Civil Engineering Reference
In-Depth Information
Fig. 3.2
Influence of network size
n
h
on the mean (
μ
) and standard error (
˃
) for the testing set for
the summer (
top
) and the winter (
bottom
)
of
n
h
. It is useful to show the relationship between the
e
RMS
and network
size
n
h
. Since the training of the networks relies on random elements, the error
e
RMS
TE
(
N
NN
)
TE
is a random variable, and hence, it is possible to compute its mean and
standard deviation. In Fig.
3.2
, the mean value for each
n
h
is plotted with a dark blue
solid line and (
(
N
NN
)
) marks for testing sets for the summer, top, and the winter, bottom.
The light blue lines above and below represent the mean plus and minus the standard
deviation, respectively. For each value of
n
h
, 50 networks are trained and tested, the
experimental mean and standard derivation are taken over these 50 trials for each
n
h
.
The mean value of
e
RMS
TE
◦
, for both the summer and winter sets, does have
a clear tendency to decrease with
n
h
. But it is clear from Fig.
3.2
that for values
of
n
h
>
(
N
NN
)
50 the mean value of
e
RMS
TE
is almost constant, that is, the reduction
in the mean value is not significant for
n
h
values greater than 50. Thus, a logical
choice is
n
h
(
N
NN
)
=
50, then the number of configurable parameters of the network is
N
p
=
50
×
(
4
+
1
)
+
50
+
1
=
301. The graphs in Fig.
3.2
indicate that a theoretical
mean RMS error about 0
01 is to be expected in both the summer and winter cases.
In Figs.
3.3
and
3.4
, the real and estimated PMV are shown for the four validation
data sets. In addition, the bottom picture of each figure shows the absolute error
associated with the four validation data sets. With respect to the summer results, the
neural network model obtains
e
RMS
VA
1
a
.
0117 and
e
RMS
VA
1
b
0079, for validation
data sets VA1a, VA1b, respectively, see Fig.
3.3
. These results are inside the expected
range obtained by the testing data set and can be considered good enough to use the
=
0
.
=
0
.
