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Neuro-fuzzy Modelling of a Linear Fresnel-type Solar Collector System as a Digital Twin

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Neuro-fuzzy Modelling of a Linear Fresnel-type Solar collector System as
A Digital Twin
William D. Chicaiza and Adolfo J. Sánchez and Antonio J. Gallego and Juan M. Escaño
Department of System Engineering and Automatic Control, University of Seville,
Camino de los Descubrimientos s/n, 41092, Seville, Spain.
wchicaiza@us.es; asanchezdelpozo@us.es; agallego2@us.es; jescano@us.es
Abstract
One of the main components of a Digital
Twin is the modeling of the virtual entity, be-
ing this a high-fidelity digital model of the
physical entity that represents the modeling
of geometry, modeling of physical proper-
ties, modeling of behavior, and modeling of
rules in the virtual world.
This paper presents a model, based on an
Adaptive Neuro-Fuzzy Inference System, of
a Fresnel linear solar collector system as
a Digital Twin, located on the roof of the
School of Engineering of the University of
Seville, which is a part of an absorption cool-
ing plant.
A distributed parameter model of the sys-
tem has been used to generate artificial data.
Real operating data were used to validate the
model.
Keywords: Digital Twin, Neuro-Fuzzy
modeling, ANFIS.
1 Introduction
Digital Twin (DT) is one of the most promising tech-
nologies applied to smart manufacturing and industry
4.0. Several DT applications have been realized in
product design, production and, prognostics and health
management (PHM) thanks to the increasing techno-
logical development, information storage, and trans-
mission speeds. The concept DT appeared in 2002
at the University of Michigan, promoting the premise
that each system has a physical entity and a virtual en-
tity. Term Digital Twin was included in Virtually Per-
fect for the conceptual model currently in use [11, 12].
The first general standard architecture that appears is
modeling in three dimensions [11]. Similarly, [26] pro-
poses a 5-layer DT modeling architecture, being this an
extension of the three-dimensional architecture. There
is also an eight-dimension architecture that describes
the behavior and context of the DT [21].
Several are the works developed regarding DTs, in
[12] argues that DT is the digital representation of a
physical object by developing a DT of a bending test
bench. Likewise, A step-by-step process of building
a DT model is presented in [17] using a commercial
drilling rig. Also, DT modeling of a 3D printing ma-
chine was performed in [7]. Industrial companies such
as General Electric and Siemens have seen the great
potential of DT [16, 27].
Deep learning shows the ability to learn and model
large-scale data sets, unlike traditional learning meth-
ods [18]. The performance of a physical entity can
be represented through artificial intelligence (AI) tech-
niques such as fuzzy logic (FL), Artificial neural net-
works (ANN), neuro-fuzzy algorithms, or optimiza-
tion techniques such as genetic algorithms (GA), parti-
cle swarm optimization (PSO), in order to solve many
problems in different areas.
The advantages of fuzzy logic and artificial neural net-
works were concatenating in an AI technique called
Neuro-Fuzzy. The most popular is the adaptive neuro-
fuzzy inference system (ANFIS) proposed by Jang
[14], which combines the learning capacity and rela-
tional structure of artificial neural networks with the
decision-making mechanism of fuzzy logic [15, 9, 23].
Several papers use ANFIS [8] presents a neuro-fuzzy
model of the temperature of an industrial autoclave to
apply nonlinear predictive control. Used to predict the
cone index values of arable soils [1], to control the
bag process by implementing an ANFIS controller [3].
Similarly, ANFIS is used to forecast monthly water use
[28, 4]. In the energy context in [29], they investigated
the interrelationship between energy consumption and
economic growth in China. Successful applications of
the neuro-fuzzy system for modeling complex nonlin-
ear hydro-resource systems have been reported [2].
Atlantis Studies in Uncertainty Modelling, volume 3
Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society
for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
Copyright © 2021 The Authors. Published by Atlantis Press International B.V.
This is an open access article distributed under the CC BY-NC 4.0 license -http://creativecommons.org/licenses/by-nc/4.0/. 242
This work uses ANFIS to model an energy system,
specifically the Linear Fresnel Collector (LFC) system
of the ETSI of the University of Seville, which is part
of the solar cooling plant installed. Since the dynamics
of this kind of systems is highly nonlinear, a complex
model is needed to describe this dynamics [6]. In order
to develop optimal control and optimization strategies
which use the prediction of the solar field temperature,
a fast model is indispensable. The use of the nonlinear
distributed parameter model to do this implies a high
computational burden and this is a great hindrance if
the problem has to be solved within a sampling time of
several seconds [5]. Faster models are very important
to be obtained. Thus the main objective of this paper
is to obtain a neuro-fuzzy model that describes the per-
formance of the real outlet temperature from the solar
field, considering the variables that affect this process
(solar radiation, water flow, ambient temperature, fluid
temperature, and the local hour that will determine the
position of the sun respect to the solar field).
