Method, system and equipment for acquiring evaluation parameters of numerical reactor and medium
By obtaining the influence parameters of the numerical reactor and its probability distribution type, determining the basis function combination terms and polynomial basis function matrix, the problem of low computational efficiency in the prior art is solved, and the efficiency of obtaining evaluation parameters and the accuracy of simulation results are improved.
Patent Information
- Application Number
- CN202411772145.3
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-04
- Publication Date
- 2025-05-13
- Estimated Expiration
- 2044-12-04
AI Technical Summary
In the prior art, the calculation efficiency of obtaining numerical reactor evaluation parameters is low, which affects the reliability and accuracy of the simulation results.
By obtaining the influence parameters of the numerical reactor and its probability distribution type, determine the basis function combination terms of the influencing parameters, and determine the polynomial basis function matrix and the downward coefficient based on the sampling results and the basis function combination terms, and finally determine the evaluation parameters of the numerical reactor.
The efficiency of obtaining numerical reactor evaluation parameters is improved, the intermediate calculation volume is reduced, and the reliability and accuracy of simulation results are enhanced.
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Figure CN119993294A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the field of data processing technology, and in particular to a method, system, device and medium for obtaining evaluation parameters of a numerical reactor. Background Art
[0002] Numerical reactor multi-physics coupling simulation is an important research direction in the field of nuclear energy. The simulation process usually involves a large number of input parameters. The uncertainty of these input parameters has an important impact on the reliability and accuracy of the simulation results. In the field of engineering analysis, sensitivity analysis, as a part of uncertainty analysis, is a method used to evaluate and understand the influence of uncertainty factors such as input parameters on the output results of engineering systems or models. Uncertainty analysis methods are used in related technologies to obtain evaluation parameters that can be used to analyze the influence of input parameters, but the calculation efficiency is low.
[0003] Application Contents
[0004] In view of this, one of the objectives of the present application is to provide a method, system, device and medium for obtaining evaluation parameters of a numerical reactor, which can improve the efficiency of obtaining the evaluation parameters of the numerical reactor.
[0005] To achieve the above purpose, the technical solution of this application is implemented as follows:
[0006] In a first aspect, an embodiment of the present application provides a method for obtaining evaluation parameters of a numerical reactor, comprising:
[0007] Obtain the influencing parameters of the numerical reactor and their probability distribution types;
[0008] According to the influencing parameters and their probability distribution types, determining the basis function combination items of the influencing parameters;
[0009] Determine the polynomial basis function matrix and the reduction coefficients according to the sampling results and the basis function combination terms, wherein the sampling results are obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type;
[0010] The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
[0011] In a possible implementation, after determining the basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type, the method further includes:
[0012] Determining a target calculation strategy according to a comparison result of the first quantity and the second quantity;
[0013] Determine the coefficients of each polynomial basis function in the polynomial basis function matrix according to the target calculation strategy;
[0014] Wherein, the first quantity includes the number of sampled samples in the sampling result, and the second quantity includes the number of terms of the basis function combination terms;
[0015] According to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters, the evaluation parameters of the numerical reactor are determined, including:
[0016] The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, coefficients of each polynomial basis function in the polynomial basis function matrix, reduced-order coefficients, influencing parameters and probability distributions corresponding to the influencing parameters.
[0017] In a possible implementation, determining a target calculation strategy according to a comparison result between the first quantity and the second quantity includes:
[0018] In the case where the comparison result indicates that the first quantity is greater than or equal to the second quantity, determining the least square method as the target calculation strategy;
[0019] When the least square method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the least square method;
[0020] When the comparison result indicates that the first number is less than the second number, determining the sparse matrix method as the target calculation strategy;
[0021] When the sparse matrix method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the sparse matrix method.
[0022] In a possible implementation, the evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, the coefficients of each polynomial basis function in the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters, and the probability distribution corresponding to the influencing parameters, including:
[0023] Determine the average value of the reduced-order coefficients according to the polynomial basis function matrix, the coefficients of each polynomial basis function, the influencing parameters and the probability distribution corresponding to the influencing parameters;
[0024] Determine the variance of the reduced-order coefficient according to the average value of the reduced-order coefficient and the reduced-order coefficient;
[0025] Determine the average value of the physical field of the numerical reactor according to the average value of the reduced-order coefficients and the polynomial basis function matrix;
[0026] Determine the variance of the physical field of the numerical reactor based on the variance of the reduced-order coefficients and the polynomial basis function matrix;
[0027] The evaluation parameters include an average value of the physical field of the numerical reactor and a variance of the physical field of the numerical reactor.
[0028] In a possible implementation, after determining the polynomial basis functions and the reduced-order coefficients according to the sampling results and the basis function combination terms, the method further includes:
[0029] Determine the key physical quantity matrix based on the sampling results and the simulation model of the numerical reactor;
[0030] When the number of key physical quantities in the key physical quantity matrix is greater than or equal to a preset number threshold, performing dimensionality reduction processing on the key physical quantity matrix;
[0031] When the least square method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the least square method, including:
[0032] For the key physical quantity matrix after dimensionality reduction, the coefficients of the polynomial basis function are determined according to the least squares method.
[0033] In a possible implementation, the dimension reduction process is performed on the key physical quantity matrix, including:
[0034] Determine the correlation matrix based on the key physical quantity matrix;
[0035] According to the non-zero eigenvalues and eigenvectors of the correlation matrix, the intrinsic orthogonal decomposition modes of the correlation matrix are determined;
[0036] According to the intrinsic orthogonal decomposition mode and key physical quantity matrix, the key physical quantity matrix after dimensionality reduction processing is determined.
[0037] In a possible implementation, determining the basis function combination item of the influencing parameter according to the influencing parameter and the probability distribution type of the influencing parameter includes:
[0038] When the dimension of the influencing parameter is determined, the basis function combination item is determined according to the dimension of the influencing parameter and the preset truncation order.
