An efficient simulation method for large-scale stochastic turbulent wind field

Abstract

The application discloses a high-efficiency simulation method of large-scale structure random turbulent wind field. n V-1D random vector process is separated into two mutually irrelevant 2 n V-1D and n V-1D two random vector processes, wherein the two n V-1D processes are simulated by using an eigen-orthogonal decomposition-spectral representation hybrid method, the two n V-1D processes are simulated by using a spectral representation method; secondly, random functions are constructed to replace orthogonal random variables in the two random vector processes, so that the number of random variables is reduced to the maximum; meanwhile, an FFT algorithm is introduced to further improve the simulation efficiency; finally, by selecting appropriate power spectrum models, space and turbulent coherence function models, the high-efficiency simulation of the large-scale structure random turbulent wind field can be carried out; compared with a traditional double eigen-orthogonal decomposition model, the application has high calculation efficiency, small computer memory occupation and good simulation precision, and the generated wind speed time history sample set has definite probability information.

Description

Technical Field

[0001] This invention relates to a simulation method, specifically an efficient simulation method for large-scale structural stochastic turbulent wind fields, belonging to the field of stochastic disaster modeling technology. Background Technology

[0002] Large-scale turbulent wind-sensitive structures such as power transmission towers and long-span bridges are lifeline projects that maintain normal urban operations and have a significant impact on the national economy and people's livelihoods. Due to the complexity of wind loads and the nonlinear behavior of the structures they cause, random turbulent wind loads have become the dominant factor in controlling the design of these large-scale wind-sensitive flexible structures.

[0003] The DPOD method for wind-turbulent flow fields is achieved through the PSD matrix at a single point and the POD decomposition of the PSD matrices at different points. However, the constraint that the number of simulation points increases affects simulation efficiency has hindered the widespread application of this method in engineering practice. Summary of the Invention

[0004] The purpose of this invention is to provide an efficient simulation method for large-scale structural stochastic turbulent wind fields in order to solve at least one of the above-mentioned technical problems.

[0005] This invention achieves the above objective through the following technical solution: an efficient simulation method for large-scale structural stochastic turbulent wind fields, comprising the following steps:

[0006] Step 1: Separate the 3nV-1D random turbulent wind field into two random vector processes: 2nV-1D and nV-1D.

[0007] Based on the assumption that the forward and vertical turbulence components are uncorrelated with the transverse turbulence component, its bilateral power spectral density (PSD) matrix can be expressed as:

[0008]

[0009] In the formula, S v (ω) represents an nV⁻¹D random vector process V(t) = [v₁(t), v₂(t), ..., vₙ(t)]. n (t)] T PSD matrix; S uw (ω) is a 2nV⁻¹D random vector process. W i (t)=[u i (t), w i (t)] T PSD matrix; W i The power spectral density matrix of (t) can be written as:

[0010]

[0011] In the formula, For the turbulent component u i (t) and w i The coherence function of (t);

[0012] Step 2: POD-SRM hybrid representation of 2nV-1D stochastic vector processes

[0013] According to spectral analysis theory:

[0014]

[0015] In the formula, complex-valued orthogonal incremental process It satisfies zero mean, and its increment Existing spectral eigentransform forms:

[0016]

[0017] in, Also a complex-valued orthogonal incremental process; spectral principal component process PSD matrix Its elements λ i (ω)=diag[λ i (2) (ω), λ i (2) (ω)] and They are respectively eigenvalues ​​and eigenvector matrices;

[0018] If the spectral eigenvalue transformation is applied to the j-th point, then and The following relationship exists:

[0019]

[0020] Taking the expectation of both sides of equation (5), we can obtain the PSD matrix of any two-point vector process:

[0021]

[0022] In the formula, For the principal component process Q i (t) and Q j The PSD matrix of (t);

[0023] Step 3: SRM Representation of nV-1D Random Vector Processes

[0024] Based on the SRM method, the PSD matrix is ​​decomposed using Cholesky decomposition. Through derivation, the nV-1D stochastic vector process V(t) = [v1(t), v2(t), ..., v...]. n (t)] T It can be represented as:

