A stationary non-gaussian wind field simulation method and system based on random waves
By combining the stochastic spectral representation and the maximum entropy method with a piecewise Hermite polynomial model, the problems of low efficiency and insufficient accuracy in wind field simulation in existing technologies are solved, achieving efficient and stable non-Gaussian wind field simulation and meeting the high-precision requirements of modern engineering structures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHONGQING JIAOTONG UNIV
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-09
AI Technical Summary
Existing wind speed field simulation methods are computationally inefficient and numerically unstable in large-scale wind field simulations. They are unable to accurately characterize the higher-order statistical properties and tail probability features of non-Gaussian wind speed fields, and thus cannot meet the requirements of modern engineering structures for high-precision and high-efficiency wind speed field simulation.
A low-level stationary Gaussian random field is generated by using random spectral representation and two-dimensional fast Fourier transform. The non-Gaussian marginal probability density function is reconstructed by combining the maximum entropy method. The mapping function is constructed by using a piecewise Hermite polynomial model, and the low-level Gaussian correlation structure is obtained by inverse calculation. This achieves high-precision non-Gaussian wind field simulation without the need for high-dimensional spectral matrix decomposition.
It significantly improves computational efficiency and numerical stability, accurately characterizes the higher-order statistical properties and tail probability features of strong non-Gaussian wind fields, provides high-precision wind speed field sample support, and provides reliable data for wind-resistant design and wind-induced response analysis of long-span bridges and super high-rise buildings.
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Figure CN122174441A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of non-Gaussian wind field simulation technology in structural wind engineering, specifically to a method and system for simulating stationary non-Gaussian wind fields based on random waves. Background Technology
[0002] In fields such as structural wind engineering, civil engineering disaster prevention and mitigation, and aeroelastic design of wind turbines, accurate simulation of multi-point wind speed fields is a core prerequisite and key foundation for conducting structural wind resistance performance assessment, wind-induced vibration response analysis, and extreme wind disaster risk prediction. As modern engineering structures develop towards larger spans, higher heights, and greater flexibility, increasingly stringent requirements are placed on the accuracy, efficiency, and adaptability of wind speed field simulations to large-scale simulation points. Current mainstream wind speed field simulation methods are mostly based on traditional spectral representation methods. The core operation of this method is to decompose the high-dimensional cross-power spectral density matrix multiple times. Common decomposition methods include Cholesky decomposition and singular value decomposition, generating multivariate random process samples that satisfy spatial correlation through matrix decomposition. However, in practical engineering applications, as the number of simulation points continuously increases, repeated decomposition operations on the high-dimensional matrix are required at multiple frequency points. This process leads to an exponential increase in computational load, significantly prolonging simulation time, reducing overall computational efficiency, and easily causing numerical instability due to matrix singularities and numerical overflow. This severely restricts the promotion and application of this method in large-scale wind field simulation scenarios.
[0003] Wind speed processes in real-world environments generally exhibit significant non-Gaussian characteristics, especially under complex meteorological conditions such as strong winds and turbulence. The probability distribution of wind speed often displays obvious skewness and kurtosis, and its tail probability characteristics are crucial for assessing extreme wind-induced structural hazards. Traditional wind field simulation methods mostly employ the Gaussian distribution assumption or use simple Hermite polynomial approximations to fit the non-Gaussian characteristics. While these methods are applicable to weak non-Gaussian wind fields, their fitting accuracy drops significantly when faced with strong non-Gaussian wind fields, making it difficult to accurately characterize the higher-order statistical properties and tail probability features of the wind speed distribution. Specifically, simple Hermite polynomial approximations often only match low-order moments of the wind speed process, resulting in poor fitting of higher-order moments reflecting the distribution pattern, such as kurtosis and skewness. This leads to significant deviations between the simulated wind speed samples and the statistical characteristics of actual wind speed processes, affecting the reliability and safety of subsequent wind-resistant structural design and failing to provide accurate and effective data support for wind-induced risk assessment of major engineering structures.
[0004] To address the shortcomings in simulating non-Gaussian wind speed fields, some researchers have attempted to introduce nonlinear transformation methods to map Gaussian random fields to non-Gaussian random fields using specific nonlinear functions, thereby simulating non-Gaussian wind speed fields. The key to these methods lies in constructing accurate nonlinear mapping functions. However, most existing nonlinear transformation methods employ a single, global mapping function, which struggles to account for the statistical differences in wind speed field characteristics across different regions. For example, some mapping functions perform well in fitting the characteristics of the middle region of the wind speed distribution but have significant errors when fitting the characteristics of the tail region. Furthermore, some mapping functions rely excessively on large amounts of measured data for parameter calibration, severely limiting their applicability when measured data is insufficient. In addition, these methods often neglect the "correlation distortion" effect between Gaussian and non-Gaussian correlation structures when constructing the nonlinear mapping function. That is, the correlation structure of a Gaussian random field changes after nonlinear transformation. If this effect is not accurately quantified and corrected, the spatial correlation of the simulated non-Gaussian wind speed field will not match reality, further reducing simulation accuracy.
[0005] In the theoretical research and engineering practice of wind speed field simulation, how to improve the computational efficiency and numerical stability of large-scale wind field simulations while ensuring simulation accuracy, and simultaneously achieve accurate characterization of the higher-order statistical properties and tail probability characteristics of strong non-Gaussian wind speed fields, has become a key scientific problem and technical bottleneck that urgently needs to be solved. Existing technical solutions either focus on improving computational efficiency at the expense of simulation accuracy, or focus on improving simulation accuracy at the expense of computational efficiency, making it difficult to achieve a balance between the two. Furthermore, existing methods mostly use discretized spectral representations when modeling spectral characteristics in the wavenumber-frequency domain, lacking an effective characterization of the evolution characteristics of wind speed fields in the continuous spatial domain, and failing to accurately reflect the coupling correlation characteristics of wind speed in the spatial and temporal dimensions. These problems seriously hinder the further development of wind speed field simulation technology and make it difficult to meet the urgent needs of modern engineering structures for high-precision, high-efficiency wind speed field simulation.
[0006] Therefore, there is an urgent need for a method to simulate stationary non-Gaussian wind fields that does not require high-dimensional spectral matrix decomposition, has high computational efficiency, and can accurately characterize strong non-Gaussian properties, in order to solve the bottleneck problem of existing technologies. Summary of the Invention
[0007] To address the aforementioned technical problems, this application discloses a method and system for simulating stationary non-Gaussian wind fields based on random waves; the method for simulating stationary non-Gaussian wind fields based on random waves specifically includes:
[0008] Obtain the autopower spectrum and coherence function of the target wind speed field;
[0009] Construct the target non-Gaussian wavenumber-frequency spectrum based on the self-power spectrum and coherence function;
[0010] The wavenumber and frequency are discretized, and a low-level stationary Gaussian random field is generated by using a random spectral representation and combining it with a two-dimensional fast Fourier transform.
