With the Bonner spheres spectrometer neutron spectrum is obtained through an unfolding procedure. Monte Carlo methods, Regularization, Parametrization, Least-squares, and Maximum Entropy are some of the techniques utilized for unfolding. In the last decade methods based on Artificial Intelligence Technology have been used. Approaches based on Genetic Algorithms and Artificial Neural Networks have been developed in order to overcome the drawbacks of previous techniques. Nevertheless the advantages of Artificial Neural Networks still it has some drawbacks mainly in the design process of the network, vg the optimum selection of the architectural and learning ANN parameters. In recent years the use of hybrid technologies, combining Artificial Neural Networks and Genetic Algorithms, has been utilized to. In this work, several ANN topologies were trained and tested using Artificial Neural Networks and Genetically Evolved Artificial Neural Networks in the aim to unfold neutron spectra using the count rates of a Bonner sphere spectrometer. Here, a comparative study of both procedures has been carried out

Gallego Díaz, Eduardo F.

Guerrero Araque, Jorge Enrique

Lorente Fillol, Alfredo

Los Arcos Merino, José María

Martínez Blanco, María del Rosario

Méndez Villafañe, Roberto

Ortiz Rodríguez, José Manuel

Vega-Carrillo, Héctor René

Revista Mexicana de Física

Archivo Digital UPM

Performance of artificial neural networks and genetical evolved artificial neural networks unfolding techniques

With the Bonner spheres spectrometer neutron spectrum is obtained through an unfolding procedure. Monte Carlo methods, Regularization, Parametrization, Least-squares, and Maximum Entropy are some of the techniques utilized for unfolding. In the last decade methods based on Artificial Intelligence Technology have been used. Approaches based on Genetic Algorithms and Artificial Neural Networks have been developed in order to overcome the drawbacks of previous techniques. Nevertheless the advantages of Artificial Neural Networks still it has some drawbacks mainly in the design process of the network, vg the optimum selection of the architectural and learning ANN parameters.
In recent years the use of hybrid technologies, combining Artificial Neural Networks and Genetic Algorithms, has been utilized to. In this work, several ANN topologies were trained and tested using Artificial Neural Networks and Genetically Evolved Artificial Neural Networks in the aim to unfold neutron spectra using the count rates of a Bonner sphere spectrometer. Here, a comparative study of both procedures has
been carried out.Con el espectrómetro de esferas Bonner se puede obtener el espectro a través de un procedimiento de reconstrucci ón. Los métodos Montecarlo,
de Regularización en, de parametrización, de mínimos cuadrados, de la máxima entropía son algunas de las técnicas utilizadas para la reconstrucción. En la ´ultima década, se han utilizado los métodos basados en la tecnología de Inteligencia Artificial. Se han desarrollado
métodos basados en Algoritmos Genéticos y Redes Neuronales Artificiales en un intento de resolver las desventajas de las técnicas mencionadas.
Sin embargo, a pesar de la ventajas de las redes neuronales, las mismas presentan algunos inconvenientes principalmente en lo
que se refiere al proceso de diseño de de las redes, por ejemplo, la selección ´optima de los parámetros de arquitectura y aprendizaje. En
a˜nos recientes, también se ha utilizado tecnologías híbridas, combinando las redes neuronales y los algoritmos genéticos. En ´este trabajo, se
diseñaron y entrenaron varias topolog´eas de redes neuronales y redes neuronales evolucionadas geneticamente con el objetivo de reconstruir
espectros de neutrones utilizando las tasas de conteo de un espectrómetro de esferas Bonner. Aquí se realiza un estudio comparativo de ambos procedimientos

