Reactor multi-physics coupling calculation uncertainty analysis method and product

Abstract

The invention provides an uncertainty analysis method and product for reactor multi-physics coupling calculation, and the method comprises the steps: obtaining a first snapshot matrix of a reference multi-physics coupling calculation result of a reactor at a plurality of moments under a plurality of first working conditions, and a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of the first snapshot matrix; according to the first reduced-order basis matrix, the first reduced-order basis coefficient matrix and the interpolation matrixes of the plurality of first working conditions and the plurality of second working conditions, determining a second snapshot matrix for predicting the multi-physics coupling calculation result of the reactor at the plurality of moments under the plurality of second working conditions; and according to the average vector and the variance vector of all row vectors in the second snapshot matrix, determining the uncertainty of the predicted multi-physics coupling calculation result of the reactor at multiple moments under multiple second working conditions. According to the method, the efficiency of uncertainty analysis of reactor multi-physical field coupling calculation can be improved, and the cost of uncertainty analysis is reduced.

Description

Technical Field

[0001] The present invention relates to the field of nuclear energy technology, and in particular to an uncertainty analysis method and product for reactor multi-physical field coupling calculation. Background Art

[0002] In the field of nuclear energy technology, uncertainty analysis of reactor multi-physics coupling calculations is usually required to determine the impact of input variables on the reliability and accuracy of reactor multi-physics coupling calculation results. In order to reduce the error of uncertainty analysis, it is usually necessary to increase the sample data of input variables. By performing statistics on expected values, variances and other indicators of reactor multi-physics coupling calculation results obtained by calculating hundreds of millions of sample data, the accuracy of uncertainty analysis of reactor multi-physics coupling calculations can be ensured.

[0003] However, most of the current uncertainty analysis methods use the reactor multi-physics field coupling calculation model to calculate hundreds of millions of sample data to obtain the reactor multi-physics field coupling calculation results. The calculation process often takes several days. When the dimension of the input variables is high, it even takes several months, resulting in low efficiency and high cost of uncertainty analysis of reactor multi-physics field coupling calculations.

[0004] How to improve the efficiency of uncertainty analysis in reactor multi-physics field coupling calculations and reduce the cost of uncertainty analysis has become an urgent problem to be solved. Summary of the invention

[0005] The main purpose of the embodiments of the present application is to propose an uncertainty analysis method and product for reactor multi-physics field coupling calculations, aiming to improve the efficiency of uncertainty analysis for reactor multi-physics field coupling calculations and reduce the cost of uncertainty analysis.

[0006] The present application provides an uncertainty analysis method for reactor multi-physics field coupling calculation, including: obtaining a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of a reactor multi-physics field; wherein the first snapshot matrix is ​​a snapshot matrix of a reference multi-physics field coupling calculation result of the reactor at multiple moments under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of values ​​of a target physical field of multiple first spatial units located in the reactor at multiple moments under each first operating condition; determining a second snapshot matrix of the reactor multi-physics field according to 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 multiple first operating conditions and multiple second The interpolation matrix of the operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under the multiple 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 multiple first spatial units located in the reactor at the multiple moments under each second operating condition; according to the average vector and variance vector of all row vectors in the second snapshot matrix, the uncertainty of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions is determined; 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 multi-physical fields.

[0007] In one embodiment, the method of obtaining a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of a reactor multi-physical field includes: performing singular value decomposition on the transposed first snapshot matrix to determine a left singular matrix, a right singular matrix and a 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 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 row vectors with position numbers greater than r in the right singular matrix from the right singular matrix to obtain a first reduced-order basis matrix of the first snapshot matrix; removing column vectors with position numbers greater than r in a matrix obtained by multiplying the left singular matrix and the singular value matrix from a 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 squares of the r selected target singular values ​​is greater than a preset value.

[0008] In one embodiment, determining the second snapshot matrix of the reactor multi-physical field according to 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 according to the first reduced-order basis coefficient matrix and the distance weight matrix; wherein the distance weight matrix is ​​a matrix of distance weight functions between each first operating condition in the multiple first operating conditions; determining the second reduced-order basis coefficient matrix according to the first interpolation matrix and the radial basis function mapping coefficient matrix; and multiplying the first reduced-order basis matrix with the second reduced-order basis coefficient matrix to obtain the second snapshot matrix of the reactor multi-physical field.

[0009] In one embodiment, the step of determining the uncertainty of the predicted multi-physics coupling calculation results of the reactor at multiple moments under the 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 multi-physics coupling calculation results of the reactor at multiple moments under the multiple second operating conditions based on the variance vector of all row vectors in the second snapshot matrix and the variance vector of all row vectors in the deviation matrix; determining the uncertainty of the predicted multi-physics coupling calculation results of the reactor at multiple moments under the 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 multi-physics field 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 the step of determining the target variance vector of the predicted multi-physics coupling calculation results of the reactor at multiple moments 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 also includes: determining a third snapshot matrix of the reactor multi-physics field 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 multi-physics coupling calculation results of the reactor at multiple moments under the multiple third operating conditions; obtaining a fourth snapshot matrix of the reactor multi-physics field; the fourth snapshot matrix is ​​a snapshot matrix of the reference multi-physics coupling calculation results of the reactor at multiple moments 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 multiple 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 multiple second operating conditions are multiple operating conditions determined by second sampling based on the probability distribution range obeyed by the 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.

