Non-Gaussian process efficient simulation method based on HPM and JTM hybrid model

Abstract

The invention discloses a non-Gaussian process efficient simulation method based on an HPM and JTM mixed model, and belongs to the technical field of structural dynamics. Through parameter estimation of the Hermite polynomial model and the Johnson conversion model based on machine learning, explicit conversion from the non-Gaussian correlation function to the Gaussian correlation function and rapid simulation of the non-Gaussian process based on the linear filtering method, the efficiency of non-Gaussian process simulation is effectively improved on the premise of ensuring the precision, and the method is suitable for large-scale popularization and application. The method is suitable for non-Gaussian process simulation in various engineering fields.

Description

Technical Field

[0001] The present invention relates to the technical field of structural dynamics, and in particular to an efficient non-Gaussian process simulation method based on a HPM and JTM hybrid model. Background Art

[0002] Due to the complexity of the actual engineering environment, the probabilistic form of external forces such as earthquakes, waves, and wind loads presents non-Gaussian characteristics. The previous Gaussian distribution assumption is no longer applicable, so it is necessary to carry out non-Gaussian process simulation.

[0003] Compared to Gaussian random process simulation, non-Gaussian random processes contain more probabilistic information at each moment, making their simulation more complex. For non-Gaussian random processes, it is necessary not only to ensure that the power spectral density function matches the target but also to ensure that the marginal probability information is correct.

[0004] According to transformation process theory, any non-Gaussian process can be converted from its corresponding standard Gaussian process via nonlinear functions. However, the mapping relationship provided by general nonlinear functions is implicit, requiring iterations in the simulation process. To address this, the Hermite polynomial model (HPM) and the Johnson transform model (JTM), which construct explicit relationships, have received considerable attention. When using these models, parameter estimation requires iterative calculations to ensure accuracy. Furthermore, harmonic synthesis methods involve multiple Fourier transforms, which consume significant computational resources and time, resulting in low simulation efficiency. Therefore, simulation methods need to be improved.

[0005] The field of machine learning has developed rapidly in recent years, and data processing techniques based on machine learning have gradually entered the engineering field. Predictive models and parameter fitting models based on machine learning have already been developed. Therefore, using machine learning tools to estimate model parameters and reduce the amount of iterative calculations will effectively improve the efficiency of simulations in actual engineering projects.

[0006] Based on this, an efficient simulation method for non-Gaussian processes based on the Hermite polynomial model and the Johnson transform mixture model is proposed. Summary of the Invention

[0007] The purpose of the present invention is to provide an efficient non-Gaussian process simulation method based on the HPM and JTM hybrid model to solve the problems in the background technology.

[0008] To achieve the above object, the present invention provides an efficient non-Gaussian process simulation method based on the HPM and JTM hybrid model, comprising the following steps:

[0009] S1. Classify each set of skewness and kurtosis data of the non-Gaussian process and determine the applicable model for each set of data; the applicable models include the Hermite polynomial model, the unbounded system of the Johnson transformation model, and the bounded system of the Johnson transformation model;

[0010] S2. Construct a non-Gaussian process parameter calculation model for different applicable models, then use the support vector machine model for training and output the model parameters;

[0011] S3, based on the results of S2, the Hermite polynomial and Johnson transformation mixed model, construct an explicit conversion formula from non-Gaussian correlation function to Gaussian correlation function, and obtain the Gaussian correlation function value;

[0012] S4. Based on the results of S3, linear filtering is used to perform fast simulation of non-Gaussian time history and output the non-Gaussian time history simulation value.

