Utility water supply forecast via a GM (1,1) weighted Markov chain  

作　　者：Yi-mei TIAN Hai-liang SHEN Li ZHANG Xiang-rui LV 

机构地区：[1]College of Environmental Science & Engineering, Tianjin University, Tianjin 300072, China [2]School of Engineering, University of Guelph, Guelph, Ontario, N1G 2W1, Canada

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2010年第9期677-682,共6页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：Project supported by the National Natural Science Foundation of China (No. 50778121);the National Basic Research Program of China (No. 2007CB407306-1);the National Water Pollution Control and Management of Science and Technology Project of China (No. 2008ZX07317-005)

摘　　要：This paper describes the procedure of using the GM (1,1) weighted Markov chain (GMWMC) to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps: (1) use GM (1,1) to fit the trend of the data, and obtain the relative error of the fitted values; (2) divide the relative error into ‘state’ data based on pre-set intervals; (3) calibrate the weighted Markov chain model: herein the parameters are the pre-set interval and the step of transition matrix (TM); (4) by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, (5) validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval (DAI) is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data.This paper describes the procedure of using the GM （1,1） weighted Markov chain （GMWMC） to forecast the utility water supply, a quantity that usually has significant temporal variability. The GMWMC is formulated into five steps： （1） use GM （1,1） to fit the trend of the data, and obtain the relative error of the fitted values; （2） divide the relative error into ‘state’ data based on pre-set intervals; （3） calibrate the weighted Markov chain model： herein the parameters are the pre-set interval and the step of transition matrix （TM）; （4） by using auto-correlation coefficient as the weight, the Markov chain provides the prediction interval. Then the mid-value of the interval is selected as the relative error for the data. Upon combining the data and its relative error, the predicted magnitude in a specific time period is obtained; and, （5） validate the model. Commonly, static intervals are used in both model calibration and validation stages, usually causing large errors. Thus, a dynamic adjustment interval （DAI） is proposed for a better performance. The proposed procedure is described and demonstrated through a case study, which shows that the DAI can usually achieve a better performance than the static interval, and the best TM may exist for certain data.

关 键 词：Dynamic adjustment interval （DAI） FORECAST GM （1 1） Markov chain Water supply 

分 类 号：O178[理学—数学] TP391.41[理学—基础数学]