Method and system for stationary non-gaussian wind pressure simulation based on machine learning enhanced hermite polynomial model

Abstract

This invention relates to a method and system for simulating stationary non-Gaussian wind pressure based on a machine learning-enhanced Hermite multinomial model. First, a multi-input, single-output machine learning model is constructed to determine the statistical moments required in the transformation function of the proposed method. Then, based on this, a neural network transformation model is established from a non-Gaussian power spectrum to a potential Gaussian power spectrum using a multi-input, multi-output model. Finally, an ML-EHPM model constructed based on dual machine learning models predicts the statistical moments required for the transformation function and the potential Gaussian power spectrum predicted by the Gaussian PSD prediction model, respectively. This potential Gaussian power spectrum representation is then used to simulate non-Gaussian wind pressure. Under conditions of strong non-Gaussian wind pressure, wind pressure exceeding the monotonic region, and bimodal wind pressure distribution, the ML-EHPM method can more realistically reproduce the target probability density function and power spectral density, significantly outperforming the traditional HPM method in simulation accuracy, especially in strong non-Gaussian samples.

Description

Technical Field

[0001] This invention belongs to the field of non-Gaussian wind pressure simulation technology, and relates to a stationary non-Gaussian wind pressure simulation method and system based on machine learning-enhanced Hermite polynomial model. The method introduces two machine learning models into the simulation process, which are used to predict the statistical moments of the transformation function from the tenth-order origin moment and the mean, and to convert the non-Gaussian power spectrum (TNPSD) to the potential Gaussian power spectrum (UGPSD). Background Technology

[0002] The wind pressure on the roof of low-rise buildings is mainly dominated by the ridge separation shear layer and the vortex in the roof corner area. Its instantaneous negative pressure peak has a short duration and high amplitude. Field measurements and multiple wind tunnel tests have shown that the probability distribution of the roof wind pressure coefficient is significantly negatively skewed, thick-tailed, or even bimodal, which exceeds the traditional Gaussian random process assumption.

[0003] Existing non-Gaussian wind pressure simulations mostly employ the "transformation process method," which first assumes a latent Gaussian process and then maps the Gaussian signal to the target non-Gaussian marginal distribution through a monotonic Hermite polynomial transform (HPM). However, when the measured wind pressure kurtosis is greater than 3 or bimodal phenomena occur, the monotonic transformation region becomes limited, requiring the introduction of higher-order moment estimation into the transformation function, which rapidly amplifies the error. Simultaneously, the latent Gaussian power spectrum (UGPSD) cannot be obtained analytically, necessitating iterative corrections that are computationally time-consuming and prone to distortion.

[0004] Therefore, there is an urgent need for a new method that does not rely on monotonic assumptions, can automatically match arbitrary kurtosis / skewness combinations, and can directly and quickly invert Gaussian power spectrum (UGPSD) from non-Gaussian power spectrum (TNPSD) to improve the simulation accuracy and efficiency of strong non-Gaussian roof wind pressure field. Summary of the Invention

[0005] In view of this, to address the problems of large higher-order moment errors and slow inversion of the potential Gaussian power spectrum caused by monotonic constraints in existing Hermite polynomial transforms under strong non-Gaussian and bimodal wind pressure conditions, resulting in time-consuming and easily distorted calculations, this invention provides a method and system for simulating stationary non-Gaussian wind pressure based on machine learning-enhanced Hermite polynomial models. This method is used for the rapid and accurate simulation of stationary non-Gaussian wind pressure. Based on the traditional moment-based HPM simulation method, two machine learning models are established to improve the accuracy and efficiency of the simulation.

