An uncertainty analysis method and product for multiphysics coupling calculations in reactors

Abstract

This application provides an uncertainty analysis method and product for reactor multiphysics coupling calculations. The uncertainty analysis method includes obtaining a first snapshot matrix of reference multiphysics coupling calculation results for the reactor at multiple times under multiple first operating conditions, and a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of the first snapshot matrix; determining a second snapshot matrix of predicted multiphysics coupling calculation results for the reactor at multiple times under multiple second operating conditions based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and interpolation matrices of multiple first operating conditions and multiple second operating conditions; and determining the uncertainty of the predicted multiphysics coupling calculation results for the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix. This application can improve the efficiency of uncertainty analysis for reactor multiphysics coupling calculations and reduce the cost of uncertainty analysis.

Description

Technical Field

[0001] This invention relates to the field of nuclear energy technology, specifically to an uncertainty analysis method and product for multiphysics coupling calculations in reactors. Background Technology

[0002] In the field of nuclear energy technology, uncertainty analysis is typically required for reactor multiphysics coupling calculations to determine the impact of input variables on the reliability and accuracy of the calculation results. To reduce the error in uncertainty analysis, it is usually necessary to increase the sample data of the input variables. Statistical analysis of the expected value, variance, and other indicators of the reactor multiphysics coupling calculation results obtained from hundreds of millions of sample data points is necessary to ensure the accuracy of the uncertainty analysis.

[0003] However, most current uncertainty analysis methods rely on reactor multiphysics coupling calculation models to perform calculations on hundreds of millions of sample data to obtain reactor multiphysics coupling calculation results. The calculation process often takes several days, and even several months when the dimensionality of the input variables is high. This results in low efficiency and high cost for reactor multiphysics coupling calculation uncertainty analysis.

[0004] Improving the efficiency and reducing the cost of uncertainty analysis in multiphysics coupling calculations for reactors is an urgent problem to be solved. Summary of the Invention

[0005] The main objective of this application is to propose an uncertainty analysis method and product for reactor multiphysics coupling calculation, aiming to improve the efficiency of uncertainty analysis in reactor multiphysics coupling calculation and reduce the cost of uncertainty analysis.

[0006] This application provides an uncertainty analysis method for reactor multiphysics coupling calculations, comprising: obtaining a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of the reactor multiphysics; wherein, the first snapshot matrix is ​​a snapshot matrix of reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each first operating condition; determining a second snapshot matrix of the reactor multiphysics based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and a first interpolation matrix; wherein, the first interpolation matrix is ​​a matrix of the first operating conditions and multiple second... The interpolation matrix for the operating conditions; the second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions; each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical field located in the multiple first spatial units in the reactor at multiple times under each second operating condition; the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is determined based on the average vector and variance vector of all row vectors in the second snapshot matrix; wherein, the multiple first spatial units are multiple spatial units in the reactor corresponding to the target physical field, and the target physical field is any physical field in the multiphysics.

[0007] In one embodiment, obtaining the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics includes: performing singular value decomposition on the transposed first snapshot matrix to determine the left singular matrix, right singular matrix, and singular value matrix of the first snapshot matrix; wherein, the singular value matrix is ​​a diagonal matrix, the elements on the diagonal of the singular value matrix are the singular values ​​of the first snapshot matrix, and the singular values ​​are arranged from top to bottom on the diagonal of the singular value matrix in descending order; removing the row vectors with position numbers greater than r in the right singular matrix from the right singular matrix to obtain the first reduced-order basis matrix of the first snapshot matrix; removing the column vectors with position numbers greater than r in the matrix obtained by multiplying the left singular matrix and the singular value matrix from the matrix obtained by multiplying the left singular matrix and the singular value matrix to obtain the first reduced-order basis coefficient matrix; wherein, r is the number of target singular values ​​selected in descending order of the singular values, and the sum of the squares of the selected r target singular values ​​is greater than a preset value.

[0008] In one embodiment, determining the second snapshot matrix of the reactor multiphysics field based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix includes: determining the radial basis function mapping coefficient matrix based on the first reduced-order basis coefficient matrix and the distance weight matrix; wherein the distance weight matrix is ​​the matrix of distance weight functions between each of the plurality of first operating conditions; determining the second reduced-order basis coefficient matrix based on the first interpolation matrix and the radial basis function mapping coefficient matrix; and multiplying the first reduced-order basis matrix and the second reduced-order basis coefficient matrix to obtain the second snapshot matrix of the reactor multiphysics field.

[0009] In one embodiment, the step of determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix includes: determining the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix; determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector of all row vectors in the second snapshot matrix, the average vector of all row vectors in the deviation matrix, and the target variance vector; wherein, the deviation matrix is ​​used to characterize the deviation of the third snapshot matrix of the reactor multiphysics determined based on the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix, and the second interpolation matrix is ​​the interpolation matrix of the multiple first operating conditions and the multiple third operating conditions.

[0010] In one embodiment, before determining the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix, the uncertainty analysis method further includes: determining a third snapshot matrix of the reactor multiphysics based on the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix; wherein the third snapshot matrix is ​​a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple third operating conditions; obtaining a fourth snapshot matrix of the reactor multiphysics; the fourth snapshot matrix is ​​a snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under the multiple third operating conditions; determining the deviation between the third snapshot matrix and the fourth snapshot matrix to obtain the deviation matrix.

