Parameter uncertainty quantification method and device for particle transport and intelligent equipment

Abstract

The invention relates to the technical field of radiation protection, particularly provides a particle transport-oriented parameter uncertainty quantification method and device and intelligent equipment, and aims to solve the problem that parameter uncertainty analysis and calculation are complex and not flexible enough. The method comprises the steps that an uncertainty model and feature data in the particle transportation process are obtained, the uncertainty model is constructed according to the relation between particle transportation parameters and responses, and the uncertainty model comprises coefficient terms and variance terms; calculating a coefficient item based on the characteristic data by adopting a numerical simulation method, wherein the coefficient item is used for reflecting the influence of parameter disturbance on response uncertainty; calculating a variance item according to a preset parameter, wherein the variance item is used for reflecting parameter correlation; and quantizing the parameter uncertainty according to an uncertainty model, the calculated coefficient item and the variance item. According to the method, a large amount of sampling statistics is not needed, the uncertainty model can be adjusted according to the parameter response relation, the flexibility of uncertainty calculation is improved, and the calculation cost is reduced.

Description

Technical Field

[0001] The present application relates to the field of radiation protection technology, and in particular to a parameter uncertainty quantification method, apparatus and intelligent device for particle transport. Background Art

[0002] Particle transport is a discipline that studies the transport and diffusion behavior of microscopic particles in matter. Studying particle transport helps to design more effective radiation protection equipment and solutions. Usually, there is a certain deviation between the calculated values ​​of particle transport software and the theoretical values ​​or experimental values. Uncertainty analysis can evaluate the impact of uncertainty and analyze the physical characteristics of the system. It is an important way to reduce the uncertainty of calculation results and optimize the design. At present, the input parameter uncertainty analysis method requires repeated large-scale sampling statistical calculations, and cannot flexibly adjust the relationship between parameters and responses.

[0003] Accordingly, the field needs a new parameter uncertainty quantification scheme for particle transport to solve the above problems. Summary of the invention

[0004] In order to overcome the above-mentioned defects, the present application is proposed to solve or at least partially solve the technical problems of high computational cost and lack of flexibility in parameter uncertainty analysis.

[0005] In a first aspect, a method for quantifying parameter uncertainty in particle transport is provided, the method comprising: obtaining an uncertainty model and characteristic data in a particle transport process, wherein the uncertainty model is constructed based on the relationship between parameters and responses of particle transport, and the uncertainty model comprises coefficient terms and variance terms; calculating the coefficient terms using a numerical simulation method based on the characteristic data, wherein the coefficient terms are used to reflect the influence of parameter disturbance on response uncertainty; calculating the variance terms according to preset parameters, wherein the variance terms are used to reflect parameter correlation; and quantifying parameter uncertainty according to the uncertainty model, the calculated coefficient terms, and the variance terms.

[0006] In a technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the method further includes: obtaining a function representing the relationship between the parameter and the response; and obtaining the uncertainty model by fitting the function and Taylor expansion.

[0007] In one technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the uncertainty model is expressed as:

[0008] U 2 =SV α S T

[0009] Where U represents the parameter uncertainty of particle transport; S represents the coefficient term; V α represents the variance term; S T represents the transpose of the coefficient term.

[0010] In a technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the characteristic data includes the particle path, path weight and contribution of the path to the response, and the coefficient term is calculated based on the characteristic data using a numerical simulation method, including: using a Monte Carlo simulation method to calculate the coefficient term according to the path, path weight and contribution of the path to the response.

[0011] In one technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the calculation formula of the coefficient term is:

[0012]

[0013] Where n represents the order of the Taylor expansion; B represents a set of reaction cross sections, b represents a reaction cross section in B; H represents a set of energy points, h represents an energy point in H; R represents the response, Σ b (h) represents the reaction cross section at energy point h, Represents ∑ b (h) to the power of n, It means to find the n-th order partial derivative; wherein the reaction cross section and the energy point are determined according to the Monte Carlo simulation method.

[0014] In a technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the uncertainty is not affected by parameter disturbances.

