Neutron shielding material optimization method based on machine learning and chaotic mapping NSGA-III

Abstract

The invention belongs to the technical field of radiation protection, and particularly relates to a neutron shielding material optimization method based on machine learning and chaotic mapping NSGA-III, and the method comprises the steps: 1, determining an optimization target, and building a multi-target neutron composite shielding material attribute optimization model; step 2, building a Monte Carlo model to simulate and calculate shielding doses of the composite shielding materials with different attributes to a neutron source, and obtaining a data set with the material component proportion and thickness as characteristic attributes and the shielding doses as labels; and step 3, optimizing initial parameters of the BP neural network by adopting an improved particle swarm optimization algorithm, improving calculation precision and operation efficiency of the neural network, and training a neural network regression model by taking the data set obtained in the step 2 as a sample to complete establishment of a shielding dose prediction model and the like. An improved particle swarm optimization algorithm for improving Levy flight mechanism strategy optimization is designed to optimize initial parameters of the BP neural network, and the precision and operation efficiency of a neural network shielding dose regression prediction model are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of radiation protection, and specifically relates to a neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III. Background Art

[0002] Radiation shielding is an important component of nuclear facilities. In actual nuclear engineering applications, multiple factors such as the structural composition, volume, weight and physical properties of the shielding body are usually considered. Traditional shielding design is mostly based on subjective experience and trial and error, which is relatively inefficient. In recent years, the use of intelligent optimization algorithms to automatically optimize the design of shielding materials has become a major development trend. Among them, evolutionary multi-objective optimization algorithms such as NSGA-Ⅱ, MOPSO and MOEA / D have fully demonstrated their advantages in solving multi-objective optimization problems with good convergence and finding diverse non-dominated solutions.

[0003] Through the study of prior art literature, it was found that the Chinese patent application number is 201510329363.4, the application publication number is CN104933245A, and the patent name is: Marine reactor shielding design optimization method based on neural network and genetic algorithm. The patent uses BP neural network to train and learn shielding dose data to achieve a prediction accuracy of less than 2% error, but does not optimize the initial parameters of the BP neural network, which increases the running time of the network fitting, and the genetic algorithm is only applicable to the optimization problem of a single target, and cannot solve three or more multi-objective optimization models; the Chinese patent application number is 202210929887.7, the application publication number is CN115374613A, and the patent name is: Multi-objective shielding optimization method and system based on non-dominated sorting genetic algorithm. During the optimization process, the patent needs to continuously call the shielding calculation program to calculate the dose rate of the randomly generated shielding scheme, which greatly increases the complexity of the optimization process and reduces the algorithm optimization efficiency. Summary of the invention

[0004] In view of the problems existing in the prior art, the purpose of the present invention is to provide a neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III. The method optimizes the initial parameters of the BP neural network by improving the PSO algorithm for optimizing the Levy flight mechanism strategy, and introduces a double chaos mapping method to optimize the NSGA-III. On the one hand, a Logistic-tent composite chaotic dynamics model is used to generate a uniform initial population, thereby improving the optimization efficiency and global search capability of the algorithm; on the other hand, a random factor chaotic sequence is generated by a Piecewise chaos mapping, and the diversity and uniformity of the population are improved while performing crossover and mutation operations; a non-dominated sorting genetic algorithm based on reference point calculation is used to maintain the diversity of the population using well-distributed reference points, and has good convergence in solving three or more multi-objective optimization problems.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution of the present invention is as follows:

[0006] A neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III comprises the following steps:

[0007] Step 1, determine the optimization target and establish a multi-objective neutron composite shielding material property optimization model;

[0008] Step 2: Build a Monte Carlo model to simulate and calculate the shielding dose of composite shielding materials with different properties to the neutron source, and obtain a data set with material component ratio and thickness as characteristic attributes and shielding dose as label;

[0009] Step 3, using the improved particle swarm optimization algorithm to optimize the initial parameters of the BP neural network, improve the calculation accuracy and efficiency of the neural network, and use the data set obtained in step 2 as a sample to train the neural network regression model to complete the establishment of the shielding dose prediction model;

[0010] Step 4: The double chaos mapping method is used to improve the non-dominated sorting genetic algorithm NSGA-Ⅲ based on reference points, and the uniform reference point calculation method and non-dominated sorting method are used to evaluate the fitness function of multi-objective individuals. After multiple population iterations, the Pareto optimal solution set is obtained;

[0011] Step 5: Analyze the Pareto solution set based on actual engineering application requirements and experience, and select the material property solution that maximizes the benefits.

