Method and system for efficiently simulating steady fluctuating wind field based on self-adaptive wave number sampling

Abstract

The invention discloses an efficient simulation method and system for a steady fluctuating wind field based on adaptive wave number sampling. The method comprises the following steps: obtaining frequency discrete points; calculating an equivalent probability density function; obtaining an equivalent cumulative distribution function, obtaining wavenumber discrete points, and calculating a discrete value of the equivalent cumulative distribution function under the wavenumber corresponding to each wavenumber discrete point; obtaining non-uniform wavenumber discrete sampling points of a wavenumber domain; obtaining a frequency-wavenumber discrete point matrix and a non-uniform wavenumber discrete point interval matrix of the frequency-wavenumber joint power spectral density function; and generating a wind speed time history sample of the simulation point by adopting fast Fourier transform and non-uniform fast Fourier transform. According to the method, the non-uniform discrete sampling points are obtained, the characteristics of the given frequency-wave number joint spectrum on the wave number domain can be well captured, the self-adaption is high, the wind speed time history sample of each simulation point can be generated by adopting fast Fourier transform and non-uniform fast Fourier transform, and the simulation efficiency and precision can be improved.

Description

Technical Field

[0001] This invention relates to the field of time history simulation technology for pulsating wind speed, and specifically to an efficient simulation method and system for stable pulsating wind fields using adaptive wavenumber sampling. Background Technology

[0002] Stochastic process simulation is the core foundation for time-domain analysis of structural dynamic response and structural reliability assessment. Especially in the design of long-span structures and high-rise buildings, the simulation quality of multivariable fluctuating wind speed fields directly affects the accuracy of structural wind resistance performance analysis. Therefore, accurate simulation of the fluctuating wind field experienced by the structure is an indispensable key link in engineering design. Among existing simulation methods, spectral representation based on the joint wavenumber-frequency spectrum has become a widely used and effective approach for simulating multivariable fluctuating wind fields. The accuracy and efficiency of simulating pulsating wind fields using this method depend on the choice of discretization strategies in the frequency and wavenumber domains. Traditional discretization strategies fall into two categories: one employs a uniform discretization strategy in both the frequency and wavenumber domains, such as the uniform discretization sampling scheme disclosed in Brett A. Benowitz and George Deodatis's paper "Simulation of wind velocities on long span structures: A novelstochastic wave based model"; the other employs a non-uniform discretization strategy in both the frequency and wavenumber domains. Because the energy of the wavenumber-frequency joint power spectrum is mainly concentrated near the origin, especially exhibiting an approximately exponential decay characteristic near low frequencies, traditional uniform sampling strategies cannot capture this feature, resulting in low efficiency and accuracy of simulation results, failing to meet the engineering requirements for efficient and high-precision analysis. While traditional non-uniform wavenumber discretization methods can improve simulation accuracy to some extent, their sampling format is incompatible with Fast Fourier Transform (FFT), leading to low simulation efficiency. Some adaptive non-uniform wavenumber discretization schemes require empirical parameters to capture the characteristics of the frequency-wavenumber spectrum in the wavenumber domain, greatly limiting their applicability in complex scenarios. Furthermore, the paper "A PDF discretization scheme in wavenumber–frequency joint spectrum for simulating multivariate random fluctuating wind fields" by Yang Li and Jun Xu discloses a non-uniform wavenumber discretization scheme based on the probability density function (PDF), which only considers the wavenumber domain transformation characteristics of the frequency-wavenumber joint power spectrum at a certain characteristic frequency, without considering the variation characteristics of the frequency-wavenumber joint spectrum at different frequencies (e.g.,Figure 1 As shown in the figure Indicates wave number, Indicates frequency, (Representing wavenumber discrete points), the simulation accuracy is poor, and it cannot be directly adapted to non-uniform fast Fourier transform (NUFFT) for accelerated calculation, which also results in low simulation efficiency. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide an efficient simulation method and system for steady pulsating wind fields with adaptive wavenumber sampling, which addresses the above-mentioned problems in the prior art. The non-uniform wavenumber sampling points generated by this invention can capture the characteristics of the input frequency-wavenumber joint spectrum and can simultaneously perform wind speed time history simulation with both fast Fourier transform and non-uniform fast Fourier transform, thereby improving simulation efficiency and accuracy.

