An Overview of AI Methods for in-Core Fuel Management: Tools for the Automatic Design of Nuclear Reactor Core Configurations for Fuel Reload, (Re)arranging New and Partly Spent Fuel
Abstract
:1. Introduction
1.1. Aims
1.2. Considerations about Artificial Intelligence for Nuclear Engineers
“(t)he separation of the problem-solving knowledge and the inference engine makes it possible to represent knowledge in a more natural fashion. If … then … rules […] are closer to the way in which human beings describe their own problem-solving techniques than a program that embeds this knowledge in lower-level computer code. […] Because the knowledge base is separated from the program’s lower-level control structures, expert system builders can focus directly on capturing and organizing problem-solving knowledge rather than on the details of its computer implementation. […] The separation of knowledge and control, along with the modularity provided by rules and other representational structures used in building knowledge bases, allows changes to be made in one part of the knowledge base without creating side effects in other parts of the program. […] The separation of the knowledge and control elements of the program allows the same control and interface software to be used in a variety of systems. […]”
“Neurally inspired models, also known as parallel distributed processing (PDP) or connectionist systems, de-emphasize the explicit use of symbols in problem solving. […] Processing in these systems is distributed across collections or layers of neurons. Problem solving is parallel in the sense that all the neurons within the collection or layer process their inputs simultaneously and independently. […] In connectionist models there is, however, a strong representational character both in the creation of input parameters as well as in the interpretation of output values. To build a neural network, for example, the designer must create a scheme for encoding patterns in the world into numerical quantities in the net. The choice of an encoding scheme can play a crucial role in the eventual success or failure of the network to learn.
In connectionist systems, processing is parallel and distributed with no manipulation of symbols as symbols. Patterns in a domain are encoded as numerical vectors. The connections between components, or neurons, are also represented as numerical values. Finally, the transformation of patterns is the result of a numerical operation, usually, matrix multiplications. These “designer choices” for a connectionist architecture constitute the inductive bias of the system.
The algorithms and architectures that implement these techniques are usually trained or conditioned rather than explicitly programmed. Indeed, this is a major strength of the approach: an appropriately designed network architecture and learning algorithm can often capture invariances in the world, even in the form of strange attractors,7 without being explicitly programmed to recognize them.”
“challenge to satisfy the energy demand using green energy resources is to balance energy supply and demand. Territory design deals with the problem of grouping geographic areas into larger geographic clusters called territories in such a way that the grouping is acceptable according to a planning criterion. The aim of this study is to group geographic areas so that energy requirement in a geographic cluster matches the available green energy potential in the same cluster. In this way, investments may be supported through region specific policies. The problem is formulated as a mixed-integer linear programming model. A location-allocation approach is employed to solve the model. The location and allocation problems are solved iteratively. In order to solve the initial location problem, a Genetic Algorithm is developed to find the results of the p-median problem. Then, the allocation problem is solved optimally using the ILOG Cplex solver.”
“Annealing is the physical process of heating up a solid until it melts, followed by cooling it down until it crystallizes into a state with a perfect lattice. During this process, the free energy of the solid is minimized. Practice shows that the cooling must be done carefully in order not to get trapped in locally optimal lattice structures with crystal imperfections.
In combinatorial optimization, we can define a similar process. This process can be formulated as the problem of finding—among a potentially very large number of solutions— a solution with minimal cost. Now, by establishing a correspondence between the cost function and the free energy, and between the solutions and the physical states, we can introduce a solution method in the field of combinatorial optimization based on a simulation of the physical annealing process. The resulting method is called Simulated Annealing.
Salient features of this method are its general applicability and its ability to obtain solutions arbitrarily close to an optimum. A major drawback however is that finding high-quality solutions may require large computational efforts.
A substantial reduction of the computational effort required by the simulated annealing algorithm may be achieved by using computational models based on massively parallel execution. An example of such a model is the Boltzmann machine.
