ارائه الگوریتم جدید برای پیش‌بینی سرعت باد مبتنی بر مدل پنهان مارکوف

نوع مقاله: مقاله تحقیقی‌ (پژوهشی‌)

نویسندگان

1 استادیار دانشگاه شهید بهشتی، تهران، ایران

2 دانشجوی دکتری دانشگاه شهید بهشتی، تهران، ایران

3 دانشیار پژوهشکده هواشناسی، تهران، ایران

چکیده

در این مقاله ضمن ارائه مبانی نظری مدل پنهان مارکوف، ساختار مناسب آن برای مدل‌سازیِ سری زمانی باد پیشنهاد و اجرا شده است. مدل پیشنهادی در شناسایی رژیم‌های حاکم در سری‌های زمانی باد سطح زمین در فرودگاه امام خمینی آزمایش و برای اجرای آن از داده جمع‌آوری‌شده طی چهار سال متوالی استفاده شده است. ضمن ارائه آزمون ایستاییِ زمانی برای مدل مارکوف مرتبه اول، این آزمون برای مدل پنهان مارکوف توسعه داده شده است و نتایج آزمون ایستایی دو روش مقایسه شده‌اند. نتایج نشان می‌دهد که آزمون ایستایی زمانی روی داده سرعت باد در مدل پیشنهادی نسبت به مدل مارکوف مرتبه اول در 70 تا 85 درصد موارد بهبود یافته است که این افزایش ایستایی زمانی به معنی به‌دست‌آوردن دقتِ بیشتر در پیش‌بینی سرعت باد با استفاده از مدل پنهان مارکوف است. اثر تغییر تعداد رژیم‌ها از دو به سه و چهار، در ماه‌های مختلف سال بررسی و نتایج آن با نتایج اجرای مدل مارکوف مرتبه اول مقایسه شده است. نتایج نشان از این دارد که با تشخیص و تفکیک رژیم با مدل پیشنهادی، در پیش‌بینی ارائه‌شده پراکندگی احتمالات کمتر می‌شود. درنهایت، با به‌دست‌آوردن پیش‌بینی سرعت باد با روش پیشنهادی و همچنین روش مارکوف مرتبه اول و مقایسه با مقادیر واقعی ثبت‌شده و محاسبه ریشه مجموع مربعات خطا برای هر دو روش، نشان داده شده است که روش پیشنهادی نتایج بهتری تولید می‌کند.

کلیدواژه‌ها


عنوان مقاله [English]

A Novel Algorithm for Wind Forecasting Based on Hidden Markov Model

نویسندگان [English]

  • Golamreza Latif Shangahi 1
  • Navid Chiniforoush 2
  • majid azadi 3
1 Associate Professor, Shahid Beheshti University, Tehran, Iran
2 PHD candidate, Shahid Beheshti University, Tehran, Iran
3 Assistant professor, Atmospheric Science and Meteorological Research Center, Tehran, Iran
چکیده [English]

Meteorological time series are used as important input for risk forecasting and related warning systems. Wind is one of the most important atmospheric parameters because of its extensive effects in many industries and fields of human life. Many researches have been carried out to improve forecasting of the wind with the aim of improving output of wind farms, issuing warning for public, detection of wind shear and turbulence in the airports and so on. Generally, there are two main groups of meteorological forecasting methods, one is based on physical relation of atmospheric parameters, and the other is based on historical data. For a long time, time series of wind have been used for forecasting the wind speed. ARMA (Auto-Regressive Moving Average) and Markov model are two important groups of time series analyzing methods. In this paper, the capability of HMM (Hidden Markov Model) is described and used for identification and classification of wind time series. Based on theoretical concept of HMM, a proper method is proposed, and utilized for simulation with real data. The proposed method is based on constructing a multinomial–HMM on wind direction time series. The whole range of possible wind direction (360 degrees) is divided into 16 groups and then categorized to different regimes. Wind forecasting is then carried out based on these separated categories. Temporal stationary test which is well known for Markov chain, is extended for the proposed method and used for its efficiency evaluation. Efficiency of the proposed model is investigated by using real data of IKIA (Imam Khomeini International Airport). A part of the collected data including wind speed and direction is used for constructing of the proposed model and another part is used for its evaluation. The achieved results show that there is improvement in temporal stationary for HMM vs simple Markov model, in 70 to 80 percent of cases. History of the observations in IKIA shows that there are two major wind directions in the area which are related to the local condition: from mountain to the desert in the day times from north-west and from the opposite direction at nights. These are the only important directions in the area in summer when there are no important meteorological phenomena, while in winter one major direction would be added from south-west because of the large scale meteorological systems. Increasing the number of regimes has also significant improvement in temporal stationary in winter times, while there is no important improvement in summer times. This has a good harmony with long term recorded data.