[0012] Further, in step 1, the multi-objective neutron composite shielding material property optimization model is:

[0013] minF(x)=(f1(x),f2(x),...,f M (x) T

[0014]

[0015] s.t. 1 ≤ x M ≤ 31

[0016] wherein, F(x) is a multi-objective function, M is the objective dimension, and f i (x) is the i-th sub-objective function, and x i represents the i-th attribute of the material.

[0017] Furthermore, in step 2, a unidirectional neutron plane source is placed at the center position of the Monte Carlo model, the thickness range of the shielding material is set, and the F2 counting card and DE, DF cards are used to evaluate the radiation dose equivalent.

[0018] Furthermore, in step 3, the following steps are included:

[0019] Step 3.1, according to the number m of sample input characteristic parameters, the number n of output labels, and the empirical formula 1 < a < 10, determine the topological structure of the BP neural network, traverse the range of the number of hidden layers, simulate and calculate the mean square error value MSE between the actual output and the predicted result of the test set, and determine the optimal number h of hidden layer nodes of the network;

[0020] Step 3.2, introduce an improved particle swarm optimization algorithm to optimize the initial weights w and biases b of the neural network, select the mean square error between the actual output and the predicted result of the test set as the fitness function, calculate the fitness value of each particle, complete the priority sorting and then perform the update iteration of the population, and output the optimized optimal population. In order to prevent the PSO algorithm from falling into local optimum and premature convergence, set the random number rand;

[0021] Step 3.3, use the optimal population output after optimization in step 3.2 as the initial value of the neural network parameters, define the number of training times, learning rate, minimum error of the training target, momentum factor, minimum performance gradient, and maximum number of failures, set the activation function, use the Levenberg-Marquardt algorithm to improve the operation speed of the network, start training until the termination condition is met, save the trained network net, and complete the establishment of the shielding dose prediction model.

[0022] Furthermore, in step 3.2, when updating the particles, if rand < 0.5, the particles are updated using the following formula:

[0023] X i (t + 1) = X i (t) + η · V i (t) + c1 · rand · (pbest i - X i(t))+c2·rand(gbest-X i (t))

[0024]

[0025] Where, X i (t+1) is the position of the i-th particle at the t+1th iteration; V i (t) is the velocity of the ith particle at the tth iteration; η represents the inertia weight; c1 and c2 are learning factors; pbest i represents the current optimal individual of population i; gbest is the current global optimal particle; T is the maximum number of iterations.

[0026] Furthermore, in step 3.2, when the particles are updated, if rand ≥ 0.5, the individuals search and update in the global space with the improved Levy flight mechanism strategy, which increases the randomness and diversity of the population and can better balance the development and exploration of the algorithm.

[0027] Further, step 4 includes the following steps:

[0028] Step 4.1, initialize the population size P, population dimension d, target dimension M, maximum number of iterations G, current number of iterations gen, individual size upper and lower limit thresholds y u ,y l , the threshold is consistent with the population dimension d, and a uniform initial population is generated using the Logistic-tent composite chaotic dynamics model;

[0029] Step 4.2, perform crossover and mutation genetic operations on the initial parent population P(0) to obtain the offspring population Pp;

[0030] Step 4.3, for two arbitrary individuals x1 and x2, if all sub-objective functions satisfy f j (x1)≤f j (x2), and there exists a sub-objective function such that f j (x1)<f j (x2), then individual x1 is said to dominate individual x2; if there is no dominance relationship between the two, x1 and x2 are said to be unrelated; merge the two generations of populations into Q(gen), and according to the above relationship, quickly sort the individuals in Q(gen) to form a non-dominated layer {F{1}, F{2}, ... F{L}} and store them in the next generation population P(gen+1) in sequence. If F{l} is the last non-dominated layer that is larger than the population size P for the first time, then P(gen+1)=F{1}∪F{2}∪...∪F{l-1}, calculate the reference point of the population in the non-dominated layer of F{l} and screen out a uniform population;

[0031] Step 4.4, set an M-1 dimensional normalized hyperplane, which has the same inclination for all target axes and the intercept on each axis is not 0;

[0032] Step 4.5, repeat steps 4.1 to 4.4, when gen≤G, the optimization ends.

