Engineering-level model integration simulation method based on Kriging proxy model

Abstract

The invention relates to an engineering-level model integration simulation method based on a Kriging agent model, and the method comprises the following steps: S1, carrying out the design of key investigation parameters of a model according to the simulation demands of a system; s2, acquiring historical data of the engineering-level model, and generating a training sample data set; s3, preprocessing the data of the training sample set; s4, constructing an agent model of the engineering-level simulation model by adopting a Kriging agent model method; s5, performing model test verification on the proxy model; s6, carrying out confidence evaluation on the agent model; s7, establishing a model management module of the agent model; and S8, integrating and deploying the proxy model in a simulation system environment. By constructing the agent model and realizing integration, the system simulation efficiency and the test optimization efficiency can be improved to the greatest extent on the premise of keeping the model precision, the efficient application of the engineering-level simulation model in the system simulation system is realized, and the performance and the efficiency of the whole system are greatly improved.

Description

Technical Field

[0001] The present invention relates to the technical field of simulation and modeling, and in particular to an engineering-level model integration simulation method based on a Kriging proxy model. Background Art

[0002] Currently, engineering-level simulation models are widely used in design and analysis fields in various professional fields as a tool to accurately describe system performance and behavior. With the development of modeling and simulation technology, it is proposed to connect engineering-level models to system-level simulation in the process of system simulation system development and research, and to carry out mixed simulation of multi-level simulation models at the mission level, combat level, and engineering level. However, there are many problems in the process of connecting existing engineering-level simulation models to the system simulation environment for simulation and operation.

[0003] First, the amount of calculation required for engineering-level models is extremely large, resulting in a long calculation time. In practical applications, especially for some system simulation scenarios with high real-time or super real-time requirements, such as aerospace and weapon systems, the long calculation time makes it impossible for the model to provide effective results in time, which seriously affects the system's response speed and decision-making efficiency.

[0004] Secondly, most engineering-level simulation models are multidisciplinary design models, and their operation is highly dependent on the specific design tools and operating environment of each discipline. They cannot be directly and independently integrated into the system simulation system, and generally adopt the traditional method of interconnecting heterogeneous systems for joint simulation. This method has a huge development workload and is inefficient. Developers need to perform tedious data interaction and interface matching between different systems, which consumes a lot of time and energy. At the same time, due to the involvement of multiple different systems and tools, the consistency and accuracy of the data are difficult to guarantee, and errors and deviations are prone to occur.

[0005] In addition, the existing heterogeneous system interconnection solutions cannot effectively balance the accuracy of the model and the computing efficiency. In order to improve the computing speed, the accuracy of the model needs to be sacrificed, resulting in reduced reliability of the simulation results; while the pursuit of high accuracy will further extend the computing time, which is a dilemma and affects the user experience.

[0006] In summary, the existing engineering-level simulation models have serious deficiencies in terms of computational complexity, integration, and efficiency, and cannot meet the requirements of today's complex system simulation systems for high efficiency, accuracy, and real-time performance. How to improve the integration capability and simulation efficiency of engineering-level simulation models in the system simulation environment while ensuring the accuracy of simulation results and ensuring user experience is an urgent problem to be solved. Summary of the invention

[0007] In order to solve the technical problems existing in the above-mentioned prior art, the purpose of the present invention is to provide an engineering-level model integration simulation method based on a Kriging proxy model, which has the characteristics of high data storage efficiency and fast loading speed.

[0008] To achieve the above-mentioned object of the invention, the present invention provides an engineering-level model integration simulation method based on a Kriging proxy model, characterized in that it comprises the following steps:

[0009] Step S1, designing key parameters of the model according to the system simulation requirements; the key parameters of the model include: design conditions, operating conditions, key parameter combinations, and performance evaluation indicators;

[0010] Step S2: Obtain historical data of the engineering-level model and generate a training sample data set;

[0011] Step S3, preprocessing the data of the training sample set;

[0012] Step S4, constructing a proxy model of the engineering-level simulation model using the Kriging proxy model method;

[0013] Step S5: performing model testing and verification on the proxy model;

[0014] Step S6, performing confidence evaluation on the proxy model;

[0015] Step S7: Establish a model management module for the proxy model to record and manage the version, parameters and training data of the proxy model;

[0016] Step S8: Integrate and deploy the agent model in a simulation system environment.

