Efficient Simulation Method for Non-Gaussian Processes Based on HPM and JTM Mixture Models

Abstract

This invention discloses an efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model, belonging to the field of structural dynamics technology. This invention achieves rapid simulation of non-Gaussian processes through parameter estimation using Hermitian polynomial and Johnson transformation models based on machine learning, explicit transformation from non-Gaussian correlation functions to Gaussian correlation functions, and fast simulation of non-Gaussian processes based on linear filtering. While ensuring accuracy, this method effectively improves the efficiency of non-Gaussian process simulation and is applicable to non-Gaussian process simulation in various engineering fields.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics technology, and in particular to an efficient simulation method for non-Gaussian processes based on a hybrid model of HPM and JTM. Background Technology

[0002] Due to the complexity of actual engineering environments, the probabilistic forms of external forces such as earthquakes, waves, and wind loads exhibit non-Gaussian characteristics, rendering the previous Gaussian distribution assumptions no longer applicable. Therefore, it is necessary to conduct simulations of non-Gaussian processes.

[0003] Compared to Gaussian random process simulations, non-Gaussian random processes are more complex to simulate because they contain more probabilistic information at each time step. Non-Gaussian random processes not only require ensuring the power spectral density function fits the target, but also guaranteeing the accuracy of their marginal probability information.

[0004] According to the theory of transformation processes, any non-Gaussian process can be obtained by transforming its corresponding standard Gaussian process through a nonlinear function. However, the mapping relationship provided by general nonlinear functions is implicit, leading to iterative simulation processes. Therefore, constructing explicit relationships using Hermitian polynomial models (HPM) and Johnson transformation models (JTM) has attracted considerable attention. When using Hermitian polynomial models and Johnson transformation models, parameter estimation requires iterative calculations to ensure accuracy; simultaneously, harmonic synthesis methods involve multiple Fourier transforms, consuming significant computational resources and time, resulting in low simulation efficiency. Therefore, simulation methods need improvement.

[0005] The field of machine learning has developed rapidly in recent years, and data processing technologies based on machine learning have gradually entered the engineering field. Precedents already exist for predictive models and parameter fitting models developed using machine learning. Therefore, estimating model parameters using machine learning tools and reducing iterative computation can effectively improve the simulation efficiency of practical engineering projects.

[0006] Based on this, an efficient simulation method for non-Gaussian processes based on a hybrid model of Hermitian polynomials and Johnson transformation is proposed. Summary of the Invention

[0007] The purpose of this invention is to provide an efficient simulation method for non-Gaussian processes based on a hybrid model of HPM and JTM, in order to solve the problems in the background art.

[0008] To achieve the above objectives, this invention provides an efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model, comprising the following steps:

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

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

[0011] S3. Based on the results of S2, a hybrid model of Hermitian polynomial and Johnson transformation is used to construct an explicit transformation analytical expression from non-Gaussian correlation function to Gaussian correlation function, and the value of Gaussian correlation function is obtained.

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

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

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

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

[0016] ① First, using the non-Gaussian skewness α3 and kurtosis α4, the dimensionless parameters h3 and h4 are calculated using the following formula:

[0017]

[0018] In the formula, κ is the scaling parameter that makes the standard deviation of the non-Gaussian process equal to 1;

[0019] ② Determine whether it satisfies If the conditions are met, then the data set falls within the applicable range of the Hermitian 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, it is classified as an unbounded system of the Johnson transformation model; if the kurtosis estimate is greater than the kurtosis data, it is classified as a bounded system of the Johnson transformation model.

[0021] The formula for calculating the intermediate variable is as follows:

[0022]

[0023] In the formula, w i The root of the intermediate variable;

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

[0025]

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

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

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

[0029] Preferably, in step (2), the parameter calculation model of the Hermitian 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] In the formula, μ Y It is the mean of variable Y, ω = exp(δ -2 ), τ and δ are JTM-S U The parameters of the model, σ Y It 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] In the formula, α 3Y α represents the skewness of variable Y. 4Y Let be the kurtosis of variable Y, u be the standard Gaussian variable, and δ be the JTM-S kurtosis. B The scaling parameter of the model, τ, is JTM-S B The model's position parameters, This represents the probability density function.

