ALGORITHM BASED ON ARTIFICIAL BEE COLONY FOR UNFOLDING OF NEUTRON SPECTRA OBTAINED WITH BONNER SPHERES

ALGORITHM BASED ON ARTIFICIAL BEE COLONY FOR UNFOLDING OF NEUTRON SPECTRA OBTAINED WITH BONNER... Abstract Occupational neutron fields usually have energies from the thermal range to some MeV and the characterization of the spectra is essential for estimation of the radioprotection quantities. Thus, the spectrum must be unfolded based on a limited number of measurements. This study implemented an algorithm based on the bee colonies behavior, named Artificial Bee Colony (ABC), where the intelligent behavior of the bees in search of food is reproduced to perform the unfolding of neutron spectra. The experimental measurements used Bonner spheres and 6LiI (Eu) detector, with irradiations using a thermal neutron flux and three reference fields: 241Am–Be, 252Cf and 252Cf (D2O). The ABC obtained good estimation of the expected spectrum even without previous information and its results were closer to expected spectra than those obtained by the SPUNIT algorithm. INTRODUCTION Occupational neutron fields usually have energies from the thermal range until some MeV, and the characterization of the spectra is essential for a correct estimation of the radioprotection quantities. However, this is a complex task due to the difficulty in obtaining reliable results for all ranges of energies observed in the facilities. This is mainly because of the lack of neutron detectors for some of these energies. Therefore, the spectrum of the actual neutron field must be unfolded based on a limited number of measurements(1). The unfolding of neutron spectra is a non-linear problem with difficult analytical solution and several mathematical methods have been used to accomplish this task, especially the method of least squares fit and methods based on artificial intelligence. However, depending on the studied neutron field, each algorithm presents advantages and limitations. Besides that, spectra obtained with different techniques may differ significantly, even using the same set of input data(1). Algorithms based on swarm intelligence are being progressively used to solve mathematical and operational problems of difficult solution, mainly those that need combinatorial attempts in large scale. For these problems, classical optimization methods present limitations and usually are strongly dependent on a good initial guess. The swarm intelligence algorithms find solutions modeling the social behavior of animal swarms, mainly in the food search and present good convergence to solutions even using poor initial guess(2). One typical and powerful swarm intelligence algorithm is the Artificial Bee Colony (ABC), based on the social behavior of the bees in the search of food sources(3). In ABC algorithm, the bees’ intelligent behavior is converted in computational rules to find near-optimum solutions of multimodal optimization problems, presenting excellent results in different applications(3, 4). Considering the good performance of the ABC algorithm in the solution of other difficult non-analytical problems, even with poor previous information (random guess solution), this study developed a new method of an unfolding of neutron spectra, based on the ABC algorithm. The ABC code was used to obtain unfolded neutron spectra from Bonner spheres measurements with 6LiI(Eu) detector in standard fields. ARTIFICIAL BEE COLONY ALGORITHM The bees have good memory and efficient systems of navigation and communication to look for food sources. A colony of bees can exploit a large number of food sources at the same time(2). There are three types of bees: employed bees that have a food source to exploit; onlooker bees that wait in the hive for information shared by employed bees; and scout bees that look for a new source to exploit. The employed bees return to the hive to share information about the food sources, performing a waggle dance. Using the position of the sun as a guide, the bee waggles its body in the direction of the source and the distance of the food is communicated by additional movements. The total time spent with the waggle dance is proportional to the quality of source(3). Good food sources attract more onlooker bees than poor sources and they can watch many dances before employing itself. During each visit to the source, the employed bee looks for new sources around the neighborhood. If the bee finds a source with better quality, it forgets the previous source and starts to exploit the new one. When a food source is exhausted, all the employed bees associated with it abandon the source, and become scouts. The scout bees perform random searches looking for a source better than its last source and, if they find one, they becomes an employed bee(3, 4). In the ABC algorithm, the bees are objects constructed using an object-oriented programming. Each food source is a possible solution for the problem and the nectar amount of the source corresponds to the quality of the solution, represented by a fitness value. The fitness works as feedback to the optimization of the solution, in