[0011] In one embodiment, the plurality of first operating conditions are a plurality of operating conditions determined by a first sampling based on the value range of a plurality of variables of the reactor in the design space; the plurality of second operating conditions are a plurality of operating conditions determined by a second sampling based on the probability distribution range followed by a plurality of variables of the reactor; and the plurality of third operating conditions are a plurality of operating conditions determined by a third sampling based on the value range of a plurality of variables of the reactor in the design space.

[0012] In one embodiment, before obtaining the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field, the uncertainty analysis method further includes: dividing the reactor at least once according to each physical field in the multiphysics field to obtain multiple spatial units of the reactor corresponding to each physical field; calculating the values ​​of each physical field located in the multiple spatial units at multiple times under each first operating condition of the reactor using a multiphysics coupling calculation model to obtain reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions; determining the snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions to obtain the first snapshot matrix.

[0013] This application also improves an uncertainty analysis system for reactor multiphysics coupling calculation, including an acquisition module, a snapshot module, and an uncertainty module; the acquisition module is used to acquire a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of the reactor multiphysics; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each first operating condition; the snapshot module is used to determine a second snapshot matrix of the reactor multiphysics based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and a first interpolation matrix; wherein, the first interpolation matrix is ​​a snapshot matrix of the reference multiphysics coupling calculation results of the reactor multiphysics at multiple times under multiple first operating conditions. The first operating condition and multiple second operating conditions are interpolation matrices. The second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions. Each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical field located in the multiple first spatial units in the reactor at multiple times under each second operating condition. The uncertainty module is used to determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix. The multiple first spatial units are multiple spatial units in the reactor corresponding to the target physical field, and the target physical field is any physical field in the multiphysics.

[0014] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the uncertainty analysis method described above.

[0015] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described uncertainty analysis method.

[0016] This application provides a method and product for uncertainty analysis of reactor multiphysics coupling calculations. By utilizing two low-order matrices of the snapshot matrix of the reference multiphysics coupling calculation results at multiple times under multiple first operating conditions: a first reduced-order basis matrix and a first reduced-order basis coefficient matrix, combined with a first interpolation matrix of multiple first operating conditions and multiple second operating conditions, the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions can be quickly determined. This improves the efficiency of uncertainty analysis of reactor multiphysics coupling calculations and reduces the cost of uncertainty analysis. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating the uncertainty analysis method for reactor multiphysics coupling calculations provided in this application embodiment;

[0018] Figure 2 yes Figure 1 A flowchart illustrating step S102 in the process;

[0019] Figure 3 yes Figure 1 A flowchart illustrating step S103 in the process;

[0020] Figure 4 This is a schematic diagram of the structure of the uncertainty analysis system for reactor multiphysics coupling calculation provided in the embodiments of this application;

[0021] Figure 5 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application;

[0022] Figure 6 This is a schematic diagram of another embodiment of the electronic device provided in this application. Detailed Implementation

[0023] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0024] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0025] The uncertainty analysis method for reactor multiphysics coupling calculations provided in this application can be applied to a terminal, a server, or software running on either a terminal or a server. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, etc.; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application that implements the uncertainty analysis method for reactor multiphysics coupling calculations, etc., but is not limited to the above forms.

[0026] The uncertainty analysis method for reactor multiphysics coupling calculation provided in this application will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0027] Please see Figure 1 This application provides an uncertainty analysis method for reactor multiphysics coupling calculations, including:

[0028] Step S101: Obtain the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each first operating condition;

[0029] Step S102: Determine the second snapshot matrix of the reactor multiphysics field based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix; wherein, the first interpolation matrix is ​​an interpolation matrix of multiple first operating conditions and multiple second operating conditions, and the second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics field coupling calculation results of the reactor at multiple times under multiple second operating conditions, and each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each second operating condition;

[0030] Step S103: Determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix;

[0031] Among them, the multiple first spatial units are multiple spatial units in the reactor that correspond to the target physical field, and the target physical field is any physical field in the multi-physics field.

[0032] This application embodiment utilizes two low-order matrices—a first reduced-order basis matrix and a first reduced-order basis coefficient matrix—of the snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions. Combined with the first interpolation matrix of multiple first operating conditions and multiple second operating conditions, the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions can be quickly determined. This improves the efficiency of uncertainty analysis in reactor multiphysics coupling calculation and reduces the cost of uncertainty analysis.

[0033] Optionally, the multiple first operating conditions are multiple operating conditions determined by first sampling from the value range of multiple variables of the reactor in the design space. The multiple variables of the reactor include variable parameters input by the user into the reactor multiphysics calculation model and variable parameters of the reactor multiphysics calculation model. For example, the variable parameters input by the user may include, but are not limited to, geometric parameters such as the reactor's height, length, and radius; nuclide densities such as the uranium loading and enrichment of the fuel; and operating states such as the temperature of the reactor inlet coolant, the position of the control rods, and the operating power level. The variable parameters of the reactor multiphysics calculation model may include, but are not limited to, the neutron-material reaction cross-section coefficient and the fitting coefficients of the model equations.

[0034] Furthermore, the design space ε for each variable can be defined. i,min ≤ε i ≤ε i,max The design space characterizes the possible range of variation for each variable, where ε i Let ε represent the i-th variable in the reactor. i,min and ε i,max Let X and Y represent the upper and lower boundaries of the range of variation of the i-th variable, respectively, such as 1cm ≤ reactor height ≤ 10m. Each variable and its value range within its design space constitutes a two-dimensional design space, which can be represented as a square region on a plane. A first sampling of the two-dimensional design space can be performed using simple random sampling (such as Monte Carlo sampling) or Latin hypercube sampling, resulting in a first sample dataset X1 with dimensions (N1, M), where N1 is the number of samples obtained from the first sampling, and M is the number of variables in the reactor. Each sample obtained from the first sampling is used as a first operating condition of the reactor, resulting in N1 first operating conditions.

