Method, system and electronic device for calibrating input parameters of a nuclear engineer software model

Abstract

The application discloses a method, system and electronic equipment for calibrating input parameters of a nuclear engineering software model, and the method comprises the following steps: generating a training data set and a verification data set according to an experimental data set related to a model to be calibrated; constructing a substitute large model corresponding to the model to be calibrated; training the substitute large model through the training data set to obtain a trained substitute large model; determining a target posterior probability distribution of input parameters of the trained substitute large model according to a prediction value set of the trained substitute large model and the verification data set; and replacing a preset prior probability distribution of the model to be calibrated through the target posterior probability distribution, wherein the preset prior probability distribution is a probability distribution corresponding to the input parameters of the model to be calibrated and set in advance. The application can improve the accuracy of the input parameters of the software model and statistically quantify the uncertainty.

Description

Technical Field

[0001] This application relates to the field of computer technology, and in particular to a calibration method, system, and electronic device for input parameters of a nuclear engineering software model. Background Technology

[0002] With the advancement of computing technology, computer numerical simulation has been widely applied in industrial practice. Large-scale industrial software with complex mathematical and physical models has been successfully applied to design and evaluation work in various scientific research and industrial fields.

[0003] For nuclear engineering design and safety analysis software, especially optimal estimation software, safety review agencies in various countries have raised the need for uncertainty quantification and sensitivity analysis when such software is applied to optimal estimation evaluation models or combined evaluation models, as an important part of software verification and validation.

[0004] In related technologies, to obtain uncertainty quantification results, software is typically used for positive uncertainty quantification analysis. However, positive uncertainty quantification requires sufficient understanding of the input uncertainty. In practical applications, the determination of many input parameters and their uncertainties often relies on expert judgment or user experience, lacking a sound physical or mathematical foundation. Furthermore, differences in expert and user understanding can lead to significant discrepancies in calculation results; in other words, positive uncertainty quantification can result in inaccurate input parameters for the software model. Summary of the Invention

[0005] This application aims to propose a calibration method, system, and electronic device for input parameters of nuclear engineering software models, which can improve the accuracy of input parameters of software models.

[0006] In a first aspect, embodiments of this application provide a method for calibrating input parameters of a nuclear engineering software model, the method comprising:

[0007] Based on the experimental dataset associated with the model to be calibrated, generate training datasets and validation datasets;

[0008] Construct a replacement large model corresponding to the model to be calibrated;

[0009] By training a replacement large model using a training dataset, a well-trained replacement large model can be obtained.

[0010] Based on the predicted value set and validation dataset of the trained alternative large model, determine the target posterior probability distribution of the input parameters of the trained alternative large model.

[0011] The preset prior probability distribution of the model to be calibrated is replaced by the target posterior probability distribution, where the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

[0012] In some implementations, an alternative large model corresponding to the model to be calibrated is constructed, including:

[0013] Obtain the number of data points N in the experimental dataset, where N is a positive integer;

[0014] If N is less than the preset value, a linear deep Gaussian process structure is selected to replace the large model.

[0015] In some implementations, after obtaining the number N of experimental data, the method further includes:

[0016] When N is greater than or equal to a preset value, the relationship between the input and output parameters of the model to be calibrated is analyzed to obtain linear analysis results, where the linear analysis results are either linear or nonlinear correlations.

[0017] If the linear analysis results show a nonlinear correlation, then a nonlinear deep Gaussian process structure is chosen to replace the large model.

[0018] If the linear analysis results show a linear correlation, then a linear deep Gaussian process structure is chosen to replace the large model.

[0019] In some implementations, after training the surrogate model using a training dataset and obtaining the trained surrogate model, before determining the target posterior probability distribution of the input parameters of the trained surrogate model based on the predicted value set and the validation dataset, the method further includes:

[0020] Calculate the mean squared error of the trained surrogate model;

[0021] Based on the predicted value set and validation dataset of the trained surrogate model, determine the target posterior probability distribution of the input parameters of the trained surrogate model, including:

[0022] If the mean squared error value meets the preset threshold range, the input data in the verification dataset will be input into the trained alternative large model to obtain the predicted value set of the trained alternative large model.

[0023] The target posterior probability distribution of the input parameters of the trained alternative large model is determined based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset that correspond to the input data.

[0024] In some implementations, the target posterior probability distribution of the input parameters of the trained surrogate model is determined based on the predicted values ​​in the predicted value set of the trained surrogate model and the true output values ​​corresponding to the input data in the validation dataset, including:

[0025] Obtain the prior probability distribution of the model to be calibrated;

[0026] The predicted values ​​in the training set of the alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison results.

[0027] Based on the comparison results and prior probability distribution, the posterior probability distribution of the input parameters of the trained alternative large model is calculated using the maximum likelihood estimation method.

[0028] If the maximum likelihood estimation method meets the preset acceptance criteria, then the posterior probability distribution will be determined as the target posterior probability distribution.

[0029] If the maximum likelihood estimation method fails to meet the preset acceptance criteria, the posterior probability distribution is used to replace the prior probability distribution, and the process returns to calculate the posterior probability distribution of the input parameters of the trained replacement large model using the maximum likelihood estimation method based on the comparison results and the prior probability distribution, until the maximum likelihood estimation method meets the preset acceptance criteria. The posterior probability distribution calculated after the maximum likelihood estimation method meets the preset acceptance criteria is then determined as the target posterior probability distribution.

[0030] In some implementations, training datasets and validation datasets are generated based on experimental datasets associated with the model to be calibrated, including:

[0031] Obtain the number of experimental data M used for training the model to be calibrated, where M is a positive integer;

[0032] Select M data points from the experimental dataset;

[0033] Generate a training dataset containing M data points.

[0034] In some implementations, training datasets and validation datasets are generated based on experimental datasets associated with the model to be calibrated, including:

[0035] Remove the training dataset from the experimental dataset to obtain the remaining experimental dataset;

[0036] Using at least a portion of the remaining experimental dataset, generate multiple subsets;

[0037] Select a preset number of first data from each subset;

[0038] The first data selected from each subset is combined to form the validation dataset.