The Boltzmann machine is a neural network and belongs to the class of connectionist models. A Boltzmann machine consists of a large network of simple computing elements, called units, that are connected in some way. The units can have two states, either ‘on’ or ‘off’, and the connections have real-valued strengths that impose local constraints on the states of the individual units. A consensus function gives a quantitative measure for the ‘goodness’ of a global configuration of the Boltzmann machine, determined by the states of all individual units.”
1.3. Preliminary Notions in Nuclear Engineering, Concerning Fuel at Nuclear Reactor Plants
2. Safety, Materials, and Options for Nonproliferation Aims
3. Computer Tools for Designing Fuel Reload Configurations
3.1. Pressurized Water Reactors
3.2. Nuclear Fuel Cycle
3.3. Manual Design Packages
“Pressurized water reactor core designs have become more complex and must meet a plethora of design constraints. Trends have been toward longer cycles with increased discharge burnup, increased burnable absorber (BA) number, 19 mixed BA types, reduced radial leakage, axially blanketed fuel, and multiple-batch feed fuel regions. Obtaining economical reload core loading patterns (LPs) that meet design criteria is a difficult task to do manually. Automated LP search tools are needed. An LP search tool cannot possibly perform an exhaustive search because of the sheer size of the combinatorial problem. On the other hand, evolving complexity of the design features and constraints often invalidates expert rules based on past design experiences.”
3.4. Expert Systems
3.5. Validation by Simulations of the Reactor Physics
“Nodal diffusion is currently the preferred neutronics model for industrial reactor core calculations, which use few-group cross-section libraries generated via standard assembly homogenization. The infinite-medium flux-weighted cross sections fail to capture the spectral effects triggered in the core environment by nonreflective boundary conditions at the fuel-assembly edges. This poses a serious limitation to the numerical simulation of current- and next-generation reactor cores, characterized by strong interassembly heterogeneity.”
3.6. Ruleset Improvement, and the Involvement of Neural Revision
Algorithm 1 Code written by Hava Siegelmann for the rule elimination rule: “Do not load a fresh assembly in such a position that is adjacent to another position where there is another assembly of the same kind, except when one of those two positions is in a corner position.” [193,194]. |
Algorithm 2 Code written by Hava Siegelmann for the rule preference rule: “If it is a once-burned assembly that is currently being considered, then choose for it — from amongst those positions that were not forbidden by Rules 1 to 6 (the elimination rules)—that position whose distance from the centre of the core is minimal.” [193,194]. |
3.7. An Expert System Based on a Genetic Algorithm
3.8. A Survey of the Application of Other Techniques: Genetic, Fuzzy, Particle Swarm, Tabu Search, Simulated Annealing
“is a metaheuristic search method employing local search methods used for mathematical optimization. Local (neighborhood) searches take a potential solution to a problem and check its immediate neighbors (that is, solutions that are similar except for very few minor details) in the hope of finding an improved solution. Local search methods have a tendency to become stuck in suboptimal regions or on plateaus where many solutions are equally fit.
Tabu search enhances the performance of local search by relaxing its basic rule. First, at each step worsening moves can be accepted if no improving move is available (like when the search is stuck at a strict local minimum). In addition, prohibitions (henceforth the term tabu) are introduced to discourage the search from coming back to previously-visited solutions.
The implementation of tabu search uses memory structures that describe the visited solutions or user-provided sets of rules. If a potential solution has been previously visited within a certain short-term period or if it has violated a rule, it is marked as “tabu” (forbidden) so that the algorithm does not consider that possibility repeatedly.”