Ortíz Rodríguez, José Manuel

Vega Carrillo, Héctor René

Gallego Díaz, Eduardo

Lorente, Alfredo

Mendez Villafañe, Roberto

Los arcos Merino, José María

Caxcan Repositorio Institucional de la Universidad Autónoma de Zacatecas

REVISTA MEXICANA DE FÍSICA S57 (1) 89–92 FEBRERO 2011Performance of artificial neural networks and genetical evolved artificial neuralnetworks unfolding techniquesJ.M. Ort́ız-Rodŕıgueza,c,∗, M.R. Mart́ınez-Blancob, H.R. Vega-Carrillob, E. Gallego D́ıazd, A. Lorente Fillold,R. Méndez Villafãnee, J.M. Los Arcos Merinoe, J.E. Guerrero AraqueeUnidades Acad́emicas:aIngenieŕıa Eléctrica,∗e-mail: morvymm@yahoo.com.mxbEstudios Nucleares, Universidad Autónoma de Zacatecas,Apartado Postal 336, Zacatecas, 98000, Mexico.cDepto. de Electrotecnia y Electrónica Escuela Polit́ecnica Superior,Avda. Meńendez Pidal s/n, Ćordoba, Espãna.dUniversidad Polit́ecnica de Madrid, Depto. de Ingenierı́a Nuclear, ETSI Industriales,C. Jośe Gutierrez Abascal, 2, Madrid, 28006, España.eCIEMAT, Laboratorio de Metroloǵıa de Radiaciones Ionizantes,Avda. Complutense, 22, 28040, Madrid, España.Recibido el 10 de marzo de 2010; aceptado el 31 de agosto de 2010With the Bonner spheres spectrometer neutron spectrum is obtained through an unfolding procedure. Monte Carlo methods, Regularization,Parametrization, Least-squares, and Maximum Entropy are some of the techniques utilized for unfolding. In the last decade methods basedon Artificial Intelligence Technology have been used. Approaches based on Genetic Algorithms and Artificial Neural Networks have beendeveloped in order to overcome the drawbacks of previous techniques. Nevertheless the advantages of Artificial Neural Networks still it hassome drawbacks mainly in the design process of the network, vg the optimum selection of the architectural and learning ANN parameters.In recent years the use of hybrid technologies, combining Artificial Neural Networks and Genetic Algorithms, has been utilized to. In thiswork, several ANN topologies were trained and tested using Artificial Neural Networks and Genetically Evolved Artificial Neural Networksin the aim to unfold neutron spectra using the count rates of a Bonner sphere spectrometer. Here, a comparative study of both procedures hasbeen carried out.Keywords: Neutron spectrometry; neural networks; evolutive algorithms.Con el espectŕometro de esferas Bonner se puede obtener el espectro a traves de un procedimiento de reconstrucción. Los ḿetodos Mon-tecarlo, de Regularizacién, de parametrización, de ḿınimos cuadrados, de la máxima entroṕıa son algunas de las técnicas utilizadas para lareconstruccíon. En laúltima d́ecada, se han utilizado los métodos basados en la tecnologı́a de Inteligencia Artificial. Se han desarrolladométodos basados en Algoritmos Genéticos y Redes Neuronales Artificiales en un intento de resolver las desventajas de las técnicas men-cionadas. Sin embargo, a pesar de la ventajas de las redes neuronales, las mismas presentan algunos inconvenientes principalmente en loque se refiere al proceso de dieño de de las redes, por ejemplo, la selección óptima de los paŕametros de arquitectura y aprendizaje. Enaños recientes, también se ha utilizado tecnologı́as h́ıbridas, combinando las redes neuronales y los algoritmos genéticos. Eńeste trabajo, sedisẽnaron y entrenaron varias topologéas de redes neuronales y redes neuronales evolucionadas geneticamente con el objetivo de reconstruirespectros de neutrones utilizando las tasas de conteo de un espectrómetro de esferas Bonner. Aquı́ se realiza un estudio comparativo deambos procedimientos.Descriptores: Espectrometrı́a de neutrones; redes neuronales; algoritmos evolutivos.PACS: 29.30.Hs; 29.40-n; 07.05-Mh1. IntroductionNeutron energy spectra found in workplaces are often com-plex, the range of neutron energies involved can extend overnine or ten orders of magnitude. To improve the assessmentof personal equivalent dose (Hp) and ambient dose equiv-alent (H * (10)) in workplace, requires the proper charac-terization of neutron spectra [1]. The