Digital Twin Design with On-Line Calibration for HVAC Systems in Buildings

Abstract

Digital twins of HVAC systems show great potential to increase efficiency through operational optimization and predictive maintenance of real processes. We introduce an IoT-based framework that allows the communication between a heat pump and its digital twin as well as further clients like a time series data base and supervisor dashboard. The obtained data is used to calibrate on-line the digital twin. Recalibration is performed to continuously improve the results. Using RMSE for evaluation and system supply temperature as target variable, we meet experimental data with RMSE<1 K automatically within a monthly time horizon.

Full text

Digital Twin Design with On-Line Calibration for HVAC Systems in Buildings
Christian Vering1, Sebastian Borges1, Daniel Coakley2, Hannah Krützfeldt1, Philipp Mehrfeld1,
Dirk Müller1,
1RWTH Aachen University, Institute for Energy Efficient Buildings and Indoor Climate, Aachen,
Germany
2Mitsubishi Electric R&D Centre Europe, Livingston, United Kingdom
Abstract
Digital twins of HVAC systems show great potential to
increase efficiency through operational optimization and
predictive maintenance of real processes. We introduce an
IoT-based framework that allows the communication
between a heat pump and its digital twin as well as further
clients like a time series data base and supervisor
dashboard. The obtained data is used to calibrate on-line
the digital twin. Recalibration is performed to
continuously improve the results. Using RMSE for
evaluation and system supply temperature as target
variable, we meet experimental data with RMSE<1 K
automatically within a monthly time horizon.
Key Innovations
 Proposal of scalable application of digital twins
 Evaluation of heat pump recalibration in a period
of one month
 Effect of plant aging on simulation models
Practical Implications
Our method is implemented in Python and can be applied
to other scenarios using FMI in the Docker environment
to couple further models or even dashboards. The
optimization algorithm automatically calibrates the model
according to measured data and is robust to different
datasets. Thus, we provide an easy-to-deploy method to
systematically roll out digital twins.
Introduction
As part of climate targets of the Paris Climate Agreement,
the EU has pledged to reduce their emissions by 80 % to
95 % by 2050 compared to 1990 levels from which 30 %
are related to buildings. Among other important
adjustment levers, reaching this ambitious goal requires
an almost climate-neutral building stock by 2050 and thus
a sustainable energy supply for the whole building sector.
To this end, particular efforts need to be made to exploit
the saving potentials of building energy supply systems.
(Bundesministerium, 2016)
Saving potentials can be exploited for example by
updating conventional technologies by new systems. In
this context, the heat pump is considered a key technology
for a sustainable building heat supply
(Bundesministerium, 2016). Furthermore, optimization of
operation can offer saving potentials (Drgona, 2020).
Operational optimization has proven to be promising for
existing as well as new systems. One possibility to
implement operation optimizations are digital twins
(Vering, 2019). Thus, digital twins gain increasing
interest in research and industry since recent years
(Bauer, 2020). They enable the digital representation of
real plants and processes and can map the characteristics
as well as the operational behavior (Schleich, 2017).
Digital twins have the potential to offer energy saving
potentials for predictive maintenance (Vering, 2019).
The basis of digital twins is the use of models to describe
and predict the behavior of real systems. Sufficient
reliability and robustness of the models is therefore
essential for the application of digital twins. For this
purpose, a calibration of the simulation models is
necessary. The goal of calibration is to minimize the
difference between simulated and measured data by
variations of certain model parameters (so-called tuner
parameters) (Mehrfeld, 2021). The minimization can be
solved automatically by implementing mathematical
optimization methods. However, aging of machinery, e.g.
due to physical object modifications, can change the
system behavior. This leads to aging of simulation
models, which were previously calibrated using measured
data that does not fit to the current system behavior
anymore. Thus, the prediction accuracy of existing
models might reduce significantly (Chong, 2019).
According to Table 1, calibration methods can be
distinguished in four groups: (1) manual calibration,
(2) graphical calibration, (3) analytical calibration and
(4) automated calibration. All methods aim for different
accuracies, but also require a different execution effort. In
general, all methods are able to offer high model
accuracy, if the method suits the calibration problem.
Automated calibration outperforms the other methods in
terms of implementation time.
Table 1: Calibration methods according to their
accuracy and implementation time.
Method
Accuracy
Implementation
time
Manual
+/-
-
Graphical
+/-
-
Analytical
+/-
-
Automated
+*
+
* Independent of technical experts
Refining the first three calibration methods, approaches of
a repeated calibration (recalibration or on-line calibration)
are already discussed in the literature, but mostly refer to

