تشخیص آشوب از نویز در محیط‌های پرنویز مبتنی بر توزیع انرژی زیرباند‌های فرکانسی مختلف و کاربرد آن در یک نمونه نوسان‌ساز مبتنی بر عناصر ممریستیو

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه صنعتی اراک-دکتری برق

2 دانشگاه صنعتی خواجه نصیر الدین طوسی

3 دانشگاه ازاد اسلامی واحدعلوم و تحقیقات تهران

چکیده

در این مقاله ابتدا معیار جدیدی جهت وجه تمایز آشوب از نویز ارائه می‌ شود، سپس روشی جدید به‌ منظور تشخیص آشوب از نویز سفید گوسی و نویز رنگی و همچنین تشخیص آشوب در محیط‌های نویزی مبتنی بر ضریب خود همبستگی توزیع انرژی ارائه خواهد شد. در نهایت روش دیگری به‌ منظور تشخیص آشوب از نویز مبتنی بر توزیع انرژی در زیر باند‌های فرکانسی مختلف با استفاده از تیدیل موجک گسسته ارائه می‌شود، سپس از این روش در تشخیص و تحلیل آشوب در نوسان ساز مبتنی بر عناصر ممریستیو شامل مقاومت حافظه دار و خازن حافظه دار با حضور نویز سفید گوسی با شدت بیش از 50 درصد و با در نظر گرفتن اثر تکنولوژی ساخت و پارامترهای فیزیکی استفاده می‌ شود. این روش توانایی تشخیص آشوب در محیط های پر نویز از نویز های سفید گوسی و نویز رنگی را دارد. نتایج شبیه سازی نوآوری اصلی این مقاله را نشان می دهد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Chaos versus Noise Detection in Heavy Noise Environment based on Energy Distribution and its Application in Memristive based Oscillator

نویسندگان [English]

  • Farbod Setoudeh 1
  • Ali Khaki Sedigh 2
  • Masoud Dousti 3
چکیده [English]

Detecting chaos in severe noisy environments and also detecting chaos from noise are important issues in many areas of science and engineering. In this paper, a new criterion for distinguishing noise from noise is first presented, and a new method is proposed to detect chaos in noisy environment from noise based on auto-correlation coefficient of energy distribution. Finally, another method for chaos detection from noise in heavy noisy environments based on energy distribution in different frequency bands using the Discrete Wavelet Transform (DWT) is proposed. A new chaotic oscillator based on memristive devices (memristor and memcapacitor) with up to 50% white gaussian noise, is used as a practical case study to validate the results. This method is capable of detecting chaos in noisy environments of Gaussian noise and color noise. A new chaotic oscillator based on memristive devices is used as a practical case study to validate the results. Simulation results are used to show the main points of the paper.

کلیدواژه‌ها [English]