[0035] Optionally, the reference multiphysics coupling calculation results of the reactor at multiple moments under multiple first operating conditions can be user-defined multiphysics coupling calculation results, or multiphysics coupling calculation results obtained by solving the multiphysics coupling calculation equations. This application does not limit the method of obtaining the reference multiphysics coupling calculation results of the reactor at multiple moments under multiple first operating conditions.

[0036] Before obtaining the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field in step S101 above, the uncertainty analysis method further includes:

[0037] The reactor is divided at least once according to each physical field in the multiphysics field to obtain multiple spatial units of the reactor corresponding to each physical field.

[0038] The multiphysics coupling calculation model is used to calculate the values ​​of each physical field in multiple spatial units of the reactor at multiple times under various first operating conditions, and to obtain the reference multiphysics coupling calculation results of the reactor at multiple times under various first operating conditions.

[0039] The first snapshot matrix is ​​obtained by determining the snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions.

[0040] Optionally, the multiphysics field of the reactor may include, but is not limited to, the reactor's fuel power field, fuel temperature field, coolant temperature field, coolant pressure field, velocity field, and neutron flux distribution field.

[0041] For example, the reactor has 157 square components in the radial direction, and each square component has 17 sub-components on each side. According to the fuel temperature field and coolant temperature field in the multiphysics field, the reactor can be divided into 30 layers in the axial direction and 4 parts in the radial direction, resulting in 157×4×30=18840 spatial units. That is, the fuel temperature field and coolant temperature field in the multiphysics field correspond to 18840 spatial units in the reactor. Each sub-component (such as fuel rod) in the reactor can also be divided into a spatial unit according to the fuel power field in the multiphysics field, resulting in 157×17×17×30=136119 spatial units. That is, the power field in the multiphysics field corresponds to 136119 spatial units in the reactor.

[0042] Furthermore, the i-th first working condition x among multiple first working conditions can be... 1i ∈X1, with dimensions (1,M), is input into the reactor multiphysics coupling calculation model, and the reactor multiphysics coupling calculation is performed to obtain the reference multiphysics coupling calculation results of the reactor at multiple times under the i-th first operating condition:

[0043] Y 1i,P (K P ,T),Y 1i,TF (K TF ,T),Y 1i,TC (K TC ,T),…=F(x 1i )

[0044] Where, F(x) 1i ) represents the multiphysics coupling computational model of the reactor, x 1i For the i-th first operating condition among multiple first operating conditions, Y 1i,P (K P (T) is a dataset containing the values ​​of the fuel power field of each spatial cell corresponding to the fuel power field in the reactor at multiple times under the i-th first operating condition. Its dimension is (K). P ,T), K P Y represents the number of spatial units corresponding to the power field. 1i,TF (K TF (T) is a dataset containing the values ​​of the fuel temperature field at multiple times for each spatial cell corresponding to the fuel temperature field in the reactor under the i-th first operating condition. Its dimension is (K). TG ,T),K YF Y represents the number of spatial units corresponding to the fuel temperature field. 1i,TC (K TC (T) is a dataset containing the values ​​of the coolant temperature field of each spatial unit corresponding to the coolant temperature field in the reactor at multiple times under the i-th first operating condition. Its dimension is (K). YC ,T), K YC The number of spatial units corresponding to the coolant temperature field, where T is the number of multiple moments (or the number of time steps).

[0045] Furthermore, the fuel power field, fuel temperature field, coolant temperature field, and other reference multiphysics field coupling calculation results of the reactor under the i-th first operating condition can be constructed into a result matrix:

[0046]

[0047] Among them, Y 1i The dimension is

[0048] Furthermore, the reference multiphysics coupling calculation results of the reactor under multiple first operating conditions can be constructed into a result matrix, resulting in the reference multiphysics coupling calculation result matrix Y1 of the reactor under multiple first operating conditions, with dimensions of...

[0049] Furthermore, a first snapshot matrix U1 is constructed from the reference multiphysics coupling calculation result matrix Y1 under multiple first operating conditions of the reactor, with dimensions of... That is, any column vector in the first snapshot matrix U1 has a dimension of It represents a set of snapshots of the values ​​of each physical field in the spatial unit corresponding to each physical field at all times under any first operating condition of the reactor.

[0050] In this embodiment, the reactor is divided at least once according to each physics field in the multiphysics model, resulting in multiple spatial units corresponding to each physics field. This refines the coupling calculation results of each physics field to the corresponding spatial units in the reactor, improving the accuracy of the reference multiphysics coupling calculation results at multiple times under multiple first operating conditions. Furthermore, by constructing a snapshot matrix of the reference multiphysics coupling calculation results at multiple times under multiple first operating conditions, the reference multiphysics coupling calculation results under multiple first operating conditions are compressed from three-dimensional space to two-dimensional space, improving the convenience of using the reference multiphysics coupling calculation results under multiple first operating conditions to determine the predicted multiphysics coupling calculation results of the reactor under other operating conditions.

[0051] In one embodiment, obtaining the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics in step S101 includes:

[0052] Perform singular value decomposition on the transposed first snapshot matrix to determine the left singular matrix, right singular matrix, and singular value matrix of the first snapshot matrix; wherein, the singular value matrix is ​​a diagonal matrix, and the elements on the diagonal of the singular value matrix are the singular values ​​of the first snapshot matrix, and the singular values ​​are arranged from top to bottom on the diagonal of the singular value matrix in descending order.

