A reactor core thermal coupling calculation method based on an embedded physical knowledge neural network.

Abstract

This invention discloses a method for calculating nuclear thermal coupling in a reactor core based on an embedded physical knowledge neural network. The steps are as follows: 1. Divide the reactor core into nodes; 2. Initialize the neutron physics field parameters and thermal-hydraulic parameters of the core; 3. Build, train, and save the embedded physical knowledge neural network model; 4. Use the saved model to predict the neutron number density at each node of the core to obtain the neutron flux distribution; 5. Calculate the core power distribution based on the neutron flux distribution; 6. Use a system analysis program to calculate and update t. n+1 7. Calculate and update the reactivity of each node in the core; 8. Determine if the specified calculation time has been reached. If yes, end the calculation; otherwise, return to step 4. This invention's method, based on an embedded physical knowledge neural network, provides an accurate and efficient calculation method for solving the neutron physics and thermal field distribution in the reactor core, which is of great significance for reactor design optimization.

Description

Technical Field

[0001] This invention belongs to the field of nuclear thermal coupling calculation technology of reactor core, and particularly relates to a nuclear thermal coupling calculation method for reactor core based on an embedded physical knowledge neural network. Background Technology

[0002] The core of a nuclear reactor contains a complex nuclear-thermal coupled physical field. Neutron kinetic parameters determine the core power distribution, thus affecting the thermal-hydraulic state. These thermal-hydraulic parameters, in turn, influence the neutron physical field through reactivity feedback and other mechanisms. A coupling interface was developed to simultaneously call both the neutron kinetics and thermal-hydraulic programs for data transfer, enabling the analysis and calculation of the nuclear-thermal coupled physical field.

[0003] Currently, one-dimensional system programs and CFD programs exist for nuclear-thermal coupling calculations of reactor cores. However, the accuracy of neutron physics field calculations using system programs is relatively low, while CFD programs have slow convergence speeds and consume significant computational resources during coupling calculations. At present, there is a lack of fast, efficient, and high-precision nuclear-thermal coupling calculation programs for reactor cores. Summary of the Invention

[0004] To fill the gaps in the existing technology, the present invention aims to provide a reactor core thermal coupling calculation method based on an embedded physical knowledge neural network, which can quickly, efficiently and accurately solve the reactor core thermal coupling physical field, and is of great significance for reactor core design optimization.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] The reactor core thermal coupling calculation method based on an embedded physical knowledge neural network includes the following steps:

[0007] Step 1: Determine the reactor core geometry and perform node division, dividing it into m nodes axially and n rings radially;

[0008] Step 2: Initialize the state parameters, which includes the following:

[0009] Step 2-1: Initialize the core fuel, coolant temperature, power, thermal-hydraulic state parameters;

[0010] Step 2-2: Initialize the reactivity and neutron number density of each node in the reactor core;

[0011] Step 3: t n At any time, an embedded physical knowledge neural network is built in the deep learning framework DeepXDE, and the built embedded physical knowledge neural network is trained and optimized to solve the neutron diffusion equation and obtain a model for calculating the neutron number density of each node in the reactor core.

[0012] Step 4: Use the trained model to predict the neutron number density n(r,t) at each node of the core and calculate the neutron flux distribution in the core;

[0013] Step 5: Convert the core neutron flux distribution obtained in Step 4 into the core power distribution using the following formula:

[0014] P(r,t)=E f Σ f5 φV

[0015] In the formula:

[0016] P(r,t): t n The power distribution of the node at time r;

[0017] E f The energy released in each fission;

[0018] Σ f5 :U 235 Macroscopic cross section of thermal neutrons;

[0019] φ: Neutron flux in the node;

[0020] V: The volume of the node;

[0021] Step 6: Input the core power distribution obtained in Step 5 as the energy source term into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR. This software is a one-dimensional system analysis program, which calculates t. n+1 At any given moment, the thermal-hydraulic state parameters of each node in the reactor core are: coolant temperature and fuel temperature.

