian additive noise. Detecting hidden periodicity under these conditions is considerably more complex than in standard cases. Using Monte Carlo simulations, we validate the proposed robust methods, demonstrating their effectiveness and superiority over traditional approaches. To further support our conclusions, we analyze real datasets where hidden periodicity has been previously confirmed in the literature. This serves as a key inspiration for our
research.

Wojciech Żuławiński

Wrocław University of Science and Technology, Poland

Fractional lower-order covariance-based autodependence measures for heavy-tailed cyclostationary time series

This presentation introduces new methods for the analysis of cyclostationary time series with infinite variance. Traditional cyclostationary analysis, based on periodically correlated (PC) processes, relies on the autocovariance function (ACVF). However, the ACVF is not suitable for data exhibiting a heavy-tailed distribution, particularly with infinite variance. Thus, we propose a novel framework for the analysis of cyclostationary time series with heavy-tailed distribution, utilizing the fractional lower-order covariance (FLOC) as an alternative to covariance. This leads to the introduction of two new autodependence measures: the periodic fractional lower-order autocorrelation function (peFLOACF) and the periodic fractional lower-order partial autocorrelation function (peFLOPACF). These measures generalize the classical periodic autocorrelation function (peACF) and periodic partial autocorrelation function (pePACF), offering robust tools for analyzing infinite-variance processes. Two practical applications of the proposed measures are explored: a portmanteau test for testing dependence in cyclostationary series and a method for order identification in periodic autoregressive (PAR) and periodic moving average (PMA) models with infinite variance. Both applications demonstrate the potential of new tools, with simulations validating their efficiency. The methodology is further illustrated through the analysis of real-world air pollution data, which showcases its practical utility. The results indicate that the proposed measures based on LOC provide reliable and efficient techniques for analyzing cyclostationary processes with heavy-tailed distributions.

Oleh Lychak

Ukrainian Academy of Sciences, Lviv, Ukraine

Using the Hilbert transform for analysis of the high-frequency modulation of periodically nonstationary vibration signals

We discuss the use of the Hilbert transform for the analysis of periodically non-stationary random signals (PNRSs), whose carrier harmonics are modulated by jointly stationary high- frequency narrow-band random processes. PNRS of this type are suitable models for numerous natural and man-made phenomena, including the vibration of a damaged mechanism. We show that the auto-covariance function of the signal and its Hilbert transform are the same, and that their cross-covariance functions differ only in their sign, meaning that the sum of squares of the signal and its Hilbert transform cannot be considered a ‘squared envelope’ and no new information is contained compared with the variance of the raw signal. A representation of the signal in the form of a superposition of high-frequency components is obtained and it is shown that these components are jointly periodically non-stationary random processes. The properties of the band-pass filtered signals are examined, and it is shown that band-pass filtering can reduce both the number of signal variance cyclic harmonics and their amplitudes. We show that it is possible to extract the quadratures of narrow-band high-frequency modulation processes using the Hilbert transform. The results obtained here theoretically substantiate the use of the Hilbert transform for the analysis of high-frequency modulation which occurs when a fault appears. They offer a new way to consider the traditional approach to vibration diagnosis. A processing technique that can be considered an alternative to envelope analysis is described, and its use in the analysis of a vibration signal is discussed.

Harry Hurd

Reproducing Kernel Hilbert Space for Continuous Time PC Processes

In this talk, we present the RKHS for continuous time PC processes. We first review the RKHS definition
and then examine the consequences of the PC structure. We develop representations based on the
RKHS structure and analyze the consequences of mean square continuity of X_t, t in R.

Andrzej Makagon

Hampton University, USA

Lecture on theory of PC sequences

In my presentation I would like to outline the theory of PC Sequences. Talk is based on my papers written in the period of 2000 – 2020, some together with Prof. Abolghassem Miamee. I think that even if you work on applications or statistics of PC sequences, it will benefit to know the mathematics behind it.

Vladas Pipiras

University of North Carolina, Chapel Hill, USA

Recent encounters of cyclical long memory

I will describe my recent encounter of a curious, physics-based model with the so-called cyclical long memory. While the usual long memory can be characterized by a divergent spectrum around the zero frequency, the spectrum of its cyclical counterpart diverges at non-zero frequency(ies). I will also discuss some implications of this phenomenon for the application in question, and some constructions of general cyclical long memory processes by means of random modulation.