[0053] Remove the row vectors with position numbers greater than r from the right singular matrix to obtain the first reduced-order basis matrix of the first snapshot matrix;

[0054] The column vectors with position numbers greater than r in the matrix obtained by multiplying the left singular matrix and the singular value matrix are removed from the matrix obtained by multiplying the left singular matrix and the singular value matrix to obtain the first reduced-order basis coefficient matrix.

[0055] Where r is the number of target singular values ​​selected in descending order of singular values, and the sum of the squares of the selected r target singular values ​​is greater than a preset value.

[0056] For example, firstly, the first snapshot matrix U1 is transposed to obtain the transpose matrix of the first snapshot matrix U1. Its dimensions are Secondly, the transpose of the first snapshot matrix Perform Singular Value Decomposition (SVD): Where S is the left singular matrix of the first snapshot matrix, which is an orthogonal matrix composed of left singular basis vectors, with dimension (N1, N1). ∑ is the singular value matrix of the first snapshot matrix, which is a matrix with dimension N1. Let V be a diagonal matrix whose diagonal elements are the singular values ​​of the first snapshot matrix, and the singular values ​​of the first snapshot matrix are arranged from top to bottom on the diagonal of the singular value matrix ∑ in descending order. Let V be the right singular matrix of the first snapshot matrix, which is an orthogonal matrix composed of right singular basis vectors, with dimension ∑.

[0057] Next, following the order of singular values ​​from largest to smallest, multiple target singular values ​​λ1, λ2, ... are selected sequentially, and the sum of squares of the selected target singular values ​​is calculated sequentially. If, when selecting the r-th target singular value, the selected r target singular values ​​satisfy the following condition:

[0058] (λ1) 2 +(λ2) 2 +...+(λ r ) 2 >0.99×(sum(λ) i ) 2 )

[0059] Then we can stop selecting the next target singular value and obtain the final value of r, where λ i Let i be the i-th singular value, 1≤i≤n, where n is the total number of singular values ​​in the singular value matrix.

[0060] Then, the row vectors with position indices greater than r in the right singular matrix V are removed from the right singular matrix V to obtain the first reduced-order basis matrix of the first snapshot matrix. Its dimensions are Alternatively, the left singular matrix S of the first snapshot matrix can be multiplied by the singular value matrix Σ of the first snapshot matrix to obtain the singular value decomposition coefficient matrix A1 of the first snapshot matrix, i.e., A1 = S × Σ. Then, the column vectors with position indices greater than r in the singular value decomposition coefficient matrix A1 are removed from the singular value decomposition coefficient matrix A1 to obtain the first reduced-order basis coefficient matrix of the first snapshot matrix. Its dimension is (N1, r).

[0061] This application embodiment decomposes the reference multiphysics coupling calculation results of the reactor under multiple first operating conditions at multiple times into two low-order matrices: a first reduced-order basis matrix and a first reduced-order basis coefficient matrix, from a high-order first snapshot matrix. This improves the efficiency of determining the predicted multiphysics coupling calculation results of the reactor under other operating conditions using the reference multiphysics coupling calculation results of the reactor under multiple first operating conditions. This improves the efficiency of uncertainty analysis of reactor multiphysics coupling calculation and reduces the cost of uncertainty analysis.

[0062] In step S102 above, the second snapshot matrix of the reactor's multiphysics field is determined based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix, including:

[0063] Step S201: Determine the radial basis function mapping coefficient matrix based on the first reduced-order basis coefficient matrix and the distance weight matrix; wherein, the distance weight matrix is ​​the matrix of the distance weight function between each of the multiple first working conditions;

[0064] Step S202: Determine the second reduced-order basis coefficient matrix based on the first interpolation matrix and the radial basis function mapping coefficient matrix;

[0065] Step S203: Multiply the first reduced-order basis matrix with the second reduced-order basis coefficient matrix to obtain the second snapshot matrix of the reactor's multiphysics field.

[0066] Optionally, the distance weight matrix in step S201 above is as follows:

[0067]

[0068] in, Let be the distance weight matrix, with dimensions (N1, N1). For the j-th first working condition among multiple first working conditions With the i-th first working condition Distance weighting function between them.

[0069] Optionally, the distance weighting function described above is as follows:

[0070]

[0071] Where c is the smoothing factor of the radial basis function (RBF), and its value varies depending on the reactor design space.

[0072] Optionally, the radial basis function mapping coefficient matrix in step S201 above is determined by the following formula:

[0073]

[0074] Where B is the radial basis function mapping coefficient matrix, and its dimension is (N1, r).

[0075] The first interpolation matrix in step S202 above is an interpolation matrix of multiple first operating conditions and multiple second operating conditions. Optionally, the multiple second operating conditions are multiple operating conditions determined by second sampling based on the probability distribution ranges followed by multiple variables of the reactor. In the specific design scheme of the reactor, the values ​​of each variable of the reactor, within the manufacturing error disturbance range, generally conform to probability distributions such as normal distribution, beta distribution, and uniform distribution. For example, in the reactor design scheme, the height of the reactor is 1m, and within its manufacturing error disturbance range, it follows a normal distribution range of 0.9m ≤ reactor height ≤ 1.1m. The probability distribution ranges followed by each variable of the reactor can be defined, and each variable and its probability distribution range constitute a joint probability distribution range of multiple variables. Furthermore, a second sampling can be performed on the joint probability distribution range using simple random sampling (such as Monte Carlo sampling) or Latin hypercube sampling, resulting in a second sample dataset X2 with dimensions (N2, M), where N2 is the number of samples obtained from the second sampling, and M is the number of variables in the reactor. The samples obtained from the second sampling are used as the second operating conditions of the reactor, resulting in N2 second operating conditions.

