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CLC number: TU991.31

On-line Access: 2010-09-07

Received: 2009-12-10

Revision Accepted: 2010-06-01

Crosschecked: 2010-08-11

Cited: 4

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Citations:  Bibtex RefMan EndNote GB/T7714

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Journal of Zhejiang University SCIENCE A 2010 Vol.11 No.9 P.677-682

http://doi.org/10.1631/jzus.A0900754


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


Author(s):  Yi-mei Tian, Hai-liang Shen, Li Zhang, Xiang-rui Lv

Affiliation(s):  College of Environmental Science & Engineering, Tianjin University, Tianjin 300072, China, School of Engineering, University of Guelph, Guelph, Ontario, N1G 2W1, Canada

Corresponding email(s):   ymtian_2000@yahoo.com.cn, shenh@uoguelph.ca

Key Words:  Dynamic adjustment interval (DAI), Forecast, GM (1, 1), Markov chain, Water supply


Yi-mei Tian, Hai-liang Shen, Li Zhang, Xiang-rui Lv. Utility water supply forecast via a GM (1,1) weighted Markov chain[J]. Journal of Zhejiang University Science A, 2010, 11(9): 677-682.

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T1 - Utility water supply forecast via a GM (1,1) weighted Markov chain
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J0 - Journal of Zhejiang University Science A
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PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.A0900754


Abstract: 
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.

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