[0039] In a second aspect, an embodiment of the present application provides a system for obtaining evaluation parameters of a numerical reactor, the system comprising:
[0040] An acquisition module, used for acquiring the influencing parameters of the numerical reactor and their probability distribution types;
[0041] A first determination module is used to determine a basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type;
[0042] A second determination module is used to determine the polynomial basis function matrix and the reduction coefficients according to the sampling results and the basis function combination items, wherein the sampling results are obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type;
[0043] The third determination module is used to determine the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
[0044] In a third aspect, an embodiment of the present application provides an electronic device, the electronic device comprising a memory and a processor, the memory storing a computer program, and when the computer program is executed by the processor, the method for obtaining evaluation parameters of a numerical reactor provided in the first aspect is implemented.
[0045] In a fourth aspect, an embodiment of the present application provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by one or more processors, the method for obtaining evaluation parameters of a numerical reactor provided in the first aspect is implemented.
[0046] The method for obtaining the evaluation parameters of the numerical reactor provided in the embodiment of the present application can determine the basis function combination items of the influencing parameters based on the influencing parameters of the numerical reactor and their probability distribution types. Then, according to the sampling results and the basis function combination items, the polynomial basis function matrix and the reduced-order coefficients are determined, and the sampling results are obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type. Finally, according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters, the evaluation parameters of the numerical reactor are determined. By sampling and involving the reduced-order coefficients in the calculation of the evaluation parameters, the intermediate calculation amount can be reduced, thereby improving the efficiency of determining the evaluation parameters. BRIEF DESCRIPTION OF THE DRAWINGS
[0047] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. It should be understood that the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.
[0048] Figure 1 A flowchart of a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0049] Figure 2 A curve diagram of a linear power density value changing over time provided in an embodiment of the present application;
[0050] Figure 3 A mean value line graph obtained by Monte Carlo analysis provided in an embodiment of the present application;
[0051] Figure 4 A variance line graph obtained by using the Monte Carlo method provided in an embodiment of the present application;
[0052] Figure 5 An energy variation diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0053] Figure 6 A probability density variation curve diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0054] Figure 7 Another probability density variation curve diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0055] Figure 8 A comparison diagram related to a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0056] Fig. 9 A schematic diagram of functional modules of a system for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application;
[0057] Fig.10 A diagram of the internal structure of an electronic device provided in an embodiment of the present application.
[0058] Description of reference numerals:
[0059] A system 900 for acquiring evaluation parameters of a numerical reactor includes an acquisition module 910 , a first determination module 920 , a second determination module 930 , and a third determination module 940 . DETAILED DESCRIPTION
[0060] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings 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. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.
[0061] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for which protection is sought, but merely represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work are within the scope of protection of the present application.
[0062] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.
[0063] In various embodiments of the present application, the expression "or" or "at least one of A or / and B" includes any combination or all combinations of the words listed at the same time. For example, the expression "A or B" or "at least one of A or / and B" may include A, may include B, or may include both A and B.
[0064] In the description of the present application, it should be noted that if the terms "upper", "lower", "inside", "outside", etc. appear to indicate an orientation or position relationship, it is based on the orientation or position relationship shown in the drawings, or is the orientation or position relationship in which the product of the invention is usually placed when used. It is only for the convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present application.
[0065] In addition, the terms “first”, “second”, etc., if used, are merely used to distinguish between the descriptions and should not be understood as indicating or implying relative importance.
[0066] It should be noted that, in the absence of conflict, the features in the embodiments of the present application may be combined with each other.
[0067] Furthermore, in the embodiments of the present application, the term "connection" may refer to "electrical connection" or "direct connection". "Electrical connection" may refer to direct electrical connection between two components or electrical connection between two components via one or more normally open tubes or other components.
[0068] To facilitate a better understanding of the solutions of the embodiments of the present application, the relevant technical terms are first introduced below.
[0069] A numerical reactor is a tool that uses computer simulation technology to perform detailed numerical simulations of the physical, thermal, hydraulic and other processes of a nuclear reactor. A numerical reactor can be regarded as a "virtual reactor" that reproduces various phenomena inside a nuclear reactor through complex mathematical models and computational algorithms.
[0070] Monte Carlo method, also known as statistical simulation method, is a numerical calculation method guided by probability statistics theory. It solves various mathematical and physical problems through random sampling, especially in solving complex integrals, solving differential equations and simulating systems with uncertainty.
[0071] In order to solve the technical problems in the background technology, the embodiments of the present application provide a method, system, device and medium for obtaining evaluation parameters of a numerical reactor. The method for obtaining evaluation parameters of a numerical reactor provided by the embodiments of the present application is first introduced below.
[0072] See also Figure 1 , Figure 1 A flowchart of a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application is provided. The method for obtaining evaluation parameters of a numerical reactor can be applied to a system and an electronic device for obtaining evaluation parameters of a numerical reactor in the following embodiments, wherein the electronic device includes a personal computer, a server, a mobile device, a cloud computing platform, and a supercomputer, etc. The method for obtaining evaluation parameters of a numerical reactor will be introduced from the perspective of application to electronic devices, and specifically includes the following steps:
[0073] Step 110, obtaining the influencing parameters of the numerical reactor and their probability distribution types.
[0074] Step 120: Determine the basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type.
[0075] Step 130, determining the polynomial basis function matrix and the reduction coefficients according to the sampling results and the basis function combination items, wherein the sampling results are obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type.