[0076] Optionally, the first interpolation matrix in step S202 above is as follows:

[0077]

[0078] in, Let be the interpolation matrix for multiple first operating conditions and multiple second operating conditions, with dimensions (N1, N2). For the j-th second working condition among multiple second working conditions With the i-th first operating condition among multiple first operating conditions Interpolation function between them.

[0079] Alternatively, the above interpolation function is as follows:

[0080]

[0081] Where c is the smoothing factor of the radial basis function (RBF), and its value varies depending on the reactor design space.

[0082] Optionally, the second reduced-order basis coefficient matrix in step S202 above is determined by the following formula:

[0083]

[0084] Here, A2 is the second reduced-order basis coefficient matrix, with dimensions (N2, r).

[0085] Optionally, the second snapshot matrix of the reactor's multiphysics field in step S203 above is determined by the following formula:

[0086]

[0087] in, This is the second snapshot matrix of the multiphysics field of the reactor, with dimensions of... This is the first reduced-order basis matrix.

[0088] This application's embodiments utilize two low-order matrices, the first reduced-order basis matrix and the first reduced-order basis coefficient matrix, to accelerate the determination of the snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple moments under multiple second operating conditions. On the other hand, by utilizing the first interpolation matrix of multiple first operating conditions and multiple second operating conditions, the determination of the snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple moments under multiple second operating conditions can be further accelerated through interpolation. This improves the efficiency of uncertainty analysis in reactor multiphysics coupling calculations and reduces the cost of uncertainty analysis.

[0089] Optionally, the average vector of all row vectors in the second snapshot matrix can be determined using the following formula:

[0090]

[0091] Optionally, the variance vector of all row vectors in the second snapshot matrix can be determined using the following formula:

[0092]

[0093] Among them, Est u The average vector of all row vectors in the second snapshot matrix, with dimensions of . Est σ Let be the variance vector of all row vectors in the second snapshot matrix, with dimension . `numpy.mean()` is a function in the NumPy open-source library that calculates the mean vector, and `numpy.var()` is a function in the NumPy open-source library that calculates the variance vector.

[0094] In one embodiment, step S103 above: determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix, including:

[0095] Based on the mean vector and variance vector of all row vectors in the second snapshot matrix, determine the upper boundary of the 95% confidence interval of the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0096] The upper boundary of the 95% confidence interval is defined as the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0097] Optionally, the upper bound of the 95% confidence interval for the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is:

[0098] |Est u |+k·Est σ

[0099] The value of k is determined based on the number of second working conditions and the specific problem definition, and usually k = 1.96.

[0100] Furthermore, we can let U = |Est u |+k·Est σ The uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is obtained.

[0101] Where U represents the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions, and its dimension is... Any element in U represents the uncertainty of the target physical field located in the first target spatial unit at the target time under multiple second operating conditions of the reactor. The first spatial unit is any spatial unit in the first spatial unit, and the target time is any time among multiple times.

[0102] This application embodiment utilizes two low-order matrices—the first reduced-order basis matrix and the first reduced-order basis coefficient matrix—of the first snapshot matrix of the reactor multiphysics field, combined with the first interpolation matrix of multiple first operating conditions and multiple second operating conditions, to quickly determine the second snapshot matrix of the reactor multiphysics field. Based on the average vector and variance vector of all row vectors in the second snapshot matrix, the uncertainty of the predicted multiphysics field coupling calculation results of the reactor under multiple second operating conditions at multiple times can be quickly determined. This can improve the efficiency of uncertainty analysis in reactor multiphysics field coupling calculation and reduce the cost of uncertainty analysis.

[0103] In another embodiment, step S103 above: determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix, including:

[0104] Step S301: Based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix, determine the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0105] Step S302: Determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector of all row vectors in the second snapshot matrix, the average vector of all row vectors in the deviation matrix, and the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0106] The deviation matrix is ​​used to characterize the deviation of the third snapshot matrix of the reactor multiphysics field determined by the first reduced basis matrix, the radial basis function mapping coefficient matrix and the second interpolation matrix. The second interpolation matrix is ​​an interpolation matrix of multiple first operating conditions and multiple third operating conditions.

[0107] Alternatively, the average vector of all row vectors in the deviation matrix can be determined using the following formula:

[0108]

[0109] in, The deviation matrix has the following dimensions: N3 represents the number of multiple third operating conditions, Err u The average vector of all row vectors in the deviation matrix, with dimensions .

[0110] Alternatively, the variance vector of all row vectors in the deviation matrix can be determined using the following formula:

[0111]

[0112] Among them, Err σ Let be the variance vector of all row vectors in the deviation matrix, with dimension .

[0113] Optionally, the target variance vector of the predicted multiphysics coupling calculation results of the reactor under multiple second operating conditions at multiple times in step S301 above is determined by the following formula:

[0114]

[0115] Among them, E σ Let be the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions, with dimensions .

[0116] Optionally, step S302 above: determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector of all row vectors in the second snapshot matrix, the average vector of all row vectors in the deviation matrix, and the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions, including:

[0117] Based on the average vector of all row vectors in the second snapshot matrix, the average vector of all row vectors in the deviation matrix, and the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions, the upper boundary of the 95% confidence interval of the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is determined.