specific, technical applications (Tügel, 2012; Chong,
2019; Doekemeijer, 2018). A modular use of simulation
models for air-source heat pumps is not addressed, so far.
Therefore, the overall goal of this contribution is to
develop a modular framework for automated recalibration
of digital twins. Through a generic structure and object-
oriented programming, arbitrary simulation models can
be integrated into the framework, thus enabling a wide
variety of applications in practice. Furthermore, a
modular integration of databases is set up.
To show the applicability of the framework for the
recalibration of digital twins, a use case consisting of a
building and an air-source heat pump is investigated for a
period of one month. For this purpose, the heat pump
model is created and parameterized with the help of the
Modelica model library called AixLib (Müller, 2016). We
test the functionality of the framework and analyze
interdependencies of calibration classes and influences of
recalibrating the simulation models on the results. This
publication is organized as follows:
 Chapter 2 shows the framework of recalibration
and explains all steps towards fully automated
on-line calibration methods.
 Chapter 3 describes the heat pump use case, the
simulation model parameters, the tuning
parameters and the conducted sensitivity
analysis.
 Chapter 4 presents calibration results.
 Chapter 5 discusses the application of the
framework, on the basis of which application
possibilities and limitations are shown.
 Chapter 6 draws conclusions and introduces
further work.
On-line Calibration
In this paper, we present a framework for repeated
calibration (on-line calibration or recalibration) of
simulation models (ReCaMo). The framework is applied
to an air-source heat pump providing heat for a real
building to show the functionality of recalibration. We use
measurement data of three days to recalibrate the heat
pump model. This is done on-line ensuring to predict the
real behaviour of the system uninterrupted by external
influences that occur during operation on the heat pump.
Thus, ReCaMo can, for example, increase model
prediction accuracy (1) or even mitigate the effect of
aging of simulation models (2). Within the short field test
period of one month, we are able to prove (1) and give a
promising outlook that we are one step closer to (2).
The structure of the framework is generic to allow the
application of any type of simulation model by using FMI
and thus to ensure modularity.
ReCaMo is implemented in Python and its structure is
schematically depicted in Figure 1. Hereafter, the six
steps are explained separately in detail.
Figure 1: Structure of the ReCaMo-framework for the
recalibration of digital twins.
Step 1: Instantiation
At First, the ReCaMo framework is instantiated by a
configuration file. This file contains information about the
simulation model (e.g. model type), the configuration for
simulation, sensitivity analysis and calibration as well as
the data source being used. The configuration file is read
and the settings are applied in the framework. In this
paper, we show its application on an air-source heat
pump. In general, the framework should be applicable to
simulations models that fit pyFMI standard (Storek,
2019).
To ensure modular use of simulation models, an API
(application programming interface) class is provided for
the link between the framework and the selected model
type. The methods of the program classes of different
model types can thus be individualized.
Step 2: Data Acquisition
After instantiation, measurement data for in- and outputs
of the model is extracted (cf. Figure 2) and cleaned
according to the specifications in the configuration file
(e.g. start and end time, designations of database and
measurement point). Furthermore, a data mapping is
provided to support the user by mapping of the measuring
point designations into the database and the
corresponding data points in the simulation model. The
mapping is defined once for each simulation model by the
user in the configuration file. Figure 2 indicates how
measurement data could look like in the data acquisition
step. It shows the measured supply temperature of a
building for an exemplary day. Obviously the data is
highly dynamic and the courses over a day differ from
each other. This dataset will be applied to ReCaMo.
Within ReCaMo an InfluxDB database is used to store and
handle data. Due to the modular structure, it is also
possible to easily integrate further databases in ReCaMo
such as SQL. InfluxDB is an open-source time series
database, which was designed to handle time series data
efficiently. The SQL-like query language is easy to learn
and understand. (Naqvi, 2017)