[0033] Further, step 4.2 includes the following operations:

[0034] A1: Chromosome crossover operation:

[0035] Pp1=0.5×((1+γ)×P1+(1-γ)×P2)

[0036] Pp2=0.5×((1-γ)×P1+(1+γ)×P2)

[0037] Pp=Pp1∪Pp2

[0038]

[0039] α=2-β -μ-1

[0040]

[0041] In the formula, two parent populations are selected: P1 = {P1(0), P3(0), ..., P N-1 (0)};P2={P2(0),P4(0),...,P N (0)}; μ is the crossover factor; α is the crossover condition factor; β is the crossover adjustment factor; γ is the crossover balance factor; Pp1 and Pp2 are the two offspring populations after crossover; for the random factor u, the chaotic sequence generated by the piecewise chaotic map can be described as:

[0042]

[0043] Where u(t) is the number of random factors at the tth iteration; p is 0.4;

[0044] A2: Chromosome mutation operation:

[0045] Pp=Pp+φ×(rand(1,d)<0.4)×(y u -y l )

[0046]

[0047]

[0048] Where Pp is the population undergoing mutation; is the variation adjustment factor; φ is the variation balance factor; rand(1,d) represents the generation of a matrix with 1 row and d columns whose elements are 0 to 1 random numbers; d is the population dimension; ν is the variation factor; u is a random factor, and the chaotic sequence is generated by Piecewise chaotic mapping.

[0049] Further, step 4.4 includes the following operations:

[0050] B1: Calculate the ideal point z for multi-objective optimization min :

[0051] For an M-dimensional objective function, there is an ideal point in the jth dimension Where j = 1, 2...M; P is the size of the population to be screened; f ij represents the objective function of the jth dimension of the ith population; Y i is the i-th population, Y i ∈F{l}, F{l} is the population set of the lth layer after non-dominated sorting. Then the ideal point of the population in this iteration is Then, the target values ​​of all individuals in F{l} are transformed with the ideal point as reference to obtain the temporary standardized translation target f i '(Y i )=f i (Y i )-z min , where the ideal point after translation becomes the zero vector;

[0052] B2: Use the following formula to calculate the extreme point z on each target axis. j,max :

[0053]

[0054] In the formula, w j represents the extreme coordinates of the j-th dimension target, w j =(ε,ε,...1,..ε) T , ε=1×10 -6 and

[0055] B3: These M extreme points form an M-1 dimensional linear hyperplane, and calculate its intercept a=[a1,a2,...,a M ], and use the intercept and temporary standardized target value to solve the standardized target value f of the individual target value according to the following formula j ” (y), complete the target structure normalization:

[0056]

[0057] In the formula, a jRepresents the intercept in the direction of the target axis of the j-th dimension.

[0058] B4: A set of uniform reference points is predefined on the hyperplane, the number of which is Where M is the number of targets to be optimized; p is the number of divisions of each target axis, and all reference points z r Connect the origin to form several reference lines c=z, and calculate the vertical distance from all individual targets to each reference line. The distance from the kth individual to each reference line is expressed as L k =(l k1 ,l k2 ,...l kH ), find the reference point corresponding to its minimum vertical distance, namely π(z r )=z r :argminL k , complete the association operations in sequence;

[0059] B5: Traverse all reference points in turn, record the number of individuals o associated with them, and determine the reference point set J with the minimum number of individuals by mino s , randomly select any reference point And add the associated individuals that match it to P(gen+1); here, if mino=0, then after deleting the corresponding reference point set, re-execute this step until P(gen+1)=P.

[0060] Furthermore, in step 5, any population of the Pareto solution set obtained is an optional solution with its own advantages, and a result in which any goal is better than other solutions can always be found; it is not that all design goals are optimal at the same time, but a collection of radiation shielding solutions in which each goal is relatively optimal but optimal overall.