[0025]

[0026] In the formula, H is a lower triangular matrix ν The elements in (ω), H ν (ω) is S v (ω) is the matrix obtained by Cholesky decomposition, i.e., S v (ω)=H ν (ω)H ν (ω) *T ;

[0027] Step 4: Simulation of stochastic turbulent wind field based on stochastic functions

[0028] By constructing a random function, the set of orthogonal random variables can be represented in the following form:

[0029]

[0030] In the formula: m, r = 1, 2, 3; p, q = 1, 2, ..., n; k, l = 1, 2, ..., N; the basic random variables Θ = (Θ1, Θ2, Θ3) are independent of each other and all follow a uniform distribution on [0, 2π).

[0031] Substituting equation (15) into equations (13) and (14), we finally obtain the 2nV-1D random vector process W. i (t) and nV-1D random vector process v i The random function expression of (t):

[0032]

[0033]

[0034] Step 5: Introduce the FFT algorithm

[0035] To further improve computational efficiency, the FFT algorithm is introduced at the frequencies in equations (16) and (17).

[0036] As a further aspect of the present invention: In step one, for the random turbulent wind field, a 3nV-1D random vector process is selected. To represent;

[0037] Among them, U i (t)=[ui (t), v i (t), w i (t)] T (i=1, 2,...,n), and u i (t), v i (t), w i (t) represents the forward, lateral, and vertical turbulence components at a single point, respectively.

[0038] As a further aspect of the present invention: In step one, based on the assumption that the vertical turbulence component is uncorrelated with both longitudinal and transverse turbulence components in the measured records, the 3nV-1D random turbulence wind field is represented as a combination of two random vector processes. At the same time, Cholesky decomposition is used as much as possible to replace the eigenvalue decomposition in the traditional model.

[0039] As a further aspect of the present invention: In step two, based on the single-point spectral principal component process Q... i Similarly, the spectral principal component process of a 2nV-1D random vector process W(t) can be expressed as Q(t) = [Q (1) (t) T Q (2) (t) T ] T ;

[0040] Its elements

[0041] Furthermore, the PSD matrix of Q(t) can be expressed as:

[0042]

[0043] Will Performing Cholesky decomposition yields... At this time, dZ Q (ω) can be expressed as:

[0044] dZ Q (ω)=H(ω)dZ R (ω) (8)

[0045] In the formula, R(t) = [R (1) (t) T R (2) (t) T ] T A 2nV⁻¹D random vector process with zero mean, whose elements dZ R (ω) satisfies I n×n Represents an n-order identity matrix;

[0046] Therefore, by using equations (5) and (8), we obtain

[0047]

[0048] In the formula, H represents the lower triangular matrix (m) The p-th column of (ω); η(ω) represents a 2n×2n matrix, which is composed of 2n×n submatrices η. (m) The set is composed of (ω)(m=1,2);

[0049] Substituting equation (9) into equation (3), W(t) can be approximately expressed as:

[0050]

[0051]

[0052] In the formula, Δω=ω u / N is the frequency step size, ω u X is the cutoff frequency, N is the frequency fraction; mpk and Y mpk An orthogonal random variable with zero mean satisfies the following condition:

[0053]

[0054] As a further aspect of the present invention: H (m) (ω) is a lower triangular matrix whose elements satisfy... so,

[0055]

[0056] As a further aspect of the present invention: In step five, taking equation (16) as an example, the corresponding calculation formula is given:

[0057]

[0058]

[0059]

[0060] In the formula, Re[·] represents the real part; l = 0, 1, 2, ..., 2N-1; generally, ΔtΔω = π / N is taken.

[0061] The beneficial effects of this invention are:

[0062] First, the 3nV-1D stochastic vector process is separated into two uncorrelated stochastic vector processes, 2nV-1D and nV-1D. The 2nV-1D process is simulated using a hybrid method of intrinsic orthogonal decomposition-spectral representation (POD-SRM), while the nV-1D process is simulated using the spectral representation method (SRM).

