A method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method

Abstract

A method for predicting reactor neutron disturbance parameters based on an unstructured grid discrete ordinate method, based on disturbance parameters, calculates frequency domain neutron noise or time domain neutron noise to obtain a neutron noise spectrum and generates a data set for training a neural network, and then predicts disturbance parameters based on the neutron noise collected in real time through the trained neural network. The present invention uses frequency domain analysis and time domain analysis to describe the neutron noise caused by random disturbance of the neutron cross section in the reactor, and uses the reactor neutron noise inversion based on an artificial neural network model to infer the actual neutron cross section disturbance parameters, providing an important basis for online monitoring and fault diagnosis of the reactor.

Description

Technical Field

[0001] The invention relates to a technology in the field of reactor control, in particular to a method for predicting reactor neutron disturbance parameters based on an unstructured grid discrete ordinate method. Background Art

[0002] In the actual process of steady-state operation of a nuclear reactor, the neutron flux density of the reactor does not ideally maintain a constant value, but is in a random fluctuation state that continuously fluctuates around the steady-state value. This random fluctuation is called the neutron noise of the reactor.

[0003] The neutron noise phenomenon indicates that there is a disturbance in the reactor, causing the reactor's operating state to deviate from normal, which has an adverse impact on the economy and safety of reactor operation. Therefore, it is necessary to establish a neutron noise calculation model and an inversion model to assist the online monitoring and fault diagnosis of the reactor. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention proposes a method for predicting reactor neutron perturbation parameters based on an unstructured grid discrete ordinate method, which uses frequency domain analysis and time domain analysis to describe the neutron noise caused by random perturbations of the neutron cross section in the reactor, and uses the reactor neutron noise inversion to infer the actual neutron cross section disturbance parameters based on an artificial neural network model, thereby providing an important basis for online monitoring and fault diagnosis of the reactor.

[0005] The present invention is achieved through the following technical solutions:

[0006] The present invention relates to a method for predicting reactor neutron disturbance parameters based on an unstructured grid discrete ordinate method. Based on disturbance parameters, a neutron noise spectrum is obtained by calculating frequency domain neutron noise or time domain neutron noise and a data set for training a neural network is generated. Then, the disturbance parameters are predicted based on the neutron noise collected in real time through the trained neural network.

[0007] The neural network model comprises: an input layer, several intermediate layers and an output layer, wherein: the input layer contains the real part Reδφ and the imaginary part Imδφ (or the amplitude and phase) of the neutron noise at the selected position; the output layer contains the spatial position coordinates r of the disturbance source , frequency f pert and amplitude A pert ; The middle layer has several neuron layers, each layer contains several neurons, and the output of each neuron Where: θ i represents the output of the neuron in the i-th layer; f represents the activation function; w i represents the weight coefficient of the neurons in the i-th layer; b i Represents the bias of the neurons in the i-th layer.

[0008] Technical Effects

[0009] The present invention establishes a frequency domain neutron noise calculation model and an inversion model based on unstructured grid neutron transport technology and artificial neural network technology. Compared with the existing frequency domain neutron noise solution technology based on discrete ordinate method, which can only establish a structured grid model of the reactor, has insufficient adaptability to reactors with complex geometric structures, and does not have the ability to invert reactor disturbance parameters based on neutron noise, the present invention uses unstructured grid technology to improve the processing ability of frequency domain and time domain neutron noise calculation models for complex geometries, and at the same time expands the ability to carry out inversion analysis based on actual neutron noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0010] Figure 1 It is a flow chart of the present invention.