[0022] Step 7: Calculate t based on the core thermal-hydraulic parameters and reactivity feedback relationship obtained in Step 6. n+1 Total reactivity of each node at any given time;

[0023] ρ=ρ0+ρ ext +ρ D +ρ f,a +ρ f,r +ρ c

[0024] In the formula:

[0025] ρ——Step length end t n+1 Total reactivity at any given time point;

[0026] ρ0——Initial step size t n Total reactivity at any given time point;

[0027] ρ ext —External reactivity introduced by nodes within the Δτ time step;

[0028] ρ D—Reactivity caused by the fuel Doppler effect within the time step Δτ;

[0029] ρ f,a —Reactivity caused by axial thermal expansion of fuel within the time step Δτ;

[0030] ρ f,r —Reactivity caused by radial thermal expansion of fuel within the time step Δτ;

[0031] ρ c —Reactivity caused by the thermal expansion of the coolant within the time step Δτ;

[0032]

[0033] ρ f,a =α f,a (T f -T f,0 )

[0034] ρ f,r =α f,r (T f -T f,0 )

[0035] ρ c =α c (T c -T c,0 )

[0036] In the formula:

[0037] K D —Fuel Doppler coefficient;

[0038] α f,a —Fuel axial thermal expansion feedback coefficient;

[0039] α f,r —Fuel radial thermal expansion feedback coefficient;

[0040] α c —Coefficient of thermal expansion of coolant;

[0041] T f ——Step length initial t n fuel temperature at any given time point;

[0042] T f,0 ——Previous step long initial t n-1 fuel temperature at any given time point;

[0043] T c ——Step length initial t n Coolant temperature at any given time point;

[0044] T c,0——Previous step long initial t n-1 Coolant temperature at any given time point;

[0045] Step 8: t n+1 Time as a new t n At each point, repeat steps 4 through 7 until the specified calculation time is reached.

[0046] Step 3 is as follows:

[0047] Step 3-1: Build the neural network structure in the deep learning framework DeepXDE;

[0048] A fully connected neural network structure is adopted, and the depth, number of neurons in the intermediate layers, activation function, boundary weights, learning rate, optimizer and training times are set. The network is initialized using Gaussian random sampling method.

[0049] Step 3-2: Record the output of the fully connected layer of the neural network built in Step 3-1: the predicted neutron number density value n for each node. pred The number density of slow-emission neutron precursor nuclei C ipred ;

[0050] Step 3-3: Calculate the loss value of the neural network with embedded physics knowledge, which includes three parts: PDE operator loss of the neutron diffusion equation, observation loss, and regularization loss.

[0051] 1) Calculate the PDE operator loss of the neutron diffusion equation, specifically including the following:

[0052] a. The neutron diffusion equation is as follows:

[0053]

[0054] In the formula:

[0055] n(r,t): t n Neutron number density at position r at time r;

[0056] S(r,t): t n External neutron number density at position r at time r;

[0057] ρ(r,t): t n Total reactivity of the node at time r;

[0058] β: Total proportion of delayed neutron emission;

[0059] Λ: Neutron generation time;

[0060] λ i : Decay constant of the i-th group of delayed neutron precursor nuclei;

[0061] C i(r,t): The number density of the i-th delayed neutron precursor nuclei at position r at time t;

[0062] β i : The share of delayed neutron emission in group i;

[0063] b. Use the automatic differentiation function in the DeepXDE deep learning framework to calculate n(r,t) and respectively. Derivatives with respect to time and space;

[0064] c. Constructing the PDE operator for the neutron diffusion equation:

[0065]

[0066] In the formula:

[0067] n (t) : n(r,t) is the first derivative with respect to time t;

[0068] n (rr) : n(r,t) is the second derivative of n(r,t) with respect to position r;

[0069] n pred The neural network's prediction of n(r,t);

[0070] C ipred Neural networks for C i Predicted value of (r,t);

[0071] d. Calculate the PDE operator loss using the DeepXDE deep learning framework. o ;