[0063] Secondly, by constructing a random function to replace the orthogonal random variables in the two random vector processes, the number of random variables is reduced to the minimum, and the FFT algorithm is introduced to further improve the simulation efficiency.

[0064] Finally, by selecting appropriate power spectrum models, spatial and turbulent coherence function models, efficient simulation of large-scale structural stochastic turbulent wind fields can be carried out.

[0065] Compared with the traditional dual eigenorthogonal decomposition (DPOD) model, this invention has higher computational efficiency, smaller computer memory usage, and better simulation accuracy. The generated wind speed time history sample set has clear probabilistic information. Attached Figure Description

[0066] Figure 1 This is a layout diagram of the structural points of a tall power transmission tower;

[0067] Figure 2 A representative point set diagram corresponding to the three basic random variables;

[0068] Figure 3 This is the 50th representative wind speed sample image at location P7;

[0069] Figure 4 A comparison chart of the relative mean error and the target value of the simulated sample at position P7.

[0070] Figure 5 A comparison chart of the relative standard deviation error and the target value of the simulated sample at position P7.

[0071] Figure 6 A comparison graph showing the simulated and target values ​​of the longitudinal turbulence component u at location P7 using the PSD function;

[0072] Figure 7 A comparison graph showing the simulated and target values ​​of the PSD function of the transverse turbulence component v at location P7;

[0073] Figure 8 A comparison graph showing the simulated and target values ​​of the PSD function for the vertical turbulence component w at location P7;

[0074] Figure 9 A comparison graph showing the simulated and target values ​​of the PSD functions for the longitudinal turbulence component u and the vertical turbulence component w at location P7;

[0075] Figure 10 A comparison graph showing the simulated and target values ​​of the longitudinal turbulence component u at positions P4 and P7 using the PSD function;

[0076] Figure 11 This is a comparison chart of the simulation efficiency of the model of this invention and the traditional DPOD model. Detailed Implementation

[0077] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0078] Example 1

[0079] like Figure 1 As shown, an efficient simulation method for large-scale structural stochastic turbulent wind fields is proposed, comprising the following steps:

[0080] Step 1: Separate the 3nV-1D random turbulent wind field into two random vector processes: 2nV-1D and nV-1D.

[0081] Based on the assumption that the forward and vertical turbulence components are uncorrelated with the transverse turbulence component, its bilateral power spectral density (PSD) matrix can be expressed as:

[0082]

[0083] In the formula, S v (ω) represents an nV⁻¹D random vector process V(t) = [v₁(t), v₂(t), ..., vₙ(t)]. n (t)] T PSD matrix; S uw (ω) is a 2nV⁻¹D random vector process. W i (t)=[u i (t), w i (t)] T PSD matrix; W i The power spectral density matrix of (t) can be written as:

[0084]

[0085] In the formula, For the turbulent component u i (t) and w i The coherence function of (t);

[0086] Step 2: POD-SRM hybrid representation of 2nV-1D stochastic vector processes

[0087] According to spectral analysis theory:

[0088]

[0089] In the formula, complex-valued orthogonal incremental process It satisfies zero mean, and its increment Existing spectral eigentransform forms:

[0090]

[0091] in, Also a complex-valued orthogonal incremental process; spectral principal component process PSD matrix Its elements λ i (ω)=diag[λ i (1) (ω), λ i (2) (ω)] and They are respectively eigenvalues ​​and eigenvector matrices;

[0092] If the spectral eigenvalue transformation is applied to the j-th point, then and The following relationship exists:

[0093]

[0094] Taking the expectation of both sides of equation (5), we can obtain the PSD matrix of any two-point vector process:

[0095]

[0096] In the formula, For the principal component process Q i (t) and Q j The PSD matrix of (t);

