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Advanced computer experiments enable to understand and optimise a model. However, using these methods require skills in programming and a deep understanding of their underlying theory. Persalys is an open-source software, based on OpenTURNS methods, which guides the user in the analysis and makes computer experiments accessible to non-programmers. This article aims to illustrate the use of Persalys on an intelligible use case : a solar collector from ThermoSysPro library. We first performed a sensitivity analysis on the Model-ica model exported as FMU. We then employed Persalys capabilities to optimize and metamodel the solar collector. We finally included the metamodel in the ThermoSysPro concentrated solar power plant to observe its performance. Persalys is developed for both Windows and Linux. We succeeded in including metamodels on both OpenModel-ica Connection Editor (OMEdit) and Dymola, in the form of Modelica block or FMU.
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Analysis and reduction of models using Persalys
Claire-Eleuthèriane Gerrer1Hubert Blervaque2Julien Schueller1Daniel Bouskela3Sylvain
1Phimeca Engineering, France, {gerrer, schueller, girard}
2Hubert Modelisation, France,
3EDF Lab Chatou, France,
Advanced computer experiments enable to understand and
optimise a model. However, using these methods require
skills in programming and a deep understanding of their
underlying theory. Persalys is an open-source software,
based on OpenTURNS methods, which guides the user in
the analysis and makes computer experiments accessible
to non-programmers. This article aims to illustrate the use
of Persalys on an intelligible use case : a solar collector
from ThermoSysPro library.
We first performed a sensitivity analysis on the Model-
ica model exported as FMU. We then employed Persalys
capabilities to optimize and metamodel the solar collector.
We finally included the metamodel in the ThermoSysPro
concentrated solar power plant to observe its performance.
Persalys is developed for both Windows and Linux. We
succeeded in including metamodels on both OpenModel-
ica Connection Editor (OMEdit) and Dymola, in the form
of Modelica block or FMU.
Keywords: FMI, FMU, OtFMI, Persalys, ThermoSysPro,
sensitivity analysis, screening, metamodelling, model re-
duction, ExternalFunction.
1 Introduction
Analysing Modelica models is necessary to understand
their functioning and assert their reliability. Modellers do
it naturally when they modify inputs or parameters and
check the output variations. This verification step how-
ever demands lots of handwork when it is performed in
modelling GUIs, be it OMEdit or Dymola.
Persalys1is a user-friendly Python-based GUI dedi-
cated to the treatment of uncertainty and the management
of variabilities. Persalys enables the analysis of Modelica
models via the FMI standard. The software can be em-
ployed on all kinds of FMUs as well as with most finite
elements models. FMUs (Functional Mockup Units) are
models, written in Modelica or another 1D-modelling lan-
guage, exported under the FMI standard. This standard
provides an interface between different languages, such as
Amesim, Simulink, Python.
Persalys is based on the Python library for the treatment
of uncertainties, risks and statistics OpenTURNS2(Baudin
et al., 2015). The GUI is developed by part of the Open-
TURNS consortium, EDF and Phimeca Engineering, to
help and guide non-specialists in model analysis (see fig-
ure 1).
Aside from model analysis, Persalys enables to per-
form metamodelling, or model reduction, in a guided
way. Metamodelling consists in learning the behaviour of
the physical model using a mathematical function whose
computation time is negligible (usually in milliseconds
and below). Metamodels are thus a handy expedient to
prohibitive computation times when many model runs are
needed. Embedding metamodels in Modelica GUIs:
• permits to connect the metamodel with Modelica
blocks for larger-scale modelling,
• enables the inclusion of (metamodelled) external
models such as finite-element models.
Our purpose is to demonstrate how to, using only GUIs,
thoroughly analyse a FMU, metamodel it and employ the
metamodel in a Modelica environment.
The Modelica use case is detailed in section 2. The be-
haviour of a ThermoSysPro component, exported as FMU,
using Persalys is explored in section 3. Section 4 shows
how we computed the corresponding reduced model and
exported it from Persalys. We finally discuss the use of the
reduced model as FMU or Modelica component in sec-
tion 5.
2 The Modelica use case
We consider a Concentrated Solar Power Plant (CSPP)
transforming solar radiation to electricity. This industrial
installation provides up to 1 MWe.
2.1 The physics of a CSPP
The most visible part of a CSPP is its large amount of
surfaces reflecting the sun. The Parabolic Trough Solar
Collector (PTSC) contains a parabolic reflective surface
and a receiver tube, see figure 2. The reflected solar en-
ergy is transferred to the transparent receiver tube, which
contains an absorber tube coated with blackened nickel to
Figure 1. Persalys methods are presented as a tree. After defining the variables and outputs of interest, the user can evaluate the
model, perform screening, optimization, etc. The no-entry sign on a method signals if a prior step was not completed. For instance,
in the current analysis, the calibration method cannot be employed as observations must be provided first.
ensure high absorption. The absorber tubes heat up the
synthetic oil it contains to nearly 400 °C.
