Fluctuating wind field simulation method and system based on frequency-dependent uniform discrete strategy

Abstract

The invention discloses a fluctuating wind field simulation method and system based on a frequency-dependent uniform discrete strategy. The method comprises the following steps: establishing a target auto-power spectral density function according to actual wind speed time-history distribution characteristics; giving an initial wavenumber cut-off upper limit, and uniformly dispersing a frequency domain and a wavenumber domain at the same time; calculating the relative error of the estimated value of the auto-power spectral density function at each frequency discrete point, if the relative error is greater than a preset error tolerance upper limit, adjusting a wave number cut-off upper limit, and uniformly discretizing the wave number domain again until an error condition is met; according to the adjusted wavenumber cut-off upper limit, redivision of the initial uniform discrete frequency interval is realized; and generating a wind speed time history of the random fluctuating wind field. According to the method, the uniform discrete frequency domain is further divided by adaptively adjusting the wave number interval and controlling the relative error of the power spectrum density function, so that the rapid attenuation of the frequency-wave number spectrum in the wave number domain can be effectively captured, the simulation accuracy is ensured, the number of required wave number discrete points is greatly reduced, and the efficiency is improved.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of computational wind engineering, and particularly relates to a high-efficiency simulation method and system for fluctuating wind field. BACKGROUND

[0002] For wind-sensitive structures such as flexible and large-span structures, the influence of wind load is one of the key design considerations. However, the wind load acting on the structure is not a constant static force, but a random process with dynamic characteristics. It will cause complex dynamic responses of the structure, including vibration, fatigue and even aeroelastic instability. In order to accurately analyze and ensure the safety and applicability of the structure under the action of wind, engineers must obtain wind load time history that can accurately reflect the characteristics of wind (such as turbulence intensity, power spectral density and spatial coherence) as input. However, it is not only costly but also often unfeasible to directly obtain a large amount of measured wind data that meets specific site and meteorological conditions.

[0003] It is under this demand that wind field simulation technology emerges as the times require and becomes an indispensable core tool in modern structural wind engineering. Wind field simulation aims to generate random wind speed sequences that meet the statistical characteristics of real atmospheric wind field in time and space through computer numerical methods. These simulated wind speed time histories provide reliable and sufficient load input for subsequent structural dynamic analysis, enabling engineers to conduct comprehensive "wind tunnel tests" in a virtual environment, thereby optimizing design and improving structural performance.

[0004] In existing research, the simulation of random fluctuating wind field based on frequency-wave number spectrum is a high-efficiency and high-precision fluctuating wind field simulation technology. This technology mainly treats fluctuating wind speed field as a continuous space-time field in time and space rather than a discrete space and continuous time, and uses spectral representation based on frequency-wave number spectrum to obtain fluctuating wind speed time history without matrix decomposition. However, in the process of using spectral representation to convert the joint power spectrum in the frequency-wave number domain to the fluctuating wind speed time history at any position in space, uniform discretization of the frequency domain and the wave number domain is required, and the number of discrete points is huge. Directly using the accumulation of harmonic components makes the computational overhead too large, and in order to improve the simulation efficiency, the FFT (Fast Fourier Transform) algorithm is generally used for calculation. However, the FFT algorithm is only suitable for equidistant random fields, and when the discretization is insufficient, the simulation accuracy in the low frequency domain is insufficient. Using non-uniform discretization strategy can reduce the computational workload, but the irregularity of the selected points due to non-uniform intervals still increases the additional computational burden, reducing the simulation efficiency. SUMMARY

[0005] The application aims to provide a fluctuating wind field simulation method and system based on a frequency-dependent uniform discrete strategy to solve the problems of low simulation accuracy and low efficiency in existing uniform discrete strategies and non-uniform discrete strategies.

[0006] The technical scheme is a fluctuating wind field simulation method based on a frequency-dependent uniform discrete strategy, comprising the following steps:

[0007] S1, obtaining atmospheric parameters of a location where an engineering is located, and establishing a target self-power spectral density function according to actual wind speed time history distribution characteristics;

[0008] S2, according to the target self-power spectral density function, giving an initial wave number upper limit, uniformly discretizing the frequency domain and the wave number domain at the same time, and solving a frequency-wave number joint evolution power spectral density function based on a spatial coherence function;

