A fast prediction method for transient multi-physics fields of micro-reactor based on reduced-order model

Abstract

A fast prediction method for transient multiphysics events in microreactors based on a reduced-order model is proposed. This method uses the changes in core parameters and time variations during the transient process as discrete parameter points in the parameter space. A response matrix is ​​established, representing the target information: core power, core reactivity, core temperature, and matrix expansion rate. The response matrix is ​​reduced to a low-dimensional matrix using Orthogonal Eigenvalue Decomposition (POD). New parameter points are input in real-time during the online phase, and radial basis functions are used to establish the relationship between the parameter points and the response vector. Rapid prediction is then performed using the low-dimensional matrix, achieving high computational accuracy with low computational cost. This invention performs transient multiphysics coupled simulation of the microreactor startup process based on the Orthogonal Eigenvalue Decomposition Radial Basis Function (POD-RBF) method, significantly improving computational efficiency while maintaining high prediction accuracy. Traditional high-fidelity simulation methods typically face high computational costs when performing multiphysics coupled calculations; this method significantly reduces the computational load while ensuring accuracy.

Description

Technical Field

[0001] This invention relates to a technology in the field of reactor control, specifically a method for rapid prediction of transient multiphysics fields in microreactors based on a reduced-order model. Background Technology

[0002] Existing simulations of microreactor startup processes typically rely on high-fidelity computational methods. While these methods offer high accuracy, their computation time is lengthy, failing to meet the demands of real-time response and efficient simulation in engineering practice. Therefore, significantly improving computational efficiency while maintaining accuracy has become a key technical challenge in microreactor transient simulation. Summary of the Invention

[0003] This invention addresses the shortcomings of existing technologies in solving transient problems of microreactors by proposing a fast multiphysics prediction method for microreactors based on a reduced-order model. It utilizes the intrinsic orthogonal decomposition radial basis function (POD-RBF) method to perform transient multiphysics coupling simulation of the microreactor startup process, thereby significantly improving computational efficiency while maintaining high prediction accuracy. Traditional high-fidelity simulation methods typically face high computational costs when performing multiphysics coupling calculations; this invention significantly reduces the computational load while ensuring accuracy.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a rapid prediction method for transient multiphysics fields in microreactors based on a reduced-order model. The method uses the changes in core parameters and time during the transient process as discrete parameter points in the parameter space. It establishes response matrices representing the target information: core power, core reactivity, core temperature, and matrix expansion rate. The response matrix is ​​reduced to a low-dimensional matrix using intrinsic orthogonal decomposition (POD). New parameter points are input in real-time during the online phase. The relationship between the parameter points and the response vector is established using radial basis functions, and rapid prediction is performed using the low-dimensional matrix, thus achieving high computational accuracy with low computational cost.

[0006] The aforementioned intrinsic orthogonal decomposition refers to taking M discrete points p1, p2, ..., p in the parameter space. M ∈R t And the response vector u1, u2, ..., u corresponding to each parameter point. M ∈R n Stored as a response matrix U = [u1…u M The singular value decomposition (SVD) of the response matrix yields: Φ = U·V, where: C·V = Λ·V, C = U T ·U, Φ∈R N×M Let be the orthogonal basis matrix of the response matrix, and let be the unitary matrix; Λ∈R M×MFor a diagonal matrix containing singular values, typically, the singular values ​​on the diagonal are arranged in descending order; V∈R M×M It is also a unitary matrix, C∈R M×M Let V be the characteristic matrix of V.

[0007] By retaining only the orthogonal basis of the first r = k columns of matrix Φ, we obtain the orthogonal basis with the response matrix truncated. parameter Where: τ is a number less than 1, usually chosen as 0.9999; λ i The diagonal elements of Λ are the singular values ​​of the response matrix. This inequality shows the proportion of the retained orthogonal basis in the total information, and the first r columns of matrix Φ are denoted as the reduced-order basis matrix. Reduce the basis matrix Applying this to the response matrix will yield the amplitude matrix of the response matrix.

[0008] The radial basis function refers to the distance between parameter points in the continuous parameter space and discrete parameter points. Where: p1, p2, ..., p M ∈R t Let there be M discrete parameter points in the parameter space. The parameter space typically contains macroscopic parameters of the micro-heap, such as substrate temperature, heat pipe temperature, and control drum angle; p∈R t For continuous parameter points in the parameter space; r is a smoothing factor, ensuring that the interpolation function matrix cond(F) < 10. 12 In this case, maximize the smoothing factor; the radial basis functions can be used to define an interpolation function matrix for M discrete parameter points. Wherein: the condition number of the interpolation function matrix depends on the smoothing factor r, ensuring that the interpolation function matrix cond(F) < 10. 12 In this case, the smoothing factor should be increased as much as possible. At the same time, to ensure interpolation accuracy, r > 0.011 must be satisfied.

