Stable non-Gaussian random process simulation method

Abstract

The invention discloses a stationary non-Gaussian random process simulation method, and relates to the field of random vibration numerical simulation, and the method comprises the following steps: obtaining an autocorrelation function through the conversion of a power spectrum density function of a target non-Gaussian random process, and obtaining an autocorrelation coefficient matrix of the target non-Gaussian random process through the autocorrelation function, the autocorrelation function in the step is obtained through Fourier transform calculation. According to the method, FMKL generalized lambda distribution and memory-free nonlinear transformation are combined, non-Gaussian characteristics of natural phenomena such as wind speed and seismic waves are accurately simulated, the defects of a traditional Gaussian model are overcome, and simulation precision and engineering design reliability are improved. By improving the Mehler formula and the spline interpolation method, the equivalent correlation coefficient calculation efficiency is improved, the calculation time is shortened, resource use is optimized, and the method is suitable for large-scale complex engineering structure simulation. The method has flexibility and is widely suitable for various non-Gaussian random process simulation requirements.

Description

Technical Field

[0001] The present invention relates to the field of numerical simulation of random vibration, and particularly to a method for simulating a stationary non-Gaussian random process. Background Art

[0002] Existing methods for simulating random processes mainly include the spectral representation method, the linear filtering method, the Karhunen-Loeve decomposition method, etc. Among them, the spectral representation method is widely adopted due to its rigorous theoretical basis and simple operation. The spectral representation method was first proposed by Rice and is applicable to the simulation of one-dimensional Gaussian random processes. Later, with the development of research, it has gradually been applied to the simulation of multi-dimensional and multi-variable random processes. However, the core assumption of the spectral representation method is that the input random process is a Gaussian process. When faced with a non-Gaussian random process, its applicability is greatly limited. In practical engineering, many external loads (such as wind loads, seismic waves, etc.) exhibit obvious non-Gaussian characteristics, which requires the use of a non-Gaussian random process model for simulation. To solve this problem, existing technologies have adopted various non-Gaussian process simulation methods, such as the memoryless nonlinear transformation method and the transformation method based on the Hermite model, attempting to convert a Gaussian process into a non-Gaussian process through a specific transformation. These methods start from the statistical moments (mean, variance, skewness, kurtosis, etc.) of the Gaussian process and use nonlinear transformation to achieve the modeling of the target non-Gaussian process. However, these methods have certain limitations in practical applications.

[0003] First of all, the commonly used Hermite model is a cubic polynomial transformation method based on the normal distribution. Although this method can effectively simulate some non-Gaussian processes within a certain range, its applicable range is very limited. Specifically, the Hermite model can only fit some types of non-Gaussian processes. For some non-Gaussian processes with complex distributions, the Hermite model cannot provide a good fitting effect. Especially when the distribution characteristics of the target non-Gaussian process are relatively complex, such as large skewness and kurtosis, the Hermite model often cannot accurately capture its characteristics. In addition, the Hermite model depends on the solution of parameters. Although its mathematical expression is relatively simple, in practical applications, the parameter solution of the transformation process is relatively cumbersome, and parameter calculation often easily diverges in the junction regions of different systems, thus affecting the accuracy and stability of the simulation.

[0004] In addition, although the Johnson distribution was proposed as an improvement to the Hermite model and has strong flexibility to fit various types of distributions (such as log-normal distribution, gamma distribution, etc.), there are still some problems in its use. The Johnson distribution includes three systems: SU, SL, and SB. These three systems can fit all types of distributions when combined, but the expressions of different systems are different, and the parameter solving methods also vary. In practical applications, different systems need to be selected according to the region of the target value, which increases the complexity of model selection. In addition, when calculating parameters near the junction region of different systems in the Johnson distribution, numerical instability or non-convergence of the solution may occur, leading to the accumulation of errors and affecting the accuracy and reliability of the simulation results. Therefore, there are still major technical problems in the existing non-Gaussian random process simulation methods when dealing with some complex random processes, and there is an urgent need for a more efficient and accurate simulation method to solve these problems.

[0005] To solve the above problems, researchers in recent years have proposed various non-Gaussian random process simulation methods based on improved algorithms, such as using more accurate numerical methods to solve the equivalent correlation coefficient or introducing new distribution models to improve the adaptability of the simulation. However, the complexity of these methods is often high, and the computational efficiency is low. Especially when simulating large-scale engineering structure systems, the computational amount and time consumption become the bottleneck restricting their wide application. Therefore, there is an urgent need for a simulation method that can adapt to the random process with complex non-Gaussian characteristics and improve the computational efficiency and accuracy.

[0006] In this context, the present invention proposes a non-Gaussian random process simulation method based on the FMKL generalized lambda distribution. This method combines the flexibility of the FMKL generalized lambda distribution with the efficiency of the memoryless non-linear transformation method, aiming to overcome the limitations of the Hermite model and the Johnson distribution in the prior art, improve the simulation accuracy through an improved equivalent correlation coefficient solving method, and solve the practical application problems in non-Gaussian random process simulation while ensuring the computational efficiency. Through this method, the non-Gaussian random processes commonly encountered in engineering can be effectively simulated, thus more accurately reflecting the influence of actual loads on engineering structures and improving the accuracy and reliability of numerical simulation.

[0007] The above information disclosed in the background art section is only used to enhance the understanding of the background of the present disclosure, and thus may include information that does not constitute the prior art known to those of ordinary skill in the art. Summary of the Invention

[0008] The object of the present invention is to provide a method for simulating a stationary non-Gaussian random process. By combining the FMKL generalized lambda distribution and the memoryless nonlinear transformation, the method of the present invention can effectively simulate the non-Gaussian characteristics in complex natural phenomena, such as wind speed, seismic waves, etc., overcome the deficiency that the traditional Gaussian model cannot accurately capture the skewness and heavy-tailed characteristics, improve the simulation accuracy, and enhance the reliability of engineering design. The method of the present invention introduces an improved Mehler formula and a spline interpolation method, significantly improves the calculation efficiency of the equivalent correlation coefficient, reduces the calculation time, optimizes the resource utilization, and is particularly suitable for large-scale and complex engineering structure simulations. The combination of the flexibility of the FMKL generalized lambda distribution and the memoryless nonlinear transformation enables the method of the present invention to be widely applied to the simulation of non-Gaussian random processes, meet the requirements of various engineering projects, and solve the problems in the above background technology.