[0015] In a technical solution of the above-mentioned parameter uncertainty quantification method for particle transport, the method further includes: calculating the influence of the parameter disturbance on the response based on the uncertainty.

[0016] In one technical solution of the above-mentioned parameter uncertainty quantification method for particle transport,

[0017] In a second aspect, a parameter uncertainty quantification device for particle transport is provided, comprising: an acquisition module, used to acquire an uncertainty model and characteristic data in a particle transport process, wherein the uncertainty model is constructed according to the relationship between the parameters and responses of the particle transport, and the uncertainty model includes coefficient terms and variance terms; a coefficient term calculation module, used to calculate the coefficient terms using a numerical simulation method based on the characteristic data, wherein the coefficient terms are used to reflect the influence of parameter disturbances on response uncertainty; a variance term calculation module, used to calculate the variance terms according to preset parameters, and the variance terms are used to reflect parameter correlation; an uncertainty quantification module, used to quantify parameter uncertainty according to the uncertainty model, the calculated coefficient terms and the variance terms.

[0018] In a third aspect, a smart device is provided, comprising at least one processor; and a memory communicatively connected to the at least one processor; wherein a computer program is stored in the memory, and when the computer program is executed by the at least one processor, the method in the first aspect or any corresponding technical solution thereof is implemented.

[0019] In a fourth aspect, a computer-readable storage medium is provided, wherein a plurality of program codes are stored therein, wherein the program codes are suitable for being loaded and run by a processor to execute the method in the above-mentioned first aspect or any corresponding technical solution thereof.

[0020] The above one or more technical solutions of the present application have at least one or more of the following beneficial effects:

[0021] In the technical solution of the present application, an uncertainty model consisting of coefficient terms and variance terms is constructed through the relationship between the parameters of particle transport and the response, and then the coefficient terms are calculated using a numerical simulation method based on the characteristic data, and the variance terms are calculated based on the preset parameters, and finally the calculated coefficient terms and variance terms are substituted into the uncertainty model to obtain the uncertainty. The present application can adjust the uncertainty model according to different parameter response relationships, thereby improving the flexibility of uncertainty calculation. The present application can also flexibly adjust the model parameters and conditions without repeating a large number of sampling statistical calculations, thereby achieving the effect of reducing the calculation cost of uncertainty analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The disclosure of the present application will become easier to understand with reference to the accompanying drawings. It is easy for those skilled in the art to understand that these drawings are only for illustrative purposes and are not intended to limit the scope of protection of the present application. Among them:

[0023] Figure 1 It is a schematic flow chart of the main steps of a parameter uncertainty quantification method for particle transport according to an embodiment of the present application;

[0024] Figure 2 It is a schematic diagram of the main structural block diagram of a parameter uncertainty quantification device for particle transport according to an embodiment of the present application;

[0025] Figure 3 The figure is a schematic diagram of the connection relationship between the processor and the memory of a smart device according to an embodiment of the present application.

[0026] Reference numerals:

[0027] 11: memory; 12: processor. DETAILED DESCRIPTION

[0028] Some embodiments of the present application are described below with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are only used to explain the technical principles of the present application and are not intended to limit the protection scope of the present application.

[0029] In the description of the present application, the terms "first", "second", etc. are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device that includes a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices. The terms "installed", "connected", and "connected" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, it can be indirectly connected through an intermediate medium, it can also be the internal communication of two elements, it can be a wireless connection, or it can be a wired connection.

[0030] In addition, "module" and "processor" may include hardware, software or a combination of the two. A module may include hardware circuits, various suitable sensors, communication ports, and memories, and may also include software parts, such as program codes, or a combination of software and hardware. The processor may be a central processing unit, a microprocessor, an image processor, a digital signal processor, or any other suitable processor. The processor has data and / or signal processing functions. The processor may be implemented in software, hardware, or a combination of the two. Computer-readable storage media include any suitable media that can store program codes, such as magnetic disks, hard disks, optical disks, flash memory, read-only memory, random access memory, etc.