[0118] The upper boundary of the 95% confidence interval of the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is determined as the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0119] Optionally, the upper bound of the 95% confidence interval for the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is:

[0120] |Est u |+|Err u |+k·E σ

[0121] The value of k is determined based on the number of second working conditions and the specific problem definition, and usually k = 1.96.

[0122] Furthermore, we can let U = |Est u |+|Err u |+k·E σ The uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions is obtained.

[0123] Where U represents the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions, and its dimension is... Any element in U represents the uncertainty of the target physical field located in the first target spatial unit at the target time under multiple second operating conditions of the reactor. The first spatial unit is any spatial unit in the first spatial unit, and the target time is any time among multiple times.

[0124] This application embodiment considers two low-order matrices—a first reduced-order basis matrix and a first reduced-order basis coefficient matrix—based on the reference multiphysics coupling calculation results of the reactor under multiple first operating conditions. Combined with a first interpolation matrix for multiple first and second operating conditions, it determines the possible deviations in the predicted multiphysics coupling calculation results of the reactor at multiple moments under multiple second operating conditions. By using the average and variance vectors of all row vectors of the deviation matrix—used to characterize the deviation of the third snapshot matrix of the reactor multiphysics determined based on the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix—the average and variance vectors of all row vectors in the second snapshot matrix of the reactor under multiple second operating conditions are corrected. This not only improves the efficiency and reduces the cost of uncertainty analysis in reactor multiphysics coupling calculations but also enhances the accuracy of uncertainty analysis in reactor multiphysics coupling calculations.

[0125] Before step S301 above: determining the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix, the uncertainty analysis method further includes:

[0126] Based on the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix, the third snapshot matrix of the reactor multiphysics is determined; wherein, the third snapshot matrix is ​​a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple third operating conditions.

[0127] Obtain the fourth snapshot matrix of the reactor multiphysics field; the fourth snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple third operating conditions;

[0128] The deviation between the third snapshot matrix and the fourth snapshot matrix is ​​determined to obtain the deviation matrix.

[0129] Optionally, the reference multiphysics coupling calculation results of the reactor at multiple moments under multiple third operating conditions can be user-defined multiphysics coupling calculation results, or multiphysics coupling calculation results obtained by solving the multiphysics coupling calculation equations. This application does not limit the method of obtaining the reference multiphysics coupling calculation results of the reactor at multiple moments under multiple third operating conditions.

[0130] Optionally, the multiple third operating conditions are multiple operating conditions determined by third sampling based on the value range of multiple variables of the reactor in the design space. The specific process of obtaining multiple third operating conditions and obtaining the fourth snapshot matrix of the reactor multiphysics field is the same as the process of obtaining multiple first operating conditions and obtaining the first snapshot matrix of the reactor multiphysics field described above, and will not be repeated here. The first sampling, second sampling, and third sampling mentioned in this application can be the same sampling method or different sampling methods.

[0131] In practical implementation, sufficient sampling can be performed based on each variable and its value range in the design space using simple random sampling (such as Monte Carlo sampling) or Latin hypercube sampling. The resulting total sample dataset is then split into a first sample dataset X1(N1,M) and a third sample dataset X3(N3,M), where N1 is the number of samples in the first sample dataset, N3 is the number of samples in the third sample dataset, and M is the number of variables in the reactor. The samples from the first sample dataset are used as the first operating conditions of the reactor, resulting in N1 first operating conditions. The samples from the third sample dataset are used as the third operating conditions of the reactor, resulting in N3 third operating conditions. The first and fourth snapshot matrices of the reactor multiphysics can also be derived by referring to the partitioning of the sample dataset. Correspondingly, the snapshot matrix of the reactor's reference multiphysics coupling calculation results obtained based on the total sample dataset is split into the first and fourth snapshot matrices of the reactor multiphysics.

[0132] Alternatively, the second interpolation matrix is ​​as follows:

[0133]

[0134] in, Let be the interpolation matrix for multiple first operating conditions and multiple third operating conditions, with dimensions (N1, N3). For the j-th third working condition among multiple third working conditions With the i-th first operating condition among multiple first operating conditions Interpolation function between them.

[0135] Alternatively, the above interpolation function is as follows:

[0136]

[0137] Where c is the smoothing factor of the radial basis function (RBF), and its value varies depending on the reactor design space.

[0138] Optionally, the third snapshot matrix of the reactor multiphysics field is determined by the following formula:

[0139]

[0140] Where A3 is the third reduced-order basis coefficient with dimension (N3×r), and B is the radial basis function mapping coefficient matrix with dimension (N1×r). Let be the first reduced-order basis matrix, with dimension . This is a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple third operating conditions, i.e., the third snapshot matrix of the reactor multiphysics, with dimensions of...

[0141] Furthermore, the deviation matrix can be determined using the following formula:

[0142]

[0143] in, The deviation matrix has the following dimensions: N3 represents the number of third operating conditions, and U3 is the snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple third operating conditions, i.e., the fourth snapshot matrix, with dimensions of...

[0144] This application embodiment uses two low-order matrices—a first reduced-order basis matrix and a first reduced-order basis coefficient matrix—based on the reference multiphysics coupling calculation results of the reactor under multiple first operating conditions, combined with a first interpolation matrix for multiple first operating conditions and multiple second operating conditions. This allows for the rapid determination of the predicted multiphysics coupling calculation results of the reactor at multiple moments under multiple second operating conditions, improving the efficiency of uncertainty analysis in reactor multiphysics coupling calculations and reducing the cost of uncertainty analysis. Furthermore, by using the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix, a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple moments under multiple third operating conditions can be determined, accurately determining the deviation matrix. Further, based on the average vector and variance vector of all row vectors in the deviation matrix, the average vector and variance vector of all row vectors in the second snapshot matrix of the reactor under multiple second operating conditions are corrected, improving the accuracy of uncertainty analysis in reactor multiphysics coupling calculations.

