Abstract:
This study investigates the potential of nonlinear
local function approximation in a Takagi–Sugeno
(TS) fuzzy model for river flow forecasting. Generally, in a
TS framework, the local approximation is performed by a
linear model, while in this approach, linear function
approximation is substituted using a nonlinear function
approximation. The primary hypothesis herein is that the
process being modeled (rainfall–runoff in this study) is
highly nonlinear, and a linear approximation at the local
domain might still leave a lot of unexplained variance by
the model. In this study, subtractive clustering technique is
used for domain partition, and neural network is used for
function approximation. The modeling approach has been
tested on two case studies: Kolar basin in India and Kentucky
basin in USA. The results of fuzzy nonlinear local
approximation (FNLLA) model are highly promising. The
performance of the FNLLA is compared with that of a pure
fuzzy inference system (FIS), and it is observed that both
the models perform similar at 1-step-ahead forecasts.
However, the FNLLA performs much better than FIS at
higher lead times. It is also observed that FNLLA forecasts
the river flow with lesser error compared to FIS. In the case
of Kolar River, more than 40 % of the total data are
forecasted with\2 % error by FNLLA at 1 h ahead, while
the corresponding value for FIS is only 20 %. In the case of
3-h-ahead forecasts, these values are 25 % for FNLLA and
15 % for FIS. Performance of FNLLA in the case of
Kentucky River basin was also better compared to FIS. It is
also found that FNLLA simulates the peak flow better than
FIS, which is certainly an improvement over the existing
models.