[0017] According to a technical solution of the present invention, in step S1, it specifically includes:

[0018] Combining the system simulation evaluation and test requirements, by taking the union of the key design parameters and test factors of the engineering-level simulation model, the key design variable parameter set is determined as X = (x 1 ,x 2 ,……,x n ), where x n Represents the key design variable parameter of the nth dimension;

[0019] By decomposing the system simulation evaluation requirements, the performance evaluation index set of the engineering-level simulation model is determined as Y=(y 1 ,y 2 ,……,y t );There is a mapping relationship between the key design variable parameter set and the performance evaluation index set.

[0020] According to a technical solution of the present invention, in the step S2, it specifically includes:

[0021] Step S21, constructing an operating environment covering various working conditions, parameter combinations and operating conditions, performing an initial simulation calculation under the premise of having an operating tool and an operating environment, and obtaining simulation response data of the engineering-level model; the data points input for the initial simulation calculation include data points of common working modes, data points of extreme conditions and data points of rare conditions;

[0022] Step S22: Perform a preliminary check on the simulation response data to form a training sample data set, expressed as (S, Q s ), where S = {s1, s2, ..., s m} represents the data value set of the design variable parameters of each data point of the engineering-level model, s m is the value of the key design variable parameter set X at the mth data point sample; Q s ={q1,q2,……,q m} represents the real simulation response data of the engineering-level model, and the real simulation response data is the response result of the performance evaluation index set Y of the engineering-level simulation model, S and Q s There is a one-to-one mapping relationship between the elements.

[0023] According to a technical solution of the present invention, in step S3, it specifically includes:

[0024] Step S31, data cleaning of the training sample set: using a data screening and verification algorithm based on a statistical analysis method to determine a reasonable range of the response result data, determining the response results of data points that exceed the range as outliers and processing them, so as to remove possible outliers, erroneous data and noise interference;

[0025] Step S32: using a standardization method to standardize the key design variable parameters of the sample points. The value of Convert to a unified interval for description.

[0026] According to a technical solution of the present invention, the normalization method is min-max normalization or z-score normalization.

[0027] According to a technical solution of the present invention, the min-max normalization is expressed as:

[0028]

[0029] In the formula, Normalized values ​​of the i-th dimension design variable parameters of the k-th data point sample, i = 1, 2, ..., n; m = 1, 2, ..., m; It is the minimum value of all data point samples on the i-th dimension design variable parameter; It is the maximum distance between all data point sample values ​​on the k-th dimension design variable parameter.

[0030] According to a technical solution of the present invention, in step S4, it specifically includes:

[0031] Step S41, determining the form of the covariance function according to the distribution characteristics and complexity of the data and the expected accuracy requirements of the model, wherein the form of the covariance function is a Gaussian covariance function or an exponential covariance function;

[0032] Step S42, construct multiple rounds of experiments, and determine the parameters of the covariance function by combining cross-validation means: divide the engineering-level simulation model historical data set into multiple subsets, use one of the subsets as the validation set in turn, and the remaining subsets as the training set, to construct multiple groups of the covariance function parameter combinations {Θ (j)}, where j represents the jth round of experiments; by comparing the performance of the Kriging surrogate model on the validation set under different covariance function parameter combinations, the optimal covariance function parameter combination is found;

[0033] Step S43: construct the proxy model according to the selected covariance function and the optimal covariance function parameter combination, which is expressed as:

[0034]

[0035] in, is the unknown data point s * The predicted response value, μ is the mean, m is the number of training data points, and λ is the k is the weight coefficient, C(s * ,s k ) is the covariance function.

[0036] According to a technical solution of the present invention, in step S5, it specifically includes:

[0037] Step S51: Perform encapsulation interface testing on the proxy model, and strictly check the stability, compatibility, accuracy and timeliness of data transmission of the proxy model interface;

[0038] Step S52: Perform a performance test on the proxy model to evaluate key performance indicators of the proxy model, where the key performance indicators include computing speed, resource consumption, and memory usage.

