Development of multicriteria nuclear dismantling management incorporated with fuzzy deep learning in nuclear power plants (NPPs)

The nuclear dismantling assessment is analyzed with the fuzzy set and deep‐learning algorithm, where the project preference time search (PPTS) has been constructed. Artificial intelligence (AI) management is applied to nuclear decommissioning for the best estimation. The basic data are from three factors, Licensee, NRC, and Public. In the analysis, the highest OUTPUT value is 0.0513151 in the 72nd year, which is the best time for decommissioning, because the confidence value in the 37th year is 78.76% compared to that of the 72nd year. In the other case of membership functions with right‐shift values, the change rate is higher in the 72nd year as being similar to the value in the 37th year near 0.09 in final confidence value. The trend is a new function that shows two peaks compared to the previous one. The other cases could be made by comparing in the interested time. Finally, the list of reactor decommissions processes with numbering is used to find out the very confident time using the final confidence value as the PPTS method.


| INTRODUCTION
The nuclear decommissioning for the best time estimation is analyzed with the fuzzy set and deeplearning algorithm, where the project preference time search (PPTS) has been constructed.Artificial intelligence (AI) management is applied to nuclear decommissioning for the best estimation.4][5][6] There are some types of membership functions in a triangular form, which will be run as the designed modeling in this study.Each membership function could be constructed and incorporated with expert judgment.Project management has been used in nuclear waste treatments, 7 which means activities including a project dealing with scope, time, cost, quality, and risk 8 in the nuclear industry.It is difficult to decide the starting time for the construction of nuclear waste repository, because of the Not-In-My-Backyard (NIMBY) phenomena against the radioactive facility.Therefore, it is important to find out the interesting step of a project such as a site selection in the nuclear waste repository.
The management of the nuclear dismantlement is investigated by the AI-based approach with deep learning (DL) in this study.One of the important purposes of solving a certain problem in the nuclear industry is to find out a simpler method with a mathematical algorithm. 9,10The brain of a human is mimicked by the neural networking algorithm with axon, synapse, and dendrite systems in AI.That is, the artificial system performs transfers, calculates, combines, and intuits the information processing of the signals.However, depending on the present technologies, there are limitations to making a robot that has some functions similar to human motions.Therefore, AI is considered the interim method to make a kind of cyborg, human-like machine, or so.The nuclear decommissioning is analyzed using machine learning (ML) where the data are connected by the neural networking method, where the artificial neural networking (ANN) is applied as a basic ML.Cao et al. 11 applied the AI to the calculations of nuclear fuel using the ultra-fine group method in core resonance.In addition, the physical similarity in thermal-hydraulics is analyzed for the local pattern simulations. 12In the application of medical imaging, 13 the convolutional neural networking (CNN) was used for radiomic features in clinical as well as experimental purposes. 14onsidering the decommissioned nuclear facilities including the operation and preparing periods, the treatment of radioactive materials has one of the important issues in the dismantled possesses where the plant structures and nuclear wastes are included in the radioactively contaminated stuff.Therefore, this study makes the modeling of a 100-year period from 0th to 100th year, where the parameters regarding nuclear decommission are related to safety and economical factors. 15Hence, the organizations of the decommission-related elements should be investigated in this study.Since this project is connected to many areas such as the networking system, issues are complex in nuclear decommissions.It is reasonable to make use of AIbased DL incorporated with neural networking.The multiple-criteria needs many complex connections of the events in the modeling of ML and the dada could be generated by a usual method of random number generation associated with fuzzy evaluations.The other critical issue is how to manage the process of dismantlement.For example, Figure 1 shows major organizations for nuclear decommissioning 16 where Licensee, NRC, and Public are combined.NRC is the legal body in the USA in charge of the Licensure process including Review, Public Meeting, Initial Notification, and Information, which eventually uses or creates the leading process for Decommissioning.Three parts of Licensee, NRC, and Public are needed to cooperate under the guidance of NRC.Hence, it is necessary to modulate the opinions of three groups.The criteria for decommissioning should be considered for the sake of the above-mentioned groups.In this study, it is assessed in the processes of decommissioning in which DL is associated with human decision-making.Especially, the dynamic concern is one of the interesting topics as the safe and economical dismantling, because the project management such as the nuclear decommissioning should ensure the dynamic trust of the public as well as the government. 17he nuclear facilities are related to many interest groups.So, the decommissioning time is one of the important matters for the groups.In addition, the many connectivities of the groups is similar to the networking in ANN.