Figure 2: Measured supply temperature with
measurement data of a day under consideration.
Step 3: Simulation and Preparation
Following the data acquisition, a first simulation of the
model is performed. ReCaMo uses all initial parameter
values specified in the model. The results of the
simulation are subsequently used in the following
preparation step. During this preparation step, the so-
called goals, tuner parameters and calibration classes are
defined.
The proposed concept of goals represent variables for the
comparison of measured and simulated values in a tabular
form (e.g. of a supply temperature in a heating circuit).
All tuner parameters specified in the simulation model,
including the initial and allowed minimal and maximal
values, are automatically identified and read by the
framework. Within the calibration process, tuner
parameters are varied to minimize a predefined
evaluation metric in a certain time period. Since each
period might have unique characteristics, calibration
classes can be introduced in ReCaMo.
The proposed concept of Calibration classes (CCs)
describes different operation modes that are calibrated
individually using the corresponding time intervals.
Operation modes for different CCs could e.g. be on-/off-
modes and the differentiation between transient and
steady state operation. The CCs thus ensure a piecewise
calibration of the entire examination area (e. g. the
calibration of one day). Each CC contains its own related
goals and tuner parameters. Depending on the
application, several CCs with different tuner parameters
and target values can be defined, as the sensitivity of the
tuner parameters may differ for different operation
modes.
Step 4: Sensitivity Analysis
The sensitivity analysis gives information about the extent
to which a change of specific parameters (tuner
parameters) influences the simulation results. Thus, in
step 4 ReCaMo identifies the impact of changes in
parameters on the simulation model output. Parameters
without significant impact are not considered during
calibration, thus simplifying the process. To analyse the
sensitivity in simulation models before calibration and
find the relevant parameters in ReCaMo, we apply the
Morris method (Morris, 1991). This method represents a
one-factor-at-a-time method. The input variables remain
unchanged for each parameter variation.
According to the analysis, the sensitive parameters for
calibration are selected semi-automatically afterwards.
For this purpose, the user has to identify all relevant tuner
parameters in the simulation model and distinguish
between sensitive and non-sensitive parameters. The
sensitive parameters then have to be declared as tuner
parameters. This first step is done manually and only once
for each simulation model. From this point on, the Morris
method can be used to automatically select the sensitive
tuner parameters according to the settings of the
configuration file. If automation is not desired by the user,
the tuner parameters can also be set manually in the
configuration file (in the case the majority of the sensitive
parameters are already known). The sensitivity analysis
step can thus be used optionally and can be deactivated
depending on the scope and application.
Step 5: Calibration
The aim of calibration is to increase the accuracy of a
model by adjusting the tuner parameters through
parameter variation, and thereby reduce the deviation
between simulation  and measured data . In the
case of automated calibration methods, calibration can be
understood as minimization of a chosen objective
function (deviation between measured and simulated
data) and thus can be formulated as a mathematical
optimization problem. Common key performance
indicators (so called “metrics”) to evaluate the deviation
are shown in Table 2. The “Mean Absolute Error” (MAE)
and “Root Mean Square Error” (RMSE) have the unit of
the target variable (e.g. K for supply temperature). By
normalizing the error measures, the dimensionless
“Normalized Root Mean Square Error” (NRMSE) and
“Coefficient of variation of Root Mean Square Error”
(CV(RMSE)) are obtained. Therefore, the mean value 
for the CV(RMSE) and the range   for the
NRMSE are used as reference values. All above
mentioned methods are implemented in our optimization
framework. Within this paper, we use RMSE and
CV(RMSE), to evaluate the calibration results.
The modular structure of ReCaMo also allows the use of
different optimization methods. In this context, we apply
Differential Evolution (DE), which represents a method
of the evolutionary algorithms (Storn, 1997).
In order to limit a scatter of the optimized values of the
tuner parameters and obtain more consistent results, a
deviation penalty function is implemented in the scope of
this work:
 