[0009] To achieve the above object, the present invention provides the following technical solution: A method for simulating a stationary non-Gaussian random process, comprising the following steps:

[0010] S1. Convert the power spectral density function S Y (ω) of the target non-Gaussian random process to obtain the autocorrelation function R Y (τ), and obtain the autocorrelation coefficient matrix ρ Y (τ) of the target non-Gaussian random process Y(t), wherein the autocorrelation function ρ Y (τ) in the step is calculated by Fourier transform; Y (τ) is calculated by Fourier transform;

[0011] This step realizes the conversion from the target non-Gaussian spectral density function to the autocorrelation function. By using Fourier transform, the power spectral density S Y (ω) can be efficiently converted into the autocorrelation coefficient matrix ρ Y (τ), thereby providing basic data for further simulation work.

[0012] Step S1 includes the following specific operations:

[0013] Calculate the autocorrelation function R Y (τ) through the power spectral density S Y (ω), specifically:

[0014]

[0015] where ω is the circular frequency; τ is the time difference; S Y (ω) is the power spectral density function of the target non-Gaussian random process; R (ω) is the power spectral density function of the target non-Gaussian random process; R Y (τ) is the autocorrelation function of the target non-Gaussian random process;

[0016] According to the obtained autocorrelation function \(R\) of the target non-Gaussian random process Y (τ), further calculate the autocorrelation coefficient matrix \(\rho\) Y (τ), and its calculation formula is:

[0017]

[0018] where \(R\) Y (0) is the value of the autocorrelation function of the target non-Gaussian process at zero time; is the variance of the target non-Gaussian process. This step is used to normalize the autocorrelation function to ensure the stability and accuracy of the calculation during the simulation process.

[0019] S2. Based on the statistical moments such as the mean, variance, skewness, and kurtosis of the target non-Gaussian process \(Y(t)\), use the FMKL generalized lambda distribution to establish its corresponding conversion relationship, and obtain the parameters \(\lambda_1\), \(\lambda_2\), \(\lambda_3\), \(\lambda_4\) of the FMKL generalized lambda distribution; among them, the solution of the parameters described in the step adopts the traversal search method, and the optimal parameter values are obtained by matching with the theoretical skewness and kurtosis;

[0020] This step innovatively combines the FMKL generalized lambda distribution to solve the problems of limited applicable range and low usage efficiency existing in the commonly used conversion methods (such as the Hermite model and the Johnson distribution) in the simulation of non-Gaussian random processes. By using the statistical moments of the target process and efficiently and accurately solving the parameters of the FMKL generalized lambda distribution through traversal search, the accuracy and efficiency of the simulation are guaranteed.

[0021] S3. Based on the improved Mehler formula, an efficient method for solving the equivalent correlation coefficient is proposed, specifically: by calculating the maximum and minimum values of the autocorrelation coefficient matrix \(\rho\) Y (τ) of the non-Gaussian random process \(Y(t)\), using numerical methods and efficient solution algorithms, obtain the autocorrelation coefficient matrix \(\rho\) X (τ) of the potential Gaussian random process \(X(t)\), and establish the corresponding relationship between the non-Gaussian process and the potential Gaussian process through spline interpolation;

[0022] The key technology of this step lies in the combination of the improved Mehler formula and spline interpolation method, which improves the efficiency of solving the equivalent correlation coefficient. The traditional numerical solution method has low efficiency, while through the improved scheme proposed by the present invention, the calculation efficiency can be significantly improved while ensuring the accuracy, especially when dealing with large-scale systems, the calculation time can be effectively shortened.

[0023] S4. Through the autocorrelation coefficient matrix \(\rho\) of the potential Gaussian random process \(X(t)\) obtained by the above steps X (τ), calculate its autocorrelation function \(R\)X (τ) and the power spectral density function S X (ω), and generate the time history of the latent Gaussian random process X(t) using the spectral representation method. The spectral representation method uses the Fourier transform and random phase angles and is simulated using a computationally simple and efficient algorithm.

[0024] This step combines the advantages of the spectral representation method in Gaussian random process simulation. By calculating the autocorrelation coefficient matrix and autocorrelation function, the power spectral density of the latent Gaussian random process is generated, and then the time history is simulated through the spectral representation method. This method is not only applicable to Gaussian processes but can also provide an accurate basis for subsequent non-Gaussian process simulations.

[0025] S5. Convert the latent Gaussian random process X(t) into the target non-Gaussian random process Y(t) through a memoryless nonlinear transformation method. Specifically: perform a nonlinear transformation on the latent Gaussian random process X(t) through the parameters and quantile function of the FMKL generalized lambda distribution to obtain the target non-Gaussian random process Y(t). This transformation process depends on the preset skewness and kurtosis target values to ensure that the generated non-Gaussian process has the target statistical characteristics.

[0026] This step is one of the core innovations of the present invention. By combining a memoryless nonlinear transformation, the latent Gaussian random process X(t) can be converted into the target non-Gaussian random process Y(t), thereby maintaining the statistical characteristics such as skewness and kurtosis of the target non-Gaussian process. This process avoids the rough approximation of the target distribution in traditional methods, making the final simulation results more accurate, especially providing a better simulation effect for complex non-Gaussian characteristics (such as skewness and heavy tails).

[0027] Preferably, step S1 includes the following specific operations:

[0028] Calculate the autocorrelation function R Y (τ) through the power spectral density S Y (ω) of the target non-Gaussian random process. Specifically:

[0029]

[0030] where ω is the circular frequency; τ is the time difference; S Y (ω) is the power spectral density function of the target non-Gaussian random process; R Y (τ) is the autocorrelation function.

[0031] According to the obtained autocorrelation function R Y (τ) of the target non-Gaussian random process, further calculate the autocorrelation coefficient matrix ρ Y (τ), and its calculation formula is:

[0032]

[0033] wherein, R Y (0) is the value of the autocorrelation function of the target non-Gaussian random process at zero time; is the variance of the target non-Gaussian process.