[0009] S3, according to the frequency-wave number joint evolution power spectral density function, calculating a self-power spectral density function estimation value at each frequency discrete point, calculating a relative error between the self-power spectral density function estimation value and a target self-power spectral density function value, and accumulating and summing up the relative error in the frequency domain range to obtain a cumulative relative error, if the cumulative relative error is greater than a preset error tolerance upper limit, adjusting the wave number upper limit, and uniformly discretizing the wave number domain again until the error relationship meets the requirements, obtaining M different wave number upper limits, M>1;

[0010] S4, according to the adjusted wave number upper limit, each frequency discrete point has a corresponding wave number upper limit under the premise of meeting the error relationship, the frequency discrete points and the wave number discrete points corresponding to the same wave number upper limit are integrated, the initial uniform discrete frequency interval is redivided, and the frequency-wave number spectrum is reconstructed into M uniformly discrete frequency-wave number spectra based on different wave number upper limits, each frequency-wave number spectrum corresponds to a different frequency domain of the initial frequency-wave number spectrum;

[0011] S5, based on the M uniformly discrete frequency-wave number spectra obtained by reconstruction, a spectrum expression method combined with a fast Fourier transform is used to generate a wind speed time history sample function for each frequency-wave number spectrum, and finally M wind speed time history sample functions are accumulated to obtain a wind speed time history of a random fluctuating wind field.

[0012] Further, the calculation formula of the frequency-wave number joint evolution power spectral density function is as follows:

[0013] ;

[0014] Wherein, S (F-W) (ω, κ) is the frequency-wave number joint evolution power spectral density function, ρ (F-W)(ω, ξ) is a spatial coherence function, S(z, ω) is a target auto-power spectral density function, ω is a frequency, κ is a wave number, ξ is a distance, and z is a height.

[0015] Further, according to the frequency-wave number joint evolution power spectral density function, the auto-power spectral density function estimate value at each frequency discrete point is calculated, including: using the frequency-wave number joint evolution power spectral density function S (F-W) (ω, κ) to integrate it with respect to the wave number κ to obtain the auto-power spectral density function estimate value S E (z, ω).

[0016] Further, the cumulative relative error calculation formula is as follows:

[0017] ;

[0018] wherein ε is the cumulative relative error; S(z, ω) is the target auto-power spectral density function, △ω is the adjacent frequency interval, N ω is the number of frequency discrete points, is the auto-power spectral density function estimate value obtained by frequency-wave number spectrum conversion, and m represents the mth discrete frequency point.

[0019] Further, the specific way of adjusting the upper limit of the wave number cutoff is to increase the initial wave number cutoff by a multiple of 2.

[0020] Further, the wind speed time history sample function is as follows:

[0021] ;

[0022] wherein FFT represents fast Fourier transform, x is a spatial position, t is a time, Re[·] is a real part, Φ lm (1) and Φ lm (2) are two groups of random phases uniformly distributed on (0, 2π] and independent of each other, ω is a frequency, κ is a wave number, △ω is an adjacent frequency interval, △κ is an adjacent wave number interval, S (F-W) (ω, κ) is a frequency-wave number joint evolution power spectral density function.

[0023] A fluctuating wind field simulation system based on a frequency-dependent uniform discrete strategy, comprising:

[0024] A target auto-power spectral density function construction module, configured to obtain atmospheric parameters at a location where an engineering project is located, and establish a target auto-power spectral density function according to actual wind speed time history distribution characteristics;

[0025] An initial discrete module is configured to discretize the frequency domain and the wave number domain uniformly according to a target self-power spectral density function and a given initial wave number cutoff upper limit, and solve a frequency-wave number joint evolution power spectral density function based on a spatial coherence function;

[0026] A cutoff wave number adjustment module is configured to calculate a self-power spectral density function estimation value at each frequency discrete point according to the frequency-wave number joint evolution power spectral density function, calculate a relative error between the self-power spectral density function estimation value and a target self-power spectral density function value, and accumulate and sum the relative errors in the frequency domain range to obtain a cumulative relative error, and if the cumulative relative error is greater than a preset error tolerance upper limit, adjust the wave number cutoff upper limit and uniformly rediscretize the wave number domain again until the error relationship meets the requirements, and obtain M different wave number cutoff upper limits, M>1.

[0027] A frequency-dependent uniform discrete module is configured to, under the premise of meeting the error relationship, have each frequency discrete point have a corresponding wave number cutoff upper limit according to the adjusted wave number cutoff upper limit, integrate the frequency discrete points and the wave number discrete points corresponding to the same wave number cutoff upper limit, redivide the initial uniformly discrete frequency interval, and reconstruct the frequency-wave number spectrum into M uniformly discrete frequency-wave number spectra based on different wave number cutoff upper limits, each of which corresponds to a different frequency domain of the initial frequency-wave number spectrum.