The paper is organized as follows: Section 2 briefly
describes the Fresnel solar field and its mathematical
model. Section 3 describes the LFC ANFIS modeling.
Section 4 shows the training and evaluation results. Fi-
nally, some concluding remarks are given in section 5.
2 Modeling of the Fresnel solar field
This section presents a brief description of the Fres-
nel solar field and the mathematical model that will be
used for the simulation of the plant and the generation
of data to train the ANFIS models.
2.1 Description of the Fresnel solar field
The Escuela Técnica Superior de Ingeniería (ETSI) of
Seville has a solar cooling plant (SCP). The SCP con-
sists of three main subsystems: (1)Fresnel-type solar
field, see Figure 1, (2) Absorption machine chiller and
(3) a PCM storage tank. This work focuses on the
LFC subsystem. The Fresnel solar field is installed on
the roof of the building with an East-West orientation
(Latitude =37.4108972,Longitude =6.0006621
).
The solar field heats up the pressurized water coming
from the chiller up to the required operation tempera-
ture (145165C). The solar field consists of 11 rows
of mirrors which focus the direct solar radiation on a
metal tube of 64 m long whereby the water is circu-
lating. A more complete description can be found in
[19].
The modeling of the Fresnel field is developed us-
ing similar equations to the case of parabolic trough
Figure 1: Fresnel solar collector.
fields modeling [24], but differ in the way of calculat-
ing the geometric efficiency, the shade factor and the
thermodynamic properties of the fluid. The LFC sys-
tem can be modeled using two different approaches: i)
the concentrated parameter model used in control ap-
plications because its simplicity [19, 20, 22] and ii) the
distributed parameter model which takes into account
the spatial distribution of the system providing a more
precise description [6, 10, 5]. The distributed parame-
ter model is used for simulation purposes.
2.2 Distributed parameter model
The distributed parameter model consists of a pair of
differential equations in partial derivatives describing
the energy balance [10] as follows:
ρmCmAm
Tm
t=IKo ptnoGHl(TmTa). . .
. . . lpHt(TmTf)
ρfCfAf
Tf
t+ρfCfqTf
l=lpHt(TmTf)
(1)
where msubindex refers to metal and fsubindex refers
to fluid. The description of the parameters is presented
in Table 1.
The calculation of the optical efficiency Kopt requires
knowledge of multiple factors such as the reflectivity
of the mirror, the absorptance of the metal tube, the
shape factor. The heat transmission coefficient, den-
sity and specific heat coefficient are obtained as poly-
nomial functions of the segment temperature and the
water flow by using thermodynamic data of the heat
transfer fluid (pressurized water), which can be found
in [6]. The geometric efficiency nois obtained using
complex trigonometric formulas, considering the ef-
fect of the cosine of the incidence angle of the solar
Atlantis Studies in Uncertainty Modelling, volume 3
243
Symbol Description Units
tTime s
lSpace m
ρDensity kg m3
CSpecific heat capacity JK1kg1
ACross sectional area m2
T(l,t)Temperature K,
C
q(t)Water flow rate m3s1
I(t)Direct solar radiation W m2
noGeometric efficiency Unitless
Kopt Optical efficiency Unitl ess
GCollector aperture m
Ta(t)Ambient temperature K,
C
HlGlobal coefficient W m2C1
of thermal loss
HtCoefficient of heat W m2C1
transmission metal-fluid
lpLength of pipe line m
STotal reflective surface m2
Table 1: Description of the parameters.
beam and the shade factor [19]. The distributed pa-
rameter model is solved with an integration time of
0.25s, dividing the tube into 64 segments of 1 m each.
The distributed parameter model is used as a simula-
tion model to generate artificial data in order to be used
to train the Neuro-fuzzy model.