[0011] Based on the finite-order statistical moments of the target wind speed process, the maximum entropy method is used to reconstruct the target non-Gaussian marginal probability density function and cumulative distribution function.
[0012] The edge distribution is embedded into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian.
[0013] Based on the relevant distortion relationship, the underlying Gaussian correlation structure is derived from the target non-Gaussian correlation structure, and the underlying Gaussian spectral characteristics are determined from the underlying Gaussian correlation structure.
[0014] Applying the piecewise translation mapping function to the underlying stationary Gaussian random field yields stationary non-Gaussian wind field samples.
[0015] Preferably, the target non-Gaussian wavenumber-frequency spectrum is constructed by performing a spatial Fourier transform on the coherence function to obtain the spectral distribution in the wavenumber dimension. The specific calculation formula is as follows: ,in, The non-Gaussian self-power spectrum of the target wind speed field. Let be the coherence function of the target wind speed field, describing the frequency domain correlation between spatial points. For wave number, For frequency, This is the spatial lag. It is the imaginary unit.
[0016] Preferably, the wavenumber and frequency are discretized, and a stationary Gaussian random field is generated by using a random spectral representation combined with a two-dimensional fast Fourier transform. Specifically, the number of wavenumber discrete segments is... With frequency discrete segment number All are chosen to be integer powers of 2, and satisfy the requirement of spatial discretization quantity. Number of time discretizations To avoid aliasing effects, the generation formula for the underlying stationary Gaussian random field is: ,in, To take the real part of a complex number, This indicates the Fast Fourier Transform operation. Indicates the inverse fast Fourier transform operation, subscript and These represent transformations performed along the wavenumber and frequency dimensions, respectively. Wavenumber-frequency domain coefficients, For frequency direction identification, For wavenumber discrete indexing, For frequency discrete indexing, , The underlying Gaussian wavenumber-frequency spectrum, For the first discrete wave values For the first A discrete frequency value, Wavenumber step size, For frequency step size, To distribute evenly in Random phase angle within the interval, For spatial location variables, It is a time variable.
[0017] Preferably, the maximum entropy method reconstructs the target non-Gaussian marginal probability density function using an exponential family density function in the form of moment constraints, as shown in the following formula: ,in, The target non-Gaussian marginal probability density function is to be reconstructed. For a random variable to take values, Let Lagrange multipliers be the ones to be solved. The order of moments is determined by the entropy increment threshold. Or the equivalence criterion determines; the Lagrange multipliers satisfy the moment constraint condition. ( ), For the target wind speed process Statistical moments of order, The integration interval is determined by a truncation strategy based on the linear displacement moment or the tail threshold of the target distribution.
[0018] Preferably, the piecewise translation mapping function uses a threshold. As the segmentation point, differentiated Hermite polynomial coefficients are used in different intervals, with the specific formula as follows:
[0019]
[0020] in, Let Gaussian be a piecewise translation function from non-Gaussian. The values are those of the underlying Gaussian random field. The median of the target non-Gaussian wind field. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. Indicated by kurtosis A Hermite polynomial model with parameters.
[0021] Preferably, the correlation distortion relationship is established through the integral relationship of the two-dimensional joint Gaussian density, and the explicit mapping between non-Gaussian correlation and Gaussian correlation is obtained through Hermite coefficient expansion. The target non-Gaussian correlation coefficient is then used to determine the correlation. Inversely calculate the underlying Gaussian correlation coefficient The formula is:
[0022]
[0023] in, For the target non-Gaussian wind field in spatial lag Time lag The correlation coefficient at the location, The correlation coefficient is the value corresponding to the underlying Gaussian random field. This is the proportionality coefficient. and These are the third and fourth order Hermite coefficients of the target non-Gaussian wind field, respectively. and These are intermediate calculation parameters. , , , , It is an intermediate parameter for calculating the target non-Gaussian correlation coefficient and the square of the fourth-order Hermite coefficient. It is an intermediate calculation parameter for the square of the third-order Hermite coefficients and the fourth-order Hermite coefficients raised to the fourth power.
[0024] Preferably, the underlying Gaussian spectral characteristics are determined by the underlying Gaussian correlation structure through the Wiener-Khintchine transform, and the specific calculation formula is as follows: ,in, For the bottom Gaussian wavenumber-frequency spectrum at the 1st Discrete wavenumbers , No. discrete frequency The value at that location, To take the real part of a complex number, For the time lag step, For spatial lag step size, For the first Spatial lag discrete value For the first Discrete values with time lag For spatially lagging discrete quantities, For discrete quantities with time lag, For the underlying Gaussian random field , The correlation coefficient at the location, It is the imaginary unit.
[0025] The described stationary non-Gaussian wind field simulation system based on random waves includes:
[0026] The spectrum construction module acquires the autopower spectrum and coherence function of the target wind speed field, and constructs the target non-Gaussian wavenumber-frequency spectrum based on the autopower spectrum and coherence function.
[0027] The underlying Gaussian field generation module discretizes the wavenumber and frequency, and uses a random spectrum representation combined with two-dimensional fast Fourier transform to generate a bottom-level stationary Gaussian random field.
[0028] The maximum entropy distribution reconstruction module reconstructs the non-Gaussian marginal probability density function and cumulative distribution function of the target wind speed process using the maximum entropy method, based on the finite-order statistical moments of the target wind speed process.
[0029] The piecewise translation mapping module embeds the edge distribution into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian.
[0030] The correlation distortion inverse calculation module inversely calculates the underlying Gaussian correlation structure from the target non-Gaussian correlation structure based on the correlation distortion relationship, and determines the underlying Gaussian spectral characteristics based on the underlying Gaussian correlation structure.
[0031] The sample output module applies the piecewise translation mapping function to the underlying stationary Gaussian random field and outputs stationary non-Gaussian wind field samples that satisfy the target statistical characteristics.
[0032] An electronic device includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the electronic device performs the aforementioned method for simulating stationary non-Gaussian wind fields based on random waves.
[0033] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is used to implement the aforementioned method for simulating stationary non-Gaussian wind fields based on random waves.
[0034] Compared with the prior art, the technical solution of this application has the following technical effects:
[0035] This invention eliminates the need to decompose the high-dimensional cross-power spectral density matrix. It generates a low-level Gaussian random field using random spectral representation and two-dimensional fast Fourier transform, reducing the computational complexity in large-scale simulation point scenarios, effectively avoiding numerical instability caused by matrix singularity, and significantly improving the computational efficiency and numerical reliability of stationary non-Gaussian wind field simulation.
[0036] This invention employs the maximum entropy method, which can accurately reconstruct the target non-Gaussian marginal distribution using only finite-order statistical moments, breaking through the dependence on a large amount of measured data. At the same time, it combines a piecewise Hermite multinomial model to construct a mapping function and uses differentiated coefficients for different intervals to improve the fitting accuracy of the probability characteristics of the tail of strong non-Gaussian wind fields, making the simulation results more consistent with the statistical characteristics of the actual wind speed field.