[0039] According to a technical solution of the present invention, in step S6, it specifically includes:

[0040] Step S61: Evaluate the accuracy of the proxy model: Based on the data points S={s1, s2, ..., s m}, perform simulation calculation in the system simulation environment to obtain the prediction results of the agent model The prediction results of the proxy model The actual simulation response data Q in the training sample data s Compare and evaluate the accuracy and error of the proxy model using mean square error and mean absolute error evaluation indicators; if the accuracy of the proxy model does not meet the requirements, return to step S42, adjust the optimal covariance function parameter combination and rebuild the proxy model;

[0041] Step S62, test the stability of the proxy model: by changing the test order of the data point samples and adding a small amount of noise to the data points, observe whether the prediction result of the proxy model is stable. If the prediction result of the proxy model is unstable, return to step S4 to re-build the proxy model.

[0042] Compared with the prior art, the present invention has the following beneficial effects:

[0043] First, in response to the problem of excessive calculation amount of engineering-level models, the present invention introduces an advanced Kriging proxy model method, which can effectively simplify and optimize the complex calculation process of engineering-level simulation models. By learning and analyzing a large amount of historical simulation data, a proxy model that can respond quickly and predict accurately is established.

[0044] Secondly, in order to solve the problem that the engineering-level simulation model cannot be independently integrated into the system simulation system, the present invention carries out customized development based on the Kriging proxy model. The proxy model is used to accurately simulate the functions and behaviors of the engineering-level model, so that it can be seamlessly integrated into the system simulation system without relying on the operating environment of the original design tool.

[0045] In addition, the improved scheme of the present invention is not just to simply build a proxy model and realize integration, but also to maximize the efficiency of system simulation and test optimization under the premise of maintaining a certain model accuracy. Through sophisticated data analysis and model optimization, the present invention ensures that the proxy model can provide accuracy similar to or even better than the original engineering-level model while reducing the amount of calculation, thereby providing reliable support for system simulation.

[0046] Through the above series of improvements, the present invention realizes the efficient application of engineering-level simulation models in the system simulation system, greatly improving the performance and efficiency of the entire system. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0048] Figure 1 The flowchart of the engineering-level model integration simulation method based on the Kriging proxy model provided in one embodiment of the present invention is schematically shown. DETAILED DESCRIPTION

[0049] The description of the embodiments of this specification should be combined with the corresponding drawings, which should be considered as part of the complete specification. In the drawings, the shape or thickness of the embodiments may be enlarged and indicated for simplification or convenience. Furthermore, the parts of each structure in the drawings will be described separately. It is worth noting that the elements not shown in the drawings or not described in words are in a form known to ordinary technicians in the relevant technical field.

[0050] The description of the embodiments herein and any reference to directions and orientations are only for the convenience of description and are not to be construed as any limitation on the scope of protection of the present invention. The following description of the preferred embodiments may involve combinations of features, which may exist independently or in combination, and the present invention is not particularly limited to the preferred embodiments. The scope of the present invention is defined by the claims.

[0051] like Figure 1 As shown, an engineering-level model integration simulation method based on a Kriging proxy model of the present invention comprises the following steps:

[0052] Step S1: Design key parameters of the model according to the system simulation requirements:

[0053] Design key parameters and indicators of engineering-level simulation models. For the engineering-level model connected to the system simulation system, design the working conditions, operating conditions, key parameter combinations and performance evaluation indicators according to the system simulation requirements. This design process can be combined with system simulation evaluation and test requirements. By taking the union of the key design parameters and test factors of the engineering-level simulation model, the key design variable parameter set X = (x 1 ,x 2 ,……,x n ), where x nRepresents the key design variable parameter of the nth dimension. By decomposing the system simulation evaluation requirements, the performance evaluation index set for the engineering-level model is determined as Y=(y 1 ,y 2 ,……,y t ). There is a mapping relationship between the key design variable parameter set and the performance evaluation index set.