[0031] In addition, if the meaning of "and / or" appears in this application, it includes three parallel solutions. Taking "A and / or B" as an example, it includes solution A, solution B, or a solution that satisfies both A and B. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the ability of ordinary technicians in this field to implement. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by this application. The term "at least one A or B" or "at least one of A and B" has a similar meaning to "A and / or B" and can include only A, only B, or A and B. The singular terms "one" and "this" can also include plural forms.

[0032] Particle transport studies the process of particle transport in matter, including particle diffusion, migration, adsorption, reaction and other behaviors. The particle transport process is not only affected by the properties and characteristics of the particles themselves, but also by the surrounding environmental factors and macroscopic effects. Particle transport research is of great significance in practical applications. Radiation protection, materials science, energy conversion and storage, environmental science, biomedicine, nanotechnology and other fields all need to design and develop new materials, technologies and processes by studying and understanding particle transport. In radiation protection work, the calculation deviation of particle transport software mainly comes from the following three aspects:

[0033] (1) Data uncertainty, including uncertainty caused by uncertainty in nuclear data, device size, and loading capacity.

[0034] (2) Modeling uncertainty, including uncertainty caused by simplification and approximation in the establishment of computational models.

[0035] (3) Methodological uncertainty, including the uncertainty caused by simplification and approximation in the software calculation method and the calculation process.

[0036] Research on uncertainty analysis at home and abroad is mainly focused on nuclear databases. Uncertainty analysis methods can be divided into two categories: output uncertainty extrapolation methods and input parameter uncertainty analysis methods. Among them, the basic idea of ​​the output uncertainty extrapolation method is to compare the program calculation results with important experimental data, obtain the program calculation accuracy, and then extrapolate the program calculation accuracy to the simulation of other systems to quantify uncertainty. The input parameter uncertainty analysis method needs to determine the probability distribution of each uncertainty parameter and other original uncertainty information, realize the transmission of uncertainty parameters in the simulation process, and finally quantify the uncertainty of the simulation results. The currently commonly used uncertainty analysis methods based on sampling statistics theory have the problems of high computational cost and poor applicability.

[0037] This embodiment provides a parameter uncertainty quantification method for particle transport, see the attached Figure 1 , Figure 1 FIG. 1 is a flow chart of the main steps of a parameter uncertainty quantification method for particle transport according to an embodiment of the present application. Figure 1 As shown, the method mainly includes the following steps S2 to S8:

[0038] Step S2, obtaining an uncertainty model and characteristic data in the particle transport process, wherein the uncertainty model is constructed according to the relationship between the parameters and responses of the particle transport, and the uncertainty model includes coefficient terms and variance terms.

[0039] In this embodiment, the uncertainty model is used to quantify parameter uncertainty, such as calculating parameter uncertainty; the characteristic data in the particle transport process includes the path and weight of particle transport, secondary particle generation, acceleration and other characteristic quantity data. It should be noted that the uncertainty model is constructed based on the relationship between the parameters and responses of particle transport, wherein the parameters and responses are determined by the specific research problem. For example, in the study of neutron leakage, the (input) parameter can be one or more of the reaction cross section, radius, and density, and the (output) response can be the average value, standard deviation, maximum value, etc. of the neutron leakage rate. This embodiment does not make specific restrictions on this, that is, the selection of parameters and responses is determined according to the specific circumstances of the actual problem to ensure that the output results can effectively support decision analysis.

[0040] In this embodiment, uncertainty analysis is performed based on generalized perturbation theory. The core idea is to calculate the behavior of a complex system under small perturbations. This method can derive an expression for the expected solution of a formal power series in some "small" parameters (also called perturbation series), thereby quantifying the deviation from the problem. Specifically, assuming that the initial value (measurement mean) of the k parameters is (α1 0 , α2 0 , ..., α k 0 ), whose response is R(α1 0 , α2 0 , ..., α k 0 ) is denoted as R 0 , the perturbations of the k parameters are (δα1, δα2, ..., δα k ), then the response after the disturbance is R(α1 0 +δα1,α2 0 +δα2,...,α k 0 +δα k ), recorded as R(α), then the parameter uncertainty can be measured using the following formula (1):

[0041]

[0042] in, Represents (relative) uncertainty, R(α)-R 0 Represents the change in response after parameter disturbance, R 0 Represents the response of the initial parameters.