[0037] This invention establishes a correlation distortion model through a two-dimensional joint Gaussian density integral relationship, and obtains an explicit mapping relationship between non-Gaussian and Gaussian correlated structures through Hermite coefficient expansion. This enables the operation of directly inverting the underlying Gaussian correlated structure from the target non-Gaussian correlated structure, avoiding complex iterative integral calculations, improving the efficiency and accuracy of correlation structure inversion, and ensuring that the spatial and temporal correlation of the simulated wind field meets expectations.
[0038] The non-Gaussian wavenumber-frequency spectrum constructed in this invention can realize wind field modeling in a continuous spatial domain. Compared with the discretized spectrum representation method, it can more accurately reflect the coupled evolution characteristics of wind speed in the spatial and temporal dimensions, while balancing computational efficiency and simulation accuracy. It provides high-precision wind speed field sample support for wind-resistant design and wind-induced response analysis of major projects such as long-span bridges and super high-rise buildings.
[0039] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the preferred embodiments of this application are described in detail below with reference to the accompanying drawings.
[0040] The above and other objects, advantages and features of this application will become more apparent to those skilled in the art from the following detailed description of specific embodiments in conjunction with the accompanying drawings. Attached Figure Description
[0041] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In all drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.
[0042] Based on the description of the figures and their corresponding technical content in the document, the titles of the figures are as follows:
[0043] Figure 1 Flowchart of the steps in the simulation method of stationary non-Gaussian wind field based on random waves;
[0044] Figure 2 : Module architecture and data flow diagram of a stationary non-Gaussian wind field simulation system based on random waves;
[0045] Figure 3 Comparison of the frequency domain characteristics of the target non-Gaussian self-power spectrum and the non-Gaussian wavenumber-frequency spectrum;
[0046] Figure 4 A comparison chart of the underlying Gaussian correlation coefficient and the target non-Gaussian correlation coefficient obtained by reverse calculation;
[0047] Figure 5 Spatial distribution maps of underlying Gaussian and non-Gaussian fields generated by different models (HPM, UHPM, PHPM);
[0048] Figure 6 Three typical simulation points ( Comparison of wind speed time histories for different models at point ).
[0049] Figure 7 A comparison of the autocorrelation coefficients and cross-correlation coefficients of different models as a function of lag.
[0050] Figure 8 A comparative graph showing the relationship between transfer function magnitude and correlation distortion for different models;
[0051] Figure 9 Three typical spatial locations ( (Comparison of simulated and target PDF at point ) Detailed Implementation
[0052] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. In the following description, specific details such as specific configurations and components are provided merely to help fully understand the embodiments of this application. Therefore, those skilled in the art should understand that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. In addition, for clarity and brevity, descriptions of known functions and structures are omitted in the embodiments.
[0053] It should be understood that the phrase "an embodiment" or "this embodiment" throughout the specification means that a specific feature, structure, or characteristic related to the embodiment is included in at least one embodiment of this application. Therefore, "an embodiment" or "this embodiment" appearing throughout the specification does not necessarily refer to the same embodiment. Furthermore, these specific features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.
[0054] Furthermore, reference numerals and / or letters may be repeated in different examples within this application. Such repetition is for the purpose of simplification and clarity and does not in itself indicate a relationship between the various embodiments and / or settings discussed.
[0055] In this article, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can mean: A exists alone, B exists alone, and A and B exist simultaneously. The term " / and" in this article describes another type of relationship between related objects, indicating that two relationships can exist. For example, A / and B can mean: A exists alone, and A and B exist alone. In addition, the character " / " in this article generally indicates that the related objects before and after it are in an "or" relationship.
[0056] In this article, the term "at least one" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, "at least one of A and B" can mean: A exists alone, A and B exist simultaneously, or B exists alone.
[0057] It should also be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion.
[0058] Example 1
[0059] This embodiment mainly describes a method for simulating stationary non-Gaussian wind fields based on random waves, such as... Figure 1 As shown, it specifically includes:
[0060] Obtain the autopower spectrum and coherence function of the target wind speed field;
[0061] Construct the target non-Gaussian wavenumber-frequency spectrum based on the self-power spectrum and coherence function;
[0062] The wavenumber and frequency are discretized, and a low-level stationary Gaussian random field is generated by using a random spectral representation and combining it with a two-dimensional fast Fourier transform.
[0063] Based on the finite-order statistical moments of the target wind speed process, the maximum entropy method is used to reconstruct the target non-Gaussian marginal probability density function and cumulative distribution function.
[0064] The edge distribution is embedded into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian.
[0065] Based on the relevant distortion relationship, the underlying Gaussian correlation structure is derived from the target non-Gaussian correlation structure, and the underlying Gaussian spectral characteristics are determined from the underlying Gaussian correlation structure.
[0066] Applying the piecewise translation mapping function to the underlying stationary Gaussian random field yields stationary non-Gaussian wind field samples.
[0067] Furthermore, the autopower spectrum and coherence function of the target wind speed field are obtained, and the non-Gaussian wavenumber-frequency spectrum of the target wind speed field is constructed. Coherence function is a core frequency domain characteristic parameter describing the energy distribution of wind speed signals at different frequencies. It accurately reflects the energy intensity distribution of wind speed processes in the frequency domain and is one of the key input parameters for wind field simulation. This is used to characterize the correlation between any two spatial points in a wind speed field under different frequency conditions. This represents the distance between two points in space, i.e., the spatial lag. Representing frequency, the coherence function effectively describes the spatial correlation of the wind speed field and is a crucial fundamental parameter for constructing the spatial domain characteristics of the wind field. In practical engineering applications, these two key parameters—power spectrum and coherence function—can be obtained through field measurements, statistical analysis of wind tunnel test data, or calculation using empirical formulas recommended by relevant technical specifications. These methods provide solid and reliable foundational data support for the subsequent construction of the non-Gaussian wavenumber-frequency spectrum.
[0068] The core task of this step is to transform the wind speed characteristics in the time and spatial domains into the wavenumber-frequency domain, and then construct the target non-Gaussian wavenumber-frequency spectrum. ,in The wave number is mainly used to characterize spatial frequency characteristics, and its specific calculation formula is as follows: In the formula The non-Gaussian self-power spectrum of the target wind speed field. Let be the coherence function of the target wind speed field, used to describe the degree of correlation between different spatial points at corresponding frequencies. This is the spatial lag, which is the distance between two spatial points. The wave number is positively correlated with the spatial frequency. Frequency represents the variation characteristics in the time domain. The imaginary unit satisfies Integral symbol Indicates spatial lag Integral operations are performed, enabling the transformation from the spatial domain to the wavenumber domain. This formula, through a spatial Fourier transform of the coherence function, effectively incorporates the spatial correlation of the wind speed field into the wavenumber-frequency spectrum, thus constructing... It can simultaneously include the frequency domain energy distribution and spatial correlation characteristics of the wind speed field, thus providing accurate and reasonable spectral input conditions for the subsequent generation of the underlying Gaussian random field.
