مهندسی مکانیک مدرس

مهندسی مکانیک مدرس

روش بهبودیافته کاهش نویز از سری زمانی آشوبناک به کمک شبکه عصبی و تحلیل طیف منفرد

نوع مقاله : پژوهشی اصیل

نویسندگان
علی‌رضا بهرامی
سعید اصیل قره باغی
دانشکده عمران، دانشگاه صنعتی خواجه نصیرالدین طوسی
10.22034/MME.24.1.53
چکیده
در تحقیق حاضر روشی بهبود یافته برای کاهش نویز از سری زمانی حاصل از یک سیستم آشوبناک ارائه شده است. اساس این روش بر مبنای روش کاهش نویز ارائه شده توسط شِریبر و گِرَسبِرگر می‌باشد که دارای عملکردی مناسب و پیچیدگی کمتر نسبت به سایر روش‌های کاهش نویز از اطلاعات آشوبناک است. در اینجا از یک مدل کلی که به کمک شبکه عصبی ایجاد شده است به منظور مدل پیش‌بینی سری زمانی آشوبناک استفاده گردیده است. بر خلاف روش اصلی، استفاده از یک مدل پیش‌بینی کلی با نتایج بهتر در مقایسه با مدل‌های محلی و همچنین بهره گرفتن از روش بازسازی تحلیل طیف منفرد سبب ارائه روشی با دقت بالاتر شده است که در عین حال از مزایای منحصر به فرد روش اصلی نیز برخوردار می‌باشد. این روش بهبود یافته به سری زمانی حاصل از حالت آشوبناک معادلات لورِنز که با نویز گاوسی آغشته شده، اعمال گردیده است. پس از اعمال روش کاهش نویز بهبود یافته، نتایج نهایی، کاهش حدود ۳۳ درصدی مقدار خطای مطلق میانگین را در مقایسه با روش اولیه نشان می‌دهند. همچنین خطای محاسبه بُعد همبستگی پس از اعمال روش بهبود یافته به ۲ درصد کاهش یافته است.
کلیدواژه‌ها
کاهش نویز
سری زمانی آشوبناک
تحلیل طیف منفرد
شبکه عصبی
مدل کلی

موضوعات

عنوان مقاله English

Improved Noise Reduction Method for Chaotic Time Series Using Neural Network and Singular Spectrum Analysis

نویسندگان English

Ali Reza Bahrami
Saeed Asil Gharebaghi
Khajeh Nasir Toosi University of Technology
چکیده English

An improved method for noise reduction from a time series obtained from a chaotic system is presented. This improved method is based on a noise reduction technique presented by Schreiber and Grassberger that has good performance and less complexity compared to other noise reduction methods from chaotic data. Here a global model created using a neural network has been used as a prediction model for chaotic time series. This global prediction model performs better compared to the local prediction model used in the original method. The improved method also takes advantage of the singular spectrum analysis reconstruction technique. Both of these improvements led to a more accurate noise reduction method while preserving the unique properties of the original. The improved method is applied to a time series obtained from the chaotic state of Lorenz equations that is polluted with Gaussian noise. The final results show a 33 percent reduction in mean absolute error values compared to the original method. Also, the error of calculating the correlation dimension from the data has been reduced to 2 percent after applying the improved method.

