Uncertainty transmission method based on data dimension reduction and Monte Carlo sampling

Abstract

The invention provides an uncertainty transmission method based on data dimension reduction and Monte Carlo sampling. Firstly, based on covariance of input parameters, a Monte Carlo method is adopted to randomly sample and generate a large number of target input parameters; secondly, through the target control equation after dimension reduction processing, numerical calculation is executed on the target input parameters obtained through sampling, and corresponding target output parameters are obtained; and finally, performing statistical analysis according to the target output parameters to determine the uncertainty condition of the target system. Obviously, original target input parameters are obtained through the Monte Carlo method, the universality of an application scene can be improved, the method can also be used for a system with nonlinear characteristics or complex parameter distribution conditions, the sampling data of the Monte Carlo method are calculated through the target control equation after dimension reduction, and the calculation efficiency is improved. The complexity of a data processing system and the calculation amount of data can be reduced, so that the data dimension in the calculation process is reduced, and the calculation efficiency of uncertainty transmission is improved.

Description

Technical Field

[0001] The present application relates to the field of data analysis, and in particular to an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling. Background Art

[0002] In the field of data analysis and data processing, data analysis work such as uncertainty transfer can be completed by deterministic methods or full Monte Carlo methods. Deterministic methods rely on analytical means and approximate formulas to transfer the uncertainty of input parameters, and have the advantage of high computational efficiency. However, since such methods assume that system parameters follow a normal distribution and that the system response is approximately linear within the range of input parameter uncertainty, their applicability is poor for complex nonlinear systems in practical application scenarios. Full Monte Carlo is a random analysis method based on statistical simulation. It generates the values ​​of input parameters by random sampling, inputs them into the model one by one for calculation, and finally analyzes the output results to obtain their statistical characteristics. The full Monte Carlo method can more realistically reflect the nonlinear effects of complex systems and the global impact of the statistical distribution of input parameters on the output. However, in order to ensure that the output results have sufficient statistical accuracy, a large number of sample simulation calculations are usually required. At the same time, the data dimensions processed by the full Monte Carlo method are large, resulting in low computational efficiency.

[0003] Therefore, in order to solve the limitations of the current uncertainty analysis methods, a data processing method that combines the principles of the two methods is needed to improve computational efficiency and reduce data costs while ensuring that the distribution information of various system parameters and the complex nonlinear response of the system can be effectively captured. Summary of the invention

[0004] The purpose of this application is to solve at least one of the above-mentioned technical defects, especially the technical defects in the prior art that the deterministic method cannot accurately reflect the distribution and response of system parameters when applied alone, and the low computational efficiency and high data cost when the Monte Carlo method is applied alone.

[0005] In a first aspect, the present application provides an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling, the method comprising:

[0006] Determine the target input parameters based on the Monte Carlo method;

[0007] According to the target control equation, data processing is performed on the target input parameters to obtain target output parameters corresponding to each of the target input parameters;

[0008] Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation;

[0009] Statistical analysis is performed on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

[0010] As an optional implementation, the data dimension reduction process includes a reduced basis method, and the reduced basis method includes:

[0011] determining a snapshot matrix corresponding to the original governing equations;

[0012] According to the snapshot matrix, a reduced basis space corresponding to the target physical field is obtained;

[0013] The target input parameters are projected onto the reduced basis space to obtain a corresponding discrete equation set as the target control equation.

[0014] As an optional implementation, the target control equation is indicated according to a first formula, and the first formula includes:

[0015]

[0016] Among them, A is the system matrix obtained by discretizing the original control equation, B is the load term, and U is the coefficient vector in the reduced basis space. Used to indicate the system function associated with BU;

[0017] Among them, if the system function is a linear function, then , where k is the eigenvalue, and in the neutron transport equation, k is the effective multiplication coefficient and U is the neutron flux;

[0018] The reduced base method specifically includes:

[0019] According to the neutron transport equation, a numerical solution corresponding to typical input parameters is determined to obtain a snapshot matrix;

[0020] Performing intrinsic orthogonal decomposition on the snapshot matrix to obtain a reduced basis space corresponding to the neutron transport equation, and determining a reduced basis matrix according to the reduced basis space;

[0021] Projecting the neutron transport equation to the reduced basis space according to the second formula to obtain a corresponding discrete equation group as the target control equation;

[0022] Wherein, the second formula includes:

[0023]

[0024] in, , is the projection vector of the coefficient vector, and Z is the reduced basis matrix.

[0025] As an optional implementation manner, the determining of the target input parameters based on the Monte Carlo method includes:

[0026] Determine the parameter distribution and covariance matrix of the initial variables corresponding to the target input parameters;

[0027] According to the parameter distribution and the covariance matrix, the target input parameter is sampled based on the Monte Carlo method to obtain the target input parameter.

[0028] As an optional implementation, the specific sampling process includes Latin hypercube sampling.

[0029] As an optional implementation manner, performing statistical analysis on the target output parameter to obtain the uncertainty characteristics corresponding to the target system includes:

[0030] Determine the sensitivity coefficient and covariance matrix corresponding to each variable in the target system;

[0031] Determining the uncertainty of the target system according to a third formula;

[0032] Wherein, the third formula includes:

[0033]

[0034] Among them, S is the sensitivity coefficient vector or sensitivity coefficient matrix corresponding to the sensitivity coefficient, M is the covariance matrix, and Δ is the uncertainty.

[0035] As an optional implementation, the method further includes:

[0036] According to the original control equation, data processing is performed on the target input parameters to obtain control output parameters corresponding to each of the target input parameters;

[0037] A first time duration for obtaining the target output parameter and a second time duration for obtaining the control output parameter are determined, and a time acceleration ratio parameter is determined according to the first time duration and the second time duration.