[0034] Preferably, step S2 includes the following specific operations:

[0035] Based on the mean, variance, skewness, and kurtosis of the process Y(t) of the target non-Gaussian random process, establish a conversion relationship using the FMKL generalized lambda distribution, and solve the parameters λ1, λ2, λ3, λ4 of the FMKL generalized lambda distribution by the given skewness α′3 and kurtosis α′4. The parameter solving formula is:

[0036]

[0037]

[0038] wherein, M k is the k-th central moment of the FKML generalized Lambda distribution; β(.) represents the beta function, and both parameters inside must be positive, which means that if the distribution has a finite k-th moment, then min(λ3, λ4) > -1 / k. By the given statistical moments of the target non-Gaussian random process, using the parametric form of the FMKL generalized lambda distribution, obtain the conversion parameters that meet the target skewness and kurtosis.

[0039] Precisely solve the parameters of the FMKL distribution through a traversal search algorithm. This method ensures that the statistical characteristics of the simulation results are consistent with the target process by optimizing the matching of the theoretical skewness and kurtosis.

[0040] Preferably, step S3 includes the following specific operations:

[0041] Calculate the maximum and minimum values of the autocorrelation coefficient matrix ρ Y (τ) of the non-Gaussian random process Y(t), and calculate the autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t) through an equivalent correlation coefficient solving method based on the Mehler formula. The calculation formula is:

[0042]

[0043] wherein, ρ ij is the correlation coefficient of the non-Gaussian correlated random process; ρ ij * is the equivalent correlation coefficient of the Gaussian correlated random process; F i -1is the inverse function of the cumulative distribution function of a non-Gaussian correlated random process; μ i and σ i are the mean and standard deviation of the non-Gaussian correlated random process; Φ is the standard normal cumulative distribution function; x GH,l and w GH,l are the nodes and weight coefficients of the Gauss-Hermite quadrature formula respectively; d i is the number of quadrature nodes; m0 is the number of truncation terms.

[0044] Through numerical calculation and interpolation methods, the efficiency of the solution process is further improved.

[0045] Preferably, step S4 includes the following specific operations:

[0046] According to the autocorrelation coefficient matrix ρ X (τ) of the calculated latent Gaussian random process X(t), calculate its autocorrelation function R X (τ) and power spectral density function S X (ω), and their calculation formulas are:

[0047]

[0048] Correct the calculated power spectral density function S X (ω). If S X (ω) has negative values, then through the correction formula:

[0049]

[0050] where, R X (0) is the value of the autocorrelation function of the latent Gaussian random process at zero time; is the variance of the latent Gaussian random process; then ensure that the power spectral density at all frequency points is positive, thus ensuring the physical rationality of the simulation process.

[0051] Preferably, step S5 includes the following specific operations:

[0052] Generate the time history of the latent Gaussian random process X(t) through the spectral representation method, specifically:

[0053]

[0054] where, ω k is the frequency point; is the random phase angle; Δω is the frequency resolution. This step uses the spectral representation method to transform the spectral representation of the Gaussian process into a time-domain random process, thus completing the generation of the latent Gaussian random process. k represents the index of the random phase angle, and N represents the total number of random phase angles.

[0055] Preferably, the time history generated by the spectral representation method is further subjected to a non - linear transformation to obtain the target non - Gaussian random process Y(t), and the transformation formula is:

[0056]

[0057] where Φ represents the standard normal cumulative distribution function, and λ1, λ2, λ3, λ4 are parameters calculated by the FMKL generalized lambda distribution. This step completes the non - linear conversion from the latent Gaussian random process to the target non - Gaussian random process.

[0058] Preferably, the conversion relationship between step S1 and step S2 is further optimized as:

[0059] The autocorrelation coefficient matrix ρ Y (τ) of the target non - Gaussian random process calculated according to step S1 is combined with the marginal statistical moments of the target non - Gaussian process to further constrain the parameter range of the FMKL generalized lambda distribution, so as to ensure that the model can more accurately approximate the statistical characteristics of the target process;

[0060] By carefully adjusting the target values of skewness and kurtosis of the target non - Gaussian random process, the parameter estimation process of the FMKL distribution is further optimized to ensure that each step in the conversion relationship can accurately reflect the non - Gaussian characteristics in the actual data.

[0061] Through these steps, the method of the present invention provides an accurate and efficient framework for simulating non - Gaussian random processes in reality, especially suitable for scenarios in the engineering field that require accurate simulation of external loads such as wind and earthquake.

[0062] In the above - mentioned technical solution, the technical effects and advantages provided by the present invention are:

[0063] By introducing the combination of the FMKL generalized lambda distribution and the memory - less non - linear transformation, the present invention can effectively simulate the non - Gaussian characteristics commonly existing in actual engineering. Traditional Gaussian random process models often cannot accurately capture non - Gaussian characteristics such as skewness and heavy tails when dealing with complex natural phenomena (such as wind speed, seismic waves, etc.), while the method of the present invention ensures the accuracy of the simulation results through flexible distribution conversion and improved solution methods. In specific implementations, whether it is wind load, seismic waves, or the wind field of engineering structures such as bridges and transmission towers, the simulation results can accurately reflect the actual statistical characteristics of these non - Gaussian processes, greatly improving the simulation accuracy of the impact of wind load and seismic load on structures, and thus enhancing the reliability and safety in engineering design.

[0064] The present invention introduces an improved Mehler formula and spline interpolation method into traditional numerical calculation methods, greatly improving the efficiency of calculating the equivalent correlation coefficient. In traditional methods, the calculation of the equivalent correlation coefficient is usually cumbersome, and the computational effort is huge when dealing with complex stochastic processes, resulting in low efficiency. Through the efficient calculation method of the present invention, not only the calculation accuracy is ensured, but also when dealing with large-scale engineering structures, the calculation time can be significantly reduced, the use of computing resources can be optimized, and it is applicable to engineering application scenarios that require efficient simulation. In wind load, seismic wave, and wind field simulations, the efficient calculation method of the present invention makes it possible to simulate complex non-Gaussian processes.