[0028] A wind speed time history simulation calculation module is configured to generate wind speed time history sample functions by using a spectral representation method combined with a fast Fourier transform for each frequency-wave number spectrum based on the M reconstructed uniformly discrete frequency-wave number spectra, and finally accumulate the M wind speed time history sample functions to obtain a wind speed time history of a random fluctuating wind field.

[0029] The application also provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs are implemented when executed by the processor to realize the fluctuating wind field simulation method based on the frequency-dependent uniform discrete strategy as described above.

[0030] The application also provides a computer readable storage medium having a computer program stored thereon, and the computer program is implemented when executed by the processor to realize the fluctuating wind field simulation method based on the frequency-dependent uniform discrete strategy as described above.

[0031] The application also provides a computer program product comprising a computer program, and the computer program is implemented when executed by the processor to realize the fluctuating wind field simulation method based on the frequency-dependent uniform discrete strategy as described above.

[0032] Advantages:

[0033] (1) The method of the present application can ensure the consistency of the calculated self-power spectral density function and the target power spectral density function by controlling the relative error of each frequency discrete position, thereby ensuring the accuracy of the simulation.

[0034] (2) The discrete strategy in the simulation method of the present application is highly efficient. The discrete strategy captures the rapid decay of the wave number domain of the frequency-wave number spectrum in the low frequency domain by adjusting the size of the cutoff wave number, thereby adapting to the huge difference in the spectrum value between the low frequency and the high frequency of the frequency-wave number spectrum, greatly reducing the number of discrete points required in the wave number domain, thereby ensuring the high efficiency of the discrete; at the same time, the discrete strategy can also combine the FFT algorithm to more efficiently convert the frequency-wave number joint evolution power spectral density function into a random fluctuating wind field, thereby ensuring the efficiency of the simulation. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 Flow chart of the fluctuating wind field simulation method based on the frequency-dependent uniform discrete strategy in the embodiment;

[0036] Figure 2 Schematic diagram of the relative error between the self-power spectral density function and the target power spectral density function in the embodiment;

[0037] Figure 3 Schematic diagram of the full frequency domain-wave number discrete points in the embodiment;

[0038] Figure 4 Schematic diagram of the wind speed time history at the 2m position of the one-dimensional spatial fluctuating wind field in the embodiment;

[0039] Figure 5 Schematic diagram of the target power spectral density function and the calculated self-power spectral density function in the embodiment;

[0040] Figure 6 Schematic diagram of the target coherence function and the calculated coherence function in the embodiment;

[0041] Figure 7 Schematic diagram of the target cross-correlation function and the calculated cross-correlation function in the embodiment;

[0042] Figure 8 Schematic diagram of the self-power spectral density function with different wave number discrete points under two kinds of uniform discrete strategies. DETAILED DESCRIPTION

[0043] The technical solutions of the present application will be further described below in conjunction with the drawings.

[0044] Embodiment One

[0045] This embodiment provides a method for simulating fluctuating wind fields based on a frequency-dependent uniform discretization strategy. This method primarily adjusts the cutoff wavenumber by calculating the relative error between the auto-power spectral density function and the target power spectral density function, thereby further dividing the uniformly discretized frequency domain. Combined with spectral representation, the time history of the random fluctuating wind field is obtained. This method is simple, efficient, and requires minimal memory. The auto-power spectrum, cross-power spectrum, coherence function, and cross-correlation function of the wind speed time history in the simulated random fluctuating wind field are all consistent with the target values, thus ensuring the accuracy of the simulation. (Refer to...) Figure 1 The method includes the following steps:

[0046] S1. Obtain the atmospheric parameters of the project location and establish the target self-power spectral density function based on the actual wind speed time history distribution characteristics;

[0047] Query and determine the relevant atmospheric parameters for the project location from meteorological information websites, including the average wind speed at a height of 10m and the surface roughness length. Select the appropriate self-power spectral density function S(z, ω) based on the wind speed time history characteristics, such as the Kaimal spectrum or Davenport spectrum.

[0048] S2. Based on the target self-power spectral density function, give an initial wavenumber cutoff upper limit, and simultaneously discretize the frequency domain and wavenumber domain uniformly. Solve the frequency-wavenumber joint evolution power spectral density function based on the spatial coherence function.