[0072] 2) Calculate the value of the total loss function, Loss:

[0073] Loss=λ d Loss d +λ o Loss o +λ reg Loss2

[0074] In the formula:

[0075] λ d : Observation loss coefficient;

[0076] λ o : PDE operator loss coefficient;

[0077] λ reg Regularization coefficient;

[0078] Loss d : Observation loss;

[0079] Loss2: L2 regularization loss;

[0080]

[0081] In the formula:

[0082] N: Number of samples;

[0083] w ij The weights connecting the i-th sample and the j-th neuron;

[0084] Step 3-4: Determine whether the target value of the training rounds or loss function set in Step 3-1 has been reached. If so, terminate the training; otherwise, proceed to Step 3-5.

[0085] Step 3-5: Repeat steps 3-2 to 3-4 to train and optimize the embedded physical knowledge neural network;

[0086] 1) Read the output of the fully connected layer in each step of step 3-2, calculate the loss function value in step 3-3 and minimize the loss;

[0087] 2) Record the total loss function value and total loss decrease data in step 3-3 after each training session;

[0088] Steps 3-6: Save the trained model used to calculate the neutron number density at each node of the reactor core.

[0089] Compared with the prior art, the present invention has the following advantages:

[0090] 1. This invention calculates thermal-hydraulic parameters based on a one-dimensional system analysis program and calculates neutron physics fields based on a neural network method with embedded physical knowledge. This ensures both high calculation accuracy of the neutron physics fields and fast convergence speed and low computational resource consumption in the entire coupled calculation process.

[0091] After the embedded physical knowledge neural network model is trained and saved, the neutron number density of each node in the core can be quickly solved by simply calling the trained model at each time step. This ensures the calculation speed of the neutron physics field, thereby improving the calculation speed of core thermal coupling, and the consumption of computing resources is low.

[0092] 2. This invention enables nuclear-thermal coupling calculation and analysis of the reactor core through bidirectional data exchange between neutron physics field parameters and thermal-hydraulic parameters in the reactor core. Attached Figure Description

[0093] Figure 1 This is a flowchart of a reactor core thermal coupling calculation method based on an embedded physical knowledge neural network.

[0094] Figure 2A schematic diagram of the core node partitioning;

[0095] Figure 3 A flowchart for solving the neutron flux distribution in the reactor core using a neural network with embedded physical knowledge. Detailed Implementation

[0096] The present invention will now be described in detail with reference to the accompanying drawings.

[0097] This invention provides a reactor core thermal coupling calculation method based on an embedded physical knowledge neural network, the specific process of which is as follows: Figure 1 As shown, it includes the following steps:

[0098] Step 1: Determine the reactor core geometry and perform node division, such as... Figure 2 As shown: The reactor core is cylindrical with a height of h and a radius of r, divided into 10 nodes axially and 4 rings radially;

[0099] Step 2: Initialize the state parameters, which includes the following:

[0100] Step 2-1: Initialize the thermal-hydraulic state parameters of each node in the reactor core: fuel temperature and coolant temperature, core power;

[0101] Step 2-2: Initialize the neutron physics parameters of each node in the core: reactivity and neutron number density;

[0102] Step 3: t n At any given time, an embedded physical knowledge neural network is built within the DeepXDE deep learning framework. This network is then trained and optimized to solve the neutron diffusion equation, resulting in a model for calculating the neutron number density at each node of the reactor core. Figure 3 Specifically, it includes the following:

[0103] Step 3-1: Build the neural network structure in the deep learning framework DeepXDE, which includes the following:

[0104] A fully connected neural network structure is used, with a depth of l=16, the number of neurons in the intermediate layers s=20, the activation function is the hyperbolic tangent function tanh, and the boundary weights P b =100, learning rate lr=0.001, optimizer selected is Adam, Gaussian distribution random sampling method is used to initialize the network, training epochs are set to N_train=100000 as the stopping condition, and the target value of the loss function is set to 0.001;

[0105] Step 3-2: Record the output of the fully connected layer of the neural network built in Step 3-1: the predicted neutron number density value n for each node. predThe number density of slow-emission neutron precursor nuclei C ipred ;

[0106] Step 3-3: Calculate the loss value of the neural network with embedded physics knowledge, which includes three parts: PDE operator loss of the neutron diffusion equation, observation loss, and regularization loss.