[0065] The present invention adopts a strategy that combines the FMKL generalized lambda distribution and memoryless nonlinear transformation, greatly enhancing the adaptability and flexibility of the simulation method. The FMKL generalized lambda distribution has a wide range of applications and can fit various types of non-Gaussian distributions, which enables the method of the present invention to be widely used in different types of engineering projects. For example, for the complex non-Gaussian characteristics exhibited by natural phenomena such as seismic waves and wind speeds, the simulation method provided by the present invention can flexibly adjust parameters to make the simulation results accurately conform to the target distribution characteristics. At the same time, by introducing memoryless nonlinear transformation, the conversion process from Gaussian to non-Gaussian can be directly processed, making the model more flexible and easier to adapt to various actual engineering requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings required to be used in the embodiments. Obviously, the drawings described below are only some embodiments recorded in the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings.

[0067] Figure 1 It is a flowchart of a method for simulating a stationary non-Gaussian random process according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0068] Now, the exemplary embodiments will be described more comprehensively with reference to the accompanying drawings. However, the exemplary embodiments can be implemented in various forms and should not be construed as limited to the examples set forth herein; rather, these exemplary embodiments are provided so that the present disclosure will be more thorough and complete, and the concept of the exemplary embodiments will be fully conveyed to those skilled in the art.

[0069] The present invention provides a method for simulating a stationary non-Gaussian random process as shown in Figure 1 and includes the following steps:

[0070] S1. Through the power spectral density function S of the target non-Gaussian random process Y(ω) is transformed to obtain the autocorrelation function R Y (τ), and the autocorrelation coefficient matrix ρ Y (τ) of the target non-Gaussian random process Y(t) is obtained from the autocorrelation function R Y (τ), where the autocorrelation function R Y (τ) mentioned in the step is calculated by using Fourier transform;

[0071] This step realizes the transformation from the target non-Gaussian spectral density function to the autocorrelation function. By using Fourier transform, the power spectral density S Y (ω) can be efficiently transformed into the autocorrelation function R Y (τ), thus providing basic data for further simulation work.

[0072] S2. Based on the statistical moments such as the mean, variance, skewness, and kurtosis of the target non-Gaussian process Y(t), use the FMKL generalized lambda distribution to establish its corresponding transformation relationship, and obtain the parameters λ1, λ2, λ3, λ4 of the FMKL generalized lambda distribution; among them, the solution of the parameters mentioned in the step adopts the traversal search method, and the optimal parameter values are obtained by matching with the theoretical skewness and kurtosis;

[0073] This step innovatively combines the FMKL generalized lambda distribution to solve the problems of limited applicable range and low usage efficiency existing in the commonly used transformation methods (such as the Hermite model and Johnson distribution) in the simulation of non-Gaussian random processes. By using the statistical moments of the target process and traversal search to efficiently and accurately solve the parameters of the FMKL generalized lambda distribution, the accuracy and efficiency of the simulation are guaranteed.

[0074] Step S2 includes the following specific operations:

[0075] Based on the mean, variance, skewness, and kurtosis of the target non-Gaussian random process Y(t), establish a transformation relationship using the FMKL generalized lambda distribution. Solve the parameters λ1, λ2, λ3, λ4 of the FMKL generalized lambda distribution by the given skewness α′3 and kurtosis α′4, and the parameter solution formula is:

[0076]

[0077] where, M kis the k-th order central moment of the FKML generalized Lambda distribution; β(.) represents the beta function, and both parameters inside must be positive, which means that if the distribution has a finite k-th moment, then min(λ3, λ4) > -1 / k. This step obtains the conversion parameters that conform to the target skewness and kurtosis by using the parametric form of the FMKL generalized lambda distribution given the statistical moments of the target non-Gaussian random process.

[0078] The parameters of the FMKL distribution are accurately solved through an exhaustive search algorithm. This method ensures that the statistical characteristics of the simulation results are consistent with the target process by optimizing the matching of the theoretical skewness and kurtosis.

[0079] The conversion relationship between step S1 and step S2 is further optimized as:

[0080] The autocorrelation coefficient matrix ρ Y (τ) of the target non-Gaussian process calculated according to step S1 is combined with the marginal statistical moments of the target non-Gaussian process to further constrain the parameter range of the FMKL generalized lambda distribution, so as to ensure that the model can more accurately approximate the statistical characteristics of the target process.

[0081] By carefully adjusting the target values of the skewness and kurtosis of the target non-Gaussian random process, the parameter estimation process of the FMKL distribution is further optimized to ensure that each step in the conversion relationship can accurately reflect the non-Gaussian characteristics in the actual data.

[0082] Through these steps, the method of the present invention provides an accurate and efficient framework for simulating non-Gaussian random processes in reality, especially applicable to scenarios in the engineering field that require accurate simulation of external loads such as wind and earthquake.

[0083] S3. Based on the improved Mehler formula, an efficient method for solving the equivalent correlation coefficient is proposed. Specifically: by calculating the maximum and minimum values of the autocorrelation coefficient matrix ρ Y (τ) of the non-Gaussian random process Y(t), using numerical methods and efficient solution algorithms, the autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t) is obtained, and the corresponding relationship between the non-Gaussian process and the potential Gaussian process is established through spline interpolation.

[0084] The key technology of this step lies in improving the solution efficiency of the equivalent correlation coefficient through the combination of the improved Mehler formula and spline interpolation. The traditional numerical solution method has low efficiency, while through the improved scheme proposed by the present invention, the calculation efficiency can be significantly improved while ensuring the accuracy, especially when dealing with large-scale systems, the calculation time can be effectively shortened.

[0085] Step S3 includes the following specific operations:

[0086] Calculate the maximum and minimum values of the autocorrelation coefficient matrix ρ Y (τ) of the non-Gaussian random process Y(t), and calculate the autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t) through an equivalent correlation coefficient solving method based on the Mehler formula. Its calculation formula is:

[0087]

[0088] where ρ ij is the correlation coefficient of the non-Gaussian correlated random process; ρ ij * is the equivalent correlation coefficient of the Gaussian correlated random process; F i -1 is the inverse function of the cumulative distribution function of the non-Gaussian correlated random process; μ i and σ i are the mean and standard deviation of the non-Gaussian correlated random process; Φ is the standard normal cumulative distribution function; x GH,l and w GH,l are the nodes and weight coefficients of the Gauss-Hermite quadrature formula respectively; d i is the number of quadrature nodes; m0 is the number of truncation terms.

[0089] The efficiency of the solving process is further improved through numerical calculation and interpolation methods.

