4. Sub-Modelling Approaches to Predict Dynamic Moisture Response in Historic Buildings
4.2 Calibration of a BES-Model
Development of a BES model using the forward approach (Chapter 1) involves prediction of the output variables using a detailed structure and parameters of the model subjected to a specific set of input variables. Models developed practicing such an approach are called white-box models [32]. In a historic building, however, not all input variables are known. As a consequence, values of some parameters are estimated. When one or more input parameters in a white-box model are estimated based on a fitting of the model to measurement data, the model becomes grey, no matter its complexity [237]. Figure 4.1 shows the approach which is also used in this work to achieve a validated BES-simulation model using calibration22.
Figure 4.1: Approach used in throughout dissertation to achieve a simulation model. Based on [239,240].
22 Model calibration is an iterative process which, through the assessment of a series of simulations with different inputs, aims to reduce the discrepancies between simulated and actual building energy behaviour [238].
DEVELOPMENT MODEL Observations / measurements to define
boundary conditions, internal gains, …
SIMULATION BASED FORECASTING MODEL CALIBRATION Gather As-built
information
Set up of simulation model of current situation
Comparison and validation with measured data
Measurement of the output of the simulation
model
Simulate different retrofitting strategies:
e.g. humidity, control, natural ventilation, visitors’
management, ...
Preservation Conditions /
Damage risk Comfort Energy use …
Refine model
4.2.1 Development model
The first step is to build a simulation model that approximates the real behaviour of the (part of the) building as well as possible. Therefore, the following is needed [241]:
As-built information to build up a simulation model (geometry of the building, envelope properties, infiltration rate, operation set-points of the heating system, …)
Survey observations or measurements to define the boundary conditions of the simulation model: occupant’s behaviour, outdoor climate measurement, behaviour of adjacent rooms, …
4.2.2 Model Calibration
Once the whole simulation model is developed, input parameters are set and measurements data have been collected, the model can be calibrated to represent more closely the actual behaviour of the building under study [36,45]. To perform the calibration, different methods exist. Roberti describes different methods applied on historical buildings [242]. In this dissertation, the calibration is done manually iterative. Other possible methods are automated, graphical and statistical methods [243,244].
Input Parameters
For the calibration process, different types of input parameters were considered. The first type contains data for which values remains unchanged and could be obtained from the building drawings, site survey and technical sheets [245]. The second type of data included parameters which were updated until an accurate model was achieved (Figure 4.2).
Figure 4.2: Schematic representation of the procedure followed in this case study to compare the moisture buffering models.
Parameters
Uncertain Input Parameters:
Building model: properties building envelope
Heating device and humidifiers controls
Light: on/off
Visitors: Number and profile
Infiltration rate Definite Input Parameters:
Building model: geometry, orientation , presence shading device
Measured outdoor climate
System specifications Result TRNSYS
simulation
SUB-MODELLING APPROACHES TO PREDICT DYNAMIC MOISTURE RESPONSE 87
To achieve accurate results, the procedure suggested by Mustafaraj et al. [246] was used in this work. Based on earlier research, the authors proposed two stages of calibration during the manual iterative method process. In the first stage, the model is built using the collected data including as-built information with realistic occupancy, operating profiles and building use. In the second stage, sensitive parameters are defined and if possible extra field measurements are performed. A sensitivity analysis of the model to the input data is for historic buildings closely related to the calibration activity in order to assess the parameter influence on the building energy performance [238]. The chosen input parameters, that will be adapt, are updated through an iterative process until the accuracy of the calibrated model is satisfactory.
Chosen simulation output to compare with measured data
It was chosen in this work to use temperature and absolute humidity to calibrate the simulation model. The reason was that for estimating the preservation condition in a (historical) building, it is important to correctly model temperature and relative humidity course as these are the two most important parameters. Absolute humidity was chosen instead of relative humidity, because the absolute humidity is not dependent on temperature, contrary to relative humidity.