[0043] Furthermore, this embodiment decomposes formula (1) and converts it into an uncertainty model represented by coefficient terms and variance terms, wherein the coefficient terms are used to reflect the influence of disturbances of different parameters on the uncertainty of the response, and the variance terms are used to reflect the correlation between multiple parameters. It should be noted that when converting, the n-order Taylor expansion can be used to fit the input and the response according to the relationship between the input and the response (such as exponential and logarithmic functions) (n=1, 2, 3..), and this embodiment does not specifically limit the conversion method.

[0044] Step S4, calculating coefficient terms using a numerical simulation method based on the characteristic data, wherein the coefficient terms are used to reflect the impact of parameter disturbance on response uncertainty.

[0045] In this embodiment, the numerical simulation method is a technology that uses a computer to perform numerical calculations and simulations, including Monte Carlo simulation method, finite difference method, finite element method, boundary element method, etc. This embodiment uses a numerical simulation method to simulate the particle transport process according to characteristic data, thereby calculating the coefficient term of the uncertainty model, which reflects the influence of parameter disturbance on the response uncertainty. Among them, the results of the numerical simulation can be controlled and optimized by adjusting the input parameters, initial conditions and calculation methods, etc., without repeating a large number of sampling statistical calculations, which greatly improves the calculation efficiency.

[0046] Step S6, calculating the variance term according to the preset parameters, where the variance term is used to reflect the parameter correlation.

[0047] In this embodiment, the preset parameters are determined according to the actual problem like the parameters and responses, such as the initial input parameters and disturbance ratio under a certain research problem. The variance term is used to reflect the correlation of parameters and can be calculated using the relative covariance matrix, correlation coefficient, etc.

[0048] Step S8, quantifying parameter uncertainty according to the uncertainty model, the calculated coefficient term and the variance term.

[0049] In this embodiment, the coefficient term and the variance term calculated in step S4 and step S6 are input into the uncertainty model to obtain the parameter uncertainty.

[0050] Based on the method described in steps S2 to S8 above, an uncertainty model consisting of coefficient terms and variance terms is constructed through the relationship between the parameters of particle transport and the response, and then the coefficient terms are calculated using a numerical simulation method based on the characteristic data, and the variance terms are calculated based on the preset parameters, and finally the calculated coefficient terms and variance terms are substituted into the uncertainty model to obtain the uncertainty. The present application can adjust the uncertainty model according to different parameter response relationships, improves the flexibility of uncertainty calculation, and uses numerical simulation methods to flexibly adjust model parameters and conditions without repeating a large number of sampling statistical calculations, thereby achieving the effect of reducing the calculation cost of uncertainty analysis.

[0051] In an optional implementation, before the above step S2, step S1 may be further included, specifically including the following steps S10 and S12:

[0052] Step S10, obtaining a function representing the relationship between parameters and responses.

[0053] In this embodiment, it is assumed that the relationship function between the parameter and the response is R(·), and the parameter uncertainty is as shown in formula (1) in the above embodiment.

[0054] Step S12, obtaining an uncertainty model according to the function and Taylor expansion fitting.

[0055] In this embodiment, based on the generalized perturbation theory, R(α) is 0 Taylor expansion is performed at α, where the order of Taylor expansion can be selected as needed. This embodiment assumes that the disturbance is small and uses the first-order Taylor expansion as an example. Specifically, R(α) at ​​α 0 The result of the first-order Taylor expansion at is shown in the following formula (2):

[0056]

[0057] in, It means that R(α) is at point α 0 Place α i The first-order partial derivative of i Represents parameter α i The corresponding perturbation, o[(α-α 0 ) 1 ] represents the parameter vector (α-α 0 ) of first order infinitesimal, α=(α1 0 +δα1,α2 0 +δα2,...,α k 0 +δα k ), α 0 =(α1 0 , α2 0, ..., α k 0 ).

[0058] By simplifying the above uncertainty calculation formula (1) using formula (2), we can obtain the following approximate uncertainty expression (3):

[0059]

[0060] Among them, k represents the number of parameters, α i 0 represents the initial value of the i-th (1≤i≤k) parameter, R 0 That is, R(α1 0 , α2 0 , ..., α k 0 ), δα i represents the perturbation of the i-th parameter.