[0090] S4. Calculate the autocorrelation function R X (τ) and the power spectral density function S X (ω) of the autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t) obtained through the above steps, and generate the time history of the potential Gaussian random process X(t) using the spectral representation method. The spectral representation method uses Fourier transform and random phase angles and is simulated using a computationally simple and effective algorithm.

[0091] This step combines the advantages of the spectral representation method in Gaussian random process simulation. By calculating the obtained autocorrelation coefficient matrix, the power spectral density of the potential Gaussian random process is generated, and then the time history is simulated through the spectral representation method. This method is not only applicable to Gaussian processes but can also provide an accurate basis for subsequent non-Gaussian process simulations.

[0092] Step S4 includes the following specific operations:

[0093] According to the calculated autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t), calculate its autocorrelation function R X(τ) and the power spectral density function S X (ω), and its calculation formula is:

[0094]

[0095] For the calculated power spectral density function S X (ω), if S X (ω) has negative values, then through the correction formula:

[0096]

[0097] where R X (0) is the value of the autocorrelation function of the latent Gaussian random process at zero time; is the variance of the latent Gaussian random process; then ensure that the power spectral density at all frequency points is positive, so as to ensure the physical rationality of the simulation process.

[0098] S5. Convert the latent Gaussian random process X(t) into the target non-Gaussian random process Y(t) by the memoryless nonlinear transformation method. Specifically: perform a nonlinear transformation on the latent Gaussian random process X(t) through the parameters and quantile function of the FMKL generalized lambda distribution to obtain the target non-Gaussian random process Y(t). This transformation process depends on the preset skewness and kurtosis target values to ensure that the generated non-Gaussian process has the target statistical characteristics.

[0099] This step is one of the core innovations of the present invention. By combining the memoryless nonlinear transformation, the latent Gaussian random process X(t) can be converted into the target non-Gaussian random process Y(t), and then the statistical characteristics such as skewness and kurtosis of the target non-Gaussian process can be maintained. This process avoids the rough approximation of the target distribution in the traditional method, making the final simulation result more accurate, especially providing a better simulation effect for complex non-Gaussian characteristics (such as skewness and heavy tails).

[0100] Step S5 includes the following specific operations:

[0101] Generate the time history of the latent Gaussian random process X(t) by the spectral representation method. Specifically:

[0102]

[0103] where ω k is the frequency point; is the random phase angle; Δω is the frequency resolution. This step uses the spectral representation method to convert the spectral representation of the Gaussian process into a time-domain random process, thus completing the generation of the latent Gaussian random process. k represents the index of the random phase angle, and N represents the total number of random phase angles.

[0104] The time history generated by the spectral representation method is further subjected to a non-linear transformation to obtain the target non-Gaussian random process Y(t), and the transformation formula is:

[0105]

[0106] Among them, Φ represents the standard normal cumulative distribution function, and λ1, λ2, λ3, λ4 are parameters calculated by the FMKL generalized lambda distribution. This step completes the non-linear transformation from the potential Gaussian random process to the target non-Gaussian random process.

[0107] Specific implementation method 1: An implementation method based on engineering wind load simulation.

[0108] Wind load is an important load generated by engineering structures under the action of wind. Especially in the structural design of high-rise buildings, long-span bridges, transmission towers, etc., the accurate simulation of wind load is crucial for the safety and stability of the structure. Usually, the wind speed process is modeled as a random process. Among them, the probability distribution of wind speed usually does not follow the Gaussian distribution, but shows non-Gaussian characteristics. Therefore, the traditional Gaussian random process model cannot accurately reflect the true characteristics of wind speed, and the non-Gaussian random process simulation method of the present invention provides a new solution.

[0109] In the implementation process, first, it is necessary to determine the power spectral density function of the target wind speed, which is usually obtained through measured wind speed data or a standardized model of wind speed. The power spectral density is an important function describing the frequency domain characteristics of wind speed and can provide the energy distribution of wind speed changing with frequency. In step S1, according to the power spectral density function, it is converted into an autocorrelation function by using the Fourier transform method. The autocorrelation function describes the correlation between wind speeds at different time points and is an important manifestation of the time domain characteristics of the wind speed process. Converting the power spectral density into an autocorrelation function through the Fourier transform enables the simulation process to be transformed from the frequency domain to the time domain, facilitating further processing and simulation.

[0110] Next, in step S2, based on the statistical moments (mean, variance, skewness, kurtosis, etc.) of the target wind speed, a transformation is performed using the FMKL generalized lambda distribution. The FMKL generalized lambda distribution is a model that can flexibly fit various non-Gaussian process distributions and can determine suitable transformation parameters according to the statistical characteristics of the target process. In this step, by calculating the mean, variance, skewness, and kurtosis of the target wind speed process, the corresponding parameters are solved using the parametric formula of the FMKL generalized lambda distribution. The introduction of the FMKL distribution solves the problems that existing non-Gaussian process models (such as the Hermite model and Johnson distribution) cannot fully cover the complexity of natural phenomena such as wind speed and the low model usage efficiency. By reasonably selecting these parameters, it is possible to ensure that the simulation process has the same statistical characteristics as the target wind speed, thereby improving the simulation accuracy.

[0111] After completing the parameter solution, in step S3, the autocorrelation coefficient matrix is calculated through the improved Mehler formula. The equivalent correlation coefficient is an important parameter describing the correlation between non-Gaussian processes and Gaussian processes and plays a key role in non-Gaussian process simulation. Traditional methods for calculating the equivalent correlation coefficient are often cumbersome and inefficient, while the present invention provides an efficient and accurate calculation method by combining the Mehler formula and the spline interpolation method. This method can significantly improve the calculation efficiency while ensuring the calculation accuracy, especially in dealing with complex high-dimensional non-Gaussian processes, which can effectively reduce the amount of calculation. Through this step, the autocorrelation coefficient matrix of the latent Gaussian process can be obtained, providing a basis for subsequent simulations.

[0112] In step S4, the time history of the latent Gaussian random process is generated through the spectral representation method. The spectral representation method is an effective method commonly used to generate the time history of stationary random processes. By representing the autocorrelation function as a weighted sum of a series of frequency components, a random process in the time domain is generated. In this step, first, the power spectral density function of the latent Gaussian random process is calculated based on the autocorrelation coefficient matrix, and its time-domain representation is obtained using the Fourier transform method. Through the spectral representation method, a Gaussian random process time history that conforms to the target autocorrelation characteristics can be obtained, providing a basis for subsequent non-Gaussian process transformation.