[0076] Step 140, determining the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
[0077] The method for obtaining the evaluation parameters of the numerical reactor provided in the embodiment of the present application can determine the basis function combination items of the influencing parameters based on the influencing parameters of the numerical reactor and their probability distribution types. Then, according to the sampling results and the basis function combination items, the polynomial basis function matrix and the reduced-order coefficients are determined, and the sampling results are obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type. Finally, according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters, the evaluation parameters of the numerical reactor are determined. By sampling and involving the reduced-order coefficients in the calculation of the evaluation parameters, the intermediate calculation amount can be reduced, thereby improving the efficiency of determining the evaluation parameters.
[0078] The following will be Figure 1 Each step of the method is described in detail.
[0079] In step 110 , the electronic device may obtain influencing parameters of the numerical reactor and probability distribution types of the influencing parameters.
[0080] The influencing parameters include the uncertain variables in the reactor, which have different degrees of influence on the reactivity and energy output of the reactor. The influencing parameters may include parameters such as geometric parameters, nuclear physics parameters, thermal hydraulic parameters, material property parameters and control system parameters. If X is used to represent the influencing parameters, then X = (x1 , x 2 , ..., x d ), d represents the number of influencing parameters.
[0081] Specifically, the geometric parameters may include parameters related to the geometry and arrangement of nuclear reactor fuel rods, fuel assemblies, cores, etc.
[0082] Nuclear physics parameters may include cross-sections of respective types of nuclear reaction channels (such as absorption, fission, scattering, etc.), energy deposition and other related parameters. Their uncertainties may come from measurement errors in experimental data, simplification of some theoretical models, etc.
[0083] Thermal hydraulic parameters may include parameters such as coolant flow, temperature and pressure, and their uncertainties may come from factors such as measurement errors, equipment failures or operator errors.
[0084] Material property parameters may include material property parameters of reactor components, such as strength, plasticity and fatigue life, which may have uncertainties, and the uncertainties may come from material defects, environmental factors (such as temperature and pressure), and aging.
[0085] Control system parameters may include gain, hysteresis, and time constants, which may be subject to uncertainty, which may come from factors such as measurement errors, equipment failures, or operator errors.
[0086] The probability distribution type can be used to indicate the probability distribution of the corresponding influencing parameters. The probability distribution of the influencing parameters can be quantitatively represented with uncertain influencing parameters. For example, for the influencing parameter of coolant flow, a normal distribution can be used to describe the fluctuation of the coolant flow around a certain average value.
[0087] In some embodiments, different probability distribution types can be distinguished by different identifiers, such as identifier 001 represents probability distribution A, and identifier 002 represents probability distribution B. In addition to Arabic numerals in the example, the identifiers may also be English, punctuation marks, or a combination of at least two of Arabic numerals, English, and punctuation marks, which will not be described in detail here.
[0088] For different influencing parameters, their probability distribution may be different depending on the type and source of the influencing parameters. For example, some influencing parameters may be assumed to obey normal distribution, uniform distribution or other common probability distributions. For other types of probability distributions, they can be obtained in the form of separation transformation. For example, if the probability distribution needs to be converted to a Gaussian distribution, corresponding transformation methods such as Box-Cox transformation or Yeo-Johnson transformation can be used. These transformations can convert the original data into data that meets the Gaussian distribution assumption. If the probability distribution needs to be converted to a Beta distribution, the inverse transformation method of the Beta distribution can be used. The inverse transformation maps the original data to the definition domain of the Beta distribution.
[0089] In some embodiments, the electronic device may obtain the influencing parameters of the numerical reactor and the probability distribution type of the influencing parameters in response to the acquisition instruction. The acquisition instruction may be used to instruct the electronic device to obtain the influencing parameters and the probability distribution type, which may be generated by manual triggering by the user or automatically generated at a preset time, which is not limited here.
[0090] In step 120, when the electronic device determines the influencing parameters and their probability distribution types based on the aforementioned step 110, it can further determine the basis function combination items of the influencing parameters, so as to facilitate the subsequent calculation of the evaluation parameters of the numerical reactor.
[0091] Specifically, for the influencing parameters whose probability distribution is uniform distribution, Legendre polynomials can be used as orthogonal basis, and the p-order polynomial can be obtained through the special.eval_legendre function in the open source scipy library. p is the order.
[0092] For the Beta distribution, Jacobi polynomials can be used as the orthogonal basis, and the p-order polynomial can be obtained through the scipy.special.jacobi function in the open source scipy library. p is the order.
[0093] For Gaussian probability distribution, Hermite polynomial can be used as an orthogonal basis, and the p-order polynomial can be obtained through the special.hermite function in the open source scipy library. p is the order.
[0094] For the i-th variable x in the d-dimensional variable space i (i.e., the i-th influencing parameter), the expression of all p-order polynomials is No. iThe polynomial is expressed as
[0095] If each influencing parameter is independent of each other, their orders are (p 1 ,…,p d ) can be expressed as the product of independent basis functions of each variable:
[0096]
[0097] Therefore, the total number of basis function combination items Nc can be expressed as follows:
[0098] N C =(P+1) d , (2)
[0099] In step 130 , the electronic device may further determine a polynomial basis function matrix and reduced-order coefficients, where the polynomial basis function matrix includes a plurality of polynomial basis functions.
[0100] The sampling result may be composed of multiple sampling samples. Specifically, the electronic device may sample the influencing parameter according to a preset sampling method based on a probability distribution function corresponding to the probability distribution of the influencing parameter, and the multiple sampling samples obtained by sampling may form the sampling result.
[0101] The preset sampling method includes at least one of random sampling and Latin hypercube sampling.
[0102] In some embodiments, the function for performing Latin hypercube sampling using the scipy open source library is scipy.stats.qmc.LatinHypercube
[0103] In some embodiments, a preset sampling number may be set, and the influencing parameters may be sampled according to a preset sampling method, including sampling the influencing parameters according to a preset sampling number of times based on a preset sampling method.
