Civil Engineering Reference
In-Depth Information
4
1
10
8
v
0
.
6
a
in
T
g
.
10
×
T
g
+
(
T
g
+
(
273
2
T
g
+
273
3
4
×
273
)
6
×
)
×
+
D
0
.
4
273
4
1
T
a
in
−
(
4
10
8
v
0
.
6
a
in
.
10
×
+
−
T
mr
+
273
)
=
0
(3.9)
D
0
.
4
ε
T
g
), subranges included in the
ranges presented in Table
3.5
are defined depending on the place where the approx-
imated models will be used. In this case the models are calculated using real data
saved during the operation of the CDdI-CIESOL-ARFRISOL bioclimatic building,
sets (GS1 for summer and GS2 for winter) each composed of 19
Moreover, for these four variables (
T
a
in
,
Rh
,
v
a
in
,
404 data points
are obtained. The set of points covers the four-dimensional space of the independent
variables (
T
a
in
,
,
T
g
), where all possible combinations among each variable
are considered. In addition, each variable changes inside a range delimited by appro-
priated values for the location of the building and with a fixed step size, see Table
3.6
.
Once these GS1 and GS2 have been defined, the PMV index can be estimated using
Eqs.
3.3
-
3.8
for all these combinations.
Following the standard methodology (Reed and Marks
1999
), each GS
X
, where
Rh
,
v
a
in
,
X
2 for winter, has been split through random sampling
without replacement in the following subsets, each composed of 9
=
1 for summer and
X
=
,
702 data points:
•
A training set (TR
X
) for obtaining both the ANN parameters using a gradient
descent algorithm and the polynomial model coefficients defined in the following
section by means of a QR factorisation (where
Q
is an orthogonal matrix and
R
is
an upper triangular matrix) with pivoting.
•
A testing set (TE
X
) for deciding both, the number of nodes in the hidden layer of
the ANN and the order of the polynomial model in the case considered in the next
section.
Although the goodness of the model is validated by the testing set, in order to see
the models' performance during real days, the models are validated by several real
data sets from the CDdI-CIESOL-ARFRISOL building to cover the most usual cases.
The obtained models' results from these real data sets are similar in all of them, and
for this reason a couple of days has been chosen for each season considered, since
different PMV models are needed for summer and winter. Each of these real data
sets corresponds to one day sampling with a sample time of
t
s
=
60 s, thus, their size
is 1,440 data points. Therefore, for summer, two data sets are considered. The first
one (VA1a) corresponds to a non-working day, where the real PMV index value is
above the comfort band since the HVAC system was disconnected. The second data
set (VA1b) refers to a working day, where the usual occupants were inside the CDdI-
CIESOL-ARFRISOL building and the HVAC system was working. Therefore, the
real PMV index value for this data set is inside the comfort band (
5, 0.5). In the
same manner, for winter, a working day and a non-working day have been selected as
real validation data sets. Moreover, the first data set (VA2a) refers to a non-working
−
0
.