3 LFC ANFIS modelling
ANFIS integrates two methods of Soft-Computing: ar-
tificial neural networks (ANN) and a fuzzy inference
system (FIS) [14]. Providing a method applicable to
fuzzy modeling, learning from a data set in order to
calculate the parameters of the membership functions
(MF) that best allow the associated FIS to follow the
input-output data [23, 13]. Fuzzy logic (FL) can model
arbitrarily complex non-linear functions. Non-linearity
and complexity are handled by rules, MF and the in-
ference process, improving performance with simpler
implementation. The fuzzy Takagi-Sugeno model can
be formulated as an ANFIS [25], except that the links
indicate the direction of signal flow and no associated
weights. The ANFIS architecture consists of five lay-
ers: fuzzification, product, normalization, defuzzifica-
tion and output. The first and fourth layers contain
adaptive nodes (square nodes) that represent the pa-
rameter sets that are adjustable, while the remaining
layers contain fixed nodes (circular nodes) that repre-
sent the parameter sets that are fixed in the system [14].
ANFIS requests a training data set, (x1,x2,· · · ,y)de-
sired input-output pair that represents the system to
model. Obtaining a dynamic model is not always easy,
either because of the complexity, randomness, or lack
of knowledge of the study system. An accurate model
in many cases will consist of a high number of equa-
tions, but in some cases, it is not always adequate to
solve uncertain systems.. The use of an ANFIS to
model the qualitative aspects and reasoning processes
of human knowledge, using fuzzy rules to describe the
performance of the system, and avoiding precise quan-
titative analysis is an alternative.
ANFIS starts from previous knowledge, or the neces-
sary information can be added to improve the model.
In this work with an ANFIS, a set of rules describ-
ing the dynamics of the solar field output temperature
has been obtained. When defining its structure we are
faced with the drawback of setting the MFs, since a
greater number of MFs determines greater knowledge.
However it generates the use of numerous rules, this
can be solved by applying clustering methods that seek
to classify data into subsets.
3.1 Input/Output data set selection
The neuro-fuzzy model represents the performance of
the real outlet temperature from the solar field, using
the variables that influence this process: solar radia-
tion, water flow, ambient temperature, fluid tempera-
ture, and the local hour that will determine the position
of the sun. The solar field evolves independently in
an open-loop from an arbitrarily given starting point to
obtain data for subsequent ANFIS training.
The distributed parameter model has been used to sim-
ulate the solar plant and obtain artificial data that will
be part of the training set. Simulations have been car-
ried out, starting from the system in a permanent state.
Initially, there has only been one input change in each
variable, of the step type, while the rest of the variables
remain constant in average values. Likewise, the levels
of the amplitudes of the steps were divided into three
regions (low, medium, high) and these have been given
for the variables water flow, inlet fluid temperature and
solar radiation. The values of the applied steps have
thus served to better capture the dynamics of the sys-
tem, in the formation of the ANFIS.
Real and artificial input-output data from the solar field
has been used, to prepare two data sets: training and
checking set. The training set is composed of real data
from two different days in the months of June, July
as shown in Figure 2(a) and artificial data obtained
from the distributed parameter model, see Figure 2(b).
While the checking data is composed of real data from
two different days in the month of August as shown
in Figure 3. The training set must contain all the rep-
resentative characteristics of the system to be modeled.
Atlantis Studies in Uncertainty Modelling, volume 3
244
This set is used by ANFIS to find a spatial input-output
relationship through repetitive analysis.
Figure 2: Training data set: (a) real data, (b) artificial
data
The checking set allows to verify the generalization ca-
pacity of the obtained ANFIS model, should be differ-
ent from the training set, so that the validation process
is not trivial and avoids overfitting. Figures 2 and 3
shows training and checking data.
0 100 200 300 400 500 600 700 800
Time [min]
80
100
120
140
160
180
200
Temperature (ºC)
20
30
40
50
60
70
Temperature (ºC)
Tin
Tout
Ta
0 100 200 300 400 500 600 700 800
Time [min]
11
11.5
12
12.5
Water Flow (m3/h)
400
500
600
700
800
900
DNI (W/m2)
Q
I
Figure 3: Checking data set.
3.2 Data processing
A process of normalization of the input-output data
set is performed. The use of normalized values pre-
vents the different nature and magnitude of the vari-
ables from affecting the neural learning process, also
helps to reduce noise, inconsistency and leads to a bet-
ter estimation of the modeling.
The original data has been normalized in the range [0
1] using Eq. 2.
Xnorm =xxmin
xmax xmin
(2)
Where xis the data to be normalized, (xmax,xmin )is the
maximum and minimum of the original data respec-
tively and Xnorm is the normalized data.