[0049] The initial frequency and wavenumber domain uniform discretization information is determined, including the number of discrete points and the discretization interval, and then the frequency and wavenumber domains are simultaneously and uniformly discretized. This is based on the spatial coherence function ρ. (F-W) Solve for the initial frequency-wavenumber joint evolution power spectral density function S (ω, ξ). (F-W) (ω, κ):

[0050]

[0051] The superscript (FW) indicates that the power spectral density function is a frequency-wavenumber spectrum.

[0052] S3. Based on the frequency-wavenumber joint evolution power spectral density function, calculate the estimated value of the self-power spectral density function at each frequency discrete point, calculate the relative error between the estimated value and the target self-power spectral density function value, and sum them up in the frequency domain to obtain the cumulative relative error. If the cumulative relative error is greater than the preset error tolerance upper limit, adjust the wavenumber cutoff upper limit and re-discrete the wavenumber domain uniformly until the error relationship meets the requirements, and obtain M different wavenumber cutoff upper limits, M>1.

[0053] Using frequency-wavenumber joint evolution of the power spectral density function S (F-W)(ω, κ), integrating it with respect to the wave number κ gives the self-power spectral density function estimate S E (z, ω), where the superscript E represents the estimate of the self-power spectral density function. A preset error tolerance upper limit ε* is set, and the self-power spectral density function estimate S E (z, ω) and the target self-power spectral density function value is solved ωi , and the cumulative sum is accumulated in the frequency domain range to obtain the cumulative relative error:

[0054]

[0055] wherein, is the target self-power spectral density function, is the self-power spectral density function obtained by converting the frequency-wave number spectrum. If the cumulative relative error is greater than the error tolerance upper limit, the wave number cutoff upper limit needs to be adjusted. In order to achieve the highest efficiency for subsequent FFT application, the initial wave number cutoff upper limit is increased by a multiple of 2. The calculation formula is: , is the wave number cutoff upper limit obtained by the nth adjustment, n = 2, 3,... M. Then steps S2-S3 are repeated until the cumulative relative error is less than the tolerance upper limit throughout the frequency domain, so that the target power spectral density function is consistent with the calculated self-power spectral density function, ensuring the accuracy of the simulation.

[0056] S4, according to the adjusted wave number cutoff upper limit, each frequency discrete point has a corresponding wave number cutoff upper limit under the premise of meeting the error relationship, the frequency discrete points and wave number discrete points corresponding to the same wave number cutoff upper limit are integrated, and the initial uniform discrete frequency interval is redivided, and the frequency-wave number spectrum is reconstructed into M uniform discrete frequency-wave number spectra based on different wave number cutoff upper limits, each frequency-wave number spectrum corresponding to a different frequency domain of the initial frequency-wave number spectrum;

[0057] Based on the generated M cutoff wave numbers, the uniform discrete frequency domain is further divided, and each corresponding uniform discrete frequency interval is represented as Instead of simply discretizing the frequency domain and the wave number domain, after redividing the frequency range, the low frequency domain is discretized with a small wave number interval. As the frequency increases, the wave number interval also increases, but the number of wave number discrete points remains unchanged, finally realizing the frequency-dependent uniform discretization strategy. Thus, without too many discrete points, the simulation can adapt to the large difference in the spectrum value of the frequency-wave number spectrum between low and high frequencies, improving the efficiency of the simulation.

[0058] S5. Based on the M uniformly discrete frequency-wavenumber spectra obtained from the reconstruction, wind speed time history sample functions are generated for each frequency-wavenumber spectrum using spectral representation combined with fast Fourier transform. Finally, the wind speed time history of the random pulsating wind field is obtained by summing the M wind speed time history sample functions.

[0059] Specifically, based on the M frequency-wavenumber spectra obtained from the reconstruction, a wind speed time history sample function V is generated for each frequency-wavenumber spectrum using spectral representation combined with FFT. M (x, t), and finally the wind speed time history V(x, t) of the random fluctuating wind field is obtained by summing the M wind speed time history sample functions.

[0060]

[0061]

[0062] Where FFT represents Fast Fourier Transform, x is the spatial location, t is the time, Re[·] is the real part, and Φ lm (1) and Φ lm (2) Let S be two sets of random phases that are uniformly distributed and independent on (0, 2π], where ω is the frequency, κ is the wavenumber, Δω is the interval between adjacent frequencies, Δκ is the interval between adjacent wavenumbers, and S is the frequency. (F-W) (ω, κ) is the power spectral density function of the frequency-wavenumber joint evolution.