[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 multi-physical field, the uncertainty analysis method also includes: dividing the reactor at least once according to each physical field in the multi-physical field to obtain a plurality of spatial units of the reactor corresponding to each physical field; calculating the values ​​of each physical field located in the plurality of spatial units at the plurality of moments under each first operating condition of the reactor through a multi-physical field coupling calculation model to obtain a reference multi-physical field coupling calculation result of the reactor at the plurality of moments under the plurality of first operating conditions; determining a snapshot matrix of the reference multi-physical field coupling calculation result of the reactor at the plurality of moments under the plurality of first operating conditions to obtain the first snapshot matrix.

[0013] The present application also improves an uncertainty analysis system for reactor multi-physics field 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 multi-physics field; wherein the first snapshot matrix is ​​a snapshot matrix of a reference multi-physics field coupling calculation result of the reactor at multiple moments under multiple first operating conditions, and each column vector in the first snapshot matrix includes a snapshot set of values ​​of a target physical field of multiple first spatial units located in the reactor at multiple moments under each first operating condition; the snapshot module is used to determine a second snapshot matrix of the reactor multi-physics field according to the first reduced-order basis matrix, the first reduced-order basis coefficient matrix and the first interpolation matrix; wherein the first interpolation matrix is ​​a snapshot matrix of the multi-physics field coupling calculation result of the reactor at multiple moments. The invention relates to an interpolation matrix of a first operating condition and a plurality of second operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at a plurality of moments under the plurality of second operating conditions, 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 located in the reactor at the plurality of moments under each second operating condition; the uncertainty module is used to determine the uncertainty of the predicted multi-physical field coupling calculation results of the reactor at a plurality of moments under the plurality of second operating conditions according to the average vector and variance vector of all row vectors in the second snapshot matrix; wherein the plurality of first spatial units are a plurality of spatial units in the reactor corresponding to the target physical field, and the target physical field is any physical field in the multi-physical fields.

[0014] The present application also provides an electronic device, which includes a memory and a processor, wherein the memory stores a computer program, and the processor implements the uncertainty analysis method as described above when executing the computer program.

[0015] The present application also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above uncertainty analysis method when executed by a processor.

[0016] The present application provides an uncertainty analysis method and product for reactor multi-physics coupling calculations. By utilizing two low-order matrices of the snapshot matrix of the reference multi-physics coupling calculation results of the reactor at multiple moments 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 multi-physics coupling calculation results of the reactor at multiple moments under multiple second operating conditions can be quickly determined, thereby improving the efficiency of uncertainty analysis of reactor multi-physics coupling calculations and reducing the cost of uncertainty analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is a flow chart of the uncertainty analysis method of reactor multi-physics field coupling calculation provided in the embodiment of the present application;

[0018] Figure 2 yes Figure 1 A schematic flow chart of step S102 in FIG.

[0019] Figure 3 yes Figure 1 Schematic diagram of the process of step S103 in ;

[0020] Figure 4 It is a structural schematic diagram of an uncertainty analysis system for reactor multi-physics field coupling calculation provided in an embodiment of the present application;

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

[0022] Figure 6 It is a structural diagram of another embodiment of the electronic device provided in the embodiment of the present application. DETAILED DESCRIPTION

[0023] The following will be combined with the drawings in the embodiments of the present application to clearly describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments in the present application belong to the scope of protection of this application.

[0024] The terms "first", "second", etc. in the specification and claims of the present application are used to distinguish similar objects, and are not used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable under appropriate circumstances, so that the embodiments of the present application can be implemented in an order other than those illustrated or described here, and the objects distinguished by "first", "second", etc. are generally of one type, and the number of objects is not limited. For example, the first object can be one or more. In addition, "and / or" in the specification and claims represents at least one of the connected objects, and the character " / " generally indicates that the objects associated with each other are in an "or" relationship.

[0025] The uncertainty analysis method for reactor multi-physics field coupling calculation provided in the embodiment of the present application can be applied to the terminal, can also be applied to the server side, and can also be software running in the terminal or the server side. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, etc.; the server side can be configured as an independent physical server, or a server cluster or distributed system composed of multiple physical servers, and can also be configured as a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms; the software can be an application of the uncertainty analysis method for reactor multi-physics field coupling calculation, etc., but is not limited to the above forms.

[0026] The uncertainty analysis method for reactor multi-physical field coupling calculation provided by the embodiment of the present application is described in detail below with reference to the accompanying drawings through specific embodiments.

[0027] See also Figure 1 The embodiment of the present application provides an uncertainty analysis method for reactor multi-physics field coupling calculation, including:

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

[0029] Step S102: determining a second snapshot matrix of the multi-physical field of the reactor according to 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, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under the 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 moments under each second operating condition;

[0030] Step S103: determining the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to the average vector and the 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 corresponding to the target physical field, and the target physical field is any physical field in the multi-physical field.

[0032] The embodiment of the present application utilizes two low-order matrices of the snapshot matrix of the reference multi-physics field coupling calculation results of the reactor at multiple moments 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, to quickly determine the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions, thereby improving the efficiency of uncertainty analysis of the reactor multi-physics field coupling calculation and reducing the cost of uncertainty analysis.