ANFIS has been provided with memory through a re-
cursive structure, using past values of the inputs and
outputs to capture the solar field dynamics. There are
no standard methods to transform human knowledge
or experience into a base of rules and data. Therefore,
it becomes the art of adjusting the ANFIS parameters
in order to minimize the error or maximize the perfor-
mance index.
4 Results
This section presents the results of the ANFIS models.
Simulations have been carried out with real data from
different days of September where the real results will
be compared with those obtained with the ANFIS mod-
els.
4.1 ANFIS training results
The training process starts with seven inputs with a
hybrid configuration [14] and the subtractive cluster-
ing (SC) method with a influence range equal to 0.70.
A total of four Gaussian type MFs are obtained for
each input. The number of epochs used during train-
ing was 200 and the evaluation criterion for estimating
accuracy of the model is performed by comparing the
RMSE at each epoch. However, as can be observed in
the ANFIS modeling parameters, the influence range
of clustering, and the number of MFs have been varied
in order to obtain a more generalized learning of the
training and checking sets. The ANFIS architecture is
also modified when the RMSEChk is considerable dur-
ing training. The number of rules is changed since re-
dundant rules lead to overfitting. Overfitting indicates
that the ANFIS model obtained is fitted too closely to
the training data set and the final performance of the
model with respect to another data set will be deficient.
The Figure 4 shows the overfitting effect considering a
high number of epochs (k=10e4), since the learning
rate also depends on the number of given epochs.
If kis small the convergence will be slow but if kis
large the convergence will be initially very fast and
will oscillate around the optimum. However, for a very
high kthe ANFIS model is fitted the training data and
the RMSEChk increases.
The obtained ANFIS architecture of the model is
shown in Table 2 and Figure 5 shows the evolution of
the training and checking RMSE index at each epoch.
The RMSE checking curve has to be observed more to
evaluate the accuracy of the model, since it indicates
Atlantis Studies in Uncertainty Modelling, volume 3
245
0246810
Epoch 104
0
0.01
0.02
0.03
0.04
0.05
RMSE
RMSETrn
RMSEChk
Figure 4: Overfitting effect on ANFIS modeling train-
ing.
if the ANFIS learning is general1. Therefore, a middle
point is sought where the learning is general for both
sets. For the rest of the paper this model will be named
as ANFIS1.
Description RMSE min
Number MFs: 3 Gaussianty pe Normalized data
Number rules: 3 RMSET rn =0.0028
Optimization method: hybrid RMSEChk =0.0105
Output MF type: linear
Influence range: 0.72
Epoch number: 200
Table 2: ANFIS1 architecture parameters obtained
with normalized data.
4.2 ANFIS evaluation results
The results of the evaluation of the model obtained are
presented when using real data from days of operation.
Two error indexes were used to compare the models,
the RMSE and the MAPE, Eqs. 3 and 4.
RMSE =rn
t=1(xtx0
t)2
n(3)
MAPE =
n
t=1
xtx0
t
xt
n(4)
We performed a simulation to evaluate the ANFIS1
model. Figure 6 shows that ANFIS1 model has a good
1If RMSET rn down and RMSEChk up, the ANFIS model-
ing is learning from one set but gets more error in the other,
which indicates that learning is not general.
0 50 100 150 200
Epoch
0
0.01
0.02
0.03
0.04
0.05
RMSE
RMSETrn
RMSEChk
Figure 5: Training and checking RMSE curves for AN-
FIS1 modeling.
performance capturing the dynamics of the LFC field
except in the last part of the day, where the error is
higher. Figure 7 shows the results of the ANFIS1
model and real data from a different day. It can show
that, although the dynamics are similar, the error in this
simulation is very high.
0 200 400 600 800 1000 1200
Samples
60
80
100
120
140
160
180
200
Temperature [°C]
Real Tout
Model
Figure 6: ANFIS1 model evaluation, model data vs
real data. Day data-set 1.
In order to obtain a model with a better overall per-
formance, a second ANFIS (ANFIS2) has been trained
with a different architecture and parameters which are
shown in Table 3. The number of epochs has been in-
creased and the range of clustering influence has been
modified to 0.70 for this ANFIS model.
It can be checked, comparing tables 2 and 3, that the
RMSE (Trn and Chk) of ANFIS2 are similar to those of
ANFIS1. The RMSE curves of training and checking
are shown in Figure 8.