4. Current Trends
“Nuclear fuel cycle studies have provided a wealth of information on the potential impacts of advanced recycling systems. Deciding on fuel cycle implementation pathways, however, requires synthesizing volumes of data and navigating trade-offs between fuel cycle options. This research presents a framework intended to aid fuel cycle decision makers by focusing on the cost reduction/waste mitigation trade-off as a lens for choosing a near-term strategy. The framework consists of a fuel cycle simulation coupled to a decision tree model that maps evolution scenarios. System scenarios are constructed by considering the technological options for fuel cycle evolution and key uncertainties expected to affect the desirability of those options. For this study, the once-through fuel cycle is compared to a self-sustaining fast reactor (FR) fuel cycle. Scenarios are compared using a value function that incorporates cost and waste metrics. …”
“Experience with modeling fuel cycle options reveals that the large amount of generated data makes it difficult to understand trade-offs among fuel cycle policies. This paper shows that numerical optimization can be used to better identify impacts of fuel cycle policies and condense the generated data against a few significant criteria. The once-through cycle is considered the baseline case, while advanced technologies with fuel recycling characterize the alternative fuel cycle options available in the future. The options include, among others, recycling the fissile materials from spent light water reactor fuel in fast reactors (FRs) as well as deployment of innovative recycling reactor technologies, such as the 235U initiated FRs. Additionally, a first-of-a-kind optimization scheme for the nuclear fuel cycle analysis is described. Optimization metrics of interest to different stakeholders in the fuel cycle (economics, fuel resource utilization, high-level waste, transuranic materials/proliferation management, and environmental impact) are utilized for two different optimization techniques: a linear one and a stochastic one. …”
“In the breed and burn (B&B) strategy,24 low-reactivity fuels are loaded in a core. It is difficult to keep criticality in operating a small core. To enhance the potential for achieving criticality, the neutron economy in a core should be improved. One improvement method is to increase the core size and reduce neutron leakage. If it is necessary to avoid the large-sized core, another method is to locate high-reactivity fuels in high-neutron-importance region continuously through an equilibrium burnup state. On the other hand, to stabilize the change of neutron flux and power distribution during the operation, the B&B regions need to be kept stationary in the same region.
5. Concluding Remarks
Remark about the References
Funding
Acknowledgments
Conflicts of Interest
References
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1 | The name FUELCON was patterned after the phrase “fuel configurations”. |
2 | The name FUELGEN is a compound of fuel and gen (etic). |
3 | An introduction to convolutional neural networks can be found in [1]. That technique is most commonly applied to analyzing visual imagery. Its inspiration is biological, in that the connectivity pattern between its artificial neurons resembles the organization of the animal visual cortex. |
4 | |
5 | |
6 | Frame-based expert systems are the subject of, e.g., [2] (Chapter 5). |
7 | Attractor networks are the subject of [2] (Section 14.6, pp. 701–711). |
8 | |
9 | |
10 | The contrast between rule-based and case-based intelligent systems from artificial intelligence should not be mistaken for the contrast (in legal studies) between such legal jurisdictions that mainly judge based on precedent (which is the case of Anglo-Saxon countries), and such jurisdictions (such as France) where adjudication is mainly based on rules as stated in law as made by legislators. Moreover, the two opposite pairs do not overlap, even when either rule-based or case-based reasoning is adopted in intelligent software systems applied to the legal domain. Bain’s JUDGE system [65,66,67] is a tool whose AI mechanism is case-based reasoning. It adopts a hybrid approach, both rule-based and case-based. JUDGE is a cognitive model of judges’ decision-making when sentencing (and indeed it was based on interviews with judges). |