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

[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 the calculation model for each parameter, 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. Then, the K-fold cross-validation method is used to score each node of the grid and select the optimal kernel function parameters and penalty coefficient for learning.

[0042] (4) Error analysis is performed using a validation set. The error analysis includes the calculation of the coefficient of determination and the mean absolute error.

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

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

[0045]

[0046] In the formula, 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 parameters of the Hermitian polynomial model;

[0047] ② Unbounded systems of Hermitian polynomial models and Johnson transformation models:

[0048]

[0049] In the formula, λ k For JTM-S U The scale parameter, δ k For JTM-S U Shape parameters, For the standard Gaussian process U j and U k The cross-correlation function, τ k For JTM-S U Position parameters;

[0050] ③ Bounded systems of Hermitian polynomial models and Johnson transformation models:

[0051]

[0052] In the formula, I l,m G represents the integral weighting coefficient. m H represents the nonlinear transformation function. l Denotes the Hermitian polynomial, ξ k JTM-S B The parameter, u p (p = 1, 2, ..., 11) is The root, w p These are the corresponding weights, calculated as follows:

[0053]

[0054] ④ Unbounded systems in the Johnson transition model and unbounded systems in the Johnson transition model:

[0055]

[0056] ⑤ Unbounded systems and bounded systems in the Johnson transition model:

[0057]

[0058] ⑥ Bounded systems of the Johnson transition model and the bounded systems of the Johnson transition model:

[0059]

[0060] Preferably, the specific process of fast simulation of non-Gaussian process in S4 is as follows: Gaussian process simulation of Gaussian correlation function is performed by linear filtering method to obtain simulated Gaussian time history, and the simulated Gaussian time history is converted into non-Gaussian time history by Hermitian polynomial and Johnson transformation hybrid model.

[0061] Therefore, the efficient simulation method for non-Gaussian processes based on a hybrid model of HPM and JTM proposed in this invention has the following beneficial effects:

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

[0063] (2) By combining Hermitian polynomials and Johnson transformation models, an explicit analytical expression covering six types of mapping scenarios was constructed, realizing the direct conversion from non-Gaussian correlation functions to Gaussian correlation functions, avoiding multiple Fourier transforms, significantly reducing computational complexity, significantly improving efficiency, and solving the computational resource bottleneck of large-scale engineering simulation.

[0064] (3) The hybrid model proposed in this invention dynamically assigns HPM and JTM-S to the 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 transformation, time history generation, and non-Gaussian transformation is highly automated, which can quickly obtain high-precision non-Gaussian time histories, solving the problems of narrow applicability and complex operation of traditional methods, and providing an efficient and reliable tool for practical applications in fields such as wind engineering and marine engineering.

[0065] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

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

[0067] Figure 2 This is a flowchart illustrating the simulation of a conventional non-Gaussian process according to an embodiment of the present invention.

[0068] Figure 3 This is a flowchart illustrating the applicable model classification process in an embodiment of the present invention.

[0069] Figure 4 A flowchart for generating relevant parameters for the non-Gaussian process parameter calculation model in this embodiment of the invention;

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

[0071] Figure 6 This is a comparison chart of simulated and theoretical power spectral density values ​​in an embodiment of the present invention. (a) represents point 1 applicable to HPM, with a skewness of 1 and a kurtosis of 20; (b) represents the value applicable to JTM-S. U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the applicability to JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5.

[0072] Figure 7 This is a comparison chart of simulated and theoretical values ​​of relevant functions in an 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 the value applicable to JTM-S U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the applicability to JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5.

[0073] Figure 8This is a schematic diagram of the probability density function of the simulated time series in an 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 the point applicable to JTM-S U Point 2 has a skewness of 2 and a kurtosis of 55; (c) represents the applicability to JTM-S B Point 3 has a skewness of 0.5 and a kurtosis of 2.5. Detailed Implementation

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

[0075] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are some embodiments of the present invention, but not all embodiments.

[0076] like Figure 2 As shown, traditional non-Gaussian process simulation methods require, given the non-Gaussian time history, first fitting a non-Gaussian correlation function, then using a Hermitian polynomial and Johnson transformation hybrid model to establish a mapping to obtain a Gaussian correlation function, then simulating the Gaussian time history using the Gaussian correlation function, and finally converting it into the time history of a non-Gaussian process.