[0145] Please see Figure 4 This application embodiment also provides an uncertainty analysis system 400 for reactor multiphysics coupling calculation, which can realize the above-mentioned uncertainty analysis method for reactor multiphysics coupling calculation. The system includes: an acquisition module 401, a snapshot module 402 and an uncertainty module 403.

[0146] The acquisition module 401 is used to acquire the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each first operating condition;

[0147] The snapshot module 402 is used to determine the second snapshot matrix of the reactor multiphysics field based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix; wherein, the first interpolation matrix is ​​an interpolation matrix of multiple first operating conditions and multiple second operating conditions, and the second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics field coupling calculation results of the reactor at multiple times under multiple second operating conditions. Each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical fields of multiple first spatial units located in the reactor at multiple times under each second operating condition.

[0148] Uncertainty module 403 is used to determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix.

[0149] Among them, the multiple first spatial units are multiple spatial units in the reactor that correspond to the target physical field, and the target physical field is any physical field in the multi-physics field.

[0150] The uncertainty analysis system for reactor multiphysics coupling calculation provided in this application embodiment can realize all the steps of the above-described uncertainty analysis method embodiment for reactor multiphysics coupling calculation and achieve the same technical effect. To avoid repetition, it will not be described again here.

[0151] Optionally, such as Figure 5 As shown, this application embodiment also provides an electronic device 500, including a processor 501 and a memory 502. The memory 502 stores a program or instructions that can run on the processor 501. When the program or instructions are executed by the processor 501, they implement the various steps of the uncertainty analysis method embodiment for reactor multiphysics coupling calculation described above, and achieve the same technical effect. To avoid repetition, they will not be described again here. It should be noted that the electronic device in this application embodiment includes the aforementioned mobile electronic device and non-mobile electronic device.

[0152] Figure 6 To illustrate the hardware structure of the electronic device according to the embodiments of this application, the electronic device includes:

[0153] The processor 601 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application.

[0154] The memory 602 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 602 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 602 and called by the processor 601 to execute the uncertainty analysis method for reactor multiphysics coupling calculations according to the embodiments of this application.

[0155] The input / output interface 603 is used to implement information input and output;

[0156] The communication interface 604 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0157] Bus 605 transmits information between various components of the device (e.g., processor 601, memory 602, input / output interface 603, and communication interface 604);

[0158] The processor 601, memory 602, input / output interface 603, and communication interface 604 are connected to each other within the device via bus 605.

[0159] The electronic device provided in this application embodiment can realize each step of the above-described uncertainty analysis method embodiment for multiphysics coupling calculation of reactors, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0160] This application also provides a computer-readable storage medium storing a program or instructions. When the program or instructions are executed by a processor, they implement the various steps of the above-described uncertainty analysis method embodiment for reactor multiphysics coupling calculation and achieve the same technical effect. To avoid repetition, they will not be described again here.

[0161] The processor is the processor in the electronic device described in the above embodiments. The computer-readable storage medium includes computer-readable storage media such as computer read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0162] This application embodiment also provides a chip, which includes a processor and a communication interface. The communication interface and the processor are coupled. The processor is used to run programs or instructions to implement the various steps of the above-described embodiment of the uncertainty analysis method for multiphysics coupling calculation of reactors, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0163] It should be understood that the chip mentioned in the embodiments of this application may also be referred to as a system-on-a-chip, system chip, chip system, or system-on-a-chip, etc.

[0164] This application provides a computer program product stored in a storage medium. The program product is executed by at least one processor to implement the various steps of the uncertainty analysis method embodiment for reactor multiphysics coupling calculation described above, and can achieve the same technical effect. To avoid repetition, it will not be described again here.

[0165] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes that element. Furthermore, it should be noted that the scope of the methods and apparatuses in the embodiments of this application is not limited to performing functions in the order shown or discussed, but may also include performing functions substantially simultaneously or in the reverse order, depending on the functions involved. For example, the described methods may be performed in a different order than described, and various steps may be added, omitted, or combined. Additionally, features described with reference to certain examples may be combined in other examples.

[0166] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a computer software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) and includes several instructions to cause a terminal (which may be a mobile phone, computer, server, or network device, etc.) to execute the methods described in the various embodiments of this application.

[0167] The embodiments of this application have been described above with reference to the accompanying drawings. However, this application is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of this application without departing from the spirit and scope of the claims, and all of these forms are within the protection scope of this application.

Claims

1. An uncertainty analysis method for multiphysics coupling calculations in a reactor, characterized in that, include: Obtain the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical field of multiple first spatial units located in the reactor at multiple times under each first operating condition; Based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix, a second snapshot matrix of the reactor multiphysics field is determined; wherein, the first interpolation matrix is ​​an interpolation matrix of the plurality of first operating conditions and the plurality of second operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics field coupling calculation results of the reactor at multiple times under the plurality of second operating conditions, and each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical field of the plurality of first spatial units in the reactor at the plurality of times under each second operating condition; Based on the average vector and variance vector of all row vectors in the second snapshot matrix, determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions; Wherein, the plurality of first spatial units are multiple spatial units in the reactor corresponding to the target physical field, and the target physical field is any one of the multiple physical fields.