[0061] The beneficial effects of the present invention are as follows:

[0062] 1. Design an improved particle swarm optimization algorithm for optimizing the strategy of Levy flight mechanism to optimize the initial parameters of BP neural network, improve the accuracy and operation efficiency of neural network shielding dose regression prediction model, and improve the problem of complex and time-consuming shielding calculation process of constantly calling MC program;

[0063] 2. The double chaos mapping method is introduced to optimize NSGA-Ⅲ. On the one hand, the Logistic-tent composite chaotic dynamics model is used to generate a uniform initial population to improve the optimization efficiency and global search ability of the algorithm; on the other hand, the random factor chaotic sequence is generated by the Piecewise chaotic mapping to perform crossover and mutation operations while improving the diversity and uniformity of the population;

[0064] 3. The non-dominated sorting genetic algorithm based on reference point calculation uses well-distributed reference points to maintain the diversity of the population. It has good convergence in solving three or more multi-objective optimization problems and can provide users with more balanced solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 This is a flow chart of a neutron shielding material optimization method based on machine learning and chaos mapping NSGA-Ⅲ;

[0066] Figure 2 This is the regression curve diagram of the optimized BP neural network training. a, b, c, and d are the regression diagrams of the training set, validation set, test set, and all data respectively;

[0067] Figure 3 Optimization convergence plot for the three-objective case. DETAILED DESCRIPTION

[0068] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0069] The present invention is a neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III, the flow chart is as follows Figure 1 As shown, the following steps are included:

[0070] Step 1, determine the optimization target and establish a multi-objective neutron composite shielding material property optimization model;

[0071] Step 2: Build a Monte Carlo model to simulate and calculate the shielding dose (the sum of the ambient dose equivalents of neutrons and secondary photons after shielding) of composite shielding materials with different properties to the neutron source, and obtain a data set with material component ratio and thickness as characteristic attributes and shielding dose as label;

[0072] Step 3, using an improved particle swarm optimization algorithm (PSO) to optimize the initial parameters of the BP neural network, improve the calculation accuracy and efficiency of the neural network, and use the data set obtained in step 2 as a sample to train the neural network regression model to complete the establishment of the shielding dose prediction model;

[0073] Step 4: The double chaos mapping method is used to improve the non-dominated sorting genetic algorithm NSGA-Ⅲ based on reference points, and the uniform reference point calculation method and non-dominated sorting method are used to evaluate the fitness function of multi-objective individuals. After multiple population iterations, the Pareto optimal solution set is obtained;

[0074] Step 5: Analyze the Pareto solution set based on actual engineering application requirements and experience, and select the material property solution that maximizes the benefits.

[0075] In Step 1, the multi-objective neutron composite shielding material property optimization model is as follows:

[0076] minF(x) = (f1(x), f2(x),..., f M (x)) T

[0077]

[0078] s.t. 1 ≤ x M ≤ 31

[0079] In the formula, F(x) is the multi-objective function, M is the objective dimension, f i (x) is the i-th sub-objective function, and x i represents the i-th property of the material.

[0080] In Step 2, a unidirectional neutron plane source with a radius of 5 cm is placed at the center of the Monte Carlo model. The thickness range of the shielding material is set, and the F2 counting card and DE, DF cards are used to evaluate the radiation dose equivalent.

[0081] In Step 3, it includes the following steps:

[0082] Step 3.1, according to the number of sample input characteristic parameters m, the number of output labels n, and the empirical formula 1 < a < 10, determine the topological structure of the BP neural network. Traverse the range of the number of hidden layers, and simulate and calculate the mean square error value MSE between the actual output and the predicted result of the test set to determine the optimal number of hidden layer nodes h of the network;

[0083] Step 3.2, introduce an improved particle swarm optimization algorithm to optimize parameters such as the initial weights w and biases b of the neural network. Initialize the population size N, the population dimension D = m·(h + 1) + h·(n + 1), the maximum number of evolutionary generations T, and define the upper and lower limits L b and U b , the particle velocity update boundary V max = (U b - L b ) × 0.15, V min = -V max . Initialize the particle positions X and velocities V, where the position of the i-th population is expressed as X i (t) = [x i1 , x i2 , x i3 ....x iD (where x ikis the randomly generated network weight or bias), select the mean square error between the actual output of the test set and the predicted result as the fitness function, calculate the fitness value of each particle, update the population iteratively after completing the priority sorting, and output the optimized optimal population.

