Fuzzy model identification based on cluster estimation for reservoir inflow forecasting

Fuzzy theory appears to be extremely effective at handling dynamic, non-linear and noisy data, especially when the underlying physical relationships are not fully understood. Since hydrologists are still uncertain about many of the aspects of the physical processes in the watershed, fuzzy theory has proved to be a very attractive tool enabling them to investigate such problems. The effectiveness of the fuzzy model lies in the identification of the antecedent membership function (MF), which is generally addressed through a fuzzy clustering approach. Most of the applications of fuzzy computing in hydrology seem to have selected the clustering algorithm quite arbitrarily. However, it is apparent that, as the antecedent parameters are based solely on the identified clusters, the method used for clustering should certainly have an impact on the overall performance of the model. This paper presents the results of a study conducted to investigate the impact of choice of clustering algorithm on the overall performance of a fuzzy-based hydrologic model. The research is illustrated through a case study of developing a Takagi-Sugeno fuzzy model for reservoir inflow forecasting in the Narmada basin, India. The model was developed using two popular clustering techniques, namely Gustafson-Kessel (GK) and subtractive clustering (SC), and was extensively evaluated for performance based on various statistical indices. The results show that the model performance is comparable at a 1 h lead forecast. However, it is observed that the GK approach results in a better performance than the SC approach in computing forecasts at higher lead times. The analysis suggest that the GK method clusters the input space based on the actual pattern, since it uses a membership-grade weighted-distance measure as the measure of closeness, whereas the SC method classifies the input space more logically according to the magnitude of flow available in the data set.