[0061] Define the first-order coefficient (coefficient term) as: 1≤i≤k. It should be noted that when the Taylor expansion order is n, the corresponding coefficient term is the coefficient of the nth order term.

[0062] So the relative uncertainty It can be expressed as:

[0063]

[0064] Where S represents the first-order coefficient matrix, S = [S1, S2, ...S i , ...S k ]; δα is (δα1, δα2,..., δα k ); α 0 That is (α1 0 , α2 0 , ..., α k 0 ).

[0065] but It can be expressed as:

[0066]

[0067] Among them, Var(·) is the variance calculation function, E[·] is the expectation calculation function, R is R(α), S T is the transposed matrix of the first-order coefficient matrix S, yes The transposed vector of . is the relative covariance matrix, i.e., the variance term, which is denoted as V α , the uncertainty Denoted as U, the uncertainty model can be expressed as:

[0068] U 2 =SV α S T (6)

[0069] In an optional implementation, the characteristic data includes the path of the particle, the path weight, and the contribution of the path to the response, and the above step S4 may further include the following step S40:

[0070] Step S40: Calculate the coefficient term according to the path, path weight and contribution of the path to the response by using a Monte Carlo simulation method.

[0071] In this embodiment, according to the n-th order Taylor expansion, the n-th order coefficient corresponding to the influence of the parameter α on the response R can be expressed as:

[0072]

[0073] It can be understood that the first-order coefficient S corresponds to the case where n is 1 in the above n-order coefficient.

[0074] In the calculation based on Monte Carlo simulation of particle transport trajectory (path), the response R can be expressed as:

[0075] R=∑ j t j q j (8)

[0076] Among them, j represents the number of paths, q j represents the weight corresponding to path j, t j represents the contribution (estimate) of path j to the response, where path refers to the trajectory (track) of the particle.

[0077] Considering the different reaction cross sections and energy groups of particles, the n-order coefficient in the above formula (7) can be expressed as:

[0078]

[0079] Where n represents the order of Taylor expansion; B represents a set of reaction cross sections, b represents a reaction cross section in B; H represents a set of energy points, h represents an energy point in H; It means to find the n-th order partial derivative, Represents ∑ b (h) to the power of n;∑ b (h) = K b (h)e v is the reaction cross section calculation formula for the energy point h particle transport process, K b(h) represents the basic item of the cross section, which can be selected according to the reaction type and is not specifically limited in this embodiment; e is a natural constant, and v represents a variable path.

[0080] Further, let Then the n-order coefficient of formula (9) can be expressed as:

[0081]

[0082] According to the Monte Carlo simulation of particle transport process, the n-order coefficient can be expressed as:

[0083] μ n =∑ i V ni w i (11)

[0084] Where i represents the i-th particle, V ni is the nth-order coefficient of particle i, w i is the weight of the i-th particle, corresponding to q j , that is, j q j =w i .

[0085] According to the equality of formula (10) and (11), expanding the n-order coefficient of particle i can obtain:

[0086]

[0087] Therefore, for a simulation of N particles, V can be calculated ni The mean value V ni :

[0088]

[0089] Since nuclear reactions may cause path bifurcation, path segment j is composed of m+1 tracks. The probability of path j is determined by the probability of the tracks that make it up, where a track refers to a path between two changes (including keeping the original particle unchanged, particles crossing the boundary, multiple nuclear reactions, etc.). Assume that the probability corresponding to each track is r k , we can get the following formula (14):

[0090]

[0091] Among them, k∈[0,m] represents m+1 segments of track, r k Indicates the probability corresponding to each track, q j represents the weight of the ith particle. Assume that the kth track starts from a neutron generated by a type a reaction, scattered from an angle θ′ to θ, and the path length is λk , the energies before and after the collision are E′ and E, and the cross section of the collision reaction type is ∑ T (E), the cross section of the boundary reaction type is X T (E), where the reaction cross section is a physical quantity that represents the probability of a specific nuclear reaction occurring. The probability r corresponding to each track is k It can be calculated by the following formula (15):

[0092]

[0093] Among them, ∑ a (E′) represents the cross section of type a reaction before collision, ∑ T (E′) represents the total cross section before collision, P a (E′→E; θ′→θ) represents the reaction (E′→E; θ′→θ), that is, the probability of energy change and angle scattering change before and after the collision. dE and dθ represent the infinitesimal elements of energy and angle, ∑ T (E) represents the total cross section after the collision, λ k Denotes the path length, dλ k A microelement representing the length of a path.