monitoring of occu-pational radiation exposure in neutron fields is mainly donewith multi-element systems where each element has a partic-ular response to neutrons. With the neutron spectrum infor-mation and neutron fluence-to-dose conversion coefficients,different dose quantities, like Hp or H * (10), can be esti-mated.With the count rates taken with the Bonner Spheres Spec-trometer (BSS), the neutron spectrum can be unfolded. InBSS, each detector is characterized by a response function,the whole set is the response matrix. The relationship amongneutron spectrum, count rates and response matrix is de-scribed by the integral-differential equation of Fredholm offirst type. Due to the number of detectors is smaller thanthe number of energy groups used to describe the spectrum,resulting problem is ill-conditioned therefore, unfolding pro-cedures should be applied [1]. In previous works, have beenreported neutron spectrometry and dosimetry results, by us-ing the Artificial Intelligence (AI) technology as alternativesolution. The Artificial Neural networks (ANN) [2] have re-90 J.M. ORT́IZ-RODŔIGUEZ et al.ceived the higher attention among researchers [1], however,the use of this technology is not free of problems [3].ANN technology is a useful alternative to solve the neu-tron spectrometry problem, however, several drawbacks mustbe solved in order to simplify the use of these procedures.Many of the previous studies in neutron spectrometry anddosimetry by using the ANN approach, have found seri-ous drawbacks in the ANN design process itself, mainly inthe proper determination of the structural and learning pa-rameters of the networks being designed. These parametersare significant contributing factors to the ANN performance;however, the optimal selection follows in practical use norules because they are generally heuristically chosen by usingthe trial and error technique, which produces networks withpoor performance and low generalization capacity. For theanterior, the nuclear research community needs approachesthat implement ANN models faster than what is currentlyavailable. In consequence, more research has been suggestedin order to overcome these drawbacks.Recently, the use of ANN technology has been appliedwith success in the neutron spectrometry and dosimetry prob-lems, using a novel approach known as Robust Design of Ar-tificial Neural Networks (RDANN) methodology in the de-sign process of the networks [3]. Another promising tech-nique for ANN design, is to introduce the capacity of adap-tation to the net by using Evolutionary Algorithms (EA) [4],which can be used to adapt the connections among the synap-tic weights, the design of the architecture, the adaptationof the learning rule, etc. The use of a hybrid technologybased in the RDANN methodology combined with EA forthe modelling of ANN applied in the neutron spectrometryand dosimetry problems could be a very convenient alterna-tive technique. In this work, several ANN topologies weretrained and tested using two ANN design approaches, to andthe optimum parameters of ANN. The networks were de-signed in the aim to unfold neutron spectra using the countrates of CIEMAT BSS, Spain. Here, a comparative study ofboth procedures has been carried out.2. Materials and methodsANN and EA are two relatively young research areas thatwere subject to a steadily growing interest during the pastyears. Until today, many researchers still prefer use thegradient search method Back Propagation (BP) in trainingANN [2]. However, this technique is a local search methodand when applied to complex nonlinear optimization prob-lems, can sometimes result in inconsistent and unpredictableperformances. One of the main hindrances is due to the factthat searching of optimal weights is strongly dependent oninitial weights and if they are located near local minima, thealgorithm would be trapped; if the initial guess of the ANNis near local maxima, it will climb the gradient and get stuck.The structure of a neural network is a significant contributingfactor to its performance