Метод інтервального прогнозування водоспоживання із використанням моделі періодичної авторегресії

Abstract

Здійснено статистичний аналіз похибок прогнозу водоспоживання на основі моделі періодичної авторегресії з метою встановлення їх ймовірнісного розподілу. Проведено верифікацію моделі водоспоживання. Встановлено некорельованість похибок прогнозу, чим підтверджено адекватність моделі водоспоживання у вигляді послідовності періодичної авторегресії. Розроблено метод інтервального прогнозування водоспоживання на основі методів непараметричної статистики.

Among the problems of water supply systems, the most significant are: zoning of water supply systems, pressure normalizing, selection of the optimal parameters for water consumption meters control. These problems can be solved by means of water consumption forecasting. The actual task is the development of water forecasting method for detection of water supply system emergency conditions: water leaks and poor service. This method must allow to estimate forecasting errors. Interval forecast is most useful in practical application. As a result they provide intervals which contain forecasting values with pre-specified probability. Conventional methods for water supply forecasting do not meet the requirements as to the stochastic and daily-cyclic nature of hourly water consumption process. This article describes new mathematical model and forecasting method, which contributes to the solution of the tasks, concerning water supply systems. The objective of this article is to show the developed method of water consumption operative interval forecasting. Hourly water consumption process has been modeled as the periodic autoregression time series, after which, forecasting errors were estimated by performing the forecasting in the known time interval. Statistical analysis of water consumption forecasting errors has been performed using periodic autoregression model. It allowed to identify probabilistic distribution of water consumption process. New model of water consumption has been verified using the Ljung-Box Q-test. Miscorrelation of water consumption errors series has been found. Thus, adequacy of the proposed water consumption model as periodic autoregression series was proved. The method of water consumption interval forecasting has been developed using the methods of nonparametric statistics. The method of water consumption interval forecasting was tested on a computer. The results of the experimental forecasting were compared with the real water consumption values for the appropriate time points. Probability of falling out of the intervals was estimated. These probability values are very close to those probability ones, specified as the input argument to the interval estimation function. Thus, the validity of this method for solving tasks of water consumption interval forecasting, has been concluded.