11 | “FirstEnergy Nuclear Operating Company’s (FENOC) Perry nuclear power plant—a 1270-MWe boiling water reactor located in North Perry, Ohio—completed its 16th refueling outage on April 3, 2017. The 29-day outage, which began on March 5, marks the shortest refueling outage in Perry’s 30 years of operation (the previous record was 34 days in 2001). More than 1400 contract workers and FENOC employees from the company’s other nuclear plants supplemented Perry’s 700-person workforce during the outage. In addition to replacing 280 of the plant’s 748 fuel assemblies, workers completed more than 9600 outage work activities. A new, massive transformer that provides power from the off-site transmission network was also installed” [73]. (p. 42). “Perry’s 1270-MWe reactor will operate for approximately 24 months until its next refuelling in spring 2019” [73] (p. 48). |
12 | The paper by Bhattacharya and Yu [76] “presents the development of comprehensive computational fluid dynamics models for unsteady flows of coolant through a string of 12 CANDU 6 fuel bundles with angular misalignments inside a pressure tube by means of large eddy simulation”. |
13 | “[T]he nuclear fuel cycle beginning at the uranium mine, where ore is removed from the earth, crushed, and concentrated into ‘yellowcake’ (U3O8). The majority of yellowcake currently comes from Canada and Australia. Next, the U3O8 is combined with fluorine to make UF6, which is solid at room temperature but changes to gas when slightly heated. UF6 gas is used in the enrichment process, during which the concentration of U 235 is increased from its natural value of less than 1% to between 4% and 5%, which is the concentration needed by today’s [i.e., 2006] nuclear power plants. Following enrichment, UF6 is converted into uranium oxide form and fabricated into ceramic fuel pellets, which are packed into fuel rods. The fuel rods are then configured into bundles called fuel elements, which are shipped to utility customers and loaded into power plants. Power plants refuel their reactors about every 12 to 24 months, replacing about one-third of the fuel bundles in the reactor core. Each refueling represents on average $12 million worth of enriched uranium fuel” at 2006 prices [77] (p. 4, col. 2). At the time [77], there were 441 nuclear power plants worldwide (of which, 103 operating nuclear plants in the USA), and they were generating 16% of the world’s total electricity production. The fraction of electricity generation as per data known at that time was 78% in France, 74% in Lithuania, 56% in Belgium, 55% in Slovakia, 47% in Ukraine, 41% in South Korea, 34% in Japan, 31% in Germany, 23% in the United Kingdom, 20% in the USA, and 15% in Russia [77]. There exists an annual reference issue of Nuclear News magazine, being the given year’s World List of Nuclear Power Plants. The 2017 World List covered data from 2016, and was the 19th Annual Reference Issue. |
14 | Waste management of spent nuclear fuel and radioactive waste disposal facilities, as well as the management of plant decommissioning, are the subject areas of the magazine Radwaste Solutions (http://www.ans.org/rs), published by the American Nuclear Society from 1994. |
15 | Monti et al. [99] discussed the design of a core—the Encapsulated Nuclear Heat Source (ENHS) core—in a “fuel self-sustaining reactor”. The reference ENHS core considered is fuelled with transuranium from spent fuel that had been used in a light water reactor (LWR) and was then cooled for 10 years, with better results if the cooling period was of nearly 32 years. Then the ENHS core is repeatedly reloaded by recycling the heavy metal discharged with the ENHS itself. The concentrations of different isotopes of plutonium were also discussed. |
16 | There also are “poisons” that are produced by the nuclear fission itself and are undesirable because they can cause an outage. “Some of the fission products generated during a nuclear reaction have a high neutron absorption capacity, such as xenon-135 (Xe-135) and samarium-149 (Sm-149). Because these two fission product poisons remove neutrons from the reactor, they will have an impact on the thermal utilization factor and thus the reactivity. The poisoning of a reactor core by these fission products may become so serious that the chain reaction comes to a standstill. Xe-135 in particular has a tremendous impact on the operation of a nuclear reactor. The inability of a reactor to be started due to the effects of Xe-135 is sometimes referred to as xenon precluded start-up. The period of time in which the reactor is unable to override the effects of Xe-135 is called the xenon dead time or poison outage. During periods of steady state operation, at a constant neutron flux level, the Xe-135 concentration builds up to its equilibrium value for that reactor power in about 40 to 50 hours. When the reactor power is increased, Xe-135 concentration initially decreases because the burn up is increased at the new higher power level” [110]. |
