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Fig. 5.24 Solar radiation as observed and estimated using the ANN model with conjugate
algorithm for the training data set. a scatter plot, b line diagram
In this section of study, various hidden layer neuron number combinations were
tested for the ANN models to find the best hidden layer node number for modelling.
We constructed a feed forward neural network with 9 neurons in hidden layer
trained using the BFGS algorithm, Conjugate Gradient algorithms and Leven-
berg
Marquardt training algorithm; and their performance was compared with that
of the LLR model (shown in Table
5.1
).
The size of training data was already determined as 770 data points through the
M-Test analysis, and the target mean-squared error (MSError) was identi
-
ed as
0.0354 (scaled) for M = 770. The resulting plots (both scatter and line plot) of
training and validation results produced by the Conjugate Gradient Algorithm based
model are shown in Figs.
5.24
a, b and
5.25
a, b. The prediction results (both scatter
plots and line diagram) of BFGS method based ANN model for training and
validation data are shown in the form of scatter plots in Figs.
5.26
a, b and
5.27
a, b.
The conjugate gradient ANN model performed better in the validation data set
than BFGS algorithm based ANN model with RMSE value of 35.417 W/m
2
(28.1 % of mean observed solar radiation) and MBE value of
0.162 W/m
2
−
whereas the latter produced 39.236 W/m
2
(29.7 % of mean observed solar radia-
0.255 W/m
2
, respectively. The Levenberg
tion) and
Marquardt algorithm based
ANN outperformed both conjugate gradient and BFGS ANNs in both the training
−
-
Fig. 5.25 Solar radiation as observed and estimated using the ANN model with conjugate
algorithm for the validation data set. a scatter plot, b line diagram
