کاربرد نظریه آشوب و شبکه عصبی مصنوعی در بررسی و تخمین تبخیر از سطح آب دریاچه‌ها

نوع مقاله : مقالات پژوهشی

نویسندگان

1 دانشگاه سمنان

2 دانشگاه علم و صنعت ایران

3 دانشگاه تبریز

چکیده

ماهیت دینامیکی پدیده‌های هیدرولوژیکی و نیز محدودیت دسترسی ابزارهای ریاضیاتی مناسب، سبب گشته که اکثر مطالعات پیشین در این زمینه، منجر به نگرشی تصادفی و احتمالاتی گردد. بررسی قطعی و یا تصادفی بودن فرآیند دینامیکی مقادیر تبخیر از سطح آب دریاچه‌ها، به منظور انتخاب روش مناسب شبیه‌سازی و بررسی قابلیت پیش‌بینی، موضوع مهم و بحث برانگیزی است که در این تحقیق به آن پرداخته شده است. در این راستا، با توجه به قابلیت فراوان نظریه آشوب و مدل هوشمند شبکه عصبی در مطالعه رفتار سیستم‌های غیر‌خطی پویا مقادیر ماهانه تبخیر سطح آب دریاچه ارومیه در شمال‌غربی ایران، طی یک دوره آماری 40 ساله (1346-1386) با استفاده از مفاهیم این دو روش مورد بررسی و پیش‌بینی قرار گرفته است. نتایج بررسی شاخص‌های تعیین ماهیت آشوبناکی داده‌‌های تبخیر؛ نمای لیاپانوف مثبت و مقدار غیر‌صحیح شیب نمودار بعد همبستگی در مقابل شعاع همبستگی، همگی نشانگر رفتار کاملا آشوبناک سری زمانی تحت بررسی می‌باشد. نتایج صحت‌سنجی حاکی از دقت بالای نظریه آشوب و مدل شبکه عصبی مصنوعی- اندکی دقت بالاتر- می‌باشد به طوریکه میانگین خطای مطلق (MAE) و جذر میانگین مربعات خطا (RMSE) در شبکه عصبی مصنوعی نسبت به نظریه آشوب به ترتیب 51/2 و 25/2 میلی‌متر کاهش یافته‌اند. همچنین نتایج مربوط به ارتفاع تجمعی تبخیر در دوره صحت‌سنجی حاکی از برتری 8/3 درصدی شبکه عصبی مصنوعی نسبت به نظریه آشوب دارد.

کلیدواژه‌ها


عنوان مقاله [English]

Application of Chaos Theory and Artificial Neural Networks to Evaluate Evaporation from Lake's Water Surface

نویسندگان [English]

  • Saeed Farzin 1
  • Reza Hajiabadi 2
  • Mohammad Hossein Ahmadi 3
1 University of Semnan
2 Iran University of Science and Technology
3 University of Tabriz
چکیده [English]