[0006] To achieve the above objectives, the present invention provides the following technical solution:

[0007] A method for simulating stationary non-Gaussian wind pressure based on a machine learning-enhanced Hermite multinomial model includes the following steps:

[0008] S1. Construct a multi-input single-output BES-XGBoost model, and use the tenth-order origin moments ( ) and the mean of the transformation function As input features, the statistical moments of the remaining transformation functions ( , , , The output features are used for training to obtain the prediction model corresponding to the four statistical moments;

[0009] S2. Construct a multi-input multi-output (BPNN) model, and use the non-Gaussian PSD and the mean of the transformation function. and the statistical moments of the transformation function ( , , , Using ) as input features and Latent Gaussian PSD as output features, a prediction model for Latent Gaussian PSD is obtained after training.

[0010] S3. Based on the ML-EHPM model constructed in steps S1 and S2, predict the statistical moments required for the transformation function. , , , The potential Gaussian power spectrum predicted by the Gaussian PSD prediction model. Using this potential Gaussian power spectrum The notation method simulates non-Gaussian wind pressure.

[0011] Furthermore, step S1 specifically involves: calculating the first ten origin moments of the simulated points (…). ) and the mean of the transformation function The input is fed into the nested BES-XGBoost model trained in step S1 to predict the statistical moments required for the transformation function. , , , ).

[0012] Furthermore, step S2 specifically involves: normalizing the target non-Gaussian PSD of the simulation points using formula (16) to obtain... ,

[0013] (16)

[0014] Normalized non-Gaussian PSD power spectrum The statistical moments of the transformation function of the simulated points predicted by the BES-XGBoost model in step S1. , , , ) and the mean of the transformation function The input is fed into the trained BPNN model to obtain the desired latent Gaussian power spectrum. .

[0015] Furthermore, step S3 specifically involves: analyzing the potential Gaussian power spectrum from step S2. The matrix is ​​subjected to Cholesky decomposition, and Gaussian time history samples are generated using the spectral representation method of multivariate stationary random processes according to formula (17). , ,

[0016] (17)

[0017] Based on the statistical moments of the transformation function of the simulated points predicted in step S1, , , , Using formulas (16)-(19), Gaussian samples of the transformation function model under different conditions are transformed. Convert to non-Gaussian samples Non-Gaussian samples Inverse normalization yields the final non-Gaussian samples. .

[0018] A stationary non-Gaussian wind pressure simulation system based on machine learning-enhanced Hermite polynomial models includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, it implements the aforementioned stationary non-Gaussian wind pressure simulation method.

[0019] A storage medium on which a computer program is stored, which, when executed by a processor, implements the steps of the above-described method for simulating stationary non-Gaussian wind pressure.

[0020] The beneficial effects of this invention are as follows:

[0021] 1. The stationary non-Gaussian wind pressure simulation method based on machine learning-enhanced Hermite multinomial models disclosed in this invention constructs two machine learning models at two crucial stages of the simulation process to assist in simulating non-Gaussian wind pressure. First, a multi-input single-output BES-XGBoost machine learning model is constructed to determine the statistical moments required in the transformation function. Then, based on this, a neural network transformation model from multi-input multi-output non-Gaussian power spectrum (TNPSD) to potential Gaussian power spectrum (UGPSD) is established. Finally, the potential Gaussian power spectrum predicted by the model and the statistical moments required in the transformation function are substituted into the ML-EHPM model to simulate the corresponding wind pressure. The transformation from the tenth-order raw moment and mean to ML-EHPM statistical moments, and from TNPSD to UGPSD, achieved through machine learning models, has proven to be a practical, efficient, and accurate method. Under conditions of strong non-Gaussian wind pressure, wind pressure exceeding the monotonic region, and bimodal wind pressure distribution, the ML-EHPM method can more realistically reproduce the target probability density function and power spectral density. Its simulation accuracy in both aspects significantly surpasses that of traditional HPM methods, especially in strongly non-Gaussian samples. When simulating multi-point rooftop wind pressure fields, the proposed method consistently demonstrates high-precision simulation capabilities, further validating its applicability and reliability in low-rise building wind pressure modeling. Overall, compared to traditional HPM methods, the proposed ML-EHPM method has a wider range of applications and higher simulation accuracy. Future research could extend this method to the simulation of non-Gaussian excitations, such as wind speed simulation in complex terrain.