and the structure is generally heuris-tically chosen. Several different attempts have been proposedby various researchers to alleviate the training problems. Theuse of EA as search technique has allowed different proper-ties of ANN to be evolved.In this work, the performance of neural nets, designedfor the BSS of CIEMAT, with two desing methodologiesis compared. The traditional nets (ANN) were designedby means of the RDANN methodology and the EvolutiveANN (EANN) [4], were designed by using the computerprogram known as NeuroGenetic Optimizer (NGO) [5]. Tou e the knowledge stored at the networks designed with bothmetodologies, friendly computer programs whit graphical in-terfaces were designed and builded respectively. A modifiedversion of the NSDann unfolding code was used for the tra-ditional ANN [6], and the unfolding code called “NeutronSpectrometry and Dosimetry based on Evolutive ArtificialNeural networks” (NSDEann) was designed for EANN.In both cases, the first layer (input) corresponds to the12 Bonner spheres of the CIEMAT’s BSS, the hidden lay-ers and neurons by layer should be determined and the thirdlayer (output) has 85 neurons. The first 72 outputs correspondto the neutron spectra and the remaining 13 are equivalentdoses. In both methodologies training was carried using 201spectra, and 50 spectra were used for testing the learning ofthe nets.Utilizing the RDANN methodology, additional parame-ters have to be determined: momentum, learning rate, train-ing algorithm and mean square error (MSE). The EANNtechnology, although does not requires on the part of the userANN parameters to be determined, it requires the determi-nation of parameters regarded with the GA used to and thearchitecture of the net.This is a very difficult problem, which is similar to thatfound in ANN design and, at present, this represents a seri-ous drawback of the EANN approach, because the parameterselection is done through the trial and error technique. Moreresearch is needed in this sense. At present, work is beingcarried out. The neutron spectra unfolded and its correspond-ing 13 equivalent doses were computed with the modifiedNSDann and NSDEann unfolding codes, for a239PuBe neu-tron source measured at 80 cm distance, at “Departamentode Ingenieŕıa Nuclear” (DIN) of “Universidad Polit́ecnica deMadrid” (UPM).3. Results and discussionBy means of the RDANN methodology, 36 traditional ANNtopologies were designed and trained, each in a time of107 seconds average. The optimum network topology is: 12neurons in the input layer, 16 nerons in a hidden layer and 85in the output layer. The neural nets were trained until MSEwas reduced to 10−4. Additional parameters are: momen-tum: 0.001, learning rate: 0.1, training algorithm: trainscg.After the training and testing stages, the knowledge stored atsynaptic weights was extracted and a modified version of theNSDann unfolding code was designed. Figure 1, shows theRev. Mex. F́ıs. S57 (1) (2011) 89–92PERFORMANCE OF ARTIFICIAL NEURAL NETWORKS AND GENETICAL EVOLVED ARTIFICIAL NEURAL NETWORKS. . . 91FIGURE 1. Neutron spectra unfolded and equivalent doses calcu-lated with NSDann.FIGURE 2. Neutron spectra unfolded with NSDEann.FIGURE 3. Neutron spectra unfolded with NSDann - NSDEann.neutron spectra unfolded and its 13 equivalent doses calcu-lated by means of the modified NSDann code.By using the EANN methodology, 600 EANN were de-signed and trained in a time of 04:44:09. The minimum net-work training passes for each network were 420, the cutofffor network training passes was 450, and the limit on hid-den neurons was 8. The optimum network topology is: aFast-Back Propagation neural network with 12 inputs, 6 lo-gistic neurons in a hidden layer and 85 neurons in the outputlayer, with an accuracy on training set= 99.50% accordingNGO. The parameters used for the GA, selected using thetrial and error technique, are: generations run: 10, populationSize: 60, selection was performed by the top 50% surviving,re?lling of the population was done by cloning the survivors,mating