کلیدواژه‌ها English

Noise Reduction
Chaotic Time Series
Singular Spectrum Analysis
Neural Network
Global Model
1. Fan G, Li J, Hao H. Vibration signal denoising for structural health monitoring by residual convolutional neural networks. Measurement. 2020;157:107651.
2. Ravizza G, Ferrari R, Rizzi E, Dertimanis V. On the denoising of structural vibration response records from low-cost sensors: A critical comparison and assessment. Journal of Civil Structural Health Monitoring. 2021;11(5):1201-24.
3. Wang X, Chakraborty J, Niederleithinger E. Noise reduction for improvement of ultrasonic monitoring using coda wave interferometry on a real bridge. Journal of Nondestructive Evaluation. 2021;40(1):14.
4. Kullaa J. Robust damage detection in the time domain using Bayesian virtual sensing with noise reduction and environmental effect elimination capabilities. Journal of Sound and Vibration. 2020;473:115232.
5. Zhang Z, Ye Y, Luo B, Chen G, Wu M. Investigation of microseismic signal denoising using an improved wavelet adaptive thresholding method. Scientific Reports. 2022;12(1):22186.
6. Dastgerdi AK, Mercorelli P. Investigating the effect of noise elimination on LSTM models for financial markets prediction using Kalman Filter and Wavelet Transform. WSEAS Trans Bus Econ. 2022;19:432-41.
7. Niu P, Sun Y, Gong Z. Research on the chaotic characteristics and noise reduction prediction of information system anomalies in equipment manufacturing enterprises. Sustainability. 2021;13(9):4911.
8. Li Y-x, Wang L. A novel noise reduction technique for underwater acoustic signals based on complete ensemble empirical mode decomposition with adaptive noise, minimum mean square variance criterion and least mean square adaptive filter. Defence Technology. 2020;16(3):543-54.
9. Grassberger P, Hegger R, Kantz H, Schaffrath C, Schreiber T. On noise reduction methods for chaotic data. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1993;3(2):127-41.
10. Han M, Liu Y, Xi J, Guo W. Noise smoothing for nonlinear time series using wavelet soft threshold. IEEE signal processing letters. 2006;14(1):62-5.
11. Shang L-J, Shyu K-K. A method for extracting chaotic signal from noisy environment. Chaos, Solitons & Fractals. 2009;42(2):1120-5.
12. Wei G, Shu H. H∞ filtering on nonlinear stochastic systems with delay. Chaos, Solitons & Fractals. 2007;33(2):663-70.
13. Billings SA, Lee KL. A smoothing algorithm for nonlinear time series. International Journal of Bifurcation and Chaos. 2004;14(03):1037-51.
14. Schreiber T, Grassberger P. A simple noise-reduction method for real data. Physics letters A. 1991;160(5):411-8.
15. Abarbanel HDI, Gollub JP. Analysis of Observed Chaotic Data. Physics Today. 1996;49(11):86-8.
16. Farmer JD, Sidorowich JJ. Exploiting Chaos to Predict the Future and Reduce Noise. Evolution, Learning And Cognition. 1989:277.
17. Hammel SM. A noise reduction method for chaotic systems. Physics letters A. 1990;148(8-9):421-8.
18. Davies M. Noise reduction schemes for chaotic time series. Physica D: Nonlinear Phenomena. 1994;79(2-4):174-92.
19. Marteau P, Abarbanel HD. Noise reduction in chaotic time series using scaled probabilistic methods. Journal of Nonlinear Science. 1991;1:313-43.
20. Pikovsky A. Discrete-time dynamic noise filtering. Sov J Commun Technol Electron. 1986;31:81.
21. Landa P, Rozenblum M. A comparison of methods for constructing a phase space and determining the dimension of an attractor from experimental data. Sov Phys-Tech Phys. 1989;34:1229-32.
22. Kostelich EJ, Yorke JA. Noise reduction: Finding the simplest dynamical system consistent with the data. Physica D: Nonlinear Phenomena. 1990;41(2):183-96.
23. Cawley R, Hsu G-H. Local-geometric-projection method for noise reduction in chaotic maps and flows. Physical review A. 1992;46(6):3057.
24. Sauer T. A noise reduction method for signals from nonlinear systems. Physica D: Nonlinear Phenomena. 1992;58(1-4):193-201.