[0022] 2. The stationary non-Gaussian wind pressure simulation method based on machine learning-enhanced Hermite multinomial models disclosed in this invention can more accurately reconstruct the target probability density function (PDF) and probability distribution density function (PSD) under conditions of strong non-Gaussian wind pressure, wind pressure exceeding the monotonic region, and bimodal wind pressure distribution. Compared with the traditional moment-based HPM method, it has higher simulation accuracy and a wider range of applicability, overcoming the limitations of the monotonic interval. Furthermore, based on the transformation function of ML-EHPM, the latent Gaussian PSD is further estimated through BPNN, allowing this invention to directly and accurately determine UGPSD, especially with strong non-Gaussian samples. It can be used to simulate single-point and multi-point non-Gaussian wind pressure based on wind tunnel test databases. When simulating multi-point roof wind pressure fields, the proposed ML-EHPM method consistently demonstrates high-precision simulation capabilities, further confirming its applicability and reliability in low-rise building wind pressure modeling.

[0023] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0024] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0025] Figure 1 This is a flowchart of the method for simulating stationary non-Gaussian wind pressure based on machine learning-enhanced Hermite polynomial models according to the present invention.

[0026] Figure 2 (a) is a comparison chart of the probability density function (PDF) of the wind pressure coefficient in the embodiment of the present invention, the HPM model, and the ML-EHPM model. Figure 2 (b) is a comparison graph of the probability density function under semi-logarithmic coordinates in the embodiments of the present invention. Figure 2 (c) is a comparison chart of power spectral density (PSD) of embodiments of the present invention. Detailed Implementation

[0027] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0028] like Figure 1 The method for simulating stationary non-Gaussian wind pressure based on a machine learning-enhanced Hermite multinomial model, as shown, includes the following steps:

[0029] S1. Construct a multi-input single-output BES-XGBoost model, and use the tenth-order origin moments ( ) and the mean of the transformation function As input features, the statistical moments of the remaining transformation functions ( , , , The first ten origin moments of the simulated points are used as output features for training to obtain the prediction model corresponding to the four statistical moments; that is, the first ten origin moments of the simulated points are used as output features for training. ) and the mean of the transformation function The input is fed into the nested BES-XGBoost model trained in step S1 to predict the statistical moments required for the transformation function. , , , ).

[0030] Tenth-order raw moment ( ) and the mean of the transformation function To the statistical moments of the transformation function ( , , , The predictive model is constructed as follows: Using the median of the original probability density function (PDF) as a boundary, it is divided into two parts: a positive side (greater than the median) and a negative side (less than the median). Two new symmetric PDFs are then constructed for each side, ensuring that their transformation functions remain consistent with the original PDF on their respective sides. Since the skewness of these two symmetric PDFs is always zero, the calculated statistical moments are no longer subject to monotonicity constraints. Assuming... Non-Gaussian component process The original PDF, then the random process The first four statistical moments on the positive side are defined as follows:

[0031] (1)

[0032] (2)

[0033] (3)

[0034] (4)

[0035] in, From the original PDF The exported median; , , and These are the newly defined mean, standard deviation, skewness, and kurtosis for the positive side; similarly, the statistical moments for the negative side are defined as follows:

[0036] (5)

[0037] (6)

[0038] (7)

[0039] (8)

[0040] in , , and These are the newly defined mean, standard deviation, skewness, and kurtosis of the negative side.

