nuclear fuel loading pattern optimisation using a neural network

Nuclear fuel loading pattern optimisation usinga neural network

Eduardo Fernandes Faria, Claubia Pereira*

Departamento de Eng. Nuclear- UFMG, PCA1—Anexo Engenharia, Av. Antonio Carlos,

6627 Pampulha 31270-901, Belo Horizonte, MG, Brazil

Received 5 November 2001; received in revised form 28 August 2002; accepted 30 August 2002

Abstract

An algorithm to optimise the fuel loading pattern (LP) in nuclear reactors was developedusing an artificial neural network (ANN) to generate arrangements for the fuel in the core.The core parameters were calculated with the WIMS-D4 and CITATION-LDI2 codes, andthe minimization of the maximum power peaking factor (FPmax) was used to choose the best

arrangements. To verify the algorithm a PWR reactor with approximately 1/3 reprocessedfuel loaded was considered. The neutronic performance of the obtained arrangements and theefficiency of the implemented method were analysed. Several configurations were found for

the core presenting better characteristics than the reference configuration adopted, so indi-cating the viability of the developed methodology. The algorithm was applied to a core con-sidering part of the loading with reprocessed fuels, however this technique can be used for

standard loadings.# 2002 Elsevier Science Ltd. All rights reserved.

1. Introduction

In the management of the fuel in the core there are some stages such as refuellingschedules, fuel loading patterns, prediction of fuel burnup and isotope build-up thathave to be programmed and evaluated. Our work will refer to the fuel distributionduring the core refuelling.The main problem in the fuel assembly position determination is the large number

of possible combinations for the fuel loading in the core. In addition, the fact that

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this is a non-linear problem create complications in the use of conventional optimi-sation techniques.Several techniques have been developed in order to automate this distribution

process for the fuel assemblies in the core. A better choice in the configurationof the fuel assemblies loading is essential to guarantee the adequate use of thefissile elements, and also to guarantee safety during the operation. Among thesetechniques we may mention: dynamic programming (Wall and French, 1965),direct search (Stout, 1973), variational techniques (Terney and Williamson 1982),backward diffusion calculation (Chao et al., 1986), reverse depletion (Downarand Kim, 1986; Kim et al., 1987), linear programming (Okafor and Aldemir,1988; Stillman et al., 1989), simulated annealing (Parks, 1990; Kropaczek andTurinsky, 1991; Smuc et al., 1994; Mahlers, 1994), genetic algorithms (Yamamoto,1997), and others that use artificial intelligence techniques. Artificial intelligencetechniques like fuzzy logic artificial neural networks (Kim et al., 1993a,b) andknowledge-based systems (Galperin and Nissan, 1988; Galperin et al., 1989) havebeen successfully tested thus accelerating the search for the best positioning of thefuel assemblies in the core.In this work an algorithm to perform loading pattern (LP) optimisation for a

PWR reactor was developed. The algorithm was implemented using an ANN togenerate the loading pattern and nuclear codes to calculate core parameters. Themain idea is to train the ANN with information on the performance of a groupof spatial configurations for the fuel assemblies, using them later for the gen-eration of new configurations that will be evaluated according to the perfor-mance of the parameters obtained through simulation with the WIMS andCITATION codes.The optimisation tests were made considering a PWR reactor with the insertion of

approximately 1/3 fuel reprocessed with the AIROX (Asquith and Grantham, 1978),Coprocessing (Pobereskin et al., 1978) and PUREX (MOX fuel) techniques. How-ever such a study also can be used for more generalized reloads.Euzimar M. Leite (1998), studied the behaviour of these reprocessed fuels

when inserted in the core of a PWR reactor, his arrangement for the fuelassemblies being adopted as the reference in the evaluation of the proposedmethod. For data comparison the same model and composition for the fuelassemblies were used.The minimization of the FPmax was the optimisation criteria proposed. The

reduction of the FPmax represents a factor of extreme importance for the reactorsafety. Also, the evolution of the effective multiplication factor (keff) was fol-lowed.The developed algorithm comes from a group of LPs, generating new patterns in

an attempt to reduce local power peaks, resulting in the reduction of the FPmax.The results showed viability in the use of the proposed technique as a backup for

the optimisation of nuclear fuel reloads, obtaining several arrangements for fuelassemblies with reduced FPmax. The best results were obtained with the pre-opti-mised reference arrangement between the initial spatial configurations necessary forthe optimisation process.