[0069] Furthermore, in order to perform efficient numerical calculations using two-dimensional Fast Fourier Transform (FFT / IFFT), it is necessary to first determine the wavenumber. and frequency Discretization is performed. Number of wavenumber discrete segments. With frequency discrete segment number Choosing all values as integer powers of 2 maximizes the computational efficiency of 2D FFT / IFFT, significantly reduces numerical computation time, and accelerates the overall simulation progress. Simultaneously, to avoid aliasing during discretization and ensure the accuracy of simulation results, the number of spatial discretization operations must be sufficient. Number of time discretizations The constraints.
[0070] The discretized wavenumber and frequency are expressed as follows: and In the formula For the first discrete wave values This is a discrete wavenumber index, with a value range of [value range missing]. arrive , The wavenumber step size is determined by the cutoff wavenumber. Wavenumber discrete segment number Sure, The cutoff wavenumber is the upper limit of the wavenumber discretization. The number of discrete segments of the wavenumber. For the first A discrete frequency value, This is a frequency discrete index, with a value range of [value range missing]. arrive , The frequency step size is determined by the cutoff frequency. and the number of discrete frequency segments Sure, The cutoff frequency is the upper limit of the frequency discrete value. This represents the number of discrete frequency segments.
[0071] After discretizing the wavenumber and frequency, the spatial location variables... and time variables It also needs to be discretized accordingly, and its discretization expressions are as follows: and ,in For the first Discrete spatial location values For spatial step size, For spatially discrete quantities, For the first discrete time values For time step, For discrete time quantities.
[0072] Subsequently, a random spectrum representation method was adopted, combined with a two-dimensional fast Fourier transform, to generate a stationary Gaussian random field at the bottom layer. The core formula is as follows: In the formula To take the real part of a complex number, This indicates the Fast Fourier Transform operation. Indicates the inverse fast Fourier transform operation, subscript and These represent transformations performed along the wavenumber and frequency dimensions, respectively. Wavenumber-frequency domain coefficients, For frequency direction identification, For wavenumber discrete indexing, For frequency discrete indexing, ,in The underlying Gaussian wavenumber-frequency spectrum, For the first discrete wave values For the first A discrete frequency value, Wavenumber step size, For frequency step size, To distribute evenly in Random phase angle within the interval, For spatial location variables, The variable is time. This formula can efficiently generate a stationary Gaussian random field that satisfies the spectral characteristics, providing a solid foundation for subsequent non-Gaussian transformations.
[0073] Furthermore, based on the maximum entropy method, the non-Gaussian marginal probability density function and cumulative distribution function of the target are reconstructed, assuming... For having the former Original Moments For the sake of ease of subsequent calculations and analysis, and without loss of generality, a stationary non-Gaussian field will be... Standardized to ,in and They are The mean and standard deviation of the values. After standardization... The first and second origin moments are equal to 0 and 1, respectively, i.e. , , The First-order origin moment It can be done It is estimated that among them It is the binomial coefficient, representing Among the elements The number of combinations of elements.
[0074] Meanwhile, the standardized non-Gaussian field This can be achieved by analyzing the underlying Gaussian field. The nonlinear memoryless transformation is defined as follows: ,in express The translation function, yes The standard Gaussian cumulative distribution function, yes The inverse function of the marginal non-Gaussian cumulative distribution function is the equation, which is also known as the standard translation formula.
[0075] cumulative distribution function By its probability density function The integral yields the result; the specific formula is as follows: ,in It is a function The independent variable, yes The probability density function.
[0076] To accurately approximate the marginal probability density function of the target non-Gaussian wind field This method employs the maximum entropy method, and its core formula is: In the formula The target non-Gaussian marginal probability density function is to be reconstructed. For a random variable to take values, Let Lagrange multipliers be the ones to be solved. The order of moments is determined by the entropy increment threshold. Alternatively, if the equivalence criterion is determined, the Lagrange multipliers satisfy the moment constraint condition. ( ), For the target wind speed process Statistical moments of order, The integration interval is determined by a truncation strategy based on the linear displacement moment or the tail threshold of the target distribution.
[0077] The formula for determining the entropy increment threshold is as follows: Among them, it is suggested , Indicates the total amount used before A moment to determine hour The entropy, i.e., in the formula It can be accessed through calculate.
[0078] Determine the integration interval At that time, a boundary determination strategy based on linear displacement moment is adopted, the core formula of which is: ,in , For linear displacement moments, The displacement parameter is used. Through the above process, it is possible to accurately reconstruct the non-Gaussian marginal probability density function and cumulative distribution function of the target under the condition that only a finite number of statistical moments are known, breaking through the dependence of traditional methods on a large amount of measured data.
[0079] Furthermore, a piecewise Hermite polynomial model is embedded and a piecewise translation mapping function is constructed. The non-Gaussian marginal distribution reconstructed by the maximum entropy method is embedded into the piecewise Hermite polynomial model (PHPM) to construct a Gaussian-to-non-Gaussian piecewise translation mapping function. This mapping function uses a threshold... As the segmentation point, differentiated Hermite polynomial coefficients are used in different intervals, with the specific formula being: In the formula Let Gaussian be a piecewise translation function from non-Gaussian. The values are those of the underlying Gaussian random field. The median of the target non-Gaussian wind field. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. Indicated by kurtosis A Hermite polynomial model with parameters.
[0080] in It is possible estimate, Let be the cumulative distribution function of the target non-Gaussian wind field. and It can be done and Similarly, calculation and It can be done and calculate.
[0081] Hermite polynomial model The expression is ,in for Hermite polynomial of order 1 These are polynomial coefficients, which are determined by kurtosis. It has been determined that the piecewise mapping function can effectively match the statistical characteristics of different intervals, significantly improving the fitting accuracy of the tail probability of strong non-Gaussian wind fields.
[0082] Furthermore, based on the correlation distortion relationship, the underlying Gaussian correlation structure is inversely derived and the underlying Gaussian spectral characteristics are determined. The correlation distortion relationship is established through the integral relationship of the two-dimensional joint Gaussian density, and the expression of the two-dimensional joint Gaussian probability density function is as follows: ,in The underlying Gaussian correlation coefficient. Let be the values of two Gaussian random variables.
[0083] Based on this joint probability density function, the non-Gaussian correlation coefficient correlation coefficient with Gaussian The mapping relationship can be represented as The explicit mapping between non-Gaussian correlation and Gaussian correlation is obtained through Hermite coefficient expansion, and the target non-Gaussian correlation coefficient is used to obtain the mapping. Inversely calculate the underlying Gaussian correlation coefficient The formula is In the formula For the target non-Gaussian wind field in spatial lag Time lag The correlation coefficient at the location, The correlation coefficient is the value corresponding to the underlying Gaussian random field. This is the proportionality coefficient. and These are the third and fourth order Hermite coefficients of the target non-Gaussian wind field, respectively. and These are intermediate calculation parameters. , , , , It is an intermediate parameter for calculating the target non-Gaussian correlation coefficient and the square of the fourth-order Hermite coefficient. It is an intermediate calculation parameter for the square of the third-order Hermite coefficients and the fourth-order Hermite coefficients raised to the fourth power.
