Geology Reference
In-Depth Information
5.4.2.3 Daily Solar Radiation Modelling with NW, W-SVM
and W-ANFIS
The conjunctive use of wavelets with neural networks is a relatively new modelling
concept
financial time series modelling in late 90s [
8
]. This
book use the discrete wavelet transforms (DWT) with data based intelligent models
like ANN, SVM and ANFIS to form hybrid models like NW, W-SVM and
W-ANFIS respectively. In order to serve this purpose, the daily solar radiation
modelling was performed at the Brue catchment using the relevant data sets
mentioned earlier (viz. like horizontal extraterrestrial radiation, daily mean air
temperature (averaged over 24 h), maximum daily air temperature, minimum daily
air temperature, daily wind speed (averaged over 24 h), and daily rainfall (summed
over 24 h)) decomposed into sub-signals of various resolution levels. The sub-
signals entered to the models like ANN, SVM and ANFIS to model the desired
daily solar radiation time series. The modelling ability of the proposed models was
compared with individual ANN-LM, ANFIS and SVM in the context of daily solar
radiation modelling. The procedure involved is explained below in the context of
NW model.
In the case of NW models, a multi-layer perceptron (MLP) feed forward ANN
model was used in conjunction with DWT. This kind of ANN was trained using the
widely used and popular back propagation training algorithm, levenberg
-
Marquardt
algorithm. The aim of the wavelet and ANN conjunction model (NW) is to predict
the daily solar radiation at time t using other inputs measured at the same time. We
didn
first introduced in the
t make an attempt to make multi time-step ahead prediction in this case of
solar radiation modelling. The employed Daubechies-4(db4) wavelet (the most
popular wavelet) decomposes the original input data series into corresponding sub-
series components. Each original input time series are decomposed into a 6 number
of DWs by DWT (3 approximations and 3 details time series). In this manner of
decomposition, each sub-signal may represent a special level of the seasonality
relationship which would be more useful for modelling than using the original
inputs. Selection of the
'
fit and appropriate DWs for construction of NW model to
estimate daily solar radiation is very tricky. The selection of the most important and
effective DWs depends largely on the hybrid model
'
s modelling ability. The con-
ventional way is estimation of correlation coef
cients between DWs and original
and desired daily solar radiation data, to provide a guideline on the selection of the
conjunction model inputs. However in this study we have used three detail series
and third approximation series for modelling, because such a combination has
mathematical validity to make the original data input. The conventional way of
making a new summed series obtained by adding the dominant DWs (obtained
based on correlation coef
cient) is in effect to cause loss of inherent information in
the actual series, and fails to reproduce the original data series. Because of these
two reasons we discarded the conventional approach and used three details and the
third approximation data series directly for modelling.
The discrete wavelet transfer model used for this modelling scheme is functioned
through two set of