[0084] In order to prevent the PSO algorithm from falling into the local optimum and premature convergence, a random number rand is set. When the particle is updated, if rand < 0.5, the particle is updated using the following formula:

[0085] X i (t+1)=X i (t)+η·V i (t)+c1·rand·(pbest i -X i (t))+c2·rand(gbest-X i (t))

[0086]

[0087] Where, X i (t+1) is the position of the i-th particle at the t+1th iteration; V i (t) is the velocity of the ith particle at the tth iteration; η represents the inertia weight; c1 and c2 are learning factors; pbest i represents the current optimal individual of population i; gbest is the current global optimal particle; T is the maximum number of iterations.

[0088] If rand ≥ 0.5, individuals search and update in the global space using the improved Levy flight mechanism strategy, which increases the randomness and diversity of the population and can better balance the development and exploration of the algorithm. The principle is as follows:

[0089]

[0090] C = 2 × rand × (1-1 / T)

[0091]

[0092] μ:N(0,σ 2 ), v:N(0,1)

[0093]

[0094] In the formula, C is the weight coefficient; rand is a random number between 0 and 1; λ is the optimization ratio coefficient; α is the step size scaling factor, which is 0.1; is a custom operator; Levy(β) is the random path of Levy flight, and β is usually 1.5; μ is the random number of Levy flight algorithm, which satisfies the normal distribution; ν is the random number that satisfies the standard normal distribution; Г is the gamma function, which satisfies Г(1+β)=β.

[0095] Step 3.3, use the optimal population output after optimization in step 3.2 as the initial value of the neural network parameters, define the number of training epochs = 1000, the learning rate lr = 0.01, the minimum error goal of the training target = 0.0001, the momentum factor mc = 0.01, the minimum performance gradient min_grad = 1e-6 and the maximum number of failures max_fail = 6, set the activation function to {'tansig', 'purelin'}, use the Levenberg-Marquardt algorithm to improve the network's computing speed, start training until the termination condition is met, save the trained network net, and complete the establishment of the shielding dose prediction model. Among them, the regression curve of the optimized BP neural network training is as follows Figure 2 shown.

[0096] Step 4 is as follows:

[0097] Step 4.1, initialize the population size P, population dimension d, target dimension M, maximum number of iterations G, current number of iterations gen, individual size upper and lower limit thresholds y u ,y l (consistent with the population dimension d), a uniform initial population is generated using the Logistic-tent compound chaotic dynamics model, the principle of which is:

[0098]

[0099] Where Y i j It represents the size of the j-th individual in the ith population, and r is the chaos coefficient, which is 0.3.

[0100] For any individual Y=(y1,y2,...y d-1 ), to ensure satisfaction 0≤y k ≤1, the spherical coordinate transformation method is used to perform floating-point encoding on the first d-1 dimensional variables of the population individuals, where:

[0101]

[0102] Step 4.2, perform crossover and mutation genetic operations on the initial parent population P(0) to obtain the offspring population Pp:

[0103] A1: Chromosome crossover operation:

[0104] Pp1=0.5×((1+γ)×P1+(1-γ)×P2)

[0105] Pp2=0.5×((1-γ)×P1+(1+γ)×P2)

[0106] Pp=Pp1∪Pp2

[0107]

[0108] α=2-β -μ-1

[0109]

[0110] In the formula, two parent populations are selected: P1 = {P1(0), P3(0), ..., P N-1 (0)};P2={P2(0),P4(0),...,P N (0)}; μ is the crossover factor; α is the crossover condition factor; β is the crossover adjustment factor; γ is the crossover balance factor; Pp1 and Pp2 are the two offspring populations after crossover; for the random factor u, the chaotic sequence generated by the piecewise chaotic map can be described as:

[0111]

[0112] Where u(t) is the number of random factors at the tth iteration; p is 0.4;

[0113] A2: Chromosome mutation operation:

[0114] Pp=Pp+φ×(rand(1,d)<0.4)×(y u -y l )

[0115]

[0116] Where Pp is the population undergoing mutation; is the variation adjustment factor; φ is the variation balance factor; rand(1,d) represents the generation of a matrix with 1 row and d columns whose elements are 0 to 1 random numbers; d is the population dimension; ν is the variation factor; u is a random factor, and the chaotic sequence is generated by Piecewise chaotic mapping.