Afterwards, once the model was calibrated on absolute humidity, relative humidity was used to estimate the preservation conditions. Simulation results of the models were compared with hourly and monthly mean temperature and absolute humidity. In addition to the average temperature and humidity course, it also is important to estimate as good as possible the short-term fluctuations. Therefore, also the daily variation in temperature and absolute humidity was used in the calibration process.
Furthermore, monitoring periods should be long enough and should allow to calibrate the model for each operation mode of the building: free floating, heating and or cooling [247]. Besides to evaluate the indoor climate, it is also advised to measure a longer time period to assess seasonal fluctuations. Therefore in this dissertation, one year was used.
Indicators to assess the fitting with measured data
To compare the deviation of the simulated results with the measured results, several data performance metrics exist. An extensive overview is provided by Afram et al [47]. In this work, the calibration process of the simulation model follows the method suggested by ASHRAE Guideline 14 [240]. ASHRAE Guideline 14 [240] suggests following two statistical indicators to calibrate the simulation model: "Mean Bias Error (MBE)" and "Coefficient of Variation of Root Mean Square Error (CV [RMSE])".
The mean Bias Error (MBE) measures how closely simulated data correspond to monitored data.
It is a non-dimensional bias measure (relative error) between measured and simulated data and is calculated by the following equation:
MBE =∑ni=1xmeas,i− xsim,i
∑n xmeas,i i=1
(4.1) Where: xmeas,i the measured data points for each model instance i,
xsim,i the simulated data points for each model instance i n number of data points
The MBE it is subject to cancellation errors. Therefore, the Root Mean Squared Error (RMSE) approach or the Coefficient of Variation (CV) of the root mean squared error values are used more frequently [45,240]. The RMSE and CV(RMSE) are not subject to cancellation errors, because the error of every data point is squared. They allow one to determine how well a model fits the data by capturing offsetting errors between measured and simulated data. The advantage of using CV(RMSE) instead of RMSE is that it allows to compare which models provide better predictions of outcome, because the CV(RMSE) is non-dimensional. Equation (4.2) shows how the CV(RMSE) is calculated. Guideline 14/2002. These are shown in Table 4.1. Although this guideline was originally developed to quantify energy saving potentials of proposed retrofit schemes, it is also used for other variables like temperature, relative humidity, energy use, … [234,246,248]. However, it is important to consider whether the requirements apply to the parameters of interest and whether the requirements lead to a sufficiently accurate simulation model. For example, an error of 10%
on 20°C allows a deviation of 2°C. In literature, only a few works were found that use the internal temperature as a calibration goal [242,249]. Three of them, applied on historical buildings, are listed Table 4.1. In this dissertation, indicators suggested by ASHRAE Guideline 14/2002 were used.
Furthermore, there was strived to never have an error larger than 5% for temperature and 10%
for relative humidity.
4.2.3 Simulation Based Forecasting
Once there is reasonable agreement between measured and simulated data, new scenarios can be tested, parameter analysis can be performed, … The authors are aware that it is inevitable that the vast volume of information that is required to describe a building model generally always leads to simplification and parameter reduction [234] and that other, more detailed methods are available calibration the simulation model. A comprehensive review of historical and current
SUB-MODELLING APPROACHES TO PREDICT DYNAMIC MOISTURE RESPONSE 89
calibration techniques and their advantages is given by Coakley, et al. [45] and by Reddy [250].
This is not in the scope of this work.
Table 4.1: Criteria used to calibrate the building simulation model described in ASHRAE Guideline 14 [240].
Source Statistical indicator Criterion
ASHRAE Guideline 14/2002 MBE Hourly: 10 % Monthly: 5 %
CV(RMSE) Hourly: 30% Monthly: 15%
Paper of Roberti et al.[242] RMSE As no standard was found they tried to find the lowest value as possible. A RMSE of 0.78K was reported.
MAE23
Book of Pretelli et al. [249] MAE 5-10%
Paper of Enriquez et al. [247] RMSE 0.5°C
¨
23 MAE is the mean absolute error. The same formula as the MBE is used. However, the absolute value of the numerator is used instead (always positive).