Acceleration method for solving neutron noise problem by Monte Carlo method

Abstract

The invention discloses an acceleration method for solving a neutron noise problem through a Monte Carlo method, and the method comprises the steps: 1, constructing a neutron transport critical problem based on reactor core parameters, calculating a noise source item, and solving the neutron noise problem; 2, pre-dividing an iteration stage into an acceleration generation, a convergence generation, a redundancy generation and a statistical generation; 3, in an acceleration generation, realizing rapid convergence of real part distribution and imaginary part distribution of particles in the noise fission library by adopting less particle number simulation; 4, switching to normal particle number simulation when convergence is carried out, and dynamically monitoring a source particle distribution convergence state based on an online convergence judgment criterion; and 5, after convergence, skipping a redundant generation, directly entering a statistical generation, and counting and outputting a result. According to the method, a staged iteration mechanism and online convergence judgment are innovatively combined, convergence is greatly accelerated, and computing resource consumption is reduced. While the calculation precision is ensured, the efficiency bottleneck of the traditional Monte Carlo method in neutron noise analysis is overcome, and an efficient solution is provided for engineering-level Monte Carlo neutron noise simulation.

Description

Technical Field

[0001] The present invention belongs to the technical fields of dynamic reactor neutron noise calculation and particle transport calculation in nuclear reactor physics calculation, and particularly relates to an acceleration method for solving neutron noise problems by the Monte Carlo method. Background Art

[0002] The numerical simulation technology of neutron noise depends on the solution of complex neutron noise problems. For a long time, there have been two mainstream methods: the deterministic method and the Monte Carlo method. Deterministic methods include, for example, the finite difference method based on diffusion approximation, the method based on SP3 approximation, the discrete ordinate method, the finite element method, etc. Deterministic methods usually rely on spatial discretization and a certain degree of physical approximation. The calculation speed of deterministic methods is usually fast, but they also involve more theories and spatial approximations, and it is difficult to handle relatively complex curved geometries.

[0003] Neutron noise simulation based on the Monte Carlo method has fewer theoretical approximations, high geometric modeling accuracy, wide applicability to special reactor types, and can also provide high-precision reference solutions for other deterministic methods.

[0004] The methods for solving neutron noise equations by traditional Monte Carlo methods include: the weight cancellation method for changing track length counting, the fixed source algorithm for introducing pseudo cross-sections, and the traditional iterative method. Among them, the weight cancellation method for changing track length counting requires large-scale reconstruction of the program; the method of introducing pseudo cross-sections requires complete simulation of long single-particle histories; while the traditional iterative method requires a large number of iterations to converge the fission source distribution, the real and imaginary parts of noise particles in the neutron noise problem, and there are problems such as slow calculation convergence and lack of convergence criteria for noise problems. Summary of the Invention

[0005] To overcome the problems of slow convergence speed and low calculation efficiency of the traditional Monte Carlo iterative method for solving neutron noise equations, the purpose of the present invention is to provide an acceleration method for solving neutron noise problems by the Monte Carlo method. Based on the characteristics of neutron noise problems and the Monte Carlo method, the present invention performs algebraic pre-partitioning on the traditional iterative neutron noise solution process, which can effectively accelerate the convergence process.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] An acceleration method for solving neutron noise problems by the Monte Carlo method, comprising the following steps:

[0008] Step 1. Use a Monte Carlo program to construct a neutron transport critical problem based on the geometric and material perturbation parameters of the reactor core, calculate the neutron noise source term, and start iteratively solving the neutron noise problem;

[0009] Step 2. Before the iteration starts, preliminarily divide the iteration phase algebra into acceleration generations, convergence generations, redundant generations, and statistical generations;

[0010] Step 3. After the iteration starts, first enter the acceleration generation, and use one-tenth to one-thousandth of the normal number of particles to simulate and achieve rapid convergence of the real and imaginary parts of the noise fission library particles;

[0011] Step 4. After the acceleration generation ends, enter the convergence generation, switch to normal particle number simulation, and dynamically monitor the convergence state of the source particle distribution based on the online convergence determination criterion for neutron noise problems;

[0012] Step 5. After convergence, skip the redundant generation and directly enter the statistical generation to count the results and output.

[0013] Compared with the prior art, the present invention has the following outstanding advantages:

[0014] 1. The present invention adds an acceleration method of algebraic preliminary division to the previous Monte Carlo iteration calculation method, which can greatly improve the calculation efficiency;

[0015] 2. An online convergence determination criterion applicable to neutron noise calculation is introduced, reducing unnecessary calculations after convergence. The present invention retains the advantage of strong geometric adaptability of the Monte Carlo method, which is of great significance for further applying the Monte Carlo method to neutron noise analysis in engineering scenarios.