The synthetic oil circuit exchanges heat with a circuit
of water undergoing a Rankine cycle. The water is heated
to dry steam and passes through a set of turbines in rota-
tion, bringing an alternator in rotation to produce electric-
ity. The water is then condensed and sent back to the heat
exchangers, where it is heated again (Ferrière, 2008).
2.2 The modelling of a CSPP
The model ConcentratedSolarPowerPlant_PTSC3is an
emblematic example of the open-source ThermoSysPro li-
brary 4. ThermoSysPro provides components in the disci-
plines of thermal hydraulics and instrumentation and con-
trol for building nuclear, gas, coal or solar power plant
models. The modelling choices concerning the concen-
trated solar power plant is detailed in (El Hefni, 2014)
and (El Hefni and Bouskela, 2019). Figure 3 shows the
entire power plant model, using ThermoSysPro v3.2.
The component in the upper part, called SolarCollec-
tor5, models the PTSC. It is connected to the weather in-
puts: the sun radiation (direct normal incidence), sun in-
cidence angle and atmospheric temperature. The Solar-
Collector component is connected to the primary circuit
(whose fluid is oil) exchanging heat with the secondary
circuit. In this secondary circuit, the water is heated in
three steps (by the economizer, heater and super-heater)
before passing through the set of turbines.
2.3 A focus on the PTSC model
Before studying the entire solar power plant model, we fo-
cused on the PTSC model SolarCollector. Our purpose is
to better understand its behaviour using statistical analysis
and to replace it in the CSPP model by its metamodel.
We connected this component to ThermoSysPro inter-
face component HeatExchangerWall and to a HeatSource
setting the temperature value. We defined as output the
heat flow produced by the solar collector.
This model, named Env_PTSC, is steady-state. We thus
considered only the heat flow final value and constant
weather inputs. We exported this model as FMU to study
it using Persalys.
3 Understanding the PTSC’s be-
Modelica parameters and inputs have similar roles for sta-
tistical analysis as we consider a steady-state model. In
the following, we call “variables” the model inputs and
parameters under study.
We focus here on understanding the effect of the vari-
ables on the model output. We pre-selected 9 variables
of the SolarCollector, with causalities input or parameter,
3located in ThermoSysPro.Examples.Book.PowerPlant
5located in ThermoSysPro.Solar.Collectors
to study their effects. We chose their variation bounds in
accordance with the physics they represent, see table 1.
We loaded the PTSC model as FMU in Persalys. To
gain insights in the model behaviour, we first ran screen-
ing and Sobol’ sensitivity analyses (see subsection 3.1).
We then checked if the optimal values of important vari-
ables correspond to our understanding of the physics (see
subsection 3.2).
3.1 Screening and sensitivity analysis
Sensitivity analysis methods enable to determine the
model variables which affect most the output. Morris
method (also called “Morris screening”) and Sobol’ in-
dices are two global sensitivity analysis methods (Iooss,
2011). Morris’ qualifies the variables as important,with
nonlinear effect and/or interactions, or without effect. Its
results are rough, but the computation is rapid even with a
large number of variables (Morris, 1991). Sobol’ method
quantifies the fraction of the output variation for which
each variable is responsible. Sobol’ indices are computa-
tionally expensive, but very precise.
We screened the important variables using Morris
method, then studied more precisely their relative effect
on the heat flow. Figure 5 shows the results of Mor-
ris screening for the 9 variables (based on 80 trajectories
and 8 levels). The atmospheric temperature and the so-
lar collector heat transfer coefficient, glass transmittivity
and tube length variations have a negligible effect on the
model output. We thus set these 4 variables "without ef-
fect" to their value in the model ConcentratedSolarPow-
We refined the analysis of the effect of the 5 variables
categorized as important using Sobol’ sensitivity analysis.
The results of Morris analysis can be used by Persalys to
define the variables probabilistic model. Only the vari-
ables declared as significant are considered as uncertain:
the others are fixed to their default value.
Figure 6 shows the results of Sobol’ analysis in Per-
salys. The first-order index quantifies the effect of a vari-
able without interaction with any other variable on the
model output. The total index accounts for the effect of an
variable alone and in interaction with the other variables,
on the output. The variables with the greatest Sobol’ in-
dices are the most influential (with respect to their given
variation range). The heat flow produced by the solar
panel thus mainly depends on the sun radiation and the
incidence angle.
3.2 Variables optimal value
The value that maximises the model output is a comple-
mentary information to the relative influence of the vari-
ables. In theory, the heat flow produced is maximum when
the sun radiation and mirror reflectivity are maximal, the
angle incidence minimal. We checked the optimal com-
bined value of the 5 variables in Persalys.