 (1)
The objective function  (e.g. the RMSE) is extended
by a penalty factor. This penalty factor is calculated from
the squared deviation of a tuner parameter  to a
benchmark 
 and thus affects the value of the objective
function. A benchmark represents the solution of all tuner
parameters of a recalibration, which has the lowest value

of the metric of all recalibrations so far. This is updated
as soon as the value of the metric of a recalibration is
lower compared to the current benchmark.  represents
the number of all tuner parameters used for calibration
and  denotes a constant weighting factor for each tuner
parameter, which can be specified by the user in the
configuration file.
Table 2: Metrics to evaluate the deviation between
simulated  and measured  results. n represents the
number of sampling points.
Metric
Formula
Shortcut
Mean absolute
error
 

 
MAE
Root-mean-square
error
 


 
RMSE
Normalized root-
mean-square error

 
NRMSE
Coefficient of
variation of root-
mean-square error


CV(RMSE)
The tuner parameters as well as the benchmark are
normalized between 0 and 1 using their limit values from
the model to ensure scale independence and thus make it
possible to compare different tuner parameter sets with
each other. According to this formulation, optimization
runs are conducted automatically.
Step 6: Overwriting
The optimized tuner parameters, metrics and goals of each
iteration are stored in the InfluxDB. The results of each
recalibration are compared continuously. If the value of
the metric decreases, all related results are overwritten in
a separate file, so that the best performant parameters are
not lost.
Figure 3: Different objective functions for different
calibration classes. Averaging of the results for the tuner
parameters  in case of two different solutions for the
same tuner parameters  and .
In the case that several CCs are used within one
recalibration step (e. g. one day), it may occur that some
tuner parameters are used in more than one CC. This can
lead to different optimal values for these tuner parameters
in the respective CCs. As a result, there are multiple
solutions for tuner parameters within a recalibration step.
Figure 3 shows the objective functions for two calibration
classes using the same tuner parameters.
Apparently, the optimal values  and  of the
tuner parameters differ after calibration for both classes.
To determine the overall solution of a recalibration step,
the results of the tuner parameters are averaged  and the
objective function is evaluated again. Due to averaging,
the calculated solution is not the optimal solution for any
of the CCs, unless the results of the CCs are the same. For
further investigations, an additional optimization step
might improve the averaging step to ensure global optimal
tuner parameters with respect to all CCs. Averaging can
be specifically prevented by not allowing overlapping of
the sensitive tuner parameters during configuration. In
this case, the tuner parameters would have to be selected
manually for each CC. Further work could deal with the
automation of this functionality.
The last step of ReCaMo is to overwrite the latest tuner
parameter, the entire process is repeated, and current
measurement data is extracted again. The optimal time
until next repetition is not investigated in the scope of this
contribution. We recalibrate a heat pump model three
times, in each week once, within one month according to
field test data. This case study is introduced in the
following Chapter.
Case Study: Heat Pump Calibration
The application of ReCaMo focusses on a heat pump,
which is being modelled and recalibrated using the
framework. We investigate one month of measurement
data. A recalibration step covers one day from 00:00:00 h
to 23:59:50 h with a sampling rate of 10 seconds. Within
this contribution, we calibrate the heat pump model once
based on the first day and we recalibrate the model
according to two other days to show the potential of our
method.
Figure 4 shows the heat pump that is modelled in
Modelica using the AixLib (Müller, 2016) heat pump
model. The refrigeration circuit is implemented as a
black-box using a characteristic curve from the
manufacturer's specifications and the heat exchangers as
semi-empirical grey-box models. This type of model
represents a compromise between computational effort
and model accuracy.
Heat capacity and heat losses are considered in the heat
exchangers. Heat source and heat sink of the heat pump
are modelled using ideal mass flows. Pressure losses in
the heat exchangers are not considered, yet, just as the
heating water circuit and hence the water pump are not
investigated, respectively. Icing effects and the control of
the system including safety functions are also
disregarded.