[0016] In summary, the present invention innovatively combines a phased iteration mechanism with an online convergence determination, greatly accelerating convergence and reducing computational resource consumption. While ensuring computational accuracy, it overcomes the efficiency bottleneck of the traditional Monte Carlo method in neutron noise analysis, providing an efficient solution for engineering-level Monte Carlo neutron noise simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a schematic flow chart of an acceleration method for solving neutron noise problems by a Monte Carlo method of the present invention.

[0018] Figure 2 It is a schematic diagram of algebraic preliminary division of an acceleration method for solving neutron noise problems by a Monte Carlo method of the present invention.

[0019] Figure 3 It is a schematic diagram of grid division of an online convergence determination criterion of an acceleration method for solving neutron noise problems by a Monte Carlo method of the present invention.

[0020] Figure 4 It is a schematic diagram of the determination effect of the real part convergence criterion in the present invention.

[0021] Figure 5 It is a schematic diagram of the determination effect of the imaginary part convergence criterion in the present invention.

[0022] Figure 6 This is a schematic diagram showing the determination effect of the real part to imaginary part ratio convergence criterion in the present invention. Specific embodiments

[0023] The present invention will be further described in detail below through specific embodiments.

[0024] As Figure 1 shown, an acceleration method for solving the neutron noise problem by a Monte Carlo method in the present invention is implemented by adopting the following technical solutions:

[0025] Step 1. Use a Monte Carlo program to construct a neutron transport critical problem based on parameters such as the geometry, materials, and perturbations of the reactor core, and calculate the neutron noise source term, and start to solve the neutron noise problem;

[0026] Step 2. As Figure 2 shown, before the start of iteration, the iteration stages are algebraically pre-divided into acceleration generations, convergence generations, redundant generations, and statistical generations;

[0027] Step 3. After the start of iteration, enter the acceleration generation, and use a small number of particles (usually dozens to thousands of times less than the normal number of particles) to simulate to achieve rapid convergence of the real part and imaginary part distributions of the noise fission library particles;

[0028] Step 4. After the acceleration generation ends, enter the convergence generation, switch to normal particle number simulation, and dynamically monitor the convergence state of the source particle distribution based on the online convergence determination criterion for the neutron noise problem; the definition process of the online convergence determination criterion is as follows:

[0029] First, as Figure 3 shown, taking the simplified C5G7 neutron noise benchmark problem as an example, the calculation region is divided into grid spaces, and the space is divided into N grid cells (as Figure 3 shown by the solid line), and then, for each grid cell, the real part weight ratio of the particles in the i-th grid is defined in turn, as shown in formula (1):

[0030]

[0031] In the formula: M i,real —— represents the sum of the real part weights of the particles in the i-th grid

[0032] M total,real —— represents the sum of the real part weights of all the particles in the grids

[0033] P i,real —— represents the share of the real part weight of the particles in the i-th grid in the total real part weight of the particles. Similarly, for each grid cell, the imaginary part weight ratio of the particles in the i-th grid is defined in turn, as shown in formula (2):

[0034]

[0035] Where: M i,imag —— Represents the sum of the imaginary part weights of the particles in the i-th grid

[0036] M total,imag —— Represents the sum of the imaginary part weights of all particles in the grids

[0037] P i,imag —— Represents the share of the imaginary part weight of the particles in the i-th grid in the total imaginary part weight of the particles. Then, the Shannon entropy of the real part is defined according to formula (1), as shown in formula (3):

[0038]

[0039] Where: H real —— Represents the Shannon entropy of the real part

[0040] Similarly, according to formula (2), the Shannon entropy of the imaginary part is defined as shown in formula (4):

[0041]

[0042] Where: H imag —— Represents the Shannon entropy of the imaginary part

[0043] Define the ratio of the imaginary part to the real part, as shown in formula (5):

[0044] R = |M total,imag / M total,real | (5)

[0045] Then, the stochastic oscillators of the real part, the imaginary part, and the ratio of the real part to the imaginary part are defined respectively as shown in formulas (6), (7), and (x):

[0046]

[0047] Where: —— Represents the Shannon entropy of the real part at the n-th iteration

[0048] —— Represents the maximum value of the Shannon entropy of the real part among p generations before the n-th iteration. p is a constant, usually taken as 20

[0049] —— Represents the minimum value of the Shannon entropy of the real part among p generations before the n-th iteration. p is a constant, usually taken as 20