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

[0078]

[0079] In the formula, f is the natural frequency, k f For Mourning coordinates, z and U z u represents the corresponding altitude and the average wind speed at that altitude. * The airflow shear velocity, K is the von Kármán constant, and z0 is the surface roughness length.

[0080] The cross spectrum of wind fields 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] In the formula, Δjk Let C be the horizontal distance between points j and k. x The attenuation coefficient is... and The average wind speeds at points j and k are respectively;

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

[0086]

[0087] Example

[0088] like Figure 1 As shown, this invention provides an efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model. This method is achieved through three parts: parameter estimation using a Hermitian multinomial model and a Johnson transformation model based on machine learning; explicit transformation of the non-Gaussian correlation function to a Gaussian correlation function; and rapid simulation of the non-Gaussian process based on linear filtering. The method includes the following steps:

[0089] S1. Classify the skewness and kurtosis data for each set of non-Gaussian processes, and determine the applicable model for each set of data. Applicable models include Hermitian polynomial models (HPM) and unbounded systems of Johnson transformation models (JTM-S). U Bounded systems of the Johnson transition model (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 Hermitian polynomial model. If so, classify it as a Hermitian polynomial model to complete the classification of the data. The specific process of judgment is as follows:

[0092] ① First, using the non-Gaussian skewness α3 and kurtosis α4, the dimensionless parameters h3 and h4 are calculated using the following formula:

[0093]

[0094] In the formula, κ is the scaling parameter that makes the standard deviation of the non-Gaussian process equal to 1;

[0095] ② Determine whether it satisfies If the conditions are met, then the data set falls within the scope of HPM, and the classification is complete;

[0096] If the condition is not met, it belongs to one of the JTM types, and step (2) is executed for a 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 roots. 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] The formula for calculating the intermediate variable w is as follows:

[0099]

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

[0101]

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

[0103] The specific construction process of the non-Gaussian process parameter calculation model is as follows:

[0104] (1) Generate a large amount of skewness, kurtosis and corresponding model parameter data according to the applicable model range. Use S1 to classify the generated data. Based on the conventional random set distribution method, construct training set, validation set and test set from the classified data. The proportions of 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 A parameter calculation model is constructed, and the generated skewness and kurtosis data are input into the model. An iterative method is used to calculate the parameters, determining the model parameters for each applicable model. (After model construction, inputting a set of non-Gaussian data allows us to determine which model category the data belongs to and directly output the relevant model parameters.) Specifically:

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

[0107]

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

[0109]

[0110] In the formula, μY It is the mean of variable Y, ω = exp(δ -2 ), τ and δ are JTM-S U The scaling parameter of the model, σ Y It is the standard deviation of variable Y, α 3Y α represents the skewness of variable Y. 4Y Kurtosis of variable Y;

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

[0112]

[0113] In the formula, α 3Y α represents the skewness of variable Y. 4Y Let be the kurtosis of variable Y, u be the standard Gaussian variable, and δ be the JTM-S kurtosis. B The scaling parameter of the model, τ, is JTM-S B The model's position parameters, This represents the probability density function.

[0114] Then, a Support Vector Machine (SVM) model from a machine learning tool was used for training. The input variables of the SVM model were the skewness and kurtosis of the non-Gaussian process, and the output variables were HPM and JTM-S. U and JTM-S B The model parameters are set, and the model is saved after training. The specific training process is as follows:

[0115] (3) Configure the radial basis kernel function, adopt 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 validation calculations on the model for each parameter, adjust and determine the number of iterations, and ensure model convergence;

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

[0118] This approach uses a large amount of data to train and build a machine learning model for parameter fitting, avoiding the non-convergence problem in traditional iterative calculations. It also avoids nested calculations in traditional iterative calculations, greatly improving fitting efficiency while ensuring accuracy. In addition, the support vector machine model uses a unified kernel function, which allows the parameters in the kernel function to be shared, thereby reducing the number of machine learning parameters and reducing model complexity and overfitting to a certain extent.