17 | The notion of burnable poisons is not identical with control rods (movable control rods, parallel to the fuel assemblies, and containing neutron-absorbing material), but is a broader concept: “to control large amounts of excess fuel reactivity without control rods, burnable poisons are loaded into the core. Burnable poisons are materials that have a high neutron absorption cross section that are converted into materials of relatively low absorption cross section as the result of neutron absorption. Due to the burn-up of the poison material, the negative reactivity of the burnable poison decreases over core life. Ideally, these poisons should decrease their negative reactivity at the same rate that the fuel’s excess positive reactivity is depleted. Fixed burnable poisons are generally used in the form of compounds of boron or gadolinium that are shaped into separate lattice pins or plates, or introduced as additives to the fuel. Since they can usually be distributed more uniformly than control rods, these poisons are less disruptive to the core’s power distribution. Fixed burnable poisons may also be discretely loaded in specific locations in the core in order to shape or control flux profiles to prevent excessive flux and power peaking near certain regions of the reactor. Current practice however is to use fixed non-burnable poisons in this service” [110]. |
18 | |
19 | A project Bernard and Washio’s category (a) was NUCLEXPERT, described by Jardon and Dubois [159]. Quite possibly, an incentive for such a focus on the first version of the task, instead of the second option, may have been grounded in an approach to (or culture of) nuclear power as known from the French national context: the state has a monopoly, and moreover the provision of fuel and the management of nuclear power plants is integrated vertically, so that the national strategy is to have reactors refuelled on a strictly annual basis, with no attempt to achieve longer operation periods between successive shutdowns of the reactor. Whereas vertical integration is also found in the United States, managers of the individual plants there (as opposed to the company-level decision-making typical of the United Kingdom) have the interest of increasing the temporal distance between shutdowns, apart from the generalized requirement that downtime periods be kept short (they usually take a few weeks). “Expert systems have also been developed to assist with scheduling the movements of fuel assemblies. One such system is CLEO, which was developed at Hanford for use in the Fast Flux Test Facility [160,161]. Moreover, EPRI [i.e., the Electric Power Research Institute in Palo Alto, California], in conjunction with Intellicorp and the Virginia Electric Power Company, developed a prototype expert system [162,163], which planned crane movements for the fuel insert shuffle of a PWR” [159] (p. 41). Samary Baranov, a former Soviet, naturalized Israeli researcher who was a colleague of mine in Beer-Sheva, at one time developed—for application at Soviet nuclear plants—a method by which a solution algorithm is Converted into an optimized logic circuit design for incorporation into the hardware, Baranov’s conversion procedure is independent of the application domain, and was exemplified in several ways, in a book of 1994 (see especially its Chapter 8 [164]) which however does not include the old, but (as I noted in 1998) unpublished application to nuclear power plants). |
20 | The following few paragraphs are based on the final section in [201]. The role, in the making of FUELGEN, of my colleague, Alan Soper (by whom, see [202]), and of our doctoral student, Jun Zhao, cannot be overstressed. They deserve credit as my senior co-authors of the text of the paragraphs about FUELGEN in my present paper. |
21 | As for robotics (biorobotics), a pheromone trail is a concept underlying neurobiologist Frank Grasso’s RoboLobster. The aim of that project is to produce a robot that would mimic a lobster’s ability to navigate pounding surf, and the intended use is in discovering the scent of chemicals and identifying their sources underwater, such as leakages (e.g., a plume of chemicals was discovered in the Red Sea, in experiments conducted in 2002 on second-generation lobster-like robots in collaboration with the Interuniversity Institute of Eilat, Israel), as well as in clearing mines from shallow water. The underwater trials were conducted at a depth of five metres. The substance to be sensed by the robot was marked with dye, so the students who were scoring the robot’s behaviour could do so by tracking its movements relative to the dye [251]. “A small underwater wheeled robot with conductivity sensors was used to test chemical orientation strategies employed by lobsters to locate odor sources” [252] (p. 779, referring to [253]; also see [254,255]). RoboLobster does not look like a lobster, except in that on its front side, it has two antennae, which are parallel with the flanks of the