[0013] Preferably, in S1, the specific process of classification is:

[0014] 1) For each set of skewness and kurtosis data, determine whether the corresponding non-Gaussian process falls within the applicable range of the Hermite polynomial model. If so, classify it as a Hermite polynomial model; otherwise, execute step 2);

[0015] The specific process of judgment is as follows:

[0016] ① First, use the non-Gaussian skewness α3 and the kurtosis value α4 to calculate the dimensionless parameters h3 and h4. The calculation formula is:

[0017]

[0018] Where κ is the scale parameter that makes the standard deviation of the non-Gaussian process equal to 1;

[0019] ② Determine whether If it satisfies, then the data set falls within the applicable range of the Hermite polynomial model;

[0020] 2) Calculate the root of the intermediate variable based on the skewness data, and calculate the kurtosis estimate based on the positive root. If the kurtosis estimate is less than the kurtosis data, classify it as an unbounded system of the Johnson transformation model; if the kurtosis estimate is greater than the kurtosis data, classify it as a bounded system of the Johnson transformation model.

[0021] The calculation formula of the intermediate variable is:

[0022]

[0023] Where w i is the root of the intermediate variable;

[0024] The formula for calculating the kurtosis estimate is:

[0025]

[0026] Preferably, in S2, the specific construction process of the non-Gaussian process parameter calculation model is:

[0027] (1) Generate multiple skewness, kurtosis and corresponding model parameter data according to the range of applicable models, use S1 to classify the generated data, and construct training sets, validation sets and test sets;

[0028] (2) Construct a parameter calculation model for each applicable model, input the generated skewness and kurtosis data into the parameter calculation model, use the iterative method to calculate the parameters, and determine the model parameters of each applicable model.

[0029] Preferably, in step (2), the parameter calculation model of the Hermite polynomial model is expressed as:

[0030]

[0031] Preferably, in step (2), the parameter calculation model of the unbounded system of the Johnson transformation model is expressed as:

[0032] μ Y =-ω 0.5 sinh(Ω);

[0033]

[0034] Where μ Y is the mean of variable Y, ω=exp(δ -2 ), τ and δ are JTM-S U The parameters of the model, σ Y is the standard deviation of variable Y.

[0035] Preferably, in step (2), the parameter calculation model of the bounded system of the Johnson transformation model is expressed as:

[0036]

[0037] Where, α 3Y is the skewness of variable Y, α 4Y is the kurtosis of variable Y, u is the standard Gaussian variable, and δ is the JTM-S B The scale parameter of the model, τ is the JTM-S B The location parameters of the model, represents the probability density function.

[0038] Preferably, in S2, the specific training process is:

[0039] (1) Configure the radial basis kernel function and define the initial kernel function parameters and penalty coefficients;

[0040] (2) Use the training set and validation set to perform preliminary validation calculations on each parameter calculation model and adjust the number of iterations;

[0041] (3) The grid search method is used to list the structural parameter values ​​required by the support vector machine model into a grid, and then the K-fold cross-validation method is used to score each node of the grid to select the optimal kernel function parameters and penalty coefficients for learning;

[0042] (4) The validation set is used for error analysis, which includes the calculation of the coefficient of determination and the mean absolute error.

[0043] Preferably, the explicit conversion analytical expression in S3 is formed by any two models of the Hermite polynomial model, the unbounded system of the Johnson conversion model, and the bounded system of the Johnson conversion model, or by repeated combinations of the same model, including the following 6 categories:

[0044] ① Hermite polynomial model and Hermite polynomial model:

[0045]

[0046] Where, represents the non-Gaussian correlation function, Represents a non-Gaussian process X j The standard deviation of (t), h 3j and h 4j represents the Hermitian polynomial model parameters;

[0047] ② Unbounded system of Hermite polynomial model and Johnson transformation model:

[0048]

[0049] Where λ k JTM-S U The scale parameter, δ k JTM-S U The shape parameters, is a standard Gaussian process U j and U k The cross-correlation function, τ k JTM-S U Positional parameters;

[0050] ③Bounded systems of Hermite polynomial model and Johnson transformation model:

[0051]

[0052] Where, I l,m Indicates the integral weight coefficient, g m represents the nonlinear transformation function, H l represents the Hermitian polynomial, ξ k Indicates JTM-S B Parameters, u p (p=1,2,…,11) is The root of w p is the corresponding weight, calculated as follows:

