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In-Depth Information
Fig. 4.19 The proposed wavelet-ANFIS (W-ANFIS) scheme
4.6.6 Wavelet-ANFIS Model (W-ANFIS)
This topic introduces another conjunction model. Wavelet-neuro-fuzzy is applied in
subsequent sections for solar radiation modeling, rainfall-runoff modeling, and
evapotranspiration estimation. Thewavelet transform, a strongmathematical tool which
provides a time
frequency representation of analyzed data in the time domain, has been
used in conjunction with a conventional ANFIS model. In this section, the particular
details of the model are explained in the context of rainfall-runoff modeling. The input
antecedent information data considered are decomposed into wavelet subseries by
DWT, and then the neuro-fuzzymodel is constructedwith appropriatewavelet subseries
as input, and desired time step of the original runoff time series as output. Each of
subseries DWs is a detailed time series and has a distinct contribution to the original time
series data [
94
]. In this topic, the proposed model is used in association with data
selection approaches, particularly the Gamma Test. The selection of dominant subseries
is an important procedure which was performed by different approaches mentioned in
Chap.
3
and compared with the co-correlation approach. The schematic diagram of the
proposed hybrid scheme is given in Fig.
4.19
. In Fig.
4.19
, D stands for details time
series and A stands for approximation time series.
-
4.6.7 Wavelet-Support Vector Machines (W-SVM) Model
Figure
4.20
illustrates the
flowchart describing the proposed hybrid SVM scheme-
based rainfall-runoff modeling carried out in this topic. In stage 1, antecedent rainfall
and runoff information of the Brue catchment were decomposed into detailed coef-
ficients (D) and three series of approximation (A) sub-time series. In the case of SVM,