[0117] Step 4.3, for two arbitrary individuals x1 and x2, if all sub-objective functions satisfy f j (x1)≤f j (x2), and there exists a sub-objective function such that f j (x1) <f j(x2), then individual x1 is said to dominate individual x2; if there is no dominance relationship between the two, x1 and x2 are said to be unrelated; the two generations of populations are merged into Q(gen), and according to the above relationship, the individuals in Q(gen) are quickly non-dominated sorted to form a non-dominated layer [F{1}, F{2}, ... F{L}} and stored in the next generation population P(gen+1) in sequence; if F{l} is the last non-dominated layer that is larger than the population size P for the first time, then P(gen+1) = F{1}∪F{2}∪...∪F{l-1}, the reference point calculation is performed on the population in the non-dominated layer of F{l} and a uniform population is screened out.

[0118] Step 4.4, set an M-1 dimensional normalized hyperplane, which has the same inclination for all target axes and the intercept on each axis is not 0.

[0119] B1: Calculate the ideal point z for multi-objective optimization min :

[0120] For an M-dimensional objective function, there is an ideal point in the jth dimension Where j = 1, 2...M; P is the size of the population to be screened; f ij represents the objective function of the jth dimension of the ith population; Y i is the i-th population, Y i ∈F{l}, F{l} is the population set of the lth layer after non-dominated sorting. Then the ideal point of the population in this iteration is Then, the target values ​​of all individuals in F{l} are transformed with the ideal point as reference to obtain the temporary standardized translation target f i '(Y i )=f i (Y i )-z min , where the ideal point after translation becomes the zero vector;

[0121] B2: Use the following formula to calculate the extreme point z on each target axis. j,max :

[0122]

[0123] In the formula, w j represents the extreme coordinates of the j-th dimension target, w j =(ε,ε,...1,..ε) T , ε=1×10 -6 and

[0124] B3: These M extreme points form an M-1 dimensional linear hyperplane, and calculate its intercept a=[a1,a2,...,aM ], and use the intercept and temporary standardized target value to solve the standardized target value f of the individual target value according to the following formula j ” (y), complete the target structure normalization:

[0125]

[0126] In the formula, a j Represents the intercept in the direction of the target axis of the j-th dimension.

[0127] B4: A set of uniform reference points is predefined on the hyperplane, the number of which is (where M is the number of targets to be optimized; p is the number of divisions of each target axis), and all reference points z r Connect the origin to form several reference lines c=z, and calculate the vertical distance from all individual targets to each reference line. The distance from the kth individual to each reference line is expressed as L k =(l k1 ,l k2 ,...l kH ), find the reference point corresponding to its minimum vertical distance, namely π(z r )=z r :argminL k , complete the association operations in sequence;

[0128] B5: Traverse all reference points in turn, record the number of individuals o associated with them, and determine the reference point set J with the minimum number of individuals by mino s , randomly select any reference point And add the associated individuals that match it to P(gen+1); here, if mino=0, then after deleting the corresponding reference point set, re-execute this step until P(gen+1)=P.

[0129] Step 4.5, repeat steps 4.1 to 4.4, when gen≤G, the optimization ends.

[0130] In step 5, any population of the Pareto solution set obtained is an optional solution with its own advantages, and we can always find a result in which any goal is better than other solutions; it is not that all design goals are optimal at the same time, but a set of radiation shielding solutions in which each goal is relatively optimal but optimal overall.

[0131] Example

[0132] Taking the three-objective optimization as an example: considering the moderation, absorption and shielding of secondary photons of neutrons, a composite material uniformly mixed with boron carbide, iron, tungsten, lead, bismuth oxide, polyethylene and NBS concrete was selected as the research object. The optimization of mass, volume and shielding effect was taken as the goal to carry out the optimization design of neutron shielding material composition and thickness based on the evolutionary multi-objective optimization algorithm. The final Pareto convergence curve is shown in Figure 3 shown.