| METHODOLOGY
The nuclear decommissioning is analyzed using the DL where the data are connected by the neural networking method.PPTS for nuclear decommission procedure is proposed in this study.The basic data are from three factors as Licensee, NRC, and Public in Figure 1.Each element in the factor is in Table 1 which shows the list of reactor decommissioning processes with numbering with a decision of operator's judgment. 16The notation is included as two layers in the hidden layer of the modeling that is showing a form of "L + Layer Number + Variable Number."In the modeling, there are two layers in the hidden layer where the first layer has Licensee and Public factors, and the second layer has the NRC factor.That is, Licensee and Public factors are leaded by the NRC factor which is seen in Figure 1.NRC is compared to the group of Licensee and Public factors.So, there are two different layers.
To achieve the best performance, the self-learning process is done by fuzzy and neural networking.Figure 2 shows the characteristics of AI in nuclear decommissioning in which the dismantling should be done as the safer and more economical state.In addition, faster and more knowledgeable performance could be accomplished, which is one of the important reasons for making use of AI-based modeling in this study.As it is explained, it is difficult to make a decision in dealing with a nuclear facility.Hence, AI-associated decision-making could be a desirable method.

| Fuzzy membership function
The basic fuzzy membership is interpreted by the algebraic form as follows. 18For the addition of the numbers in a set, where A and B are the crisp sets, μ is the degree of membership function.A ̅ and B ̅ are the fuzzy sets.Furthermore, the multiplication is interpreted by the algebraic form as The above algorithms are performed in the modeling of this study.As a basic fuzzy membership function, the triangular form is easily treated to manage the modeling in this study, although it is possible to use the other kinds of membership functions.In constructing a triangular fuzzy set form, where, A x ¯( ) is the membership function and the fuzzy number is given as a triplet (a, b, c) with membership numbers between 0.0 and 1.0, which is in Figure 3A.
There are three types of membership functions in a triangular form, which will be run as the Current 1 in the result.This has been used in the core power controller of nuclear power plants (NPPs). 19,20Furthermore, nuclear reliability analysis has been studied. 21,22The core power controller and nuclear reliability as the critical characteristics in NPPs could affect to construct the functions associated with expert judgments.Figure 3B means the triangular membership function used in L101 where the minimum value is 0.2, the mean value is 0.5 and the maximum value is 0.9.In the operations of the modeling, fuzzy arithmetic calculations are applied.The number is obtained dynamically in the specified time and then it is calculated by addition or multiplication.Comparing the conventional tree-type assessment method, the OR gate is presented by the addition and the AND gate is produced by the multiplication.

| DL
AI is applied to the decision-making of nuclear dismantlement where the decision tree is associated with the DL method. 23It is shown that the combined pipeline of the events flows is constructed where the networking training is performed.The typical neural networking is seen in Figure 4 as three stages of the input layer, hidden layer, and output layer.Especially, there could be multiple layers in the hidden layer.There are initial data in the input layer and the results are produced in the output layer.
There is the neutral networking with two layers in the hidden layer where the first layer has Licensee and Public factors, and the second layer has the NRC factor.This means that the NRC factor leads to Licensee and Public factors.Machine learning with collaborative learning processes is discussed for the project program in the nuclear dismantlement where the guideline for the tasks was developed. 24