[0033] Optionally, the multiple 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, wherein the multiple variables of the reactor include variable parameters input by the user into the reactor multi-physics field calculation model, and variable parameters of the reactor multi-physics field calculation model. Exemplarily, the variable parameters input by the user may include, but are not limited to, geometric parameters such as the height, length, and radius of the reactor, uranium loading of the fuel, enrichment and other nuclide densities, the temperature of the reactor inlet coolant, the position of the control rod, the operating power level and other operating conditions. The variable parameters of the reactor multi-physics field calculation model may include, but are not limited to, the reaction cross-section coefficient of neutrons and materials and the fitting coefficient of the model equation group.

[0034] Furthermore, the design space ε of each variable can be defined i,min ≤ε i ≤ε i,max , the design space represents the possible range of variation of each variable, where ε i represents the i-th variable in the reactor, ε i,min and ε i,max Respectively represent the upper and lower boundaries of the variation range of the i-th variable, such as 1cm≤reactor height≤10m. Each variable and its value range in the design space constitutes a two-dimensional design space, which can be represented as a square area on the plane. Simple random sampling (such as Monte Carlo sampling) or Latin hypercube sampling can be used to perform the first sampling of the two-dimensional design space to obtain the first sample data set X 1 , whose dimension is (N 1 ,M), where N 1 is the number of samples obtained by the first sampling, and M is the number of variables of the reactor. Each sample obtained by the first sampling is used as a first operating condition of the reactor, that is, N 1 The first operating condition.

[0035] Optionally, the reference multi-physics field coupling calculation results of the reactor at multiple moments under multiple first operating conditions may be multi-physics field coupling calculation results set by the user, or may be multi-physics field coupling calculation results obtained by solving multi-physics field coupling calculation equations. This application does not limit the method for obtaining the reference multi-physics field 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 multi-physical field in the above step S101, the uncertainty analysis method further includes:

[0037] According to each physical field in the multi-physical field, the reactor is divided at least once to obtain a plurality of spatial units of the reactor corresponding to each physical field;

[0038] By using a multi-physics field coupling calculation model, the values ​​of each physical field located in multiple space units at multiple times under each first operating condition of the reactor are calculated to obtain reference multi-physics field coupling calculation results of the reactor at multiple times under the multiple first operating conditions;

[0039] A snapshot matrix of the reference multi-physics field coupling calculation results of the reactor at multiple moments under multiple first operating conditions is determined to obtain a first snapshot matrix.

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

[0041] Exemplarily, there are 157 square components in the radial direction of the reactor, and each side of each square component has 17 sub-components. According to the fuel temperature field and coolant temperature field in the multi-physical field, the reactor can be divided into 30 layers in the axial direction and 4 parts in the radial direction, and 157×4×30=18840 space units are obtained, that is, the fuel temperature field and coolant temperature field in the multi-physical field correspond to 18840 space units in the reactor. According to the fuel power field in the multi-physical field, each sub-component in the reactor (such as fuel rods) can be divided into a space unit, and 157×17×17×30=136119 space units are obtained, that is, the power field in the multi-physical field corresponds to 136119 space units in the reactor.

[0042] Furthermore, the i-th first operating condition x among the plurality of first operating conditions can be 1i ∈X 1 , whose dimension is (1, M), is input into the reactor multi-physics field coupling calculation model, and the reactor multi-physics field coupling calculation is performed to obtain the reference multi-physics field coupling calculation results of the reactor at multiple moments 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] Among them, F(x 1i ) represents the reactor multi-physics field coupling calculation model, x 1i is the i-th first operating condition among multiple first operating conditions, Y 1i,P (K P ,T) is a data set of the fuel power field values ​​of each spatial unit corresponding to the fuel power field in the reactor at multiple times under the first operating condition of the reactor, and its dimension is (K P ,T),K P is the number of spatial units corresponding to the power field; Y 1i,TF (K TF ,T) is a data set of the fuel temperature field values ​​of each spatial unit corresponding to the fuel temperature field in the reactor at multiple times under the first operating condition of the reactor, and its dimension is (K TG ,T),K YF is the number of spatial units corresponding to the fuel temperature field; Y 1i,TC (K TC ,T) is a data set of the coolant temperature field values ​​of each spatial unit corresponding to the coolant temperature field in the reactor at multiple times under the first operating condition of the reactor, and its dimension is (K YC ,T),K YC is the number of spatial units corresponding to the coolant temperature field, and 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 multi-physics 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 multi-physics field coupling calculation results of the reactor under multiple first operating conditions can be constructed into a result matrix to obtain the reference multi-physics field coupling calculation result matrix Y of the reactor under multiple first operating conditions. 1 , whose dimensions are

[0049] Further, a reference multi-physics field coupling calculation result matrix Y of the reactor under multiple first operating conditions is constructed 1 The first snapshot matrix U 1 , whose dimensions are That is, the first snapshot matrix U 1 Any column vector in , with dimension It represents a collection 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] The embodiment of the present application divides the reactor at least once according to each physical field in the multi-physical field to obtain multiple spatial units of the reactor corresponding to each physical field, and can refine the coupling calculation results of each physical field to the spatial units in the reactor corresponding to each physical field, which can improve the accuracy of the reference multi-physical field coupling calculation results of the reactor at multiple moments under multiple first operating conditions. In addition, by constructing a snapshot matrix of the reference multi-physical field coupling calculation results of the reactor at multiple moments under multiple first operating conditions, the reference multi-physical field coupling calculation results of the reactor under multiple first operating conditions are compressed from three-dimensional space to two-dimensional space, thereby improving the convenience of using the reference multi-physical field coupling calculation results of the reactor under multiple first operating conditions to determine the predicted multi-physical field coupling calculation results of the reactor under other operating conditions.

