A UNIVERSAL DIAGNOSTIC AND PROGNOSTIC MODULE FOR CONDITION MONITORING SYSTEMS
OF COMPLEX MECHANICAL STRUCTURES OPERATING IN THE PRESENCE OF NON-GAUSSIAN DISTURBANCES AND VARIABLE OPERATING CONDITIONS


    Funding agency: National Centre for Research and Development (NCBiR), Poland

    Funding period: 1.10.2021-31.12.2023

    Partners: Faculty of Mathematics (WMat) WUST, Faculty of Geoengineering, Mining and Geology (WGGG) WUST, AMC Tech

    Budget for WUST: 1 926 000 PLN (c.a. 421 500 Euro)

    A key personnel consists of: prof. Agnieszka Wyłomańska (WMat), prof. Tomasz Barszcz (AMC Tech), prof. Radoslaw Zimroz (WGGG/KG/DMC).

    More details - see the link

    Job offer - see the link

    ANOMALOUS DIFFUSION PROCESSES
    AND THEIR APPLICATION TO REAL DATA MODELLING


      Grant no.: 2016/21/B/ST1/00929 (OPUS)

      Funding agency: National Science Centre (NCN), Poland

      Funding period: 27.01.2017-26.01.2020

      Budget: 485 000 PLN

      Research team

      1. Agnieszka Wyłomańska (leader of the project, principal investigator)
      2. Janusz Gajda (investigator)
      3. Aleksandra Grzesiek (Ph.D. student)
      4. Piotr Kruczek (Ph.D. student)
      5. Rafał Połoczański (Ph.D. student)
      6. Katarzyna Maraj (student)
      7. Wojciech Żuławiński (student)
      8. Aleksei Chechkin (international collaborator, Potsdam University, Germany)
      9. Arun Kumar (international collaborator, IIT Ropar, India)
      10. Diego Krapf (international collaborator, Colorado State University, USA)
      11. S. Sundar (international collaborator, IIT Madras, India)
      12. Samudrajit Thapa (international collaborator, Potsdam University, Germany)
      13. Prashant Giri (international collaborator, IIT Madras, India)
      14. Anna Panorska (international collaborator, University of Nevada, USA)
      15. Tomasz Kozubowski (international collaborator, University of Nevada, USA)
      16. Holger Kantz (international collaborator, Max Planck Institute, Dresden, Germany)
      17. Marc Hoell (international collaborator, Max Planck Institute, Dresden, Germany)
      18. Denis Grebenkov (international collaborator, Ecole Polytechnique, France)
      19. Yann Lanoiselee (international collaborator, Ecole Polytechnique, France)

      Key words: anomalous difussion, subordinated process, stochastic modeling, statistical identification

      Tasks

      1. Analysis of subordinated processes with stationary increments
      2. Analysis of subordinated processes with inverse subordinators
      3. Analysis of long memory processes

