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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Project supported by the National Natural Science Foundation of China (No. 50778121), the National Basic Research Program of China (No. 2007CB407306-1), and the National Water Pollution Control and Management of Science and Technology Project of China (No. 2008ZX07317-005)
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Tian, Ym., Shen, Hl., Zhang, L. et al. Utility water supply forecast via a GM (1,1) weighted Markov chain. J. Zhejiang Univ. Sci. A 11, 677–682 (2010). https://doi.org/10.1631/jzus.A0900754
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DOI: https://doi.org/10.1631/jzus.A0900754