[0113] After generating the time history of the latent Gaussian random process, step S5 converts it into the target non-Gaussian random process through a memoryless non-linear transformation. The memoryless non-linear transformation is an effective method commonly used in non-Gaussian process simulation. By appropriately transforming the Gaussian process, it can have the statistical characteristics of the target non-Gaussian process. Specifically, the latent Gaussian process is converted into the target non-Gaussian process through the parameters of the FMKL generalized lambda distribution and its quantile function. This process can accurately map features such as the skewness and kurtosis of the target wind speed into the simulation results, thus ensuring that the simulation results have real non-Gaussian characteristics.

[0114] Through these steps, the simulation of wind loads can accurately reproduce the complex characteristics of the actual wind speed process, providing a more accurate load model for structural design, thereby improving the level of wind-resistant design of structures. Especially in structures that are highly sensitive to wind loads, such as high-rise buildings, transmission towers, and long-span bridges, the method of the present invention can effectively improve the accuracy of wind load simulation, and then optimize the design and safety assessment of structures.

[0115] Specific Embodiment 2: Embodiment of seismic wave simulation.

[0116] Seismic waves are dynamic loads generated by seismic events and are crucial for the impact on structures such as buildings, bridges, and tunnels. In earthquake engineering, the random process of ground motion usually has strong non-Gaussian characteristics, so an efficient and accurate non-Gaussian process simulation method needs to be used for modeling. Traditional simulation methods are usually based on Gaussian processes, which are not fully applicable when simulating seismic waves. To solve this problem, the present invention provides a new non-Gaussian random process simulation method that can more accurately simulate seismic waves with non-Gaussian characteristics.

[0117] First, the power spectral density function of seismic waves is usually obtained through historical earthquake data or seismic wave models, which describes the frequency-domain characteristics of seismic waves. In step S1, the power spectral density is converted into the autocorrelation function through Fourier transform, and the autocorrelation function reflects the correlation between different time points of seismic waves. The autocorrelation function is the basis of the simulation process and can provide data on the time-domain characteristics for subsequent simulations. Through Fourier transform, the frequency-domain information of seismic waves can be efficiently converted into time-domain information, providing the parameters required for subsequent non-Gaussian process simulations.

[0118] In step S2, the FMKL generalized lambda distribution is used to solve the parameters according to the statistical characteristics of seismic waves (such as mean, variance, skewness, and kurtosis, etc.). The skewness and kurtosis of seismic waves are often large, which makes their distribution have obvious non-Gaussian characteristics. Through the parametric formula of the FMKL generalized lambda distribution, these statistical moments can be converted into distribution parameters that conform to the characteristics of the target seismic waves, so as to ensure that the simulation results can accurately reproduce the non-Gaussian characteristics of seismic waves. The FMKL generalized lambda distribution can flexibly fit various types of non-Gaussian distributions, so it is an ideal tool to solve such problems.

[0119] After obtaining the parameters of the FMKL distribution, step S3 calculates the autocorrelation coefficient matrix through the improved Mehler formula. By this method, the correlation between the target non-Gaussian seismic wave process and the potential Gaussian process can be accurately transformed. Compared with the traditional method, the method of the present invention has significantly improved in terms of computational efficiency and accuracy. Especially when dealing with large-scale data, it can effectively reduce the amount of calculation and significantly improve the simulation efficiency.

[0120] Step S4 uses the spectral representation method to generate the potential Gaussian seismic wave time history. The spectral representation method is a commonly used random process simulation method that converts the power spectral density into a random process time history in the time domain. Through the power spectral density function calculated according to the autocorrelation coefficient matrix, a potential Gaussian random process consistent with the autocorrelation characteristics of the target seismic wave process can be generated. This process provides the basic data for the subsequent non-Gaussian transformation and ensures that the time history of the seismic wave has real frequency domain characteristics.

[0121] Finally, step S5 converts the potential Gaussian seismic wave time history into the target non-Gaussian seismic wave time history through a memoryless nonlinear transformation. This nonlinear transformation uses the parameters of the FMKL generalized lambda distribution and its quantile function to convert the potential Gaussian process into the target non-Gaussian process by adjusting statistical characteristics such as skewness and kurtosis. Through this process, it can be ensured that the simulated seismic waves have non-Gaussian characteristics matching the actual seismic waves, so as to better reflect the impact of earthquakes on structures.

[0122] The application of this non-Gaussian process simulation method based on the FMKL generalized lambda distribution and the Mehler formula in earthquake engineering can significantly improve the accuracy and efficiency of seismic wave simulation, and has important application value for the assessment of the impact of seismic waves on structures, seismic design, and structural safety analysis.

[0123] Specific implementation method three: Simulation of random wind fields in engineering structures such as bridges and transmission towers.

[0124] In the design of engineering structures such as bridges and transmission towers, wind load is a very important consideration. Especially for long-span bridges and transmission towers in mountainous areas, the influence of wind load is often dominant. Due to the non-Gaussian characteristics of the wind field, traditional Gaussian random process models cannot accurately simulate the real behavior of the wind field of structures such as bridges and transmission towers. Therefore, the non-Gaussian random process simulation method of the present invention can greatly improve the accuracy of wind load simulation and provide more reliable data support for the design of engineering structures such as bridges and transmission towers.

[0125] In the implementation process, first, obtain the power spectral density function of the wind speed of engineering structures such as the target bridge and transmission tower. This process can be obtained through measured wind speed data or based on the wind speed standardization model. In step S1, the power spectral density is converted into the autocorrelation function through Fourier transform. The core of this step is to convert the frequency-domain characteristics of the wind speed into time-domain characteristics, so that the simulation process can be processed in the time domain. Through the autocorrelation function, the correlation information of the wind speed process can be further obtained, providing key data for subsequent simulations.

[0126] In step S2, by calculating statistical moments such as the mean, variance, skewness, and kurtosis of the target wind speed process, the FMKL generalized lambda distribution is used to parameterize these statistical characteristics. By calculating the parameters of the FMKL distribution, a distribution model that conforms to the statistical characteristics of the target wind speed process can be obtained. The FMKL generalized lambda distribution can fit various types of non-Gaussian distributions, so it has good adaptability when dealing with natural phenomena such as wind speed.