[0011] Figure 2 This is a flow chart of the frequency domain neutron noise calculation method;

[0012] Figure 3 It is a flow chart of the time domain neutron noise calculation method;

[0013] Figure 4 This is a schematic diagram of the neural network structure of the neutron noise inversion model;

[0014] Figure 5 Flowchart of a method for generating training data for a neutron noise inversion model;

[0015] Figure 6 The flowchart of neural network training for neutron noise inversion model;

[0016] Figure 8 is the spatial distribution diagram of the normalized fast group neutron noise spectrum amplitude;

[0017] Fig. 9 is the spatial distribution diagram of the normalized thermal group neutron noise spectrum amplitude;

[0018] Fig.10 is the normalized sub-diagonal direction fast group neutron noise spectrum amplitude distribution diagram;

[0019] Fig.11 It is the distribution diagram of the normalized sub-diagonal direction thermal group neutron noise spectrum amplitude. DETAILED DESCRIPTION

[0020] like Figure 1 As shown, this embodiment relates to a method for predicting reactor neutron disturbance parameters based on an unstructured grid discrete ordinate method, comprising:

[0021] Step 1: Figure 5 As shown, the data set is generated by the neutron noise calculation model, including:

[0022] 1.1) Set the hyperparameters for dataset generation and generate a set of perturbation parameters required for neutron noise calculation;

[0023] 1.2) According to the basic parameters of the reactor and the disturbance parameters of its neutron noise behavior, construct the frequency domain neutron noise equation or the time domain neutron dynamics equation;

[0024] The frequency domain neutron noise equation is specifically:

[0025] Of which: Equivalent dynamic total cross section Equivalent Dynamic Fission Spectrum Noise source terms

[0026] The time domain neutron dynamics equation is specifically:

[0027] in: v g represents the neutron velocity of the gth group; μ m , η m , m H represents the cosine of the angle between the m direction and the three coordinate axes in the Cartesian coordinate system; z Indicates the height of the node along the z-axis; Σ t,g (r, t) represents the total cross section of the gth group; represents the neutron angular flux density of the gth group in the m direction; G represents the energy group number; I represents the number of delayed neutron precursor nuclei; χ g represents the prompt neutron energy spectrum of the fission reaction of group g; k eff represents the effective proliferation factor; β represents the total delayed neutron fraction; (νΣ f ) g represents the neutron production cross section of the gth group;

[0028] Σ g′→g (r, t) represents the scattering cross section from the g'th group to the gth group; φ g (r, t) represents the neutron flux density of the g-th group; χ i,g represents the delayed neutron energy spectrum of the gth group in the i-th group of delayed neutron precursor nuclei; λ i represents the decay constant of the i-th group of delayed neutron precursor nuclei; C i (r, t) represents the nuclear density of the i-th group of delayed neutron precursors.

[0029] 1.3) Solving the frequency domain neutron noise equation or the time domain neutron dynamics equation constructed in step 1.2 to obtain the neutron noise spectrum;

[0030] like Figure 2As shown, the method for solving the frequency domain neutron noise equation to obtain the neutron noise spectrum specifically includes: using a discrete ordinate transport solver to solve the frequency domain neutron noise equation to obtain the complex form of the angular neutron noise Integrating it over the angle gives the neutron noise spectrum Where: w m represents the weight in the m direction;

[0031] like Figure 3 As shown, the method for solving the time-domain neutron kinetic equation to obtain the neutron noise spectrum specifically includes:

[0032] Step i, constructing a space-time neutron dynamics equation group of the reactor according to the basic parameters of the reactor and the disturbance parameters of the neutron noise behavior of the reactor, and determining the time step of the transient solution;

[0033] Step ii, using transient solution technology to calculate the space-time neutron dynamics equations, obtain the neutron flux at all time steps, and form a series of neutron flux time series;

[0034] Step iii: using discrete Fourier transform to transform the neutron flux time series into a neutron noise spectrum.

[0035] 1.4) Repeat steps 1.2 to 1.3 until all perturbation parameters are traversed, and the perturbation parameters and their corresponding neutron noise spectra are used as data pairs to obtain a data set for training the neural network model.