[0053]

[0054] ④Unbounded system of Johnson transformation model and unbounded system of Johnson transformation model:

[0055]

[0056] ⑤Unbounded system and bounded system of Johnson transformation model:

[0057]

[0058] ⑥Bounded system of Johnson transformation model and bounded system of Johnson transformation model:

[0059]

[0060] Preferably, the specific process of the rapid simulation of the non-Gaussian process in S4 is: using a linear filtering method to simulate the Gaussian process on the Gaussian correlation function to obtain a simulated Gaussian time history, and using a Hermite polynomial and Johnson transformation mixed model to convert the simulated Gaussian time history into a non-Gaussian time history.

[0061] Therefore, the present invention provides an efficient non-Gaussian process simulation method based on the HPM and JTM hybrid model, which has the following beneficial effects:

[0062] (1) By introducing machine learning (support vector machine model), a direct mapping relationship from the statistical characteristics of non-Gaussian processes (skewness, kurtosis) to model parameters was constructed. The model was trained using massive pre-generated data, avoiding the loop nested calculation in the traditional iterative process. While ensuring accuracy, the parameter calculation time was significantly shortened, the convergence failure problem that may be caused by iteration was solved, and the stability and reliability of the simulation were significantly improved.

[0063] (2) By combining the Hermite polynomials with the Johnson transformation model, an explicit analytical expression covering six types of mapping scenarios was constructed, which achieved the direct conversion of non-Gaussian correlation functions to Gaussian correlation functions, avoided multiple Fourier transforms, greatly reduced the computational complexity, significantly improved the efficiency, and solved the computational resource bottleneck of large-scale engineering simulations.

[0064] (3) The hybrid model proposed in this invention dynamically allocates HPM, JTM-S to data through a classification mechanism. U or JTM-S B The model significantly broadens its applicable boundaries; at the same time, the entire process from parameter estimation, correlation function conversion, time history generation, to non-Gaussian conversion is highly automated, and high-precision non-Gaussian time history can be quickly obtained, solving the problems of narrow application scope and complex operation of traditional methods, and providing efficient and reliable tools for practical applications in wind engineering, marine engineering and other fields.

[0065] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a flowchart of efficient simulation of non-Gaussian processes according to an embodiment of the present invention;

[0067] Figure 2 This is a flow chart of a traditional non-Gaussian process simulation according to an embodiment of the present invention;

[0068] Figure 3 This is a flow chart of classification of applicable models according to an embodiment of the present invention;

[0069] Figure 4 A flowchart of generating relevant parameters for a non-Gaussian process parameter calculation model according to an embodiment of the present invention;

[0070] Figure 5 A schematic diagram of a machine learning training process according to an embodiment of the present invention;

[0071] Figure 6 The comparison diagram of the simulated value and theoretical value of the power spectrum density of the embodiment of the present invention, wherein (a) represents point 1 applicable to HPM, with a skewness of 1 and a kurtosis of 20; (b) represents point 1 applicable to JTM-S U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the point that is suitable for JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5;

[0072] Figure 7 The simulation value and theoretical value comparison diagram of the correlation function of the embodiment of the present invention are shown in FIG1 , where (a) represents point 1 applicable to HPM, with a skewness of 1 and a kurtosis of 20; (b) represents point 1 applicable to JTM-S U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the point that is suitable for JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5;

[0073] Figure 8Schematic diagram of the probability density function of the simulated time series according to the embodiment of the present invention, where (a) represents point 1 applicable to HPM, with a skewness of 1 and a kurtosis of 20; (b) represents point 1 applicable to JTM-S U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the point that is suitable for JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5. DETAILED DESCRIPTION

[0074] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0075] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0076] like Figure 2 As shown in the figure, the traditional non-Gaussian process simulation method requires that, under the premise of known non-Gaussian time history, the non-Gaussian correlation function is first fitted, and then the Hermite polynomial and Johnson transformation mixed model is used to establish a mapping to obtain the Gaussian correlation function, and then the Gaussian correlation function is simulated to obtain the Gaussian time history, and finally converted into the time history of the non-Gaussian process.