604 E.F. Faria, C. Pereira /Annals of Nuclear Energy 30 (2003) 603–613

2. The optimisation algorithm

To optimise the LP, an ANN based on error backpropagation attached to theWIMS and CITATION nuclear codes were used.The core model assumes two dimensions and four groups of energy, being one

fast, another thermal and two groups in the resonance energy range. A PWR reactorwith 121 fuel assemblies was simulated. Fig. 1 shows the core geometry.Considering the symmetry, the calculations of the reactor core were made using

only 1=4 of it. For the optimisation process 1/8 of it was considered. This allowed a

Fig. 1. PWR-type core used and regions considered in the model.

E.F. Faria, C. Pereira /Annals of Nuclear Energy 30 (2003) 603–613 605

great simplification for the optimisation models and the core simulation, resulting ina considerable reduction in the processing time.To obtain the cross sections required for core simulation with the CITATION-

LDI2 code the WIMS-D4 code was used.The option for the use of ANNs was chosen because of their capacity to emulate

any function, with a certain error, after training. The critical point in the use ofANNs is within the training stage, which sometimes takes a long time without cer-tain of convergence. But at the end of the training stage, the answer to an inputexcitation is immediate.There are some works where ANNs were used to accelerate the optimisation of

nuclear fuel reloads. These ANNs are usually used in substitution for nuclear codesin order to faster calculate the reactor core parameters, like keff and FPmax. Theseparameters are then used to determine the fuel arrangement by some other tech-nique. In contrast, in this work the ANN is used to get the new arrangement for thefuels assemblies in the core. The core parameters for optimisation are obtainedthrough the simulation of these loading patterns using the nuclear codes mentioned.The parameter used for optimisation was the average power peaking factor

(defined as the ratio between the fuel assembly power and the core power) for eachfuel assembly with the objective of reducing the local peaking factors, and conse-quently the FPmax. Fig. 2 shows a diagram of the implemented algorithm, which isdetailed next.A backpropagation (Fausett, 1994; Freeman and Skapura, 1991) ANN with

three layers (input, output and hidden) was used. Fig. 3 shows the schematic ofthe ANN. Sigmoid functions were used as activation functions for all the neu-rons. The input layer is composed of a neuron relating to each fuel assemblyposition in the core, being 21 neurons for 21 positions (using 1/8 of the core ofthe considered PWR). Each input neuron receives the value of the averagepower factor for the fuel assembly in the position it represents. On the outputlayer, for each position of the core there is a neuron for each type of fuel assembly(each region) possible, being in this case eight different fuel types (eight regions) tobe loaded in 21 positions which makes 8�21=168 output neurons. Each position isthen represented by n neurons where n is the number of different fuels. Each outputis considered activated if ‘1’ and disabled if ‘0’. In this way for each position onlyone of the n outputs will be activated, thus representing the fuel type considered inthe position.In this way, it is expected that after training the ANN is able to emulate a func-

tion, in such a way that when a radial power profile in the input is presented, thecorresponding spatial distribution of the fuel assemblies in the output is given.In the algorithm described in Fig. 2, initially a group of random loading patterns

for fuel assemblies is generated. Each of these configurations for the nuclear fuel inthe core is simulated using the WIMS and CITATION codes. The obtained data onthe radial profile of the average power factor together with the associated spatialconfiguration of the fuel assemblies form the pattern basis for the ANN training.The cases with the lowest FPmax are selected for the ANN training. This selection ismade because, if all cases are used, the ANN training shall become very slow.