[0063] Example 2

[0064] In this embodiment, the technical solution of the present invention is further explained by simulating the pulsating wind field at a height of 50m on the bridge deck of a bridge with a main span of 1600m.

[0065] This embodiment of a method for simulating fluctuating wind fields based on a frequency-dependent uniform discretization strategy includes the following steps:

[0066] Step 101: Determine the required engineering parameters and power spectral density function.

[0067] By consulting the engineering information, we can find that the average wind speed at a height of 10 m at the bridge location is 40 m / s, the surface roughness length is 0.005 m, and the flow shear velocity is selected as 2.105 m / s. Since the required simulated wind field height is 50 m, we do not consider the variation of wind speed with height, and can choose the Kaimal spectrum as the intrinsic power spectral density function. The corresponding target power spectral density function is as follows: Figure 3 :

[0068] (1)

[0069] in

[0070] (2)

[0071] In the formula, z is the selected bridge deck height, U(z) is the average wind speed at height z, and u * Where is the flow shear velocity, k is the von Kármán constant, usually taken as 0.4, z0 is the surface roughness length, and ω represents the value corresponding to the frequency discrete point.

[0072] Step 102, preset the initial wavenumber cutoff upper limit κ1 (u) =16 / π, and the frequency domain and wavenumber domain are uniformly discretized:

[0073] (3)

[0074] (4)

[0075] The initial wavenumber cutoff upper limit is obtained from the pre-simulation. Choosing 16 / π ensures a small initial wavenumber interval, which satisfies the accuracy of the frequency-wavenumber spectrum in the low-frequency domain. If the initial wavenumber cutoff upper limit is chosen too large, the accuracy in the low-frequency domain will be insufficient. If the initial wavenumber cutoff upper limit is chosen too small, the number of subsequent frequency intervals will be too large, which will increase the computational load required for subsequent spectral representation.

[0076] In equations (3) to (4), N ω N represents the number of frequency discrete points, and Δω represents the frequency interval. These can be set to 1024 and 8π rad / s, respectively. κ The number of wavenumber discrete points can be set to 1024. Δκ1 is the initial wavenumber interval, which should satisfy Δκ1≤2π / L. L is the length of the simulated wind field, which is 1600 m.

[0077] Step 103: Using the power spectral density function described in formula (1), the Davenport spatial coherence function is used to perform a Fourier transform with respect to spatial distance to solve for the corresponding frequency-wavenumber joint evolution power spectral density function:

[0078] (5)

[0079] in

[0080] (6)

[0081] In equations (5) to (6), ξ is the distance between the two spatial points of interest, λ is the attenuation constant, and U 10 The average wind speed at a height of 10 m can be set as ξ = 1 m, λ = 10, and κ is the wave number.

[0082] Step 104, the frequency wave number joint evolution power spectrum density function S (F-W) (ω, κ) is solved from the power spectrum density function using the following formula (7):

[0083] (7)

[0084] Step 105, preset the truncation error ε*, use the following formula (8) to calculate the cumulative relative error ε at all frequency discrete points, and through error analysis, the accuracy of the power spectrum density function calculation can be effectively improved:

[0085] (8)

[0086] Step 106, if the cumulative relative error ε calculated is greater than the preset truncation error ε*, the cutoff wave number is increased by a factor of 2 based on the preset upper limit of the cutoff wave number to facilitate the efficient use of subsequent FFT:

[0087] (9)

[0088] Step 107, repeat steps 104-106 until the cumulative relative error is less than or equal to the preset truncation error throughout the frequency domain. The corresponding cumulative relative error calculation result is shown in Figure 2

[0089] Step 108, based on the M different cutoff wave numbers generated in step 107:

[0090]

[0091] Induction of the same cutoff wave number κ M (u) Corresponding to different frequency discrete point intervals ω M (u) The initial uniformly dispersed frequency domain is further divided into M segments, and the corresponding uniformly dispersed frequency interval is represented as:

[0092]

[0093] Therefore, after re-dividing the frequency segments, the low frequency domain realizes smaller wave number interval discretization. As the frequency increases, the wave number interval also increases, but the number of wave number discrete points remains the same, ultimately realizing a frequency-dependent uniform discretization strategy. The corresponding full frequency domain-wave number domain discrete point number of the frequency-dependent uniform discretization strategy is shown in Figure 3 ​As shown, there are 1024 wave number discrete points corresponding to each frequency point. Traditional uniform discrete uniformly discretizes in both frequency domain and wave number domain, but the accuracy is insufficient when the number of wave number domain discrete points is small, because the wind field energy is concentrated in low frequency, and the large wave number interval in low frequency domain will result in insufficient accuracy. The frequency-dependent uniform discrete strategy can control the wave number interval size while controlling the relative error of power spectral density accumulation to meet the requirements in different frequency intervals, capture the rapid decay of frequency-wave number spectrum in wave number domain, ensure accuracy while greatly reducing the number of wave number discrete points required, and improve computational efficiency.