[0038] In a second aspect, the present application provides an uncertainty transfer device based on data dimensionality reduction and Monte Carlo sampling, the device comprising:

[0039] A determination module, used for determining target input parameters based on a Monte Carlo method;

[0040] A processing module, used for performing data processing on the target input parameters according to the target control equation to obtain target output parameters corresponding to each of the target input parameters;

[0041] Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation;

[0042] The processing module is further used to perform statistical analysis on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

[0043] In a third aspect, the present application provides a computer device comprising one or more processors and a memory, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the one or more processors, the steps of the method described in the first aspect are performed.

[0044] In a fourth aspect, the present application provides a storage medium storing computer-readable instructions, which, when executed by one or more processors, causes the one or more processors to perform the steps of the method described in the first aspect.

[0045] It can be seen from the above technical solutions that the embodiments of the present application have the following advantages:

[0046] Based on any of the above embodiments, the method provided by the present application combines the advantages of Monte Carlo sampling and data dimensionality reduction methods, and improves the computational efficiency and reduces the cost of data processing and data requirements while ensuring that the distribution information of various system parameters and the complex nonlinear response of the system can be effectively captured. The present application first determines the target input parameters through the Monte Carlo method, and then performs data processing on the sampled target input parameters through the target control equation after dimensionality reduction processing to obtain the corresponding target output parameters, thereby performing statistical analysis based on the target output parameters to determine the uncertainty of the target system. Obviously, obtaining the original target input parameters through the Monte Carlo method can improve the universality of the application scenario, and can be used for systems with nonlinear characteristics or complex parameter distributions. Processing the sampled data of the Monte Carlo method through the target control equation after dimensionality reduction can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission. 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. Obviously, 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 creative labor.

[0048] Figure 1A schematic diagram of a flow chart of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application;

[0049] Figure 2 A schematic diagram of an application scenario of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application;

[0050] Figure 3 A schematic diagram of the effect of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application;

[0051] Figure 4 A schematic diagram of the effect of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application;

[0052] Figure 5 This is a diagram of the internal structure of a computer device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0053] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0054] Uncertainty quantification has important applications in many fields such as metrology and calibration, scientific research and engineering applications, quality control, etc. In recent years, with the improvement of computer performance and the improvement of physical calculation methods, the uncertainty introduced by calculation methods and model approximations has been decreasing, while the uncertainty of simulation results caused by the uncertainty of the parameters themselves (geometric dimensions, material composition, etc.) has gradually become the focus of attention. Therefore, studying the transmission of parameter uncertainty is of great significance to all related fields.

[0055] In the field of data processing, uncertainty transfer methods generally include two categories, namely deterministic methods and complete Monte Carlo methods.

[0056] The deterministic method relies on analytical means and approximate formulas to transfer the uncertainty of input parameters, and has the advantage of high computational efficiency. However, since this method assumes that the system parameters follow a normal distribution and the system response is approximately linear within the range of input parameter uncertainty, its applicability is poor for complex nonlinear systems. The Total Monte Carlo method (TMC) is a random analysis method based on statistical simulation. It generates the values ​​of input parameters by random sampling, and inputs them into the model one by one for calculation. Finally, the output results are analyzed to obtain their statistical characteristics. Therefore, the Total Monte Carlo method can more realistically reflect the nonlinear effects of complex systems and the global impact of the statistical distribution of input parameters on the output. However, in order to ensure that the output results have sufficient statistical accuracy, a large number of sample simulation calculations are usually required, resulting in low computational efficiency.

[0057] Specifically, the deterministic method obtains the sensitivity coefficient of the response function with respect to the input model parameters through perturbation theory, and then calculates the uncertainty of the response function based on the covariance matrix of the parameters through the first-order Taylor expansion, the so-called "sandwich formula". The methods of sensitivity analysis mainly include direct numerical perturbation method, generalized perturbation theory and traditional perturbation theory. Among them, the direct numerical perturbation method is the most commonly used. This method calculates the sensitivity coefficient of the input parameter to the response parameter based on the idea of ​​replacing the differential with the differential.

[0058] The complete Monte Carlo method samples the parameters according to the distribution information of the input parameters and the covariance matrix to generate a large number of input parameters, and then calculates the response function according to these parameters in turn. The final calculation results are statistically analyzed (the mean, variance, etc. are obtained by fitting the probability density function) to quantify the distribution and uncertainty of the response function.

[0059] The deterministic method has the limitation of not being able to accurately reflect the uncertainty transfer of parameter distribution in nonlinear systems, and although the complete Monte Carlo method can capture the uncertainty transfer effect of complex nonlinear systems, its high computational cost limits its practical application. However, the two methods have their own advantages: the deterministic method is suitable for the case where the input parameters are normally distributed and the relationship with the response function is approximately linear, and only two calculations are required for each parameter to obtain the sensitivity coefficient, which has high computational efficiency; while the complete Monte Carlo method is suitable for complex nonlinear systems and has no arbitrary preset restrictions on parameter distribution, but because a large number of sampled parameters need to be calculated one by one, the cost is high and the efficiency is low.

[0060] Therefore, the present application aims to combine the advantages of reduced basis and full Monte Carlo, and propose an uncertainty transfer method that combines the two. This method effectively increases computational efficiency and reduces computational cost while ensuring the capture of system parameter distribution information and complex nonlinear responses of the system. It solves the problem that the deterministic method cannot fully capture parameter probability distribution and nonlinear response, and also solves the technical problem that the full Monte Carlo method requires a large amount of calculation and low computational efficiency to obtain high-precision results. In order to more accurately describe the uncertainty transfer effect in nonlinear systems and overcome the shortcomings of the full Monte Carlo method, which has a large amount of calculation and low efficiency, the present application proposes an uncertainty transfer method that combines reduced basis and full Monte Carlo in a specific application scenario. The full Monte Carlo method is inefficient because it requires sampling to calculate the responses of a large number of input parameters. The reduced basis method obtains the snapshot matrix of the numerical solution by solving the control equations of typical input parameters, and obtains the reduced basis of each physical field by performing a comprehensive intrinsic orthogonal decomposition on the matrix. The control equations corresponding to the input parameters sampled by the full Monte Carlo method are then projected onto the low-dimensional subspace formed by the reduced basis to obtain a set of discrete equations with a greatly reduced number of degrees of freedom, thereby effectively reducing the computational cost, accelerating the convergence speed, and improving the computational efficiency, while retaining the advantage of the full Monte Carlo method in being applicable to complex nonlinear systems.