[0039] In some implementations, multiple subsets are generated using at least a portion of the remaining experimental dataset, including:

[0040] Determine the input variables of the model to be calibrated;

[0041] Obtain the target range, which includes at least one of the ranges of input variables and the ranges of input parameters;

[0042] If the target range is within the range corresponding to the remaining experimental dataset, multiple subsets are generated using the data in the remaining experimental dataset that are within the target range;

[0043] If the target range is larger than the range corresponding to the remaining experimental dataset, then all data in the remaining experimental dataset will be used to generate multiple subsets.

[0044] Secondly, embodiments of this application also provide a calibration system for input parameters of a nuclear engineering software model, the system comprising:

[0045] The dataset generation module is used to generate training and validation datasets based on the experimental datasets associated with the model to be calibrated.

[0046] The large model building module is used to build a replacement large model corresponding to the model to be calibrated.

[0047] The large model training module is used to train a replacement large model using a training dataset to obtain a trained replacement large model.

[0048] The probability distribution determination module is used to determine the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted value set of the trained alternative large model and the validation dataset.

[0049] The input parameter calibration module is used to replace the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution. The preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

[0050] Thirdly, embodiments of this application also provide an electronic device, including at least one control processor and a memory for communicatively connecting to the at least one control processor; the memory stores instructions executable by the at least one control processor, which, when executed by the at least one control processor, enable the at least one control processor to perform a calibration method for nuclear engineering software model input parameters as described in the first aspect.

[0051] Fourthly, embodiments of this application also provide a computer-readable storage medium storing computer-executable instructions for causing a computer to perform a calibration method for input parameters of a nuclear engineering software model as described in the first aspect.

[0052] In this embodiment, a training dataset and a validation dataset are generated based on experimental datasets related to the model to be calibrated; a replacement large model corresponding to the model to be calibrated is constructed; the replacement large model is trained using the training dataset to obtain a trained replacement large model; the target posterior probability distribution of the input parameters of the trained replacement large model is determined based on the predicted value set of the trained replacement large model and the validation dataset; the preset prior probability distribution of the model to be calibrated is replaced by the target posterior probability distribution, where the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated. Thus, by training the replacement large model using existing experimental data and then replacing the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution of the input parameters of the trained replacement large model, uncertainty can be statistically quantified. This solves the problem of discrepancies in positive uncertainty quantification results caused by human bias in input uncertainty, thereby improving the accuracy of the input parameters of the software model. Attached Figure Description

[0053] The above and / or additional aspects and advantages of this application will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0054] Figure 1 This is a flowchart illustrating an embodiment of the calibration method for input parameters of nuclear engineering software models provided in this application;

[0055] Figure 2 This is a flowchart illustrating the preferred embodiment of the calibration method for input parameters of nuclear engineering software models provided in this application;

[0056] Figure 3 This is a schematic diagram of the structure of an embodiment of the calibration system for input parameters of nuclear engineering software models provided in this application;

[0057] Figure 4 This is a schematic diagram of the structure of an embodiment of the electronic device provided in this application. Detailed Implementation

[0058] The embodiments of this application are described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain this application, and should not be construed as limiting this application.

[0059] In the description of this application, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or the order of the technical features indicated.

[0060] In the description of this application, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application.

[0061] In the description of this application, it should be noted that, unless otherwise explicitly defined, terms such as "setup," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this application in conjunction with the specific content of the technical solution.

[0062] With the advancement of computing technology, computer numerical simulation has been widely applied in industrial practice. Large-scale industrial software with complex mathematical and physical models has been successfully applied to design and evaluation work in various scientific research and industrial fields.

[0063] In the nuclear industry, software simulation is widely used in design and safety analysis. For nuclear design and safety analysis software, especially optimal estimation software, safety review agencies in various countries have proposed the requirement for positive uncertainty quantification and sensitivity analysis when such software is applied to optimal estimation evaluation models or combined evaluation models, as an important component of software verification and validation. In related technologies, to obtain uncertainty quantification results, it is usually necessary to use software for positive uncertainty quantification analysis. However, positive uncertainty quantification requires sufficient understanding of input uncertainties. In practical applications, the determination of many input parameters and their uncertainties comes from expert judgment or user experience, lacking reasonable physical or mathematical support. Furthermore, due to differences in expert and user understanding, the calculation results may vary significantly, meaning that positive uncertainty quantification can lead to inaccurate input parameters in the software model.

[0064] To address the issue of potentially significant discrepancies in calculation results due to differing expert and user perceptions, this application proposes a calibration method, system, and electronic device for input parameters of nuclear engineering software models.

[0065] Reference Figure 1 This application provides a schematic flowchart of a calibration method for input parameters of a nuclear engineering software model. This calibration method for input parameters of a nuclear engineering software model is applied to an electronic device, which may be a server or a mobile terminal, etc. Figure 1 As shown, the calibration method for the input parameters of this nuclear engineering software model may include the following steps:

[0066] Step 110: Generate a training dataset and a validation dataset based on the experimental dataset related to the model to be calibrated;

[0067] Step 120: Construct a replacement large model corresponding to the model to be calibrated;

[0068] Step 130: Train the replacement large model using the training dataset to obtain the trained replacement large model;

[0069] Step 140: Based on the predicted value set and validation dataset of the trained alternative large model, determine the target posterior probability distribution of the input parameters of the trained alternative large model.

[0070] Step 150: Replace the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution, wherein the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

[0071] In this embodiment, a training dataset and a validation dataset are generated based on the experimental dataset related to the model to be calibrated; a replacement large model corresponding to the model to be calibrated is constructed; the replacement large model is trained using the training dataset to obtain a trained replacement large model; the target posterior probability distribution of the input parameters of the trained replacement large model is determined based on the predicted value set of the trained replacement large model and the validation dataset; the preset prior probability distribution of the model to be calibrated is replaced by the target posterior probability distribution, where the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated. Thus, by training the replacement large model using existing experimental data and then replacing the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution of the input parameters of the trained replacement large model, uncertainty can be statistically quantified. This addresses the problem of discrepancies in positive uncertainty quantification results caused by human bias in input uncertainty, thereby improving the accuracy of the software model's input parameters.

[0072] In step 110 above, the electronic device generates a training dataset and a validation dataset based on the experimental dataset associated with the model to be calibrated.