[0094] Step 109, determine the time domain discrete characteristics of the fluctuating wind field using the following formula (10):

[0095] (10)

[0096] In the formula, T is the duration of the wind speed time history, Δt is the time interval, N t is the number of time discrete points, which are T=256(s), Δt=0.125(s), N t =2048, respectively. Here, the number of time discrete points is selected to be twice the number of frequency discrete points, and the ratio of the number of space discrete points to the number of wave number discrete points is the same.

[0097] Step 110, use the following formulas (11)-(14) to solve the one-dimensional random fluctuating wind field V(x,t):

[0098] (11)

[0099] where

[0100] (12)

[0101] In order to be suitable for FFT, formula (12) can be modified as:

[0102] (13)

[0103] where

[0104] (14)

[0105] Using the FFT symbol, formula (13) can be converted to:

[0106] (15)

[0107] In formulas (11)-(14), x is the spatial position, t is the time, Re[·] is the real part, Φ lm (1) and Φ lm(2) are two sets of random phases uniformly distributed on (0, 2π] and independent of each other. In equation (15), the FFT and IFFT functions can be directly used for implementation.

[0108] Since a random process is simulated, the number of samples of the wind field simulation is selected as 500, and the sample mean is taken for verification analysis. A wind speed time history sample at point P1 (2, 50) of the generated fluctuating wind field is shown in FIG. 6. Figure 4

[0109] To verify the accuracy of the simulation, based on the wind speed time history of the 500 sets of generated fluctuating wind fields, the wind speed time history at P1 (2, 50) and P2 (8, 50) is focused on, Figure 5 The wind speed time histories at P1 and P2 are compared, the Fourier transform is used to obtain the self-power spectral density function, and the comparison results with the target self-power spectral density function Kaimal spectrum are compared to verify that the simulated time history meets the target requirements.

[0110] Figure 6 The coherence function between P1 and P2 is compared with the target Davenport function, which shows that the simulation meets the expected spatial coherence.

[0111] Figure 7 The difference between the cross-correlation functions at P1 and P2 is compared with the target cross-correlation function. The cross-power spectral density function of the response signals at the two positions is calculated, and the cross-correlation function is generated again by inverse Fourier transform combined with the coherence function. The results are well fitted with the target cross-correlation function obtained by the target Kaimal spectrum and the Davenport coherence function, which shows that the wind speed time history of the simulated wind field at each position has good spatial coherence.

[0112] To verify the accuracy and efficiency advantage of the discrete strategy in simulating the fluctuating wind field, based on the same frequency domain discrete characteristics, the number of discrete points in the wave number domain of the traditional uniform discrete strategy is set to 2 12 , 2 13 , 2 14 , 2 15 , and the number of discrete points in the wave number domain of the frequency-dependent discrete strategy is set to 2 10 , Figure 8 The difference between the self-power spectral density function and the target self-power spectral density function Kaimal spectrum under the traditional uniform discrete strategy and the frequency-dependent uniform discrete strategy is compared, and the accuracy comparison of the energy concentration of the wind field, i.e. the low frequency domain, is highlighted. The results show that the frequency-dependent uniform discrete strategy has higher accuracy and fewer discrete points, and the calculation efficiency is significantly improved.

[0113] Example Three

[0114] ​Based on the same technical concept as the first method embodiment, the present embodiment provides a fluctuating wind field simulation system based on a frequency-dependent uniform discretization strategy, comprising:

[0115] A target auto-power spectral density function construction module is configured to acquire atmospheric parameters at a location where the project is located, and to establish a target auto-power spectral density function according to actual wind speed time history distribution characteristics;

[0116] An initial discretization module is configured to discretize the frequency domain and the wave number domain uniformly based on a given initial wave number upper limit, and to solve a frequency-wave number joint evolution power spectral density function based on a spatial coherence function according to the target auto-power spectral density function;

[0117] A wave number cut-off adjustment module is configured to calculate an auto-power spectral density function estimate value at each frequency discretization point based on the frequency-wave number joint evolution power spectral density function, to calculate a relative error between the auto-power spectral density function estimate value and a target auto-power spectral density function value, and to accumulate and sum the relative errors in the frequency domain range to obtain a cumulative relative error, and if the cumulative relative error is greater than a preset error tolerance upper limit, to adjust the wave number upper limit and to uniformly discretize the wave number domain again until the error relationship meets the requirements, thereby obtaining M different wave number upper limits, M>1.