Introduction: Dynamic nature of hydrological phenomena and the limited availability of appropriate mathematical tools caused the most previous studies in this field led to the random and the probabilistic approach. So selection the best model for evaluation of these phenomena is essential and complex. Nowadays different models are used for evaluation and prediction of hydrological phenomena. Damle and Yalcin (2007) estimated river runoff by chaos theory. khatibi et al (2012) used artificial neural network and gene expression programming to predict relative humidity. Zounemat and Kisi (2015) evaluated chaotic behavior of marine wind-wave system of Caspian sea. One of the important hydrological phenomena is evaporation, especially in lakes. The investigation of deterministic and stochastic behavior of water evaporation values in the lakes in order to select the best simulation approach and capable of prediction is an important and controversial issue that has been studied in this research.
Materials and Methods: In the present paper, monthly values of evaporation are evaluated by two different models. Chaos theory and artificial neural network are used for the analysis of stochastic behavior and capability of prediction of water evaporation values in the Urmia Lake in northwestern of Iran. In recent years, Urmia Lake has unpleasant changes and drop in water level due to inappropriate management and climate change. One of the important factors related to climate change, is evaporation. Urmia Lake is a salt lake, and because of existence valuable ecology, environmental issues and maintenance of ecosystems of this lake are very important. So evaporation can have an essential role in the salinity, environmental and the hydrological cycle of the lake.
In this regard, according to the ability of chaos theory and artificial neural network to analysis nonlinear dynamic systems; monthly values of evaporation, during a 40-year period, are investigated and then predicted. So that, 10 years of data are applied to model validation and a four-year time horizon is predicted by each model. In the present paper, a multi-layer perceptron network with a hidden layer are used. Number of neurons in the hidden layer is determined by try and error. Also different input combinations are used to find out the best artificial neural network model. Prediction accuracy of models is evaluated by three indexes. These three indexes are mean absolute error (MAE), root mean squared error (RMSE) and determination coefficient (R2).
Results and Discussion: Results of chaotic parameters such as a positive lyapunov exponent and the correlation dimension non-integer slope indicate that evaporation values in the Urmia Lake have chaotic behavior. So these values have not stochastic behavior and can be predicted by suitable models. Chaos theory and artificial neural network are used for prediction in this paper. Values of MAE, RMSE and R2 for validation data are 10.96, 14.67 and 0.97 for artificial neural network and 13.47, 16.92 and 0.97 for chaos theory, respectively. The determination coefficient is the same in the two models while the values of MAE and RMSE is lower in the artificial neural network. So error indexes indicate that the artificial neural network is slightly better than the chaos theory. In order to prediction by artificial neural network, The best input combination includes four time delays that they are values of a month ago, two months ago, eleven and twelve months ago. Because in the chaos theory only the evaporation time series is applied, in order to better comparison of artificial neural network and chaos theory, in the artificial neural network model only the evaporation time series is used. Results of the four-year time horizon indicate somewhat similar behavior of two models especially in the minimum and maximum values of time series. In the maximum and minimum value chaos theory and artificial neural network predict similar values while in the other values there are some difference and the artificial neural network model predicted values less than chaos theory.
Conclusions: The results obtained from the chaotic nature determination parameters of the evaporation data, positive lyapunov exponent and the correlation dimension non-integer slope; indicate the chaotic behavior of study time series. Therefore, the system has a hidden pattern (i.e., the system isn’t Stochastic). The verification results indicate the high accuracy of chaos theory and neural network models - a little more accurate - and it was found that both models have similar accuracy in prediction of the future evaporation values or data that haven't been recorded in the past.

کلیدواژه‌ها [English]

