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Fig. 7.40 Sensitivity versus complexity
—
case study: evaporation modeling
achievable best error for the models. It has been observed that the RMSE decreases
with increasing complexity as the basic hypothesis. The more complex NNARX
and SVM models have shown more erroneous prediction than the relatively simple
LLR and ANN-LM models in the case study on data based modeling on evapo-
ration. The better prediction in terms of error is exhibited by the NW model,
followed by the W-ANFIS, ANFIS, and W-SVM models. To
find the modeling
sensitivity of the model to the inputs, we have changed all the inputs in the range
−
30 to +30 % and analyzed the variation of output in relation to the change in
inputs. The sensitivity diagrams were drawn for each model, averaging the change
in outputs with the percentage change in inputs. The slopes of these sensitivity
diagrams are estimated and each slope value is considered as the measure of sen-
sitivity. The sensitivity curves for different models are shown in Fig.
7.39
.
The variation of the sensitivity of different models on daily evaporation data with
the corresponding complexity values are shown in Fig.
7.40
. The sensitivity-
complexity relation shows a positive linear trend with increasing complexity with
an R
2
value of 0.728. Models such as ANN-LM, LLR, and NNARX fall very close
in this plot. It has been observed that the higher value of complexity and sensitivity
was associated with the W-SVM model in this case study. Even so, the W-ANFIS
model is somewhat complex in structure, and the sensitivity value was observed
close to that of basic ANFIS model. Even though the NW model has a complex
structure, in this particular case study, the model achieved the designated target
accuracy in less time, and thus the complexity value is less.
Table
7.10
shows the different models and the variation of different modeling
attributes which decide overall utility of the models.
The normal range of overall model utility index (U) is 0 and 1. The model with
higher U value is considered to be the model with better utility in terms of modeling
aspects such as uncertainty and complexity. The utility diagram of the models used
in the evaporation modeling is shown in Fig.
7.41
. It is seen that the NW model has
the higher utility in this modeling case study with U value of 0.342. The relatively