[0118] A frequency-dependent uniform discretization module is configured to integrate the frequency discretization points and the wave number discretization points corresponding to the same wave number upper limit to redivide the initial uniform discretization frequency interval based on the adjusted wave number upper limit under the premise that the error relationship is met, and to reconstruct the frequency-wave number spectrum into M uniformly discretized frequency-wave number spectra based on different wave number upper limits, each of which corresponds to a different frequency domain of the initial frequency-wave number spectrum.

[0119] A wind speed time history simulation calculation module is configured to generate wind speed time history sample functions for each frequency-wave number spectrum by using a spectral representation method combined with a fast Fourier transform based on the M reconstructed uniformly discretized frequency-wave number spectra, and to finally accumulate the M wind speed time history sample functions to obtain a wind speed time history of a random fluctuating wind field.

[0120] It should be understood that the fluctuating wind field simulation system based on the frequency-dependent uniform discretization strategy in the present embodiment can implement all the technical solutions in the above method embodiments, and the functions of each functional module can be implemented according to the methods in the above method embodiments, and the specific implementation process can be referred to the related descriptions in the above embodiments, which will not be described here in detail.

[0121] Embodiment Four

[0122] The embodiment provides an electronic device, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the program is implemented by the processor to implement the method for simulating fluctuating wind field based on frequency-dependent uniform discrete strategy as described above.

[0123] Embodiment five

[0124] The embodiment provides a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and the computer program is implemented by the processor to implement the method for simulating fluctuating wind field based on frequency-dependent uniform discrete strategy as described above.

[0125] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, device (system), electronic device or computer program product. Therefore, the present application can adopt a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer usable program codes.

[0126] The present application is described with reference to flowcharts according to the method of the embodiments of the present application. It should be understood that each flow in the flowchart and the combination of the flows in the flowchart can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device produce a means for implementing the functions specified in the flow Figure 1 The device specified in one flow or multiple flows.

[0127] These computer program instructions can also be stored in a computer readable memory capable of guiding the computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer readable memory produce a product including instruction means, which implements the functions specified in the flow Figure 1 The device specified in one flow or multiple flows.

[0128] These computer program instructions can also be loaded into the computer or other programmable data processing device, so that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the flow Figure 1 The device specified in one flow or multiple flows.

Claims

1. A method for simulating fluctuating wind fields based on a frequency-dependent uniform discretization strategy, characterized in that, Includes the following steps: S1. Obtain the atmospheric parameters of the project location and establish the target self-power spectral density function based on the actual wind speed time history distribution characteristics; S2. Based on the target self-power spectral density function, give an initial wavenumber cutoff upper limit, and simultaneously discretize the frequency domain and wavenumber domain uniformly. Solve the frequency-wavenumber joint evolution power spectral density function based on the spatial coherence function. S3. Based on the frequency-wavenumber joint evolution power spectral density function, calculate the estimated value of the self-power spectral density function at each frequency discrete point, calculate the relative error between the estimated value of the self-power spectral density function and the target self-power spectral density function value, and sum them up in the frequency domain to obtain the cumulative relative error. If the cumulative relative error is greater than the preset error tolerance upper limit, adjust the wavenumber cutoff upper limit and re-discrete the wavenumber domain uniformly until the error relationship meets the requirements, and obtain M different wavenumber cutoff upper limits, M>1; S4. Based on the adjusted upper limit of the wavenumber cutoff, under the premise of satisfying the error relationship, each frequency discrete point has a corresponding upper limit of the wavenumber cutoff. The frequency discrete points and wavenumber discrete points corresponding to the same upper limit of the wavenumber cutoff are integrated to realize the re-division of the initial uniform discrete frequency interval. The frequency-wavenumber spectrum is reconstructed into M uniform discrete frequency-wavenumber spectra based on different upper limits of the wavenumber cutoff. Each frequency-wavenumber spectrum corresponds to a different frequency domain of the initial frequency-wavenumber spectrum. S5. Based on the M uniformly discrete frequency-wavenumber spectra obtained from the reconstruction, wind speed time history sample functions are generated for each frequency-wavenumber spectrum using spectral representation combined with fast Fourier transform. Finally, the wind speed time history of the random pulsating wind field is obtained by summing the M wind speed time history sample functions.