[0051] In one embodiment, the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multi-physical field are obtained in the above step S101, including:

[0052] Performing singular value decomposition on the transposed first snapshot matrix to determine a left singular matrix, a right singular matrix and a singular value matrix of the first snapshot matrix; wherein the singular value matrix is ​​a diagonal matrix, elements on the diagonal of the singular value matrix are 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 row vectors whose position numbers in the right singular matrix are greater than r from the right singular matrix to obtain a first reduced-order basis matrix of the first snapshot matrix;

[0054] The column vectors whose position numbers are 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 a first reduced-order basis coefficient matrix;

[0055] Among them, r is the number of target singular values ​​selected in order from large to small, and the sum of squares of the selected r target singular values ​​is greater than a preset value.

[0056] For example, first, the first snapshot matrix U 1 Transpose to get the first snapshot matrix U 1 The transposed matrix of Its dimension is Next, the transposed matrix of the first snapshot matrix is 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 and has a dimension of (N 1 ,N 1 ). ∑ is the singular value matrix of the first snapshot matrix, which is of dimension The diagonal matrix of , 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. V is the right singular matrix of the first snapshot matrix, which is an orthogonal matrix composed of right singular basis vectors with a dimension of

[0057] Next, select multiple target singular values ​​λ in order from large to small. 1 , 2 , ..., and calculate the sum of squares of multiple selected target singular values ​​in turn. If the rth target singular value is selected in turn, the selected r target singular values ​​meet the following conditions:

[0058] (λ 1 ) 2 +(λ 2 ) 2 +...+(λ r ) 2 >0.99×(sum(λ i ) 2 )

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

[0060] Then, the row vectors with position numbers 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 dimension is In addition, 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 A of the first snapshot matrix: 1 , that is: A 1=S×∑, and the singular value decomposition coefficient matrix A 1 The column vectors with position numbers greater than r in the singular value decomposition coefficient matrix A 1 Remove from the matrix to obtain the first reduced-order basis coefficient matrix of the first snapshot matrix Its dimension is (N 1 ,r).

[0061] The embodiment of the present application decomposes the reference multi-physical field coupling calculation results of the reactor at multiple moments under multiple first operating conditions from a high-order first snapshot matrix into two low-order matrices, a first reduced-order basis matrix and a first reduced-order basis coefficient matrix. This can improve the efficiency of determining the predicted multi-physical field coupling calculation results of the reactor under other operating conditions by utilizing the reference multi-physical field coupling calculation results of the reactor under multiple first operating conditions, thereby improving the efficiency of uncertainty analysis of the reactor multi-physical field coupling calculation and reducing the cost of uncertainty analysis.

[0062] In the above step S102, the second snapshot matrix of the multi-physical field of the reactor is determined according to the first reduced-order basis matrix, the first reduced-order basis coefficient matrix and the first interpolation matrix, including:

[0063] Step S201: determining a radial basis function mapping coefficient matrix according to a first reduced-order basis coefficient matrix and a distance weight matrix; wherein the distance weight matrix is ​​a matrix of distance weight functions between each of a plurality of first operating conditions;

[0064] Step S202: determining a second reduced-order basis coefficient matrix according to the first interpolation matrix and the radial basis function mapping coefficient matrix;

[0065] Step S203: multiply the first reduced-order basis matrix by the second reduced-order basis coefficient matrix to obtain a second snapshot matrix of the multi-physical field of the reactor.

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

[0067]

[0068] in, is the distance weight matrix, whose dimension is (N 1 , N 1 ), is the jth first operating condition among the multiple first operating conditions With the i-th first working condition The distance weight function between .

[0069] Optionally, the distance weight function is as follows:

[0070]

[0071] Wherein, c is the smoothing factor of the radial basis function (RBF), and its value varies according to the change of the reactor design space.

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

[0073]

[0074] Among them, B is the radial basis function mapping coefficient matrix, and its dimension is (N 1 , r).

[0075] The first interpolation matrix in the above step S202 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 the second sampling based on the probability distribution range obeyed by multiple variables of the reactor. In the specific design scheme of the reactor, the values ​​of each variable of the reactor generally conform to the probability distribution such as normal distribution, beta distribution, uniform distribution, etc. within the manufacturing error disturbance range. For example, in the design scheme of the reactor, the height of the reactor is 1m, and within the manufacturing error disturbance range, the normal distribution range it obeys is 0.9m≤reactor height≤1.1m. The probability distribution range obeyed by each variable of the reactor can be defined, and each variable and the probability distribution range it obeys constitute a joint probability distribution range of multiple variables. Further, a simple random sampling (such as Monte Carlo sampling) or a sampling method such as Latin hypercube sampling can be used to perform a second sampling on the joint probability distribution range to obtain a second sample data set X 2 , whose dimension is (N 2 ,M), where N 2 is the number of samples obtained by the second sampling, and M is the number of variables in the reactor. The samples obtained by the second sampling are used as the second operating condition of the reactor, that is, N 2 A second operating condition.