a heuristic process. Each employed bee has a solution associated to it and the exploitation of the food source corresponds to searches of neighboring solutions using a Monte Carlo method. For each iteration of the algorithm, a source is considered exhausted when the maximum number of attempts to find a better neighboring solution is reached without success. The waggle dance corresponds to a computational process executed when an employed bee find a solution better than its current solution. In this process, there is a probability of an onlooker bee to assume the solution of the employed bee. If the solution has a good fitness, the probability that the onlookers choose it is greater. Progressively more bees search neighboring solutions around the current best solution of the problem. Despite the convergence to be a process looked for all optimization algorithms, the quick convergence to local solutions can be a problem because these solutions can be far of the optimal solution. The process associated to the scout bees avoids this quick convergence and can be considered the one of the main advantages of ABC in relation to the other algorithms. Unfolding of neutron spectra using ABC Computational methods and parameter based on the ABC algorithm were developed in this study to perform the unfolding of neutron spectra with Bonner sphere measurements. Each solution associated to a bee corresponds to a neutron spectrum and all the employed bees are initialized with the guess spectrum previously defined. In each iteration, the employed bees look for spectra with better fitness (closer to the experimental measurements). Neighboring solutions are those for which the fluence associated to only one energy bin changes randomly. After this small change, the fitness of the new solution is evaluated and if it is better than the previous solution, the employed bee’s memory is updated. In the end of each iteration, the solution with the best fitness is stored. After all the iterations, the best solution is returned as the unfolded spectrum. For calculation of the fitness (Ft) of the current solution (unfolded spectrum), Equation (1) is used:   Ft=∑i=1M(CCi−Cexpi)2Cexpi2, (1)where M is the number of spheres; CCi is the calculated counts rate of the sphere i and Cexpi is the measured counts rate of the sphere i. Equation (2) is used to calculate of the CCi:   CCi=∑j=1NRji×ϕj, (2)where CCi is the calculated counts rate of the sphere i; N is the number of energy bins; Rji is the value of response matrix to bin j of the sphere i and Φj is the fluence of bin j. The main steps of the ABC algorithm developed in this study are summarized below. Initial solution: Each employed bee object is initialized with a guess spectrum. Neighboring solutions: For each employed bee, slightly different spectra are generated changing randomly the fluence of one energy bin. Fitness evaluation: The generated spectrum is evaluated using the results of Bonner spheres. Exploitation of the food source: If the number of attempts to found a better spectrum is reached, the spectrum is abandoned and the bee becomes scout. Waggle dance: If an employed bee finds a better spectrum, the waggle process is executed and onlooker bees can adopt the employed bee’s spectrum. Scout process: Scout bees look for better spectra. Best solution: The spectrum with the best fitness must be memorized. Repeated cycle: The steps 2–7 is repeated until the stopping criterion is met. The user of the ABC algorithm can determine: the initial number of each type of bee, the total number of iterations and the maximum number of visits to one source (attempts of to find better solutions). The user can choose too: the guess spectrum, the response matrix and which spheres will be considered. The default guess spectrum is a flat spectrum with zero fluence for all the energy bins, but the user can insert any specific spectra. MATERIALS AND METHODS The counting rate measurements were performed in the low scattering laboratory of the Brazilian National Metrology Laboratory of Ionizing Radiations (LNMRI), using a detector of 6LiI(Eu) (4 mm × 4 mm) and a set of Bonner spheres: 2″, 3″, 5″, 8″, 10″ and 12″. Measurements with the bare detector were also performed (0″). Bonner spheres spectrometry was used for measurements of standard neutron spectra to the 241Am–Be, 252Cf(D2O) and 252Cf, besides the LNMRI standard thermal neutron flux(5). All measurements were done without shadow cone. The response matrices were taken from the TRS-403 of the IAEA(6). For evaluation of the code, the spectra unfolded using ABC were compared to the PTB measured reference neutron spectra, without use of shadow cone(6). These spectra were also compared to the calculated ISO reference spectra(6) and to those obtained by the SPUNIT algorithm(7). SPUNIT was chosen because it lies behind some of the most accessible and widely used unfolding codes such as NSDUAZ(8), used in this study, and mainly the BUNKI code(9). RESULTS Figures 1–3 present, respectively, the results of the neutron spectrum unfolding for: bare 241Am–Be, 252Cf(D2O) and bare 252Cf. Figure 