Figure 4: Scheme of the heat pump model, which is
(re)calibrated using ReCaMo.
Figure 4 shows a scheme of the heat pump model with the
basic components compressor, condenser, expansion
valve and evaporator. For the simulation of the heat pump,
the return temperature  (water inlet to the condenser),
the ambient temperature  (air inlet to the evaporator),
the water mass flow , air mass flow , and the
relative speed of the compressor  are required (circled
dashed). The output variables of the model (circled solid)
are the supply temperature  (water outlet from the
condenser) and the electrical power  of the heat pump
compressor. Only the supply temperature is used for
calibration, since the electrical power of the compressor
is not measured separately. Using this setup and
measurement data such as shown in Figure 2, we can use
ReCaMo for calibration of the model.
Calibration Results
In the following, we evaluate the results from the
ReCaMo framework for recalibration of digital twins by
presenting a sensitivity analysis (I), the first calibration
(II) and the recalibration (III) based on one month. In most
cases, we use one CC for calibration purposes and a
weighting factor for the deviation penalty function of
  is set heuristically a priori. An adjustment of this
weighting can be necessary, when ReCaMo is to be
applied to further simulation model calibrations based on
field test data.
Results I: Sensitivity analysis
The relevant tuner parameters from the model for the
sensitivity analysis are shown in Table 3. They are
evaluated within the Morris method using the absolute
mean value of the elementary effects μ*, which represents
the ratio of the variation of the output with respect to the
variation of the input between two points within the
examination range by applying a standardized relative
amount (Morris, 1991). The number of parameter
variations (called trajectories) is 100, the number of
possible parameter values (called grid levels) is 4. The
CV(RMSE) is chosen for the evaluation of the sensitivity
of the supply temperature.
Table 3: Notation of relevant tuner parameters.
Parameter
Notation
Parameter
Notation
ω
Cut-off
frequency
(inertia)

Pressure
drop
evaporator

Pressure drop
condenser

Volume
evaporator

Volume
condenser

Heat loss
to ambient
evaporator

Heat loss
to ambient
condenser

Heat loss
to exchanger
evaporator

Heat loss
to exchanger
condenser

Heat
capacity
evaporator

Heat capacity
condenser
Figure 5 shows the results of the absolute mean values μ*
of the sensitivity analysis with measurement data from the
first day for the given tuner parameters. Evidently, the
volume of the condenser , the cut-off frequency ω and
the heat loss parameters  and  dominate the impact
on the target variable. The sensitivity of the heat capacity
of the condenser  is negligible. The absolute mean
values of the evaporator-specific parameters (, ,
, ) are barely sensitive to the target variable. This
corresponds to the expectations, as the outlet temperature
is directly connected only to the condenser and not the
evaporator. Furthermore, the pressure losses in evaporator
 and condenser  have no influence on the supply
temperature. This is due to the fact, that the heating circuit
and the fan are represented by ideal mass flow sources.
Figure 5: Results of the sensitivity analysis with
measurement data of day one.
The results obtained on the other days of the study period
match those obtained on day one (cf. Figure 5). According
to the sensitivity analysis, further evaluations within the
calibrations are based on the four highest ranked tuner
parameters ω, ,  and .
Results II: First calibration day
Figure 6 shows the measured and simulated data after the
first calibration of the supply temperature of the first day
of the investigation from 01:08:30 h to 06:03:30 h. The
results of the simulation after calibration are similar to the
measured data which yields an RMSE of the whole
calibration day of only 0.60 K. Temperature peaks can be
predicted by the model. Apparently, the temperatures are