[0036] Step 2) Use the generated dataset to Figure 6 The training process shown is as follows Figure 4 The neural network model shown specifically includes:

[0037] 2.1) Set the hyperparameters of the neural network and initialize the neural network, and randomly generate the weights and biases of each neuron in the neural network;

[0038] 2.2) After the neutron noise spectrum in the training set is input into the neural network in sequence to obtain the corresponding disturbance parameter prediction value, the loss between it and the actual disturbance parameter is calculated, specifically: Where: Reδφ is the real part of the neutron noise spectrum; Imδφ is the imaginary part of the neutron noise spectrum; r source,i , are the predicted value and actual value of the disturbance position respectively; f pert,i , are the predicted value and actual value of the disturbance frequency respectively; A pert,i , are the predicted value and actual value of the disturbance amplitude respectively; λ r,i , f,i ,

[0039] λ A,i are the hyper parameters of each item.

[0040] 2.3) Using the loss function and optimization algorithm, optimize the parameters of each neuron in the current neural network until all the data in the training set are traversed;

[0041] 2.4) Calculate the loss function of the current neural network. If the loss function is less than the allowable error range, the training ends; otherwise, re-execute steps 2.2) to 2.3);

[0042] Step 3) Using the trained neural network model, the reactor disturbance parameters are predicted based on the neutron noise spectrum.

[0043] After specific actual experiments, the neutron noise benchmark C4V of two groups of four components is calculated as an example. The core consists of two UO2 fuel assemblies and two MOX fuel assemblies. Figure 7 As shown. Each component consists of 17×17 square grid cells, the side length of the square grid cell is 1.26cm, of which 25 grid cells are guide tubes and the remaining grid cells are fuel grid cells. The absorption cross section of the fuel grid cell with coordinates (19, 16) is disturbed, the disturbance amplitude is 5% of the steady-state absorption cross section, and the disturbance frequency is 1Hz. The neutron noise calculation for this core obtains the spatial distribution of the normalized neutron noise spectrum amplitude, as shown in Figures 8 to 11 Compared with the calculated results of the time-domain neutron noise spectrum, the maximum relative errors of the normalized sub-diagonal neutron noise spectrum amplitudes in the fast group and the thermal group are 0.67% and 2.99%, respectively.

[0044] The present invention adopts an unstructured grid transport method to establish a neutron noise calculation model and performs neutron noise inversion based on an artificial neural network. Compared with the existing structured grid diffusion method, it has high-fidelity calculation capabilities for processing complex geometries.

[0045] The above-mentioned specific implementation can be partially adjusted in different ways by those skilled in the art without departing from the principle and purpose of the present invention. The protection scope of the present invention shall be based on the claims and shall not be limited by the above-mentioned specific implementation. Each implementation scheme within its scope shall be subject to the constraints of the present invention.