[0119] After training, based on the calculated parameters, input and output datasets are constructed according to the classification. 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 a validation set. The error analysis includes determining the coefficients R0. 2 Calculation of Mean Absolute Error (MAE).

[0121] S3. Explicit Transformation from Non-Gaussian Correlation Function to Gaussian Correlation Function: Based on the results of S2, and a hybrid model of Hermite polynomial and Johnson transformation, an explicit transformation analytical expression for the transformation from non-Gaussian correlation function to Gaussian correlation function is constructed, yielding the Gaussian correlation function values ​​at discrete points. According to the transformation process theory, the relationship between the non-Gaussian process correlation function and the standard Gaussian process correlation function is as follows:

[0122]

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

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

[0125] ①HPM and HPM:

[0126]

[0127] In the formula, 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 parameters of the Hermitian polynomial model;

[0128] ②HPM and JTM-S U :

[0129]

[0130] In the formula, λ k For JTM-S U The scale parameter, δ k For JTM-S U Shape parameters, For the standard Gaussian process U j and U k The cross-correlation function, τ k For JTM-S U Position parameters;

[0131] ③HPM and JTM-S B :

[0132]

[0133] In the formula, I l,m G represents the integral weighting coefficient. m H represents the nonlinear transformation function. l Denotes the Hermitian polynomial, ξ k JTM-S B The parameter, u p (p = 1, 2, ..., 11) is The root, w p These are the corresponding weights, 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 Hermitian polynomial (HPM) and Johnson transform (JTM) models, enabling efficient and accurate simulation of multivariable non-Gaussian processes with a wide range of applicability. Furthermore, by solving the correlation function of the standard Gaussian process numerically, it avoids the iterative process and to some extent solves the problems of time-consuming iterative processes and poor convergence in the parameter estimation of non-Gaussian processes.

[0142] S4. Fast simulation of non-Gaussian processes based on linear filtering: Based on the results of S3, a fast simulation of non-Gaussian time histories is performed using linear filtering, and the simulated non-Gaussian time histories are output. Specifically, a Gaussian process simulation is performed on the Gaussian correlation function using linear filtering to obtain the simulated Gaussian time histories. The simulated Gaussian time histories are then converted into non-Gaussian time histories using a hybrid model of Hermitian polynomials and Johnson transformation, and the simulated non-Gaussian time histories are output.

[0143] Tests have shown that, taking non-Gaussian wind field simulation as an example, this invention can significantly shorten the running time of non-Gaussian process simulations (as shown in Table 1). The method proposed in this invention can be directly applied to actual engineering structures, achieving efficient computation in the field and saving computational resources and costs.

[0144] Table 1 Comparison of Simulation Efficiency for Non-Gaussian Wind Fields

[0145]

[0146] The non-Gaussian time history data simulated using this method has the following key applications 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 (wave load assessment of platforms) and earthquake engineering (non-Gaussian ground motion simulation), the generated time history data can accurately reproduce the non-Gaussian statistical characteristics of actual loads, avoid the underestimation of the probability of extreme events by traditional Gaussian models, and significantly improve the reliability of structural safety margin calculation.

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

[0149] ③ Promote intelligent disaster prevention decision-making systems: The generated high-precision non-Gaussian time histories can serve as the core input of digital twin systems, predicting disaster evolution in real time (such as the wind vibration response of building clusters under typhoon paths), providing data support for emergency dispatch in smart cities, and enhancing urban resilience.

[0150] In summary, the time-history data output by this solution is the core foundation for ensuring the disaster resistance performance 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, this invention provides an efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model. The constructed non-Gaussian process parameter calculation model can shorten the calculation time of non-Gaussian process parameters while ensuring accuracy. It overcomes the low efficiency caused by traditional iteration in the simulation of non-Gaussian processes in actual engineering structures, and has the characteristics of being fast, fully automatic, and highly accurate. The training method of this invention has a small computational load, low model complexity, high degree of automation, and good training efficiency, sensitivity, and accuracy. Through machine learning and linear filtering, the efficiency of parameter calculation and time history simulation in non-Gaussian processes is improved.