25. Davies M. Noise reduction by gradient descent. International Journal of Bifurcation and Chaos. 1993;3(01):113-8.
26. Robins V, Abernethy J, Rooney N, Bradley E. Topology and intelligent data analysis. Intelligent Data Analysis. 2004;8(5):505-15.
27. Robins V, Rooney N, Bradley E. Topology-based signal separation. Chaos: An Interdisciplinary Journal of Nonlinear Science. 2004;14(2):305-16.
28. Alexander Z, Bradley E, Garland J, Meiss J. Iterated Function System Models in Data Analysis: Detection and Separation; CU-CS-1087-11. 2011.
29. Wang W-B, Zhang X-D, Chang Y, Wang X-L, Wang Z, Chen X, et al. Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating. Chinese Physics B. 2015;25(1):010202.
30. Wang M, Zhou Z, Li Z, Zeng Y. An adaptive denoising algorithm for chaotic signals based on improved empirical mode decomposition. Circuits, Systems, and Signal Processing. 2019;38:2471-88.
31. Tang G, Yan X, Wang X. Chaotic signal denoising based on adaptive smoothing multiscale morphological filtering. Complexity. 2020;2020:1-14.
32. Nichols J, Trickey S, Todd M, Virgin L. Structural health monitoring through chaotic interrogation. Meccanica. 2003;38(2):239-50.
33. Takens T. Detecting Strange Attractors in Turbulence. Lecture Notes in Math. 1981;898:336-81.
34. Kostelich EJ, Schreiber T. Noise reduction in chaotic time-series data: A survey of common methods. Physical Review E. 1993;48(3):1752.
35. Fraser AM, Swinney HL. Independent coordinates for strange attractors from mutual information. Physical review A. 1986;33(2):1134.
36. Broomhead DS, King GP. Extracting qualitative dynamics from experimental data. Physica D: Nonlinear Phenomena. 1986;20(2-3):217-36.
37. Vautard R, Yiou P, Ghil M. Singular-spectrum analysis: A toolkit for short, noisy chaotic signals. Physica D: Nonlinear Phenomena. 1992;58(1-4):95-126.
38. Karunasinghe DS, Liong S-Y. Chaotic time series prediction with a global model: Artificial neural network. Journal of Hydrology. 2006;323(1-4):92-105.
39. Han M, Zhong K, Qiu T, Han B. Interval Type-2 Fuzzy Neural Networks for Chaotic Time Series Prediction: A Concise Overview. IEEE transactions on cybernetics. 2019;49(7):2720-31.
40. Fan H, Jiang J, Zhang C, Wang X, Lai Y-C. Long-term prediction of chaotic systems with machine learning. Physical Review Research. 2020;2(1):012080.
41. Ouyang T, Huang H, He Y, Tang Z. Chaotic wind power time series prediction via switching data-driven modes. Renewable Energy. 2020;145:270-81.
42. Sun W, Chen H, Liu F, Wang Y. Point and interval prediction of crude oil futures prices based on chaos theory and multiobjective slime mold algorithm. Annals of Operations Research. 2022:1-31.
43. Burden F, Winkler D. Bayesian regularization of neural networks. Artificial neural networks: methods and applications. 2009:23-42.
44. Feng Q, Li Y. Denoising Deep Learning Network Based on Singular Spectrum Analysis—DAS Seismic Data Denoising With Multichannel SVDDCNN. IEEE Transactions on Geoscience and Remote Sensing. 2022;60:3071189.
45. Zheng Y-B, Huang T-Z, Zhao X-L, Jiang T-X, Ma T-H, Ji T-Y. Mixed noise removal in hyperspectral image via low-fibered-rank regularization. IEEE Transactions on Geoscience and Remote Sensing. 2019;58(1):734-49.
46. Lorenz EN. Deterministic nonperiodic flow. Journal of atmospheric sciences. 1963;20(2):130-41.
47. Theiler J. Efficient algorithm for estimating the correlation dimension from a set of discrete points. Physical review A. 1987;36(9):4456.
48. Grassberger P, Procaccia I. Measuring the strangeness of strange attractors. Physica D: nonlinear phenomena. 1983;9(1-2):189-208.
49. Carrassi A, Bocquet M, Demaeyer J, Grudzien C, Raanes P, Vannitsem S. Data assimilation for chaotic dynamics. Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications (Vol IV). 2022:1-42.
مهندسی مکانیک مدرس
دوره 24، شماره 1
دی 1402
صفحه 53-63