[0061] In summary, the technical concept of the present application is that the method provided by the present application combines the advantages of Monte Carlo sampling and data dimensionality reduction methods, and improves the computational efficiency and reduces the cost of data processing and data requirements while ensuring that the distribution information of various system parameters and the complex nonlinear response of the system can be effectively captured. The present application first determines the target input parameters through the Monte Carlo method, and then performs data processing on the sampled target input parameters through the target control equation after dimensionality reduction processing to obtain the corresponding target output parameters, thereby performing statistical analysis based on the target output parameters to determine the uncertainty of the target system. Obviously, obtaining the original target input parameters through the Monte Carlo method can improve the universality of the application scenario, and can be used for systems with nonlinear characteristics or complex parameter distributions. Processing the sampled data of the Monte Carlo method through the target control equation after dimensionality reduction can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0062] The method provided in this application is described in detail below based on corresponding implementation methods in some practical application scenarios.

[0063] See also Figure 1 , Figure 1 A flowchart of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling is provided for an embodiment of the present application, such as Figure 1 As shown, the method includes:

[0064] S101. Determine target input parameters based on the Monte Carlo method;

[0065] Specifically, as an optional implementation, the determining of the target input parameters based on the Monte Carlo method includes:

[0066] Determine the parameter distribution and covariance matrix of the initial variables corresponding to the target input parameters;

[0067] According to the parameter distribution and the covariance matrix, sampling the target input parameter based on the Monte Carlo method to obtain the target input parameter;

[0068] In this embodiment, the parameter distribution and covariance matrix corresponding to the initial variables are first determined based on previous experimental data or the distribution estimated according to physical principles. Then, the determined parameter distribution and covariance matrix can provide a data basis for Monte Carlo sampling, and further provide a data basis for the optimization of the Monte Carlo sampling process, further improving the uniformity and rationality of the data distribution in the sampling process, so as to improve the effectiveness of uncertainty data processing.

[0069] As an optional implementation, the specific sampling process includes Latin hypercube sampling.

[0070] Latin hypercube sampling can perform partition sampling according to parameter distribution to improve the uniformity and rationality of data distribution, thereby improving the effectiveness of the original target input parameters, thereby improving the effectiveness of the final uncertainty data processing.

[0071] For example, in one application scenario, Latin hypercube sampling is performed on the input parameters to ensure that the sampling has higher coverage and uniformity. The mean of the input parameters is set to 0.085 cm -1 , with an uncertainty of 1.2%. 500 sets of data were generated through Latin hypercube sampling as input for subsequent parameter calculations.

[0072] S102, performing data processing on the target input parameters according to the target control equation to obtain target output parameters corresponding to each of the target input parameters;

[0073] Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation;

[0074] In the present application, a reduced basis method is used as a means of data dimensionality reduction, combined with the aforementioned Monte Carlo sampling and applied. For details, please refer to the relevant implementation method.

[0075] S103: Perform statistical analysis on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

[0076] In this part, the sensitivity coefficient can be calculated based on the direct perturbation method through the target control equation, and then the uncertainty can be calculated in combination with the covariance matrix corresponding to the target input parameters. For specific calculation processes and examples, please refer to the relevant content of other implementation methods.

[0077] In the data processing process of uncertainty analysis, this embodiment combines the advantages of Monte Carlo sampling and data dimension reduction methods, and improves the computational efficiency and reduces the cost of data processing and data demand while ensuring that the distribution information of various system parameters and the complex nonlinear response of the system can be effectively captured. Specifically, this method first determines the target input parameters by Monte Carlo sampling, and then performs data processing on the sampled target input parameters through the target control equation after dimensionality reduction processing to obtain the corresponding target output parameters, thereby performing statistical analysis based on the target output parameters to determine the uncertainty of the target system. Obviously, obtaining the original target input parameters through the Monte Carlo method can improve the universality of the application scenario, and can be used for systems with nonlinear characteristics or complex parameter distribution. Processing the sampled data of the Monte Carlo method through the target control equation after dimensionality reduction can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0078] As an optional implementation, the data dimension reduction process includes a reduced basis method, and the reduced basis method includes:

[0079] determining a snapshot matrix corresponding to the original governing equations;

[0080] According to the snapshot matrix, a reduced basis space corresponding to the target physical field is obtained;

[0081] The target input parameters are projected onto the reduced basis space to obtain a corresponding discrete equation set as the target control equation.

[0082] The method provided in this embodiment can perform the corresponding data dimension reduction process through the reduced basis method, determine the typical numerical solution of the target input parameters according to the original control equation to form a snapshot matrix, and further obtain the reduced basis space corresponding to the physical field indicated by the control equation according to the snapshot matrix. The vectors in the reduced basis space are mutually orthogonal, and the degree of freedom is significantly reduced. Finally, the target input parameters can be projected to the reduced basis space after the degree of freedom is reduced, and the corresponding discrete equation group is obtained as the target control equation to achieve data dimension reduction. In this way, the sampled data of the Monte Carlo method can be processed through the target control equation after dimension reduction, which can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0083] It should be noted that the reduced basis method is an optional implementation method given by this application based on specific application scenarios. Depending on the different data processing principles of specific application scenarios, the corresponding data features may also be different. Therefore, it is also feasible to use other data dimensionality reduction methods in combination with the Monte Carlo method. Technicians in related fields can choose some of these methods for application. For example, in some fields, feasible data dimensionality reduction supporting methods in the Monte Carlo method may include:

[0084] 1. Principal Component Analysis (PCA):

[0085] principle:

[0086] PCA finds the main components (principal components) in the data by eigendecomposing the data covariance matrix. These principal components are linear combinations of the original data variables. It can transform high-dimensional data into low-dimensional space while retaining the variance information of the data as much as possible.