کلیدواژه‌ها [English]

  • Hidden Markov Model
  • Temporal stationary
  • wind speed
  • regime separation
  • Forecasting

چینی­فروش، ن. و لطیف شبانگاهی، غ.، 2018، تجهیزات انداز‌ه‌گیری سرعت و جهت باد: روش‌ها، چالش­ها و روند فنّاوری: پژوهش­های اقلیم شناسی، 33، 43-62.

Ailliot, P., Bessac, J., Monbet, V., and Pene, F., 2015, Non-homogeneous hidden Markov-switching models for wind time series: Journal of Statistical Planning Inference, 160, 75-88.

Ailliot, P., and Monbet, V., 2012, Markov-switching autoregressive models for wind time series: Environmental Modelling Software, 30, 92-101.

Billinton, R., Chen, H., and Ghajar, R., 1996, Time-series models for reliability evaluation of power systems including wind energy: Microelectronics Reliability, 36(9), 1253-1261.

Bitner-Gregersen, E. M., Bhattacharya, S. K., Chatjigeorgiou, I. K., Eames, I., Ellermann, K., Ewans, K., Hermanski, G., Johnson, M. C., Ma, N., and Maisondieu, Ch., 2014, Recent developments of ocean environmental description with focus on uncertainties: Ocean Engineering, 86, 26-46.

Callaway, D. S., 2010, Sequential reliability forecasting for wind energy: Temperature dependence and probability distributions: IEEE Transactions on Energy Conversion, 25(2), 577-585.

Carta, J. A., Ramirez, P., and Velazquez, S., 2009, A review of wind speed probability distributions used in wind energy analysis: Case studies in the Canary Islands: Renewable Sustainable Energy Reviews, 13(5), 933-955.

D’Amico, G., Petroni, F., and Prattico, F., 2012, Wind speed modeled as a semi-Markov process: Environmetrics, 24(6), 367-376.

D’Amico, G., Petroni, F., and Prattico, F., 2014, Wind speed and energy forecasting at different time scales: A nonparametric approach: Statistical Mechanics and its Applications, 406, 59-66.Hocaoglu, F. O., Gerek, O. N., and Kurban, M., 2008, The effect of Markov chain state size for synthetic wind speed generation: paper presented at the Proceedings of the 10th International Conference on Probablistic Methods Applied to Power Systems, IEEE, 1-4.

Jiang, Y., Song, Z., and Kusiak, A., 2013, Very short-term wind speed forecasting with

 

Bayesian structural break model: Renewable Energy, 50, 637-647.

Karatepe, S., and Corscadden, K., 2013, Wind speed estimation: incorporating seasonal data using Markov chain models: ISRN Renewable Energy.

Lei, M., Shiyan, L., Chuanwen, J., Hongling, L., and Yan, Z., 2009, A review on the forecasting of wind speed and generated power: Renewable and Sustainable Energy Reviews, 13(4), 915-920.

Leroux, B., 1989, Maximum likelihood estimation for mixture distributions and hidden Markov models: University of British Columbia.

Lou, H. L., 1995, Implementing the Viterbi algorithm: IEEE Signal processing magazine, 12(5), 42-52.

Picard, F., 2007, An introduction to mixture models, 7.

Pinson, P., and Madsen, H., 2012, Adaptive modelling and forecasting of offshore wind power fluctuations with Markov switching autoregressive models: Journal of forecasting, 31(4), 281-313.

Schlipf, D., Schlipf, D. J., and Kühn, M., 2013, Nonlinear model predictive control of wind turbines using LIDAR: Wind Energy, 16(7), 1107-1129.

Scholz, T., Lopes, V. V., and Estanqueiro, A., 2014, A cyclic time-dependent Markov process to model daily patterns in wind turbine power production: Energy, 67, 557-568.

Shamshad, A., Bawadi, M. A., Hussin, W. W., Majid, T. A., and Sanusi, S., 2005, First and second order Markov chain models for synthetic generation of wind speed time series: Energy, 30(5), 693-708.

Suomalainen, K., Silva, C. A., Ferrão, P., and Connors, S., 2012, Synthetic wind speed scenarios including diurnal effects: Implications for wind power dimensioning: Energy, 37(1), 41-50.

Tagliaferri, F., Hayes, B. P., Viola, I. M., Djokić, S. Z., 2016, Wind modelling with nested Markov chains: Journal of Wind Engineering Industrial Aerodynamics, 157, 118-124.

Wang, X., Guo, P., and Huang, X., 2011, A review of wind power forecasting models: Energy Procedia, 12, 770-778.

Xie, K., Liao, Q., Tai, H.M., and Hu, B., 2017, Non-Homogeneous Markov wind speed time series model considering daily and seasonal variation characteristics: IEEE Transactions on Sustainable Energy, 8(3), 1281-1290.