[0133] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. A neutron shielding material optimization method based on machine learning and chaos mapping NSGA-Ⅲ, characterized in that: The following steps are involved: Step 1, determine the optimization target and establish a multi-objective neutron composite shielding material property optimization model; Step 2: Build a Monte Carlo model to simulate and calculate the shielding dose of composite shielding materials with different properties to the neutron source, and obtain a data set with material component ratio and thickness as characteristic attributes and shielding dose as label; Step 3, using the improved particle swarm optimization algorithm to optimize the initial parameters of the BP neural network, improve the calculation accuracy and efficiency of the neural network, and use the data set obtained in step 2 as a sample to train the neural network regression model to complete the establishment of the shielding dose prediction model; Step 4: The double chaos mapping method is used to improve the non-dominated sorting genetic algorithm NSGA-Ⅲ based on reference points, and the uniform reference point calculation method and non-dominated sorting method are used to evaluate the fitness function of multi-objective individuals. After multiple population iterations, the Pareto optimal solution set is obtained; Step 5: Analyze the Pareto solution set based on actual engineering application requirements and experience, and select the material property solution that maximizes the benefits.

2. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 1, characterized in that: In step 1, the multi-objective neutron composite shielding material property optimization model is: minF(x)=(f1(x),f2(x),...,f M (x)) T s.t.1≤x M ≤31 In the formula, F(x) is a multi-objective function, M is the target dimension, and f i (x) is the ith sub-objective function, x i represents the i-th property of the material.

3. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 1, characterized in that: In step 2, a unidirectional neutron surface source is placed at the center of the Monte Carlo model, the thickness range of the shielding material is set, and the radiation dose equivalent is evaluated using an F2 counting card and DE and DF cards.

4. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 1, characterized in that: Step 3 includes the following steps: Step 3.1, according to the number of sample input feature parameters m, the number of output labels n, and the empirical formula 1 < a < 10 to determine the topological structure of the BP neural network, traverse the range of the number of hidden layers, simulate and calculate the mean square error value MSE between the actual output and the predicted result of the test set, and determine the optimal number of hidden layer nodes h of the network; Step 3.2, introduce the improved particle swarm optimization algorithm to optimize the initial weight w and bias b of the neural network, select the mean square error between the actual output of the test set and the predicted result as the fitness function, calculate the fitness value of each particle, and update the population after priority sorting, and output the optimized optimal population. In order to prevent the improved particle swarm optimization algorithm from falling into the local optimum and premature convergence, set the random number rand; Step 3.3, use the optimal population output after optimization in step 3.2 as the initial value of the neural network parameters, define the number of training times, learning rate, training target minimum error, momentum factor, minimum performance gradient and maximum number of failures, set the activation function, use the Levenberg-Marquardt algorithm to improve the network's computing speed, start training until the termination condition is met, save the trained network net, and complete the establishment of the shielding dose prediction model.

5. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 4, characterized in that: In step 3.2, when the particle is updated, if rand < 0.5, the particle is updated using the following formula: X i (t+1)=X i (t)+η·V i (t)+c1·rand·(pbest i -X i (t))+c2·rand(gbest-X i (t)) Where, X i (t+1) is the position of the i-th particle at the t+1th iteration; V i (t) is the velocity of the ith particle at the tth iteration; η represents the inertia weight; c1 and c2 are learning factors; pbest i represents the current optimal individual of population i; gbest is the current global optimal particle; T is the maximum number of iterations.

6. The method for optimizing neutron shielding materials based on machine learning and chaos mapping NSGA-III as claimed in claim 4, characterized in that: In step 3.2, when the particles are updated, if rand ≥ 0.5, the individuals search and update in the global space with the improved Levy flight mechanism strategy, which increases the randomness and diversity of the population and can better balance the development and exploration of the algorithm.

7. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 1, characterized in that: Step 4 includes the following steps: Step 4.1, initialize the population size P, population dimension d, target dimension M, maximum number of iterations G, current number of iterations gen, individual size upper and lower limit thresholds y u ,y l , the threshold is consistent with the population dimension d, and a uniform initial population is generated using the Logistic-tent composite chaotic dynamics model; Step 4.2, perform crossover and mutation genetic operations on the initial parent population P(0) to obtain the offspring population Pp; Step 4.3, for two arbitrary individuals x1 and x2, if all sub-objective functions satisfy f j (x1)≤f j (x2), and there exists a sub-objective function such that f j (x1)<f j (x2), then individual x1 is said to dominate individual x2; if there is no dominance relationship between the two, x1 and x2 are said to be unrelated; merge the two generations of populations into Q(gen), and according to the above relationship, quickly sort the individuals in Q(gen) to form a non-dominated layer {F{1}, F{2}, ... F{L}} and store them in the next generation population P(gen+1) in sequence. If F{l} is the last non-dominated layer that is larger than the population size P for the first time, then P(gen+1)=F{1}∪F{2}∪...∪F{l-1}, calculate the reference point of the population in the non-dominated layer of F{l} and screen out a uniform population; Step 4.4, set an M-1 dimensional normalized hyperplane, which has the same inclination for all target axes and the intercept on each axis is not 0; Step 4.5, repeat steps 4.1 to 4.4, when gen≤G, the optimization ends.