[0054] Step S2: Obtain historical data of the engineering-level model and generate a training sample data set:

[0055] By building an operating environment covering various working conditions, parameter combinations and operating conditions, and with the operating tools and operating environment, initial simulation calculations are performed to obtain the simulation response data of the engineering-level model. These operating inputs and model response data should be comprehensive, complete and diverse, including data points for common working modes as well as extreme and rare situations. A preliminary check is performed on the collected historical simulation data of the engineering-level simulation model to ensure the accuracy and rationality of the data. All data points S = {s1, s2, ..., s m} and simulation response data Q s ={q1,q2,……,q m} constitutes the training sample data set (S,Q s ), the real simulation response data is the performance evaluation index response result.

[0056] Step S3: preprocess the data of the training sample set:

[0057] Preprocessing operations are performed on the collected massive data. This process includes multiple rounds of data cleaning and normalization. Specifically, step S3 includes:

[0058] Step S31, data cleaning process: Use data screening and verification algorithms based on statistical analysis methods to determine the reasonable range of response result data, determine the response results of data points that are out of range as outliers and process them, so as to remove possible outliers, erroneous data and noise interference.

[0059] Step S32, data normalization process: Considering the different properties, expressions and value ranges of the key design variable parameters, standardization methods such as min-max normalization and z-score normalization are used to normalize the design variables of the sample points. The value of Convert to a unified interval for description. The min-max normalization is as follows:

[0060]

[0061] In the formula, Normalized values ​​of the i-th dimension design variable parameters of the k-th data point sample, i = 1, 2, ..., n; k = 1, 2, ..., m; It is the minimum value of all data point samples on the i-th dimension design variable parameter; It is the maximum distance between all data point sample values ​​on the i-th dimension design variable parameter.

[0062] Converting data into a standardized and consistent standard format will help improve the stability and convergence speed of the model, and create convenient conditions for subsequent analysis and processing.

[0063] Step S4: Use Kriging proxy model method to build a proxy model of the engineering-level simulation model

[0064] The Kriging surrogate model method is used to construct a surrogate model of the engineering-level simulation model. The Kriging model is an interpolation model based on spatial correlation. Its interpolation result is defined as the linear weighting of the known sample function response value. Its core principle is to accurately predict the value of unknown points through in-depth analysis and mining of known sample points.

[0065] In the modeling process, the first step is to comprehensively consider the distribution characteristics, complexity and expected accuracy requirements of the data to determine the appropriate Kriging proxy model parameters. The model parameters refer to the covariance function parameters of the random process model part in the Kriging proxy model. The second step is to select the covariance function form of the random process model by comparing the performance of different types of spatial correlation functions on the fitted data. In addition, in the process of constructing parameters, the optimal parameter combination is selected through iterative testing and optimization combined with cross-validation methods.

[0066] Specifically, step S4 includes:

[0067] Step S41, covariance function selection: The core of the Kriging proxy model is the random process covariance function. It describes the spatial correlation between sample points. According to the distribution characteristics and complexity of the data and the expected accuracy requirements of the model, a covariance function form such as a Gaussian covariance function and an exponential covariance function is selected.

[0068] Step S42, iterative optimization of covariance function parameters: construct multiple rounds of experiments, and determine the parameters of the covariance function by combining cross-validation methods. Divide the historical data set of the engineering-level simulation model into multiple subsets, use one of the subsets as the validation set, and the remaining subsets as the training set, and construct multiple groups of the covariance function parameter combinations {Θ (j)}, where j represents the jth round of trials. The covariance function parameter combination Θ is only a related model parameter in a mathematical sense and has no actual physical meaning. By comparing the performance of the Kriging surrogate model on the validation set under different covariance function parameter combinations, the optimal covariance function parameter combination is found.

[0069] Step S43: construct a proxy model based on the selected covariance function and the optimal covariance function parameter combination:

[0070] Based on the selected covariance function and optimized parameters, a Kriging proxy model is constructed. The model is expressed as:

[0071]

[0072] in, is the unknown data point s * The predicted response value, μ is the mean, m is the number of training data points, and λ is the k is the weight coefficient, C(s * ,s k ) is the covariance function.

[0073] By solving the linear equations, the weight coefficient λ can be determined i And mean μ, thus completing the construction of the model.

[0074] Step S5: Perform model testing and verification on the proxy model:

[0075] After constructing the Kriging surrogate model, the model is tested and verified.