[0050] K n,real —— Represents the stochastic oscillator of the real part at the n-th iteration

[0051]

[0052] In the formula: —— represents the imaginary part Shannon entropy of the nth iteration

[0053] —— represents the maximum value of the imaginary part Shannon entropy between p generations before the nth iteration. p is a constant, generally taken as 20

[0054] —— represents the minimum value of the imaginary part Shannon entropy between p generations before the nth iteration. p is a constant, generally taken as 20

[0055] K n,imag —— represents the random oscillator of the imaginary part of the nth iteration

[0056]

[0057] In the formula: R n —— represents the ratio of the real part to the imaginary part of the nth iteration

[0058] —— represents the maximum value of the ratio of the real part to the imaginary part between p generations before the nth iteration. p is a constant, generally taken as 20

[0059] —— represents the minimum value of the ratio of the real part to the imaginary part between p generations before the nth iteration. p is a constant, generally taken as 20

[0060] K n,ratio —— represents the random oscillator of the ratio of the real part to the imaginary part of the nth iteration

[0061] When the calculation reaches convergence, R n The sequence will randomly oscillate around the convergence stable value. It can be seen from formula (6), formula (7), and formula (8) that at convergence, since the random oscillator is a certain value between the maximum and minimum values of a period of its history, the random oscillator will oscillate between 0 and 1. The random oscillator K n,real , K n,imag and K n,ratio The expected value at convergence is 0.5. Based on this characteristic, the online convergence judgment criterion is defined as that the convergence is satisfied when the inequalities (9), (10), and (11) are simultaneously satisfied:

[0062]

[0063] In the formula: ε—— constant, used to constrain the range of the random oscillator deviating from 0.5, generally taken as 0.1

[0064] —— represents the random oscillator of the real part of the (n - m + 1)-th generation before the n-th iteration. m is a constant, generally taken as 50

[0065] —— represents the average value of the random oscillators of the real parts of these m generations from the (n - m + 1)-th generation to the n-th generation before the n-th iteration. m is a constant, generally taken as 50

[0066] —— represents the random oscillator of the imaginary part of the (n - m + 1)-th generation before the n-th iteration. m is a constant, generally taken as 50

[0067] —— represents the average value of the random oscillators of the imaginary parts of these m generations from the (n - m + 1)-th generation to the n-th generation before the n-th iteration. m is a constant, generally taken as 50

[0068] —— represents the random oscillator of the ratio of the real part to the imaginary part of the (n - m + 1)-th generation before the n-th iteration. m is a constant, generally taken as 50

[0069] —— represents the average value of the random oscillators of the ratios of the real part to the imaginary part of these m generations from the (n - m + 1)-th generation to the n-th generation before the n-th iteration. m is a constant, generally taken as 50.

[0070] Step 5. After determining convergence using the convergence criterion, skip redundant generations, directly enter the statistical generation, and statistically record the results and output them.

[0071] Taking the simplified C5G7 neutron noise benchmark problem as an example, the method of the present invention is applied to neutron noise calculation, and the Shannon entropy of the real part, the imaginary part, and the ratio of the real part to the imaginary part in its iterative process is recorded. The results are as Figures 4 to 5 shown. As Figure 4 shown, it is a schematic diagram of the determination effect of the real part convergence criterion. It can be seen from the figure that the real part converges relatively fast and reaches convergence quickly at the beginning of the calculation. As Figure 5 shown, it is a schematic diagram of the determination effect of the imaginary part convergence criterion in the present invention. It can be seen from the figure that the imaginary part increases very regularly after the start of the calculation and reaches convergence at about 300 generations. As Figure 6 shown, it is a schematic diagram of the determination effect of the convergence criterion of the ratio of the real part to the imaginary part in the present invention. It can be seen from the figure that this ratio gradually increases after the start of the calculation. By applying this convergence determination criterion, its convergence point can be accurately determined as the 677-th generation. After reaching convergence, statistics start, and unnecessary calculation iterations are discarded. In the simplified C5G7 neutron noise benchmark problem, the present invention can accurately determine the convergence point, and applying this method greatly improves the calculation efficiency.

