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.
This paper presents a method to calibrate pipe roughness coefficient (i.e., Manning n-factor) with genetic algorithm (GA) under multiple loading conditions. Due to the old pipe age as well as deleting valves and blends in the skeleton of distribution network, most of the pipes in hydraulic model of practical water distribution system (WDS) are rough. The commonly used Hazen-Williams C-factor is therefore replaced by Manning n-factor in calibrating WDS hydraulic model. Adjustment to GA is designed, and the program efficiency is improved. A case study shows that the adjustment can save 60% of the total runtime. About 90% of the relative differences between simulated and observed pressures at monitoring locations are lower than 3%, which suggests that the proposed adjustment to the calibration is efficient and effective.