[0073] The aforementioned model to be calibrated can be a nuclear software model to be calibrated in nuclear design and safety analysis software.

[0074] The aforementioned model to be calibrated can be determined by the user based on the Phenomenon Identification and Ranking Table (PIRT table). By analyzing different accident conditions in the PIRT table, the key phenomena related to the accident conditions are identified, and then expert judgment is made to determine the model to be calibrated related to the key phenomena.

[0075] The experimental datasets related to the model to be calibrated may include multiple experimental data generated from separation effect experiments and overall effect experiments related to the model to be calibrated.

[0076] The aforementioned separation effect experiment can be a separation effect test (SET) rig that needs to be established based on the similarity ratio law during the safety assessment of nuclear reactors and nuclear power plants, providing data support for safety performance verification and assessment.

[0077] The aforementioned overall effect experiment can be an overall effect test (IET) rig established based on the similarity ratio law during the safety assessment of nuclear reactors and nuclear power plants, providing data support for safety performance verification and evaluation. An overall effect experiment refers to a full-system simulation experiment of a thermal process involving multiple effects, used to observe the interactions and feedback relationships between various effects, and to verify, improve, and refine the computer program describing the process.

[0078] An example of a global effect experiment: natural circulation experiment of reactor primary loop, small and large breach accident experiment of reactor coolant system, global effect experiment of droplet entrainment and deentrainment process during core reflooding.

[0079] The above-mentioned generation of training and validation datasets based on the experimental datasets related to the model to be calibrated can be achieved by selecting a certain amount of data from the experimental datasets related to the model to be calibrated as the data in the training and validation datasets. The amount of data in the training and validation datasets can be unequal.

[0080] Before generating the training and validation datasets, we first need to check whether the separation effect experiments and overall effect experiments corresponding to the experimental datasets cover the key phenomena related to the model to be calibrated. If they cover the key phenomena, the experimental datasets are usable; if they do not, the experimental datasets are not usable. If the experimental datasets are not usable, we need to select new experimental datasets.

[0081] In step 120 above, an alternative large model corresponding to the model to be calibrated is constructed.

[0082] This application does not limit the type or structure of the alternative large model. In some embodiments, the alternative large model corresponding to the model to be calibrated described above may be an alternative large model constructed using a deep Gaussian process structure. In other embodiments, alternative large models constructed using existing deep machine learning algorithms, such as deep neural network structures, may also be used.

[0083] In step 130 above, the alternative large model is trained by training the training dataset to obtain the trained alternative large model.

[0084] This application does not limit the training method of the alternative large model; any method that can be used to train the alternative large model falls within the protection scope of this application. In some embodiments, the above-mentioned method of training the alternative large model using a training dataset to obtain a trained alternative large model can be achieved by using the maximum likelihood estimation method to train the alternative large model using a training dataset to obtain a trained alternative large model.

[0085] The maximum likelihood estimation method described above is an important and general approach for finding estimators. It explicitly uses a probabilistic model, aiming to find a phylogenetic tree that generates the observed data with a high probability.

[0086] In step 140 above, the target posterior probability distribution of the input parameters of the trained alternative large model is determined based on the predicted value set of the trained alternative large model and the validation dataset.

[0087] The set of predictions from the trained alternative large model includes at least one prediction, each of which is obtained by feeding one of the input data from the validation dataset into the trained alternative large model for prediction.

[0088] The target posterior probability distribution of the input parameters of the trained alternative large model can be determined by using the maximum likelihood estimation method based on the predicted value set and the validation dataset of the trained alternative large model.

[0089] The target posterior probability distribution of the input parameters of the trained alternative large model can also be determined by using the maximum a posteriori estimation method based on the predicted value set and the validation dataset of the trained alternative large model.

[0090] In step 150 above, the preset prior probability distribution of the model to be calibrated is replaced by the target posterior probability distribution, wherein the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

[0091] The input parameters of the above-mentioned model to be calibrated can be determined by the user based on the PIRT table, analyzing different accident conditions, identifying key phenomena related to the accident conditions, and then conducting expert judgment to determine the input parameters of the model to be calibrated related to the key phenomena.

[0092] The above method of replacing the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution can achieve the calibration of the input parameters of the model to be calibrated.

[0093] Since the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated, while the target posterior probability distribution is a determined, trained target posterior probability distribution that replaces the preset prior probability distribution, the input parameters of the model to be calibrated can be calibrated by replacing the preset prior probability distribution with the target posterior probability distribution.

[0094] In some implementations, constructing an alternative large model corresponding to the model to be calibrated may include:

[0095] Obtain the number of data points N in the experimental dataset, where N is a positive integer;

[0096] If N is less than the preset value, a linear deep Gaussian process structure is selected to replace the large model.

[0097] In this embodiment, when the number of data points N in the experimental dataset is less than a preset value, a linear deep Gaussian process structure is selected to construct an alternative large model. This effectively reduces the requirements for training data, allowing training with limited data to form an effective alternative large model. Furthermore, the target posterior probability distribution of the input parameters of the trained alternative large model is used to replace the preset prior probability distribution of the model to be calibrated for input parameter calibration, resulting in greater accuracy in the later stages.

[0098] The experimental dataset mentioned above can be an integration of multiple experimental datasets related to the model to be calibrated.

[0099] The above-mentioned choice of using a linear deep Gaussian process structure to replace the large model when N is less than the preset value can be used when the overall data volume in the experimental dataset is relatively small.

[0100] The above-mentioned linear deep Gaussian process structure can be a deep Gaussian process with a single hidden layer or multiple hidden layers using linear activation functions.

[0101] In some implementations, after acquiring the number N of experimental data, the method may further include:

[0102] When N is greater than or equal to a preset value, the relationship between the input and output parameters of the model to be calibrated is analyzed to obtain linear analysis results, where the linear analysis results are either linear or nonlinear correlations.

[0103] If the linear analysis results show a nonlinear correlation, then a nonlinear deep Gaussian process structure is chosen to replace the large model.

[0104] If the linear analysis results show a linear correlation, then a linear deep Gaussian process structure is chosen to replace the large model.