[0107] 1) Calculate the PDE operator loss for the neutron diffusion equation, specifically including the following:

[0108] a. The neutron diffusion equation is as follows:

[0109]

[0110] In the formula:

[0111] n(r,t): t n Neutron number density at position r at time r;

[0112] S(r,t): t n External neutron number density at position r at time r;

[0113] ρ(r,t): t n Total reactivity of the node at time r;

[0114] β: Total proportion of delayed neutron emission;

[0115] Λ: Neutron generation time;

[0116] λ i : Decay constant of the i-th group of delayed neutron precursor nuclei;

[0117] C i (r,t): The number density of the i-th delayed neutron precursor nuclei at position r at time t;

[0118] β i : The share of delayed neutron emission in group i;

[0119] b. Use the automatic differentiation function in the deep learning framework DeepXDE to calculate the first derivative of n(r,t) with respect to time t and the second derivative with respect to spatial position r in the neutron diffusion equation;

[0120] c. Constructing the PDE operator for the neutron diffusion equation:

[0121]

[0122] In the formula:

[0123] n (t) : n(r,t) is the first derivative with respect to time t;

[0124] n (rr): n(r,t) is the second derivative of n(r,t) with respect to position r;

[0125] n pred The neural network's prediction of n(r,t);

[0126] C ipred Neural networks for C i d. Predicted value of (r,t); d. Calculate the PDE operator loss using the deep learning framework DeepXDE. o Specifically:

[0127] Loss o =PDE 2

[0128] 2) Calculate the value of the total loss function, Loss:

[0129] Loss=λ d Loss d +λ o Loss o +λ reg Loss2

[0130] In the formula:

[0131] λ d : Observation loss coefficient;

[0132] λ o : PDE operator loss coefficient;

[0133] λ reg Regularization coefficient;

[0134] Loss d : Observation loss;

[0135] Loss o : PDE operator loss;

[0136] Loss2: L2 regularization loss;

[0137] Because this invention uses a neural network based on embedded physical knowledge for nuclear thermal coupling calculations, which is a regression problem, the mean squared error is chosen as the observation loss function. d :

[0138]

[0139] In the formula:

[0140] N: Number of samples;

[0141] w ij The weights connecting the i-th sample and the j-th neuron;

[0142] Step 3-4: Determine whether the target value of the training rounds or loss function set in Step 3-1 has been reached. If so, terminate the training; otherwise, proceed to Step 3-5.

[0143] Step 3-5: Repeat steps 3-2 to 3-4 to train and optimize the embedded physical knowledge neural network;

[0144] 1) Read the output of the fully connected layer in each step of step 3-2, calculate the loss function value in step 3-3 and minimize the loss;

[0145] 2) Record the total loss function value and total loss decrease data in step 3-3 after each training session;

[0146] Steps 3-6: Save the trained model used to calculate the neutron number density at each node of the reactor core;

[0147] Step 4: Use the trained model to predict the neutron number density n(r,t) at each node of the core, and calculate the neutron flux distribution in the core:

[0148] φ(r,t)=n(r,t)v

[0149] v: neutron speed;

[0150] φ(r,t): t n Neutron flux at time point;

[0151] Step 5: Take the t obtained in Step 4 n The neutron flux distribution in the reactor core at any given time can be converted into the core power distribution using the following formula:

[0152] P(r,t)=E f Σ f5 φV

[0153] In the formula:

[0154] P(r,t): t n The power distribution of the node at time r;

[0155] E f The energy released in each fission;

[0156] Σ f5 :U 235 Macroscopic cross section of thermal neutrons;

[0157] φ: Neutron flux in the node;

[0158] V: The volume of the node;

[0159] Step 6: Input the core power distribution obtained in Step 5 as the energy source term into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR. This software is a one-dimensional system analysis program, which calculates t. n+1 At any given moment, the thermal-hydraulic state parameters of each node in the reactor core are: coolant temperature and fuel temperature.