[0041] Statistical moments of transformation function ( , , , Based on different combinations of positive and negative kurtosis, four different transformation function models are constructed: two softening processes (case 1), a semi-softening and semi-hardening process (case 2), a semi-hardening and semi-softening process (case 3), and two hardening processes (case 4), which are given by the following equation:

[0042] Case 1 ( >3, >3):

[0043] (9)

[0044] Case 2 ( >3, <3):

[0045] (10)

[0046] Case 3 ( <3, >3):

[0047] (11)

[0048] Case 4 ( <3, <3):

[0049] (12)

[0050] in, , , and It is determined using the newly defined statistical moments and the following equation:

[0051] (13)

[0052] and , , and It is determined using the following equation:

[0053] (14)

[0054] (15)

[0055] As can be seen from the above equations, in each case, the piecewise transformation function... All places are continuous; therefore, It is a memoryless and monotonically increasing transition function.

[0056] Step S1 is as follows:

[0057] S11. Construct a pairing training dataset

[0058] Estimate the first ten original moments and the target probability density function (PDF) based on measured data, and obtain the mean of the transformation function through formula (1). The input is used as the input, and then the statistical moments of the transformation function are calculated using formulas (2), (4), (6), and (8) respectively. , , , As output data, the training dataset is constructed to provide basic data for model training;

[0059] S12, Training the BES-XGBoost model

[0060] For the four statistical moments of the transformation function ( , , , Four independent BES-XGBoost models were constructed. During training, the BES algorithm was used to optimize the key hyperparameters of XGBoost (number of iterations, tree depth, and learning rate, etc.) to improve prediction accuracy and model generalization ability.

[0061] S13. Establish a nested input structure

[0062] To further improve prediction stability and accuracy, a nested input structure is introduced; that is, the BES-XGBoost model is used to predict the standard deviation of the positive and negative sides. , The predicted standard deviation is used as a new input feature, and the same BES-XGBoost model is used to predict the kurtosis. , );

[0063] S14, Statistical Moments of Predictive Transition Function

[0064] After training, the first ten order origin moments of the target ( ) and the corresponding mean of the transformation function ( The input is fed into the trained BES-XGBoost model, and the statistical moments of the transformation function are directly output. , , , ).

[0065] S2. Construct a multi-input multi-output (BPNN) model, and use the non-Gaussian PSD and the mean of the transformation function. and the statistical moments of the transformation function ( , , , Using the latent Gaussian PSD as the input feature and the latent Gaussian PSD as the output feature, a prediction model of the latent Gaussian PSD is obtained after training; that is, the target non-Gaussian PSD of the simulated points is normalized using formula (16) to obtain the model. Normalized non-Gaussian PSD power spectrum The statistical moments of the transformation function of the simulated points predicted by the BES-XGBoost model in step S1. , , , ) and the mean of the transformation function calculated by formulas (1) and (5) , The input is fed into the trained BPNN model to obtain the desired latent Gaussian power spectrum. .

[0066] (16)

[0067] S3. Based on the ML-EHPM model constructed in steps S1 and S2, predict the statistical moments required for the transformation function. , , , The potential Gaussian power spectrum predicted by the Gaussian PSD prediction model. Using this potential Gaussian power spectrum The non-Gaussian wind pressure is simulated using the representation method. Specifically, the potential Gaussian power spectrum from step S2 is used. The matrix is ​​subjected to Cholesky decomposition, and Gaussian time history samples are generated using the spectral representation method of multivariate stationary random processes according to formula (17). , Based on the statistical moments of the transformation function of the simulated points predicted in step S1 , , , Using formulas (9)-(12), Gaussian samples of the transformation function model under different conditions are transformed. Convert to non-Gaussian samples Non-Gaussian samples Inverse normalization yields the final non-Gaussian samples. .

[0068] (17)

[0069] Example

[0070] Specifically, the following simulation of the wind pressure coefficient time history at three measurement points in a single-point simulation further illustrates the invention:

[0071] Without loss of generality, this study uses two methods to simulate the time histories of wind pressure coefficients at measurement points 162, 77, and 215, respectively. These represent strong non-Gaussian wind pressure data, wind pressure data outside the monotonic region, and wind pressure data with a bimodal distribution.