[0104] Specifically, the electronic device can substitute the sample Sx (dimension is Ng*d, Ng represents the number of sample) in the sampling result into Nc to obtain the polynomial basis function matrix: (The dimension is Ng*Nc), then, the electronic device can determine the reduced-order coefficients according to the polynomial basis function matrix.
[0105] In step 140, the electronic device can quickly determine the evaluation parameters of the numerical reactor based on the relevant parameters such as the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters obtained in the aforementioned steps 110 to 130. Among them, the evaluation parameters of the numerical reactor may include the average value of the physical field of the numerical reactor and the variance of the physical field of the numerical reactor. Based on the two evaluation parameters of the average value and the variance, the electronic device can further determine the degree of influence of the influencing parameters on the engineering system or model output results simulated by the numerical reactor, and complete the sensitivity analysis of the influencing parameters.
[0106] In a possible implementation, after determining the polynomial basis functions and the reduced-order coefficients according to the sampling results and the basis function combination terms, the method further includes:
[0107] Determine the key physical quantity matrix based on the sampling results and the simulation model of the numerical reactor;
[0108] When the number of key physical quantities in the key physical quantity matrix is greater than or equal to a preset number threshold, performing dimensionality reduction processing on the key physical quantity matrix;
[0109] When the least square method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the least square method, including:
[0110] For the key physical quantity matrix after dimensionality reduction, the coefficients of the polynomial basis function are determined according to the least squares method.
[0111] The embodiment of the present application can reduce the amount of data to be processed and thus improve the efficiency of determining the evaluation parameters of the numerical reactor by performing dimensionality reduction processing on the key physical quantity matrix when it is judged that the key physical quantity matrix is too large, that is, greater than or equal to a preset number.
[0112] Specifically, the electronic device can input the sampling samples Sx (with a dimension of Ng*d) in the sampling results into a simulation model of a numerical reactor such as M(x) to obtain a key physical quantity matrix Q (with a dimension of Ng*Nq).
[0113] It should be noted that by inputting each sample (which can be regarded as a design scheme in the design space) into the simulation model M(x) of the numerical reactor, the physical field (physical quantity of interest) under each design scheme can be obtained, and the simulation model of the numerical reactor can output Nq physical quantities of interest. Considering that the grid division of the physical field is very fine, such as the number of grids will exceed tens of thousands or millions, and there are multiple physical fields such as nuclear (neutron field)-thermal (temperature, pressure, flow)-force (geometric deformation, stress field)-chemical (corrosion product distribution, sediment distribution), etc., which leads to a sharp increase in the physical quantity of interest, the value of Nq can be very large.
[0114] The x in M(x) represents the sample, that is, the true value obtained by sampling the influencing parameter.
[0115] As a specific embodiment, the number of sampling samples Ng = 10000, each sample has 7 influencing parameters, and the 10000 sampling samples are input into the simulation model M(x) of the numerical reactor to obtain the key physical quantity matrix Q. Taking the reactor transient behavior as an example, the i-th physical quantity Q i The dimension is 5024*100, which means the neutron flux (or linear power density) value at 5024 discrete points in space in 100 time steps. The unit of linear power density is watt / cm2 (W / cm2). If the maximum linear power density value of the whole reactor is displayed as a curve over time, it can be obtained Figure 2 , Figure 2 A curve diagram showing the change of linear power density value over time provided in an embodiment of the present application.
[0116] exist Figure 2 In the figure, the horizontal axis represents time (in seconds) and the vertical axis represents linear power density (in watts / cm), which shows the linear power density of the first 300 samples (represented by curves of different colors) over time. It can be found that when the time is close to 0 seconds, the linear power density of all samples remains near a relatively low value, that is, at the initial moment, the linear power density of all samples is at a relatively low level. As time increases, the linear power density of each sample increases rapidly, and after reaching the peak value, it decreases and stabilizes near a value. Although the overall change trends of the first 300 samples are similar, there are still certain differences in the height of the peak and the process of decline, reflecting the differences in the online power density change characteristics of different samples.
[0117] The peak values of the line power density at all times are counted and their average values are determined as follows: Figure 3 , and the variance is Figure 4 . Figure 3 A mean value line graph obtained by Monte Carlo analysis is provided in an embodiment of the present application. Figure 4 A variance line graph obtained by using the Monte Carlo method provided in an embodiment of the present application, Figure 3 and Figure 4 The horizontal axes of the two figures represent the number of samples (in units), and the vertical axes represent the peak linear power density (in units of watts / cm2).
[0118] It can be found that Figure 3 and Figure 4 In the process of obtaining the mean and variance of the peak value of the line power density using Monte Carlo random sampling, a certain number of samples, such as a number of samples greater than 4000, is required to obtain a relatively stable and accurate mean and variance.
[0119] The preset quantity threshold can be set according to actual needs and is not limited here.
[0120] After the dimensionality reduction processing is performed on the key physical quantity matrix in the embodiment of the present application, the number of samples required is less than 4000. By reducing the number of samples, the calculation time can be reduced, thereby improving the efficiency of determining the evaluation parameters of the numerical reactor.
[0121] In a possible implementation, the dimension reduction process is performed on the key physical quantity matrix, including:
[0122] Determine the correlation matrix based on the key physical quantity matrix;
[0123] According to the non-zero eigenvalues and eigenvectors of the correlation matrix, the intrinsic orthogonal decomposition modes of the correlation matrix are determined;
[0124] According to the intrinsic orthogonal decomposition mode and key physical quantity matrix, the key physical quantity matrix after dimensionality reduction processing is determined.
[0125] Specifically, the correlation matrix R can be expressed as follows:
[0126] R=Q T Q, (3)
[0127] in,
[0128] Determine the non-zero eigenvalues λ of the correlation matrix R j and the eigenvector φ j , and determine the correlation matrix R acting on the eigenvector φ j The above results are expressed as follows:
[0129] Rφ j =λ j φ j , (4)
[0130] Where j = 1, 2, ..., Nq, λ 1 >>λ 2 >>…>>λ Nq >0.