8. The method for optimizing neutron shielding materials based on machine learning and chaos mapping NSGA-III as claimed in claim 7, characterized in that: Step 4.2 includes the following operations: A1: Chromosome crossover operation: Pp1=0.5×((1+γ)×P1+(1-γ)×P2) Pp2=0.5×((1-γ)×P1+(1+γ)×P2) Pp=Pp1∪Pp2 α＝2-β -μ-1 In the formula, two parent populations are selected: P1 = {P1(0), P3(0), ..., P N-1 (0)};P2={P2(0),P4(0),...,P N (0)}; μ is the crossover factor; α is the crossover condition factor; β is the crossover adjustment factor; γ is the crossover balance factor; Pp1 and Pp2 are the two offspring populations after crossover; for the random factor u, the chaotic sequence generated by the piecewise chaotic map can be described as: Where u(t) is the number of random factors at the tth iteration; p is 0.4; A2: Chromosome mutation operation: Pp=Pp+φ×(rand(1,d)<0.4)×(y u -y l ) Where Pp is the population undergoing mutation; is the variation adjustment factor; φ is the variation balance factor; rand(1,d) represents the generation of a matrix with 1 row and d columns whose elements are 0 to 1 random numbers; d is the population dimension; ν is the variation factor; u is a random factor, and the chaotic sequence is generated by Piecewise chaotic mapping.

9. The method for optimizing neutron shielding materials based on machine learning and chaos mapping NSGA-III according to claim 7, characterized in that: Step 4.4 includes the following operations: B1: Calculate the ideal point z for multi-objective optimization min : For an M-dimensional objective function, there is an ideal point in the jth dimension Where j = 1, 2...M; P is the size of the population to be screened; f ij represents the objective function of the jth dimension of the ith population; Y i is the i-th population, Y i ∈F{l}, F{l} is the population set of the lth layer after non-dominated sorting. Then the ideal point of the population in this iteration is Then, the target values ​​of all individuals in F{l} are transformed with the ideal point as reference to obtain the temporary standardized translation target f i '(Y i ) = f i (Y i )-z min , where the ideal point after translation becomes the zero vector; B2: Use the following formula to calculate the extreme point z on each target axis. j,max : In the formula, w j represents the extreme coordinates of the j-th dimension target, w j =(ε,ε,...1,..ε) T , ε=1×10 -6 and B3: These M extreme points form an M-1 dimensional linear hyperplane, and calculate its intercept a=[a1,a2,...,a M ], and use the intercept and temporary standardized target value to solve the standardized target value f″ of the individual target value according to the following formula j (y), complete the target structure normalization: In the formula, a j Represents the intercept in the direction of the target axis of the j-th dimension. B4: A set of uniform reference points is predefined on the hyperplane, the number of which is Where M is the number of targets to be optimized; p is the number of divisions of each target axis, and all reference points z r Connect the origin to form several reference lines c=z, and calculate the vertical distance from all individual targets to each reference line. The distance from the kth individual to each reference line is expressed as L k =(l k1 ,l k2 ,...l kH ), find the reference point corresponding to its minimum vertical distance, namely π(z r )=z r :argminL k , complete the association operations in sequence; B5: Traverse all reference points in turn, record the number of individuals o associated with them, and determine the reference point set J with the minimum number of individuals by mino s , randomly select any reference point And add the associated individuals that match it to P(gen+1); here, if mino=0, then after deleting the corresponding reference point set, re-execute this step until P(gen+1)=P.

10. The neutron shielding material optimization method based on machine learning and chaos mapping NSGA-III as claimed in claim 1, characterized in that: In step 5, any population of the Pareto solution set obtained is an optional solution with its own advantages, and a result in which any goal is better than other solutions can always be found; it is not that all design goals are optimal at the same time, but a collection of radiation shielding solutions in which each goal is relatively optimal but optimal overall.

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