[0084] Calculate the underlying Gaussian correlation coefficient Subsequently, the underlying Gaussian spectral characteristics were determined using the Wiener-Khintchine transform, with the specific calculation formula as follows: In the formula For the bottom Gaussian wavenumber-frequency spectrum at the 1st Discrete wavenumbers , No. discrete frequency The value at that location, To take the real part of a complex number, For the time lag step, For spatial lag step size, For the first Spatial lag discrete value For the first Discrete values with time lag For spatially lagging discrete quantities, For discrete quantities with time lag, For the underlying Gaussian random field , The correlation coefficient at the location, The imaginary unit is used. This process enables efficient and accurate determination of the underlying Gaussian spectral characteristics, providing a crucial basis for the generation of underlying Gaussian random fields.
[0085] Furthermore, a piecewise translation mapping function is applied to obtain stationary non-Gaussian wind field samples, which are then used to generate a bottom-level stationary Gaussian random field. Substitute into the constructed piecewise translation mapping function The standard non-Gaussian field is obtained. Then, the final stationary non-Gaussian wind field sample is obtained through inverse normalization transformation, and its calculation formula is as follows: In the formula For the final generated stationary non-Gaussian wind field sample, Let be the mean of the target non-Gaussian wind field. The standard deviation of the target non-Gaussian wind field. It is a standard non-Gaussian field.
[0086] In the actual verification process, the accuracy of the simulation results can also be verified by calculating the correlation function of the target non-Gaussian wind field. It can be calculated from the non-Gaussian wavenumber-frequency spectrum using the Wiener-Khintchine transform, as shown in the formula: Its discretized FFT computation form is as follows ;
[0087] Through the above steps, a stable non-Gaussian wind field sample that meets the target statistical characteristics and related structures can be generated, providing high-precision data support for the wind-resistant design and wind-induced response analysis of structural wind engineering.
[0088] This embodiment details how the invention significantly improves the computational efficiency and numerical stability of large-scale wind field simulations by eliminating the need to decompose high-dimensional cross-power spectral density matrices; it accurately characterizes the high-order statistical properties and tail probabilities of strong non-Gaussian wind fields by combining the maximum entropy method with a piecewise Hermite polynomial model; and it ensures the spatial and temporal correlation of wind fields by inversely determining the underlying Gaussian correlation structure through explicit correlation distortion relationships, thus providing high-precision data support for wind-resistant design of major engineering projects.
[0089] Example 2 describes in detail a stationary non-Gaussian wind field simulation system based on random waves, such as... Figure 2 As shown, it includes:
[0090] The spectrum construction module acquires the autopower spectrum and coherence function of the target wind speed field, and constructs the target non-Gaussian wavenumber-frequency spectrum based on the autopower spectrum and coherence function.
[0091] The underlying Gaussian field generation module discretizes the wavenumber and frequency, and uses a random spectrum representation combined with two-dimensional fast Fourier transform to generate a bottom-level stationary Gaussian random field.
[0092] The maximum entropy distribution reconstruction module reconstructs the non-Gaussian marginal probability density function and cumulative distribution function of the target wind speed process using the maximum entropy method, based on the finite-order statistical moments of the target wind speed process.
[0093] The piecewise translation mapping module embeds the edge distribution into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian.
[0094] The correlation distortion inverse calculation module inversely calculates the underlying Gaussian correlation structure from the target non-Gaussian correlation structure based on the correlation distortion relationship, and determines the underlying Gaussian spectral characteristics based on the underlying Gaussian correlation structure.
[0095] The sample output module applies the piecewise translation mapping function to the underlying stationary Gaussian random field and outputs stationary non-Gaussian wind field samples that satisfy the target statistical characteristics.
[0096] Furthermore, the spectrum construction module is responsible for the basic input processing of wind field simulation. It obtains the autopower spectrum and coherence function of the target wind speed field by connecting to the field measurement database, wind tunnel test data interface or standard empirical formula library. Then, it converts the statistical characteristics of the time-space domain into the spectral density distribution of the wavenumber-frequency domain through spatial Fourier transform. The generated target non-Gaussian wavenumber-frequency spectrum contains both frequency domain energy distribution and spatial correlation, providing accurate spectral input for subsequent random field generation.
[0097] Furthermore, the underlying Gaussian field generation module is the core computational unit of the simulation process. It first discretizes the wavenumber and frequency by powers of 2 to adapt to the two-dimensional fast Fourier transform, and then generates a stationary Gaussian random field that satisfies the characteristics of the underlying Gaussian spectrum based on the random spectral representation. This module can improve the computational efficiency of large-scale simulation point scenarios by more than 50% through parallel two-dimensional FFT / IFFT operations, while avoiding the numerical instability problem caused by high-dimensional matrix decomposition in traditional spectral representation.
[0098] Furthermore, the maximum entropy distribution reconstruction module takes the finite-order statistical moments of the target wind speed process as input. Using the maximum entropy principle, and under the condition of satisfying moment constraints, it reconstructs the most realistic non-Gaussian marginal probability density function and cumulative distribution function. This module does not rely on a large amount of measured data; it can accurately characterize the skewness, kurtosis, and tail probability characteristics of strong non-Gaussian wind fields using only the first 4-6 orders of statistical moments, providing a reliable distribution basis for subsequent nonlinear mapping.
[0099] Furthermore, the piecewise translation mapping module embeds the edge distribution output by the maximum entropy distribution reconstruction module into a piecewise Hermite multinomial model. Using the median of the target non-Gaussian wind field as the segment threshold, differentiated Hermite multinomial coefficients are employed to construct the mapping function across different intervals. This piecewise design effectively matches the statistical characteristics of different wind field intervals, improving the fitting accuracy for the tail probability of strong non-Gaussian wind fields by more than 30% compared to traditional global single mapping functions.
[0100] Furthermore, the correlation distortion inverse calculation module establishes a correlation distortion model through a two-dimensional joint Gaussian density integral relationship. After Hermite coefficient expansion, an explicit mapping between the non-Gaussian and Gaussian correlation structures is obtained. This allows for the direct inverse calculation of the underlying Gaussian correlation structure from the target non-Gaussian correlation structure, and the underlying Gaussian spectral characteristics are determined through the Wiener-Khintchine transform. This module avoids complex iterative integral calculations, improving the efficiency and accuracy of correlation structure inverse calculation by more than 40% compared to traditional methods.
[0101] Furthermore, the sample output module inputs the output of the underlying Gaussian field generation module into a piecewise translation mapping function to obtain a standard non-Gaussian field, which is then transformed through inverse normalization to obtain the final stationary non-Gaussian wind field sample. The output sample contains two-dimensional spatial-temporal wind speed data, which can be directly exported to a format compatible with engineering software for wind-resistant design and wind-induced response analysis of major projects such as long-span bridges and super high-rise buildings.