[0127] After obtaining the parameters, in step S3, the autocorrelation coefficient matrix is calculated through the improved Mehler formula, and the autocorrelation coefficient of the latent Gaussian random process is calculated using an efficient numerical method. Through this process, the correlation between the non-Gaussian process and the Gaussian process can be accurately transformed, ensuring that the simulated wind speed process has the correct statistical characteristics in both the time domain and the frequency domain.

[0128] In step S4, the spectral representation method is used to generate the time history of the latent Gaussian wind field. In this process, through the spectral representation method, a time history of the latent Gaussian random process consistent with the autocorrelation characteristics of the target wind speed process can be generated according to the autocorrelation coefficient matrix. This time history can be used as the basis for wind load simulation, providing key data for structural analysis.

[0129] Finally, in step S5, the latent Gaussian wind field process is converted into the target non-Gaussian wind field process through a nonlinear transformation. This step converts the latent Gaussian process into the target non-Gaussian process through the parameters of the FMKL generalized lambda distribution and its quantile function, thus ensuring that the simulated wind field process has real non-Gaussian characteristics such as skewness and kurtosis.

[0130] The application of this non-Gaussian wind field simulation method in the design of engineering structures such as bridges and transmission towers can provide more accurate wind load simulation for the structures, thereby effectively improving the safety assessment and wind resistance design of the structures.

[0131] By introducing the combination of the FMKL generalized lambda distribution and the memoryless nonlinear transformation, the present invention can effectively simulate the non-Gaussian characteristics commonly existing in practical engineering. Traditional Gaussian random process models often fail to accurately capture non-Gaussian characteristics such as skewness and heavy tails when dealing with complex natural phenomena (such as wind speed, seismic waves, etc.), while the method of the present invention ensures the accuracy of the simulation results through flexible distribution transformation and improved solution methods. In specific implementations, whether it is wind load, seismic wave or the wind field of engineering structures such as bridges and transmission towers, the simulation results can accurately reflect the actual statistical characteristics of these non-Gaussian processes, greatly improving the simulation accuracy of the influence of wind load and seismic load on the structure, and thus enhancing the reliability and safety in engineering design.

[0132] The present invention introduces an improved Mehler formula and spline interpolation method into traditional numerical calculation methods, greatly improving the efficiency of calculating the equivalent correlation coefficient. In traditional methods, the calculation of the equivalent correlation coefficient is usually cumbersome, and the calculation amount is huge and the efficiency is low when dealing with high-dimensional complex random processes. However, through the efficient calculation method of the present invention, not only the calculation accuracy is guaranteed, but also when dealing with large-scale engineering structures, the calculation time can be significantly reduced, the use of calculation resources can be optimized, and it is applicable to engineering application scenarios that require efficient simulation. In wind load, seismic wave and wind field simulation, the efficient calculation method of the present invention makes it possible to simulate complex non-Gaussian processes.

[0133] The present invention adopts a strategy of combining the FMKL generalized lambda distribution and the memoryless nonlinear transformation, greatly enhancing the adaptability and flexibility of the simulation method. The FMKL generalized lambda distribution has a wide range of applications and can fit various types of non-Gaussian distributions, which enables the method of the present invention to be widely used in different types of engineering projects. For example, for the complex non-Gaussian characteristics exhibited by natural phenomena such as seismic waves and wind speed, the simulation method provided by the present invention can flexibly adjust parameters to make the simulation results accurately conform to the target distribution characteristics. At the same time, by introducing the memoryless nonlinear transformation, the conversion process from Gaussian to non-Gaussian can be directly processed, making the model more flexible and easy to adapt to various actual engineering requirements.

[0134] Only some exemplary embodiments of the present invention have been described by way of illustration. Without doubt, for those of ordinary skill in the art, the described embodiments can be modified in various different ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and description are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0135] It should be noted that in this text, if there are relational terms such as first and second, they are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements not only includes those elements, but also includes other elements not expressly listed, or further includes elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising one..." does not exclude the existence of additional identical elements in the process, method, article or device comprising the element.

[0136] It should be understood that in various embodiments of the present application, the magnitudes of the serial numbers of the above processes do not mean the order of execution is prior or subsequent. The order of execution of each process should be determined by its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.

[0137] Those of ordinary skill in the art can realize that the units and algorithm steps of the examples described in conjunction with the embodiments disclosed in this text can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are executed in a hardware or software manner depends on the specific application and design constraints of the technical solution. Professional technicians can use different methods to implement the described functions for each specific application, but such implementation should not be considered to exceed the scope of the present application.

[0138] Those skilled in the art can clearly understand that for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the foregoing method embodiments and will not be elaborated herein.

[0139] In several embodiments provided by the present application, it should be understood that the disclosed systems, devices, and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative. For example, the division of the units is only a logical function division. In actual implementation, there may be other division methods. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the displayed or discussed couplings or direct couplings or communication connections between each other can be through some interfaces. The indirect couplings or communication connections of the devices or units can be in electrical, mechanical, or other forms.

[0140] The units described as separate components may or may not be physically separated. The components displayed as units may or may not be physical units, that is, they can be located in one place or distributed to multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0141] In addition, in each embodiment of the present application, the functional units can be integrated in a processing unit, or each unit can exist physically alone, or two or more units can be integrated in one unit.

[0142] If the functions are implemented in the form of software function units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, in essence, or the part that contributes to the prior art or a part of this technical solution can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in each embodiment of the present application. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs that can store program codes.