[0097] Step 3: SRM Representation of nV-1D Random Vector Processes

[0098] Based on the SRM method, the PSD matrix is ​​decomposed using Cholesky decomposition. Through derivation, the nV-1D stochastic vector process V(t) = [v1(t), v2(t), ..., v...]. n (t)] T It can be represented as:

[0099]

[0100] In the formula, H is a lower triangular matrix ν The elements in (ω), H ν (ω) is S v (ω) is the matrix obtained by Cholesky decomposition, i.e., Sv (ω)=H ν (ω)H ν (ω) *T ;

[0101] By combining equations (13) and (14), a stochastic turbulent wind field model can be obtained. Since all elements above the diagonal of the matrix obtained after Cholesky decomposition of the PSD matrix in the SRM method are zero, this model can significantly save computer memory and improve the simulation efficiency of stochastic turbulent wind fields.

[0102] Step 4: Simulation of stochastic turbulent wind field based on stochastic functions

[0103] Furthermore, the traditional DPOD model for wind field simulation uses Monte Carlo sampling, which requires a large number of random variables to ensure simulation accuracy. Moreover, the probability information of the generated random turbulent wind speed time history samples is unclear, making it impossible to perform a refined analysis of the structural dynamic response at the probability density level. Here, we overcome the above constraints by constructing a random function and combining it with number theory point selection methods.

[0104] By constructing a random function, the set of orthogonal random variables can be represented in the following form:

[0105]

[0106] In the formula: m, r = 1, 2, 3; p, q = 1, 2, ..., n; k, l = 1, 2, ..., N; the basic random variables Θ = (Θ1, Θ2, Θ3) are independent of each other and all follow a uniform distribution on [0, 2π).

[0107] Substituting equation (15) into equations (13) and (14), we finally obtain the 2nV-1D random vector process W. i (t) and nV-1D random vector process v i The random function expression of (t):

[0108]

[0109]

[0110] Step 5: Introduce the FFT algorithm

[0111] To further improve computational efficiency, the FFT algorithm is introduced at the frequencies of equations (16) and (17).

[0112] Example 2

[0113] In addition to all the technical features included in Embodiment 1, this embodiment also includes:

[0114] In step one, for the stochastic turbulent wind field, a 3nV⁻¹D stochastic vector process is selected. To represent;

[0115] Among them, U i (t)=[u i (t), v i (t), w i (t)] T (i=1, 2,...,n), and u i (t), v i (t), w i (t) represents the forward, lateral, and vertical turbulence components at a single point, respectively.

[0116] In step one, based on the assumption that the vertical turbulence component is uncorrelated with both longitudinal and transverse turbulence components in the measured wind field, the 3nV-1D stochastic turbulent wind field is represented as a combination of two stochastic vector processes. At the same time, Cholesky decomposition is used as much as possible to replace the eigenvalue decomposition in the traditional model.

[0117] Example 3

[0118] In addition to all the technical features included in Embodiment 1, this embodiment also includes:

[0119] In step two, based on the single-point spectral principal component process Q i Similarly, the spectral principal component process of a 2nV-1D random vector process W(t) can be expressed as Q(t) = [Q (1) (t) T Q (2) (t) T ] T ;

[0120] Its elements

[0121] Furthermore, the PSD matrix of Q(t) can be expressed as:

[0122]

[0123] Traditional methods involve further eigenvalue decomposition of the PSD of Q(t); this application will... Performing Cholesky decomposition yields... At this time, dZ Q (ω) can be expressed as:

[0124] dZ Q (ω)=H(ω)dZ R (ω) (8)

[0125] In the formula, R(t) = [R (1)(t) T R (2) (t) T ] T A 2nV⁻¹D random vector process with zero mean, whose elements dZ R (ω) satisfies I n×n Represents an oak-order unit square;

[0126] Therefore, by using equations (5) and (8), we obtain

[0127]

[0128] In the formula, H represents the lower triangular matrix (m) The p-th column of (ω); η(ω) represents a 2n×2n matrix, which is composed of 2n×n submatrices η. (m) The set is composed of (ω)(m=1,2);