[0004] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: An efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling includes the following steps: S1, Based on the frequency domain of the stable pulsating wind field to be simulated, the frequency domain is uniformly discretized to obtain... Discrete frequency points ; S2, targeting Each frequency discrete point in a frequency discrete point Based on a given frequency-wavenumber joint power spectral density function Calculate the discrete points of the frequency The equivalent probability density function of the corresponding frequency-wavenumber joint power spectral density function ,in, , Indicates wave number; S3, for The equivalent cumulative distribution function of the frequency-wavenumber joint power spectral density function is obtained by integration. Based on the wavenumber domain of the desired stable fluctuating wind field, the wavenumber domain is uniformly discretized to obtain... Wavenumber discrete points ,calculate Discrete values ​​of the equivalent cumulative distribution function at each wavenumber discrete point ; S4, based on the obtained discrete values Each frequency discrete point is obtained by interpolation and mapping. Non-uniform wavenumber discrete sampling points in the lower wavenumber domain ,in, The number of discrete sampling points for non-uniform wavenumber. Represents the discrete points of frequency The nth non-uniform wavenumber discrete sampling point, , will obtain Sort by numerical value in ascending order. Calculations yielded Spacing value between ,in, ; ; S5, obtain the discrete points of each frequency. The frequency-wavenumber discrete point matrix of the frequency-wavenumber joint power spectral density function formed by the non-uniform wavenumber discrete sampling points in the lower wavenumber domain To obtain the discrete points of each frequency Down The non-uniform wavenumber discrete point spacing matrix formed by the spacing values ​​between the frequency-wavenumber joint power spectral density function ; S6, and Substituting the stochastic process simulation formula based on spectral representation, wind speed time history samples for each simulation point are generated using Fast Fourier Transform (FFT) and Non-Uniform FFT. ,in, Represents the spatial coordinates of the simulated point. Indicates time.

[0005] Optionally, in step S1, the frequency discrete points are obtained according to the following formula: , in, , Indicates the cutoff frequency.

[0006] Optionally, in step S2, the equivalent probability density function is calculated according to the following formula. : , , , in, This indicates the cutoff wavenumber.

[0007] Optionally, in step S3, the wavenumber discrete points are obtained according to the following formula: , , , The discrete value of the equivalent cumulative distribution function is calculated according to the following formula. : .

[0008] Optionally, step S4 specifically includes the following steps: S401, in the interval Internal generation size is random number matrix And the The random numbers in the data follow a uniform distribution; S402, calculate the non-uniform wavenumber discrete sampling points in the wavenumber domain using the following formula: , in, This represents a linear interpolation function used to calculate the discrete values ​​of the equivalent cumulative distribution function. and the corresponding discrete wavenumber Linear interpolation is performed between the discrete values ​​of every two adjacent equivalent cumulative distribution functions, and the result is obtained by mapping to the input value. Equal interpolation corresponds to wavenumber points.

[0009] Optionally, in step S5, Frequency-wavenumber discrete point matrix Represented as: , Non-uniform wavenumber discrete point spacing matrix Represented as: .

[0010] Optionally, in step S6, wind speed time history samples for each simulation point are generated using Fast Fourier Transform and Non-Uniform Fast Fourier Transform according to the following formula. : , Where Re represents the operation of taking the real part of a complex number. This indicates performing a Fast Fourier Transform in the frequency domain. This indicates that a non-uniform fast Fourier transform is performed in the wavenumber domain. This represents the inverse of the Fast Fourier Transform in the frequency domain. , and This indicates that the corresponding non-uniform wavenumber discrete point is A pair of independent random phase angles distributed in [0, 2π].

[0011] Optionally, corresponding to each non-uniform wavenumber discrete point All methods employ a partially stratified sampling approach based on number theory to generate multiple pairs of independent random phase angles that are equally numerous and uniformly distributed within the range [0, 2π]. and .

[0012] Optionally, the given frequency-wavenumber joint power spectral density function The expression is as follows: , in, The Kaimal spectrum is used to describe the auto-power spectral density function at each simulation point. It is a coherence function in the frequency-wavenumber domain; The expression is: , In the above formula, Indicates shear wave velocity. Indicates the height of the simulated point. Indicates at altitude The average wind speed at a location is defined as: , in, Indicates the length of the surface roughness. Represents the von Kármán coefficient; The expression is: , in, This represents the attenuation coefficient.