[0102] The electronic device includes a processor and a memory, in which a computer program is stored. When the computer program is executed by the processor, the electronic device will sequentially call the various functional modules of the simulation system: first, the target non-Gaussian wavenumber-frequency spectrum is generated through the spectrum construction module; then, the underlying stationary Gaussian random field is generated through the underlying Gaussian field generation module; then, the maximum entropy distribution reconstruction, piecewise translation mapping construction, and correlation distortion inverse calculation are executed in sequence, and finally, a stationary non-Gaussian wind field sample is output.
[0103] The electronic equipment can utilize multi-core CPUs or GPUs for accelerated computing, supporting large-scale parallel processing. It can complete a wind field simulation of 1000 simulation points and 1000 seconds in 10 minutes, meeting the timeliness requirements of engineering applications. Simultaneously, the equipment's built-in numerical stability monitoring module can monitor numerical errors in key processes such as matrix operations and FFT transformations in real time, ensuring the reliability of the simulation results.
[0104] A computer program containing the method is stored on a readable storage medium. When this program is executed by a processor, it loads and runs the various modules of the simulation system, automating the entire process from spectral input to sample output.
[0105] The storage medium can be a solid-state drive, cloud storage server, or dedicated storage array, supporting shared access from multiple devices and facilitating collaborative wind farm simulation and analysis by engineering teams. The stored computer program has version iteration capabilities, allowing for further improvements in simulation accuracy and efficiency through algorithm module updates. It is also compatible with mainstream operating systems such as Windows and Linux, demonstrating excellent cross-platform applicability.
[0106] This embodiment describes in detail how modular collaboration enables the full automation of the simulation process for stable non-Gaussian wind fields, significantly improving simulation efficiency and numerical stability. It accurately reconstructs the non-Gaussian distribution characteristics, maintains the relevant structure of the wind field, and outputs wind field samples that closely match actual statistical characteristics, providing high-precision data support for wind-resistant design of major engineering projects.
[0107] Based on Embodiment 1 or 2, this embodiment verifies the technical reliability, data accuracy, and engineering applicability of the stationary non-Gaussian wind field simulation method based on random waves of the present invention. Measured strong wind data from a long-span suspension bridge site over 72 consecutive hours were selected as the verification benchmark. The simulation points were set at 150, the spatial span at 1200m, the total duration at 800s, and the sampling frequency at 25Hz, resulting in over 120,000 sets of verification data. A multi-index evaluation system was constructed using four core dimensions: frequency domain characteristics, the rationality of the correlation structure, spatial-temporal distribution characteristics, and probability distribution fitting accuracy. Hermite multinomial model (HPM) and unified Hermite multinomial model (UHPM) were introduced as control groups.
[0108] Starting with frequency domain characteristic verification, this is the basic input condition for wind field simulation, and the corresponding results are as follows: Figure 3 As shown. Figure 3 The graph comprises two sub-graphs: the left graph shows the target non-Gaussian autospectrum, and the right graph shows the target non-Gaussian wavenumber-frequency spectrum. As seen in the left graph, the target non-Gaussian autospectrum exhibits a significant peak in the low-frequency range (0.05-0.5Hz), reaching a peak density of 185 m² / (s³). With increasing frequency, the spectral density gradually decreases, stabilizing above 5Hz (approximately 5 m² / (s³)). This perfectly matches the actual physical characteristics of low-frequency energy concentration in strong wind fields. The autospectral curve constructed by the method of this invention achieves a 97.8% overlap with the target curve, with a spectral density of 182.3 m² / (s³) at the peak frequency (0.3Hz), a deviation of only 1.4%. In contrast, the HPM model has a deviation of 11.7% at this peak, and the UHPM model has a deviation of 8.3%. In the wavenumber-frequency spectrum shown in the right figure, the high-value region of spectral density is concentrated in the intersection of wavenumber 0-0.03 rad / m and frequency 0.05-0.5 Hz, with a maximum value of 2200 m² / (s³·rad / m). The spatial matching degree between the spectral density distribution generated by the method of this invention and the target distribution reaches 96.5%, with no obvious numerical oscillations or distortions. In contrast, the traditional model shows obvious spectral density overflow in the wavenumber 0.01-0.02 rad / m region, with a deviation exceeding 15%. This result fully demonstrates that the target frequency domain statistical characteristics constructed by this invention through the autospectrum and coherence function can provide accurate and effective input conditions for subsequent random field generation, and the reliability of the frequency domain basic data is verified.
[0109] Based on the validity of the frequency domain input, the next step is to verify the correlation distortion relationship and the rationality of the inverse calculation process. The corresponding results are as follows: Figure 4 As shown. Figure 4 It contains two subgraphs. Figure 4 (a) is the Gaussian correlation coefficient obtained by reverse calculation. Figure 4(b) shows the target non-Gaussian correlation coefficient. As can be seen from the figure, the target non-Gaussian correlation coefficient decreases exponentially with the increase of spatial lag. The correlation coefficient is 1 at a spatial lag of 0m, decreasing to 0.35 at 300m and 0.12 at 600m. It also gradually decreases with the increase of time lag, being 1 at 0s, decreasing to 0.28 at 10s and 0.09 at 15s. This conforms to the physical law that the spatial correlation of wind fields weakens with distance and the temporal correlation weakens with time. The bottom-level Gaussian correlation coefficient obtained by the method of this invention has a completely consistent trend with the target non-Gaussian correlation coefficient across the entire range of spatial lag (0-600m) and time lag (0-15s). The absolute value of the correlation coefficient difference is only 0.023 on average, with the largest difference occurring at a spatial lag of 500m and a time lag of 12s, at 0.057. In comparison, the average difference between the correlation coefficient obtained by the HPM model and the target value is 0.112, while that of the UHPM model is 0.078, with a significant trend deviation appearing in the large lag region. To quantify the evaluation, a correlation inversion accuracy comparison table (Table 1) was constructed, comparing the mean absolute error (MAE), root mean square error (RMSE), and maximum error (ME). The data shows that all error indicators of the method of this invention are significantly lower than those of the traditional model, fully verifying the accuracy of the correlation distortion relationship and the rationality of the inversion process, and providing a reliable correlation structure foundation for the subsequent generation of the underlying Gaussian random field.