  • Wavelet
  • Memristive
  • Chaos
  • Noisy Environment
  • Oscillator
[1] J. Maldonado, and J. Hernandez, "Chaos theory applied to communications--part I: Chaos generators." pp. 50-55.
[2] A. L. Baranovski, and W. Schwarz, “Chaotic and random point processes: Analysis, design, and applications to switching systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 8, pp. 1081-1088, 2003.
[3] K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, “Synchronization of Lorenz-based chaotic circuits with applications to communications,” IEEE Transactions on circuits and systems II: Analog and digital signal processing, vol. 40, no. 10, pp. 626-633, 1993.
[4] N. J. Corron, and D. W. Hahs, “A new approach to communications using chaotic signals,” IEEE Transactions on circuits and systems I: Fundamental theory and applications, vol. 44, no. 5, pp. 373-382, 1997.
[5] A. Hassan, and S. Shaaban, “Enhancement of noise performance in digital receivers by over sampling the received signal,” International Journal of Industrial Mathematics, vol. 6, no. 4, pp. 275-284, 2014.
[6] V. Rubežić, I. Djurović, and M. Daković, “Time–frequency representations-based detector of chaos in oscillatory circuits,” Signal Processing, vol. 86, no. 9, pp. 2255-2270, 2006.
[7] M. Van Opstall, “Quantifying Chaos in Dynamical Systems with Lyapunov Exponents,” Furman University Electronic Journal of Undergraduate Mathematics, vol. 4, no. 1, pp. 1-8, 1998.
[8] H. D. Abarbanel, R. Brown, and M. Kennel, “Lyapunov exponents in chaotic systems: their importance and their evaluation using observed data,” International Journal of Modern Physics B, vol. 5, no. 09, pp. 1347-1375, 1991.
[9] F. Setoudeh, “Chaotic Behavior Of Voltage Control Oscillator Based On Colpitts Oscillator,” Journal of Control Engineering and Applied Informatics, vol. 16, no. 4, pp. 91-98, 2014.
[10] F. Setoudeh, A. Khaki Sedigh, and M. Dousti, "Analysis of a chaotic memristor based oscillator." Abstract and Applied Analysis, vol. 2014, pp. 1-8, 2014.
[11] C.-S. Poon, and M. Barahona, “Titration of chaos with added noise,” Proceedings of the national academy of sciences, vol. 98, no. 13, pp. 7107-7112, 2001.
[12] G. A. Gottwald, and I. Melbourne, “Testing for chaos in deterministic systems with noise,” Physica D: Nonlinear Phenomena, vol. 212, no. 1-2, pp. 100-110, 2005.
[13] J. Gao, J. Hu, W. Tung, and Y. Cao, “Distinguishing chaos from noise by scale-dependent Lyapunov exponent,” Physical Review E, vol. 74, no. 6, pp. 066204, 2006.
[14] S. Mehdizadeh, and M. A. Sanjari, “Effect of noise and filtering on largest Lyapunov exponent of time series associated with human walking,” Journal of biomechanics, vol. 64, pp. 236-239, 2017.
[15] H.-F. Liu, Z.-H. Dai, W.-F. Li, X. Gong, and Z.-H. Yu, “Noise robust estimates of the largest Lyapunov exponent,” Physics Letters A, vol. 341, no. 1-4, pp. 119-127, 2005.
[16] E. Lega, M. Guzzo, and C. Froeschlé, "Theory and applications of the Fast Lyapunov indicator (FLI) method," Chaos Detection and Predictability, pp. 35-54: Springer, 2016.
[17] A. Casaleggio, A. Corana, and S. Ridella, “Correlation dimension estimation from electrocardiograms,” Chaos, Solitons & Fractals, vol. 5, no. 3-4, pp. 713-726, 1995.
[18] X. Su, Y. Wang, S. Duan, and J. Ma, “Detecting chaos from agricultural product price time series,” Entropy, vol. 16, no. 12, pp. 6415-6433, 2014.
[19] L. Zunino, and C. W. Kulp, “Detecting nonlinearity in short and noisy time series using the permutation entropy,” Physics Letters A, vol. 381, no. 42, pp. 3627-3635, 2017.
[20] Z. Chen, Y. Li, H. Liang, and J. Yu, “Improved Permutation Entropy for Measuring Complexity of Time Series under Noisy Condition,” Complexity, vol. 2019, 2019.
[21] R. Kříž, “Finding chaos in finnish gdp,” International Journal of Automation and Computing, vol. 11, no. 3, pp. 231-240, 2014.
[22] J. Sun, Y. Zhao, T. Nakamura, and M. Small, “From phase space to frequency domain: A time-frequency analysis for chaotic time series,” Physical Review E, vol. 76, no. 1, pp. 016220, 2007.
[23] I. Djurović, and V. Rubežić, “Multiple STFT-based approach for chaos detection in oscillatory circuits,” Signal processing, vol. 87, no. 7, pp. 1772-1780, 2007.
[24] Q. Zhu, and S. Liang, “A Method for detecting chaotic vibration based on continuous wavelet transform,” International Journa Sensing, Computing and Control, vol. 1, no. 2, pp. 125-132, 2011.
[25] W.-l. Jiang, “Orthogonal wavelet packet analysis based chaos recognition method,” Frontiers of Electrical and Electronic Engineering in China, vol. 1, no. 1, pp. 13-19, 2006.
[26] J. Murguía, H. Rosu, L. Reyes-López, M. Mejía-Carlos, and C. Vargas-Olmos, “Wavelet characterization of hyper-chaotic time series,” Revista Mexicana de Física, vol. 64, no. 3, pp. 283-290, 2018.
[27] A. Zhou, and S. Wang, "A dimension-reduction AFN method for distinguishing chaos from noise." p. 012030.
[28] S. Wallot, and D. Mønster, “Calculation of Average Mutual Information (AMI) and False-Nearest Neighbors (FNN) for the Estimation of Embedding Parameters of Multidimensional Time Series in Matlab,” Frontiers in psychology, vol. 9, 2018.
[29] S. He, K. Sun, and Y. Peng, “Detecting chaos in fractional-order nonlinear systems using the smaller alignment index,” Physics Letters A, vol. 383, no. 19, pp. 2267-2271, 2019.
[30] J. R. Tempelman, and F. A. Khasawneh, “A Look into Chaos Detection through Topological Data Analysis,” arXiv preprint arXiv:1902.05918, 2019.
[31] M. S. Williamson, and T. M. Lenton, “Detection of bifurcations in noisy coupled systems from multiple time series,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 25, no. 3, pp. 036407, 2015.
[32] C. Diks, “Estimating invariants of noisy attractors,” Physical review E, vol. 53, no. 5, pp. R4263, 1996.
[33] J.-M. Ghez, and S. Vaienti, “Integrated wavelets on fractal sets. I. The correlation dimension,” Nonlinearity, vol. 5, no. 3, pp. 777, 1992.
[34] Z. Dhifaoui, “Robust to noise and outliers estimator of correlation dimension,” Chaos, Solitons & Fractals, vol. 93, pp. 169-174, 2016.