[0087] Application in Monte Carlo:

[0088] Before the Monte Carlo simulation, the input data is processed by PCA. For example, in financial risk assessment, if there are multiple risk factors (such as interest rate fluctuations, exchange rate changes, stock price fluctuations, etc.) as input data, PCA can convert these factors into a few independent principal components that can explain most of the variance of the data. Then, these principal components after dimensionality reduction are used as input variables for Monte Carlo sampling.

[0089] 2. Factor Analysis:

[0090] principle:

[0091] Factor analysis assumes that the observed data are the result of the interaction of some potential common factors and special factors. It attempts to find these potential common factors that can explain the correlation between multiple observed variables.

[0092] Application in Monte Carlo:

[0093] In Monte Carlo simulation scenarios, such as studying atmospheric pollutant diffusion models in environmental science, there may be multiple meteorological factors (such as wind speed, wind direction, temperature, humidity, etc.) and pollution source emission parameters (such as emission volume, emission height, etc.) as input variables. Factor analysis can reduce these variables to several potential factors, such as meteorological conditions and pollution source intensity factors. These common factors are then sampled and the simulated values ​​of the original variables are obtained by inverse analysis based on the factor model.

[0094] 3. Clustering Analysis:

[0095] principle:

[0096] Cluster analysis is to divide data objects into different clusters so that data objects in the same cluster have high similarity, while data objects in different clusters have great differences.

[0097] Application in Monte Carlo:

[0098] In Monte Carlo simulation, cluster analysis can be used to group data and group similar data points together. For example, in a supply chain logistics simulation, there are many different suppliers and customers with different geographical locations, order sizes, delivery time requirements, and other attributes. Through cluster analysis, suppliers and customers can be divided into different groups based on factors such as geographical location and business type, and then each cluster can be sampled instead of all data points, thereby reducing the scale of sampling and the amount of calculation.

[0099] 4. Sparse Representation:

[0100] principle:

[0101] Sparse representation is a method to find the sparsest representation of data. It assumes that high-dimensional data can be represented by a linear combination of a few basis vectors (atoms), and the combination coefficients are sparse (that is, most of the coefficients are zero).

[0102] Application in Monte Carlo:

[0103] In scenarios with high-dimensional data, such as uncertainty quantification simulations of high-resolution images (such as medical images and remote sensing images), sparse representation can find a set of dictionaries so that the image data can be represented by a linear combination of a small number of atoms in this set of dictionaries. In Monte Carlo simulations, sampling with coefficients after sparse representation as variables can effectively reduce the representation dimension of the data and reduce the number of variables in Monte Carlo simulations.

[0104] 5. Auto-Encoder Neural Network:

[0105] principle:

[0106] An autoencoder is a neural network architecture consisting of an encoder and a decoder. The encoder maps the input data into a low-dimensional latent space representation, while the decoder reconstructs this low-dimensional representation back to the original data space.

[0107] Application in Monte Carlo:

[0108] In complex industrial process simulations (such as monitoring data from multiple sensors in a chemical process), the input data may contain a large number of sensor readings, which are very high-dimensional. The autoencoder compresses these high-dimensional data into a low-dimensional latent space by learning the intrinsic structure of the data. After training, for new data, the encoder is used to convert it into a low-dimensional representation, which is used as the input variable of the Monte Carlo simulation.

[0109] 6. Random Projection

[0110] principle:

[0111] Random projection is a dimensionality reduction method based on the Johnson-Lindenstrauss Lemma, which states that a set of points in a high-dimensional space can be randomly linearly projected into a low-dimensional space, and the distance relationship between the points can be approximately preserved with a certain probability.

[0112] Application in Monte Carlo:

[0113] In Monte Carlo simulation, for high-dimensional input data, such as in uncertainty simulation of text classification tasks, each document may be represented by a high-dimensional word vector, and random projection can randomly project these high-dimensional word vectors into a low-dimensional space. Then these low-dimensional data are used as input for sampling.

[0114] As an optional implementation, the target control equation is indicated according to a first formula, and the first formula includes:

[0115]

[0116] Among them, A is the system matrix obtained by discretizing the original control equation, B is the load term, and U is the coefficient vector in the reduced basis space. Used to indicate the system function associated with BU;

[0117] Among them, if the system function is a linear function, then , where k is the eigenvalue, and in the neutron transport equation, k is the effective multiplication coefficient and U is the neutron flux;

[0118] The reduced base method specifically includes:

[0119] According to the neutron transport equation, a numerical solution corresponding to typical input parameters is determined to obtain a snapshot matrix;

[0120] Performing intrinsic orthogonal decomposition on the snapshot matrix to obtain a reduced basis space corresponding to the neutron transport equation, and determining a reduced basis matrix according to the reduced basis space;

[0121] Projecting the neutron transport equation to the reduced basis space according to the second formula to obtain a corresponding discrete equation group as the target control equation;

[0122] Wherein, the second formula includes:

[0123]

[0124] in, , is the projection vector of the coefficient vector, and Z is the reduced basis matrix.

[0125] See also Figure 2 , Figure 2 A schematic diagram of an application scenario of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application, Figure 2 Specifically, a schematic diagram of the structure of a 3D benchmark nuclear reactor of the International Atomic Energy Agency (IAEA) is shown. The following are the structures and annotations in the figure:

[0126] Regional structure:

[0127] Region 1 (dark blue stripes): These stripes may represent control rod channels, which regulate the rate of nuclear reactions, or coolant channels, which carry away the heat generated by the reactor.