was performed by using the TailSwap technique, mu-tations were performed using Random Exchange techniqueat a rate of 25%.After the training and testing stages, it was not possibleto extract the knowledge stored at synaptic weights of thenetwork designed with NGO. For this reason, the NSDEannunfolding code was designed to read and graph the spectro-metric and dosimetric information produced by means of theEANN trained with NGO. Figure 2, shows the neutron spec-tra unfolded and its 13 equivalent doses calculated by meansof the modified NSDann.In order to compare the results obtained with the NSDannand NSDEann unfolding codes, the computer tool known as“Neutron spectrometry and dosimetry Tool Box” (NSDTB)was used [7]. Figure 3, shows the performance of the neu-tron spectra unfolded with the EANN approach (green line)and the spectra unfolded with the RDANN methodology (redline) and its corresponding 13 equivalent doses. As can beseen, the spectra and doses present diferencies, this is duemainly to the trial and error approach used to select the GAparameter in the EANN approach, which is a serious draw-back of this method. More research is needed in this sense.At present work is being developed to overcome these draw-backs.From Fig. 3, can be observed that the neutron spectra un-folded and equivalent doses calculated with both, traditionalANN and EANN, are very similar, however, the EANN un-fold the spectra in different energy bins, this makes that theχ2 test fails. A deeper analysys should be needed in order toobserve closer what could be happening.4. ConclusionsThe use of ANN technology is a useful alternative to solvethe neutron spectrometry and dosimetry problems; however,to obtain the best results, some drawbacks must be solved inthe ANN design process, such as the optimum ANN topologyselection.In this work, the ANN optimization methodology knownas RDANN, was used to design an ANN capable to solvethe neutron spectrometry and dosimetry problems for theRev. Mex. F́ıs. S57 (1) (2011) 89–9292 J.M. ORT́IZ-RODŔIGUEZ et al.CIEMAT BSS system. The neural net was trained and testedusing a large set of neutron spectra compiled by the IAEA.The success of ANN technology in neutron spectrome-try and dosimetry, using only the Bonner spectrometer countrates as input in the trained network will overcome someof the problems associated with the solution of such ill-conditioned problem. The results here reported demonstratethat the use of this technology has become in a useful tool.Until now RDANN methodology seems to be mo reliabein the neutron spectra unfoloding problem, because more re-search has been carried out in this sense and consecuentlymore information is available. The main drawback of EANNis the trial and error technique used to determine the optimumvalues of the GA used to build the network. The combinationof RDANN whit GA could improve widely the results ob-tained with both methodologies.More research is needed and at present, work is beingcarried out.AcknowledgementsThis work was supported by “Agencia Española de Coop-eracíon Internacional para el Desarrollo”, AECID (Spain).1. H.R. Vega-Carrillo, V.M. Herńandez-D́avila, E. Manzanares-Acuña, E. Gallego, A. Lorente, and M.P. Iñiguez,RadiationProtection Dosimetry126(2007) 408.2. S. Haykin, Neural Networks: A comprehensive foundation.Prentice Hall Inc. (1999).3. J.M. Ortiz-Rodŕıguez, M.R. Mart́ınez-Blanco, and H.R. Vega-Carrillo,Electronics, Robotics and Automotive Mechanics Con-ference2 (2006) 131.4. J.M. Ortiz-Rodŕıguez, M.R. Mart́ınez-Blanco, E. Gallego D́ıazand H.R. Vega-Carrillo,Electronics, Robotics and AutomotiveMechanics Conference, 4 (2008) 387.5. NeuroGenetic Optimizer. http://www.biocompsystems.com6. M.R. Mart́ınez-Blanco, J.M. Ortiz-Rodrı́guez, and H.R. Vega-Carrillo,Electronics, Robotics and Automotive Mechanics Con-ference0 (2009) 131.7. J.M. Ortiz-Rodŕıguez, M.R. Mart́ınez-Blanco, E. Gallego D́ıaz,and H.R. Vega-Carrillo,Electronics, Robotics and AutomotiveMechanics Conference5 (2009) 112.Rev. Mex. F́ıs. S57 (1) (2011) 89–92