[0160] Step 7: Calculate t based on the core thermal-hydraulic parameters and reactivity feedback relationship obtained in Step 6. n+1 Total reactivity of each node at any given time;

[0161] ρ=ρ0+ρ ext +ρ D +ρ f,a +ρ f,r +ρ c

[0162] In the formula:

[0163] ρ——Step length end t n+1 Total reactivity at any given time point;

[0164] ρ0——Initial step size t n Total reactivity at any given time point;

[0165] ρ ext —External reactivity introduced by nodes within the Δτ time step;

[0166] ρ D —Reactivity caused by the fuel Doppler effect within the time step Δτ;

[0167] ρ f,a —Reactivity caused by axial thermal expansion of fuel within the time step Δτ;

[0168] ρ f,r —Reactivity caused by radial thermal expansion of fuel within the time step Δτ;

[0169] ρ c —Reactivity caused by the thermal expansion of the coolant within the time step Δτ;

[0170]

[0171] ρ f,a =α f,a (T f -T f,0 )

[0172] ρ f,r =α f,r (T f -T f,0 )

[0173] ρ c =αc (T c -T c,0 )

[0174] In the formula:

[0175] K D —Fuel Doppler coefficient;

[0176] α f,a —Fuel axial thermal expansion feedback coefficient;

[0177] α f,r —Fuel radial thermal expansion feedback coefficient;

[0178] α c —Coefficient of thermal expansion of coolant;

[0179] T f ——Step length initial t n fuel temperature at any given time point;

[0180] T f,0 ——Previous step long initial t n-1 fuel temperature at any given time point;

[0181] T c ——Step length initial t n Coolant temperature at any given time point;

[0182] T c,0 ——Previous step long initial t n-1 Coolant temperature at any given time point;

[0183] Step 8: t n+1 Time as a new t n At each point, repeat steps 4 through 7 until the specified calculation time is reached.

[0184] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A reactor core thermal coupling calculation method based on an embedded physical knowledge neural network, characterized in that: Includes the following steps: Step 1: Determine the reactor core geometry and perform node division, dividing it into m nodes axially and n rings radially; Step 2: Initialize the state parameters, which includes the following: Step 2-1: Initialize the core fuel, coolant temperature, power, thermal-hydraulic state parameters; Step 2-2: Initialize the reactivity and neutron number density of each node in the reactor core; Step 3: t n At any time, an embedded physical knowledge neural network is built in the deep learning framework DeepXDE, and the built embedded physical knowledge neural network is trained and optimized to solve the neutron diffusion equation and obtain a model for calculating the neutron number density of each node in the reactor core. Step 4: Use the trained model to predict the neutron number density n(r,t) at each node of the core and calculate the neutron flux distribution in the core; Step 5: Convert the core neutron flux distribution obtained in Step 4 into the core power distribution using the following formula: P(r,t)=E f Σ f5 φV In the formula: P(r,t): t n The power distribution of the node at time r; E f The energy released in each fission; Σ f5 :U 235 Macroscopic cross section of thermal neutrons; φ: Neutron flux in the node; V: The volume of the node; Step 6: Input the core power distribution obtained in Step 5 as the energy source term into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR. This software is a one-dimensional system analysis program, which calculates t. n+1 At any given moment, the thermal-hydraulic state parameters of each node in the reactor core are: coolant temperature and fuel temperature. Step 7: Calculate t based on the core thermal-hydraulic parameters and reactivity feedback relationship obtained in Step 6. n+1 Total reactivity of each node at any given time; p=p0+p ext +r D +r f,a +r f,r +r c In the formula: ρ——Step length end t n+1 Total reactivity at any given time point; ρ0——Initial step size t n Total reactivity at any given time point; ρ ext —External reactivity introduced by nodes within the Δτ time step; ρ D —Reactivity caused by the fuel Doppler effect within the time step Δτ; ρ f,a —Reactivity caused by axial thermal expansion of fuel within the time step Δτ; ρ f,r —Reactivity caused by radial thermal expansion of fuel within the time step Δτ; ρ c —Reactivity caused by the thermal expansion of the coolant within the time step Δτ; r f,a =a f,a (T f -T f,0 ) r f,r =a f,r (T f -T f,0 ) r c =a c (T c -T c,0 ) In the formula: K D —Fuel Doppler coefficient; α f,a —Fuel axial thermal expansion feedback coefficient; α f,r —Fuel radial thermal expansion feedback coefficient; α c —Coefficient of thermal expansion of coolant; T f ——Step length initial t n fuel temperature at any given time point; T f,0 ——Previous step long initial t n-1 fuel temperature at any given time point; T c ——Step length initial t n Coolant temperature at any given time point; T c,0 —Previous step long initial t n-1 Coolant temperature at any given time point; Step 8: t n+1 Time as a new t n At each point, repeat steps 4 through 7 until the specified calculation time is reached.