[0077] Taking vertical wind field simulation as an example, the self-spectrum S X (f) Using Panofsky spectrum, it is expressed as follows:

[0078]

[0079] Where f is the natural frequency, k f For the coordinates of Morning, z and U z Indicates the corresponding height and the average wind speed at that height, u * is the air flow shear velocity, K is the von Karman constant, and z0 is the ground roughness length.

[0080] The wind field cross spectrum is calculated using the following formula:

[0081]

[0082] ω=2πf,Coh(Δ jk ,ω) is a non-Gaussian process X j (t) and X k The coherence function between (t) is expressed as:

[0083]

[0084] Where, Δjk is the horizontal distance between point j and point k, C x is the attenuation coefficient, and are the average wind speeds at points j and k, respectively;

[0085] Non-Gaussian spectrum The non-Gaussian correlation function is obtained by inverse Fourier transform The calculation formula is as follows:

[0086]

[0087] Example

[0088] like Figure 1 As shown, the present invention provides an efficient non-Gaussian process simulation method based on the HPM and JTM hybrid model, which is implemented through three parts: Hermite polynomial model and Johnson transformation model parameter estimation based on machine learning, explicit conversion of non-Gaussian correlation function to Gaussian correlation function, and fast non-Gaussian process simulation based on linear filtering method, including the following steps:

[0089] S1. Classify each set of skewness and kurtosis data of non-Gaussian process and determine the applicable model for each set of data. The applicable models include Hermite polynomial model (HPM), Johnson transformation model unbounded system (JTM-S U ), Johnson Transformation Model Bounded System (JTM-S B );

[0090] The specific process of classification is as follows:

[0091] (1) For each set of skewness and kurtosis data, determine whether the corresponding non-Gaussian process falls within the applicable range of the Hermite polynomial model. If so, classify it as a Hermite polynomial model to complete the classification of the reorganized data. The specific process of judgment is:

[0092] ① First, use the non-Gaussian skewness α3 and the kurtosis value α4 to calculate the dimensionless parameters h3 and h4. The calculation formula is:

[0093]

[0094] Where κ is the scale parameter that makes the standard deviation of the non-Gaussian process equal to 1;

[0095] ② Determine whether If satisfied, the data set falls within the HPM applicable scope and the classification is completed;

[0096] If not, it belongs to one of the JTMs and step (2) is executed for the second classification.

[0097] (2) Calculate the three roots of the intermediate variable w based on the skewness data α3, and calculate the kurtosis estimate α'4 based on the positive root. If the kurtosis data is greater than the kurtosis estimate α4>α'4, it is classified as an unbounded system JTM-S of the Johnson Transformation Model. U If the kurtosis data is less than the kurtosis estimate α4<α'4, it is classified as a bounded system of the Johnson Transformation Model JTM-S B , complete the secondary classification;

[0098] Among them, the calculation formula of the intermediate variable w is:

[0099]

[0100] The calculation formula for the kurtosis estimate α'4 is:

[0101]

[0102] S2. Parameter estimation of Hermite polynomial models and Johnson transformation models based on machine learning: Construct non-Gaussian process parameter calculation models for different applicable models, then use machine learning tools to train them and output relevant parameters;

[0103] Among them, the specific construction process of the non-Gaussian process parameter calculation model is:

[0104] (1) Generate a large amount of skewness, kurtosis and corresponding model parameter data according to the scope of the applicable model, use S1 to classify the generated data, and construct a training set, a validation set and a test set from the classified data according to the conventional random clustering method. The proportions of the training set, validation set and test set are 70%, 20% and 10% respectively;

[0105] (2) For each applicable model HPM, JTM-S U 、JTM-S B Construct a parameter calculation model, input the generated skewness and kurtosis data into the parameter calculation model, use the iterative method to calculate the parameters, and determine the model parameters of each applicable model (after the model is built, input a set of non-Gaussian data to determine which type of model the data belongs to and directly output the relevant model parameters). Specifically:

