Water leakage forecasting: the application of a modified fuzzy evolving algorithm

Abstract

This paper investigates the use of evolving fuzzy algorithms in forecasting. An evolving Takagi-Sugeno (eTS) algorithm, which is based on a recursive version of the subtractive algorithm is considered. It groups data into several clusters based on Euclidean distance between the relevant independent variables. The Mod eTS algorithm, which incorporates a modified dynamic update of cluster radii while accommodating new available data is proposed. The created clusters serve as a base for fuzzy If-Then rules with Gaussian membership functions which are defined using the cluster centres and have linear functions in the consequent i.e., Then parts of rules. The parameters of the linear functions are calculated using a weighted version of the Recursive Least Squares algorithm. The proposed algorithm is applied to a leakage forecasting problem faced by one of the leading UK water supplying companies. Using the real world data provided by the company the forecasting results obtained from the proposed modified eTS algorithm, Mod eTS, are compared to the standard eTS algorithm, exTS, eTS+ and fuzzy C-means clustering algorithm and some standard statistical forecasting methods. Different measures of forecasting accuracy are used. The results show higher accuracy achieved by applying the algorithm proposed compared to other fuzzy clustering algorithms and statistical methods. Similar results are obtained when comparing with other fuzzy evolving algorithms with dynamic cluster radii. Furthermore the algorithm generates typically a smaller number of clusters than standard fuzzy forecasting methods which leads to more transparent forecasting models.