+ - دوره ۱۱ ‏()
+ - دوره ۱۰ ‏(۱۳۹۵)
+ - دوره ۹ ‏(۱۳۹۴)
+ - دوره ۸ ‏(۱۳۹۳)
+ - دوره ۷ ‏(۱۳۹۲)
+ - دوره ۶ ‏(۱۳۹۱)
+ - دوره ۵ ‏(۱۳۹۰)
+ - دوره ۴ ‏(۱۳۸۹)
+ - دوره ۳ ‏(۱۳۸۸)
+ - دوره ۲ ‏(۱۳۸۷)
+ - دوره ۱ ‏(۱۳۸۶)
رويكرد نظريه آشوب در تحليل سري زماني دبي رودخانه (مطالعه موردي: رودخانه کشکان)
عنوان (انگلیسی): Using chaos theory approach for time series analysis of river flow (Case study: Kashkan river)
نشریه: پژوهش آب ايران
شماره: پژوهش آب ايران (دوره: ۱۰، شماره: ۲)
نویسنده: انيس حسيني، مسعود ، ذاكرمشفق، محمد
کلیدواژه‌ها : بعد فراكتالي ، رودخانه كشكان ، فضاي فاز ، نظريه آشوب. ، حساسيت
کلیدواژه‌ها (انگلیسی): Fractal dimension , Phase space , Chaos theory , Kashkan River , Sensitivity to initial conditions
چکیده:

در سال‌هاي اخير نظريه آشوب راهي را پيش پاي پژوهش‌گران قرار داده که برخي از رفتار‌هاي در ظاهر تصادفي را ناشي از يک تعيين‌پذيري ساده مي‌داند و اين تعيين‌پذيري ساده مي‌تواند در فضاي فاز بهينه،‏ آشکار شود. بر اين اساس،‏ سري زماني دبي روزانه رودخانه کشکان تحليل آشوبناکي شده است. در اين پژوهش،‏ روش جديدي براي تخمين زمان تأخير بهينه در بازسازي فضاي فاز بر مبناي روش ميانگين اطلاعات متقابل پيشنهاد شده است. بر اين اساس،‏ به جاي در نظر گرفتن اولين كمينه موضعي تابع اطلاعات متقابل،‏ زمان وقوع كمترين مقدار تابع اطلاعات متقابل،‏ به عنوان زمان تأخير بهينه انتخاب مي‌شود. اين روش،‏ در مورد سري زماني دبي روزانه رودخانه كشكان به كار گرفته شده و كارايي آن در تخمين بعد فراكتالي سيستم حاكم بر جريان رودخانه كشكان،‏ بيشتر ارزيابي شده است. روش‌هاي نزديک‌ترين همسايگان كاذب و بعد همبستگي براي بررسي جاذب فراکتالي استفاده شده‌اند كه علاوه بر نشان ‌دادن وجود جاذب فراكتالي،‏ برتري روش جديد بازسازي فضاي فاز را نتيجه گرفته‌اند. همچنين،‏ حساسيت به شرايط اوليه،‏ به عنوان ويژگي ديگر سيستم‌هاي آشوبناك،‏ با روش‌هاي توان لياپانوف و بي‌نظمي كلموگروف در اين سري زماني بررسي شده است. در مجموع،‏ نتايج نشان از وجود آشوب در اين سري زماني و تناسب مدل‌هاي مبتني بر نظريه آشوب با سيستم حاکم بر جريان رودخانه کشکان است.

چکیده (انگلیسی):

Random-like behaviors in various natural phenomena led researchers to apply more accurate forecasting methods. While statistical models are more traditional to use for such complex behaviors, Chaos theory has been emerging as a new way to hydrologists and water engineers. In the Chaos theory viewpoint, random-like behavior can be related to a simple determinism which is hidden in the background of system dynamics and can be shown in an optimized phase space. If the conditions of a chaotic system which Chaos theory has been stated dominate the system behavior, dynamics in the phase space follows a fractal pattern which is aforementioned hidden determinism and called the attractor. The case study is the Kashkan River, which is located in Lorestan province, southwestern of Iran, where semi- arid climate is predominant. While the average number of dry days reach to 185 in a year, average precipitation is 375.3 mm during a water year. In the present study, the daily runoff time series of the Kashkan River have been analyzed using Chaos theory, following its observed random-like behavior. To perform chaotic analysis, a phase space should be reconstructed by determining optimize time delay and embedding dimension. So far, various methods have been suggested to calculate the time delay, including the Average Mutual Information method which have gained more popularity among the others. In this paper, a new method has been presented to estimate optimum time delay in the base of the AMI method. Therefore, instead of using the first local minimum of Mutual Information Function, its overall minimum has been considered to estimate optimum time delay. This method has been applied to daily runoff time series of the Kashkan River and its efficiency has been studied in fractal dimension estimation methods. While False Nearest Neighbors and Correlation Dimension methods have been employed to evaluate fractal dimension of system attractor, sensitivity to initial conditions have been studied using Lyapunov Exponent and Kolmogorov Entropy methods as the other major feature of chaotic behavior.
In the first part of this study, the AMI method and Mutual Information Function have been examined theoretically by evaluating its performance in a chaotic map called Rossler Map. It has been shown that the first minimum of MIF can be an optimum option to form best illustration of system chaotic attractor. While the first local minimum is more effective to mathematical functions such as RM, some other issues should be considered when the case study is a natural system, the MIF can have many minimums in different local sections. As mentioned earlier, the overall minimum of MIF have been used to determine the time delay as a new method phase space reconstruction which is obtained τ =107 days. False Nearest Neighbors and Correlation Dimension method have been used to evaluate fractal dimension, which showed the existence of a fractal attractor in phase space, and also the superiority of this new method for phase space reconstruction. Positive Lyapunov Exponent is a sign of sensitivity to initial conditions and therefore, chaotic behavior in system, which is more emphasized by calculating Kolmogorov Entropy in 3 different radius. Regardless of the selected radius, KE reaches to a finite number which is an evidence of chaotic behavior. While a certain number can not be calculated for Kolmogorov Entropy, it can be observed that by selecting a smaller radius, KE reaches to a finite positive number. Hence, the system entropy is consistent and follows a chaotic pattern.
Results indicated Chaos existence in this time series and suitability of Chaos theory-based models for governing system of flow in the Kashkan River. Sensitivity to initial conditions and fractal attractor as two major characteristics of chaotic system have been observed. In addition, a new AMI-based method to determine the optimum time delay has been showed better indication of system chaotic behavior in phase space. Compared with a traditional approach, the attractor which has been formed in reconstructed phase space behaves more constantly by increasing the embedding dimension in both FNN and CD methods. In comparison to similar studies analyzed the times series with different lengths, it can be concluded that the length of a time series cannot effectively adjust overall conclusion in the chaotic analysis of the Kashkan river flow governing system. Generally, evidences of chaotic behavior in the Kashkan river flow time series have been confirmed. Hence, employing chaotic models can be very helpful to forecast these time series.

فایل مقاله : [دریافت (2.2 MB)] ‏147 دریافت تاكنون
صاحب امتیاز:
دانشگاه شهرکرد
مدیر مسئول:
دکتر حسين صمدی
سردبیر:
دکتر منوچهر حيدرپور
مدیر داخلی:
دکتر محمدعلی نصراصفهانی