[0009] The coefficient matrix B∈R^ is established by inverting the interpolation function matrix F to obtain the parameter points and the amplitude matrix. For a new parameter p, we can obtain an approximate value for its response vector u(p): in:

[0010] This invention relates to a system for implementing the above-mentioned method, comprising: a data generation unit, a POD-RBF modeling unit, a fast prediction unit, and a verification unit, wherein: the data generation unit calculates the response matrix (power distribution and reactivity) corresponding to the input parameters using OpenMC based on input parameters such as core geometry, temperature, and material properties; the POD-RBF modeling unit, based on the generated training data, uses the POD method to reduce the order of the physical quantities of the core (such as power distribution and reactivity) and extract the dominant feature patterns; subsequently, it models these low-dimensional features using radial basis function (RBF) interpolation, thereby generating a low-dimensional approximate model of the core response; the fast prediction unit predicts the core power distribution and reactivity, etc., under new input parameters in real time based on the low-dimensional model generated by the POD-RBF modeling unit; it can quickly respond to new transient conditions and provide efficient calculation results while ensuring accuracy; the verification unit verifies the calculation results of the fast prediction unit and evaluates the accuracy of the prediction by comparing them with the simulation results of a high-fidelity model.

[0011] Technical effect

[0012] This invention utilizes transient data from microreactors to derive the relationship between parameter points and response vectors through intrinsic orthogonal decomposition and radial basis functions. This allows for rapid prediction of transient multiphysics fields in microreactors, yielding key physical quantities such as transient neutron flux, power distribution, core temperature, and stress distribution. This information can be applied to the rapid prediction and safety analysis of microreactor states. Compared to existing technologies, this invention reduces the computation time per time step from 800 seconds to 3 seconds, and shortens the overall startup simulation time from 74 days to 7.5 hours, improving efficiency by approximately 99.6%. Simultaneously, this invention maintains high prediction accuracy while ensuring high computational efficiency. The average error for power distribution prediction is 0.77%, with a maximum error not exceeding 3.04%. The average error for reactivity prediction is less than 50 pcm, with a maximum not exceeding 100 pcm. Attached Figure Description

[0013] Figure 1 This is a flowchart of the present invention;

[0014] Figure 2 This is a flowchart of an implementation example;

[0015] Figure 3 A comparison of power distribution predictions between the example and the high-resolution model;

[0016] Figure 4 Here are the error distribution histograms for the example and the high-resolution model;

[0017] Figure 5 A graph showing the temperature and power variations during the low-power startup of a microreactor.

[0018] Figure 6 This is a graph showing the temperature and power changes during the power regulation phase of a microreactor. Detailed Implementation

[0019] like Figure 1 As shown, this embodiment illustrates a fast prediction method for transient multiphysics fields in micro-heaps based on a reduced-order model, comprising:

[0020] Step 1: Determine the input parameters and divide the training and test sets: Select the input parameters and their value ranges, and divide 80% of the input parameters into the training set and 20% into the test set. This is used to build and correct the low-dimensional approximation model and to verify the prediction accuracy and stability of the model.

[0021] The input parameters include temperature, geometric dimensions, and control drum angle.

[0022] Step 2: Use OpenMC to calculate the response vector for each input parameter point: Under the parameter combination determined by the training set samples, call OpenMC to perform multiphysics simulation calculations on the micro-heap to obtain the corresponding response vector.

[0023] The response vector includes: power distribution, reactivity, and temperature distribution.

[0024] Step 3: Construct a low-dimensional approximate model using the intrinsic orthogonal decomposition radial basis function (POD-RBF) method: Use intrinsic orthogonal decomposition (POD) to extract feature patterns or dominant physical modes from the response vector to obtain a low-dimensional matrix.

[0025] Step 4: Use the radial basis function (RBF) interpolation method to fit or interpolate the data at different parameter points of the low-dimensional matrix to obtain a reduced-order approximate model that can quickly predict the system response.

[0026] Step 5: Use OpenMC to simulate the input parameter points in the test set to obtain the corresponding response vectors (including physical quantities such as power distribution and reactivity). Use these high-fidelity results as benchmark data and compare them point by point with the prediction results of the low-dimensional approximation model to calculate the error.

[0027] like Figure 2 As shown, in specific scenarios, this is achieved in the following ways:

[0028] 1) Set initial parameters: Select control drum angle 150°-50°, step size 10°, fuel temperature 300K-1000K, step size 100K, a total of 88 samples, including 70 training sets and 18 test sets. The core power distribution and reactivity were rapidly predicted by a reduced-order model based on POD-RBF.

[0029] 2) Establish a nuclear thermal model of the reactor core;

[0030] 3) Calculate the core temperature field and statistically analyze the matrix and fuel temperatures; calculate the heat pipe temperature and update the boundary conditions of the core thermodynamic model; calculate the core axial and radial geometric changes and update the core mesh; use POD-RBF to predict reactivity and power distribution based on neutron, temperature, and geometric information; adjust the control drum according to the reactivity to keep the reactivity near 0 and cycle until the temperature change is less than the convergence condition;

[0031] 4) The control drum uses a PID controller to track the target power until the rated power is reached.

