---

Journal of Applied Nonlinear Dynamics 6(3) (2017) 427--443 | DOI:10.5890/JAND.2017.09.009

Raoul R. Nigmatullin$^{1}$,$^{3}$, Wei Zhang$^{2}$ , Domenico Striccoli$^{4}$

$^{1}$ The Radioelectronic and Informative -Measurements Technics (R&IMT) Department, Kazan National Research Technical University (KNRTU-KAI), 10 Karl Marx str., 420011, Kazan, Tatarstan, Russian Federation

$^{2}$ Jinan University, College of Information Science and Technology, Department of Electronic Engineering, 510632, Shi-Pai, Guangzhou, Guangdong, China

$^{3}$ JNU-KNRTU(KAI) Joint Lab of FracDynamics and Signal Processing, JNU, Guangzhou, China

$^{4}$ Department of Electrical and Information Engineering (DEI), Via E. Orabona 4, 70125, Bari, Italy

Download Full Text PDF

 

Abstract

The authors suggest an effective scheme for quantitative description of complex systems, when the number of measurements is relatively small. It has a great importance for quantitative description of expensive and rare experiments when the volume of the sampling is small. They proposed a simple theory that is based on the previous results associated with conception of the intermediate model (IM). The previous results can be generalized and applicable for description of complex systems with short samplings when the influence of the uncontrollable factors becomes significant. As an example, we consider the description of acoustic signals recorded from turbine bearings. It can be proved that the real signals have self-similar (fractal) properties. It helps to compress the length of the initial files (number of data points N = 44100) at least in 88 times and reduced essentially the number of the fitting parameters. The obtained results can be used for diagnosis of different defects during the process of technical exploitation. Each failure has own acoustic “picture” i.e. the amplitude-frequency response (AFR) expressed in terms of the generalized Prony spectrum (GPS). This AFR can be used as a “specific” fingerprint for identification of the unexpected failure and preventing a possible breakdown.

Acknowledgments

The authors want to express their thanks for the support of academic exchanges from“High-and Experts Recruitment Program” of Guangdong province, China. The authors appreciate the support of the research project from the grant “3D Ultrasound magnetic locating of parturition monitoring by fractaldynamic signal processing” of the Guangdong Scientific Planning Program (No. 2014A050503046) in the frame of JNU-KNRTU(KAI) Joint-Lab. “FracDynamics and Signal Processing”. One of us (RRN) wants to express his acknowledgements to Prof. V. M. Larionov (Kazan Federal University) for the receiving of vibrational role bearings data that were used in this research.

References

1. [1]	Nigmatullin, R.R., Zhang, W., and Striccoli, D. (2015), General theory of experiment containing reproducible data: The reduction to an ideal experiment. Communications in Nonlinear Science and Numerical Simulation, 27, 175-192.

2. [2]	Peng, C.K., Buldyrev, S.V., Havlin, S., Simons, M., Stanley, H.E., and Goldberger, A.L. (1994), Mosaic organization of DNA nucleotides. Phys. Rev. E, 49, 1685-1689.

3. [3]	Peng, C.K., Havlin, S., Stanley, H.E., and Goldberger, A.L. (1995), Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series. Chaos, 5(1), 82-87.

4. [4]	Wolf, A., Swift, J.B., Swinney, H.L., and Vastano, J.A. (1985), Determining Lyapunov exponents from a time series. Physica D: Nonlinear Phenomena, 16(3), 285-317.

5. [5]	Nigmatullin, R.R., Ionescu, C.M., Osokin, S.I., Baleanu, D., and Toboev, V.A. (2012), Non-invasive methods applied for complex signals. Romanian Reports in Physics, 64(4), 1032-1045.

6. [6]	Nigmatullin, R.R., Baleanu, D., Al-Zhrani, A.A., Alhamed, Y.A., Zahid, A.H., and Youssef, T.E. (2013), Spectral analysis of HIV drugs for acquired immunodeficiency syndrome within modified non-invasive methods. Revista de Chimie, 64(9), 987-993.

7. [7]	Nigmatullin, R.R., Baleanu, D., Povarova, D., Salah, N., Habib, S.S., and Memic, A. (2013), Raman spectra of nanodiamonds: New treatment procedure directed for improved Raman signal marker detection. Mathematical Problems in Eng., 2013, 1-11.

8. [8]	Sturt, A. and Strbac, G. (2013), Times-series modelling for the aggregate Great Britain wind output circa 2030. IET Renewable Power Generation, 7(1), 36-44.

9. [9]	Angelosante, D., Giannakis, G.B., and Sidiropoulos, N.D. (2013), Sparse Parametric Models for Robust Nonstationary Signal Analysis: Leveraging the Power of Sparse Regression, IEEE Signal Processing Magazine, 30(6), 64-73.

10. [10]	Grabocka, J., Wistuba, M., and Schmidt-Thieme, L. (2015), Scalable Classification of Repetitive Time Series Through Frequencies of Local Polynomials. IEEE Transactions on Knowledge and Data Engineering, 27(6), 1683-1695.

11. [11]	Korolko, N., Sahinoglu, Z., and Nikovski, D. (2016), Modeling and Forecasting Self-Similar Power Load Due to EV Fast Chargers. IEEE Transactions on Smart Grid, 7(3), 1620-1629.

12. [12]	Sanquer, M., Chatelain, F., El-Guedri, M., and Martin, N. (2013), A Smooth Transition Model for Multiple- Regime Time Series. IEEE Transactions on Signal Processing, 61(7), 1835-1847.

13. [13]	Laner, M., Svoboda, P., and Rupp, M. (2013), Parsimonious Fitting of Long-Range Dependent Network Traffic Using ARMA Models. IEEE Communications Letters, 17(2), 2368-2371.

14. [14]	Tenyakov, A., Mamon, R., and Davison, M. (2016), Filtering of a Discrete-Time HMM-Driven Multivariate Ornstein-Uhlenbeck Model With Application to Forecasting Market Liquidity Regimes, IEEE Journal of Selected Topics in Signal Processing, 10(6), 994-1005.

15. [15]	Comert, G. and Bezuglov, A. (2013), An Online Change-Point-BasedModel for Traffic Parameter Prediction. IEEE Transactions on Intelligent Transportation Systems, 14(3), 1360-1369.

16. [16]	Le, A.D., Herath, S.P., Tran, N.H., Duong, T.Q., and Shetty, S. (2015), Achievable rates and outage probability of cognitive radio with dynamic frequency hopping under imperfect spectrum sensing. IET Communications, 9(17), 2160-2167.

17. [17]	Kwapien, J. and Drozdz, S. (2012), Physical approach to complex systems., Physics Reports, 515, 115.

18. [18]	Feder, J. (1988), Fractals, Plenum Press, NY&London.

19. [19]	Nigmatullin, R.R., Maione, G.,Lino, P., Sapponaro, F., and Zhang, W. The General Theory of the Quasi- Reproducible Experiments: How to Describe the Measured Data of Complex Systems? Communications in Nonlinear Science and Numerical simulation (accepted for publication).