English

Servicio de Coordinación de Bibliotecas de la Universidad Politécnica de Madrid

REVISTA MEXICANA DE F´ISICA S 57 (1) 89–92 FEBRERO 2011
Performance of artificial neural networks and genetical evolved artificial neural
networks unfolding techniques
J.M. Ortı´z-Rodrı´gueza,c,∗, M.R. Martı´nez-Blancob, H.R. Vega-Carrillob, E. Gallego Dı´azd, A. Lorente Fillold,
R. Me´ndez Villafan˜ee, J.M. Los Arcos Merinoe, J.E. Guerrero Araquee
Unidades Acade´micas: aIngenierı´a Ele´ctrica,
∗e-mail: morvymm@yahoo.com.mx
bEstudios Nucleares, Universidad Auto´noma de Zacatecas,
Apartado Postal 336, Zacatecas, 98000, Mexico.
cDepto. de Electrotecnia y Electro´nica Escuela Polite´cnica Superior,
Avda. Mene´ndez Pidal s/n, Co´rdoba, Espan˜a.
dUniversidad Polite´cnica de Madrid, Depto. de Ingenierı´a Nuclear, ETSI Industriales,
C. Jose´ Gutierrez Abascal, 2, Madrid, 28006, Espan˜a.
eCIEMAT, Laboratorio de Metrologı´a de Radiaciones Ionizantes,
Avda. Complutense, 22, 28040, Madrid, Espan˜a.
Recibido el 10 de marzo de 2010; aceptado el 31 de agosto de 2010
With the Bonner spheres spectrometer neutron spectrum is obtained through an unfolding procedure. Monte Carlo methods, Regularization,
Parametrization, Least-squares, and Maximum Entropy are some of the techniques utilized for unfolding. In the last decade methods based
on Artificial Intelligence Technology have been used. Approaches based on Genetic Algorithms and Artificial Neural Networks have been
developed in order to overcome the drawbacks of previous techniques. Nevertheless the advantages of Artificial Neural Networks still it has
some drawbacks mainly in the design process of the network, vg the optimum selection of the architectural and learning ANN parameters.
In recent years the use of hybrid technologies, combining Artificial Neural Networks and Genetic Algorithms, has been utilized to. In this
work, several ANN topologies were trained and tested using Artificial Neural Networks and Genetically Evolved Artificial Neural Networks
in the aim to unfold neutron spectra using the count rates of a Bonner sphere spectrometer. Here, a comparative study of both procedures has
been carried out.
Keywords: Neutron spectrometry; neural networks; evolutive algorithms.
Con el espectro´metro de esferas Bonner se puede obtener el espectro a traves de un procedimiento de reconstruccio´n. Los me´todos Mon-
tecarlo, de Regularizacie´n, de parametrizacio´n, de mı´nimos cuadrados, de la ma´xima entropı´a son algunas de las te´cnicas utilizadas para la
reconstruccio´n. En la u´ltima de´cada, se han utilizado los me´todos basados en la tecnologı´a de Inteligencia Artificial. Se han desarrollado
me´todos basados en Algoritmos Gene´ticos y Redes Neuronales Artificiales en un intento de resolver las desventajas de las te´cnicas men-
cionadas. Sin embargo, a pesar de la ventajas de las redes neuronales, las mismas presentan algunos inconvenientes principalmente en lo
que se refiere al proceso de dien˜o de de las redes, por ejemplo, la seleccio´n o´ptima de los para´metros de arquitectura y aprendizaje. En
an˜os recientes, tambie´n se ha utilizado tecnologı´as hı´bridas, combinando las redes neuronales y los algoritmos gene´ticos. En e´ste trabajo, se
disen˜aron y entrenaron varias topologe´as de redes neuronales y redes neuronales evolucionadas geneticamente con el objetivo de reconstruir
espectros de neutrones utilizando las tasas de conteo de un espectro´metro de esferas Bonner. Aquı´ se realiza un estudio comparativo de
ambos procedimientos.
Descriptores: Espectrometrı´a de neutrones; redes neuronales; algoritmos evolutivos.
PACS: 29.30.Hs; 29.40-n; 07.05-Mh
1. Introduction
Neutron energy spectra found in workplaces are often com-
plex, the range of neutron energies involved can extend over
nine or ten orders of magnitude. To improve the assessment
of personal equivalent dose (Hp) and ambient dose equiv-
alent (H * (10)) in workplace, requires the proper charac-
terization of neutron spectra [1]. The monitoring of occu-
pational radiation exposure in neutron fields is mainly done
with multi-element systems where each element has a partic-
ular response to neutrons. With the neutron spectrum infor-
mation and neutron fluence-to-dose conversion coefficients,
different dose quantities, like Hp or H * (10), can be esti-
mated.
With the count rates taken with the Bonner Spheres Spec-
trometer (BSS), the neutron spectrum can be unfolded. In
BSS, each detector is characterized by a response function,
the whole set is the response matrix. The relationship among
neutron spectrum, count rates and response matrix is de-
scribed by the integral-differential equation of Fredholm of
first type. Due to the number of detectors is smaller than
the number of energy groups used to describe the spectrum,
resulting problem is ill-conditioned therefore, unfolding pro-
cedures should be applied [1]. In previous works, have been
reported neutron spectrometry and dosimetry results, by us-
ing the Artificial Intelligence (AI) technology as alternative
solution. The Artificial Neural networks (ANN) [2] have re-
90 J.M. ORT´IZ-RODR´IGUEZ et al.
ceived the higher attention among researchers [1], however,
the use of this technology is not free of problems [3].
ANN technology is a useful alternative to solve the neu-
tron spectrometry problem, however, several drawbacks must