[0131] The proper orthogonal decomposition mode (POD mode) that forms the correlation matrix can be expressed as follows:
[0132]
[0133] Wherein, j=1, 2, ..., Nq, S represents the snapshot matrix in the POD method.
[0134] Then select only the first r modes: The principle of selection is to solve the smallest r and satisfy the following conditions:
[0135]
[0136] In some embodiments, τ takes a value of 0.999.
[0137] Next, the electronic device can construct a modal matrix based on the selected first r-order modes as follows:
[0138]
[0139] in,
[0140] According to the definition of the mode, the multi-physics field Q of the simulation model of the numerical reactor under the i-th sample i It can be expressed as follows:
[0141]
[0142] We can choose α=[α 1 …α r ], and define the modal coefficient matrix:
[0143]
[0144] Calculate the projection matrix Y:
[0145] Y=Qφ, (9)
[0146] According to the intrinsic orthogonal decomposition mode and the key physical quantity matrix, determine the key physical quantity matrix A after dimensionality reduction, including using the least squares method, and optionally using the open source mathematical library numpy for solving. The solution formula is as follows:
[0147] A=np.linalg.lstsq(φ.T,YT), (10)
[0148] Wherein, “.T” indicates the transpose operation of the matrix, and the dimension of A is Ng*r.
[0149] For example, if the key physical quantity matrix Q in this embodiment is determined based on the sampling results of only 1000 sampling samples and the simulation model of the numerical reactor, the core space-time distribution field (dimension is 5024100) can be obtained for the 1000 sampling samples, and the λ corresponding to the reduced-order mode is i See also Figure 5 , Figure 5 An energy variation diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application.
[0150] exist Figure 5 In the figure, the horizontal axis represents the number of modes, and the two vertical axes represent the modal energy (10 1 Up to 106 ) and cumulative energy contribution (0.5 to 1.0). According to the red dotted line, as the number of modes increases, the cumulative energy contribution gradually approaches 1.0, indicating that the first few modes contribute most of the energy, and the cumulative energy contribution of the following modes gradually decreases. In practical applications, only the first few modes need to be considered to capture most of the energy response of the system. In the case of τ = 0.99, there are 11 reduced-order modes, corresponding to 11 reduced-order coefficients, that is, Ng = 11.
[0151] In a possible implementation, after determining the basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type, the method further includes:
[0152] Determining a target calculation strategy according to a comparison result of the first quantity and the second quantity;
[0153] Determine the coefficients of each polynomial basis function in the polynomial basis function matrix according to the target calculation strategy;
[0154] Wherein, the first quantity includes the number of sampled samples in the sampling result, and the second quantity includes the number of terms of the basis function combination terms;
[0155] According to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters, the evaluation parameters of the numerical reactor are determined, including:
[0156] The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, coefficients of each polynomial basis function in the polynomial basis function matrix, reduced-order coefficients, influencing parameters and probability distributions corresponding to the influencing parameters.
[0157] The embodiment of the present application determines the coefficients used to calculate each polynomial basis function in the polynomial basis function matrix by comparing the number of sampling samples and the number of terms in the basis function combination terms, and then involves the coefficients of each polynomial basis function in the calculation of the evaluation parameters of the numerical reactor. By determining a suitable target calculation strategy, the efficiency of determining the evaluation parameters of the numerical reactor can be further improved.
[0158] Specifically, the number of basis function combination terms is Nc in the aforementioned embodiment, and the coefficients of the polynomial basis function can determine the specific form and properties of the polynomial basis function. The electronic device can accurately and quickly calculate the coefficients of the polynomial basis function by determining a suitable target calculation strategy, thereby improving the accuracy and reliability of determining the evaluation parameters of the numerical reactor.
[0159] In a possible implementation, determining a target calculation strategy according to a comparison result between the first quantity and the second quantity includes:
[0160] In the case where the comparison result indicates that the first quantity is greater than or equal to the second quantity, determine the least squares method as the target calculation strategy;
[0161] In the case where the least squares method is determined as the target calculation strategy, determine the coefficients of the polynomial basis function according to the least squares method;
[0162] In the case where the comparison result indicates that the first quantity is less than the second quantity, determine the sparse matrix method as the target calculation strategy;
[0163] In the case where the sparse matrix method is determined as the target calculation strategy, determine the coefficients of the polynomial basis function according to the sparse matrix method.
[0164] Specifically, the comparison result indicates that the first quantity is greater than or equal to the second quantity, that is, Ng≥Nc, which can indicate that the sampling samples are sufficient. In the case of sufficient sampling samples, the electronic device can use the least squares method to determine the coefficients of the polynomial basis function. It should be noted that in the case of sufficient sampling samples, using the least squares method can effectively average out the random noise in the data and improve the reliability of solving the coefficients of the polynomial basis function.
[0165] The comparison result indicates that the first quantity is less than the second quantity, that is, Ng<Nc, which can indicate that the sampling samples are insufficient. In the case of insufficient sampling samples, the electronic device can use the sparse matrix method to determine the coefficients of the polynomial basis function. It should be noted that considering that there are multiple influencing parameters in the numerical reactor and the multiple influencing parameters are not equally important. Generally, only a few influencing parameters play a decisive role in the simulation system of the numerical reactor. At this time, from the perspective of the coefficient matrix composed of the coefficients of the polynomial basis function to be solved, there are a large number of coefficient characteristics (that is, the coefficients of some polynomial basis functions are very small, such as approaching zero). Therefore, high-order polynomial fitting accuracy can be obtained by relying on a small number of sampling calculations. However, the computational workload and computing time of a single sampling in the simulation system of the numerical reactor are very large. When Ng<Nc, the sparse matrix method can be used to estimate the coefficient matrix U composed of the coefficients of the polynomial basis function to be solved, which can reduce the computational workload and computing time.