[0105] In this embodiment, when N is greater than or equal to a preset value, the relationship between the input and output parameters of the model to be calibrated is analyzed to obtain linear analysis results. If the linear analysis results show a nonlinear correlation, a nonlinear deep Gaussian process structure is selected to replace the large model; if the linear analysis results show a linear correlation, a linear deep Gaussian process structure is selected to replace the large model. Thus, when dealing with large datasets, analyzing the relationship between input and output parameters to select a suitable deep Gaussian process structure to replace the large model, and subsequently using the target posterior probability distribution of the input parameters of the trained replacement large model to replace the preset prior probability distribution of the model to be calibrated for input parameter calibration, the results are more accurate.

[0106] The output parameters mentioned above can correspond to the input parameters of the model to be calibrated; that is, the input parameters of the model to be calibrated will correspond to the output parameters.

[0107] The above analysis of the relationship between the input and output parameters of the model to be calibrated when N is greater than or equal to the preset value can be performed when the overall data volume of the experimental dataset is relatively large.

[0108] The relationship between the input and output parameters of the model to be calibrated can be determined by expert judgment, or by calculating the linear correlation coefficient between the input and output parameters of the model through sensitivity analysis, such as using Pearson correlation coefficient, Kendall correlation coefficient, and Spearman correlation coefficient to determine linearity.

[0109] The aforementioned input and output parameters can be derived from multiple key phenomena, and one key phenomenon can correspond to multiple input and output parameters.

[0110] The aforementioned deep Gaussian process can be viewed as a multilayer perceptron (MLP) with a single hidden layer and an infinite number of hidden layer nodes. The deep Gaussian process (DGP) is a Gaussian process obtained by extending the MLP from a single hidden layer to multiple hidden layers, that is, an MLP with multiple hidden layers and an infinite width.

[0111] The above-mentioned linear deep Gaussian process structure can be a deep Gaussian process with a single hidden layer or multiple hidden layers using linear activation functions.

[0112] The aforementioned nonlinear deep Gaussian process structure can be a deep Gaussian process with a single or multiple hidden layers using a nonlinear activation function.

[0113] In some implementations, after training the surrogate model using a training dataset to obtain the trained surrogate model, and before determining the target posterior probability distribution of the input parameters of the trained surrogate model based on the predicted value set and the validation dataset, the method may further include:

[0114] Calculate the mean squared error of the trained surrogate model;

[0115] Based on the predicted value set and validation dataset of the trained surrogate model, determine the target posterior probability distribution of the input parameters of the trained surrogate model, including:

[0116] If the mean squared error value meets the preset threshold range, the input data in the verification dataset will be input into the trained alternative large model to obtain the predicted value set of the trained alternative large model.

[0117] The target posterior probability distribution of the input parameters of the trained alternative large model is determined based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset that correspond to the input data.

[0118] In this embodiment, by comparing the mean squared error of the trained surrogate model with a preset threshold range, a set of predicted values ​​for the trained surrogate model that meets the preset threshold range is obtained. Then, based on the predicted values ​​in the set of predicted values ​​of the trained surrogate model and the true output values ​​in the validation dataset corresponding to the input data, the target posterior probability distribution of the input parameters of the trained surrogate model is determined. This improves the accuracy of the calculation, thereby improving the accuracy of the input parameters of the model to be calibrated later. Furthermore, the surrogate model is constructed using a deep Gaussian process structure. After the model is built and tested, the waste of computational resources caused by repeatedly running computational software can be reduced, thus improving computational efficiency.

[0119] The mean square error mentioned above can be a measure of the degree of difference between the estimator and the estimated quantity.

[0120] The aforementioned preset threshold range can be set according to the user's actual needs and can be changed according to the actual situation. This embodiment does not impose specific restrictions.

[0121] If the mean squared error value does not meet the preset threshold range, the replacement large model will be retrained until the mean squared error value of the trained replacement large model meets the preset threshold range.

[0122] The above method of determining the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset corresponding to the input data can be achieved by using the maximum likelihood estimation method to determine the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset corresponding to the input data.

[0123] In some implementations, determining the target posterior probability distribution of the input parameters of the trained surrogate model based on the predicted values ​​in the predicted value set of the trained surrogate model and the true output values ​​corresponding to the input data in the validation dataset may include:

[0124] Obtain the prior probability distribution of the model to be calibrated;

[0125] The predicted values ​​in the training set of the alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison results.

[0126] Based on the comparison results and prior probability distribution, the posterior probability distribution of the input parameters of the trained alternative large model is calculated using the maximum likelihood estimation method.

[0127] If the maximum likelihood estimation method meets the preset acceptance criteria, then the posterior probability distribution will be determined as the target posterior probability distribution.

[0128] If the maximum likelihood estimation method fails to meet the preset acceptance criteria, the posterior probability distribution is used to replace the prior probability distribution, and the process returns to calculate the posterior probability distribution of the input parameters of the trained replacement large model using the maximum likelihood estimation method based on the comparison results and the prior probability distribution, until the maximum likelihood estimation method meets the preset acceptance criteria. The posterior probability distribution calculated after the maximum likelihood estimation method meets the preset acceptance criteria is then determined as the target posterior probability distribution.

[0129] In this embodiment, the predicted values ​​in the prediction set of the trained alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison result. Then, based on the comparison result and the prior probability distribution, the maximum likelihood estimation method is used to calculate the posterior probability distribution of the input parameters of the trained alternative large model. This process continues until the maximum likelihood estimation method reaches the preset acceptance criteria to obtain the target posterior probability distribution. This results in a relatively accurate posterior probability distribution, laying the foundation for improving the accuracy of the input parameters of the model to be calibrated in the later stages.

[0130] The aforementioned preset acceptance criteria can be user-defined acceptance criteria.

[0131] The above-mentioned acquisition of the prior probability distribution of the model to be calibrated can be to obtain an initial prior probability distribution, which is a pre-set probability distribution. However, the prior probability distribution will be updated as the maximum likelihood estimation method iterates.

[0132] The above-mentioned method of calculating the posterior probability distribution of the input parameters of the trained alternative large model using the maximum likelihood estimation method based on the comparison results and prior probability distribution can be achieved by inputting the comparison results and prior probability distribution into the maximum likelihood estimation method to calculate the posterior probability distribution of the input parameters of the trained alternative large model.