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

Claims

1. A non-Gaussian process high-efficiency simulation method based on a mixed model of HPM and JTM, characterized in that, Includes the following steps: S1. In the field of structural dynamics, the probabilistic forms of external forces such as earthquakes, waves, and wind loads exhibit non-Gaussian characteristics, rendering the Gaussian distribution assumption inapplicable. Therefore, non-Gaussian process simulations are conducted, and each set of skewness and kurtosis data for the non-Gaussian process is classified to determine the applicable model for each set of data. Applicable models include Hermitian polynomial models, unbounded systems of Johnson transformation models, and bounded systems of Johnson transformation models. S2. Construct non-Gaussian process parameter calculation models for different applicable models, then train them using a support vector machine model and output the model parameters. S3. Based on the results of S2, a hybrid model of Hermitian polynomial and Johnson transformation is used to construct an explicit transformation analytical expression from non-Gaussian correlation function to Gaussian correlation function, and the value of Gaussian correlation function is obtained. S4. Based on the results of S3, linear filtering is used to perform fast simulation of non-Gaussian time history and output non-Gaussian time history simulation values. For vertical wind field simulation, self-spectrum Using the Panofsky spectrum, it is represented as follows: ； In the formula, For natural frequency, For Mourning coordinates, ; and This represents the corresponding altitude and the average wind speed at that altitude. The airflow shear velocity, K is the von Kármán constant. The length of the surface roughness; The cross spectrum of wind fields is calculated using the following formula: ； , Let Xj(t) and Xk(t) be the coherence function between the non-Gaussian processes, expressed as: ； In the formula, for Point and Horizontal distance between points The attenuation coefficient is... and They are respectively Point and Average wind speed at the point; Non-Gaussian spectrum The non-Gaussian correlation function is obtained through inverse Fourier transform. The calculation formula is as follows: ； This method is applied to practical engineering structures in the field of engineering. In wind engineering high-rise buildings, wind-resistant design of long-span bridges, wave load assessment of marine engineering platforms, and non-Gaussian ground motion simulation in earthquake engineering, the generated time history data reproduces the non-Gaussian statistical characteristics of actual loads, avoiding the underestimation of the probability of extreme events by traditional Gaussian models.

2. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 1, characterized in that, In S1, the specific process of classification is as follows: 1) For each set of skewness and kurtosis data, determine whether the corresponding non-Gaussian process falls within the applicable range of the Hermitian polynomial model. If so, classify it as a Hermitian polynomial model. Otherwise, proceed 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, it is classified as an unbounded system of the Johnson transformation model; if the kurtosis estimate is greater than the kurtosis data, it is classified as a bounded system of the Johnson transformation model.

3. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 1, characterized in that, In S2, the specific construction process of the non-Gaussian process parameter calculation model is as follows: (1) Generate multiple skewness, kurtosis and corresponding model parameter data according to the applicable model range, and use S1 to classify the generated data to construct training set, validation set and test set; (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 for each applicable model.

4. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 3, characterized in that, In step (2), the bounded system parameter calculation model of the Johnson transformation model is expressed as: ； In the formula, For variables skewness, For variables peak, It is a standard Gaussian variable. It is JTM- S B The model's scaling parameters It is JTM- S B The model's position parameters, yes The mean, yes standard deviation This represents the probability density function.

5. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 3, characterized in that, In S2, the specific training process is as follows: (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 verification calculations on the calculation model for each parameter, 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. Then, the K-fold cross-validation method is used to score each node of the grid and select the optimal kernel function parameters and penalty coefficients for learning. (4) Error analysis is performed using a validation set. The error analysis includes the calculation of the coefficient of determination and the mean absolute error.

6. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 1, characterized in that: The explicit transformation analytical expression in S3 is formed by repeated combinations of any two models or the same model from the Hermitian polynomial model, the unbounded system of the Johnson transformation model, and the bounded system of the Johnson transformation model.

7. The efficient simulation method for non-Gaussian processes based on a hybrid HPM and JTM model according to claim 1, characterized in that, The specific process of fast simulation of non-Gaussian process in S4 is as follows: Gaussian process simulation is performed on Gaussian correlation function using linear filtering method to obtain simulated Gaussian time history, and the simulated Gaussian time history is converted into non-Gaussian time history using Hermitian polynomial and Johnson transformation hybrid model.

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