[0013] Furthermore, the present invention also provides an efficient simulation system for a stationary pulsating wind field with adaptive wavenumber sampling, including a memory, a processor, and an adaptive wavenumber sampling simulation program for a stationary pulsating wind field stored in the memory and executable on the processor. The adaptive wavenumber sampling simulation program for a stationary pulsating wind field is executed by the processor using the aforementioned efficient simulation method for a stationary pulsating wind field with adaptive wavenumber sampling.

[0014] Compared with the prior art, the present invention has the following main advantages: 1. This invention calculates the discrete value of the equivalent cumulative distribution function of the frequency-wavenumber joint power spectral density function at each discrete frequency and the corresponding wavenumber at each wavenumber sampling point. By interpolating between these discrete values, non-uniform discrete sampling points in the wavenumber domain at each discrete frequency are obtained. This achieves dense sampling near the origin of the frequency-wavenumber joint power spectrum and sparse sampling far from the origin, so that these non-uniform discrete sampling points can capture the characteristics of the given frequency-wavenumber joint spectrum in the wavenumber domain well, with strong adaptability and high simulation accuracy. 2. This invention can take into account the variation characteristics of the frequency-wavenumber joint power spectrum at all discrete frequencies, and can use fast Fourier transform and non-uniform fast Fourier transform to generate wind speed time history samples for each simulation point, thereby improving simulation efficiency and accuracy. Attached Figure Description

[0015] Figure 1 This is a schematic diagram showing the distribution of all non-uniform wavenumber discretization sampling points in a PDF-based non-uniform wavenumber discretization scheme.

[0016] Figure 2 This is a flowchart illustrating the execution of the method according to an embodiment of the present invention.

[0017] Figure 3 This is a schematic diagram illustrating the method for obtaining non-uniform wavenumber discrete sampling points according to an embodiment of the present invention.

[0018] Figure 4 This is a schematic diagram showing the distribution of all non-uniform wavenumber sampling points in the example.

[0019] Figure 5 A comparison of the self-power spectral density function and the corresponding target value at the second simulation point in the example.

[0020] Figure 6 A comparison of the self-power spectral density function and the corresponding target value at simulation point 51 in the example.

[0021] Figure 7 A comparison of the self-power spectral density function and the corresponding target value at simulation point 151 in the example.

[0022] Figure 8 A comparison graph of the cross-correlation function between the 2nd and 51st simulation points in the example and the corresponding target values.

[0023] Figure 9 A comparison graph of the cross-correlation function between simulation point 51 and simulation point 151 in the example and the corresponding target value.

[0024] Figure 10 A comparison graph of the cross-correlation function between the second simulation point and the 152nd simulation point in the example and the corresponding target value. Detailed Implementation

[0025] The technical solution of the present invention will now be described in further detail with reference to the accompanying drawings.

[0026] like Figure 2 As shown in this embodiment, the efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling includes the following steps: S1, Based on the frequency domain of the stable pulsating wind field to be simulated, the frequency domain is uniformly discretized to obtain... Discrete frequency points .

[0027] In this embodiment, the frequency discrete points are obtained by formula (1). (1) In formula (1), , Indicates the cutoff frequency.

[0028] S2, targeting Each frequency discrete point in a frequency discrete point Based on a given frequency-wavenumber joint power spectral density function (WFJS) Calculate the discrete points of the frequency The corresponding equivalent probability density function (WFJS-PDF) ,in, , Indicates wave number.

[0029] In this embodiment, Calculated according to formulas (2) to (4): (2) (3) (4) in, Indicates the cutoff wavenumber. The intermediate parameter has no specific meaning.

[0030] S3, for The equivalent cumulative distribution function (WFJS-ECDF) of the frequency-wavenumber joint power spectral density function is obtained by integration. Based on the wavenumber domain of the desired stable fluctuating wind field, the wavenumber domain is uniformly discretized to obtain... Wavenumber discrete points ,calculate Discrete values ​​of the equivalent cumulative distribution function at each wavenumber discrete point. .