[0128] Area 2 (blue area): This is the main part of the reactor core and may contain nuclear fuel assemblies. As can be seen from the figure, this part occupies the main volume of the core.

[0129] Area 3 (red area): part of the reflector. The reflector is used to reflect neutrons leaking from the core back to the core, improving neutron utilization and thus improving reactor efficiency.

[0130] Area 4 (Green Blocks): These green blocks are located at the top of the reactor and are part of the control rod drive mechanism or other top structure.

[0131] Area 5 (yellow top): This is the top structure of the reactor, which may contain cooling systems, control equipment, etc.

[0132] Annotation:

[0133] The function of the reflector is to reduce neutron leakage and allow more neutrons to participate in the nuclear fission reaction, thereby improving the efficiency of the reactor.

[0134] This indicates that the reactor model may have some symmetry in its design, which helps to simplify reactor physics calculations and analysis.

[0135] This model is a three-dimensional model proposed by the International Atomic Energy Agency for benchmark testing of nuclear reactor physics calculations. Through this benchmark model, researchers can compare the accuracy and reliability of different calculation methods and software in nuclear reactor physics analysis. This figure mainly shows a three-dimensional benchmark model used for nuclear reactor physics research and calculation, which includes important structures such as the core, control rod channel, and reflector layer, and emphasizes the symmetry of the model and the role of the reflector layer.

[0136] Specifically, as an optional implementation, the reduced basis method provided in the present application is used to process the neutron transport SP3 equation, and the neutron transport SP3 equation is indicated according to a first formula, and the first formula includes:

[0137]

[0138] Where A is the system matrix obtained by discretizing the original control equation, B is the load term, U is the coefficient vector (neutron flux) in the reduced basis space, and k eff is the effective proliferation coefficient;

[0139] The reduced base method specifically includes:

[0140] According to the neutron transport SP3 equation, a numerical solution corresponding to typical input parameters is determined to obtain a snapshot matrix;

[0141] Performing intrinsic orthogonal decomposition on the snapshot matrix to obtain a reduced basis space corresponding to the neutron transport equation, and determining a reduced basis matrix according to the reduced basis space;

[0142] Projecting the neutron transport SP3 equation to the reduced basis space according to the second formula to obtain a corresponding discrete equation group as the target control equation;

[0143] Wherein, the second formula includes:

[0144]

[0145] in, , is the projection vector of the coefficient vector, and Z is the reduced basis matrix.

[0146] The core idea of ​​the reduced basis method is to obtain the snapshot matrix by solving the numerical solution of the control equation under typical input parameters. ,in In the input parameter set The solution of the governing equations under . Perform proper orthogonal decomposition (POD) to obtain a set of orthogonal reduced bases , where the dimension N of the reduced basis space is much smaller than the original degrees of freedom. Then, the input parameters generated by the full Monte Carlo method are The corresponding governing equations are projected onto the reduced basis space. For example, for the neutron transport SP3 equation, ,in is the system matrix obtained by discretizing the control equations, is the load term, is the coefficient vector (neutron flux) in the reduced basis space. In the reduced basis space, the above equation is projected as: .in, , Z is the reduced basis matrix, and the column vector is the orthogonal basis The degree of freedom of this set of equations is greatly reduced, which can significantly improve the solution efficiency.

[0147] In this embodiment, a nuclear physics application scenario applicable to the reduced basis method is provided, and the relevant steps of the reduced basis method can be performed on the parameters in the neutron transport SP3 equation to achieve data dimensionality reduction in the nuclear physics scenario and improve the practicality of data processing. The sampled data of the Monte Carlo method can be processed through the target control equation after dimensionality reduction, which can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0148] Based on the above application scenarios, Figure 3 and Figure 4 A schematic diagram of the effect of an uncertainty transfer method based on data dimensionality reduction and Monte Carlo sampling provided in one embodiment of the present application, wherein Figure 3 A histogram based on Latin hypercube sampling provided by an embodiment of the present invention, Figure 4The distribution diagram of the reactor effective proliferation coefficient results provided by the embodiment of the present invention. As an example, in this application, a large number of input parameters are firstly generated by sampling the parameters according to the distribution information of the input parameters and the covariance matrix through the complete Monte Carlo method, such as the neutron absorption cross section in the above example with a mean of 0.085 cm -1 , and a normal distribution with an uncertainty of 1.2%. Several cross-sectional data are generated through Latin hypercube sampling as input for subsequent calculation of the effective proliferation coefficient. Then, the response function is calculated in turn according to these parameters, and the final calculation results are statistically analyzed (the mean, variance, etc. are obtained by fitting the probability density function) to quantify the distribution and uncertainty of the response function. Figure 3 500 neutron absorption cross section samples were obtained. Figure 4 Calculation results of the neutron effective multiplication factor are shown.

[0149] For the aforementioned statistical analysis process, as an optional implementation, the statistical analysis of the target output parameter to obtain the uncertainty characteristics corresponding to the target system includes:

[0150] Determine the sensitivity coefficient and covariance matrix corresponding to each variable in the target system;

[0151] Determining the uncertainty of the target system according to a third formula;

[0152] Wherein, the third formula includes:

[0153]

[0154] Among them, S is the sensitivity coefficient vector or sensitivity coefficient matrix corresponding to the sensitivity coefficient, M is the covariance matrix, and Δ is the uncertainty.

[0155] In this application, the deterministic method obtains the sensitivity coefficient of the response function with respect to the input model parameters through the perturbation theory, and then calculates the uncertainty of the response function according to the covariance matrix of the parameters through the first-order Taylor expansion, the so-called "sandwich formula". The methods of sensitivity analysis mainly include direct numerical perturbation method, generalized perturbation theory and traditional perturbation theory. Among them, the direct numerical perturbation method is the most commonly used. This method calculates the sensitivity coefficient of the input parameter to the response parameter based on the idea of ​​replacing the differential with the differential.