4 shows the results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo simulation(5). Figure 1. View largeDownload slide Result of the ABC unfolding code to a 241Am–Be source without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 1. View largeDownload slide Result of the ABC unfolding code to a 241Am–Be source without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 2. View largeDownload slide Result of the ABC unfolding code to a 252Cf+D2O field without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 2. View largeDownload slide Result of the ABC unfolding code to a 252Cf+D2O field without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 3. View largeDownload slide Result of the ABC unfolding code to a 252Cf source with good previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 3. View largeDownload slide Result of the ABC unfolding code to a 252Cf source with good previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 4. View largeDownload slide Results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo. Figure 4. View largeDownload slide Results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo. For the unfolded spectra showed in Figures 1 and 2, a flat spectrum with the same fluence for all the energy bins was used as guess spectrum. For the 252Cf spectra, presented in Figure 3, the same input file containing a guess spectrum based on the 252Cf ISO reference spectrum was inserted in both unfolding codes(6). For the spectra showed in Figure 4, a guess spectrum based on a generic thermal field, suggested by the NSDUAZ(8), was used by the unfolding codes. Table 1 presents the count rates calculated by ABC and SPUNIT for comparison with the measurements of each Bonner sphere for the LNMRI standard thermal neutron flux. For a quantitative evaluation of the unfolded spectrum, Table 2 presents values of radiological protection quantities and other parameters calculated by the codes, at 1 m distance to the 241Am–Be source, based on coefficients presented by TRS-403 of the IAEA. Table 1. Count rates calculated by the unfolding codes for the LNMRI standard thermal neutron flux spectrum. Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Table 1. Count rates calculated by the unfolding codes for the LNMRI standard thermal neutron flux spectrum. Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Table 2. Radiological protection quantities and other parameters calculated by the ABC and SPUNIT. Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Table 2. Radiological protection quantities and other parameters calculated by the ABC and SPUNIT. Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  In Figures 1–3, spectra unfolded by ABC are closer to the reference spectra than those obtained by SPUNIT (for the PTB and ISO references). The analysis of the spectra of 241Am–Be of Figure 1 reveals that, even without any previous information about the neutron field, the spectrum unfolded by ABC is very similar to the measured spectrum from the PTB reference neutron field. As the scattering was considered, because the measurements were obtained without shadow cone, some differences between the unfolded spectrum and the calculated ISO reference spectrum are observed. Figure 4 shows that when the ABC receives a good guess spectrum as input, it presents excellent results as the NSDUAZ code. Table 1 indicates that ABC presents very accurate results when the calculated counts rate is compared to the measured ones. Table 2 shows that the values of the radiological protection quantities calculated by the ABC are very similar to those obtained by SPUNIT, indicating that the use of the ABC code is promising in the evaluation of radiological safety issues. Besides that, taking into account scattering neutrons, the fluence averaged energy calculated by ABC can be considered close to the expected value of 4.16 MeV(6). Further developments, comparisons and evaluations of the ABC code can validate its use for evaluation of the quantities presented in Table 2. CONCLUSIONS For the studied neutron fields, the unfolded spectra generated by ABC can be considered similar to the reference spectra. Besides that, the fluence averaged energy calculated by ABC is closer to the expected value than that calculated by SPUNIT. The promising performance presented by the ABC algorithm indicates that this new method is valid for unfolding of neutron spectra with Bonner spheres measurements. Despite similar irradiation conditions, differences between the low scattering laboratories (LNMRI and PTB) must contribute to the divergences between the unfolded spectra using ABC and the PTB reference spectra. The differences between the unfolded spectra and the ISO reference spectra must be related to the expected discrepancies between measured spectra with scattering neutron and calculated ones. Finally, the uncertainties of the experimental measurements and the limitations associated to the stochastic methods, can also justify the disagreements between results. The results of the unfolding of neutron spectra, performed in this study, indicate that the ABC algorithm may obtain good estimation of the expected spectrum even without previous information. Therefore, despite of the use of the good guess spectra to be recommended to improve the results of the ABC code, this algorithm could be a good alternative to situations where poor or no information about the neutron field is available. REFERENCES 1 Matzke, M. Unfolding procedures. Radiat. Prot. Dosim.  