2. The uncertainty analysis method as described in claim 1, characterized in that, The first reduced-order basis matrix and the first reduced-order basis coefficient matrix for obtaining the first snapshot matrix of the reactor multiphysics field include: Singular value decomposition is performed on the transposed first snapshot matrix to determine the left singular matrix, right singular matrix, and singular value matrix of the first snapshot matrix; wherein, the singular value matrix is ​​a diagonal matrix, the elements on the diagonal of the singular value matrix are the singular values ​​of the first snapshot matrix, and the singular values ​​are arranged from top to bottom on the diagonal of the singular value matrix in descending order. Remove the row vectors with position numbers greater than r from the right singular matrix to obtain the first reduced-order basis matrix of the first snapshot matrix; The column vectors with position numbers greater than r in the matrix obtained by multiplying the left singular matrix and the singular value matrix are removed from the matrix obtained by multiplying the left singular matrix and the singular value matrix to obtain the first reduced-order basis coefficient matrix; Where r is the number of target singular values ​​selected in descending order of the singular values, and the sum of the squares of the selected r target singular values ​​is greater than a preset value.

3. The uncertainty analysis method as described in claim 1, characterized in that, The step of determining the second snapshot matrix of the reactor multiphysics field based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix includes: Based on the first reduced-order basis coefficient matrix and the distance weight matrix, the radial basis function mapping coefficient matrix is ​​determined; wherein, the distance weight matrix is ​​the matrix of the distance weight function between each of the plurality of first working conditions; The second reduced-order basis coefficient matrix is ​​determined based on the first interpolation matrix and the radial basis function mapping coefficient matrix; Multiplying the first reduced-order basis matrix with the second reduced-order basis coefficient matrix yields the second snapshot matrix of the multiphysics field of the reactor.

4. The uncertainty analysis method as described in claim 3, characterized in that, The step of determining the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix includes: Based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix, the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions is determined. The uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions is determined based on the average vector of all row vectors in the second snapshot matrix, the average vector of all row vectors in the deviation matrix, and the target variance vector. The deviation matrix is ​​used to characterize the deviation of the third snapshot matrix of the reactor multiphysics field determined according to the first reduced basis matrix, the radial basis function mapping coefficient matrix and the second interpolation matrix, wherein the second interpolation matrix is ​​the interpolation matrix of the plurality of first operating conditions and the plurality of third operating conditions.

5. The uncertainty analysis method as described in claim 4, characterized in that, Before the step of determining the target variance vector of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions based on the variance vectors of all row vectors in the second snapshot matrix and the variance vectors of all row vectors in the deviation matrix, the uncertainty analysis method further includes: Based on the first reduced-order basis matrix, the radial basis function mapping coefficient matrix, and the second interpolation matrix, the third snapshot matrix of the reactor multiphysics is determined; wherein, the third snapshot matrix is ​​a snapshot matrix of the predicted multiphysics coupling calculation results of the reactor at multiple times under multiple third operating conditions; Obtain the fourth snapshot matrix of the reactor multiphysics field; the fourth snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple third operating conditions; The deviation matrix is ​​obtained by determining the deviation between the third snapshot matrix and the fourth snapshot matrix.

6. The uncertainty analysis method as described in claim 4, characterized in that, The plurality of first operating conditions are multiple operating conditions determined by first sampling based on the value range of multiple variables of the reactor in the design space. The plurality of second operating conditions are multiple operating conditions determined by second sampling based on the probability distribution range followed by multiple variables of the reactor. The multiple third operating conditions are multiple operating conditions determined by third sampling based on the value range of multiple variables of the reactor in the design space.

7. The uncertainty analysis method as described in claim 1, characterized in that, Before obtaining the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field, the uncertainty analysis method further includes: The reactor is divided at least once according to each physical field in the multiphysics field to obtain multiple spatial units of the reactor corresponding to each physical field. Using a multiphysics coupling calculation model, the values ​​of each physical field located in the multiple spatial units of the reactor at multiple times under each first operating condition are calculated, and reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions are obtained. The first snapshot matrix is ​​obtained by determining the snapshot matrix of the reference multiphysics coupling calculation results of the reactor at multiple times under multiple first operating conditions.

8. An uncertainty analysis system for multiphysics coupling calculations in a reactor, characterized in that, It includes an acquisition module, a snapshot module, and an uncertainty module; The acquisition module is used to acquire the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multiphysics field; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multiphysics field coupling calculation results of the reactor at multiple times under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of the values ​​of the target physical fields located in multiple first spatial units in the reactor at multiple times under each first operating condition; The snapshot module is used to determine a second snapshot matrix of the reactor multiphysics field based on the first reduced-order basis matrix, the first reduced-order basis coefficient matrix, and the first interpolation matrix; wherein, the first interpolation matrix is ​​an interpolation matrix of the plurality of first operating conditions and the plurality of second operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multiphysics field coupling calculation results of the reactor at multiple times under the plurality of second operating conditions, and each row vector in the second snapshot matrix includes a snapshot set of the values ​​of the target physical field of the plurality of first spatial units in the reactor at the plurality of times under each second operating condition; The uncertainty module is used to determine the uncertainty of the predicted multiphysics coupling calculation results of the reactor at multiple times under the multiple second operating conditions based on the average vector and variance vector of all row vectors in the second snapshot matrix. Wherein, the plurality of first spatial units are multiple spatial units in the reactor corresponding to the target physical field, and the target physical field is any one of the multiple physical fields.

9. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the uncertainty analysis method as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the uncertainty analysis method as described in any one of claims 1 to 7.

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