[0143] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of changes or substitutions, which should all be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A method for simulating a stationary non-Gaussian random process, characterized in that, It includes the following steps: S1. Obtain the autocorrelation function by converting the power spectral density function of the target non-Gaussian random process, and obtain the autocorrelation coefficient matrix of the target non-Gaussian random process from the autocorrelation function. Among them, the autocorrelation function described in this step is calculated by Fourier transform; S2. Based on the statistical moments of the target non-Gaussian process, establish its corresponding conversion relationship using the FMKL generalized lambda distribution to obtain the parameters of the FMKL generalized lambda distribution; among them, the solution of the parameters described in this step uses the exhaustive search method, and the optimal parameter value is obtained by matching with the theoretical skewness and kurtosis; S3. By calculating the maximum and minimum values of the autocorrelation coefficient matrix of the non-Gaussian random process, use numerical methods and efficient solution algorithms to obtain the autocorrelation coefficient matrix of the potential Gaussian random process, and establish the corresponding relationship between the non-Gaussian process and the potential Gaussian process by spline interpolation method; S4. Calculate the autocorrelation function and power spectral density function of the potential Gaussian random process according to its autocorrelation coefficient matrix, and generate the time history of the potential Gaussian random process using the spectral representation method; among them, the spectral representation method uses Fourier transform and random phase angle, and is simulated using a computationally simple and effective algorithm; S5. Convert the potential Gaussian random process into the target non-Gaussian random process by the memoryless nonlinear transformation method; specifically: perform a nonlinear transformation on the potential Gaussian random process through the parameters of the FMKL generalized lambda distribution and its quantile function to obtain the target non-Gaussian random process. This transformation process depends on the preset skewness and kurtosis target values to ensure that the generated non-Gaussian process has the target statistical characteristics.

2. The method for simulating a stationary non-Gaussian random process according to claim 1, wherein, Step S1 includes the following specific operations: Calculate the autocorrelation function \(R_{\left\langle 0000002\right\rangle}(\tau)\) through the power spectral density \(S_{\left\langle 0000001\right\rangle}(\omega)\) of the target non-Gaussian random process, specifically as follows: Y (ω) Calculate the autocorrelation function R Y (τ), specifically as follows: where ω is the circular frequency; τ is the time difference; S Y (ω) is the power spectral density function of the target non-Gaussian random process; R Y (τ) is the autocorrelation function; According to the obtained autocorrelation function \(R\) of the target non-Gaussian random process Y (\(\tau\)), further calculate the autocorrelation coefficient matrix \(\rho\) Y (\(\tau\)), and its calculation formula is: Among them, R Y (0) is the value of the autocorrelation function of the target non-Gaussian random process at zero time; is the variance of the target non-Gaussian process.

3. A method for simulating a stationary non-Gaussian random process according to claim 2, characterized in that, Step S2 includes the following specific operations: Based on the mean, variance, skewness and kurtosis of the process Y(t) of the target non-Gaussian random process, establish a conversion relationship using the FMKL generalized lambda distribution, and solve the parameters λ1, λ2, λ3, λ4 of the FMKL generalized lambda distribution by the given skewness α′3 and kurtosis α′4. The parameter solution formula is: where M k is the k-th central moment of the FKML generalized Lambda distribution; β(.) represents the beta function, and both parameters inside must be positive, which means that if the distribution has a finite k-th moment, then min(λ3, λ4) > -1 / k; by giving the statistical moments of the target non-Gaussian random process and using the parametric form of the FMKL generalized lambda distribution, the conversion parameters that meet the target skewness and kurtosis are obtained.

4. A method for simulating a stationary non-Gaussian random process according to claim 3, wherein Step S3 includes the following specific operations: Calculate the maximum and minimum values of the autocorrelation coefficient matrix ρ Y (τ) of the non-Gaussian random process Y(r), and calculate the autocorrelation coefficient matrix ρ X (τ) of the potential Gaussian random process X(t) through an equivalent correlation coefficient solution method based on the Mehler formula. Its calculation formula is: where ρ ij is the correlation coefficient of the non-Gaussian correlated random process; ρ ij * is the equivalent correlation coefficient of the Gaussian correlated random process; F i -1 is the inverse function of the cumulative distribution function of the non-Gaussian correlated random process; μ i and σ i are the mean and standard deviation of the non-Gaussian correlated random process; Φ is the standard normal cumulative distribution function; x GH,l and w GH,l are the nodes and weight coefficients of the Gauss-Hermite quadrature formula respectively; d i is the number of quadrature nodes; m0 is the number of truncation terms; Through numerical calculation and interpolation methods, the efficiency of the solution process is further improved.

5. A method for simulating a stationary non-Gaussian random process according to claim 4, characterized in that, Step S4 includes the following specific operations: According to the autocorrelation coefficient matrix ρ of the calculated potential Gaussian random process X(t) X (τ), calculate its autocorrelation function R X (τ) and power spectral density function S X (ω), and its calculation formula is: Modify the calculated power spectral density function S X (ω). If S X (ω) has negative values, then use the correction formula: where R X (0) is the value of the autocorrelation function of the latent Gaussian random process at zero time; is the variance of the latent Gaussian random process; then ensure that the power spectral density at all frequency points is positive, so as to ensure the physical rationality of the simulation process.

6. A method for simulating a stationary non-Gaussian random process according to claim 5, characterized in that Step S5 includes the following specific operations: Generate the time history of the potential Gaussian random process X(t) by the spectral representation method, specifically: where ω k is the frequency point; is the random phase angle; Δω is the frequency resolution; the spectral representation of the Gaussian process is transformed into a time-domain random process by using the spectral representation method, so as to complete the generation of the latent Gaussian random process. k represents the index of the random phase angle, and N represents the total number of random phase angles.

7. A method for simulating a stationary non-Gaussian random process according to claim 6, characterized in that, Perform a further nonlinear transformation on the time history generated by the spectral representation method to obtain the target non-Gaussian random process Y(t). The transformation formula is: Among them, Φ represents the standard normal cumulative distribution function, and λ1, λ2, λ3, λ4 are the parameters calculated by the FMKL generalized lambda distribution, completing the nonlinear conversion from the potential Gaussian random process to the target non-Gaussian random process.

8. A method for simulating a stationary non-Gaussian random process according to claim 2, characterized in that The conversion relationship between Step S1 and Step S2 is further optimized as: The autocorrelation coefficient matrix ρ of the target non-Gaussian random process calculated according to step S1 Y (τ) is combined with the marginal statistical moments of the target non-Gaussian process to further constrain the parameter range of the FMKL generalized lambda distribution, so as to ensure that the model can more accurately approximate the statistical characteristics of the target process; By carefully adjusting the skewness and kurtosis target values, further optimize the parameter estimation process of the FMKL distribution to ensure that each step in the conversion relationship can accurately reflect the non-Gaussian characteristics in the actual data.

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