CLC number: TU991.31
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2010-08-11
Cited: 4
Clicked: 5640
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.
@article{title="Utility water supply forecast via a GM (1,1) weighted Markov chain",
author="Yi-mei Tian, Hai-liang Shen, Li Zhang, Xiang-rui Lv",
journal="Journal of Zhejiang University Science A",
volume="11",
number="9",
pages="677-682",
year="2010",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0900754"
}
%0 Journal Article
%T Utility water supply forecast via a GM (1,1) weighted Markov chain
%A Yi-mei Tian
%A Hai-liang Shen
%A Li Zhang
%A Xiang-rui Lv
%J Journal of Zhejiang University SCIENCE A
%V 11
%N 9
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%@ 1673-565X
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0900754
TY - JOUR
T1 - Utility water supply forecast via a GM (1,1) weighted Markov chain
A1 - Yi-mei Tian
A1 - Hai-liang Shen
A1 - Li Zhang
A1 - Xiang-rui Lv
J0 - Journal of Zhejiang University Science A
VL - 11
IS - 9
SP - 677
EP - 682
%@ 1673-565X
Y1 - 2010
PB - Zhejiang University Press & Springer
ER -
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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