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

[0077]

[0078] in, is an interpolation matrix of multiple first working conditions and multiple second working conditions, and its dimension is (N 1 , N 2 ), is the jth second operating condition among the plurality of second operating conditions and the i-th first operating condition among the plurality of first operating conditions The interpolation function between .

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

[0080]

[0081] Wherein, c is the smoothing factor of the radial basis function (RBF), and its value varies according to the change of the reactor design space.

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

[0083]

[0084] Among them, A 2 is the second reduced-order basis coefficient matrix, whose dimension is (N 2 ,r).

[0085] Optionally, the second snapshot matrix of the multi-physical field of the reactor in the above step S203 is determined by the following formula:

[0086]

[0087] in, is the second snapshot matrix of the multiphysics field of the reactor, and its dimension is is the first reduced-order basis matrix.

[0088] On the one hand, the embodiment of the present application utilizes two low-order matrices, namely the first reduced-order basis matrix and the first reduced-order basis coefficient matrix, which can speed up the determination of the snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under multiple second operating conditions. On the other hand, the first interpolation matrix of multiple first operating conditions and multiple second operating conditions is utilized. Through interpolation, the speed of determining the snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under multiple second operating conditions can be further accelerated, thereby improving the efficiency of uncertainty analysis of reactor multi-physical field coupling calculations and reducing the cost of uncertainty analysis.

[0089] Optionally, the average vector of all row vectors in the second snapshot matrix is ​​determined by the following formula:

[0090]

[0091] Optionally, the variance vector of all row vectors in the second snapshot matrix is ​​determined by the following formula:

[0092]

[0093] Among them, Est uis the average vector of all row vectors in the second snapshot matrix, and its dimension is Est σ is the variance vector of all row vectors in the second snapshot matrix, and its dimension is numpy.mean() is a function in the numpy open source library that solves the mean vector, and numpy.var() is a function in the numpy open source library that solves the variance vector.

[0094] In one embodiment, the above step S103: determining the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to the average vector and the variance vector of all row vectors in the second snapshot matrix, includes:

[0095] Determine the upper boundary of a 95% confidence interval of uncertainty of predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to the average vector and the variance vector of all row vectors in the second snapshot matrix;

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

[0097] Optionally, the upper boundary of the 95% confidence interval of the uncertainty of the predicted multi-physics field 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 according to the number of the second operating conditions and the specific problem definition, and k is usually 1.96.

[0100] Furthermore, we can set U = |Est u |+k·Est σ , and obtain the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0101] Among them, U is the uncertainty of the predicted multi-physics field 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 space unit at the target time under multiple second operating conditions of the reactor. The first space unit is any space unit in the first space unit, and the target time is any time among multiple times.

[0102] The embodiment of the present application utilizes two low-order matrices, namely the first reduced-order basis matrix and the first reduced-order basis coefficient matrix, of the first snapshot matrix of the reactor multi-physics 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 multi-physics field. Based on the average vector and variance vector of all row vectors in the second snapshot matrix, the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions can be quickly determined, thereby improving the efficiency of uncertainty analysis of the reactor multi-physics field coupling calculation and reducing the cost of uncertainty analysis.

[0103] In another embodiment, the above step S103: determining the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to the average vector and the variance vector of all row vectors in the second snapshot matrix, includes:

[0104] Step S301: determining a target variance vector of a predicted multi-physics field coupling calculation result of the reactor at multiple moments under multiple second operating conditions according to variance vectors of all row vectors in the second snapshot matrix and variance vectors of all row vectors in the deviation matrix;

[0105] Step S302: determining the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to 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 multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions;

[0106] Among them, the deviation matrix is ​​used to characterize the deviation of the third snapshot matrix of the reactor multi-physical field determined according to the first reduced-order basis matrix, the radial basis function mapping coefficient matrix and the second interpolation matrix, and the second interpolation matrix is ​​an interpolation matrix of multiple first operating conditions and multiple third operating conditions.

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

[0108]

[0109] in, is the deviation matrix, whose dimension is N 3 is the number of multiple third operating conditions, Err u is the average vector of all row vectors in the deviation matrix, and its dimension is

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

[0111]

[0112] Among them, Err σ is the variance vector of all row vectors in the bias matrix, and its dimension is

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

[0114]

[0115] Among them, E σ is the target variance vector of the predicted multi-physics coupling calculation results of the reactor at multiple times under multiple second operating conditions, and its dimension is

[0116] Optionally, the above step S302: determining the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to 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 multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions, includes:

[0117] Determine the upper boundary of a 95% confidence interval of uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to 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 multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions;

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

[0119] Optionally, the upper boundary of the 95% confidence interval of the uncertainty of the predicted multi-physics field 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 according to the number of the second operating conditions and the specific problem definition, and k is usually 1.96.

[0122] Furthermore, we can set U = |Est u |+|Err u |+k·E σ , and obtain the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple times under multiple second operating conditions.

[0123] Among them, U is the uncertainty of the predicted multi-physics field 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 space unit at the target time under multiple second operating conditions of the reactor. The first space unit is any space unit in the first space unit, and the target time is any time among multiple times.