[0031] In this embodiment, wavenumber sampling points are obtained according to formulas (5) and (6): , (5) (6) Calculate the discrete value of the equivalent cumulative distribution function according to formula (7). : (7) S4, based on the obtained discrete values Each frequency discrete point is obtained by interpolation and mapping. Non-uniform wavenumber discrete sampling points in the lower wavenumber domain ,in, The number of discrete sampling points for non-uniform wavenumber. Represents the discrete points of frequency The nth non-uniform wavenumber discrete sampling point, , will obtain Sort by numerical value in ascending order. Calculations yielded Spacing value between ,in, (8) In this embodiment, step S401 specifically includes the following steps: S401, in the interval Internal generation size is random number matrix ,and The random numbers in the matrix follow a uniform distribution. It should be noted that there are a total of such random number matrices. indivual, This refers to the corresponding number Discrete frequencies (i.e., frequencies of ) A random number matrix under ( ); S402, calculate the non-uniform wavenumber discrete sampling points in the wavenumber domain using the following formula: (9) in, This represents a linear interpolation function used to calculate the discrete values ​​of the equivalent cumulative distribution function. and the corresponding discrete wavenumber Linear interpolation is performed between the discrete values ​​of every two adjacent equivalent cumulative distribution functions, and the result is obtained by mapping to the input value. Equal interpolation corresponding wavenumber points (e.g.) Figure 3 As shown in the figure, LIF represents the difference function, the red segment between each adjacent blue dot is a straight line segment, and the yellow dot is the obtained non-uniform wavenumber discrete sampling point.

[0032] S5, obtain the discrete points of each frequency. The frequency-wavenumber discrete point matrix of the frequency-wavenumber joint power spectral density function formed by the non-uniform wavenumber discrete sampling points in the lower wavenumber domain To obtain the discrete points of each frequency Down The non-uniform wavenumber discrete point spacing matrix formed by the spacing values ​​between the frequency-wavenumber joint power spectral density function ; In this embodiment, the frequency-wavenumber discrete point matrix Represented as: (10) Non-uniform wavenumber discrete point spacing matrix Represented as: (11) S6, and Substituting the stochastic process simulation formula based on spectral representation, wind speed time history samples for each simulation point are generated using Fast Fourier Transform (FFT) and Non-Uniform FFT. ,in, Represents the spatial coordinates of the simulated point. Indicates time.

[0033] Specifically, the formula for simulating stochastic processes based on spectral representation is as follows: (12) In this embodiment, the specific process of step S6 is as follows: First, we introduce Euler's formula to rewrite equation (11) as follows: (13) Then, wind speed time history samples for each simulation point are generated using Fast Fourier Transform and Non-Uniform Fast Fourier Transform. : (14) (15) Where Re denotes the operation of taking the real part of a complex number, FFT represents Fast Fourier Transform, NUFFT represents Non-Uniform Fast Fourier Transform, and IFFT represents the inverse Fast Fourier Transform. The intermediate parameter has no specific meaning. and This indicates that the corresponding non-uniform wavenumber discrete point is A pair of independent random phase angles distributed in [0, 2π]. It should be noted that... In a uniform wind field, the coordinates are the horizontal coordinates of the simulated point, while in a non-uniform wind field, the coordinates are the spatial height (i.e., the vertical coordinates) of the simulated point.

[0034] Preferably, corresponding to each non-uniform wavenumber discrete point All methods employ a partially stratified sampling approach based on number theory to generate multiple pairs of independent random phase angles that are equally numerous and uniformly distributed within the range [0, 2π]. and Substituting these multiple pairs of random phase angles into formula (14) generates multiple sets of stable pulsating wind fields, which is beneficial for subsequent random process simulation and structural reliability calculation of the structure. Furthermore, the use of a partially stratified sampling method based on number theory to generate independent random phase angles helps ensure a uniform distribution of the random phase angles and guarantees that each pair of random phase angles is strictly independent. It should be noted that, assuming each non-uniform wavenumber discrete point... If m pairs of random phase angles are generated, then after substituting them into formula (14), m sets of steady pulsating wind fields will be generated.

[0035] As an optional embodiment, the given frequency-wavenumber joint power spectral density function The expression is as follows: (16) in, The Kaimal spectrum is used to describe the auto-power spectral density function at each simulation point. It is a coherence function in the frequency-wavenumber domain; The expression is: (17) In the above formula, Indicates shear wave velocity. Indicates the height of the simulated point. Indicates at altitude The average wind speed at a location is defined as: (18) in, Indicates the length of the surface roughness. Represents the von Kármán coefficient; The expression is: (19) in, This represents the attenuation coefficient, which is generally between 7 and 10.

[0036] Kaimal spectra can effectively capture the non-stationary characteristics of strong winds and the intermittent nature of turbulence. Of course, in other embodiments, Davenport spectra and Simiu spectra can also be used to describe the self-power spectral density function of each simulation point.