[0106] ① The HPM model parameters are iteratively calculated using the following formula:

[0107]

[0108] ②JTM-S U The model parameters are iteratively calculated using the following formula:

[0109]

[0110] Where μY is the mean of variable Y, ω=exp(δ -2 ), τ and δ are JTM-S U The scale parameter of the model, σ Y is the standard deviation of variable Y, α 3Y is the skewness of variable Y, α 4Y is the kurtosis of variable Y;

[0111] ③JTM-S B The model parameters are iteratively calculated using the following formula:

[0112]

[0113] Where, α 3Y is the skewness of variable Y, α 4Y is the kurtosis of variable Y, u is the standard Gaussian variable, and δ is the JTM-S B The scale parameter of the model, τ is the JTM-S B The location parameters of the model, represents the probability density function.

[0114] Then the support vector machine model in the machine learning tool is used for training. The input variables of the support vector machine model are the skewness and kurtosis of the non-Gaussian process, and the output variables are HPM, JTM-S U and JTM-S B The parameters of the model are saved after training. The specific training process is as follows:

[0115] (3) Configure the radial basis kernel function, use the Gaussian kernel function, and define the initial kernel function parameter γ and the penalty coefficient C;

[0116] (4) Use the training set and validation set to perform preliminary verification calculations on each parameter calculation model, adjust and determine the number of iterations to ensure model convergence;

[0117] (5) The grid search method is used to list the structural parameter values ​​(hyperparameter kernel function parameter γ and penalty coefficient C) required for the support vector machine model into a grid, and then the K-fold cross-validation method is used to score each node of the grid, and the optimal kernel function parameter and penalty coefficient are selected for learning; the search range of this embodiment is set to: kernel function parameter γ is [1, 50]; penalty coefficient C is [1, 10].

[0118] This solution uses a large amount of data training to build a machine learning model for parameter fitting, avoiding the problem of non-convergence in traditional iterative calculations; at the same time, it avoids the loop nested calculations in the traditional iterative calculation process, greatly improving the fitting efficiency while ensuring accuracy; in addition, the support vector machine model uses a unified kernel function, so that the various parameters in the kernel function can be shared, thereby achieving the purpose of reducing the number of machine learning parameters, which can reduce the model complexity and reduce overfitting to a certain extent.

[0119] After the training is completed, the input data and output data sets are constructed according to the calculated parameters. For HPM, the input vector is [α3, α4] and the output vector is [h3, h4]; for JTM-S U , input vector [α3, α4], output vector [ω, Ω]; for JTM-S B , input vector [α3, α4], output vector [τ, δ].

[0120] (6) Error analysis is performed using the validation set, including the coefficient of determination R 2 , mean absolute error MAE calculation.

[0121] S3. Explicit conversion of non-Gaussian correlation function to Gaussian correlation function: Based on the results of S2, the Hermite polynomial model and the Johnson transformation mixed model, an explicit conversion expression from non-Gaussian correlation function to Gaussian correlation function is constructed, and the Gaussian correlation function value of the discrete point is obtained; according to the conversion process theory, the relationship between the non-Gaussian process correlation function and the standard Gaussian process correlation function is as follows:

[0122]

[0123] Where, represents the non-Gaussian correlation function, j and k represent different measurement points, E[·] represents the expected value, X j (t0) represents the random process X j The value at time t0, g m (·) represents the conversion function, u1=u j (t0);u2=u k (t0+t); φ[·] is the joint probability density function of the standard Gaussian variables u1 and u2;

[0124] The explicit transformation expressions are formed by any two models from the Hermitian polynomial model, the unbounded system of the Johnson transformation model, and the bounded system of the Johnson transformation model, or by repeated combinations of the same model. There are six types in total, specifically:

[0125] ①HPM and HPM:

[0126]

