Environmental Engineering Reference
In-Depth Information
between
d¼
24 and
d¼
36, Figure 8.13a suggests
that the performance on the three peaks is
not significantly reduced. For
d¼
48 the error on
the first peak is significantly increased although
accuracy remains high for peaks 2 and 3
(see Fig. 8.12a). Overall, these results appear to
be comparable with those obtained using the
TF-Kalman filter model proposed by Romanowicz
et al. (2006).
both LID3 and ULID3 is shown as a time series in
Figure 8.10a together with the actual measure-
ment values. Figure 8.10b shows a scatter plot of
predicted against actual values for both algo-
rithms. The three highest peaks shown in
Figure 8.10a (labelled peak 1, peak 2 and peak 3)
resulted in significant flooding and it is therefore
crucial that any effective prediction algorithm
should accurately predict these peak values with
as long a lead time as possible.
All three peaks in the test data exceed the max-
imal output domain values present in the training
data. These new data are therefore very hard to
predictwithout updating themodel. Consider peak
1, the highest peak shown in Figure 8.10a. LID3 is
unable to interpolate beyond the range of values in
the training data and consequently fails to predict
the peak accurately. Figure 8.10a shows that
ULID3 is more accurate than LID3 on the three
peak values, although improvement on peak 1 is
limited by the fact that since we are predicting 24
hours ahead there is a 24-hour delay before updat-
ing can occur. Further significant improvements
are shown for peaks 2 and 3.
Figures 8.11 and 8.12 show the performance of
ULID3 with lead times of
d¼
36 hours and
d¼
48
hours. Table 8.2 gives the RMSE for both LID3 and
ULID3 for lead times ranging from
d¼
24 to
d¼
72.
Although there is a notable difference in RMSE
Conclusions
In this chapter we have presented two AI learning
algorithms within the Label Semantics frame-
work. These can automatically generate fuzzy
rule-based models from data and also incorporate
probabilistic uncertainty. These methods have
been shown to perform well across a number of
case study problems in flood forecasting. Indeed,
their predictive accuracy is comparable and some-
times better than that of more black-box ap-
proaches such as Neural Networks and Support
Vector Machines. We have also given examples of
rules extracted from the fuzzy models that give
transparency to the forecasting process.
References
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Table 8.2
Comparison of results with LID3 and ULID3
for prediction of river level at Buildwas at various lead
times
Accuracy (RMSE)
t
þ
d
hours
LID3
ULID3
þ
72 h
0.91
0.88
t
t
þ
66 h
0.86
0.82
þ
60 h
0.78
0.75
t
þ
54 h
0.70
0.67
t
þ
48 h
0.64
0.59
t
t
þ 42 h
0.54
0.50
t
þ 36 h
0.45
0.41
t
þ 30 h
0.38
0.33
t
þ 24 h
0.33
0.28
RMSE,.