[0094] If the track starts at a collision and ends at the boundary, then:

[0095]

[0096] Among them, X a (eE′) represents the cross section of the boundary reaction before the collision, X T (E′) represents the total cross section before collision, X T (E) represents the total cross section after the collision.

[0097] If the track starts at the boundary and ends at the collision, then:

[0098]

[0099] If the track starts and ends at boundaries, then:

[0100]

[0101] In summary, in Monte Carlo simulation, we only need to count the relevant data of each track of the particle (such as the type of the starting and ending points of the track, the path length, the particle energy before and after the collision, the collision type, the cross section of the reaction type, the probability of the reaction, etc.) to calculate the corresponding n-order coefficient V ni For N particles, the mean can be calculated by formula (13): Then, the n-order term coefficient is calculated by formula (11), such as the first-order term coefficient.

[0102] In an optional embodiment, the variance term The calculation can be performed according to the covariance matrix calculation method in the prior art. After obtaining the coefficient term and the variance term, the uncertainty can be calculated using the uncertainty model, that is, formula (6):

[0103] In one implementation, the preset parameters may be obtained by querying from a core database.

[0104] In an optional implementation, this embodiment uses a numerical simulation method to calculate the first-order term coefficient, and then combines the covariance to perform uncertainty calculation. In the process of calculating the first-order term coefficient, the value of the partial differential does not change with the disturbance ratio. The covariance calculated according to the database is a physical property and has nothing to do with the disturbance. Therefore, the relative uncertainty calculated based on the two does not change with the disturbance ratio. At the same time, the disturbance does not affect the Monte Carlo calculation process of the physical quantity, so the neutron flux and its statistical error, etc. do not change with the disturbance. Finally, the total uncertainty calculated by combining the statistical error of the physical quantity and the data uncertainty is a stable uncertainty that is not affected by parameter disturbances.

[0105] In an application scenario according to an embodiment of the present application, the integral leakage rate experiment on bismuth balls conducted by the Institute of Physics and Power Engineering (IPPE) of Russia between 1992 and 1997 was used to verify the correctness of the nuclear calculation program. This embodiment selects a typical perturbation setting, and the calculation uncertainty is compared and analyzed. Specifically, the outer radius of the bismuth shell is 12.0 cm, the inner radius is 3.0 cm, the bismuth thickness is 9 cm, and a cylindrical hole with a radius of 2.5 cm is opened on the shell for placing the neutron source, and the point neutron source is distributed at the center of the bismuth ball. The atomic density of the bismuth material is 0.0282 (e24 / cm3), the nuclide composition is Bi-209, and the atomic fraction is 1.0. The database used is ENDF-B-VII.1, there are 150 energy groups, the selected perturbation particle is neutron n, the influence gate element is cell3, the nuclide is Bi-209, and the reaction channels involved include 1, 2, 4, 16 and 102. The cross-sectional disturbance ratios of all reaction channels are the same and can be selected from the following disturbance ratios: 0.05%, 0.1%, 0.3%, 0.6% and 1%.

[0106] In this embodiment, the relevant data of each track of neutron n (such as the type of the starting point and end point of the track, the path length, the particle energy before and after the collision, the collision type, the cross section of the reaction type, the probability of the reaction, etc.) are obtained by Monte Carlo simulation based on the above data, and then the coefficient term of the uncertainty model is calculated; the variance term is calculated by querying the database, and finally the uncertainty calculation result shown in Table 1 below is obtained based on the coefficient term and the variance term:

[0107] Table 1. Uncertainty calculation results Experiment No. Perturbation ratio Uncertainty 1 0.05％ 0.24％ 2 0.1％ 0.24％ 3 0.3％ 0.24％ 4 0.6％ 0.24％ 5 1％ 0.24％

[0108] It can be seen from Table 1 that the uncertainty is not affected by parameter disturbance, which is consistent with the theoretical analysis.