[0133] In some implementations, generating training and validation datasets based on experimental datasets associated with the model to be calibrated may include:

[0134] Obtain the number of experimental data M used for training the model to be calibrated, where M is a positive integer;

[0135] Select M data points from the experimental dataset;

[0136] Generate a training dataset containing M data points.

[0137] In this embodiment, the training dataset is selected first, which ensures the independence of large model training and provides higher reliability.

[0138] The number of experimental data M used for training the model to be calibrated can be determined according to the user's specific needs. The number of experimental data M can be changed according to the actual situation, and this embodiment does not impose specific restrictions.

[0139] Before selecting M data points from the experimental dataset, it is necessary to check whether the separation effect experiment and the overall effect experiment corresponding to the experimental dataset cover the key phenomena related to the model to be calibrated. If they cover the key phenomena, the experimental dataset is usable; otherwise, it is not usable. If the experimental dataset is unusable, it is necessary to select a new experimental dataset.

[0140] In some implementations, generating training and validation datasets based on experimental datasets associated with the model to be calibrated may include:

[0141] Remove the training dataset from the experimental dataset to obtain the remaining experimental dataset;

[0142] Using at least a portion of the remaining experimental dataset, generate multiple subsets;

[0143] Select a preset number of first data from each subset;

[0144] The first data selected from each subset is combined to form the validation dataset.

[0145] In this embodiment, since the validation dataset is selected from the remaining experimental dataset, which is the dataset after removing the training dataset from the experimental dataset, the validation dataset is selected by using cross-validation, which ensures the independence of the large model availability evaluation and provides higher reliability.

[0146] The above method of generating multiple subsets using at least a portion of the data in the remaining experimental dataset can be based on either a portion of the data in the remaining experimental dataset or all the data in the remaining experimental dataset.

[0147] The above-mentioned preset quantity can be set according to user needs and can be changed according to actual conditions. This embodiment does not impose specific limitations.

[0148] The above-mentioned combination of the first data selected from each subset into a verification dataset can be achieved by combining a preset number of the first data selected from each subset to obtain the verification dataset.

[0149] For example, N_val experimental data points (i.e., a preset number of first data points) are randomly selected from each subset, and then the N_val experimental data points selected from each subset are combined into a validation dataset A_val.

[0150] In some implementations, generating multiple subsets using at least a portion of the remaining experimental dataset may include:

[0151] Determine the input variables of the model to be calibrated;

[0152] Obtain the target range, which includes at least one of the ranges of input variables and the ranges of input parameters;

[0153] If the target range is within the range corresponding to the remaining experimental dataset, multiple subsets are generated using the data in the remaining experimental dataset that are within the target range;

[0154] If the target range is larger than the range corresponding to the remaining experimental dataset, then all data in the remaining experimental dataset will be used to generate multiple subsets.

[0155] In this embodiment, by generating multiple suitable subsets based on the range of input variables and the range of input parameters, a good data foundation is laid for selecting a more suitable validation dataset in the later stage.

[0156] The input variables for determining the model to be calibrated can be determined by the user based on the PIRT table. For different accident conditions being analyzed, the key phenomena related to the accident conditions are identified, and then expert judgment is made to determine the input variables of the model to be calibrated related to the key phenomena.

[0157] The input variables mentioned above can be boundary conditions or initial conditions.

[0158] The range of the above-mentioned input variables and input parameters can be determined by the range of operating condition parameters related to the key phenomena to be analyzed.

[0159] The range of operating parameters related to the key phenomena mentioned above can be obtained from the analysis range of the PIRT table.

[0160] The above operating parameters may be input parameters or input variables.

[0161] If the target range is within the range corresponding to the remaining experimental dataset, multiple subsets can be generated using the data in the remaining experimental dataset that are within the target range. This can be achieved when the range of the operating parameters related to the key phenomenon in the remaining experimental dataset can cover the range of the input variables and the range of the input parameters. At least one of the ranges of the input variables and the ranges of the input parameters can be divided into a preset number of groups to obtain the range of each group. Then, experimental data corresponding to the range of each group can be selected from the remaining experimental dataset to obtain multiple subsets. The number of data in each subset is the same, and the number of subsets is equal to the preset number of groups.

[0162] For example, if an input variable has a range of [0, N), and needs to be divided into n subsets, then the grouping range of each subset is [0, N / n), [N / n, 2N / n), ..., [(n-1)N / n, N). Then, based on the grouping range of each subset, experimental data can be selected from the remaining experimental dataset to obtain the experimental data contained in each subset.

[0163] The above-mentioned preset number of groups can be grouped according to the user's actual needs and can be changed according to the actual situation. This embodiment does not impose specific restrictions.

[0164] If the target range is larger than the range corresponding to the remaining experimental dataset, then all the data in the remaining experimental dataset is used to generate multiple subsets. For example, when the range of the operating parameters related to the key phenomenon corresponding to the remaining experimental dataset cannot cover the range of the input variables and the range of the input parameters, the range corresponding to the remaining experimental dataset is divided into a preset number of groups to obtain the range of each group. Then, experimental data corresponding to the range of each group are selected from the remaining experimental dataset to obtain multiple subsets. The number of data in each subset is the same, and the number of multiple subsets is equal to the preset number of groups.

[0165] The target range mentioned above includes at least one of the range of input variables and the range of input parameters, or the target range may include the range of input variables and the range of input parameters.

[0166] When the target range includes both the range of input variables and the range of input parameters, if one range is within the range corresponding to the remaining experimental dataset and the other range is greater than the range corresponding to the remaining experimental dataset, then the range within the range corresponding to the remaining experimental dataset will be divided into a preset number of groups on an average basis.

[0167] It should be noted that the various implementation methods provided in the embodiments of this application can be implemented independently or in combination without conflict with each other. The specific implementation method can be determined according to actual needs, and the embodiments of this application do not limit it.