rather underestimated in the simulation. This can be
caused by the fact that a rotational speed dependency of
the heat pump characteristic curve is only approximated
by using , since only a characteristic curve at a fixed
rotational speed is available for modelling the heat pump.
This heat pump model can now be used as digital twin
until the next calibration process is conducted. In this
paper, we conduct a second calibration one week later.
Figure 6: Measured (blue) and simulated (red) supply
temperature in Kelvin (goals) from 01:08:30 h until
06:03:30 h from day 1. RMSE of the whole calibration
day: 0.60 K.
Results III: One month results
Figure 7 shows a decrease of the RMSE during the
investigated period. Accordingly, a reduction of the
metric on the following days of consideration can be
achieved by recalibration. Thus, the accuracy of the
simulation results increases continuously. This can be
explained by the different measurement data and its
information content for the ReCaMo procedure of the
calibration days.
Figure 7: Continuous reduction of the metrics value
through recalibration from about 0.60 to 0.38.
Table 4 shows the general settings of the framework and
the results of the tuner parameters of the second day
investigation.
Table 4: Recalibration with measurement data from
recalibration day 7 using the RMSE.
CC: Improvement RMSE
Setup
Results
Target

ω [Hz]
0.00607
Start
00:03:20 h
 [m³]
0.00055
End
23:59:50 h
 [W/K]
11.84
Metric
RMSE
 [W/K]
0.0
RMSE
0.38 K
Results IV: Use of penalty function
In the following, the influence of the weighting factor 
of the squared deviation on the results of the tuner
parameters is investigated. The recalibration with the
target variable  is carried out over all 31 days from
00:00 h to 24:00 h. Figure 8 shows the results of the tuner
parameters with a weighting factor  (left) and
 (right) and the corresponding boundaries of the
tuner parameters (red line). When comparing the
parameter values on the left and on the right, it can be
observed that the scatter of the results is reduced by the
deviation penalty function. The deviation penalty function
can thus be used efficiently to contain the range of results
of the tuner parameters.
Figure 8: Tuner parameter results of the recalibration of
all 31 calibration days with and without the usage of the
introduced deviation penalty function (Eqn. 1).
Left side: ; Right side: .
However, a too high weighting factor will also reduce or
even prevent necessary changes in the parameters during
recalibration. Thus, with higher weighting factors the
impact of the very first calibration increases, as the results
of following recalibrations will strongly depend on it. If
this first result is of poor quality, e.g. due to faults in the
measurement data, this has a negative effect on all further
calibration results. Therefore, the choice of the weighting
factor  must be carefully chosen for each particular case.
Table 5 shows the results of the recalibration with a
weighting factor  (left) and thus without
application of the deviation penalty function as well as
 (right) day 14. The results of the tuner
parameters differ significantly, while the result for the
CV(RMSE) is similar in both cases. The application of the
deviation penalty function therefore does not necessarily
have a negative effect on the calibration results.

Table 5: Results of recalibration day 14 without
() and with () the deviation penalty
function.
Results day 14, w=0.0
Results day 14, w=0.4
ω
0.10374
ω
0.00688