[0124] The embodiment of the present application considers two low-order matrices, namely, a first reduced-order basis matrix and a first reduced-order basis coefficient matrix, based on the reference multi-physics coupling calculation results of the reactor under multiple first operating conditions, and combines the first interpolation matrix of multiple first operating conditions and multiple second operating conditions to determine the possible deviations in the predicted multi-physics coupling calculation results of the reactor at multiple moments under multiple second operating conditions. By using the average vector and variance vector of all row vectors of the deviation matrix used to characterize the deviation of the third snapshot matrix of the reactor multi-physics field determined according to the first reduced-order basis matrix, the radial basis function mapping coefficient matrix and the second interpolation 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. This can not only improve the efficiency of uncertainty analysis of reactor multi-physics coupling calculations and reduce the cost of uncertainty analysis, but also improve the accuracy of uncertainty analysis of reactor multi-physics coupling calculations.

[0125] Before the above step S301: determining the target variance vector of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to 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] Determine a third snapshot matrix of the multi-physics field of the reactor according to 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 multi-physics field coupling calculation results of the reactor at multiple moments under multiple third operating conditions;

[0127] Obtaining a fourth snapshot matrix of the reactor multi-physics field; the fourth snapshot matrix is ​​a snapshot matrix of the reference multi-physics field coupling calculation results of the reactor at multiple moments under multiple third operating conditions;

[0128] Determine the deviation between the third snapshot matrix and the fourth snapshot matrix to obtain a deviation matrix.

[0129] Optionally, the reference multi-physics coupling calculation results of the reactor at multiple moments under multiple third operating conditions may be multi-physics coupling calculation results set by a user, or may be multi-physics coupling calculation results obtained by solving multi-physics coupling calculation equations. This application does not limit the method for obtaining the reference multi-physics 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 the third sampling based on the value range of multiple variables of the reactor in the design space. The specific process of obtaining the multiple third operating conditions and obtaining the fourth snapshot matrix of the reactor multi-physical field refers to the above-mentioned process of obtaining the multiple first operating conditions and obtaining the first snapshot matrix of the reactor multi-physical field, which 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 actual implementation, sufficient sampling can be performed based on each variable and the value range of each variable in its design space using simple random sampling (such as Monte Carlo sampling) or Latin hypercube sampling, and the total sample data set obtained is split into the first sample data set X 1 (N 1 ,M) and the third sample data set X 3 (N 3 ,M), where N 1 is the number of samples in the first sample data set, N 3 is the number of samples in the third sample data set, and M is the number of variables in the reactor. The samples in the first sample data set obtained by sampling are used as the first operating condition of the reactor, that is, N 1 The samples in the third sample data set obtained by sampling are used as the third operating condition of the reactor, that is, N 3 The first snapshot matrix of the reactor multi-physics field and the fourth snapshot matrix of the reactor multi-physics field can also refer to the division of the sample data set, and correspondingly the snapshot matrix of the reference multi-physics field coupling calculation result of the reactor obtained based on the total sample data set is split into the first snapshot matrix of the reactor multi-physics field and the fourth snapshot matrix of the reactor multi-physics field.

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

[0133]

[0134] in, is an interpolation matrix of multiple first working conditions and multiple third working conditions, and its dimension is (N 1 , N 3 ), is the jth third operating condition among the plurality of third operating conditions and the i-th first operating condition among the plurality of first operating conditions The interpolation function between .

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

[0136]

[0137] Wherein, c is the smoothing factor of the radial basis function (RBF), and its value varies according to the change of the reactor design space.

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

[0139]

[0140] Among them, A 3 is the third reduced-order basis coefficient, whose dimension is (N 3 ×r), B is the radial basis function mapping coefficient matrix, and its dimension is (N 1 ×r), is the first reduced-order basis matrix, whose dimension is is the snapshot matrix of the predicted multi-physics coupling calculation results of the reactor at multiple times under multiple third operating conditions, that is, the third snapshot matrix of the reactor multi-physics field, and its dimension is

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

[0142]

[0143] in, is the deviation matrix, whose dimension is N 3 is the number of the third operating conditions, U 3 is the snapshot matrix of the reference multi-physics field coupling calculation results of the reactor at multiple times under multiple third operating conditions, that is, the fourth snapshot matrix, whose dimension is

[0144] The embodiment of the present application uses two low-order matrices, namely the first reduced-order basis matrix and the first reduced-order basis coefficient matrix, of the reference multi-physics coupling calculation results of the reactor under multiple first operating conditions, combined with the first interpolation matrix of multiple first operating conditions and multiple second operating conditions, to quickly determine the predicted multi-physics coupling calculation results of the reactor at multiple moments under multiple second operating conditions, which can improve the efficiency of uncertainty analysis of reactor multi-physics coupling calculations and reduce the cost of uncertainty analysis. In addition, the snapshot matrix of the predicted multi-physics coupling calculation results of the reactor at multiple moments under multiple third operating conditions is determined through the first reduced-order basis matrix, the radial basis function mapping coefficient matrix and the second interpolation matrix, which can accurately determine the deviation matrix, and further based on the average vector and variance vector of all row vectors of 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, which can improve the accuracy of uncertainty analysis of reactor multi-physics coupling calculations.

[0145] See also Figure 4 The embodiment of the present application also provides an uncertainty analysis system 400 for reactor multi-physical field coupling calculation, which can implement the above-mentioned uncertainty analysis method for reactor multi-physical field coupling calculation. The system includes: an acquisition module 401, a snapshot module 402 and an uncertainty module 403.