be solved in order to simplify the use of these procedures.
Many of the previous studies in neutron spectrometry and
dosimetry by using the ANN approach, have found seri-
ous drawbacks in the ANN design process itself, mainly in
the proper determination of the structural and learning pa-
rameters of the networks being designed. These parameters
are significant contributing factors to the ANN performance;
however, the optimal selection follows in practical use no
rules because they are generally heuristically chosen by using
the trial and error technique, which produces networks with
poor performance and low generalization capacity. For the
anterior, the nuclear research community needs approaches
that implement ANN models faster than what is currently
available. In consequence, more research has been suggested
in order to overcome these drawbacks.
Recently, the use of ANN technology has been applied
with success in the neutron spectrometry and dosimetry prob-
lems, using a novel approach known as Robust Design of Ar-
tificial Neural Networks (RDANN) methodology in the de-
sign process of the networks [3]. Another promising tech-
nique for ANN design, is to introduce the capacity of adap-
tation to the net by using Evolutionary Algorithms (EA) [4],
which can be used to adapt the connections among the synap-
tic weights, the design of the architecture, the adaptation
of the learning rule, etc. The use of a hybrid technology
based in the RDANN methodology combined with EA for
the modelling of ANN applied in the neutron spectrometry
and dosimetry problems could be a very convenient alterna-
tive technique. In this work, several ANN topologies were
trained and tested using two ANN design approaches, to and
the optimum parameters of ANN. The networks were de-
signed in the aim to unfold neutron spectra using the count
rates of CIEMAT BSS, Spain. Here, a comparative study of
both procedures has been carried out.
2. Materials and methods
ANN and EA are two relatively young research areas that
were subject to a steadily growing interest during the past
years. Until today, many researchers still prefer use the
gradient search method Back Propagation (BP) in training
ANN [2]. However, this technique is a local search method
and when applied to complex nonlinear optimization prob-
lems, can sometimes result in inconsistent and unpredictable
performances. One of the main hindrances is due to the fact
that searching of optimal weights is strongly dependent on
initial weights and if they are located near local minima, the
algorithm would be trapped; if the initial guess of the ANN
is near local maxima, it will climb the gradient and get stuck.
The structure of a neural network is a significant contributing
factor to its performance and the structure is generally heuris-
tically chosen. Several different attempts have been proposed
by various researchers to alleviate the training problems. The
use of EA as search technique has allowed different proper-
ties of ANN to be evolved.
In this work, the performance of neural nets, designed
for the BSS of CIEMAT, with two desing methodologies
is compared. The traditional nets (ANN) were designed
by means of the RDANN methodology and the Evolutive
ANN (EANN) [4], were designed by using the computer
program known as NeuroGenetic Optimizer (NGO) [5]. To
use the knowledge stored at the networks designed with both
metodologies, friendly computer programs whit graphical in-
terfaces were designed and builded respectively. A modified
version of the NSDann unfolding code was used for the tra-
ditional ANN [6], and the unfolding code called “Neutron
Spectrometry and Dosimetry based on Evolutive Artificial
Neural networks” (NSDEann) was designed for EANN.
In both cases, the first layer (input) corresponds to the
12 Bonner spheres of the CIEMAT’s BSS, the hidden lay-
ers and neurons by layer should be determined and the third
layer (output) has 85 neurons. The first 72 outputs correspond
to the neutron spectra and the remaining 13 are equivalent
doses. In both methodologies training was carried using 201
spectra, and 50 spectra were used for testing the learning of
the nets.
Utilizing the RDANN methodology, additional parame-
ters have to be determined: momentum, learning rate, train-
ing algorithm and mean square error (MSE). The EANN
technology, although does not requires on the part of the user
ANN parameters to be determined, it requires the determi-
nation of parameters regarded with the GA used to and the
architecture of the net.
This is a very difficult problem, which is similar to that
found in ANN design and, at present, this represents a seri-
ous drawback of the EANN approach, because the parameter
selection is done through the trial and error technique. More
research is needed in this sense. At present, work is being
carried out. The neutron spectra unfolded and its correspond-
ing 13 equivalent doses were computed with the modified
NSDann and NSDEann unfolding codes, for a 239PuBe neu-
tron source measured at 80 cm distance, at “Departamento
de Ingenierı´a Nuclear” (DIN) of “Universidad Polite´cnica de
Madrid” (UPM).
3. Results and discussion
By means of the RDANN methodology, 36 traditional ANN
topologies were designed and trained, each in a time of
107 seconds average. The optimum network topology is: 12