[0110] Table 1. Comparison of the accuracy of inverse correlation coefficient calculation
[0111] After the relevant structure verification was passed, the spatial distribution and temporal history characteristics of the generated non-Gaussian random field were further verified, and the corresponding results are as follows: Figure 5 and Figure 6 As shown. Figure 5The figure contains five sub-figures, showing the spatial distribution of the underlying Gaussian field (shared by HPM and PHPM), the underlying Gaussian field (UHPM), the non-Gaussian field (HPM), the non-Gaussian field (UHPM), and the non-Gaussian field (PHPM). The horizontal axis represents spatial location, and the vertical axis represents wind speed. As can be seen from the figure, the spatial distribution of the underlying Gaussian field exhibits a relatively uniform fluctuation characteristic, with no obvious extreme value concentration areas. After nonlinear mapping, the non-Gaussian fields generated by the three models all show an asymmetric distribution. However, the spatial distribution of the non-Gaussian field generated by the method of this invention (PHPM) is more regular, forming obvious wind speed extreme value areas at spatial locations of 200-300m and 700-800m, with extreme wind speeds reaching 4.8 m / s. This is completely consistent with the spatial extreme value distribution location of the measured wind field, and the range of the extreme value area (about 100m) deviates from the measured result by only 5m. The extreme region of the non-Gaussian field generated by the HPM model is blurred, with an extreme wind speed of only 3.6 m / s, which deviates from the measured value by 1.2 m / s; the extreme wind speed of the UHPM model is 4.1 m / s, but the extreme region is offset by about 30 m. Figure 5 There are three simulation points ( The wind speed time history comparison chart shows the time history curves of three models: PHPM (this invention), HPM, and UHPM. The extreme values of 2.5 m / s at nodes such as 50s and 150s of the PHPM curve are consistent with the measured fluctuations and amplitudes. The HPM curve is flat with no obvious extreme values, and the extreme value of UHPM deviates by 8s. The peak pulse of PHPM at 2.8 m / s deviated from the measured time by less than 2 s, the peak pulse of HPM was only 1.8 m / s, and the peak pulse of UHPM lagged by 5 s. The PHPM peak value of 3.0 m / s perfectly matches the measured value, while HPM shows no significant peak value and UHPM peak value is only 2.3 m / s. It can be seen that the time history generated by PHPM closely matches the measured value in terms of fluctuation frequency, extreme value amplitude, and peak time, accurately reproducing the high-frequency oscillation and pulse characteristics of non-Gaussian wind fields, while HPM and UHPM are insufficient in terms of extreme values or synchronicity.
[0112] The performance differences of different models in preserving correlation coefficients were verified, and the corresponding results are as follows: Figure 7 As shown. Figure 7 It contains two subgraphs. Figure 7 (a) Comparison of autocorrelation coefficients Figure 7 (b) is a comparison of cross-correlation coefficients. Figure 7 In (a), the autocorrelation coefficient curve of the method of the present invention almost completely coincides with the target curve. In the entire range of time lag from 0 to 15 s, the absolute value of the fitting deviation is only 0.018 on average. The deviation of the HPM model gradually increases after a time lag of 5 s, with an average deviation of 0.097. The average deviation of the UHPM model is 0.063. Figure 7In (b), the cross-correlation coefficient curve of the method of the present invention shows a 98.5% fit with the target curve within a spatial lag range of 0-600m, and the correlation coefficient at a spatial lag of 300m is 0.34, with a deviation of only 0.01 from the target value of 0.35; while the correlation coefficient of the HPM model at this position is 0.27, with a deviation of 0.08; and the UHPM model is 0.30, with a deviation of 0.05. To further analyze the mechanism of the difference in correlation preservation, Figure 8 This demonstrates the relationship between the transfer function and the associated distortion. Figure 8 (a) shows the comparison of transfer functions, with the horizontal axis representing frequency and the vertical axis representing the magnitude of the transfer function. Figure 8 (b) shows the correlation distortion relationship, with the horizontal axis representing the Gaussian correlation coefficient at the bottom level and the vertical axis representing the non-Gaussian correlation coefficient. Figure 8 In (a), the transfer function curve of the method of the present invention is smoother, with an amplitude fluctuation range of only 0.02-0.03 over the entire frequency range, while the fluctuation range of the HPM model is 0.05-0.08 and that of the UHPM model is 0.04-0.06. This indicates that the piecewise translation strategy of the present invention causes less disturbance to the frequency characteristics. Figure 8 In (b), the correlation distortion curve of the method of the present invention deviates the least from the ideal straight line (no distortion), and the correlation distortion is only 1 / 3 of that of the HPM model. This is because the present invention uses piecewise Hermite polynomial coefficients, which can accurately adjust the mapping relationship according to the statistical characteristics of different intervals, effectively reducing the distortion of the correlation structure by nonlinear mapping, thereby ensuring the accurate preservation of autocorrelation and cross-correlation coefficients. For quantitative comparison, a correlation coefficient preservation accuracy comparison table (Table 2) is constructed, and the results are evaluated from three indicators: autocorrelation fitting accuracy (ACF), cross-correlation fitting accuracy (CCF), and correlation distortion (CDD). The data further confirm the significant advantages of the method of the present invention in terms of correlation preservation.
[0113] Table 2 Comparison of Correlation Coefficient Preservation Accuracy
[0114] By comparing probability density functions (PDFs), the final verification of the fitting accuracy for non-Gaussian distributions is completed, and the corresponding results are as follows: Figure 9 As shown. Figure 9 It contains three sub-graphs, namely the one with a spatial location of 520m ( ), 570m ), 670m ( The PDF comparison curves at the points shown are plotted with wind speed on the horizontal axis and probability density value on the vertical axis. As can be seen from the three sub-plots, the target PDF exhibits a clear non-Gaussian characteristic, characterized by a narrow main range and a wide tail. Even at wind speeds of ±5 m / s, it still shows a significant probability density value (approximately 0.02 1 / m / s), consistent with the extreme value distribution characteristics of strong wind fields. The PDF curve generated by the method of this invention shows a 98.1% overlap with the target curve in the main range (-3 to 3 m / s) and a 96.8% overlap in the tail range (>3 m / s or <-3 m / s). Particularly noteworthy is the probability density value of 0.019 1 / m / s at a wind speed of 5 m / s, deviating from the target value of 0.020 1 / m / s by only 0.001 1 / m / s. The HPM model shows an overlap of 89.3% in the main interval but only 82.5% in the tail interval, with a probability density of 0.012 1 / m / s at 5 m / s and a deviation of 0.008 1 / m / s. The UHPM model shows an overlap of 93.5% in the main interval and 90.1% in the tail interval, with a deviation of 0.004 1 / m / s at 5 m / s. From a distributional perspective, the PDF curve of this invention perfectly replicates the asymmetry and wide tail of the target distribution, while the curve of the traditional model is relatively thin, with excessively rapid tail decay, failing to accurately capture the extreme probability characteristics of strong non-Gaussian wind fields. This result demonstrates that this invention, combining the maximum entropy method and the piecewise Hermite multinomial model, can accurately reconstruct the target non-Gaussian marginal distribution under finite-order statistical moments. It achieves high-precision fitting for both the conventional probability characteristics of the main interval and the extreme probability characteristics of the tail interval, ultimately verifying the overall effectiveness and superiority of the method.
[0115] The method of this invention shows significant advantages in all core aspects. The generated stable non-Gaussian wind field samples are highly consistent with the measured wind field in four dimensions: frequency domain characteristics, correlation structure, spatial-temporal distribution, and probability distribution. It can provide high-precision data support for the wind-resistant design of major projects and fully meet the reliability requirements of engineering applications.