107, 155– 174 ( 2003). Google Scholar CrossRef Search ADS   2 Nayak, V., Suthar, H. and Gadit, J. Implementation of artificial bee colony algorithm. IAES Int. J. Artif. Intell.  1, 112– 120 ( 2012). 3 Karaboga, D. , Gorkemli, B., Ozturk, C., Karaboga, N. A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev . 42, 21– 57 ( 2014). Google Scholar CrossRef Search ADS   4 McCaffrey, J. Use bee colony algorithms to solve impossible problems. Microsoft J. Dev. V  6, 56– 70 ( 2011). 5 Astuto, A., Salgado, A. P., Leite, S. P., Patrão, K. C. S., Fonseca, E. S., Pereira, W. W. and Lopes, R. T. Thermal neutron calibration channel at LNMRI/IRD. Radiat. Prot. Dosim.  161, 1– 5 ( 2014). Google Scholar CrossRef Search ADS   6 International Atomic Energy Agency. Compendium of neutron spectra and detector responses for radiation protection purposes: supplement to technical reports series no. 318. Technical reports series no. 403. IAEA, ( 2001). 7 Doroshenko, J. J., Kraitor, S. N., Kuznetsova, T. V., Kushnereva, K. K. and Lenov, E. S. New methods for measuring neutron energy spectra with energy from 0.4 to 10 MeV by track and activation detectors. Nucl. Technol.  33, 296– 304 ( 1977). Google Scholar CrossRef Search ADS   8 Vega-Carrillo, H. R., Ortiz-Rodríguez, J. M. and Martínez-Blanco, M. R. NSDUAZ unfolding package for nêutron spectrometry and dosimetry with Bonner spheres. Appl. Radiat. Isot.  71, 87– 91 ( 2012). Google Scholar CrossRef Search ADS PubMed  9 Lowry, K. A. and Johnson, T. L. Modifications to recursion unfolding algorithms to find more appropriate neutron spectra. Health Phys.  47, 587– 593 ( 1984). Google Scholar CrossRef Search ADS PubMed  © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Radiation Protection Dosimetry Oxford University Press

ALGORITHM BASED ON ARTIFICIAL BEE COLONY FOR UNFOLDING OF NEUTRON SPECTRA OBTAINED WITH BONNER SPHERES

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Abstract

Abstract Occupational neutron fields usually have energies from the thermal range to some MeV and the characterization of the spectra is essential for estimation of the radioprotection quantities. Thus, the spectrum must be unfolded based on a limited number of measurements. This study implemented an algorithm based on the bee colonies behavior, named Artificial Bee Colony (ABC), where the intelligent behavior of the bees in search of food is reproduced to perform the unfolding of neutron spectra. The experimental measurements used Bonner spheres and 6LiI (Eu) detector, with irradiations using a thermal neutron flux and three reference fields: 241Am–Be, 252Cf and 252Cf (D2O). The ABC obtained good estimation of the expected spectrum even without previous information and its results were closer to expected spectra than those obtained by the SPUNIT algorithm. INTRODUCTION Occupational neutron fields usually have energies from the thermal range until some MeV, and the characterization of the spectra is essential for a correct estimation of the radioprotection quantities. However, this is a complex task due to the difficulty in obtaining reliable results for all ranges of energies observed in the facilities. This is mainly because of the lack of neutron detectors for some of these energies. Therefore, the spectrum of the actual neutron field must be unfolded based on a limited number of measurements(1). The unfolding of neutron spectra is a non-linear problem with difficult analytical solution and several mathematical methods have been used to accomplish this task, especially the method of least squares fit and methods based on artificial intelligence. However, depending on the studied neutron field, each algorithm presents advantages and limitations. Besides that, spectra obtained with different techniques may differ significantly, even using the same set of input data(1). Algorithms based on swarm intelligence are being progressively used to solve mathematical and operational problems of difficult solution, mainly those that need combinatorial attempts in large scale. For these problems, classical optimization methods present limitations and usually are strongly dependent on a good initial guess. The swarm intelligence algorithms find solutions modeling the social behavior of animal swarms, mainly in the food search and present good convergence to solutions even using poor initial guess(2). One typical and powerful swarm intelligence algorithm is the Artificial Bee Colony (ABC), based on the social behavior of the bees in the search of food sources(3). In ABC algorithm, the bees’ intelligent behavior is converted in computational rules to find near-optimum solutions of multimodal optimization problems, presenting excellent results in