Atlantis Studies in Uncertainty Modelling, volume 3
246
0 200 400 600 800 1000 1200 1400 1600
Samples
40
60
80
100
120
140
160
180
200
Temperature [°C]
Real Tout
Model
Figure 7: ANFIS1 model evaluation, model data vs
real data. Day data-set 2.
Description RMSE min
Number MFs: 4 Gaussianty pe Normalized data
Number rules: 4 RMSET rn =0.0026
Optimization method: hybrid RMSEChk =0.0106
Output MF type: linear
Influence range: 0.70
Epoch number: 1000
Table 3: ANFIS2 architecture parameters.
Figure 9 show the evolution of ANFIS2 model vs the
real data, for day data-set 1. as in the previous case
(ANFIS1), showing that ANFIS2 model also provides
a good performance in capturing the LFC system dy-
namics but with a better performance along the day.
ANFIS2 model has also been evaluated in another day
of real data day data-set 2, shown in Figure 10, where
it can be observed the good performance of the model
evolution along the day.
In order to compare the results of both models (AN-
FIS1 and ANFIS2), a set of three simulations results
are shown in Table 4 where the RMSE and MAPE in-
dexes are shown for the different test days. It can be
observed that ANFIS2 model presents lower error rates
than ANFIS1, concluding that this model presents bet-
ter results in the estimation of the outlet temperature
from the solar field.
ANFIS2 captures the actual output temperature dy-
namics of the solar field in a better way, with twice as
many epochs compared to the previous model. How-
ever, the benefit obtained is appreciable with the ad-
vantage of not having a very high number of epochs.
The optimum number of epochs would be in this range.
Regarding the influence range, the optimum range
Figure 8: Training and checking RMSE curves for best
ANFIS modeling with normalized data.
0 200 400 600 800 1000 1200
Samples
60
80
100
120
140
160
180
200
Temperature [°C]
Real Tout
Model
Figure 9: ANFIS2 model evaluation, model data vs
real data. Day data-set 1.
should be in the interval [0.70.72].
Finally, a simulation of the distributed parameter
model and the ANFIS2 neuro-fuzzy model has been
performed to compare the computational load of each
of them. The execution time of the distributed parame-
ter model was 35.03[ms]while that of the ANFIS2 sys-
tem was 634.98[us]. In conclusion, the computational
burden of ANFIS2 concerning the distributed param-
eter model is 55 times faster, which makes it suitable
for real-time control applications where the dynamic
model of the plant is required. Also, the number of
learning parameters of ANFIS is much lower concern-
ing the distributed parameter model.
Atlantis Studies in Uncertainty Modelling, volume 3
247
0 200 400 600 800 1000 1200 1400 1600
Samples
40
60
80
100
120
140
160
180
200
Temperature [°C]
Real Tout
Model
Figure 10: ANFIS2 model evaluation, model data vs
real data. Day data-set 2.
Error ANFIS1 ANFIS2
indexes model model
Day Test 1
RMSE 6.9890 4.42
MAPE 2.69% 2.27%
Day Test 2
RMSE 12.9572 3.6726
MAPE 8.54% 2.58%
Day Test 3
RMSE 8.58 7.5141
MAPE 5.69% 4.51%
Table 4: RMSE and MAPE indexes obtained for AN-
FIS1 and ANFIS2.
5 Conclusion
In this work ANFIS has been applied to capture the dy-
namics of real outlet temperature from a Fresnel-type
solar field, obtaining satisfactorily a series of mod-
els which differ in the number of rules.Specifically,
the range of influence of clustering and the number of
epochs have been varied to obtain a better model with
a lower error coefficient at the instant of evaluation.
The use of output feedback allows the capture of the
dynamics of the process to be modelled. The result is a
recurrent neural network, whose convergence is more
complex. The ANFIS model obtained in this work is
auto-regressive of second order.
Modifying various parameters, several ANFIS models
have been obtained. One of them has been chosen,
with an acceptable validation error, to follow the dy-
namic evolution of the process. This paper lays the
foundations for creating a framework with which to de-
sign ANFIS-based digital twins for plants of this type.
In future works, the error must be improved by learn-
ing with continuous operating data.
Acknowledgement
The authors want to thank the European Commis-
sion for funding this work under project DENiM.
This project has received funding from the European
Union’s Horizon 2020 research and innovation pro-
gramme under grant agreement No 958339.
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