[0116] The above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. For those skilled in the art, the present invention can have various modifications and variations. Any changes, modifications, substitutions, integrations, and parameter changes made to these embodiments within the spirit and principles of the present invention, without departing from the principles and spirit of the present invention, through conventional substitutions or to achieve the same function, fall within the scope of protection of the present invention.
Claims
1. A method for simulating stationary non-Gaussian wind fields based on random waves, characterized in that, include: Obtain the autopower spectrum and coherence function of the target wind speed field; Construct the target non-Gaussian wavenumber-frequency spectrum based on the self-power spectrum and coherence function; The wavenumber and frequency are discretized, and a low-level stationary Gaussian random field is generated by using a random spectral representation and combining it with a two-dimensional fast Fourier transform. Based on the finite-order statistical moments of the target wind speed process, the maximum entropy method is used to reconstruct the target non-Gaussian marginal probability density function and cumulative distribution function. The edge distribution is embedded into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian. Based on the relevant distortion relationship, the underlying Gaussian correlation structure is derived from the target non-Gaussian correlation structure, and the underlying Gaussian spectral characteristics are determined from the underlying Gaussian correlation structure. Applying the piecewise translation mapping function to the underlying stationary Gaussian random field yields stationary non-Gaussian wind field samples.
2. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 1, characterized in that, The target non-Gaussian wavenumber-frequency spectrum is constructed by performing a spatial Fourier transform on the coherence function to obtain the spectral distribution in the wavenumber dimension. The specific calculation formula is as follows: ,in, The non-Gaussian self-power spectrum of the target wind speed field. Let be the coherence function of the target wind speed field, describing the frequency domain correlation between spatial points. For wave number, For frequency, This is the spatial lag. It is the imaginary unit.
3. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 2, characterized in that, The wavenumber and frequency are discretized, and a random spectral representation is used in conjunction with a two-dimensional fast Fourier transform to generate a stationary Gaussian random field at the underlying level. Specifically, the number of wavenumber discrete segments is calculated. With frequency discrete segment number All are chosen to be integer powers of 2, and satisfy the requirement of spatial discretization quantity. Number of time discretizations To avoid aliasing effects, the generation formula for the underlying stationary Gaussian random field is: ,in, To take the real part of a complex number, This indicates the Fast Fourier Transform operation. Indicates the inverse fast Fourier transform operation, subscript and These represent transformations performed along the wavenumber and frequency dimensions, respectively. Wavenumber-frequency domain coefficients, For frequency direction identification, For wavenumber discrete indexing, For frequency discrete indexing, , The underlying Gaussian wavenumber-frequency spectrum, For the first discrete wave values For the first A discrete frequency value, Wavenumber step size, For frequency step size, To distribute evenly in Random phase angle within the interval, For spatial location variables, It is a time variable.
4. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 1, characterized in that, The maximum entropy method reconstructs the target non-Gaussian marginal probability density function using an exponential family density function in the form of moment constraints. The specific formula is as follows: ,in, The target non-Gaussian marginal probability density function is to be reconstructed. For a random variable to take values, Let Lagrange multipliers be the ones to be solved. The order of moments is determined by the entropy increment threshold. Or the equivalence criterion determines; the Lagrange multipliers satisfy the moment constraint condition. ( ), For the target wind speed process Statistical moments of order, The integration interval is determined by a truncation strategy based on the linear displacement moment or the tail threshold of the target distribution.
5. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 1, characterized in that, The piecewise translation mapping function uses a threshold As the segmentation point, differentiated Hermite polynomial coefficients are used in different intervals, with the specific formula as follows: in, Let Gaussian be a piecewise translation function from non-Gaussian. The values are those of the underlying Gaussian random field. The median of the target non-Gaussian wind field. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. for The standard deviation of the target non-Gaussian wind field corresponding to the interval. for The target non-Gaussian wind field kurtosis corresponds to the interval. Indicated by kurtosis A Hermite polynomial model with parameters.
6. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 1, characterized in that, The correlation distortion relationship is established through the integral relationship of the two-dimensional joint Gaussian density. An explicit mapping between non-Gaussian and Gaussian correlations is obtained through Hermite coefficient expansion. The target non-Gaussian correlation coefficient is then used to determine the correlation. Inversely calculate the underlying Gaussian correlation coefficient The formula is: in, For the target non-Gaussian wind field in spatial lag Time lag The correlation coefficient at the location, The correlation coefficient is the value corresponding to the underlying Gaussian random field. This is the proportionality coefficient. and These are the third and fourth order Hermite coefficients of the target non-Gaussian wind field, respectively. and These are intermediate calculation parameters. , , , , It is an intermediate parameter for calculating the target non-Gaussian correlation coefficient and the square of the fourth-order Hermite coefficient. It is an intermediate calculation parameter for the square of the third-order Hermite coefficients and the fourth-order Hermite coefficients raised to the fourth power.
7. The method for simulating stationary non-Gaussian wind fields based on random waves according to claim 6, characterized in that, The underlying Gaussian spectral characteristics are determined by the underlying Gaussian correlation structure through the Wiener-Khintchine transform. The specific calculation formula is as follows: ,in, For the bottom Gaussian wavenumber-frequency spectrum at the 1st Discrete wavenumbers , No. discrete frequency The value at that location, To take the real part of a complex number, For the time lag step, For spatial lag step size, For the first Spatial lag discrete value For the first Discrete values with time lag For spatially delayed discrete quantities, For discrete quantities with time lag, For the underlying Gaussian random field , The correlation coefficient at the location, It is the imaginary unit.
8. A stationary non-Gaussian wind field simulation system based on random waves, characterized in that, include: The spectrum construction module acquires the autopower spectrum and coherence function of the target wind speed field, and constructs the target non-Gaussian wavenumber-frequency spectrum based on the autopower spectrum and coherence function. The underlying Gaussian field generation module discretizes the wavenumber and frequency, and uses a random spectrum representation combined with two-dimensional fast Fourier transform to generate a bottom-level stationary Gaussian random field. The maximum entropy distribution reconstruction module reconstructs the non-Gaussian marginal probability density function and cumulative distribution function of the target wind speed process using the maximum entropy method, based on the finite-order statistical moments of the target wind speed process. The piecewise translation mapping module embeds the edge distribution into a piecewise Hermite polynomial model to construct a piecewise translation mapping function from Gaussian to non-Gaussian. The correlation distortion inverse calculation module inversely calculates the underlying Gaussian correlation structure from the target non-Gaussian correlation structure based on the correlation distortion relationship, and determines the underlying Gaussian spectral characteristics based on the underlying Gaussian correlation structure. The sample output module applies the piecewise translation mapping function to the underlying stationary Gaussian random field and outputs stationary non-Gaussian wind field samples that satisfy the target statistical characteristics.
9. An electronic device, characterized in that, The device includes a processor and a memory, wherein the memory stores a computer program, and when the computer program is executed by the processor, the electronic device performs a method for simulating a stationary non-Gaussian wind field based on random waves as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, It stores a computer program, which, when executed by a processor, is used to implement a method for simulating a stationary non-Gaussian wind field based on random waves, as described in any one of claims 1 to 7.