[0032] like Figure 3 As shown, this is a comparison between the POD-RBF model and the high-resolution model in power distribution prediction. Figure 4 As shown in the figure, the error distribution of the power prediction by the POD-RBF model and the high-resolution model is as follows: the maximum error of the power distribution prediction is 3.04%, and the average error is 0.77%; the average error of the reactivity prediction is less than 50 pcm, and the maximum error does not exceed 100 pcm. Using the POD-RBF method, the computation time for each time step of the startup process is reduced from 800 seconds to 3 seconds, and the computation time for the entire startup process is reduced from 74 days to 7.5 hours, improving efficiency by approximately 99.6%. In the microreactor startup process, the fast prediction model based on the POD-RBF method is applied to quickly predict the reactivity and power distribution of the microreactor, obtaining stable and convergent multiphysics coupling results. This effectively improves the computational efficiency of transient multiphysics coupling problems, meets the requirements of real-time simulation and dynamic response, and has high engineering application value.

[0033] like Figure 5 As shown, the temperature and power variation trends during the low-power startup phase of a microreactor are illustrated, verifying the dynamic prediction capability of the POD-RBF method in the low-power phase. This demonstrates that the method can effectively reflect the temperature and power variation patterns while maintaining a certain level of accuracy. Figure 6 As shown, the temperature and power change trends during the power regulation phase of the microreactor further verify the stability of the POD-RBF method during reactor startup, demonstrating that the method can significantly improve computational efficiency while ensuring accuracy.

[0034] In summary, this method, by introducing a fast prediction model based on POD-RBF, reduces the computation time for each time step from 800 seconds to 3 seconds, shortening the overall startup computation time from 74 days to 7.5 hours, improving efficiency by approximately 99.6%. Furthermore, the POD-RBF model maintains high accuracy in power distribution and reactivity prediction, with a maximum power prediction error of only 3.04% and an average reactivity prediction error of less than 50 pcm, with a maximum of no more than 100 pcm. Through these technological innovations, this invention not only significantly reduces computational costs but also provides efficient, real-time prediction results, meeting the real-time simulation requirements of nuclear reactor startup processes and possessing significant engineering application value.

[0035] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A fast prediction method for transient multiphysics fields of micro-heaps based on a reduced-order model, characterized in that, Using the changes in core parameters and time during the transient process as discrete parameter points in the parameter space, a response matrix is ​​established to represent the target information: core power, core reactivity, core temperature, and matrix expansion rate. The response matrix is ​​then reduced to a low-dimensional matrix using intrinsic orthogonal decomposition (POD). New parameter points are input in real time during the online phase, and the relationship between the parameter points and the response vector is established using radial basis functions. The low-dimensional matrix is ​​then used for rapid prediction, thus achieving high computational accuracy with low computational cost. The aforementioned intrinsic orthogonal decomposition refers to: taking the parameter space discrete points And the response vector corresponding to each parameter point. Stored as a response matrix The response matrix is ​​obtained by singular value decomposition: ,in: , , The orthogonal basis matrix of the response matrix is ​​a unitary matrix; It is a diagonal matrix containing singular values; It is also a unitary matrix. for The feature matrix; When only the matrix is ​​retained forward The orthogonal basis of the columns will yield an orthogonal basis with the response matrix truncated. ,parameter ,in: For numbers less than 1, for The diagonal elements are the singular values ​​of the response matrix. The inequality shows the proportion of the retained orthogonal basis in the total information. The former The column is denoted as a reduced-order basis matrix. Reduce the order basis matrix Applying this to the response matrix will yield the amplitude matrix of the response matrix. : ; The radial basis function refers to the distance between parameter points in the continuous parameter space and discrete parameter points. ,in: For parameter space Discrete parameter points, For continuous parameter points in the parameter space; The smoothing factor is defined by the radial basis functions. Interpolation function matrix for discrete parameter points Where: the condition number of the interpolation function matrix depends on the smoothing factor .

2. The fast prediction method for transient multiphysics fields of micro-heaps based on a reduced-order model according to claim 1, characterized in that, While ensuring the interpolation function matrix While ensuring interpolation accuracy .

3. The fast prediction method for transient multiphysics fields of micro-heaps based on a reduced-order model according to claim 1, characterized in that, By analyzing the interpolation function matrix Inverse the equation to establish the coefficient matrix of the parameter points and the amplitude matrix. , For new parameters Obtain its response vector Approximate value: .

4. A fast prediction system for transient multiphysics fields of micro-heaps based on a reduced-order model, implementing the method described in any of claims 1-3, characterized in that, include: The system comprises a data generation unit, a POD-RBF modeling unit, a fast prediction unit, and a verification unit. Specifically: the data generation unit calculates the response matrix corresponding to the input core geometry, temperature, and material properties using OpenMC; the POD-RBF modeling unit, based on the generated training data, uses the POD method to reduce the order of the core's physical quantities, extracts the dominant feature patterns, and then models these low-dimensional features using radial basis function (RBF) interpolation, thereby generating a low-dimensional approximate model of the core response; the fast prediction unit predicts the core power distribution and reactive physical quantities in real time under new input parameters based on the low-dimensional model generated by the POD-RBF modeling unit; and the verification unit verifies the calculation results of the fast prediction unit by comparing them with the simulation results of the high-fidelity model to evaluate the accuracy of the predictions.

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