[0109] In an optional implementation, the method may further include the following step S9:

[0110] Step S9: Calculate the influence of the parameter disturbance on the response according to the uncertainty.

[0111] In this embodiment, the variation of the response under different parameter disturbance ratios can be determined according to the calculated uncertainty.

[0112] This embodiment introduces the generalized perturbation theory method for uncertainty analysis based on the particle transport characteristics of radiation protection. It does not need to repeat a large number of sampling statistics. Only one neutron transport simulation is needed to obtain the uncertainty impact of each input parameter on the result, which improves the calculation efficiency of uncertainty. The Monte Carlo method is used for sampling simulation to calculate the relative uncertainty of particle transport in radiation protection, which achieves the purpose of flexibly adjusting the relationship between parameters and responses and the coefficient calculation method, is conducive to analyzing the correlation of variables, and judging the main source of uncertainty. It is suitable for various radiation protection designs and optimizations.

[0113] It should be pointed out that although the various steps in the above embodiments are described in a specific order, those skilled in the art can understand that in order to achieve the effect of the present application, different steps do not have to be executed in such an order. They can be executed simultaneously (in parallel) or in other orders. These adjusted schemes are equivalent to the technical schemes described in this application, and therefore will also fall within the scope of protection of this application.

[0114] Another aspect of the present application also provides a parameter uncertainty quantification device for particle transport, such as Figure 2As shown, it includes: an acquisition module 2, which is used to obtain an uncertainty model and characteristic data in a particle transport process, wherein the uncertainty model is constructed according to the relationship between the parameters of particle transport and the response, and the uncertainty model includes coefficient terms and variance terms; a coefficient term calculation module 4, which is used to calculate the coefficient terms based on the characteristic data using a numerical simulation method, wherein the coefficient terms are used to reflect the influence of parameter disturbances on response uncertainty; a variance term calculation module 6, which is used to calculate the variance terms according to preset parameters, and the variance terms are used to reflect parameter correlation; an uncertainty quantification module 8, which is used to quantify parameter uncertainty according to the uncertainty model, the calculated coefficient terms and the variance terms.

[0115] It is understood that the above-mentioned parameter uncertainty quantification device for particle transport is used to perform Figure 1 The embodiment of the parameter uncertainty quantification method for particle transport shown in the figure has similar technical principles, technical problems solved and technical effects produced. Technicians in this technical field can clearly understand that for the convenience and conciseness of description, the specific working process and related instructions of the parameter uncertainty quantification device for particle transport can refer to the contents described in the embodiment of the parameter uncertainty quantification method for particle transport, which will not be repeated here.

[0116] It is understood by those skilled in the art that all or part of the processes in the method for implementing the above-mentioned embodiment of the present application can also be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable storage medium may include: any entity or device, medium, U disk, mobile hard disk, disk, optical disk, computer memory, read-only memory, random access memory, electrical carrier signal, telecommunication signal and software distribution medium, etc. that can carry the computer program code.

[0117] Another aspect of the present application also provides a computer-readable storage medium.

[0118] In an embodiment of a computer-readable storage medium according to the present application, the computer-readable storage medium can be configured to store a program for executing the above-mentioned method embodiment for parameter uncertainty quantification method for particle transport, and the program can be loaded and run by a processor to implement the above-mentioned parameter uncertainty quantification method for particle transport. For ease of explanation, only the parts related to the embodiment of the present application are shown. For specific technical details not disclosed, please refer to the method part of the embodiment of the present application. The computer-readable storage medium can be a storage device formed by various electronic devices. Optionally, the computer-readable storage medium in the embodiment of the present application is a non-temporary computer-readable storage medium.

[0119] Another aspect of the present application also provides a smart device.

