Some studies on differential evolution variants for application to nuclear reactor core design

During the design of nuclear reactor cores, reactor cell parameters such as dimensions, enrichment and materials must be adjusted considering restrictions such as the average thermal flux, criticality and sub-moderation. Due to the complexity of this problem, trial-and-error methods do not necessarily guarantee acceptable solutions. Thus, the necessity of formulating the design of a nuclear reactor core as an optimization problem, where the decision variables are optimized taking constraints into account. Once the problem is formulated in such way, global search methods may be used in order to generate candidate solutions, that is, sets of core design parameters, to be analyzed by programs that simulate the neutron interactions in the reactor core. The Differential Evolution (DE) algorithm is one of those state-of-art global search methods, whose application has outperformed competitive algorithms in several optimization problems including the optimization problem of nuclear core design. Modifications in the DE such as the Trigonometric Mutation Operator and the Opposition-based learning have been reported in the literature, with considerable advances in the results of many problems. This performance motivated us to apply these two variants of differential evolution to the nuclear core design problem, which is the aim of this paper. The results are promising, demonstrating that the improvements are applicable in nuclear science and engineering applications.     

Design and optimization of an equilibrium reload with MOX fuel with minor actinides

In this work the design and optimization of an equilibrium core for a boiling water reactor (BWR), loaded with fuel composed of plutonium and minor actinides (Np, Am and Cm), is presented. The plutonium and minor actinides are obtained from the recycling of the spent fuel of a BWR, and are mixed with depleted uranium obtained from the enrichment tails. The design and optimization of the equilibrium reload is achieved in two steps. In the first step, the fuel assembly is adjusted and the reload pattern is designed, in order to obtain the target cycle length. In order to improve the shutdown margin, two actions were taken: to increase the boron-10 content in the control rods, and to add a burnable absorber (gadolinia) in some fuel rods. In the second step, the reload pattern, obtained in the first step, is optimized to maximize the energy, under the thermal and reactivity margins constraints; a system based on Genetic Algorithms was used in the optimization process. Results show that 5% more energy was obtained with the optimized reload.     

Development of an automated system for fuel reload patterns design

In this paper an automated system to generate fuel reload patterns for a boiling water reactor (BWR), based on heuristic search methods using engineers expertise is presented. The main components of the system are the knowledge base, the inference engine, the 3D BWR simulator PRESTO-B and the user interface. The knowledge base includes a generation knowledge base and a modification knowledge base, which are concerned with the way human experts generate reload patterns. The system has been developed and applied to the Laguna Verde Nuclear Power Plant, achieving similar patterns to those used in the operation. No optimization algorithm has been incorporated in this system, therefore the generated reload patterns are the best estimate according the knowledge and experience of the nuclear engineers. Future works are being developed in this area using evolutionary optimization techniques as a complement of this system.     

A nuclear reactor core fuel reload optimization using artificial ant colony connective networks

The core of a nuclear Pressurized Water Reactor (PWR) may be reloaded every time the fuel burn-up is such that it is not more possible to maintain the reactor operating at nominal power. The nuclear core fuel reload optimization problem consists in finding a pattern of burned-up and fresh-fuel assemblies that maximize the number of full operational days. This is an NP-Hard problem, meaning that complexity grows exponentially with the number of fuel assemblies in the core. Moreover, the problem is non-linear and its search space is highly discontinuous and multi-modal.     

核电厂化学生产经营自动化、智能化管理探讨

核电厂化学生产经营工作涉及面广、接口部门多、工作量大、操作流程要求精细,对分析准确度、精确度要求高,各项工作相互关联、相互衔接、相互影响。核电厂化学生产经营自动化、智能化管理体系,以化学智能管理系统为核心,强化人工智能专家诊断,减少人工干预,标准化、流程化、平台化、智能化操作管控,满足核电厂化学生产经营管理的实际需求,实现核电厂化学生产经营的自动化、智能化管理。     

Estimation of research reactor core parameters using cascade feed forward artificial neural networks

The pattern of the core reload program is very important for an optimize use of research reactors. Reactor safety issues and economic efficiency should be considered during pattern studies. In order to find the best core pattern for a research reactor, its reloading program should be solved as a multi-objective and constrained optimization problem. If considered objective functions of the optimization problem can be estimated in very short time, the optimal fuel reloading pattern can be used effectively. In this research a very fast estimation system for suggested core parameters has been developed using cascade feed-forward type of artificial neural networks (ANNs). Four main core parameters are suggested to optimize reactor core adequately. And also to get larger thermal fluxes in the desired irradiation box, a new flexible method was selected. A Software package has been developed to prepare and reform required data for ANNs training. The gradient descent method with momentum weight/bias learning rule has been used to train ANNs. To get the best conditions for considered ANNs training a vast study has been performed. It includes the effects of variation of hidden neurons, hidden layers, activation functions, learning and momentum coefficients, and also the number of training data sets on the training and simulation results. Some experimental convergence criteria are used to study them. A comparison selection rule has been used to adjust desirable conditions. Final training and simulation results show that developed ANNs can be trained and estimate suggested core parameters of research reactors very quickly. It improves effectively pattern optimization process of core reload program.     