[0076] Specifically, step S5 includes:

[0077] Step S51, package model interface test: strictly check the stability, compatibility, accuracy and timeliness of data transmission of the interface;

[0078] Step S52, performance testing: evaluating key performance indicators such as the model's computing speed, resource consumption, and memory usage.

[0079] Step S6: Conduct confidence assessment on the proxy model:

[0080] Through statistical analysis and hypothesis testing methods, the confidence interval and predictive ability of the model are quantitatively evaluated to ensure that the packaged test model strictly complies with the model integration packaging standards and performance requirements.

[0081] Specifically, step S6 includes:

[0082] Step S61: Evaluate the accuracy of the proxy model: Based on the engineering-level simulation model data points S = {s1, s2, ..., sm}, perform simulation calculations in the system simulation environment to obtain the prediction results of the proxy model The prediction results of the surrogate model The actual simulation response data Q of the engineering-level simulation model s Compare and use mean square error and mean absolute error evaluation indicators to evaluate the accuracy and error of the model. If the model accuracy does not meet the requirements, return to the parameter optimization step, adjust the parameters and rebuild the model.

[0083] Step S62, stability test: Perform a stability test on the model by changing the test order of the sample points and adding a small amount of noise to the data points to observe whether the prediction results of the model are stable. If the model is unstable, it is necessary to reselect the design variables and build the model.

[0084] Step S7: Model version management:

[0085] Establish a model management module for the engineering-level simulation model Kriging proxy model to manage and record the model version, parameters, training data, etc. Use the version control system to record the iteration process and change history of the model; store model parameters and training data through a database or data warehouse, and establish a data index and query mechanism to facilitate subsequent tracing, analysis, and reuse. Store model attribute configuration content such as model interface parameters, model operation parameters, model output, and customize visualization methods based on the physical effects of the test model.

[0086] Step S8: Model integration application:

[0087] After completing the Kriging proxy model calculation efficiency, execution degree, and interface test evaluation, the proxy model can be optionally integrated and deployed in the system simulation environment. At the same time, in order to improve the calculation efficiency of the model, a distributed computing method is used to allocate computing tasks based on the selected strategy, build a data parallel processing process, speed up the calculation speed of the model, and meet the strict real-time requirements of the system simulation system. Improve the overall operation efficiency and cost-effectiveness of the system.

[0088] It should be noted that, in this article, the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or terminal 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 terminal device. In the absence of further restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, article or terminal device including the elements.

[0089] Finally, it should be noted that the above is a preferred embodiment of the present invention. It should be pointed out that although the preferred embodiment of the present invention has been described, for those skilled in the art, once the basic creative concept of the present invention is known, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention. Therefore, the attached claims are intended to be interpreted as including the preferred embodiment and all changes and modifications that fall within the scope of the embodiments of the present invention.

Claims

1. An engineering-level model integration simulation method based on Kriging proxy model, characterized in that: The following steps are involved: Step S1: Design key parameters of the model according to system simulation requirements; The key parameters of the model include: working conditions, operating conditions, key parameter combinations, and performance evaluation indicators; Step S2: Obtain historical data of the engineering-level model and generate a training sample data set; Step S3, preprocessing the data of the training sample set; Step S4, constructing a proxy model of the engineering-level simulation model using the Kriging proxy model method; Step S5: performing model testing and verification on the proxy model; Step S6, performing confidence evaluation on the proxy model; Step S7: Establish a model management module for the proxy model to record and manage the version, parameters and training data of the proxy model; Step S8: Integrate and deploy the agent model in a simulation system environment.

2. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 1, characterized in that: In the step S1, it specifically includes: Combining the system simulation evaluation and test requirements, by taking the union of the key design parameters and test factors of the engineering-level simulation model, the key design variable parameter set is determined as X = (x 1 ,x 2 ,……,x n ), where x n Represents the key design variable parameters of the nth dimension; By decomposing the system simulation evaluation requirements, the performance evaluation index set of the engineering-level simulation model is determined as Y=(y 1 ,y 2 ,……,y t ). There is a mapping relationship between the key design variable parameter set and the performance evaluation index set.

3. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 2, characterized in that: In the step S2, it specifically includes: Step S21, constructing an operating environment covering various working conditions, parameter combinations and operating conditions, performing an initial simulation calculation under the premise of having an operating tool and an operating environment, and obtaining simulation response data of the engineering-level model; the data points input for the initial simulation calculation include data points of common working modes, data points of extreme conditions and data points of rare conditions; Step S22: Perform a preliminary check on the simulation response data to form a training sample data set, expressed as (S, Q s ), where S = {s1, s2, ..., s m } represents the data value set of the design variable parameters of each data point of the engineering-level model, s m is the value of the key design variable parameter set X at the mth data point sample; Q s ={q1,q2,……,q m } represents the real simulation response data of the engineering-level model, and the real simulation response data is the response result of the performance evaluation index set Y of the engineering-level simulation model, S and Q s There is a one-to-one mapping relationship between the elements.

4. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 3 is characterized in that: In the step S3, it specifically includes: Step S31, data cleaning of the training sample set: using a data screening and verification algorithm based on a statistical analysis method to determine a reasonable range of the response result data, determining the response results of data points that exceed the range as outliers and processing them, so as to remove possible outliers, erroneous data and noise interference; Step S32: Considering the different properties, expressions and value ranges of the key design variable parameters, a standardization method is used to standardize the key design variable parameters of the sample points. The value of Convert to a unified interval for description.

5. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 4 is characterized in that: The normalization method is min-max normalization or z-score normalization.

6. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 5 is characterized in that: The min-max normalization is expressed as: In the formula, Normalized values ​​of the i-th dimension design variable parameters of the k-th data point sample, i = 1, 2, ..., n; k = 1, 2, ..., m; It is the minimum value of all data point samples on the i-th dimension design variable parameter; It is the maximum distance between all data point sample values ​​on the i-th dimension design variable parameter.

7. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 6 is characterized in that: In the step S4, it specifically includes: Step S41, covariance function selection: determine the form of the covariance function according to the distribution characteristics and complexity of the data and the expected accuracy requirements of the model, the form of the covariance function is a Gaussian covariance function or an exponential covariance function; Step S42, iterative optimization of covariance function parameters: construct multiple rounds of experiments, combine cross-validation methods, determine the parameters of the covariance function; divide the engineering-level simulation model historical data set into multiple subsets, use one of the subsets as the validation set in turn, and the remaining subsets as the training set to construct multiple groups of covariance function parameter combinations {Θ (j) }, where j represents the jth round of experiments; by comparing the performance of the Kriging surrogate model on the validation set under different covariance function parameter combinations, the optimal covariance function parameter combination is found; Step S43: construct the proxy model according to the selected covariance function and the optimal covariance function parameter combination, which is expressed as: in, is the unknown data point s * The predicted response value, μ is the mean, m is the number of training data points, and λ is the k is the weight coefficient, C(s * ,s k ) is the covariance function.

8. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 6 is characterized in that: In the step S5, it specifically includes: Step S51: Perform encapsulation interface testing on the proxy model, and strictly check the stability, compatibility, accuracy and timeliness of data transmission of the proxy model interface; Step S52: Perform a performance test on the proxy model to evaluate key performance indicators of the proxy model, where the key performance indicators include computing speed, resource consumption, and memory usage.

9. The engineering-level model integration simulation method based on the Kriging proxy model according to claim 7, characterized in that: In the step S6, it specifically includes: Step S61: Evaluate the accuracy of the proxy model: Based on the data points S={s1, s2, ..., s m }, perform simulation calculation in the system simulation environment to obtain the prediction results of the agent model The prediction results of the proxy model The actual simulation response data Q in the training sample data s Compare and evaluate the accuracy and error of the proxy model using mean square error and mean absolute error evaluation indicators; if the accuracy of the proxy model does not meet the requirements, return to step S42, adjust the optimal covariance function parameter combination and rebuild the proxy model; Step S62, test the stability of the proxy model: by changing the test order of the data point samples and adding a small amount of noise to the data points, observe whether the prediction result of the proxy model is stable. If the prediction result of the proxy model is unstable, return to step S4 to re-build the proxy model.

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