  • prediction
  • Hydrological phenomena
  • Urmia Lake
  • Lyapunov exponent
1- Abarbanel H. 1996. Analysis of observed chaotic data. Springer, Verlag, New York.
2- Banks J., Dragan V. and Jones A. 2003. Chaos, a mathematical introduction. Cambridge University Press.
3- Cao L. 1997. Practical method for determining the minimum embedding dimension of scalar time series. Physica D: Nonlinear Phenomena, 110:43-50.
4- Damle C., and Yalcin A. 2007. Flood prediction using time series data mining. Journal of Hydrology, 333:305-316.
5- Doung N.H., Nguyen T.H., Snasel V. 2015. A hybrid approach for predicting river runoff. Intelligent Data analysis and Applications, 370:61-71.
6- Elshorbagy A., Simonovic S.P., and Panu U.S. 2002. Estimation of missing stream flow data using principles of chaos theory. Journal of Hydrology, 255:123–133.
7- Frazier C., and Kockelman K. 2004. Chaos theory and transportation systems: An instructive example. Procof 83th Annual Meeting of the Transportation ResearchBoard, Washington D.C., USA.
8- Ghaheri A., Ghorbani M.A., Del Afrooz H., Malekani L. 2012. Evaluation of stream flow using chaos theory. Iran Water Research Journal, 6(10):177-186. (in Persian with English Abstract)
9- Grassberger P., Procaccia I. 1983. Characterization of strange attractors. Physical Review Letters, 50 (14):346-349.
10- Hassanzadeh, E. 2010. Partitioning impacts of climate and hydraulic structures on water level of Urmia lake (Master Thesis). University of Tabriz, Iran. (in Persian with English Abstract)
11- Hassanzadeh Y., Aalami M.T., Farzin S., Sheikholeslami S.R., Hassanzadeh E. 2012. Study of chaotic nature of daily water level fluctuations in Urmia lake. Journal of Civil Engineering and Environment, 42(1):9-20. (in Persian with English Abstract)
12- Hassanzadeh Y., Lotfollahi-Yaghin M.A., Shahverdi S., Farzin S., Farzin N. 2013. De-noising and prediction of time series based on the wavelet algorithm and chaos theory (case study: SPI drought monitoring index of Tabriz city). Iran-Water Resources Research, 8(3):1-13. (in Persian with English Abstract)
13- Hilborn R.C. 2000. Chaos and Nonlinear Dynamics. Oxford University Press.
14- Khatibi R., Ghorbani M.A., Aalami M.T., Kocak K., Makarynskyy O., Makarynska D., and Aalinezhad M. 2011. Dynamics of hourly sea level at Hillarys Boat harbour, Western Australia: a chaos theory perspective. Ocean Dynamics, 61:1797–1807.
15- Khatibi R., Naghipour L., Ghorbani M.A., Aalami M.T. 2013. Predictability of relative humidity by two artificial intelligence techniques using noisy data from two Californian gauging stations. Neural Computing and Appliccations, 23(7):2241-2252.
16- Khan S., Ganguly A.R., and Saigal S. 2005. Detection and predictive Modeling of chaos in finite hydrologycal time series. Nonlinear Processes in Geophysics, 12: 41-53.
17-Kim S., Shiri J., Kisi O., Singh V.P. 2013. Estimating daily pan evaporation using different data-driven methods and lag-time pattern. Water Resources Management, 27:2267-2286.
18- Kocak K., Bali A., and Bektasoglu B. 2007. Prediction of monthly flows by using chaotic approach. p. 553-559. International Congress on River Basin Management, 22-24 March, Antalya, Turkey, 4 (117).
19- Ng W., Panu U., Lenoxx W. 2007. Based analytical techniques for daily extreme hydrological observations. International Journal of Hydrology, 342:17-41.
20- Regonda S.K., Sivakumar V., and Jain A. 2004. Temporal scaling in the river flow: Can it be chaotic? Hydrological Sciences Journal, 49(3):373-385.
21- Shang P., Na X., and Kamae S. 2009. Chaotic analysis of time series in the sediment transport phenomenon. Chaos Solitons and Fractals, 41:368–379.
22- Sivakumar B. 2000. Chaos theory in hydrology: important issues and interpretations. Journal of Hydrology, 227: 1-20.
23- Solomatine D.P., Velickov S., and Wust J.C. 2001. Predicting water levels and currents in the north sea using chaos theory and neural networks. p. 1-11. Proceeding of the Congress-International Association for Hydraulic Research, 29th Iahr Congress, Beijing, China.
24- Stehlik J. 1999. Deterministic chaos in runoff series. Journal of Hydrololy and Hydromechanics, 47(4):271–287.
25- Sterman J.D. 2000. Business dynamics. McGraw-Hill, Book Co, Boston.
26-Terzi O. 2013. Daily pan evaporation estimation using gene expression programming and adaptive neural-based fuzzy inference system. Neural Computing and Applications, 23(3):1035-1044.
27- Wu J., Lu J., and Wang J. 2009. Application of chaos and fractal models to water quality time series prediction. Environmental Modeling & Software, 24:632–636.
28- Yu H.H., Jenq N.H. 2002. Handbook of neural network signal processing. CRC Press.
29-Zounemat-Kermani M., Kisi O. 2015. Time series analysis on marine wind-wave characteristics using chaos theory. Ocean Engineering, 100:46-53.