| Modeling
In the modeling, the input data construction begins which is in the input layer of the neural networking.Using the Vensim code system, the neural networking modeling is constructed where the left one is the input layer, the middle two layers are hidden layers, and the right layer is the output layer.Figure 5 has the modeling for AI in nuclear decommissioning where there are two layers in the hidden layer of the neural networking.There is a schematic of the workflow for the ANN model in Figure 6. Figure 7 shows the modeling for (a) INPUT, (b) L101, and (c) L21.INPUT is constructed by the random numbers where the constraints are given to produce by the expert's judgment.The general algorithm of random number-based quantification has been used in many areas for the assessment simulations in the interested tasks.The number of confidence is constructed by the random numbers.The equation is written using Vensim Professional for Window Version 8.1.2code 25 as follows: if then else(random 0 1() < 0.2, 0, 1). (4) That is to say, if the generated random number between 0.0 and 1.0 is lower than 0.2, the number is 0.0.Otherwise, it is 1.0.Therefore, the numbers are produced as Boolean values.
Then, in the first layer of the hidden layer by the neural networking, the fuzzy weighted values are produced.In the case of L101, the equation is constructed newly as follows, (5) So, the fuzzy set is presented as "RANDOM TRIANGULAR(0, 1, 0.2, 0.5, 0.9, 1000)" where the triangular function has the representative values showing the random numbers in the INPUT stage that the minimum value is 0.2, the mean value is 0.5, and the maximum value is 0.9.Table 2 shows the list of membership functions, which is decided by the expert's judgments.In the second layer of the hidden layer, the L21 is as follows, ( The fuzzy set is presented as "RANDOM TRIAN-GULAR(0, 1, 0.2, 0.5, 0.9, 1000)" where the triangular function has the representative values showing the random numbers in the previous stage of multiplemultiplications as "L101 × L102 × L103 × L104 × L105 × L106 × L107 × L108 × L109 × L110" that the minimum value is 0.1, the mean value is 0.5 and the maximum value is 0.9.The simulations are performed by networking-based modeling which is mentioned in the above section.Figure 8 shows the result for nuclear decommissioning in which the final confidence values are obtained.In the 72nd year, the highest OUTPUT value is 0.0513151.Therefore, it is the best time for decommissioning.That is, the other time is not relatively confident.For example, in the 37th year, the value is 0.0404136.So, (0.0404136/0.0513151) × 100 = 78.76(%).(7)   The confident value in the 37th year is 78.76% compared to that of the 72nd year.The other cases could be made by comparing in the interested time.
In addition, it is reasonable that the values are modified by changing the mean, maximum, and minimum values of the membership form.The mean values increase to present the importance of each event.In the case of Initial notification (L101), the three values increase reflecting the importance of Initial notification.This means that the mean values are higher than those types in Figure 4.There is another case of a right-shift one of triangular membership function in Figure 9A with Table 3. Especially, the variables of NRC have the rightest part as type 1 of Current 2. This means that the characteristics of the government part present a much stronger leadership.The comparisons between the two cases are shown in Figure 9B and the list of the membership function is in Table 4.The change rate is in Table 5 where there is the higher change rate in the 72nd year as being similar to the value of the 37th year near 0.09 in the final confidence value, in which the sensitivity is shown by the variations of three layers.The | 3535 trend in Current 2 shows two peaks compared to the trend of Current 1. So, it is found that the higher minimum, mean, and maximum values can show the trend of the event clearly if the variables used by each type are not changed.Finally, the list of reactor decommissions processes with numbering 16 in Table 1 is used to find out the very confident time by PPTS in Figure 10 using the final confidence value rotated in Figure 9. So, it is the very confident time in Approval/Denial of NRC in Figure 10A.Otherwise, if the very confident time is focused on Decommissioning of License in Figure 10B, the early procedure is done in the wider order and the later procedure is done in the narrower order.Then, the Decommissioning report is done before the 40th year in Figure 10A and it is done after the 40th year in Figure 10B.So, one can modulate the whole procedure considering the emphasized step following the fuzzy DL-based simulation result.The emphasized step can be made by the expert's decision.
• The dismantlement of NPPs is focused on safe and economical matters.• The project processes are compared by the fuzzy DL method.• Results show the dynamic assessment of the nuclear decommission.
Considering the nuclear characteristics, the radioactive materials should be cleaned up thoroughly, and eventually, the place should be returned to the previous site without any hazards stuff.The new kind of guideline as the regulation could be published after the specified site dismantling in the future.
The nuclear decommission by PPTS method could be applied to the other industry such as the oil refinery complex or ironworks plant where the facility includes the waste as well as the equipment.So, although the major meaning of dismantling is to throw away the garbage, it is important to manage the cleaning-up and hygiene matter where the toxic and dirty things should be removed and the remained land should be returned to its original condition state.Considering the non-nuclear cases, there is no radioactive material.Hence, the shielding against radiation or a half-life in radioactivity is not necessary to consider to make the planning of the decommission.In addition, in the case of emergent life-extension of the existed NPPs such as the European natural gas crisis, the optimized deconditioning could be delayed due to the political decisions of the public.As it is done in this study, the plural cases in the designed period and in the current (different membership function set) could enhance the reliability of the assessment.
In the case of the space nuclear technology for the cleaning-up, the nuclear power generator like the radioisotope thermoelectric generator is simply to be removed, because the system is structured as the modular type that the whole systems in one casing are controlled by one-time handling.This situation is also applied to the small modular reactor which is promised in the near-term commercialized NPPs.This could be a kind of technological concept for future advanced NPPs.That is, in the stage of the manufacturing of NPPs, the modular system is to make a regulation for easier and faster decommissioning, even though the modular system was originally designed as a safety enhancement.This is a topic of this study as safe and economical dismantling using AI of fuzzy DL.

F I G U R E 5
Modeling for artificial intelligence (AI) in nuclear decommissioning F I G U R E 6 The schematic of the workflow for ANN model.ANN, artificial neural networking.

9
Graphs for (A) triangular membership function with a right-shift one (Current 2) and (B) comparison of results between two cases (Current 1 and Current 2) PPTS.PPTS, project preference time search.T A B L E 3 List of membership functions for a right-shift one (Current 2)

F
I G U R E 10 The procedure of confidence value associated with NRC process (A) Linearly proportional process and (B) "Decommissioning" emphasized process.