      Selected publications

      1. A. Grzesiek, M. Teuerle, G. Sikora, A. Wyłomańska: Spatio-temporal dependence measures for alpha-stable bivariate AR(1) models , Journal of Time Series Analysis 2020, https://doi.org/10.1111/jtsa.12517
      2. A. Grzesiek, M. Teuerle, A. Wyłomańska:Cross-codifference for bidimensional VAR(1) time series with infinite variance, Communications in Statistics - Simulation and Computation 2020, https://doi.org/10.1080/03610918.2019.1670840
      3. A. Grzesiek, A. Wyłomańska: Subordinated Processes with Infinite Variance, In: Chaari F., Leskow J., Zimroz R., Wyłomańska A., Dudek A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16, 111-135, Springer, Cham, 2020
      4. P. Poczynek, P. Kruczek, A. Wyłomańska: Ornstein-Uhlenbeck Process Delayed by Gamma Subordinator , In: Chaari F., Leskow J., Zimroz R., Wyłomańska A., Dudek A. (eds) Cyclostationarity: Theory and Methods – IV. CSTA 2017. Applied Condition Monitoring, vol 16, 147-165, Springer, Cham, 2020
      5. P. Kruczek, W. Żuławiński, P. Pagacz, A. Wyłomańska: Fractional lower order covariance based-estimator for Ornstein-Uhlenbeck process with stable distribution, Mathematica Applicanda 47, 259-292, 2019
      6. M. Szmigiel, A. Grzesiek, A. Wyłomańska, H. Kasprzak: Stable distribution in application to fixational eye movement description, Optica Applicata 49 (2), 365-377, 2019
      7. A. Kumar, A. Maheshwari, A. Wyłomańska: Linnik Levy Process and Its Generalization , Physica A 529, 121539, 2019
      8. G. Sikora, Ł. Bielak, A. Michalak, P. Miśta, A. Wyłomańska: Stochastic modelling of currency exchange rates with novel validation techniques, Physica A 523, 1202-1215, 2019
      9. A. Kumar, A. Wyłomańska, R. Połoczański, J. Gajda: Fractional Brownian motion delayed by tempered and inverse tempered stable subordinators, Methodology and Computing in Applied Probability 21(1), 185-202, 2019
      10. A. Grzesiek, S. Sundar, A. Wyłomańska: Fractional lower order covariance-based estimator for bidimensional AR(1) model with stable distribution, International Journal of Advances in Engineering Sciences and Applied Mathematics 11(3), 217-229, 2019
      11. J. Gajda Janusz, A. Wyłomańska, A. Kumar: Fractional Levy stable motion time-changed by gamma subordinator, Communications in Statistics - Theory and Methods 48, (24), 5953–5968, 2019
      12. A. Kumar, N. S. Upadhye, A. Wyłomańska, J. Gajda: Tempered Mittag-Leffler Levy Process, Communications in Statistics - Theory and Methods 48 (2), 396–411, 2019
      13. Y. Lanoiselee, D.S. Grebenkov, G. Sikora, A. Grzesiek, A. Wylomanska: Optimal parameters for anomalous diffusion exponent estimation from noisy data , Phys. Rev. E 98, 062139, 2018
      14. J. Gajda, A. Wyłomańska, H. Kantz, A. Chechkin, G. Sikora:Large deviations of time-averaged statistics for Gaussian processes , Statistics and Probability Letters 143, 47-55, 2018
      15. G. Sikora, A. Wyłomańska, D. Krapf:Recurrence statistics for anomalous diffusion regime change detection , Computational Statistics & Data Analysis 128, 380-394, 2018
      16. P. Kruczek, M. Polak, A. Wyłomańska, W. Kawalec, R. Zimroz: Application of compound Poisson process for modelling of ore flow in a belt conveyor system with cyclic loading,Journal International Journal of Mining, Reclamation and Environment 32(6), 376-391, 2018
      17. A. Grzesiek, J. Gajda, A. Wyłomańska, S. Sundar: Discriminating between scaled and fractional Brownian motion via p-variation statistics, International Journal of Advances in Engineering Sciences and Applied Mathematics 10(1), 9-14, 2018
      18. D. Kucharczyk, A. Wyłomańska, G. Sikora: Variance change point detection for fractional Brownian motion based on the likelihood ratio test, Physica A 490, 439-450, 2018
      19. G. Sikora, A. Wyłomańska, J. Gajda, L. Sole, E. J. Akin, M. M. Tamkun, D. Krapf: Elucidating distinct ion channel populations on the surface of hippocampal neurons via single-particle tracking recurrence analysis, Phys. Rev. E 96, 062404, 2017
      20. G. Sikora, M. Teuerle, A. Wyłomańska, D. Grebenkov: Statistical properties of the anomalous scaling exponent estimator based on time averaged mean square displacement, Phys. Rev. E 96, 022132, 2017
      21. A. Kumar, A. Wyłomańska, J. Gajda: Stable Levy motion with inverse Gaussian subordinator, Physica A 482, 486–500, 2017
      22. G. Sikora, K. Burnecki, A. Wyłomańska: Mean-squared displacement statistical test for fractional Brownian motion, Phys. Rev. E 95, 032110, 2017
      23. A. Kumar, A. Wyłomańska, J. Gajda: Generalized fractional Laplace motion, Statistics and Probability Letters 124, 101-109, 2017
      24. M. Jabłońska, M. Teuerle, A. Wyłomańska: Bivariate sub-Gaussian model for stock indices returns, Physica A 486(15), 628–637, 2017