rather flat box which constitutes its body. There is one wheel on each of the flanks of its lower part (a box with a trapeze section), which is surmounted by a parallelepiped of clear plastic. Natural lobsters sense chemicals which may or may not be produced by their own kind. For example, in his book on pheromones, Wyatt [256] (p. 62, caption of Figure 3.10) shows: “a female lobster […], attracted by a male’s chemical ‘song’, jets her own urine towards a male in his shelter. He responds by retreating to the opposite entrance and fanning his pleopods. […]”. Wyatt’s corresponding text [256] (p. 61) explains: “males of the lobster Homarus americanus create odour currents from their dens, thus ‘singing a chemical song’ […] [citing [257]]. Females choose the locally dominant male by his urine signals”. Wyatt [256] (pp. 219–220) explains: “turbulent odour plumes form as air or water currents disperse odour molecules from their source. Odour plumes are of course normally invisible but swirling smoke clouds from a chimney provide a good visual analogy of the important features”, and: “the smoke forms a meandering cloud that snakes down. If you get closer, you can see the fine-scale structure within the clouds, with filaments of high concentration interspersed with cleaner air. As a cloud of odour molecules moves from the source, turbulence tears apart the cloud into elongated odour-containing filaments, each only a few millimetres wide, separated by ‘clean’ water or air”. Importantly for communication: “this fine filament structure is central to the responses evolved by orienting animals. The turbulent effects are greater than diffusion (which is comparatively slow) and an important consequence is that a plume is far from a uniform cloud of pheromone drifting downwind; rather, it is composed of filaments that remain relatively concentrated. Thus the pheromone concentrations within the filaments will be above the response threshold much further downstream than a diffusion model would predict—but in a spreading plume, far down stream, the odour filaments may be widely spaced” [256] (ibid.). |
22 | Nuclear Science and Engineering is the flagship of the ANS, and the most prestigious journal in nuclear engineering. It is a journal in print, with several volumes per year (for a total of 12 issues) but abstracts and (for purchase) articles can be accessed through the website http://www.new.ans.org/pubs/journals/nse/. |
23 | For example, an editorial in Nuclear News of October 2017, trying to maintain an upbeat tone, after mentioning a step taken by the USA Secretary of Energy with a request of his to the Federal Energy Regulatory Commission (FERC), spelled out the difficult situation of the nuclear sector: “and the FERC rulemaking, if successful, should go a long way in helping plants that are struggling to compete in a faulty energy market keep humming along. With the industry struggling to bring new construction projects to the market, preserving the existing fleet is more important than ever if we want to reap the benefits of clean, reliable nuclear energy” [271]. There has also been a persistent downturn in the uranium market. |
24 | As Qvist and Greenspan point out [277]: “for a reactor to establish a sustainable breed-and-burn (B&B) mode of operation, its fuel has to reach a minimum level of average burnup. The value of the minimum required average discharge burnup strongly depends on the core design details. Using the extended neutron balance method, it is possible to quantify the impact of major core design choices on the minimum required burnup in a B&B core. Relevant design variables include the fuel chemical form, nonactinide mass fraction of metallic fuel, feed-fuel fissile fraction, fuel rod pitch-to-diameter ratio (P/D), average neutron flux level, and fraction of neutron loss. Metallic fuels have been found to be the only viable fuel options for a realistic near-term B&B reactor. …”. |
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Nissan, E. An Overview of AI Methods for in-Core Fuel Management: Tools for the Automatic Design of Nuclear Reactor Core Configurations for Fuel Reload, (Re)arranging New and Partly Spent Fuel. Designs 2019, 3, 37. https://doi.org/10.3390/designs3030037
Nissan E. An Overview of AI Methods for in-Core Fuel Management: Tools for the Automatic Design of Nuclear Reactor Core Configurations for Fuel Reload, (Re)arranging New and Partly Spent Fuel. Designs. 2019; 3(3):37. https://doi.org/10.3390/designs3030037
Chicago/Turabian StyleNissan, Ephraim. 2019. "An Overview of AI Methods for in-Core Fuel Management: Tools for the Automatic Design of Nuclear Reactor Core Configurations for Fuel Reload, (Re)arranging New and Partly Spent Fuel" Designs 3, no. 3: 37. https://doi.org/10.3390/designs3030037