[0072] The roof wind pressure coefficient at measuring point 162 exhibits significant strong non-Gaussian characteristics: its first ten raw moments estimated based on measured samples are 0, 1, -0.99, 7.003, -26.30, 164.9, -965.02, 0.6×10⁴, -0.4×10⁵, and 3×10⁵, respectively. Since this combination of third and fourth moments falls within the monotone effective region of the Hermite polynomial model (HPM), theoretically, HPM can be directly used for simulation. To compare with the traditional HPM model, nested BES-XGBoost was used to predict the "lateral statistical moments" required for ML-EHPM. The predicted transformation function statistical moments ( , , , The values ​​are 1.12 and 7.995, and 0.887 and 3.202, respectively. Since the kurtosis on both sides is greater than 3, the wind pressure coefficient of Tap 162 exhibits two "softening" non-Gaussian characteristics.

[0073] Following the standard simulation procedures of HPM and ML-EHPM, this paper generates 2000 sets of wind pressure coefficient samples for each, and the first to fourth moments of the target samples and simulation samples are listed in Table 1.

[0074] Table 1

[0075]

[0076] It is evident that the statistical moments of the samples generated by ML-EHPM almost perfectly match the target value, while the statistical moments of the samples generated by HPM show significant deviations in indicators such as kurtosis. Figure 2 The comparison of the simulated sample PDF and the target PDF in (a)–(b) further validates the advantages of ML-EHPM: the PDF obtained by ML-EHPM closely follows the target distribution across the entire domain, and is particularly effective in capturing significant negative tail features. A comparison of the power spectra of the simulated samples and the target power spectra of the two methods is shown below. Figure 2 As shown in (c), the two methods have comparable simulation accuracy for the target power spectral density, indicating that the improvement of the proposed method mainly stems from the higher fidelity of the edge statistical features.

[0077] In summary, for strong non-Gaussian roof wind pressure, the machine learning-enhanced ML-EHPM method of this invention is significantly more accurate than the traditional HPM method in reproducing PDF, while maintaining the consistency of the power spectrum, thus exhibiting particularly strong performance in fitting edge statistical features.

[0078] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. 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 be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for simulating stationary non-Gaussian wind pressure based on a machine learning-enhanced Hermite polynomial model, characterized in that, Includes the following steps: S1. Construct a multi-input single-output BES-XGBoost model, and use the tenth-order origin moments ( ) and the mean of the transformation function As input features, the statistical moments of the remaining transformation functions ( , , , The output features are used for training to obtain the prediction model corresponding to the four statistical moments; Assumption Non-Gaussian component process The original PDF, then the random process The first four statistical moments of the positive side are defined as follows: （1） （2） （3） （4） in, From the original PDF The exported median; , , and These are the newly defined mean, standard deviation, skewness, and kurtosis for the positive side; similarly, the statistical moments for the negative side are defined as follows: （5） （6） （7） （8） in , , and These are the newly defined negative-side mean, standard deviation, skewness, and kurtosis; Step S1 is as follows: S11. Construct a pairing training dataset Based on measured data, the first ten original moments and the target probability density function are estimated, and the mean of the transformation function is obtained through formula (1). The transition function statistical moments are calculated using formulas (2), (4), (6), and (8), respectively. , , , As output data, the training dataset is constructed to provide basic data for model training; S12, Training the BES-XGBoost model For the four statistical moments of the transformation function ( , , , Four independent BES-XGBoost models were constructed. During training, the BES algorithm was used to optimize the key hyperparameters of XGBoost, namely the number of iterations, tree depth and learning rate, in order to improve prediction accuracy and model generalization ability. S13. Establish a nested input structure To further improve prediction stability and accuracy, a nested input structure is introduced; that is, the BES-XGBoost model is used to predict the standard deviation of the positive and negative sides. , The predicted standard deviation is used as a new input feature, and the same BES-XGBoost model is used to predict the kurtosis. , ); S14, Statistical Moments of Predictive Transition Function After training, the first ten order origin moments of the target ( ) and the corresponding mean of the transformation function ( The input is fed into the trained BES-XGBoost model, and the statistical moments of the transformation function are directly output. , , , ); S2. Construct a multi-input multi-output (BPNN) model, and use the non-Gaussian PSD and the mean of the transformation function. and the statistical moments of the transformation function ( , , , Using ) as input features and Latent Gaussian PSD as output features, a prediction model for Latent Gaussian PSD is obtained after training. S3. Based on the ML-EHPM model constructed in steps S1 and S2, predict the statistical moments required for the transformation function. , , , The potential Gaussian power spectrum predicted by the Gaussian PSD prediction model. Using this potential Gaussian power spectrum The notation method simulates non-Gaussian wind pressure.