[0127] Where, represents the non-Gaussian correlation function, Represents a non-Gaussian process X j The standard deviation of (t), h 3j and h 4j represents the Hermitian polynomial model parameters;

[0128] ②HPM and JTM-S U :

[0129]

[0130] Where λ k JTM-S U The scale parameter, δ k JTM-S U The shape parameters, is a standard Gaussian process U j and U k The cross-correlation function, τ k JTM-S U Positional parameters;

[0131] ③HPM and JTM-S B :

[0132]

[0133] Where, I l,m Indicates the integral weight coefficient, g m represents the nonlinear transformation function, H l represents the Hermitian polynomial, ξ k Indicates JTM-S B Parameters, u p (p=1,2,…,11) is The root of w p is the corresponding weight, calculated as follows:

[0134]

[0135] ④JTM-S U With JTM-S U :

[0136]

[0137] ⑤JTM-S U With JTM-S B :

[0138]

[0139] ⑥JTM-S BWith JTM-S B :

[0140]

[0141] This step combines the advantages of the Hermite polynomial model (HPM) and the Johnson transform model (JTM), and can simulate multivariable non-Gaussian processes efficiently and accurately, and has a wide range of applicability. It also solves the related functions of the standard Gaussian process through numerical methods, avoiding the iterative process, and to a certain extent solving the problems of time-consuming iterative process and poor convergence in the parameter estimation of non-Gaussian processes.

[0142] S4. Rapid simulation of non-Gaussian processes based on linear filtering method: Based on the results of S3, linear filtering is used to perform rapid simulation of non-Gaussian time history, and the simulated value of non-Gaussian time history is output. Specifically: the Gaussian correlation function is simulated by linear filtering method to obtain the simulated Gaussian time history, and the simulated Gaussian time history is converted into non-Gaussian time history by using the Hermite polynomial and Johnson transformation mixed model, and the simulated Gaussian time history is output.

[0143] The present invention has been tested, using non-Gaussian wind field simulation as an example, to significantly shorten the runtime of non-Gaussian process simulations (as shown in Table 1). The proposed method can be directly applied to actual engineering structures, enabling efficient computation in the field and saving computing resources and costs.

[0144] Table 1 Comparison of non-Gaussian wind field simulation efficiency

[0145]

[0146] The non-Gaussian time history data simulated by this solution has the following key uses and importance in the engineering field:

[0147] ① Improve the accuracy of extreme load analysis: In wind engineering (wind-resistant design of high-rise buildings and long-span bridges), marine engineering (platform wave load assessment), and earthquake engineering (non-Gaussian seismic motion simulation), the generated time history data can accurately reproduce the non-Gaussian statistical characteristics of actual loads, avoiding the underestimation of the probability of extreme events by traditional Gaussian models, and significantly improving the calculation reliability of structural safety margins.

[0148] ②Optimize fatigue life and reliability assessment: For critical structures such as aerospace and nuclear power facilities, non-Gaussian time history can accurately simulate the transient impact effects of random vibration loads (such as sudden changes in turbulent wind pressure and wave impact), support more realistic fatigue damage accumulation analysis, avoid life prediction deviations caused by load simplification, and reduce operation and maintenance risks.

[0149] ③ Promote intelligent disaster prevention decision-making systems: The generated high-precision non-Gaussian time history can be used as the core input of the digital twin system to predict disaster evolution in real time (such as the wind-induced vibration response of buildings under a typhoon path), provide data support for emergency dispatch in smart cities, and enhance urban resilience.

[0150] In summary, the time series data output by this solution is the core foundation for ensuring the disaster resistance of major projects and extending their service life, and provides key technical support for emerging fields such as new energy (offshore wind power) and smart infrastructure.