[0146] Wherein, the acquisition module 401 is used to obtain the first reduced-order basis matrix and the first reduced-order basis coefficient matrix of the first snapshot matrix of the reactor multi-physical field; wherein, the first snapshot matrix is ​​a snapshot matrix of the reference multi-physical field coupling calculation results of the reactor at multiple moments 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 moments under each first operating condition;

[0147] The snapshot module 402 is used to determine a second snapshot matrix of the multi-physical field of the reactor according to 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, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments 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 moments under each second operating condition;

[0148] The uncertainty module 403 is used to determine the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under multiple second operating conditions according to the average vector and the 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 corresponding to the target physical field, and the target physical field is any physical field in the multi-physical field.

[0150] The uncertainty analysis system for reactor multi-physical field coupling calculations provided in the embodiment of the present application can implement the various steps of the above-mentioned uncertainty analysis method embodiment for reactor multi-physical field coupling calculations, and can achieve the same technical effect. To avoid repetition, it will not be repeated here.

[0151] Alternatively, if Figure 5 As shown, the embodiment of the present application also provides an electronic device 500, including a processor 501 and a memory 502, the memory 502 stores a program or instruction that can be run on the processor 501, and the program or instruction is executed by the processor 501 to implement the various steps of the uncertainty analysis method embodiment of the reactor multi-physical field coupling calculation, and can achieve the same technical effect, to avoid repetition, it is not repeated here. It should be noted that the electronic device in the embodiment of the present application includes the above-mentioned mobile electronic device and non-mobile electronic device.

[0152] Figure 6 A schematic diagram of the hardware structure of an electronic device for implementing an embodiment of the present application is provided, wherein the electronic device includes:

[0153] The processor 601 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (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 the present application;

[0154] The memory 602 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 602 can store an operating system and other application programs. When the technical solution provided in the embodiment of this specification is implemented by software or firmware, the relevant program code is stored in the memory 602, and the processor 601 calls and executes the uncertainty analysis method for reactor multi-physics field coupling calculation in the embodiment of this application;

[0155] Input / output interface 603, used to implement information input and output;

[0156] Communication interface 604, used to realize communication interaction between the device and other devices, which can be realized by wired mode (such as USB, network cable, etc.) or wireless mode (such as mobile network, WIFI, Bluetooth, etc.);

[0157] Bus 605 , which 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 , the memory 602 , the input / output interface 603 and the communication interface 604 are connected to each other in communication within the device via a bus 605 .

[0159] The electronic device provided in the embodiment of the present application can implement each step of the uncertainty analysis method embodiment of the above-mentioned reactor multi-physical field coupling calculation, and can achieve the same technical effect. To avoid repetition, it will not be repeated here.

[0160] An embodiment of the present application also provides a computer-readable storage medium, on which a program or instruction is stored. When the program or instruction is executed by a processor, each step of the uncertainty analysis method embodiment of the above-mentioned reactor multi-physical field coupling calculation is implemented, and the same technical effect can be achieved. To avoid repetition, it will not be repeated here.

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

[0162] An embodiment of the present application further provides a chip, which includes a processor and a communication interface, wherein the communication interface and the processor are coupled, and the processor is used to run programs or instructions to implement the various steps of the uncertainty analysis method embodiment of the above-mentioned reactor multi-physical field coupling calculation, and can achieve the same technical effect. To avoid repetition, it will not be repeated here.

[0163] It should be understood that the chip mentioned in the embodiments of the present application can also be called a system-level chip, a system chip, a chip system or a system-on-chip chip, etc.

[0164] An embodiment of the present application provides a computer program product, which is 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 of the reactor multi-physical field coupling calculation as described above, and can achieve the same technical effect. To avoid repetition, it will not be repeated here.

[0165] It should be noted that, in this article, the terms "comprise", "include" or any other variant thereof are intended to cover non-exclusive inclusion, so that the process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise one..." do not exclude the presence of other identical elements in the process, method, article or device including the element. In addition, it should be pointed out that the scope of the methods and devices in the embodiments of the present application is not limited to performing functions in the order shown or discussed, and may also include performing functions in a substantially simultaneous manner or in reverse order according to the functions involved, for example, the described method may be performed in an order different from that described, and various steps may also be added, omitted, or combined. In addition, the features described with reference to certain examples may be combined in other examples.

[0166] Through the description of the above implementation methods, those skilled in the art can clearly understand that the above-mentioned embodiment methods can be implemented by means of software plus a necessary general hardware platform, and of course by hardware, but in many cases the former is a better implementation method. Based on such an understanding, the technical solution of the present application, or the part that contributes to the prior art, can be embodied in the form of a computer software product, which is stored in a storage medium (such as ROM / RAM, a disk, or an optical disk), and includes a number of instructions for a terminal (which can be a mobile phone, a computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present application.

[0167] The embodiments of the present application are described above in conjunction with the accompanying drawings, but the present application is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the guidance of the present application, ordinary technicians in this field can also make many forms without departing from the purpose of the present application and the scope of protection of the claims, all of which are within the protection of the present application.