157组燃料组件组成的堆芯燃料管理研究

本文应用SCIENCE程序包对157组燃料组件组成的压水堆堆芯进行换料优化燃料管理研究,给出了3个年换料和2个18个月换料共5个设计方案,每个设计方案给出了从首循环到第8循环共8个循环的主要计算结果,并进行了分析比较。综合来看,OUT-IN装载的设计方案功率峰值偏低,IN-OUT装载的设计方案功率峰值偏高,但均在设计限值以内;1/4堆芯换料设计方案的平均卸料燃耗最深,表明其组件燃耗得最充分,经济性较好。     

基于径向基代理模型与小生境遗传算法的铅铋反应堆堆芯智能优化

为解决铅铋反应堆多因素耦合影响下的复杂非线性多维优化问题,构建了基于径向基（RBF）代理模型预测、正交拉丁超立方抽样（OLHS）和小生境遗传算法（NGA）寻优的堆芯智能优化方法,开发了包含抽样、蒙卡程序耦合处理、堆芯参数预测寻优等功能的铅铋反应堆设计优化平台,并以堆芯最小燃料装载量为优化目标进行方案寻优验证。研究结果表明:RBF代理模型可准确快速地预测铅铋反应堆堆芯特性参数,与蒙卡程序计算值比较,其预测的堆芯有效增殖因子（k_eff）相对误差在±0.1%以内;该智能优化方法应用于铅铋反应堆堆芯优化是可行的,能找到多因素共同变化约束下的最优目标方案,且极大缩减了设计方案的搜索计算时间。本研究建立的堆芯智能优化方法可为铅铋反应堆多物理、多变量、多约束耦合影响的优化设计提供思路。      

空间核反应堆本体参数最优化研究

空间技术是具有重大潜在前景的技术,对国家的科学、国防、政治、经济具有重要意义。为了满足空间条件及发射条件的要求,并使空间核反应堆经济性最大化,对空间核反应堆本体的结构设计方案和参数最优化进行了研究。在调研多种国外空间核反应堆方案设计的基础上,提出了空间核反应堆堆型与堆本体结构设计方案。建立了堆本体数学模型,将设计最优化的工程学问题转化为求解非线性整数优化的数学问题,采用编写Matlab程序语言的方法,利用数学软件求解了最优化问题,在理论上得到了所建立模型的最优化参数设计并探讨了旋转控制鼓数量变化与堆芯燃料半径变化对堆本体总质量的影响。堆本体总质量较初始模型下降了14.3%,为今后完成更进一步的空间核反应堆设计提供了参考。     

Azcatl-CRP: An ant colony-based system for searching full power control rod patterns in BWRs

We show a new system named AZCATL-CRP to design full power control rod patterns in BWRs. Azcatl-CRP uses an ant colony system and a reactor core simulator for this purpose. Transition and equilibrium cycles of Laguna Verde Nuclear Power Plant (LVNPP) reactor core in Mexico were used to test Azcatl-CRP. LVNPP has 109 control rods grouped in four sequences and currently uses control cell core (CCC) strategy in its fuel reload design. With CCC method only one sequence is employed for reactivity control at full power operation. Several operation scenarios are considered, including core water flow variation throughout the cycle, target different axial power distributions and Haling conditions. Azcatl-CRP designs control rod patterns (CRP) taking into account safety aspects such as k_eff core value and thermal limits. Axial power distributions are also adjusted to a predetermined power shape.     

压水堆核电厂堆芯功率能力验证分析

介绍了压水堆核电厂换料堆芯功率能力验证分析的原理和方法。利用中子学计算程序对换料堆芯正常运行工况（一类工况或工况I）和中等频率事故工况（二类工况或工况II）中可能的堆芯功率分别进行模拟。从反应堆物理和热工水力学的角度论证反映一、二类工况堆芯安全性的线功率密度裕量和偏离泡核沸腾比（DNBR）裕量。从而验证一类工况反应堆运行区域和二类工况超漏、超功率保护限值。本文还给出了大亚湾核电站18个月换料堆芯功率能力验证分析的结果。     

PWR fuel management optimization using continuous particle swarm intelligence

The objective of nuclear fuel management is to minimize the cost of electrical energy generation subject to operational and safety constraints. In the present work, a core reload optimization package using continuous version of particle swarm optimization, CRCPSO, which is a combinatorial and discrete one has been developed and mapped on nuclear fuel loading pattern problems. This code is applicable to all types of PWR cores to optimize loading patterns. To evaluate the system, flattening of power inside a WWER-1000 core is considered as an objective function although other variables such as K_eff along power peaking factor, burn up and cycle length can be included. Optimization solutions, which improve the safety aspects of a nuclear reactor, may not lead to economical designs. The system performed well in comparison to the developed loading pattern optimizer using Hopfield along SA and GA.     