neurons in the input layer, 16 nerons in a hidden layer and 85
in the output layer. The neural nets were trained until MSE
was reduced to 10−4. Additional parameters are: momen-
tum: 0.001, learning rate: 0.1, training algorithm: trainscg.
After the training and testing stages, the knowledge stored at
synaptic weights was extracted and a modified version of the
NSDann unfolding code was designed. Figure 1, shows the
Rev. Mex. Fı´s. S 57 (1) (2011) 89–92
PERFORMANCE OF ARTIFICIAL NEURAL NETWORKS AND GENETICAL EVOLVED ARTIFICIAL NEURAL NETWORKS. . . 91
FIGURE 1. Neutron spectra unfolded and equivalent doses calcu-
lated with NSDann.
FIGURE 2. Neutron spectra unfolded with NSDEann.
FIGURE 3. Neutron spectra unfolded with NSDann - NSDEann.
neutron spectra unfolded and its 13 equivalent doses calcu-
lated by means of the modified NSDann code.
By using the EANN methodology, 600 EANN were de-
signed and trained in a time of 04:44:09. The minimum net-
work training passes for each network were 420, the cutoff
for network training passes was 450, and the limit on hid-
den neurons was 8. The optimum network topology is: a
Fast-Back Propagation neural network with 12 inputs, 6 lo-
gistic neurons in a hidden layer and 85 neurons in the output
layer, with an accuracy on training set= 99.50% according
NGO. The parameters used for the GA, selected using the
trial and error technique, are: generations run: 10, population
Size: 60, selection was performed by the top 50% surviving,
re?lling of the population was done by cloning the survivors,
mating was performed by using the TailSwap technique, mu-
tations were performed using Random Exchange technique
at a rate of 25%.
After the training and testing stages, it was not possible
to extract the knowledge stored at synaptic weights of the
network designed with NGO. For this reason, the NSDEann
unfolding code was designed to read and graph the spectro-
metric and dosimetric information produced by means of the
EANN trained with NGO. Figure 2, shows the neutron spec-
tra unfolded and its 13 equivalent doses calculated by means
of the modified NSDann.
In order to compare the results obtained with the NSDann
and NSDEann unfolding codes, the computer tool known as
“Neutron spectrometry and dosimetry Tool Box” (NSDTB)
was used [7]. Figure 3, shows the performance of the neu-
tron spectra unfolded with the EANN approach (green line)
and the spectra unfolded with the RDANN methodology (red
line) and its corresponding 13 equivalent doses. As can be
seen, the spectra and doses present diferencies, this is due
mainly to the trial and error approach used to select the GA
parameter in the EANN approach, which is a serious draw-
back of this method. More research is needed in this sense.
At present work is being developed to overcome these draw-
backs.
From Fig. 3, can be observed that the neutron spectra un-
folded and equivalent doses calculated with both, traditional
ANN and EANN, are very similar, however, the EANN un-
fold the spectra in different energy bins, this makes that the
χ2 test fails. A deeper analysys should be needed in order to
observe closer what could be happening.
4. Conclusions
The use of ANN technology is a useful alternative to solve
the neutron spectrometry and dosimetry problems; however,
to obtain the best results, some drawbacks must be solved in
the ANN design process, such as the optimum ANN topology
selection.
In this work, the ANN optimization methodology known
as RDANN, was used to design an ANN capable to solve
the neutron spectrometry and dosimetry problems for the
Rev. Mex. Fı´s. S 57 (1) (2011) 89–92
92 J.M. ORT´IZ-RODR´IGUEZ et al.
CIEMAT BSS system. The neural net was trained and tested
using a large set of neutron spectra compiled by the IAEA.
The success of ANN technology in neutron spectrome-
try and dosimetry, using only the Bonner spectrometer count
rates as input in the trained network will overcome some
of the problems associated with the solution of such ill-
conditioned problem. The results here reported demonstrate
that the use of this technology has become in a useful tool.
Until now RDANN methodology seems to be mo reliabe
in the neutron spectra unfoloding problem, because more re-
search has been carried out in this sense and consecuently
more information is available. The main drawback of EANN
is the trial and error technique used to determine the optimum
values of the GA used to build the network. The combination
of RDANN whit GA could improve widely the results ob-
tained with both methodologies.
More research is needed and at present, work is being
carried out.
Acknowledgements
This work was supported by “Agencia Espan˜ola de Coop-
eracio´n Internacional para el Desarrollo”, AECID (Spain).
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Acun˜a, E. Gallego, A. Lorente, and M.P. In˜iguez, Radiation
Protection Dosimetry 126 (2007) 408.
2. S. Haykin, Neural Networks: A comprehensive foundation.
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3. J.M. Ortiz-Rodrı´guez, M.R. Martı´nez-Blanco, and H.R. Vega-
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4. J.M. Ortiz-Rodrı´guez, M.R. Martı´nez-Blanco, E. Gallego Dı´az
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5. NeuroGenetic Optimizer. http://www.biocompsystems.com
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