Claims

1. A method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method, characterized in that: Based on the disturbance parameters, the neutron noise spectrum is obtained by calculating the frequency domain neutron noise or the time domain neutron noise and generating a data set for training the neural network. Then, the disturbance parameters are obtained by predicting the neutron noise collected in real time through the trained neural network, which specifically includes: Step 1: Generate a data set through a neutron noise calculation model, including: 1.1) Set the hyperparameters for dataset generation and generate a set of perturbation parameters required for neutron noise calculation; 1.2) According to the basic parameters of the reactor and the disturbance parameters of its neutron noise behavior, construct the frequency domain neutron noise equation or the time domain neutron dynamics equation; The frequency domain neutron noise equation is specifically: in: is the equivalent dynamic total cross section, Equivalent dynamic fission spectrum, S g Noise source term, μ m , η m , m H represents the cosine of the angle between the m direction and the three coordinate axes in the Cartesian coordinate system; z Indicates the height of the node along the z-axis; represents the neutron noise spectrum of the g-th group in the m direction; G represents the energy group number; (νΣ f ) k represents the neutron production cross section of the kth group; Σ k→g (r) represents the scattering cross section from the kth group to the gth group; The time domain neutron dynamics equation is specifically: in: i=1,2,...,I,v g represents the neutron velocity of the gth group; μ m , η m , m H represents the cosine of the angle between the m direction and the three coordinate axes in the Cartesian coordinate system; z Indicates the height of the node along the z-axis; Σ t,g (r, t) represents the total cross section of the gth group; represents the neutron angular flux density of the gth group in the m direction; G represents the energy group number; I represents the number of delayed neutron precursor nuclei; χ g represents the prompt neutron energy spectrum of the fission reaction of group g; k eff represents the effective proliferation factor; β represents the total delayed neutron fraction; (νΣ f ) k represents the neutron production cross section of the kth group; Σ k→g (r, t) represents the scattering cross section from the kth group to the gth group; φ k (r, t) represents the flux density of the sub-scalar in the kth group; χ i,g represents the delayed neutron energy spectrum of the gth group in the i-th group of delayed neutron precursor nuclei; λ i represents the decay constant of the i-th group of delayed neutron precursor nuclei; C i (r, t) represents the nuclear density of the delayed neutron precursors in the i-th group; 1.3) Solving the frequency domain neutron noise equation or the time domain neutron dynamics equation constructed in step 1.2 to obtain the neutron noise spectrum; 1.4) Repeat steps 1.2 to 1.3 until all disturbance parameters are traversed, and the disturbance parameters and their corresponding neutron noise spectra are used as data pairs to obtain a data set for training the neural network model; Step 2) Use the generated data set to train the neural network model, specifically including: 2.1) Set the hyperparameters of the neural network and initialize the neural network, and randomly generate the weights and biases of each neuron in the neural network; 2.2) After the neutron noise spectrum in the training set is input into the neural network in sequence to obtain the corresponding disturbance parameter prediction value, the loss between it and the actual disturbance parameter is calculated, specifically: Where: Reδφ is the real part of the neutron noise spectrum; Imδφ is the imaginary part of the neutron noise spectrum; r source,i , are the predicted value and actual value of the disturbance position respectively; f pert,i , are the predicted value and actual value of the disturbance frequency respectively; A pert,i , are the predicted value and actual value of the disturbance amplitude respectively; λ r,i , f,i , A,i are the hyperparameters of each item respectively; 2.3) Using the loss function and optimization algorithm, optimize the parameters of each neuron in the current neural network until all the data in the training set are traversed; 2.4) Calculate the loss function of the current neural network. If the loss function is less than the allowable error range, the training ends; otherwise, re-execute steps 2.2) to 2.3); Step 3) Using the trained neural network model, the reactor disturbance parameters are predicted based on the neutron noise spectrum.

2. The method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method according to claim 1 is characterized in that: The neural network model comprises: an input layer, several intermediate layers and an output layer, wherein: the input layer contains the real part Reδφ and the imaginary part Imδφ of the neutron noise spectrum at the selected position; the output layer contains the spatial position coordinates r of the disturbance source , frequency f pert and amplitude A pert ; The middle layer has several neuron layers, each layer contains several neurons, and the output of each neuron Where: θ i represents the output of the neuron in the i-th layer; f represents the activation function; w i represents the weight coefficient of the neurons in the i-th layer; b i Represents the bias of the neurons in the i-th layer.

3. The method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method according to claim 1, characterized in that: The neutron noise spectrum is obtained by constructing a frequency domain neutron noise equation or a time domain neutron noise equation and correspondingly calculating the frequency domain neutron noise or the time domain neutron noise.

4. The method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method according to claim 1, characterized in that: The method for solving the frequency domain neutron noise equation to obtain the neutron noise spectrum specifically includes: using a discrete ordinate transport solver to solve the frequency domain neutron noise equation to obtain the complex form of angular neutron noise Integrating it over the angle gives the neutron noise spectrum Where: w m Represents the weight in the m direction.

5. The method for predicting reactor neutron disturbance parameters based on unstructured grid discrete ordinate method according to claim 1, characterized in that: The method of solving the time-domain neutron dynamics equation to obtain the neutron noise spectrum specifically includes: Step i, constructing a space-time neutron dynamics equation group of the reactor according to the basic parameters of the reactor and the disturbance parameters of the neutron noise behavior of the reactor, and determining the time step of the transient solution; Step ii, using transient solution technology to calculate the space-time neutron dynamics equations, obtain the neutron flux at all time steps, and form a series of neutron flux time series; Step iii: using discrete Fourier transform to transform the neutron flux time series into a neutron noise spectrum.

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