2. The method for simulating steady non-Gaussian wind pressure as described in claim 1, characterized in that, Step S1 specifically involves: calculating the first ten origin moments of the target at the simulated points ( ) and the mean of the transformation function The input is fed into the nested BES-XGBoost model trained in step S1 to predict the statistical moments required for the transformation function. , , , ).

3. The method for simulating steady non-Gaussian wind pressure as described in claim 2, characterized in that, Step S2 specifically involves: using formula (16) to normalize the non-Gaussian PSD of the simulated points to obtain... , （16） Normalized non-Gaussian PSD power spectrum The statistical moments of the transformation function of the simulated points predicted by the BES-XGBoost model in step S1. , , , ) and the mean of the transformation function The input is fed into the trained BPNN model to obtain the desired latent Gaussian power spectrum. .

4. The method for simulating steady non-Gaussian wind pressure as described in claim 2, characterized in that, Step S1: Tenth-order origin moment ( ) and the mean of the transformation function To the statistical moments of the transformation function ( , , , The prediction model is constructed as follows: the original probability density function is divided into two parts, positive and negative, with the median as the boundary. The original probability density function is referred to as PDF. The positive side represents the part greater than the median, and the negative side represents the part less than the median. Two new symmetric PDFs are constructed, and their transformation functions are kept consistent with those of the original PDF on their respective sides. Since the skewness of these two symmetric PDFs is always zero, the statistical moments calculated by them will no longer be subject to monotonicity constraints.

5. The method for simulating steady non-Gaussian wind pressure as described in claim 2, characterized in that, In step S1, the statistical moments of the transformation function ( , , , Based on different combinations of positive and negative kurtosis, four different transformation function models are constructed: two softening processes (representing case 1), a semi-softening and semi-hardening process (representing case 2), a semi-hardening and semi-softening process (representing case 3), and two hardening processes (representing case 4), which are given by the following formula: Case 1, >3, >3: （9） Scenario 2, >3, <3: （10） Scenario 3, <3, >3: （11） Situation 4, <3, <3: （12） in, , , and It is determined using the newly defined statistical moments and the following equation: （13） and , , and It is determined using the following equation: （14） （15） As can be seen from the above equations, in each case, the piecewise transformation function... All places are continuous; therefore, It is a memoryless and monotonically increasing transition function.

6. The method for simulating steady non-Gaussian wind pressure as described in claim 5, characterized in that, Step S3 specifically involves: analyzing the potential Gaussian power spectrum from step S2. The matrix is ​​subjected to Cholesky decomposition, and Gaussian time history samples are generated using the spectral representation method of multivariate stationary random processes according to formula (17). , , （17） Based on the statistical moments of the transformation function of the simulated points predicted in step S1, , , , Using formulas (9)-(12), Gaussian samples of the transformation function model under different conditions are transformed. Convert to non-Gaussian samples Non-Gaussian samples Inverse normalization yields the final non-Gaussian samples. .

7. A stationary non-Gaussian wind pressure simulation system based on a machine learning-enhanced Hermite polynomial model, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steady non-Gaussian wind pressure simulation method according to any one of claims 1 to 6.

8. A storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method for simulating stationary non-Gaussian wind pressure as described in any one of claims 1 to 6.

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