Azcaxalli: A system based on Ant Colony Optimization algorithms,applied to fuel reloads design in a Boiling Water Reactor

This paper presents some results of the implementation of several optimization algorithms based on ant colonies, applied to the fuel reload design in a Boiling Water Reactor. The system called Azcaxalli is constructed with the following algorithms: Ant Colony System, Ant System, Best–Worst Ant System and MAX–MIN Ant System. Azcaxalli starts with a random fuel reload. Ants move into reactor core channels according to the State Transition Rule in order to select two fuel assemblies into a 1/8 part of the reactor core and change positions between them. This rule takes into account pheromone trails and acquired knowledge. Acquired knowledge is obtained from load cycle values of fuel assemblies. Azcaxalli claim is to work in order to maximize the cycle length taking into account several safety parameters. Azcaxalli’s objective function involves thermal limits at the end of the cycle, cold shutdown margin at the beginning of the cycle and the neutron effective multiplication factor for a given cycle exposure. Those parameters are calculated by CM-PRESTO code. Through the Haling Principle is possible to calculate the end of the cycle. This system was applied to an equilibrium cycle of 18 months of Laguna Verde Nuclear Power Plant in Mexico. The results show that the system obtains fuel reloads with higher cycle lengths than the original fuel reload. Azcaxalli results are compared with genetic algorithms, tabu search and neural networks results.     

Kuosheng BWR/6 stability analysis with LAPUR5 code

Unstable power/flow oscillation of a nuclear power reactor core is one of the main reasons that cause minor core damage. Stability analysis to determine system’s decay ratio needs to be performed at each core reload design to prevent core instability events from happening. Making use of LAPUR5 and SIMULATE-3 codes, we have established a methodology to conduct such analysis. Comparisons made with vendor’s STAIF results indicated close agreements, within acceptable ±0.2 in decay ratios, for Kuosheng NPP Unit2 Cycle 17 reloads design. Sensitivity studies have shown that density reactivity coefficient, delayed-neutron fractions (β) and decay constants (λ), total core flow, and core power axial shape are the most important parameters that might affect the accuracy of decay ratios. We have also found that core conditions at EOC result in larger decay ratios than those at BOC.     

Identification of nuclear power plant transients using the Particle Swarm Optimization algorithm

In order to help nuclear power plant operator reduce his cognitive load and increase his available time to maintain the plant operating in a safe condition, transient identification systems have been devised to help operators identify possible plant transients and take fast and right corrective actions in due time. In the design of classification systems for identification of nuclear power plants transients, several artificial intelligence techniques, involving expert systems, neuro-fuzzy and genetic algorithms have been used. In this work we explore the ability of the Particle Swarm Optimization algorithm (PSO) as a tool for optimizing a distance-based discrimination transient classification method, giving also an innovative solution for searching the best set of prototypes for identification of transients. The Particle Swarm Optimization algorithm was successfully applied to the optimization of a nuclear power plant transient identification problem. Comparing the PSO to similar methods found in literature it has shown better results.     

“华龙一号”反应堆堆芯与安全设计研究

“华龙一号”是我国自主设计研发的具有完整知识产权的第三代百万千瓦级压水堆核电技术。本文介绍了“华龙一号”的产生历程，系统论述了“华龙一号”反应堆堆芯与安全设计特点，包括“华龙一号”研发过程中开展的堆芯核设计、热工水力设计、安全设计、设计验证及“华龙一号”持续开展的设计改进与优化等内容，通过采用新的设计理念和设计技术，全面提高了“华龙一号”作为三代核电技术的经济性、灵活性和安全性。      

Basic investigations related to genetic algorithms in core designs

The use of genetic algorithms as a tool to improve nuclear reactor core design optimization is proposed. A method based on genetic algorithms are developed to solve optimization problems that involve cell parameters adjustment. In this paper we address a global optimization approach to nuclear reactor core design problems. In previous work, a great variety of local optimization method have been applied in such a kind of problems. In order to illustrate the performance, we apply the method based on genetic algorithms to two traditional test problems that have been considered in literature. These test problems describe the principal framework of the approach proposed, because they have known optimal solutions. Due to the global exploitation capacity and independence of prior knowledge of the search space characteristics proportioned by the genetic algorithms the application scope was extended. The method was applied to optimize a more complex problem, to which traditional methods do not apply. The goal of this third problem is to minimize the average peak factor in a three enrichment zone reactor by the adjust of the fuel radii, cladding thickness, equivalent radii, the three zone enrichments, fuel material and cladding material. In this case a qualitative analysis of the results is made.     

低泄漏堆芯燃料管理的一种多循环优化方法

提出一种用于指导压水堆低泄漏堆芯燃料管理的多循环优化方法。该方法将多循环优化问题分解为３步优化处理：首先用线性规划确定满足多循环总体目标最优的各个单循环优化目标参数,然后以此为条件,对多循环中相继的各个单循环进行燃料组件的优化布置,最后进行可燃毒物的优化配置。本文着重讨论第一步优化方法,并给出主要计算结果。     

核工程中人工智能技术的应用与进展

介绍了在核工程领域内各国开展人工智能技术研究的概况。评述了在反应堆故障诊断、控制和运行、维护、报警和显示、事故管理、机器人等领域内的专家系统及其发展方向。