[0166] Assume that the i-th reduced-dimensional coefficient of the physical field of interest is expressed as follows:
[0167]
[0168] where, Ψ i,j is the j-th polynomial basis function, u i,j is the coefficient of the j-th polynomial basis function, which is the coefficient to be solved. The coefficients of all polynomial basis functions can form a coefficient matrix U, then there is:
[0169] Q = ΨU, (12)
[0170] U=Ψ + Q, (13)
[0171] Among them, the dimension of Ψ is N g ×N C , the dimension of U is N c ×r, the dimension of Q is N g ×r.Ψ + represents the pseudo-inverse (or generalized inverse) of Ψ. In some embodiments, the pseudo-inverse can be solved using the linalg.pinv function in the open source numpy library, or using the open source scipy.linalg.pinv.
[0172] In the above embodiment, for the key physical quantity matrix after dimensionality reduction processing, the coefficients of the polynomial basis function are determined according to the least squares method. It is only necessary to replace Q in formula (12) with the key physical quantity matrix A after dimensionality reduction processing, that is:
[0173] A=ΨU, (14)
[0174] Among them, the key physical quantity matrix obtained after the order reduction process is represented by the modal coefficient matrix A, and the modal coefficient matrix is composed of α Ng The modal coefficients consist of
[0175] Furthermore, for Figure 5 The corresponding 11 reduced-order coefficients are taken as fitting objects, and they are expanded according to the Polynomial Chaos Expansion (PCE) proxy model to obtain 11 chaotic polynomials with reduced-order coefficients. The corresponding probability density change curve is shown in Figure 6 As shown, Figure 6 A probability density variation curve diagram of a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application. Figure 6 In the figure, the horizontal axis represents the coefficient value, the vertical axis represents the probability density, and the probability density is the probability density obtained based on the kernel density estimation (KDE), and p represents the degree of the polynomial (such as p = 2 is a quadratic polynomial expansion). It can be found that the probability density changes significantly under different degrees of polynomial expansion.
[0176] If the sampling results are obtained by using a fifth-order polynomial, the probability density corresponding to 1,000 samples is close to the probability density corresponding to 10,000 samples obtained by using Monte Carlo sampling. For details, please refer to Figure 7 , Figure 7 Another probability density variation curve diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application. It can be found that: Figure 7 The two curves in Figures (a), (b), (c), (d), (i) and (k) are relatively close, that is, the embodiment of the present application can use a smaller sample such as 1000, and can also obtain a convergent and highly accurate average value and variance.
[0177] Among them, d represents the order of the polynomial, and the curve corresponding to KDE MC represents the change curve of the probability density corresponding to 10,000 sampling samples obtained by Monte Carlo sampling.
[0178] In a possible implementation, the evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, the coefficients of each polynomial basis function in the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters, and the probability distribution corresponding to the influencing parameters, including:
[0179] Determine the average value of the reduced-order coefficients according to the polynomial basis function matrix, the coefficients of each polynomial basis function, the influencing parameters and the probability distribution corresponding to the influencing parameters;
[0180] Determine the variance of the reduced-order coefficient according to the average value of the reduced-order coefficient and the reduced-order coefficient;
[0181] Determine the average value of the physical field of the numerical reactor according to the average value of the reduced-order coefficients and the polynomial basis function matrix;
[0182] Determine the variance of the physical field of the numerical reactor based on the variance of the reduced-order coefficients and the polynomial basis function matrix;
[0183] The evaluation parameters include an average value of the physical field of the numerical reactor and a variance of the physical field of the numerical reactor.
[0184] Specifically, determine the average value E(a i ) can be calculated using the following formula:
[0185]
[0186] Where x represents the influencing parameter, p(x) represents the probability distribution function of the influencing parameter x, and u i,j represents the coefficient of the jth polynomial basis function, Ψ i,j represents the jth polynomial basis function, u i,1 A constant term representing the polynomial expansion.
[0187] The method of reducing the coefficient D(a i ) can be calculated using the following formula:
[0188]
[0189] The average value E(Q) of the physical field of the numerical reactor can be calculated using the following formula:
[0190]
[0191] in, and both represent 1*Nq vectors.
[0192] The variance of the physical field of the numerical reactor can be calculated using the following formula:
[0193]
[0194] in, Represents a 1*Nq vector.
[0195] In order to clearly demonstrate that the embodiment of the present application can obtain a relatively stable average value and variance through a small number of samples such as 1000, please refer to Figure 8 , Figure 8 A comparison diagram involved in a method for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application. Figure 8 (a) in the figure shows the average change of peak line power density of different sample numbers. Figure 8 (b) in the figure represents the variance change curve of the peak line power density with different sample numbers. Among them, the curve corresponding to MC represents the mean value change / variance change corresponding to the simulation using the Monte Carlo method, MC(10000) represents the fitted mean value / variance corresponding to the simulation using 1000 samples and the Monte Carlo method, and the curve corresponding to PCE p=4 represents the mean value change / variance change corresponding to the simulation using the above method of the embodiment of the present application. It can be found that the Monte Carlo method generally requires more than 3000 samples to obtain a relatively stable mean value and variance, while the simulation using the method corresponding to the embodiment of the present application only requires about 1000 samples to obtain a relatively stable mean value and variance.
[0196] In a possible implementation, determining the basis function combination item of the influencing parameter according to the influencing parameter and the probability distribution type of the influencing parameter includes:
[0197] When the dimension of the influencing parameter is determined, the basis function combination item is determined according to the dimension of the influencing parameter and the preset truncation order.