[0156] Optionally, for a response function f indicated by the control equation, the sensitivity coefficient is calculated as:

[0157]

[0158] in, For the In this scenario, the example given in this application only includes one parameter, the neutron absorption cross section, so i=1.

[0159] Alternatively, the direct perturbation method, that is, by using central differences instead of differentials, is calculated as:

[0160]

[0161] in, and Respectively represent the values ​​of the independent variable after the introduction of positive and negative disturbances, and Respectively and The corresponding response function value. For example, in a practical application scenario, and Take the neutron absorption cross section as 0.085 cm -1 The disturbance values ​​are 0.085009 cm -1 and 0.084997 cm -1 , and is the corresponding neutron effective multiplication factor (k eff ) calculated values, taking the 3D seed diffusion benchmark of the International Atomic Energy Agency (IAEA) as an example, are 1.03305 and 1.03316 respectively, and the calculated sensitivity coefficient is S=-9.16667.

[0162] Optionally, as described in the third formula, the calculation formula for uncertainty is:

[0163]

[0164] in, is the covariance matrix of the kernel data, and S is the sensitivity vector or matrix. There is only one parameter, the neutron absorption cross section, so The variance of the neutron absorption cross section is 1.0404×10 -6 cm -2 , substituting the sensitivity coefficient S = -9.16667 into =0.0094.

[0165] In this implementation, the sensitivity coefficient of each variable based on the control equation response function and the covariance matrix of each variable itself are first determined, and then the uncertainty is quantitatively calculated through the sandwich formula, which improves the physical interpretability and effectiveness of uncertainty data processing and reduces the limitations of a single method.

[0166] As an optional implementation, the method further includes:

[0167] According to the original control equation, data processing is performed on the target input parameters to obtain control output parameters corresponding to each of the target input parameters;

[0168] A first time duration for obtaining the target output parameter and a second time duration for obtaining the control output parameter are determined, and a time acceleration ratio parameter is determined according to the first time duration and the second time duration.

[0169] In this application, the samples obtained by sampling based on the Monte Carlo method can be solved and calculated one by one, and the time required for solving by the full-order method and the reduced basis method can be recorded respectively;

[0170] The full-order method uses a high-precision code to solve the neutron transport equation and calculate the neutron flux distribution and effective multiplication coefficient under different parameter combinations. The calculation time is 80141.28 seconds.

[0171] The solution of the reduced basis method is based on the low-dimensional basis function set constructed in the offline phase, and the effective proliferation coefficient is calculated. This phase only takes 3.028 seconds to complete the calculation.

[0172] Comparing the calculation results of the full-order method and the reduced-base method, it is found that the effective multiplication coefficients obtained by the two methods are exactly the same. This shows that the calculation results of the reduced-base method are highly accurate and have small errors. The time speedup ratio of the reduced-base method is about 26,000.

[0173] This embodiment provides a method for determining the effect of data dimensionality reduction, in which data processing is performed on the original control equation and the control equation after dimensionality reduction respectively, and the time consumption of executing the same data processing process before and after dimensionality reduction is calculated to determine the time acceleration ratio parameter. In addition, the effect of data dimensionality reduction can be determined based on the saving of data volume or the saving of system computing resources. In this way, the effect of the corresponding method of this application in the actual application scenario can be quantified, thereby improving the practicality and effectiveness of the corresponding scheme of this application.

[0174] also, Figure 4 A more accurate data fitting method is also provided. In step S103, according to the specific application scenario provided in this application, the target output parameter is statistically analyzed to obtain the uncertainty characteristics corresponding to the target system, which specifically includes:

[0175] The direct perturbation method of the deterministic method in uncertainty analysis is used to calculate the sensitivity coefficient of the input parameter, namely the neutron absorption cross section. Combined with the mean and variance of the input parameter, the uncertainty of the effective multiplication coefficient is calculated using the "sandwich formula". The final calculated uncertainty standard deviation of the effective multiplication coefficient is 0.0094.

[0176] Gaussian fitting was performed on the uncertainty of the effective multiplication coefficient results, and the mean of the effective multiplication coefficient was 1.0336 and the standard deviation was 0.0089. However, statistical analysis showed that the output response data had significant non-normal distribution characteristics, which were right-skewed and had heavy tails. The normal distribution assumption may lead to deviations in the uncertainty transfer analysis results. 1.0336 is also consistent with the average cross-section of 0.085 cm -1 The calculated value of 1.0331 is inconsistent. Therefore, the traditional deterministic method cannot accurately present the uncertainty of this response function.

[0177] In order to more accurately characterize the output response distribution characteristics, the GCAS model (an extended Gaussian distribution model) was used for fitting, which effectively captured the asymmetry and tail characteristics of the response variable. Finally, the mean of the effective proliferation coefficient was 1.0330 and the standard deviation was 0.0088.

[0178] The embodiment of the present application further provides an uncertainty transfer device based on data dimension reduction and Monte Carlo sampling, the device comprising:

[0179] A determination module, used for determining target input parameters based on a Monte Carlo method;

[0180] A processing module, used for performing data processing on the target input parameters according to the target control equation to obtain target output parameters corresponding to each of the target input parameters;

[0181] Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation;

[0182] The processing module is further used to perform statistical analysis on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

[0183] In the data processing process of uncertainty analysis, this embodiment combines the advantages of Monte Carlo sampling and data dimension reduction methods, and improves the computational efficiency and reduces the cost of data processing and data demand while ensuring that the distribution information of various system parameters and the complex nonlinear response of the system can be effectively captured. Specifically, this method first determines the target input parameters by Monte Carlo sampling, and then performs data processing on the sampled target input parameters through the target control equation after dimensionality reduction processing to obtain the corresponding target output parameters, thereby performing statistical analysis based on the target output parameters to determine the uncertainty of the target system. Obviously, obtaining the original target input parameters through the Monte Carlo method can improve the universality of the application scenario, and can be used for systems with nonlinear characteristics or complex parameter distribution. Processing the sampled data of the Monte Carlo method through the target control equation after dimensionality reduction can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0184] As an optional implementation, the processing module is used to perform a data dimension reduction process on the original control equation to obtain the target control equation, the data dimension reduction process includes a reduced basis method, and the specific manner in which the processing module executes the reduced basis method includes:

[0185] determining a snapshot matrix corresponding to the original governing equations;

[0186] According to the snapshot matrix, a reduced basis space corresponding to the target physical field is obtained;

[0187] The target input parameters are projected onto the reduced basis space to obtain a corresponding discrete equation set as the target control equation.