[0168] To facilitate understanding by those skilled in the art, a set of preferred embodiments is provided below:

[0169] This embodiment will establish an alternative large model using deep learning algorithms to calibrate the input parameters of the software model and quantify inverse uncertainty, thereby replacing methods for determining input uncertainty that may cause human bias, such as expert judgment and user experience. (Refer to...) Figure 2 The specific process is as follows:

[0170] Step (1) Determine the computational model of the software to be analyzed. The computational model of the software to be analyzed is nuclear engineering design and safety analysis software, which contains multiple models, such as models for calculating heat transfer and models for calculating flow. The model to be calibrated is one of the models in the computational model of the software to be analyzed. Determine the input variables and input model parameters (i.e., input parameters) related to the model to be calibrated.

[0171] Step (2) Linear analysis: Perform a preliminary analysis of the linear relationship between the output parameters of the model to be calibrated and the input model parameters to determine whether a linear assumption can be made for the model to be calibrated.

[0172] Linearity analysis can be determined by expert judgment or by calculating linear correlation coefficients through sensitivity analysis, such as Pearson, Kendall, and Spearman coefficients, to determine linearity and establish linear hypotheses.

[0173] Step (3) Select the training dataset and the validation dataset. Select the appropriate training and validation datasets for the problem requiring quantification. Ensure the training dataset is sufficient and the validation dataset covers the validation scope. Coverage refers to the degree to which the separation effect experiments and overall effect experiments in the dataset cover all key phenomena. The experimental data should cover all key phenomena and have redundancy. This determines whether the training and validation datasets are usable or not. The specific implementation steps are as follows:

[0174] 1) Collect experimental data A from separation effect experiments and overall effect experiments related to the model to be calibrated, determine the number of usable experimental data N, and number the experimental data;

[0175] 2) Select the initial training dataset: Determine the number of experimental data N_test to be used for training based on the user's specific needs, and randomly select N_test of the collected experimental data A as the training dataset A_test.

[0176] 3) Select the validation dataset: In the (A-A_test) dataset (i.e. the remaining experimental dataset), the (A-A_test) dataset is grouped into n subsets according to the range of the input variables and the range of the input model parameters. Then, N_val experimental data are randomly selected from each subset. Finally, the experimental data in each subset are combined to form the validation experimental dataset A_val.

[0177] Step (4) Constructing an alternative large model: Deep learning training is implemented using a Deep Gaussian Process (DGP). This method can effectively reduce the requirements for training data. For the common problem of insufficient relevant experimental data in the nuclear industry, training can be performed using limited data to form an effective alternative large model. The alternative large model is constructed based on the characteristics of the software model to be analyzed and the amount of experimental dataset, specifically as follows:

[0178] 1) The relationship between the output parameters and input parameters of the computational model of the software to be analyzed is nonlinear: Select a nonlinear DGP structure. The hidden layers in the DGP structure use nonlinear activation functions with single or multiple hidden layers to fit the nonlinear relationship existing in the nuclear engineering software.

[0179] 2) If the relationship between the output parameters and input parameters of the computational model of the software to be analyzed is linear or the number of experimental datasets is small: Select a linear DGP structure. The hidden layers in the DGP structure use linear activation functions of single or multiple hidden layers to fit the linear relationship existing in the nuclear engineering software.

[0180] Step (5) Training the alternative large model: Based on the training experimental dataset, the constructed alternative large model is trained using the maximum likelihood estimation method.

[0181] Step (6) Evaluate model usability: Calculate the mean squared error (MSE) value of the trained alternative large model to determine whether the DGP performance meets the requirements. By setting an acceptance threshold (i.e., a preset threshold range), when the MSE value meets the acceptance threshold, it can be determined that the DGP performance meets the requirements; when the MSE value does not meet the acceptance threshold, the alternative large model can be retrained.

[0182] Step (7) Model calibration or inverse uncertainty quantification: Use the established DGP to replace the original software to calculate the predicted output value of the model.

[0183] Specifically, the validation experimental dataset includes input data (i.e., experimental conditions) and the corresponding true output values ​​(i.e., known experimental results). The input data in the validation experimental dataset is input into the alternative large model selected in step (6) for prediction to obtain a set of predicted values ​​(i.e., since the validation experimental dataset includes multiple input data, each input data will have a corresponding predicted value). The predicted values ​​in the set of predicted values ​​are compared with the true output values ​​in the validation experimental dataset to obtain a comparison result. Finally, based on the comparison result and the prior probability distribution (the prior probability distribution when the maximum likelihood estimation method is first calculated is the initial prior probability distribution preset by the user), the maximum likelihood estimation method is used to estimate the posterior probability distribution of the input parameters of the alternative large model. The posterior probability distribution obtained after the maximum likelihood estimation method reaches the preset acceptance standard replaces the initial prior probability distribution (i.e., the preset prior probability distribution), which can realize the calibration of the input parameters of the model to be calibrated.

[0184] In this embodiment, the input parameters of the nuclear engineering software model are calibrated based on existing experimental data, and the uncertainty is statistically quantified. The overall process can minimize human bias caused by the introduction of expert judgment or user effect, and can solve the problem of differences in positive uncertainty quantification results caused by human bias due to input uncertainty.

[0185] A large-scale alternative model is constructed using deep machine learning algorithms. After its establishment and testing, this alternative model replaces the original computational model of the software to be analyzed, rather than replacing the model to be calibrated. This is because some models are not within the scope of calibration, and running the entire computational model of the software to be analyzed would increase the computational load. Therefore, using the large-scale alternative model to replace the original computational model of the software to be analyzed can both reduce the waste of computational resources caused by repeatedly running the computational software and improve computational efficiency, while also calibrating the parameters of the model to be calibrated. The deep Gaussian process method effectively reduces the requirements for training data. For the problem of a lack of relevant experimental data commonly found in the nuclear industry, limited data can be utilized to form an effective alternative model. Cross-validation is used to separately select experimental datasets for training and validation, ensuring the independence of the construction, training, and usability evaluation of the large-scale alternative model, and providing higher reliability.

[0186] Reference Figure 3 This is a schematic diagram of the structure of a calibration system for input parameters of a nuclear engineering software model provided in an embodiment of this application. The system may include:

[0187] The dataset generation module 310 is used to generate training datasets and validation datasets based on the experimental datasets related to the model to be calibrated.

[0188] Large model building module 320 is used to build a replacement large model corresponding to the model to be calibrated;

[0189] The large model training module 330 is used to train a replacement large model using a training dataset to obtain a trained replacement large model.