Figure 7 shows that the maximal heat flow is reached
for maximal sun radiation and mirror reflectivity with
Figure 2. An example of PTSC. Source: (Tagle-Salazar et al., 2020)
Figure 3. Modelica model of a concentrated solar power plant, designed by El Hefni and Bouskela (El Hefni, 2014).
Variable group Name Unit Role Value Bounds
Geometric parameters
L m Length of the PTSC tube 450 [400, 500]
solarCollector.RimAngle Rim angle 70 [65, 75]
solarCollector.f m Focal length 1.79 [1, 2]
solarCollector.h W/m2/KHeat transfer coefficient between
ambient air and glass envelope 3.06 [2.5, 5]
Cleanliness parameters solarCollector.R - Mirror reflectivity 0.93 [0.6, 0.95]
solarCollector.TauN - Glass transmittivity 0.95 [0.5, 0.95]
Weather inputs
T_atm.k K Atmospheric temperature 300 [273, 303]
angle_incidence.k Sun incidence angle (0° at zenith) 0 [0, 89]
radiation.k W/m2Direct Normal Irradiance 700 [0, 1000]
Table 1. Description of the 9 pre-selected variables of the PTSC models.
Figure 4. The Env_PTSC model relates the sun radiation, en-
vironment temperature and sun incidence to the heat flow pro-
duced by the SolarCollector.
minimal incidence angle as expected. The rim angle and
the focal length are maximal, meaning that the mirrors
have a large surface and “wrap” the tube. These results
must be considered with care, as the optimal point for the
5 variables may not be the same for each variable individ-
After gaining insights in the PTSC behaviour, we sta-
tistically learned this behaviour, i.e. we metamodelled the
Env_PTSC model. In existing solar power plants, the ge-
ometric parameters of the collectors cannot be modified:
only the weather inputs and the mirror cleanliness param-
eter evolve. Persalys enables us to reduce the PTSC model
with respect to these 3 variables.
4 Training and export of the meta-
Metamodelling, aka model reduction, consists in learn-
ing the model behaviour by a mathematical function. A
general purpose for metamodelling is to lower the compu-
tational cost, especially if many model runs are required
(e.g. to perform statistics or real-time simulations). We
reduced the PTSC model (a steady-state model) by learn-
ing the heatFlow final value with respect to the 3 afore-
mentioned variables with constant value.
Prior steps to metamodelling are the definition of a de-
sign of experiment and the simulation on these points, see
figure 1. We considered a Full Factorial Design (Friedman
et al., 2001) with 10 levels for each of the 3 variables, i.e.
1000 simulations. The metamodel is computed by Kriging
with constant mean and squared exponential covariance.
Figure 8 shows the metamodel validation by K-fold: the
cross-validation coefficient Q2is equal to 0.996, which is
very satisfying.
We saved the metamodel as a Python pickle object6
from the Persalys command line (see listing 1).
Listing 1. Save Persalys’ metamodel as Python Pickle object
import persalys as pls
import pickle
study = pls.Study.GetInstances()[0]
metamodel = study.getPhysicalModels()[1].
filename = "solar_collector.pkl"
with open(filename, ’wb’) as f:
pickle.dump(metamodel, f)
The pickled metamodel can be loaded in Python and ex-
ported as a Modelica graphical component and/or a FMU.
5 Using a Persalys metamodel in Mod-
elica GUI
Using the metamodel in a modelling environment enables
to connect it graphically to other components. We inserted
the metamodel as a power source in the concentrated solar
power plant model to show the validity of the interface be-
tween Persalys and Modelica GUIs. Following the same
methodology, metamodels reproducing the behaviour of
models from other environments (Excel, Amesim, Mat-
lab...) can be employed as blocks or FMUs in Modelica
The metamodel is a mathematical function, com-
puted by Persalys using OpenTURNS. The Python library
OTFMI interfaces FMUs with OpenTURNS objects, and
reciprocally (Girard and Yalamas, 2017)7.
We compare the advantages of exporting Persalys meta-
models as Modelica blocks or FMUs in subsection 5.1. We
show the insertion of the metamodel in a Modelica model
using a GUI in subsection 5.2.
5.1 Modelica block versus FMU
The metamodel can be used in Modelica as a block or as
a FMU. The FMU has the advantage to be standalone: it
embeds the contents required to run the metamodel, i.e.
a C function and C libraries. The “block” is a Modelica
wrapper of the C functions and XML file in which the
metamodel is stored. The simulation is faster, as unzip-
ping the FMU to access the underlying C is not necessary.