different applications(3, 4). Considering the good performance of the ABC algorithm in the solution of other difficult non-analytical problems, even with poor previous information (random guess solution), this study developed a new method of an unfolding of neutron spectra, based on the ABC algorithm. The ABC code was used to obtain unfolded neutron spectra from Bonner spheres measurements with 6LiI(Eu) detector in standard fields. ARTIFICIAL BEE COLONY ALGORITHM The bees have good memory and efficient systems of navigation and communication to look for food sources. A colony of bees can exploit a large number of food sources at the same time(2). There are three types of bees: employed bees that have a food source to exploit; onlooker bees that wait in the hive for information shared by employed bees; and scout bees that look for a new source to exploit. The employed bees return to the hive to share information about the food sources, performing a waggle dance. Using the position of the sun as a guide, the bee waggles its body in the direction of the source and the distance of the food is communicated by additional movements. The total time spent with the waggle dance is proportional to the quality of source(3). Good food sources attract more onlooker bees than poor sources and they can watch many dances before employing itself. During each visit to the source, the employed bee looks for new sources around the neighborhood. If the bee finds a source with better quality, it forgets the previous source and starts to exploit the new one. When a food source is exhausted, all the employed bees associated with it abandon the source, and become scouts. The scout bees perform random searches looking for a source better than its last source and, if they find one, they becomes an employed bee(3, 4). In the ABC algorithm, the bees are objects constructed using an object-oriented programming. Each food source is a possible solution for the problem and the nectar amount of the source corresponds to the quality of the solution, represented by a fitness value. The fitness works as feedback to the optimization of the solution, in a heuristic process. Each employed bee has a solution associated to it and the exploitation of the food source corresponds to searches of neighboring solutions using a Monte Carlo method. For each iteration of the algorithm, a source is considered exhausted when the maximum number of attempts to find a better neighboring solution is reached without success. The waggle dance corresponds to a computational process executed when an employed bee find a solution better than its current solution. In this process, there is a probability of an onlooker bee to assume the solution of the employed bee. If the solution has a good fitness, the probability that the onlookers choose it is greater. Progressively more bees search neighboring solutions around the current best solution of the problem. Despite the convergence to be a process looked for all optimization algorithms, the quick convergence to local solutions can be a problem because these solutions can be far of the optimal solution. The process associated to the scout bees avoids this quick convergence and can be considered the one of the main advantages of ABC in relation to the other algorithms. Unfolding of neutron spectra using ABC Computational methods and parameter based on the ABC algorithm were developed in this study to perform the unfolding of neutron spectra with Bonner sphere measurements. Each solution associated to a bee corresponds to a neutron spectrum and all the employed bees are initialized with the guess spectrum previously defined. In each iteration, the employed bees look for spectra with better fitness (closer to the experimental measurements). Neighboring solutions are those for which the fluence associated to only one energy bin changes randomly. After this small change, the fitness of the new solution is evaluated and if it is better than the previous solution, the employed bee’s memory is updated. In the end of each iteration, the solution with the best fitness is stored. After all the iterations, the best solution is returned as the unfolded spectrum. For calculation of the fitness (Ft) of the current solution (unfolded spectrum), Equation (1) is used:   Ft=∑i=1M(CCi−Cexpi)2Cexpi2, (1)where M is the number of spheres; CCi is the calculated counts rate of the sphere i and Cexpi is the measured counts rate of the sphere i. Equation (2) is used to calculate of the CCi:   CCi=∑j=1NRji×ϕj, (2)where CCi is the calculated counts rate of the sphere i; N is the number of energy bins; Rji is the value of response matrix to bin j of the sphere i and Φj is the fluence of bin j. The main steps of the ABC algorithm developed in this study are summarized below. Initial solution: Each employed bee object is initialized with a guess spectrum. Neighboring solutions: For each employed bee, slightly different spectra are generated changing randomly the fluence of one energy bin. Fitness evaluation: The generated spectrum is evaluated using the results of Bonner spheres. Exploitation