[0188] The method provided in this embodiment can perform the corresponding data dimension reduction process through the reduced basis method, determine the typical numerical solution of the target input parameters according to the original control equation to form a snapshot matrix, and further obtain the reduced basis space corresponding to the physical field indicated by the control equation according to the snapshot matrix. The vectors in the reduced basis space are mutually orthogonal, and the degree of freedom is significantly reduced. Finally, the target input parameters can be projected to the reduced basis space after the degree of freedom is reduced, and the corresponding discrete equation group is obtained as the target control equation to achieve data dimension reduction. In this way, the sampled data of the Monte Carlo method can be processed through the target control equation after dimension reduction, which can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0189] As an optional implementation, the reduced basis method is used to process the neutron transport SP3 equation, and the neutron transport SP3 equation is indicated according to a first formula, and the first formula includes:

[0190]

[0191] Where A is the system matrix obtained by discretizing the original control equation, B is the load term, U is the coefficient vector (neutron flux) in the reduced basis space, and k eff is the effective proliferation coefficient;

[0192] The specific manner in which the processing module performs the reduced base method includes:

[0193] According to the neutron transport SP3 equation, a numerical solution corresponding to typical input parameters is determined to obtain a snapshot matrix;

[0194] Performing intrinsic orthogonal decomposition on the snapshot matrix to obtain a reduced basis space corresponding to the neutron transport equation, and determining a reduced basis matrix according to the reduced basis space;

[0195] Projecting the neutron transport SP3 equation to the reduced basis space according to the second formula to obtain a corresponding discrete equation group as the target control equation;

[0196] Wherein, the second formula includes:

[0197]

[0198] in, , is the projection vector of the coefficient vector, and Z is the reduced basis matrix.

[0199] In this embodiment, a nuclear physics application scenario applicable to the reduced basis method is provided, and the relevant steps of the reduced basis method can be performed on the parameters in the neutron transport SP3 equation to achieve data dimensionality reduction in the nuclear physics scenario and improve the practicality of data processing. The sampled data of the Monte Carlo method can be processed through the target control equation after dimensionality reduction, which can reduce the complexity of the data processing system and the amount of data calculation, reduce the dimension of the processed data, and improve the data processing efficiency of uncertainty transmission.

[0200] As an optional implementation manner, the determination module determines the specific manner of the target input parameter based on the Monte Carlo method, including:

[0201] Determine the parameter distribution and covariance matrix of the initial variables corresponding to the target input parameters;

[0202] According to the parameter distribution and the covariance matrix, sampling the target input parameter based on the Monte Carlo method to obtain the target input parameter;

[0203] In this embodiment, the parameter distribution and covariance matrix corresponding to the initial variables are first determined based on previous experimental data or the distribution estimated according to physical principles. Then, the determined parameter distribution and covariance matrix can provide a data basis for Monte Carlo sampling, and further provide a data basis for the optimization of the Monte Carlo sampling process, further improving the uniformity and rationality of the data distribution in the sampling process, so as to improve the effectiveness of uncertainty data processing.

[0204] As an optional implementation, the specific process of the determination module performing sampling includes Latin hypercube sampling.

[0205] This implementation method improves the uniformity and rationality of data distribution during the sampling process through Latin hypercube sampling, thereby improving the effectiveness of the original target input parameters, thereby improving the effectiveness of the final uncertainty data processing.

[0206] As an optional implementation manner, the processing module performs statistical analysis on the target output parameter to obtain a specific manner of uncertainty characteristics corresponding to the target system, including:

[0207] Determine the sensitivity coefficient and covariance matrix corresponding to each variable in the target system;

[0208] Determining the uncertainty of the target system according to a third formula;

[0209] Wherein, the third formula includes:

[0210]

[0211] Among them, S is the sensitivity coefficient vector or sensitivity coefficient matrix corresponding to the sensitivity coefficient, M is the covariance matrix, and Δ is the uncertainty.

[0212] In this implementation, the sensitivity coefficient of each variable based on the control equation response function and the covariance matrix of each variable itself are first determined, and then the uncertainty is quantitatively calculated through the sandwich formula, which improves the physical interpretability and effectiveness of uncertainty data processing and reduces the limitations of a single method.

[0213] As an optional implementation manner, the processing module is further used for:

[0214] According to the original control equation, data processing is performed on the target input parameters to obtain control output parameters corresponding to each of the target input parameters;

[0215] A first time duration for obtaining the target output parameter and a second time duration for obtaining the control output parameter are determined, and a time acceleration ratio parameter is determined according to the first time duration and the second time duration.

[0216] This embodiment provides a method for determining the effect of data dimensionality reduction, in which data processing is performed on the original control equation and the control equation after dimensionality reduction respectively, and the time consumption of executing the same data processing process before and after dimensionality reduction is calculated to determine the time acceleration ratio parameter. In addition, the effect of data dimensionality reduction can be determined based on the saving of data volume or the saving of system computing resources. In this way, the effect of the corresponding method of this application in the actual application scenario can be quantified, thereby improving the practicality and effectiveness of the corresponding scheme of this application.