2. The method according to claim 1, characterized in that, The formula for calculating the power spectral density function of the frequency-wavenumber joint evolution is as follows: ； Among them, S (F-W) (ω, κ) is the power spectral density function of the joint frequency-wavenumber evolution, ρ (F-W) (ω, ξ) is the spatial coherence function, S(z, ω) is the target self-power spectral density function, ω is the frequency, κ is the wave number, ξ is the distance, and z is the altitude.

3. The method according to claim 2, characterized in that, Based on the frequency-wavenumber joint evolution power spectral density function, calculate the estimated value of the self-power spectral density function at each discrete frequency point, including: using the frequency-wavenumber joint evolution power spectral density function S (F-W) (ω, κ), integrating it with respect to the wavenumber κ yields the estimated value of the self-power spectral density function S. E (z, ω).

4. The method according to claim 3, characterized in that, The formula for calculating the cumulative relative error is as follows: ； Where ε is the cumulative relative error; S(z, ω) is the target self-power spectral density function, Δω is the adjacent frequency interval, and N ω The number of discrete points in the frequency range. This is the estimated value of the self-power spectral density function obtained from the frequency-wavenumber spectrum conversion. This represents the m-th discrete frequency point.

5. The method according to claim 1, characterized in that, The specific method for adjusting the wavenumber cutoff upper limit is as follows: increase the initial wavenumber cutoff upper limit by multiples of 2.

6. The method according to claim 1, characterized in that, The wind speed time history sample function is as follows: ； Where FFT represents Fast Fourier Transform, x is the spatial location, t is the time, Re[·] is the real part, and Φ lm (1) and Φ lm (2) Let S be two sets of random phases that are uniformly distributed and independent on (0, 2π], where ω is the frequency, κ is the wavenumber, Δω is the interval between adjacent frequencies, Δκ is the interval between adjacent wavenumbers, and S is the frequency. (F-W) (ω, κ) is the power spectral density function of the frequency-wavenumber joint evolution.

7. A pulsating wind field simulation system based on a frequency-dependent uniform discretization strategy, characterized in that, include: The target self-power spectral density function construction module is used to obtain atmospheric parameters at the location of the project and establish the target self-power spectral density function based on the actual wind speed time history distribution characteristics. The initial discretization module is used to uniformly discretize the frequency domain and wavenumber domain simultaneously based on the target self-power spectral density function and an initial wavenumber cutoff upper limit, and solve the frequency-wavenumber joint evolution power spectral density function based on the spatial coherence function. The cutoff wavenumber adjustment module is used to calculate the estimated value of the self-power spectral density function at each frequency discrete point based on the frequency-wavenumber joint evolution power spectral density function, calculate the relative error between the estimated value of the self-power spectral density function and the target self-power spectral density function value, and sum them up in the frequency domain to obtain the cumulative relative error. If the cumulative relative error is greater than the preset error tolerance upper limit, the wavenumber cutoff upper limit is adjusted, and the wavenumber domain is re-discrete uniformly until the error relationship meets the requirements, resulting in M ​​different wavenumber cutoff upper limits, where M>1. The frequency-dependent uniform discrete module is used to integrate the frequency discrete points and wavenumber discrete points with the same wavenumber cutoff upper limit according to the adjusted wavenumber cutoff upper limit, under the premise of satisfying the error relationship, so that each frequency discrete point has a corresponding wavenumber cutoff upper limit. The initial uniform discrete frequency interval is re-divided. The frequency-wavenumber spectrum is reconstructed into M uniform discrete frequency-wavenumber spectra based on different wavenumber cutoff upper limits, and each frequency-wavenumber spectrum corresponds to a different frequency domain of the initial frequency-wavenumber spectrum. The wind speed time history simulation module is used to generate wind speed time history sample functions for each frequency-wave number spectrum based on the M uniformly discrete frequency-wave number spectra obtained by reconstruction, using spectral representation combined with fast Fourier transform. Finally, the wind speed time history of the random pulsating wind field is obtained by accumulating the M wind speed time history sample functions.

8. An electronic device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the pulsating wind field simulation method based on the frequency-dependent uniform discretization strategy as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the pulsating wind field simulation method based on the frequency-dependent uniform discretization strategy as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the pulsating wind field simulation method based on the frequency-dependent uniform discretization strategy as described in any one of claims 1-6.

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