Claims

1. A method for uncertainty analysis of reactor multi-physics field coupling calculation, characterized in that: include: Obtaining a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of a multi-physical field of a reactor; wherein the first snapshot matrix is ​​a snapshot matrix of a reference multi-physical field coupling calculation result at multiple moments under multiple first operating conditions of the reactor, and each column vector in the first snapshot matrix includes a snapshot set of values ​​of a target physical field of multiple first spatial units located in the reactor at multiple moments under each first operating condition of the reactor; Determine a second snapshot matrix of the reactor multi-physics field according to 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 multiple first operating conditions and the multiple second operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple 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 multiple first spatial units located in the reactor at the multiple moments under each second operating condition; Determine the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to the average vector and the 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 multi-physical field.

2. The uncertainty analysis method according to claim 1, characterized in that: The method of obtaining a first reduced-order basis matrix and a first reduced-order basis coefficient matrix of a first snapshot matrix of a reactor multi-physical field includes: Performing singular value decomposition on the transposed first snapshot matrix to determine a left singular matrix, a right singular matrix, and a singular value matrix of the first snapshot matrix; wherein the singular value matrix is ​​a diagonal matrix, elements on the diagonal of the singular value matrix are 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 row vectors with position numbers greater than r in the right singular matrix from the right singular matrix to obtain a first reduced-order basis matrix of the first snapshot matrix; Remove the column vectors whose position numbers are 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; Among them, r is the number of target singular values ​​selected in order from large to small, and the sum of squares of the selected r target singular values ​​is greater than a preset value.

3. The uncertainty analysis method according to claim 1, characterized in that: Determining a second snapshot matrix of the reactor multi-physics field according to the first reduced-order basis matrix, the first reduced-order basis coefficient matrix and the first interpolation matrix includes: Determine a radial basis function mapping coefficient matrix according to the first reduced-order basis coefficient matrix and the distance weight matrix; wherein the distance weight matrix is ​​a matrix of distance weight functions between each of the plurality of first operating conditions; Determining a second reduced-order basis coefficient matrix according to the first interpolation matrix and the radial basis function mapping coefficient matrix; The first reduced-order basis matrix is ​​multiplied by the second reduced-order basis coefficient matrix to obtain a second snapshot matrix of the multi-physical field of the reactor.

4. The uncertainty analysis method according to claim 3, characterized in that: The step of determining the uncertainty of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to the average vector and the variance vector of all row vectors in the second snapshot matrix comprises: Determine a target variance vector of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to 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 uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to 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; Among them, the deviation matrix is ​​used to characterize the deviation of the third snapshot matrix of the reactor multi-physical field determined according to 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.

5. The uncertainty analysis method according to claim 4, characterized in that: Before the step of determining the target variance vector of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to 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: Determine a third snapshot matrix of the reactor multi-physics field according to 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 multi-physics field coupling calculation results of the reactor at multiple moments under the multiple third operating conditions; Acquire a fourth snapshot matrix of the multi-physical field of the reactor; the fourth snapshot matrix is ​​a snapshot matrix of the reference multi-physical field coupling calculation results of the reactor at multiple moments under the multiple third operating conditions; Determine the deviation between the third snapshot matrix and the fourth snapshot matrix to obtain the deviation matrix.

6. The uncertainty analysis method according to claim 4, characterized in that: The plurality of first operating conditions are a plurality of operating conditions determined by first sampling based on a value range of a plurality of variables of the reactor in a design space; The plurality of second operating conditions are a plurality of operating conditions determined by second sampling based on a probability distribution range obeyed by a plurality of variables of the reactor; The plurality of third operating conditions are a plurality of operating conditions determined by third sampling based on the value range of the plurality of variables of the reactor in the design space.

7. The uncertainty analysis method according to 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 multi-physical field, the uncertainty analysis method further includes: According to each physical field in the multi-physical field, the reactor is divided at least once to obtain a plurality of spatial units of the reactor corresponding to each physical field; Calculate the values ​​of each physical field located in the multiple space units at the multiple moments under the first operating conditions of the reactor by using a multi-physical field coupling calculation model, and obtain reference multi-physical field coupling calculation results of the reactor at the multiple moments under the first operating conditions; Determine a snapshot matrix of reference multi-physics field coupling calculation results of the reactor at multiple moments under multiple first operating conditions to obtain the first snapshot matrix.

8. An uncertainty analysis system for reactor multi-physics field coupling calculation, characterized in that: Includes acquisition module, snapshot module and 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 a multi-physical field of a reactor; wherein the first snapshot matrix is ​​a snapshot matrix of a reference multi-physical field coupling calculation result at multiple moments under multiple first operating conditions of the reactor, and each column vector in the first snapshot matrix includes a snapshot set of values ​​of a target physical field of multiple first spatial units located in the reactor at multiple moments under each first operating condition of the reactor; The snapshot module is used to determine the second snapshot matrix of the reactor multi-physical field according to 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 multiple first operating conditions and the multiple second operating conditions, the second snapshot matrix is ​​a snapshot matrix of the predicted multi-physical field coupling calculation results of the reactor at multiple moments under the multiple 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 multiple first spatial units located in the reactor at the multiple moments under each second operating condition; The uncertainty module is used to determine the uncertainty of the predicted multi-physics field coupling calculation results of the reactor at multiple moments under the multiple second operating conditions according to the average vector and the 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 multi-physical field.

9. An electronic device, characterized in that: The electronic device comprises a memory and a processor, the memory stores a computer program, and the processor implements the uncertainty analysis method according to any one of claims 1 to 7 when executing the computer program.

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

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