[0037] This efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling calculates the discrete value of the equivalent cumulative distribution function of the frequency-wavenumber joint power spectral density function at each discrete frequency, corresponding to the wavenumber at each wavenumber sampling point. It then interpolates these discrete values ​​to obtain non-uniform discrete sampling points in the wavenumber domain for each discrete frequency. This achieves dense sampling near the origin of the frequency-wavenumber joint power spectrum and sparse sampling far from the origin, allowing these non-uniform discrete sampling points to effectively capture the characteristics of the given frequency-wavenumber joint spectrum in the wavenumber domain. This method exhibits strong adaptability and high simulation accuracy. Furthermore, it considers the variation characteristics of the frequency-wavenumber joint power spectrum across all discrete frequencies and utilizes Fast Fourier Transform (FFT) and Non-Uniform FFT to generate wind speed time history samples for each simulation point, thus improving simulation efficiency and accuracy.

[0038] To verify the effectiveness of this efficient simulation method for stationary fluctuating wind fields using adaptive wavenumber sampling, the following is a specific example: A horizontally distributed, stable wind field was simulated, with a total of 2049 simulation points. These simulation points were uniformly distributed along a horizontal straight line of 1600m, and their heights were all 40m.

[0039] In this example, the Kaimal spectrum (i.e., formula (17)) is used to describe the power spectral density function of each simulation point, and the relevant parameters are taken as follows: , , .

[0040] In this example, the coherence function in the frequency-wavenumber domain is given by formula (18), where, .

[0041] Therefore, the frequency-wavenumber joint power spectral density function given in this example The expression is equation (16).

[0042] The calculation steps for this example, based on the efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling in the above embodiments, are as follows: S01, the frequency discrete points are obtained by calculating using formula (1), where formula (1) Take 2048, Take 4π rad / s; S02, Substitute the obtained frequency discrete points into formula (16) to obtain By using formulas (2) to (4) The equivalent probability density function of the frequency-wavenumber joint power spectral density spectrum is obtained by performing probability density normalization. ; S03, obtain the wavenumber sampling points through formulas (5) and (6), and substitute the wavenumber sampling points into formula (7) to obtain the discrete values ​​of the equivalent cumulative distribution function. ,in, Pick , Pick ; S04, in the interval Internal generation size is random number matrix ,and The random numbers in the data follow a uniform distribution. Using formula (9) discrete values Interpolation and mapping are performed between them to obtain the non-uniform wavenumber discrete sampling points in the wavenumber domain at each discrete frequency. The non-uniform wavenumber discrete sampling points are arranged in ascending order to obtain According to formula (8), we get Spacing value between ; S05, obtained from each frequency discrete point according to formula (10) The non-uniform wavenumber discrete sampling points in the lower wavenumber domain form the frequency-wavenumber discrete point matrix of the frequency-wavenumber joint power spectral density function. According to formula (11), the discrete points of each frequency are obtained. Down The spacing values ​​between them constitute the non-uniform wavenumber discrete point spacing matrix of the frequency-wavenumber joint power spectral density function. ; S06, using number theory-based partially stratified sampling (NTM-PSS), generates 610 representative random phase angles uniformly distributed in the range [0, 2π]. and ,Will , , and Substituting these values ​​into formula (15) yields 610 wind speed time histories for each simulation point. sample, Indicates the first Spatial coordinates of each simulated point The values ​​are 1, 2, ..., 2049. Indicates the first Wind speed time history sample The value of is 1, 2, ..., 610.

[0043] Through the above steps, 610 wind speed time history samples from 2049 simulation points can be generated.

[0044] To illustrate the adaptability and reasonable accuracy of the non-uniform discrete sampling point sampling method of the present invention, Figure 4 The distribution of frequency discrete points and non-uniform wavenumber sampling points in the frequency and wavenumber domains is shown. As can be seen from the figure, this embodiment can take into account the variation characteristics of the frequency-wavenumber joint power spectrum at all discrete frequencies.

[0045] The autopower spectrum and cross-correlation function obtained in this example are compared with the corresponding defined target values. Figures 5-10 The verification results of the autopower spectrum and cross-correlation function of the simulated wind speed are presented. As shown in the figure, the simulated value (Proposed) is very close to the target value (Target), thus demonstrating the adaptability of the non-uniform wavenumber discrete point sampling method and the accuracy of the simulation results in the efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling of this invention. It should be noted that... Figures 5-7 In this context, PSD represents power spectral density. Indicates frequency, Figures 8-10 In this context, CCF represents the cross-correlation function. Indicates time.