[0120] In an embodiment of an intelligent device according to the present application, the intelligent device may include at least one processor; and a memory connected to the at least one processor in communication; wherein a computer program is stored in the memory, and when the computer program is executed by the at least one processor, the method described in any of the above embodiments is implemented. Figure 3 , Figure 3 FIG. 4 exemplarily shows that the memory 11 and the processor 12 are communicatively connected via a bus.

[0121] In some embodiments of the present application, the smart device may further include at least one sensor, and the sensor is used to sense information. The sensor is communicatively connected to any type of processor mentioned in the present application. Optionally, the smart device described in the present application may be, but is not limited to, a mobile phone, a tablet computer, a desktop, a laptop, a handheld computer, a notebook computer, and the like, and the embodiments of the present application are not limited thereto.

[0122] So far, the technical solution of the present application has been described in conjunction with an embodiment shown in the accompanying drawings, but it is easy for those skilled in the art to understand that the protection scope of the present application is obviously not limited to these specific embodiments. Without departing from the principles of the present application, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present application.

Claims

1. A parameter uncertainty quantification method for particle transport, characterized in that: include: Acquire an uncertainty model and characteristic data in a particle transport process, wherein the uncertainty model is constructed according to a relationship between a parameter and a response of the particle transport, and the uncertainty model includes a coefficient term and a variance term; Calculate the coefficient term by using a numerical simulation method based on the characteristic data, wherein the coefficient term is used to reflect the influence of parameter disturbance on response uncertainty; Calculate the variance term according to preset parameters, where the variance term is used to reflect parameter correlation; Parameter uncertainty is quantified according to the uncertainty model, the calculated coefficient term, and the variance term.

2. The method according to claim 1, characterized in that The method further comprises: Obtaining a function representing the relationship between the parameter and the response; The uncertainty model is obtained by fitting the function and Taylor expansion.

3. The method according to claim 1 or 2, characterized in that: The uncertainty model is expressed as: IN 2 =SV α WITH T Where U represents the parameter uncertainty of particle transport; S represents the coefficient term; V α represents the variance term; S T represents the transpose of the coefficient term.

4. The method according to claim 2, characterized in that: The characteristic data includes the path of the particle, the path weight and the contribution of the path to the response, and the coefficient term is calculated based on the characteristic data by using a numerical simulation method, including: The coefficient term is calculated according to the path, path weight and contribution of the path to the response by using Monte Carlo simulation method.

5. The method according to claim 4, characterized in that The calculation formula of the coefficient term is: Where n represents the order of the Taylor expansion; B represents a set of reaction cross sections, b represents a reaction cross section in B; H represents a set of energy points, h represents an energy point in H; R represents the response, ∑ b (h) represents the reaction cross section at energy point h, Represents Σ b (h) to the power of n, It means to find the n-th order partial derivative; wherein the reaction cross section and the energy point are determined according to the Monte Carlo simulation method.

6. The method according to claim 1, characterized in that The uncertainty is not affected by parameter perturbations.

7. The method according to claim 6, characterized in that The method further comprises: The effect of the parameter disturbance on the response is calculated based on the uncertainty.

8. A parameter uncertainty quantification device for particle transport, characterized in that: include: An acquisition module, used to acquire an uncertainty model and characteristic data in a particle transport process, wherein the uncertainty model is constructed according to the relationship between the parameters and responses of the particle transport, and the uncertainty model includes a coefficient term and a variance term; A coefficient term calculation module, used for calculating the coefficient term by a numerical simulation method based on the characteristic data, wherein the coefficient term is used to reflect the influence of parameter disturbance on response uncertainty; A variance term calculation module, used to calculate the variance term according to preset parameters, wherein the variance term is used to reflect parameter correlation; The uncertainty quantification module is used to quantify the parameter uncertainty according to the uncertainty model, the calculated coefficient term and the variance term.

9. A smart device, characterized in that: include: at least one processor; and, a memory communicatively coupled to the at least one processor; The memory stores a computer program, and when the computer program is executed by the at least one processor, the method according to any one of claims 1 to 7 is implemented.

10. A computer-readable storage medium storing a plurality of program codes, characterized in that: The program code is suitable for being loaded and executed by a processor to execute the method according to any one of claims 1 to 7.

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