0.00368

0.00048

0.55

57.06

0.0

0.0
CV(RMSE)
0.002469
CV(RMSE)
0.002323
Results V: Use of calibration classes
Previous calibration results refer to calculations with one
CC. The calibration is performed continuously using one
day for training. Since the model behaviour and thus the
results of the calibration depend on the operating mode of
the system, it makes sense to examine the modes
separately with respect to the calibration in different CCs.
The selection of the CCs is done based on the relative
speed of the compressor. For the investigation, we chose
the time interval between 01:08:30 h and 06:03:30 h of
day 1. Figure 9 shows the measured supply temperature
and the relative speed of the compressor in the
investigated time interval at red highlighted background.
Figure 9: Measured data of supply temperature (top)
and relative compressor speed (bottom) of day 1.
The classification of the CCs is based on the periods in
which the compressor is switched on and off. For the
investigated time interval, this gives 18 sections. By
merging CCs of the same type, the number can be reduced
to 2: compressor switched on and switched off.
The calibration of the investigated period shown in
Figure 6 is used as the reference case with only one CC.
The RMSE in this case is 0.73 K. By using the merged
CCs (cf. Figure 10), an improvement of about 15 % of the
metric can be achieved having an RMSE of 0.63 K. In
addition, the results of the tuner parameters of the classes
“compressor on” and “compressor off” are averaged (see
section 5.6) to compare the RMSE with the calibration of
a single CC.
Despite the decrease of the metric due to averaging
(cf. Figure 3), the accuracy of the simulation results can
be increased by using well-chosen CCs.
Figure 10: Goals of the investigated period with two
calibration classes, compressor on (top) and compressor
off (bottom). The grey areas are not taken into account,
the red areas are the CCs, respectively. The right plot is
a zoom of the highlighted area on the left.
Capabilities and Limitations
This section discusses the obtained results to show
potential for refinement of the method.
Capabilities
The analysis shows that the calibration using the ReCaMo
framework provides physically reasonable results.
Furthermore, continuous recalibration of the simulation
model within specific calibration intervals can
continuously increase the performance. The use of CCs
for different operating phases can further increase the
simulation accuracy.
Due to the aging effects of machinery, updates of
simulation models during operation is necessary.
ReCaMo automatically recalibrates simulation models
based on current measurement data after the configuration
and instantiation. A sufficient quality of the simulation
results can thus be ensured over the entire application
period of the framework and the aging effects can be
considered in the simulation model.
In the literature, the implementation of recalibration is
limited to specific simulation models and applications. A
continuous recalibration using the framework of the
present study is designed for a modular use of simulation
models. This ensures a generic usage of the framework.
ReCaMo has already been successfully tested on several
heat pumps internally. In order to ensure a user-friendly
application, the stability of the framework is increased by
the implementation of an error handling of the user inputs.
A deviation penalty function is implemented to limit
scattering of the optimized tuner parameters obtained
from calibration. The results are thus more physically
reasonable.
Limitations
A potential use of the CCs is limited at this point to a
manual identification of the operating phases of the
measured data. For an automated usage of the CCs, the
integration of an automated pattern recognition of the
measurement data is necessary or a digital twin of the
controller must be known a-prior.
So far, ReCaMo does not allow any intervention in the
operating process of the real plant, e.g. by control signals
or anything similar. The results of the calibrations can

