Civil Engineering Reference
In-Depth Information
Table 4.3
Results from the
analysis of the LTI
temperature model
Parameter
Validation test
]
◦
C
Interval
[
24
.
99
−
30
.
15
16
◦
C
Rng
5
.
N
6312
49
◦
C
MAE
0
.
75
◦
C
MaxAE
2
.
02
◦
C
MRE
0
.
54
◦
C
S
N
1
.
NMAE
9
.
49 %
standard deviation (
S
N
) and the variation NormalisedMean Absolute Error (NMAE),
see Eqs.
4.11
-
4.16
.
Rng
=|
max
(
x
)
−
min
(
x
)
|
(4.11)
N
1
N
MAE
=
1
|
x
(
i
)
−
x
(
i
,Ψ)
|
(4.12)
i
=
N
1
N
|
x
(
i
)
−
x
(
i
,Ψ)
|
MRE
=
(4.13)
x
(
i
)
i
=
1
MaxAE
=
max
(
AE
(
x
,
x
(Ψ )))
(4.14)
2
N
1
N
S
N
=
x
(
i
,Ψ)
−
x
(Ψ )
(4.15)
i
=
1
N
i
=
1
|
x
(
i
)
−
x
(
i
,Ψ)
|
×
100
MAE
×
100
NMAE
=
=
(4.16)
Rng
|
max
(
x
)
−
min
(
x
)
|
In the previous equations, E
qs.
4.
11
-
4.16
,
x
are the real values measured inside
the modelled room,
represent the results obtained from the model
using the unknown parameters set defined by
x
(Ψ )
and
x
(Ψ )
, and the mean value of these results,
respectively, and finally,
AE
represents the absolute error.
As a function of the previous analysis and, as observed in Fig.
4.6
, the dynamic
of the system is captured by the ARX model, although at the end of the experiment
there is a little offset between the real and modelled indoor air temperature, which
is responsible for an NMAE around 10 %. The linear difference equation which
represents the identified ARX model can be observed in Eq.
4.17
.
Ψ
