**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/m^{2} 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 m^{2}. For the 1-D case the g-value [-]

The input signals are: *θ _{i}(t)*, the internal air temperature at time t, in °C and

*θ*, the external air temperature at time t, in °C respectively, the solar radiation,

_{e}(t)*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/m

^{2}. 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:

- Experimental boundary conditions.
- Measurement error.
- 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:

*Q(t) = G(q) u(t) + H(q) e(t)* when *H(q) = 1*

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**

IQ Test Third Training Session / Final Workshop – Outcome

System Identification Competition (SIC) 1 – including data for analysis

System Identification Competition (SIC) 2 – including data for analysis

Software Tools:

Matlab and the System Identification Toolbox.

Lord – Available from PASLINK without costs for registered people only.

CTSM – Flexible Toolbox for Continuous Time Stochastic Modelling

Web Training Book