of the food source: If the number of attempts to found a better spectrum is reached, the spectrum is abandoned and the bee becomes scout. Waggle dance: If an employed bee finds a better spectrum, the waggle process is executed and onlooker bees can adopt the employed bee’s spectrum. Scout process: Scout bees look for better spectra. Best solution: The spectrum with the best fitness must be memorized. Repeated cycle: The steps 2–7 is repeated until the stopping criterion is met. The user of the ABC algorithm can determine: the initial number of each type of bee, the total number of iterations and the maximum number of visits to one source (attempts of to find better solutions). The user can choose too: the guess spectrum, the response matrix and which spheres will be considered. The default guess spectrum is a flat spectrum with zero fluence for all the energy bins, but the user can insert any specific spectra. MATERIALS AND METHODS The counting rate measurements were performed in the low scattering laboratory of the Brazilian National Metrology Laboratory of Ionizing Radiations (LNMRI), using a detector of 6LiI(Eu) (4 mm × 4 mm) and a set of Bonner spheres: 2″, 3″, 5″, 8″, 10″ and 12″. Measurements with the bare detector were also performed (0″). Bonner spheres spectrometry was used for measurements of standard neutron spectra to the 241Am–Be, 252Cf(D2O) and 252Cf, besides the LNMRI standard thermal neutron flux(5). All measurements were done without shadow cone. The response matrices were taken from the TRS-403 of the IAEA(6). For evaluation of the code, the spectra unfolded using ABC were compared to the PTB measured reference neutron spectra, without use of shadow cone(6). These spectra were also compared to the calculated ISO reference spectra(6) and to those obtained by the SPUNIT algorithm(7). SPUNIT was chosen because it lies behind some of the most accessible and widely used unfolding codes such as NSDUAZ(8), used in this study, and mainly the BUNKI code(9). RESULTS Figures 1–3 present, respectively, the results of the neutron spectrum unfolding for: bare 241Am–Be, 252Cf(D2O) and bare 252Cf. Figure 4 shows the results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo simulation(5). Figure 1. View largeDownload slide Result of the ABC unfolding code to a 241Am–Be source without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 1. View largeDownload slide Result of the ABC unfolding code to a 241Am–Be source without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 2. View largeDownload slide Result of the ABC unfolding code to a 252Cf+D2O field without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 2. View largeDownload slide Result of the ABC unfolding code to a 252Cf+D2O field without previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 3. View largeDownload slide Result of the ABC unfolding code to a 252Cf source with good previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 3. View largeDownload slide Result of the ABC unfolding code to a 252Cf source with good previous information about the neutron field. Reference spectra and the result of the SPUNIT are presented. Figure 4. View largeDownload slide Results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo. Figure 4. View largeDownload slide Results of unfolding to the LNMRI thermal neutron flux spectrum, using the ABC and NSDUAZ (SPUNIT) codes compared to the spectrum obtained by Monte Carlo. For the unfolded spectra showed in Figures 1 and 2, a flat spectrum with the same fluence for all the energy bins was used as guess spectrum. For the 252Cf spectra, presented in Figure 3, the same input file containing a guess spectrum based on the 252Cf ISO reference spectrum was inserted in both unfolding codes(6). For the spectra showed in Figure 4, a guess spectrum based on a generic thermal field, suggested by the NSDUAZ(8), was used by the unfolding codes. Table 1 presents the count rates calculated by ABC and SPUNIT for comparison with the measurements of each Bonner sphere for the LNMRI standard thermal neutron flux. For a quantitative evaluation of the unfolded spectrum, Table 2 presents values of radiological protection quantities and other parameters calculated by the codes, at 1 m distance to the 241Am–Be source, based on coefficients presented by TRS-403 of the IAEA. Table 1. Count rates calculated by the unfolding codes for the LNMRI standard thermal neutron flux spectrum. Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Table 1. Count rates calculated by the unfolding codes for the LNMRI standard thermal neutron flux spectrum. Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Sphere  Measured (s−1)  ABC (s−1)  SPUNIT (s−1)  0′  23.15  23.14  23.20  2′  22.37  22.43  22.29  3′  23.20  23.04  22.98  5′  16.91  17.08  17.40  8′  7.91  7.74  7.74  10′  4.22  4.24  4.20  12′  2.25  2.29  2.27  Table 2. Radiological protection quantities and other parameters calculated by the ABC and SPUNIT. Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Table 2. Radiological protection quantities and other parameters calculated by the ABC and SPUNIT. Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  Quantity  ABC  SPUNIT  Fluence averaged energy (MeV)  4.03  3.77  Total fluence (cm−2)  68.2  66.5  Effective dose rate (pSv/s)  2.69 × 104  2.60 × 104  Personal dose equivalent rate (pSv/s)  2.82 × 10−2  2.74 × 10−2  Ambient dose equivalent rate (pSv/s)  2.67 × 10−2  2.59 × 10−2  In Figures 1–3, spectra unfolded by ABC are closer to the reference spectra than those obtained by SPUNIT (for the PTB and ISO references). The analysis of the spectra of 241Am–Be of Figure 1 reveals that, even without any previous information about the neutron field, the spectrum unfolded by ABC is very similar to the measured spectrum from the PTB reference neutron field. As the scattering was considered, because the measurements were obtained without shadow cone, some differences between the unfolded spectrum and the calculated ISO reference spectrum are observed. Figure 4 shows that when the ABC receives a good guess spectrum as input, it presents excellent results as the NSDUAZ code. Table 1 indicates that ABC presents very accurate results when the calculated counts rate is compared to the measured ones. Table 2 shows that the values of the radiological protection quantities calculated by the ABC are very similar to those obtained by SPUNIT, indicating that the use of the ABC code is promising in the evaluation of radiological safety issues. Besides that, taking into account scattering neutrons, the fluence averaged energy calculated by ABC can be considered close to the expected value of 4.16 MeV(6). Further developments, comparisons and evaluations of the ABC code can validate its use for evaluation of the quantities presented in Table 2. CONCLUSIONS For the studied neutron fields, the unfolded spectra generated by ABC can be considered similar to the reference spectra. Besides that, the fluence averaged energy calculated by ABC is closer to the expected value than that calculated by SPUNIT. The promising performance presented by the ABC algorithm indicates that this new method is valid for unfolding of neutron spectra with Bonner spheres measurements. Despite similar irradiation conditions, differences between the low scattering laboratories (LNMRI and PTB) must contribute to the divergences between the unfolded spectra using ABC and the PTB reference spectra. The differences between the unfolded spectra and the ISO reference spectra must be related to the expected discrepancies between measured spectra with scattering neutron and calculated ones. Finally, the uncertainties of the experimental measurements and the limitations associated to the stochastic methods, can also justify the disagreements between results. The results of the unfolding of neutron spectra, performed in this study, indicate that the ABC algorithm may obtain good estimation of the expected spectrum even without previous information. Therefore, despite of the use of the good guess spectra to be recommended to improve the results of the ABC code, this algorithm could be a good alternative to situations where poor or no information about the neutron field is available. REFERENCES 1 Matzke, M. Unfolding procedures. Radiat. Prot. Dosim.  107, 155– 174 ( 2003). Google Scholar CrossRef Search ADS   2 Nayak, V., Suthar, H. and Gadit, J. Implementation of artificial bee colony algorithm. IAES Int. J. Artif. Intell.  1, 112– 120 ( 2012). 3 Karaboga, D. , Gorkemli, B., Ozturk, C., Karaboga, N. A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev . 42, 21– 57 ( 2014). Google Scholar CrossRef Search ADS   4 McCaffrey, J. Use bee colony algorithms to solve impossible problems. Microsoft J. Dev. V  6, 56– 70 ( 2011). 5 Astuto, A., Salgado, A. P., Leite, S. P., Patrão, K. C. S., Fonseca, E. S., Pereira, W. W. and Lopes, R. T. Thermal neutron calibration channel at LNMRI/IRD. Radiat. Prot. Dosim.  161, 1– 5 ( 2014). Google Scholar CrossRef Search ADS   6 International Atomic Energy Agency. Compendium of neutron spectra and detector responses for radiation protection purposes: supplement to technical reports series no. 318. Technical reports series no. 403. IAEA, ( 2001). 7 Doroshenko, J. J., Kraitor, S. N., Kuznetsova, T. V., Kushnereva, K. K. and Lenov, E. S. New methods for measuring neutron energy spectra with energy from 0.4 to 10 MeV by track and activation detectors. Nucl. Technol.  33, 296– 304 ( 1977). Google Scholar CrossRef Search ADS   8 Vega-Carrillo, H. R., Ortiz-Rodríguez, J. M. and Martínez-Blanco, M. R. NSDUAZ unfolding package for nêutron spectrometry and dosimetry with Bonner spheres. Appl. Radiat. Isot.  71, 87– 91 ( 2012). Google Scholar CrossRef Search ADS PubMed  9 Lowry, K. A. and Johnson, T. L. Modifications to recursion unfolding algorithms to find more appropriate neutron spectra. Health Phys.  47, 587– 593 ( 1984). Google Scholar CrossRef Search ADS PubMed  © The Author(s) 2018. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

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Radiation Protection DosimetryOxford University Press

Published: Apr 13, 2018

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