Then the supervised training of the ANN with the selected cases takes place. Thetraining consists of systematically presenting groups of LPs and the radial profile ofthe average power factor at the output and at the input, respectively. The weights ofthe ANNs are recalculated through the error backpropagation until the ANN pre-sents in its output an error below the minimum stipulated value.In the next stage, four radial profiles of average power factors are selected in order

to be evaluated and tested in the ANN. One of these is a pre-defined optimal radialprofile of average power factor. Two others are selected from among the most suc-cessful cases, in other words the ones that present the lowest FPmax, up till thismoment. Another is randomly selected from among all the cases. These last threeprofiles of average power are flattened as shown in Fig. 4 in such a way as to pro-portionally reduce the power peaks.

Fig. 2. Block diagram of the implemented algorithm.


The four radial profiles of average power factor are applied at the input of theANN, been propagated through the layers to the output. So the spatial distributionsof the fuel assemblies that would be necessary, according to the ANN, to obtain theradial power profiles applied at the input are obtained. If two of the configurationsfor the fuel assemblies are similar, another pattern will be selected to be flattenedand applied at the ANN input.To ensure that the loading pattern maintains the inventory of a reload core the

following procedure is used:

� For each core position showed in Fig. 1 it is assigned the fuel type indicatedby the neuron with the highest output for that position, start from position 1(center of the core);

� If all the available fuel types to be assigned have already been used, the sec-ond highest neuron output will determine the fuel type to be loaded in thatposition. If all of that fuel types have also been used, then, the next highestneuron output is taken until there are available fuel to assign to the position.

Fig. 3. Illustrative example of power shape flattening for evaluation in ANN.


Each sole combination of enrichment, composition and burnup defines a fuel type.The obtained LPs are simulated in the reactor’s core through the WIMS and

CITATION codes. The obtained results concerning the radial profiles of the averagepower factor, together with the associated spatial configuration of the fuel assem-blies will be part of the group of cases for the next ANN training.This process is repeated until an arrangement for the fuel assemblies that satisfies

the desirable requirements for the FPmax is obtained.To optimise the core two basic pieces of information are necessary: composition

and quantity of each different type of fuel assembly.An important characteristic of the developed methodology is the existing detach-

ment of the ANN, the nuclear codes and other blocks of the algorithm. In this waythe calculation of the core using other nuclear codes can be implemented withoutaffecting the main part of the algorithm.Just to give an idea of the problem complexity, considering three regions and 1/8

of the core (21 fuel assemblies in this case), we will have 399,072,960 possible load-ing patterns. In other words, if we use 100 cases to train the ANN, we will berepresenting the problem with a subgroup of data representing only 2.5�10�5 % ofthe data universe.

3. Characterization of the tests

The tests with the developed algorithm were based on the core used by EuzimarM. Leite (1998), considering the same available fuel assemblies. Only the fuel posi-tions in the core were modified during the optimisation. Altogether there are eightdifferent fuel types (eight regions), being five with UO2 and three with the repro-cessed fuel. Fuels reprocessed using the AIROX, Coprocessing and PUREX (MOXFuel) techniques, were considered.Initial pattern configurations are generated by random distribution of the fuel

assemblies in the available positions in the core, being simulated with the codes inorder to obtain the average power factor radial shape. Thirty random LPs weregenerated to be used in all the tests.In the generation of the initial pattern configurations, the random positioning of

the fuel assemblies was chosen in order to extract different samples from the solution

Fig. 4. ANN backpropagation with one hidden layer.


space for the ANN training, making it possible to be associated with the existingrelations in different samples.For each reprocessing method two tests were made. For the first test only the 30

random configurations were used as initial patterns. For the second, besides therandom configurations, the reference configuration was used, resulting in 31 initialpatterns. In Table 1 the tests made are listed.For all the tests the ANN used 30 neurons in the hidden layer, with 30% error (the

difference between the expected and real response value at the ANN output fortraining patterns) and 0.9 learning steps (it is a number below a unit, this parametersets how large will be the adjustment in the ANN weights in each interaction; highervalue implies in faster calculation, but could impair the convergence). Because theANN output is binary, even with a 30% error a good response is achieved. Duringthe tests the minimum number of patterns for the ANN was established in 30, beingselected among the cases with the lowest FPmax.