[0190] The probability distribution determination module 340 is used to determine the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted value set of the trained alternative large model and the validation dataset.

[0191] The input parameter calibration module 350 is used to replace the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution, wherein the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

[0192] In some implementations, the large model building module 320 can be specifically used for:

[0193] The number of experimental data points N is obtained, where N is a positive integer;

[0194] If N is less than the preset value, a linear deep Gaussian process structure is selected to replace the large model.

[0195] In some implementations, the large model building module 320 can be specifically used for:

[0196] When N is greater than or equal to a preset value, the relationship between the input and output parameters of the model to be calibrated is analyzed to obtain linear analysis results, where the linear analysis results are either linear or nonlinear correlations.

[0197] If the linear analysis results show a nonlinear correlation, then a nonlinear deep Gaussian process structure is chosen to replace the large model.

[0198] If the linear analysis results show a linear correlation, then a linear deep Gaussian process structure is chosen to replace the large model.

[0199] In some implementations, the probability distribution determination module 340 can be specifically used for:

[0200] Calculate the mean squared error of the trained surrogate model;

[0201] Based on the predicted value set and validation dataset of the trained surrogate model, determine the target posterior probability distribution of the input parameters of the trained surrogate model, including:

[0202] If the mean squared error value meets the preset threshold range, the input data in the verification dataset will be input into the trained alternative large model to obtain the predicted value set of the trained alternative large model.

[0203] The target posterior probability distribution of the input parameters of the trained alternative large model is determined based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset that correspond to the input data.

[0204] In some implementations, the probability distribution determination module 340 can be specifically used for:

[0205] Obtain the prior probability distribution of the model to be calibrated;

[0206] The predicted values ​​in the training set of the alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison results.

[0207] Based on the comparison results and prior probability distribution, the posterior probability distribution of the input parameters of the trained alternative large model is calculated using the maximum likelihood estimation method.

[0208] If the maximum likelihood estimation method meets the preset acceptance criteria, then the posterior probability distribution will be determined as the target posterior probability distribution.

[0209] If the maximum likelihood estimation method fails to meet the preset acceptance criteria, the posterior probability distribution is used to replace the preset prior probability distribution. Then, the process returns to calculate the posterior probability distribution of the input parameters of the trained replacement large model using the maximum likelihood estimation method based on the comparison results and the prior probability distribution, until the maximum likelihood estimation method meets the preset acceptance criteria. The posterior probability distribution calculated after the maximum likelihood estimation method meets the preset acceptance criteria is then determined as the target posterior probability distribution.

[0210] In some implementations, the dataset generation module 310 may be specifically used for:

[0211] Obtain the amount of experimental data M used for training the model to be calibrated;

[0212] Select M data points from the experimental dataset;

[0213] Generate a training dataset containing M data points.

[0214] In some implementations, the dataset generation module 310 may be specifically used for:

[0215] Determine the input variables of the model to be calibrated;

[0216] Remove the training dataset from the experimental dataset to obtain the remaining experimental dataset;

[0217] Using at least a portion of the remaining experimental dataset, generate multiple subsets;

[0218] Select a predetermined number of first datasets from each subset;

[0219] The first dataset selected from each subset is combined to form the validation dataset.

[0220] In some implementations, the dataset generation module 310 may be specifically used for:

[0221] Obtain the target range, which includes at least one of the ranges of input variables and the ranges of input parameters;

[0222] If the target range is within the range corresponding to the remaining experimental dataset, multiple subsets are generated using the data in the remaining experimental dataset that are within the target range;

[0223] If the target range is larger than the range corresponding to the remaining experimental dataset, then all data in the remaining experimental dataset will be used to generate multiple subsets.

[0224] It should be noted that since the calibration device for the input parameters of a nuclear engineering software model in this embodiment is based on the same inventive concept as the calibration method for the input parameters of a nuclear engineering software model described above, the corresponding content in the method embodiment is also applicable to this system embodiment, and will not be described in detail here.

[0225] Reference Figure 4 This application also provides an electronic device, which may include:

[0226] At least one memory;

[0227] At least one processor;

[0228] At least one program;

[0229] The program is stored in memory, and the processor executes at least one program to implement the calibration method for the input parameters of the nuclear software model described above in this disclosure.

[0230] This electronic device can be any smart terminal, including mobile phones, tablets, personal digital assistants (PDAs), and in-vehicle computers.

[0231] The electronic devices according to embodiments of this application will now be described in detail.

[0232] The processor 410 can be implemented using a general-purpose central processing unit (CPU), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this disclosure.

[0233] The memory 420 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 420 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 420 and is called by the processor 410 to execute the calibration method for the input parameters of the nuclear engineering software model in the embodiments of this disclosure.

[0234] Input / output interface 430 is used to realize information input and output;

[0235] The communication interface 440 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, network cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0236] Bus 450 transmits information between various components of the device (e.g., processor 410, memory 420, input / output interface 430, and communication interface 440);

[0237] The processor 410, memory 420, input / output interface 430 and communication interface 440 are connected to each other within the device via bus 450.

[0238] This disclosure also provides a storage medium, which is a computer-readable storage medium storing computer-executable instructions for causing a computer to execute the calibration method for the input parameters of the nuclear engineering software model described above.

[0239] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0240] The embodiments described in this disclosure are for the purpose of more clearly illustrating the technical solutions of this disclosure and do not constitute a limitation on the technical solutions provided by this disclosure. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by this disclosure are also applicable to similar technical problems.

[0241] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this disclosure, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0242] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0243] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0244] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0245] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0246] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0247] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0248] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0249] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause an electronic device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks. The embodiments of this application have been described in detail above with reference to the accompanying drawings, but this application is not limited to the above embodiments. Various changes can be made within the scope of knowledge possessed by those skilled in the art without departing from the spirit of this application.