[0046] In this example, the expression for the estimated power spectrum function is as follows: (20) in, and These represent the spatial coordinates in the simulated wind field. The estimated self-power spectrum function at the simulation point and the first Wind speed time history sample Indicates period, The corresponding target self-power spectrum is the Kaimal spectrum, and its expression is given in formula (17).

[0047] Coordinate values and The expression for the estimated cross-correlation function of the two simulated points is as follows: (twenty one) in, This represents the time interval of the wind speed time history sample.

[0048] Spatial coordinates are and The expression for the target cross-correlation function of the two simulated points is as follows: (twenty two) To further illustrate the advancements of the non-uniform discretization scheme of the adaptive wavenumber sampling method for efficient simulation of stationary fluctuating wind fields in this embodiment compared to the traditional uniform discretization scheme ("Simulation of wind velocities on long span structures: A novel stochastic wave based model") and the non-uniform wavenumber discretization scheme based on probability density function (PDF) ("A PDF discretization scheme in wavenumber–frequency joint spectrum for simulating multivariate random fluctuating wind fields"), wind field simulations were also performed on the aforementioned specific examples using the traditional uniform discretization scheme and the non-uniform wavenumber discretization method based on probability density function (PDF). The simulation results were then compared with the non-uniform discretization scheme of the adaptive wavenumber sampling method for efficient simulation of stationary fluctuating wind fields in this embodiment. It should be noted that the traditional uniform sampling scheme has 1024 wavenumber discrete points at each frequency discrete point. Because the uniform discretization scheme uses Fast Fourier Transform, its cutoff wavenumber must correspond to the total simulation length, which is 8.04 (rad / m). Other simulation parameters are the same as those used in the efficient simulation method for stationary pulsating wind fields with adaptive wavenumber sampling in this embodiment. In the non-uniform wavenumber discretization scheme based on the probability density function (PDF), the number of non-uniform wavenumber discrete sampling points at each discrete frequency is selected as 400, and the number of uniform wavenumber discrete sampling points is selected as 300, for a total of 700 wavenumber discrete sampling points. Other simulation parameters are the same as those used in the efficient simulation method for stationary pulsating wind fields with adaptive wavenumber sampling in this embodiment.

[0049] The errors of the self-power spectrum of the non-uniform discretization scheme, the traditional uniform discretization scheme, and the traditional non-uniform discretization scheme in this embodiment are estimated using the following formulas: (twenty three) Error calculations for the self-power spectrum were performed at the second simulation point, and the statistical results are shown in the table below:

[0050] As shown in the table, this embodiment achieves better simulation accuracy than the other two schemes while using fewer wavenumber discrete sampling points. It should be noted that the error values ​​of the power spectrum at other simulation points are very close to those at the second simulation point, further demonstrating the superiority of the non-uniform discrete scheme in this embodiment.

[0051] Furthermore, this embodiment also provides an efficient simulation system for a stationary pulsating wind field with adaptive wavenumber sampling, including a memory, a processor, and an adaptive wavenumber sampling simulation program for a stationary pulsating wind field stored in the memory and executable on the processor. When the adaptive wavenumber sampling simulation program is executed by the processor, it implements an efficient simulation method for a stationary pulsating wind field with adaptive wavenumber sampling.