[0198] The embodiments of the present application can indirectly improve the efficiency of obtaining the evaluation parameters of the numerical reactor by reducing the number of basis function combination terms.
[0199] According to the above formula (2), when the parameter d is large, the number of terms of the basis function combination type is likely to explode. The p in , that is, the preset truncation order, is used to reduce the basis function combination terms, thereby indirectly improving the efficiency of obtaining the evaluation parameters of the numerical reactor. The present embodiment of the application does not specifically limit the preset truncation order p.
[0200] The number of cross-combination terms of the truncated basis functions is:
[0201]
[0202] Among them, p limit A preset truncation order can be expressed.
[0203] In some embodiments, the electronic device may further truncate high-order terms of certain influencing parameters, such as influencing parameters of a single variable, based on the first preset parameters, thereby reducing basis function combination terms.
[0204] In some embodiments, the electronic device can also limit the number of variable intersections in the basis function combination terms based on a preset crossover threshold. For example, the preset crossover threshold is 2, which may mean that in the process of determining the basis function combination terms, only the crossover terms of two variables are considered, and the crossover terms of three or more variables are not considered.
[0205] In some embodiments, the electronic device may limit the total order of the cross terms based on the second preset parameter, such as considering only low-order cross terms for the cross terms between two variables.
[0206] Corresponding to the above method embodiment, the present application embodiment also provides a system for obtaining evaluation parameters of a numerical reactor, see Fig. 9 , Fig. 9 A functional module diagram of a system for obtaining evaluation parameters of a numerical reactor provided in an embodiment of the present application, wherein the system 900 for obtaining evaluation parameters of a numerical reactor includes:
[0207] An acquisition module 910 is used to acquire the influencing parameters of the numerical reactor and their probability distribution types;
[0208] A first determination module 920 is used to determine a basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type;
[0209] A second determination module 930 is used to determine the polynomial basis function matrix and the reduction coefficients according to the sampling result and the basis function combination term, wherein the sampling result is obtained by sampling the influencing parameters according to the probability distribution indicated by the probability distribution type;
[0210] The third determination module 940 is used to determine the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
[0211] The system for obtaining the evaluation parameters of the numerical reactor provided in the embodiment of the present application can achieve the following Figure 1 The various processes implemented in the method embodiments can achieve similar or identical technical effects, and will not be described again here to avoid repetition.
[0212] In a possible implementation, the system 900 for obtaining evaluation parameters of a numerical reactor further includes a fourth determination module, which is used to:
[0213] Determining a target calculation strategy according to a comparison result of the first quantity and the second quantity;
[0214] Determine the coefficients of each polynomial basis function in the polynomial basis function matrix according to the target calculation strategy;
[0215] Wherein, the first quantity includes the number of sampled samples in the sampling result, and the second quantity includes the number of terms of the basis function combination terms;
[0216] The third determining module 940 is further specifically configured to:
[0217] The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, coefficients of each polynomial basis function in the polynomial basis function matrix, reduced-order coefficients, influencing parameters and probability distributions corresponding to the influencing parameters.
[0218] In a possible implementation, the fourth determining module includes a first determining submodule, and the first determining submodule is used to:
[0219] Determining a target calculation strategy according to a comparison result between the first quantity and the second quantity includes:
[0220] In the case where the comparison result indicates that the first quantity is greater than or equal to the second quantity, determining the least square method as the target calculation strategy;
[0221] When the least square method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the least square method;
[0222] When the comparison result indicates that the first number is less than the second number, determining the sparse matrix method as the target calculation strategy;
[0223] When the sparse matrix method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the sparse matrix method.
[0224] In a possible implementation manner, the third determining module 940 is further specifically configured to:
[0225] Determine the average value of the reduced-order coefficients according to the polynomial basis function matrix, the coefficients of each polynomial basis function, the influencing parameters and the probability distribution corresponding to the influencing parameters;
[0226] Determine the variance of the reduced-order coefficient according to the average value of the reduced-order coefficient and the reduced-order coefficient;
[0227] Determine the average value of the physical field of the numerical reactor according to the average value of the reduced-order coefficients and the polynomial basis function matrix;
[0228] Determine the variance of the physical field of the numerical reactor based on the variance of the reduced-order coefficients and the polynomial basis function matrix;
[0229] The evaluation parameters include an average value of the physical field of the numerical reactor and a variance of the physical field of the numerical reactor.
[0230] In a possible implementation, the system 900 for obtaining evaluation parameters of a numerical reactor further includes a fifth determination module, which is used to:
[0231] Determine the key physical quantity matrix based on the sampling results and the simulation model of the numerical reactor;
[0232] When the number of key physical quantities in the key physical quantity matrix is greater than or equal to a preset number threshold, performing dimensionality reduction processing on the key physical quantity matrix;
[0233] When the least square method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the least square method, including:
[0234] For the key physical quantity matrix after dimensionality reduction, the coefficients of the polynomial basis function are determined according to the least squares method.
[0235] In a possible implementation, the fifth determining module includes a second determining submodule, and the second determining submodule is used to:
[0236] Determine the correlation matrix based on the key physical quantity matrix;
[0237] According to the non-zero eigenvalues and eigenvectors of the correlation matrix, the intrinsic orthogonal decomposition modes of the correlation matrix are determined;
[0238] According to the intrinsic orthogonal decomposition mode and key physical quantity matrix, the key physical quantity matrix after dimensionality reduction processing is determined.
[0239] In a possible implementation manner, the first determining module 920 is further specifically configured to:
[0240] When the dimension of the influencing parameter is determined, the basis function combination item is determined according to the dimension of the influencing parameter and the preset truncation order.