Claims

1. A method for calibrating input parameters of a nuclear engineering software model, characterized in that, The method includes: Based on the experimental dataset associated with the model to be calibrated, generate training datasets and validation datasets; Constructing an alternative large model corresponding to the model to be calibrated includes: Obtain the number N of data in the experimental dataset, where N is a positive integer; If N is less than a preset value, a linear deep Gaussian process structure is selected to replace the large model; When N is greater than or equal to the preset value, the relationship between the input parameters and output parameters of the model to be calibrated is analyzed to obtain linear analysis results, wherein the linear analysis results are linear correlation or nonlinear correlation; If the linear analysis results are nonlinearly correlated, then a nonlinear deep Gaussian process structure is selected to replace the large model; If the linear analysis results show a linear correlation, then a linear deep Gaussian process structure is selected to replace the large model. The alternative large model is trained using the training dataset to obtain a trained alternative large model. Based on the predicted value set of the trained alternative large model and the validation dataset, determine the target posterior probability distribution of the input parameters of the trained alternative large model, including: Obtain the prior probability distribution of the model to be calibrated; The predicted values ​​in the training set of the alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison results. Based on the comparison results and the prior probability distribution, the posterior probability distribution of the input parameters of the trained alternative large model is calculated using the maximum likelihood estimation method. If the maximum likelihood estimation method meets the preset acceptance criteria, then the posterior probability distribution is determined as the target posterior probability distribution. If the maximum likelihood estimation method fails to meet the preset acceptance criteria, the posterior probability distribution is used to replace the prior probability distribution, and the process of calculating the posterior probability distribution of the input parameters of the trained alternative large model using the maximum likelihood estimation method based on the comparison results and the prior probability distribution is returned, until the maximum likelihood estimation method meets the preset acceptance criteria, and the posterior probability distribution calculated after the maximum likelihood estimation method meets the preset acceptance criteria is determined as the target posterior probability distribution. The preset prior probability distribution of the model to be calibrated is replaced by the target posterior probability distribution, wherein the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

2. The calibration method for input parameters of nuclear engineering software models according to claim 1, characterized in that, After training the alternative large model using the training dataset to obtain the trained alternative large model, and before determining the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted value set of the trained alternative large model and the validation dataset, the method further includes: Calculate the mean squared error of the trained alternative large model; The step of determining the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted value set of the trained alternative large model and the validation dataset includes: If the mean square error value meets the preset threshold range, then the input data in the verification dataset is input into the trained alternative large model to obtain the predicted value set of the trained alternative large model; The target posterior probability distribution of the input parameters of the trained alternative large model is determined based on the predicted values ​​in the predicted value set of the trained alternative large model and the true output values ​​in the validation dataset corresponding to the input data.

3. The calibration method for input parameters of nuclear engineering software models according to claim 1, characterized in that, The step of generating training and validation datasets based on experimental datasets related to the model to be calibrated includes: Obtain the number M of experimental data used for training the model to be calibrated, where M is a positive integer; Select M data points from the experimental dataset; Generate a training dataset that includes the M data points.

4. The calibration method for input parameters of nuclear engineering software models according to claim 1, characterized in that, The step of generating training and validation datasets based on experimental datasets related to the model to be calibrated includes: Remove the training dataset from the experimental dataset to obtain the remaining experimental dataset; Using at least a portion of the data from the remaining experimental dataset, generate multiple subsets; Select a preset number of first data from each subset; The first data selected from each subset are combined to form a validation dataset.

5. The calibration method for input parameters of nuclear engineering software models according to claim 4, characterized in that, The process of generating multiple subsets using at least a portion of the remaining experimental dataset includes: Determine the input variables of the model to be calibrated; Obtain a target range, wherein the target range includes at least one of the ranges of the input variables and the ranges of the input parameters; If the target range is within the range corresponding to the remaining experimental dataset, multiple subsets are generated using the data in the remaining experimental dataset that are within the target range; If the target range is larger than the range corresponding to the remaining experimental dataset, then multiple subsets are generated using all the data in the remaining experimental dataset.

6. A calibration system for input parameters of a nuclear engineering software model, characterized in that, The system includes: The dataset generation module is used to generate training and validation datasets based on the experimental datasets associated with the model to be calibrated. The large model construction module is used to construct an alternative large model corresponding to the model to be calibrated, including: Obtain the number N of data in the experimental dataset, where N is a positive integer; If N is less than a preset value, a linear deep Gaussian process structure is selected to replace the large model; When N is greater than or equal to the preset value, the relationship between the input parameters and output parameters of the model to be calibrated is analyzed to obtain linear analysis results, wherein the linear analysis results are linear correlation or nonlinear correlation; If the linear analysis results are nonlinearly correlated, then a nonlinear deep Gaussian process structure is selected to replace the large model; If the linear analysis results show a linear correlation, then a linear deep Gaussian process structure is selected to replace the large model. The large model training module is used to train the alternative large model using the training dataset to obtain the trained alternative large model. The probability distribution determination module is used to determine the target posterior probability distribution of the input parameters of the trained alternative large model based on the predicted value set of the trained alternative large model and the validation dataset, including: Obtain the prior probability distribution of the model to be calibrated; The predicted values ​​in the training set of the alternative large model are compared with the true output values ​​in the validation dataset to obtain the comparison results. Based on the comparison results and the prior probability distribution, the posterior probability distribution of the input parameters of the trained alternative large model is calculated using the maximum likelihood estimation method. If the maximum likelihood estimation method meets the preset acceptance criteria, then the posterior probability distribution is determined as the target posterior probability distribution. If the maximum likelihood estimation method fails to meet the preset acceptance criteria, the posterior probability distribution is used to replace the prior probability distribution, and the process of calculating the posterior probability distribution of the input parameters of the trained alternative large model using the maximum likelihood estimation method based on the comparison results and the prior probability distribution is returned, until the maximum likelihood estimation method meets the preset acceptance criteria, and the posterior probability distribution calculated after the maximum likelihood estimation method meets the preset acceptance criteria is determined as the target posterior probability distribution. The input parameter calibration module is used to replace the preset prior probability distribution of the model to be calibrated with the target posterior probability distribution, wherein the preset prior probability distribution is a pre-set probability distribution corresponding to the input parameters of the model to be calibrated.

7. An electronic device, characterized in that, It includes at least one control processor and a memory for communicatively connecting to the at least one control processor; The memory stores instructions that can be executed by at least one control processor to enable the at least one control processor to perform the calibration method for the input parameters of the nuclear software model as claimed in any one of claims 1 to 5.

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