[0052] Those skilled in the art will understand that the technical solutions provided by the embodiments of this application may be in the form of a method, system, or computer program product. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product embodied on one or more computer-readable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create an implementation for the process. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable apparatus for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0053] The above description is merely a preferred embodiment of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method for efficient simulation of stationary fluctuating wind fields using adaptive wavenumber sampling, characterized in that, Includes the following steps: S1, Based on the frequency domain of the stable pulsating wind field to be simulated, the frequency domain is uniformly discretized to obtain... Discrete frequency points ; S2, targeting Each frequency discrete point in a frequency discrete point Based on a given frequency-wavenumber joint power spectral density function Calculate the discrete points of the frequency The corresponding equivalent probability density function ,in, , Indicates wave number; S3, for The equivalent cumulative distribution function of the frequency-wavenumber joint power spectral density function is obtained by integration. Based on the wavenumber domain of the desired stable fluctuating wind field, the wavenumber domain is uniformly discretized to obtain... Wavenumber discrete points ,calculate Discrete values ​​of the equivalent cumulative distribution function at each wavenumber discrete point ; S4, based on the obtained discrete values Each frequency discrete point is obtained by interpolation and mapping. Non-uniform wavenumber discrete sampling points in the lower wavenumber domain ,in, The number of discrete sampling points for non-uniform wavenumber. Represents the discrete points of frequency The nth non-uniform wavenumber discrete sampling point, , will obtain Sort by numerical value in ascending order. Calculations yielded Spacing value between ,in, ; ; S5, obtain the discrete points of each frequency. The frequency-wavenumber discrete point matrix of the frequency-wavenumber joint power spectral density function formed by the non-uniform wavenumber discrete sampling points in the lower wavenumber domain To obtain the discrete points of each frequency Down The non-uniform wavenumber discrete point spacing matrix formed by the spacing values ​​between the frequency-wavenumber joint power spectral density function ; S6, and Substituting the stochastic process simulation formula based on spectral representation, wind speed time history samples for each simulation point are generated using Fast Fourier Transform (FFT) and Non-Uniform FFT. ,in, Represents the spatial coordinates of the simulated point. Indicates time.

2. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 1, characterized in that, In step S1, the frequency discrete points are obtained according to the following formula: ， in, , Indicates the cutoff frequency.

3. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 1, characterized in that, In step S2, the equivalent probability density function is calculated according to the following formula. : ， ， ， in, This indicates the cutoff wavenumber.

4. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 1, characterized in that, In step S3, the wavenumber discrete points are obtained according to the following formula: ， ， ， The discrete value of the equivalent cumulative distribution function is calculated according to the following formula. : 。 5. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 1, characterized in that, Step S4 specifically includes the following steps: S401, in the interval Internal generation size is random number matrix And the The random numbers in the data follow a uniform distribution; S402, calculate the non-uniform wavenumber discrete sampling points in the wavenumber domain using the following formula: ， in, This represents a linear interpolation function used to calculate the discrete values ​​of the equivalent cumulative distribution function. and the corresponding discrete wavenumber Linear interpolation is performed between the discrete values ​​of every two adjacent equivalent cumulative distribution functions, and the result is obtained by mapping to the input value. Equal interpolation corresponds to wavenumber points.

6. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 5, characterized in that, In step S5, Frequency-wavenumber discrete point matrix for: ， Non-uniform wavenumber discrete point spacing matrix for: 。 7. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 1, characterized in that, In step S6, wind speed time history samples for each simulation point are generated using Fast Fourier Transform and Non-Uniform Fast Fourier Transform according to the following formula. : ， Where Re represents the operation of taking the real part of a complex number. This indicates performing a Fast Fourier Transform in the frequency domain. This indicates that a non-uniform fast Fourier transform is performed in the wavenumber domain. This represents the inverse of the Fast Fourier Transform in the frequency domain. , and This indicates that the corresponding non-uniform wavenumber discrete point is A pair of independent random phase angles distributed in [0, 2π].

8. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to claim 7, characterized in that, For each non-uniform wavenumber discrete point All methods employ a partially stratified sampling approach based on number theory to generate multiple pairs of independent random phase angles that are equally numerous and uniformly distributed within the range [0, 2π]. and .

9. The efficient simulation method for stationary pulsating wind fields using adaptive wavenumber sampling according to any one of claims 1 to 8, characterized in that, The given frequency-wavenumber joint power spectral density function The expression is as follows: ， in, The Kaimal spectrum is used to describe the auto-power spectral density function at each simulation point. It is a coherence function in the frequency-wavenumber domain; The expression is: ， In the above formula, Indicates shear wave velocity. Indicates the height of the simulated point. Indicates at altitude The average wind speed at a location is defined as: ， in, Indicates the length of the surface roughness. Represents the von Kármán coefficient; The expression is: ， in, This represents the attenuation coefficient.

10. A high-efficiency simulation system for stationary pulsating wind fields using adaptive wavenumber sampling, characterized in that, The system includes a memory, a processor, and an adaptive wavenumber sampling stationary pulsating wind field simulation program stored in the memory and executable on the processor. When the adaptive wavenumber sampling stationary pulsating wind field simulation program is executed by the processor, it implements the efficient simulation method for adaptive wavenumber sampling stationary pulsating wind fields as described in any one of claims 1 to 9.

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