However, the C files need to be all stored and the wrapper
path must be updated manually if the user moves the C
The metamodel can be exported in both formats using
OTFMI, see listing 2. The function export_model exports
the given metamodel in a Modelica wrapper. If the gui op-
tion is prescribed, input and output connectors are gener-
ated, which enables to connect the wrapper to other Mod-
elica blocks. Otherwise inputs and outputs are defined us-
ing the Modelica language, which enables to simulate the
Figure 5. Top: Graph µ/σdrawn in Persalys GUI. The "no effect boundary" must be set by the user.
Bottom: Interpretation of the graphs µ/σand µ/µin Persalys GUI.
Figure 6. Top: the first-order and total Sobol’ indices of the 5 variables considered.
Bottom: the computed Sobol’ indices. Insufficient convergence of the estimates is signalled by warning panels.
Figure 7. Display of optimisation results in Persalys GUI. The heat flow is in watt ; the variable units are detailed in Table 1.
Figure 8. Metamodel validity using the K-fold method.
model via OMCompiler. The function export_fmu gener-
ates a FMU from a temporary Modelica wrapper. Both
ModelExchange or CoSimulation formats are supported.
Listing 2. Export the metamodel as component or FMU
fe = otfmi.FunctionExporter(metamodel,
fe.export_model(path_model, verbose=False,
fe.export_fmu(path_fmu, verbose=False)
These functionalities are supported on Windows and
Linux platforms. The generated component can be in-
cluded in OpenModelica Connection Editor (OMEdit) as
well as in Dymola.
5.2 Inserting the metamodel in a Modelica
We wrapped the metamodel in a Modelica block with
graphical input and output connectors. Figure 9 shows
the ThermoSysPro ConcentratedSolarPowerPlant_PTSC
model, whose solar panel has been replaced by the heat
source whose value is prescribed by the metamodel. We
call this model PartlyReducedCSPP. We successfully cali-
brated and ran the PartlyReducedCSPP model in Dymola.
At every time step of the simulation, the metamodel
value is queried by the solver (it is not co-simulation). The
initialization and integration steps last longer for the partly
reduced CSPP model than for the original CSPP, see ta-
ble 3. Table 2 shows that, even though the metamodel is
computationally less expensive than the Modelica model,
its inclusion in the Modelica environment increases the
simulation time.
Metamodel Env_PTSC
Simulation tool Python Modelica Modelica
Run time (s) 5 ×1050.5 3 ×103
Table 2. The metamodel simulates in Python up to 100 times
faster than the corresponding model in Modelica.
We have two hypotheses to explain this difference.
First, the computation of the metamodel derivatives (nec-
essary to set the solver time steps) is possibly difficult.
Each derivative must be estimated by the Modelica solver
as the metamodel analytical function is not accessible.
This increase in simulation time could thus be due to a
larger number of calls to the metamodel.
Second, three different languages (Python, C and Mod-
elica) are employed for one computation of the metamodel
in the Modelica environment. This could be improved in
the following by using the C implementation of the Open-
TURNS library, instead of its Python implementation.
6 Conclusion and perspectives
Asserting the behaviour of a model and exploiting its re-
sults are very important tasks for a modeller. We presented
in this paper technological solutions to meet these needs
while staying (mostly) in graphical interface.
The Persalys software enables the statistical analysis of
Modelica (and others) models. Its strength resides in the
guidance for the analysis, performed in a very visual way.
We showed the use of Persalys for selecting the influen-
tial variables of the PTSC by Morris and Sobol’ sensi-
tivity analyses. We leveraged the results of these analy-
ses and our physical knowledge to successfully reduce the
model. We showed that the reduced model can be easily
imported in a Modelica GUI, be it OMEdit or Dymola,
and connected to other Modelica blocks. This technolog-
ical bridge can be used in a large scope of applications,
for instance to introduce reduced finite-elements models
in the Modelica environment.
The implementation in Persalys of statistical methods
for time-dependent outputs is underway. This will open
new possibilities to study models which output(s) evolve
over time without reaching a steady state. We also intend
to increase the simulation speed of the reduced model by
suppressing the underlying call to Python and directly us-
ing the C-implementation of OpenTURNS.
We thank warmly Arnaud Barthet, Pan Zhou and Li Xiao
(M4G team, EDF Chine) for sharing with us their experi-
ence of solar collectors.
This work was partially supported by the Paris region
through the FUI research project “Modeliscale”, a collab-
oration with Dassault Systèmes, Inria, EDF, Engie, CEA
INES, DPS, Eurobios and Phimeca Engineering.
Figure 9. The PartlyReducedCSPP model, based on ThermoSysPro emblematic ConcentratedSolarPowerPlant_PTSC.
PartlyReducedCSPP ConcentratedSolarPowerPlant_PTSC
CPU time for initialization (s) 0.345 0.179
CPU time for integration (s) 993 109
Table 3. The initialization and integration times of the partly reduced CSPP are larger than for the original ThermoSysPro model.
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