[0241] The present application also provides an electronic device. The present application also provides an electronic device. Fig.10 , Fig.10An internal structure diagram of an electronic device provided for an embodiment of the present application. The electronic device includes a processor, a memory, and a network interface connected via a system bus. The memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium of the electronic device stores an operating system and may also store a computer program, which, when executed by the processor, enables the processor to implement the method for obtaining the evaluation parameters of a numerical reactor applied to the electronic device in the above-mentioned embodiment. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to execute the method for obtaining the evaluation parameters of a numerical reactor. Those skilled in the art will appreciate that Fig.10 The structure shown in the figure is merely a block diagram of a partial structure related to the scheme of the present application, and does not constitute a limitation on the electronic device to which the scheme of the present application is applied. The specific electronic device may include more or fewer components than shown in the figure, or combine certain components, or have a different arrangement of components.
[0242] The embodiment of the present application further discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for obtaining evaluation parameters of a numerical reactor as described in the method embodiment is implemented.
[0243] 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 processes of the embodiment of the method for obtaining the evaluation parameters of a numerical reactor as described above, and can achieve similar or identical technical effects. To avoid repetition, it will not be described here.
[0244] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
[0245] The technical features of the above embodiments may be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
Claims
1. A method for obtaining evaluation parameters of a numerical reactor, characterized in that: The method comprises: Obtain the influencing parameters of the numerical reactor and their probability distribution types; Determining a basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type; Determining a polynomial basis function matrix and reduced-order coefficients according to a sampling result and the basis function combination term, wherein the sampling result is obtained by sampling the influencing parameter according to the probability distribution indicated by the probability distribution type; The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
2. The method according to claim 1, characterized in that After determining the basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type, the method further includes: Determining a target calculation strategy according to a comparison result of the first quantity and the second quantity; Determining coefficients of each polynomial basis function in the polynomial basis function matrix according to the target calculation strategy; Wherein, the first number includes the number of sampled samples in the sampling result, and the second number includes the number of terms of the basis function combination terms; Determining the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters includes: The evaluation parameters of the numerical reactor are determined according to the polynomial basis function matrix, the coefficients of each polynomial basis function in the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
3. The method according to claim 2, characterized in that The step of determining the target calculation strategy according to the comparison result between the first quantity and the second quantity includes: In a case where the comparison result indicates that the first number is greater than or equal to the second number, determining the least square method as the target calculation strategy; In the case where the least squares method is determined as the target calculation strategy, determining coefficients of the polynomial basis function according to the least squares method; When the comparison result indicates that the first number is less than the second number, determining a sparse matrix method as the target calculation strategy; When the sparse matrix method is determined as the target calculation strategy, the coefficients of the polynomial basis function are determined according to the sparse matrix method.
4. The method according to claim 3, characterized in that Determining the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the coefficients of each polynomial basis function in the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters includes: Determining an average value of the reduced-order coefficients according to the polynomial basis function matrix, coefficients of each of the polynomial basis functions, the influencing parameters and probability distributions corresponding to the influencing parameters; Determining a variance of the reduced order coefficient according to an average value of the reduced order coefficient and the reduced order coefficient; Determining an average value of a physical field of the numerical reactor according to an average value of the reduced-order coefficients and the polynomial basis function matrix; Determining the variance of the physical field of the numerical reactor according to the variance of the reduced-order coefficients and the polynomial basis function matrix; The evaluation parameters include an average value of the physical field of the numerical reactor and a variance of the physical field of the numerical reactor.
5. The method according to claim 3, characterized in that After determining the polynomial basis function and the reduced-order coefficients according to the sampling results and the basis function combination terms, the method further comprises: Determining a key physical quantity matrix according to the sampling results and the simulation model of the numerical reactor; When the number of key physical quantities in the key physical quantity matrix is greater than or equal to a preset number threshold, performing dimensionality reduction processing on the key physical quantity matrix; In the case where the least squares method is determined as the target calculation strategy, determining the coefficients of the polynomial basis function according to the least squares method includes: For the key physical quantity matrix after dimensionality reduction processing, the coefficients of the polynomial basis function are determined according to the least squares method.
6. The method according to claim 5, characterized in that The dimensionality reduction processing of the key physical quantity matrix includes: Determine a correlation matrix according to the key physical quantity matrix; Determining an intrinsic orthogonal decomposition mode of the correlation matrix according to non-zero eigenvalues and eigenvectors of the correlation matrix; According to the intrinsic orthogonal decomposition mode and the key physical quantity matrix, a key physical quantity matrix after dimensionality reduction processing is determined.
7. The method according to claim 1, characterized in that The determining, according to the influencing parameters and the probability distribution type of the influencing parameters, the basis function combination item of the influencing parameters comprises: When the dimension of the influencing parameter is determined, the basis function combination item is determined according to the dimension of the influencing parameter and a preset truncation order.
8. A system for obtaining evaluation parameters of a numerical reactor, characterized in that: The system comprises: An acquisition module, used for acquiring the influencing parameters of the numerical reactor and their probability distribution types; A first determination module, used to determine a basis function combination item of the influencing parameter according to the influencing parameter and its probability distribution type; A second determination module is used to determine a polynomial basis function matrix and a reduction coefficient according to a sampling result and the basis function combination term, wherein the sampling result is obtained by sampling the influencing parameter according to the probability distribution indicated by the probability distribution type; The third determination module is used to determine the evaluation parameters of the numerical reactor according to the polynomial basis function matrix, the reduced-order coefficients, the influencing parameters and the probability distribution corresponding to the influencing parameters.
9. An electronic device, characterized in that: The electronic device comprises a memory and a processor, wherein a computer program is stored in the memory, and the computer program implements the method according to any one of claims 1 to 7 when executed by the processor.
10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by one or more processors, the method according to any one of claims 1 to 7 is implemented.
Citation Information
Patent Citations
Quantitative analysis method and device for result uncertainty of reactor core thermal hydraulic program
CN111353232A