Full Text:   <2163>

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

Clicked: 4611

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

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


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.

@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",
publisher="Zhejiang University Press & Springer",

%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
%P 677-682
%@ 1673-565X
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0900754

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

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Deng, J., 2005. The Primary Methods of Gray System Theory. Huazhong University of Science and Technology Press, Wuhan, China (in Chinese).

[2]Gai, C., Pei, Y., 2003. Study of the GM (1,1)-Markov chain model on highway freight forecast. China Journal of Highway and Transport, 16(3):113-116 (in Chinese).

[3]Geng, B., Wang, J., Zhang, X., 2007. GM (1,1)-Markov model for prediction of bridge technical condition. Journal of Wuhan University of Technology (Transportation Science & Engineering), 31(1):107-110 (in Chinese).

[4]Gong, L., 2006. The NN model based on annealing arithmetic of genetic simulation under the application of water-demand forecast in Shaanxi Province. Underground Water, 28(5):10-13, 20 (in Chinese).

[5]He, Y., Huang, M., 2005. A grey-Markov forecasting model for the electric power requirement in China. LNCS, 3789:574-582.

[6]Li, G., Yamaguchi, D., Nagai, M., 2007. A GM (1,1)-Markov chain combined model with an application to predict the number of Chinese international airlines. Technological Forecasting & Social Change, 74(8):1465-1481.

[7]Liao, G., Tsao, T., 2004. Application of fuzzy neural networks and artificial intelligence for load forecasting. Electric Power System Research, 70(3):237-244.

[8]Liu, H., Zhang, H., 2002. Comparison of the city water consumption short-term forecasting methods. Transactions of Tianjin University, 8(3):211-215 (in Chinese).

[9]Tien, T., 2005. A research on the prediction of machining accuracy by the deterministic grey dynamic model DGDM(1, 1, 1). Applied Mathematics and Computation, 161(3):923-945.

[10]Yao, Q., Li, C., Ma, H., Zhang, S., 2007. Novel network traffic forecasting algorithm based on grey model and Markov chain. Journal of Zhejiang University (Science Edition), 34(4):396-400 (in Chinese).

[11]Zhou, G., Wang, H., Wang, D., Zhang, G., 2004. Urban water consumption forecast based on neural network model. Information and Control, 33(3):364-368 (in Chinese).

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE