DATA ANALYSIS
Thermal
Parameters
Definitions of the physical parameters of interest derived from
the energy balance equation:
| UA |
is the
heat transmission coefficient: the heat flow rate in the steady state divided
by the temperature difference between the surroundings on each side of the
system or component, in W/K. For the 1-D case the U-value, in W/m2 K. |
| gA |
is the
total solar energy transmittance or solar aperture: the heat flow rate leaving
the component at the inside surface, under steady state conditions, caused
by solar radiation incident at the outside surface, divided by the intensity
of incident solar radiation on the component, in m2. For the 1-D case the
g-value [-] |
The input signals are: 
,
the internal air temperature at time t, in °C and 
,
the external air temperature at time t, in °C respectively, the solar radiation,
Qsolar and the auxiliary heat, Qheater, applied to disturb the
system. The flow of heat, Qhf through the envelope (excluding the component
under test) is measured also. All flows are in W/m2. Examining the energy balance
equation it should be noticed that long experiments are necessary to achieve
results with sufficient accuracy. The problem of small temperature differences
should be considered too.
PASLINK approach to System Identification
Applying system identification techniques on physical systems
requires throughout knowledge of the physical system. For buildings it is important
to know what the impact is of cold-bridges, corner effects, etc. The researchers
goal is to estimate physical parameters by using mathematical models. In most
cases the calculation from mathematical parameters, which derive from the chosen
model, to physical parameters, in this case the heat resistance and solar aperture,
introduces another point for discussion between physicists and mathematicians.
Physicists like to compare the obtained values of the estimates from different
methods, however they do not always realise that the way they are obtained from
mathematics might be different.
On the other hand, for the determination of the thermal and solar
characteristics the knowledge of the heat flow through the test room envelope
is an absolute must, in order to be able to obtain the properties of the test
component decoupled from the test cell. This asks for a separate calibration test.
For the characterisation of different approaches it is necessary clearly to define
the terms model/ method/ tool:
| A
model |
is
a mathematical description of a physical system or process. By definition
it is a simplification of the reality |
| A
method, |
here
a system identification technique, consists of two major parts: the mathematical
model (e.g. an ARMAX model) and the routine to estimate the parameters by
a specific algorithm (e.g. least squares method). |
| A
tool |
is a sophisticated software program which allows the user to a method
in a user friendly way.
|
The resulting accuracy of
the estimates, model as well as physical parameters, depends on three types of
errors:
1. Experimental boundary
conditions.
2. Measurement error.
3. Error introduced by the analysis method.
In general two types of
criteria for parameter identification can be distinguished:
The Prediction Error Method (PEM) and
The Output Error Method (OEM)
The OEM is a special case
of the PEM when one takes the following formula in consideration:
when 
For the evaluation of the
test results in terms of dynamic properties a parameter identification software
tool is required. Over the last 10 years several tools have been developed and
tested on simulated data (Bloem, 1996). The use of such tools requires specific
experience. A detailed checklist assists the user, covering the successive steps
to be followed in the identification process.
The same test cells are
also used for the purpose of validating thermal models of building components.
As the preparation and execution of a test is a time consuming task, the test
strategy has been set up in such a way that both purposes may be served with
the same procedure. The main difference will be that in case of model validation
specific extra sensors may be required in order to have a more detailed insight
in the physical processes, while a 'black box' type of approach is used in case
of the determination of the specimen's thermal characteristics.
Activities