Claims

1. An acceleration method for solving the neutron noise problem by the Monte Carlo method, characterized in that, The method includes the following steps: Step 1. Use a Monte Carlo program to construct a neutron transport critical problem based on the geometric and material perturbation parameters of the core, calculate the neutron noise source term, and start iteratively solving the neutron noise problem; Step 2. Before the iteration starts, pre-divide the iteration stage algebra into acceleration generations, convergence generations, redundant generations, and statistical generations; Step 3. After the iteration starts, first enter the acceleration generation, and use one-tenth to one-thousandth of the normal number of particles to simulate and achieve rapid convergence of the real and imaginary parts of the noise fission library particles; Step 4. After the acceleration generation ends, enter the convergence generation, switch to normal particle number simulation, and dynamically monitor the convergence state of the source particle distribution based on the online convergence determination criterion for the neutron noise problem; Step 5. After convergence, skip the redundant generation and directly enter the statistical generation, and then statistically output the results.

2. The acceleration method for solving the neutron noise problem by the Monte Carlo method according to claim 1, wherein An online convergence determination criterion similar to Shannon entropy, which includes real and imaginary parts and is applicable to neutron noise Monte Carlo calculations, is used. The specific definition and application method of this online convergence determination criterion are as follows: First, divide the neutron noise calculation region into grid spaces, divide the space into N grid cells, and then, for each grid cell, sequentially define the proportion of the real part weight of the particles in the i-th grid, as shown in formula (1): In the formula: M i,real —— represents the sum of the real part weights of the particles in the i-th grid M total,real —— represents the sum of the real part weights of the particles in all grids P i,real —— represents the share of the real - part weight of the particles in the \(i\) - th grid in the total real - part weight of the particles Similarly, for each grid cell, sequentially define the proportion of the imaginary part weight of the particles in the i-th grid, as shown in formula (2): In the formula: M i,imag —— represents the sum of the imaginary part weights of the particles in the i-th grid M total,imag —— Represents the sum of the imaginary part weights of the particles in all grids P i,imag —— represents the share of the imaginary part weight of the particles in the i-th grid in the total imaginary part weight of the particles. Next, the Shannon entropy of the real part is defined according to formula (1), as shown in formula (3): Where: H real —— Shannon entropy representing the real part Similarly, according to formula (2), define the Shannon entropy of the imaginary part as shown in formula (4): where: H imag —— Shannon entropy representing the imaginary part Define the ratio of the imaginary part to the real part, as shown in formula (5): R = |M total,imag / M total,real |(5) Then, respectively define the random oscillators of the real part, the imaginary part, and the ratio of the real part to the imaginary part as shown in formula (6), formula (7), and formula (8): In the formula: —— represents the real part of the Shannon entropy for the n-th iteration —— Represents the maximum value of the real - part Shannon entropy among p generations before the n - th iteration —— Represents the minimum value K of the real - part Shannon entropy among p generations before the n - th iteration n,real —— Represents the stochastic oscillator of the real part in the n - th iteration In the formula: —— represents the imaginary part Shannon entropy of the n-th iteration —— Represents the maximum value of the imaginary part Shannon entropy among p generations before the nth iteration —— Represents the minimum value K of the imaginary part Shannon entropy among p generations before the nth iteration n,imag —— Represents the stochastic oscillator of the imaginary part in the nth iteration In the formula: R n —— represents the ratio of the real part to the imaginary part in the n-th iteration —— represents the maximum value of the ratio of the real part to the imaginary part among p generations before the nth iteration —— represents the minimum value of the ratio of the real part to the imaginary part between p generations before the nth iteration K n,ratio —— a random oscillator representing the ratio of the real part to the imaginary part in the n-th iteration When the calculation reaches convergence, R n the sequence will randomly oscillate around the convergence stable value; it can be seen from formulas (6), (7), and (8) that at convergence, since the stochastic oscillator is a value between the maximum and minimum of a period of its history, the stochastic oscillator will oscillate between 0 and 1; the stochastic oscillator K n,real , K n,imag and K n,ratio has an expected value of 0.5 at convergence. Based on this property, the online convergence judgment criterion is defined as that convergence is achieved when inequalities (9), (10), and (11) are satisfied simultaneously: In the formula: ε——constant, used to constrain the range of the random oscillator deviating from 0.5 —— represents a random oscillator of the real part of the (n - m + 1)-th generation before the n-th iteration —— represents the average value of the real part of the random oscillator for these m generations between the (n - m + 1)-th generation and the n-th generation before the n-th iteration —— represents a random oscillator of the imaginary part of the (n - m + 1)-th generation before the n-th iteration —— represents the average value of the imaginary part of the random oscillators of these m generations between the (n - m + 1)-th generation and the n-th generation before the n-th iteration —— a random oscillator representing the ratio of the real part to the imaginary part of the (n - m + 1)-th generation before the n-th iteration —— represents the average value of the random oscillator of the ratio of the real part to the imaginary part of these m generations between the (n - m + 1)-th generation and the n-th generation before the n-th iteration.

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