2. The reactor core thermal coupling calculation method based on an embedded physical knowledge neural network according to claim 1, characterized in that: Step 3 is as follows: Step 3-1: Build the neural network structure in the deep learning framework DeepXDE; A fully connected neural network structure is adopted, and the depth, number of neurons in the intermediate layers, activation function, boundary weights, learning rate, optimizer and training times are set. The network is initialized using Gaussian random sampling method. Step 3-2: Record the output of the fully connected layer of the neural network built in Step 3-1: the predicted neutron number density value n for each node. pred The number density of slow-emission neutron precursor nuclei C ipred ; Step 3-3: Calculate the loss value of the neural network with embedded physics knowledge, which includes three parts: PDE operator loss of the neutron diffusion equation, observation loss, and regularization loss. 1) Calculate the PDE operator loss of the neutron diffusion equation, specifically including the following: a. The neutron diffusion equation is as follows: In the formula: n(r,t): t n Neutron number density at position r at time r; S(r,t): t n External neutron number density at position r at time r; ρ(r,t): t n Total reactivity of the node at time r; β: Total proportion of delayed neutron emission; Λ: Neutron generation time; λ i : Decay constant of the i-th group of delayed neutron precursor nuclei; C i (r,t): The number density of the i-th delayed neutron precursor nuclei at position r at time t; β i : The share of delayed neutron emission in group i; b. Use the automatic differentiation function in the DeepXDE deep learning framework to calculate n(r,t) and respectively. Derivatives with respect to time and space; c. Constructing the PDE operator for the neutron diffusion equation: In the formula: n (t) : n(r,t) is the first derivative with respect to time t; n (rr) : n(r,t) is the second derivative of n(r,t) with respect to position r; n pred The neural network's prediction of n(r,t); C ipred Neural networks for C i Predicted value of (r,t); d. Calculate the PDE operator loss using the DeepXDE deep learning framework. o ; 2) Calculate the value of the total loss function, Loss: Loss=λ d Loss d +λ o Loss o +λ reg Loss2 In the formula: λ d : Observation loss coefficient; λ o : PDE operator loss coefficient; λ reg Regularization coefficient; Loss d : Observation loss; Loss2: L2 regularization loss; In the formula: N: Number of samples; w ij The weights connecting the i-th sample and the j-th neuron; Step 3-4: Determine whether the target value of the training rounds or loss function set in Step 3-1 has been reached. If so, terminate the training; otherwise, proceed to Step 3-5. Step 3-5: Repeat steps 3-2 to 3-4 to train and optimize the embedded physical knowledge neural network; 1) Read the output of the fully connected layer in each step of step 3-2, calculate the loss function value in step 3-3 and minimize the loss; 2) Record the total loss function value and total loss decrease data in step 3-3 after each training session; Steps 3-6: Save the trained model used to calculate the neutron number density at each node of the reactor core.

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