4. Optimisation results

The tests were made using PENTIUM 166 MHz PCs. The adopted evaluationcriterion for the optimisation was FPmax, which should present the lowest possiblevalue. All tests considered beginning of cycle.On average 50 new LPs were generated in every 24 h of the execution of the pro-

gram. Considering an average of 300 cases as the necessary quantity to obtain thefirst satisfactory results, this corresponds to approximately 6 days in the execution ofthe algorithm. With the use of more powerful equipment such as workstations therequired time would be much shorter.Each test was continued until it presented at least one configuration with the

FPmax lower than the reference. Another stop criterion adopted was: if after 400generated configurations (including the initial patterns) no configuration with FPmax

lower than 1.35 was obtained. The test with the Coprocessing Fuel, without areference was the only one terminated on this stop criterion. All the others foundconfigurations with a lower value for the FPmax than the reference value.The results obtained are briefly presented in Table 2.

Table 1

Implemented tests

Test Reprocessed fuel used Reference configuration used

1 AIROX No

2 AIROX Yes

3 Coprocessing No

4 Coprocessing Yes

5 MOX No

6 MOX Yes


From the six tests made, only the test with the coprocessing fuel without using thereference configuration did not reach lower FPmax than the reference.Considering each two cases with same reprocessing technique, most of the tests

without the reference case presented higher keff for the cases with lower FPmax, thanthe tests with reference.

5. Conclusions

In all the optimisations tests several optimal arrangements for the fuel assemblieswere found, presenting different neutronic characteristics. This group of arrange-ments makes available configurations with different values of keff and FPmax, makingnecessary a more detailed study to select the arrangement that best suits the para-meters of interest.With the exception for test 3 with the coprocessing fuel, without reference, con-

figurations with lower FPmax and also presenting higher effective multiplication fac-tors were obtained, when compared with reference LP.From the results, we may observe that the implemented process is quite dependent

on the initial configurations chosen. The restart with new randomly generatedtraining set would lead to different solutions, but within similar searching time andcore conditions.The use of the reference case, as an optimal initial pattern, had great influence in

the generation of the new LPs by the ANN, resulting in better results, with lowernumbers of generated cases.A negative point is that the developed procedure does not guarantee that the

result obtained is the global optimum. However, a group of good LPs is obtainedwhich should be further considered through a more detailed analysis with regard tothe desired characteristics for core parameters, such as better neutronic performanceand better burnup, besides having to satisfy the necessary safety requirements.In a general way the developed algorithm presented a satisfactory result con-

sidering that this is an initial study. In spite of being trained with only a very tinypart of the solution space of the problem, the ANN was able to generate LPs withbetter characteristics than the reference LP.

Table 2

Results using the optimisation algorithm

Test Reference loading Optimal loading Total

generated LPs

Total number of LPs with

lower FPmax than the reference

FPmax keff FPmax keff

1 1,27376 1,0895 1,26607 1,1059 550 1

2 1,27376 1,0895 1,22364 1,0916 100 8

3 1,23831 1,0859 – – 400 0

4 1,23831 1,0859 1,23762 1,0861 250 2

5 1,26873 1,0832 1,25563 1,0837 450 2

6 1,26873 1,0832 1,25678 1,0836 100 2


Next studies could adapt this algorithm to consider the maximization in dischargeburnup as the objective function, using, for example, the burnup distribution asinput for the ANN. Another improvement would be the use of an economic func-tion.This study is a preliminary analysis to verify the applicability of the presented

methodology. In the real core reload fuel rotation it is very important to find anacceptable loading pattern, as well as the use of burnable absorbers. These resourcesneed to be added in subsequently algorithms. Since the fuel composition is not inputfor the ANN, burnable absorbers can be considered in the core models as a fuel typewithout the change in the optimisation algorithm.

Acknowledgements

The authors are grateful to CNPq (Brasil) and CAPES (Brasil) for supporting thisresearch.

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nuclear fuel loading pattern optimisation using a neural network

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