[0151] Therefore, the present invention provides an efficient non-Gaussian process simulation method based on the HPM and JTM hybrid model, and a non-Gaussian process parameter calculation model constructed therefrom can shorten the time for non-Gaussian process parameter calculation while ensuring accuracy, overcome the low efficiency caused by the use of traditional iteration in the non-Gaussian process simulation of actual engineering structures, and has the characteristics of being fast, fully automatic, and highly accurate; the training method of the present invention has a small amount of calculation, low model complexity, a high degree of automation, and good training efficiency, sensitivity, and accuracy; and through machine learning and linear filtering methods, the efficiency of parameter calculation and time-history simulation in the non-Gaussian process is improved.

[0152] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. An efficient simulation method for non-Gaussian processes based on the HPM and JTM hybrid model, characterized in that: The following steps are involved: S1. Classify each set of skewness and kurtosis data of the non-Gaussian process and determine the applicable model for each set of data; the applicable models include the Hermite polynomial model, the unbounded system of the Johnson transformation model, and the bounded system of the Johnson transformation model; S2. Construct a non-Gaussian process parameter calculation model for different applicable models, then use the support vector machine model for training and output the model parameters; S3. Based on the results of S2, the Hermite polynomial and Johnson transformation mixed model is used to construct an explicit conversion expression from non-Gaussian correlation function to Gaussian correlation function, and the Gaussian correlation function value is obtained; S4. Based on the results of S3, linear filtering is used to perform fast simulation of non-Gaussian time history and output the non-Gaussian time history simulation value.

2. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 1, wherein: In S1, the specific process of classification is: 1) For each set of skewness and kurtosis data, determine whether the corresponding non-Gaussian process falls within the scope of application of the Hermite polynomial model. If so, classify it as a Hermite polynomial model; Otherwise, go to step 2); 2) Calculate the root of the intermediate variable based on the skewness data, and calculate the kurtosis estimate based on the positive root. If the kurtosis estimate is less than the kurtosis data, classify it as an unbounded system of the Johnson transformation model; if the kurtosis estimate is greater than the kurtosis data, classify it as a bounded system of the Johnson transformation model.

3. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 1, wherein: In S2, the specific construction process of the non-Gaussian process parameter calculation model is: (1) Generate multiple skewness, kurtosis and corresponding model parameter data according to the range of applicable models, use S1 to classify the generated data, and construct training sets, validation sets and test sets; (2) Construct a parameter calculation model for each applicable model, input the generated skewness and kurtosis data into the parameter calculation model, use the iterative method to calculate the parameters, and determine the model parameters of each applicable model.

4. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 3, characterized in that: In step (2), the bounded system parameter calculation model of the Johnson transformation model is expressed as: Where, α 3Y is the skewness of variable Y, α 4Y is the kurtosis of variable Y, u is the standard Gaussian variable, and δ is the JTM-S B The scale parameter of the model, τ is the JTM-S B The location parameter of the model, μ Y is the mean of Y, σ Y is the standard deviation of Y, represents the probability density function.

5. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 3, characterized in that: In S2, the specific training process is: (1) Configure the radial basis kernel function and define the initial kernel function parameters and penalty coefficients; (2) Use the training set and validation set to perform preliminary validation calculations on each parameter calculation model and adjust the number of iterations; (3) The grid search method is used to list the structural parameter values ​​required by the support vector machine model into a grid, and then the K-fold cross-validation method is used to score each node of the grid to select the optimal kernel function parameters and penalty coefficients for learning; (4) The validation set is used for error analysis, which includes the calculation of the coefficient of determination and the mean absolute error.

6. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 1, wherein: The explicit conversion expression in S3 is formed by combining any two models of the Hermite polynomial model, the unbounded system of the Johnson conversion model, and the bounded system of the Johnson conversion model, or by repeatedly combining the same model.

7. The method for efficiently simulating non-Gaussian processes based on a hybrid model of HPM and JTM according to claim 1, wherein: The specific process of the non-Gaussian process fast simulation in S4 is: using the linear filtering method to simulate the Gaussian process of the Gaussian correlation function to obtain a simulated Gaussian time history, and using the Hermite polynomial and Johnson transformation mixed model to convert the simulated Gaussian time history into a non-Gaussian time history.

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