[0217] It should be noted that it should be understood that the division of the various modules of the above device is only a division of logical functions. In actual implementation, they can be fully or partially integrated into one physical entity, or they can be physically separated. And these modules can all be implemented in the form of software called by processing elements; they can also be all implemented in the form of hardware; some modules can also be implemented in the form of software called by processing elements, and some modules can be implemented in the form of hardware. For example, the processing module can be a separately established processing element, or it can be integrated in a chip of the above device. In addition, it can also be stored in the memory of the above device in the form of program code, and called and executed by a processing element of the above device. The function of the above-determined module. The implementation of other modules is similar. In addition, these modules can be fully or partially integrated together, or they can be implemented independently. The processing element here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each module above can be completed by an integrated logic circuit of hardware in the processor element or instructions in the form of software.

[0218] Indicatively, if Figure 5 As shown, Figure 5 This is a schematic diagram of the internal structure of a computer device provided in an embodiment of the present application. The computer device 300 may be provided as a server. Figure 5 , the computer device 300 includes a processing component 302, which further includes one or more processors, and a memory resource represented by a memory 301, for storing instructions that can be executed by the processing component 302, such as an application. The application stored in the memory 301 may include one or more modules, each corresponding to a set of instructions. In addition, the processing component 302 is configured to execute instructions to perform the method of any of the above embodiments.

[0219] The computer device 300 may further include a power supply component 303 configured to perform power management of the computer device 300, a wired or wireless network interface 304 configured to connect the computer device 300 to a network, and an input / output (I / O) interface 305. The computer device 300 may operate based on an operating system stored in the memory 301, such as Windows Server TM, Mac OS X TM, Unix TM, Linux TM, Free BSD TM, or the like.

[0220] Those skilled in the art will understand that Figure 5 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0221] An embodiment of the present application provides a storage medium, in which computer-readable instructions are stored. When the computer-readable instructions are executed by one or more processors, the one or more processors execute a method provided in any embodiment.

[0222] Finally, it should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the presence of other identical elements in the process, method, article or device including the elements.

[0223] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The various embodiments can be combined as needed, and the same or similar parts can refer to each other.

[0224] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present application. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An uncertainty transfer method based on data dimension reduction and Monte Carlo sampling, characterized in that: The method comprises: Determine the target input parameters based on the Monte Carlo method; According to the target control equation, data processing is performed on the target input parameters to obtain target output parameters corresponding to each of the target input parameters; Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation; Statistical analysis is performed on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

2. The method according to claim 1, characterized in that The data dimension reduction process includes a reduced basis method, and the reduced basis method includes: determining a snapshot matrix corresponding to the original governing equations; According to the snapshot matrix, a reduced basis space corresponding to the target physical field is obtained; The target input parameters are projected onto the reduced basis space to obtain a corresponding discrete equation set as the target control equation.

3. The method according to claim 2, characterized in that The target control equation is indicated according to a first formula, which includes: Among them, A is the system matrix obtained by discretizing the original control equation, B is the load term, and U is the coefficient vector in the reduced basis space. Used to indicate the system function associated with BU; Among them, if the system function is a linear function, then , where k is the eigenvalue, and in the neutron transport equation, k is the effective multiplication coefficient and U is the neutron flux; The reduced base method specifically includes: According to the neutron transport equation, a numerical solution corresponding to typical input parameters is determined to obtain a snapshot matrix; Performing intrinsic orthogonal decomposition on the snapshot matrix to obtain a reduced basis space corresponding to the neutron transport equation, and determining a reduced basis matrix according to the reduced basis space; Projecting the neutron transport equation to the reduced basis space according to the second formula to obtain a corresponding discrete equation group as the target control equation; Wherein, the second formula includes: in, , is the projection vector of the coefficient vector, and Z is the reduced basis matrix.

4. The method according to claim 1, characterized in that: The method of determining the target input parameters based on the Monte Carlo method includes: Determine the parameter distribution and covariance matrix of the initial variables corresponding to the target input parameters; According to the parameter distribution and the covariance matrix, the target input parameter is sampled based on the Monte Carlo method to obtain the target input parameter.

5. The method according to claim 4, characterized in that The specific process of the sampling includes Latin hypercube sampling.

6. The method according to claim 1, characterized in that The performing statistical analysis on the target output parameter to obtain the uncertainty characteristics corresponding to the target system includes: Determine the sensitivity coefficient and covariance matrix corresponding to each variable in the target system; Determining the uncertainty of the target system according to a third formula; Wherein, the third formula includes: Among them, S is the sensitivity coefficient vector or sensitivity coefficient matrix corresponding to the sensitivity coefficient, M is the covariance matrix, and Δ is the uncertainty.

7. The method according to any one of claims 1 to 6, characterized in that: The method further comprises: According to the original control equation, data processing is performed on the target input parameters to obtain control output parameters corresponding to each of the target input parameters; A first time duration for obtaining the target output parameter and a second time duration for obtaining the control output parameter are determined, and a time acceleration ratio parameter is determined according to the first time duration and the second time duration.

8. An uncertainty transfer device based on data dimension reduction and Monte Carlo sampling, characterized in that: The device comprises: A determination module, used for determining target input parameters based on a Monte Carlo method; A processing module, used for performing data processing on the target input parameters according to the target control equation to obtain target output parameters corresponding to each of the target input parameters; Wherein, the target control equation is used to indicate the response of the target system based on the input parameters, and the target control equation is obtained by performing a data dimension reduction process on the original control equation; The processing module is further used to perform statistical analysis on the target output parameters to obtain uncertainty characteristics corresponding to the target system.

9. A computer device, characterized in that: The method comprises one or more processors and a memory, wherein the memory stores computer-readable instructions, and when the computer-readable instructions are executed by the one or more processors, the steps of the method according to any one of claims 1 to 7 are performed.

10. A storage medium, characterized in that: The storage medium stores computer-readable instructions, and when the computer-readable instructions are executed by one or more processors, the one or more processors execute the steps of the method according to any one of claims 1 to 7.

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