Journal of Zhejiang University-SCIENCE A

, Volume 11, Issue 9, pp 677–682

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

• Yi-mei Tian
• Hai-liang Shen
• Li Zhang
• Xiang-rui Lv
Article

## 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.

### Key words

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

TU991.31

## Preview

### References

1. Deng, J., 2005. The Primary Methods of Gray System Theory. Huazhong University of Science and Technology Press, Wuhan, China (in Chinese).Google Scholar
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).Google Scholar
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).Google Scholar
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).Google Scholar
5. He, Y., Huang, M., 2005. A grey-Markov forecasting model for the electric power requirement in China. LNCS, 3789:574–582. [doi:10.1007/11579427_58]Google Scholar
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. [doi:10.1016/j.techfore.2006.07.010]
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. [doi:10.1016/j.epsr.2003.12.012]
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).Google Scholar
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. [doi:10.1016/j.amc.2003.12.061]
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).Google Scholar

© Zhejiang University and Springer-Verlag Berlin Heidelberg 2010

## Authors and Affiliations

• Yi-mei Tian
• 1
• Hai-liang Shen
• 2
• Li Zhang
• 1
• Xiang-rui Lv
• 1
1. 1.College of Environmental Science & EngineeringTianjin UniversityTianjinChina
2. 2.School of EngineeringUniversity of GuelphGuelphCanada