provide information for control applications such as
model predictive control or methods for forecasting and
fault detection and diagnostics (FDD) of technical
processes. Furthermore, the calibration is performed in
fixed time intervals specified by the user. A deviation-
based calibration, e.g. by real-time simulations and
continuous control of a selected error measure between
simulated and measured data, is not implemented, yet.
Equation 1 shows that the penalty factor is calculated for
each tuner parameter of the calibration. Thus, the value of
the penalty factor depends on the number of calibrated
tuner parameters. In this contribution, four tuner
parameters are calibrated. If an application of the
ReCaMo aims e.g. at the simulation of building physics
for building energy management, the number of sensitive
tuner parameters can be significantly higher. This leads to
an increase of the penalty factor, which leads to an
increased limitation of the results of the tuner parameters
by the deviation penalty function. In addition, the
sensitivity of the tuner parameters is not considered when
calculating the penalty factor. Each parameter is equally
weighted within the deviation penalty function by the
weighting factor . For a further usage of the deviation
penalty function, the weighting factor  can be chosen
depending on the number and sensitivity of the tuner
parameters, which would improve the calibration process
Conclusion and Outlook
Within this contribution, we introduce ReCaMo as a
framework for repeated calibration of simulation models
and apply it to a heat pump model. Using one month of
field test data, we proved functionality of our framework
and assessed our results using RMSE.
Comparing three different days, we calibrated a heat
pump model from the AixLib utilizing an a-priori
sensitivity analysis to systematically reduce calibration
effort. Thus, we are able to decrease the RMSE of the heat
pump supply temperature between the model and the
simulation results from day to day, which was always
below 1 K within our use case. To further improve our
results we introduced calibration classes, which again
decreased RMSE by considering whether the heat pump
is switched on or switched off.
For future investigations, we suggest to enhance the
choice of calibration classes to improve calibration
results. Furthermore, ReCaMo should be tested with other
system configurations to examine the modularity of the
whole framework. Increasing the development of such
frameworks and proving them in real world applications
accelerates the introduction of digital twins in the building
sector. This is important to significantly decrease
emissions in that sector.
Acknowledgement
We gratefully acknowledge the support of Mitsubishi
Electric R&D Centre Europe.
References
Bauer, L. (2020): Digital.Trend.Studie. Digital Twin-
Zwischen den Welten: Potential, Reifegrad und
Einsatzgebiete Digitaler Zwillinge fur die DB. 2020.
https://www.dbsystel.de/resource/blob/5654212/b0c1
fa2596dc441d8525c6f53e3ff856/200930_Digital-
Trend-Studie_Digital-Twin_FINAL-data.pdf.
Bundesministerium für Umwelt (2016). Naturschutz und
nukleare Sicherheit: Klimaschutzplan 2050 -
Klimaschutzpolitische Grundsatze und Ziele der
Bundesregierung,
https://www.bmu.de/fileadmin/Daten_BMU/Downlo
ad_PDF/Klimaschutz/klimaschutzplan_2050_bf.pdf.
Chong, A. et al. (2019). A Framework For The
Continuous Calibration Of Building Energy Models
With Uncertainty. Building Simulation Conference
2019, Rome.
Doekemeijer, B. M. et al. (2018). Online model
calibration for a simplified LES model in pursuit of
real-time closed-loop wind farm control. Wind Energy
Science 3(2), pp. 749–765.
Drgona, J. et al. (2020). All you need to know about
model predictive control for buildings. Annual
Reviews in Control 50, pp. 190-232.
Mehrfeld, P. et al. (2021): Model Calibration of an Air
Source Heat Pump System for Transient Simulations
in Modelica. Heat Pump Conference, 2021, Jeju.
Morris, M. D. (1991). Factorial sampling plans for
preliminary computational experiments.
Technometrics 33(2), 161-174.
Müller, D. et al. (2016). AixLib - An Open-Source
Modelica Library within the IEA-EBC Annex 60
Framework. BauSIM Conference 2016, Dresden.
Naqvi, S. N. Z. et al. (2017). Time series databases and
influxdb. Seminar paper, Université Libre de
Bruxelles.
Schleich, B. et al. (2017). Shaping the digital twin for
design and production engineering. CIRP Annals
66(1).
Storek, T. et al. (2019). Applying Machine Learning to
Automate Calibration for Model Predictive Control of
Building Energy Systems. Building Simulation
Conference 2019, Rome.
Storn, R. and K. Price (1997). Differential evolution – a
simple and efficient heuristic for global optimization
over continuous spaces. Journal of Global
Optimization, 341-359.
Tügel, E. (2012). The airframe digital twin: some
challenges to realization. 53rd
AIAA/ASME/ASCE/AHS/ASC Structures, Structural
Dynamics and Materials Conference 20th
AIAA/ASME/AHS Adaptive Structures Conference
14th AIAA, 1812.
Vering, C. et al. (2019). Unlocking Potentials of Building
Energy Systems’ Operational Efficiency: Application
of Digital Twin Design for HVAC systems. Building
Simulation Conference 2019, Rome.