[0129] Substituting equation (9) into equation (3), W(t) can be approximately expressed as:

[0130]

[0131]

[0132] In the formula, Δω=ω u / N is the frequency step size, ω u X is the cutoff frequency, N is the frequency fraction; mpk and Y mpk An orthogonal random variable with zero mean satisfies the following condition:

[0133]

[0134] The H (m) (ω) is a lower triangular matrix whose elements satisfy... so,

[0135] In step five, taking equation (16) as an example, the corresponding calculation formula is given:

[0136]

[0137]

[0138]

[0139] In the formula, Re[·] represents the real part; l = 0, 1, 2, ..., 2N-1; generally, ΔtΔω = π / N is taken.

[0140] Example 4

[0141] like Figures 2 to 8 As shown in Table 1, with the vertical wind field of the transmission tower as the engineering background, the simulation parameters and values ​​of the random turbulent wind field are shown in Table 1.

[0142] Table 1 Simulation parameters and values ​​of random turbulent wind field:

[0143]

[0144]

[0145] An efficient simulation method for large-scale structural stochastic turbulent wind fields includes:

[0146] Step 1: The two-sided power spectral density (PSD) matrix of the separated random turbulent wind field is expressed as follows:

[0147]

[0148] In the formula, S v (ω) represents an nV⁻¹D random vector process V(t) = [v₁(t), v₂(t), ..., vₙ(t)]. n (t)] T PSD matrix; S uw (ω) is a 2nV⁻¹D random vector process. W i (t)=[u i (t), w i (t)] T PSD matrix; W i The power spectral density matrix of (t) can be written as:

[0149]

[0150] In the formula, For the turbulent component u i (t) and w i The coherence function of (t).

[0151] Step 2: Select the Kaimal spectrum to describe the stochastic turbulent wind field; its two-sided self-PSD function is:

[0152]

[0153] In the formula, Let z be the flow shear velocity, and z be the ground clearance. Furthermore, The values ​​are 200, 15, and 3.36 respectively; d u d v d wThe values ​​are 50, 9.5, and 10, respectively.

[0154] Turbulent coherence function between the forward and vertical turbulent components at a single point The following model is adopted:

[0155]

[0156] In the formula, β u =6-1.1×arctan[ln(z0)+1.75],β w =0.25β u When z < 200m, the turbulent integral scale L w =0.1L u .

[0157] Step 3: POD-SRM hybrid representation of 2nV-1D stochastic vector processes

[0158] According to spectral analysis theory:

[0159]

[0160] In the formula, complex-valued orthogonal incremental process It satisfies zero mean, and its increment Existing spectral eigentransform forms:

[0161]

[0162] in, Also a complex-valued orthogonal incremental process; spectral principal component process PSD matrix Its elements λ i (ω)=diag[λ i (2) (ω), λ i (2) (ω)] and They are respectively The eigenvalues ​​and eigenvector matrices.

[0163] If the spectral eigenvalue transformation is applied to the j-th point, then and The following relationship exists:

[0164]

[0165] Taking the expectation of both sides of equation (7), we can obtain the PSD matrix of any two-point vector process:

[0166]

[0167] In the formula, For the principal component process Q i (t) and Q j The PSD matrix of (t).

[0168] Different spectral principal component processes and The cross power spectral density (CPSD) functions are not correlated, while the CPSD functions of the same principal component of the spectrum are... The analytical solution is:

[0169]

[0170] In the formula, For turbulent components o i (t) and o j The CPSD function of (t) (o=u, w), C = cosθ is the spatial coherence function between two distinct points. i (ω)cosθ j (ω), D=sinθ i (ω)sinθ j (ω).

[0171] In this embodiment, the spatial coherence function Coh zε (ξ, ω) are modeled using the Solari model:

[0172]

[0173] In the formula, the attenuation coefficient C zu =10, C zv =C zw =6.5; Δ z The perpendicular distance between the two points is denoted as .

[0174] Based on the single-point spectral principal component process Q i Similarly, the spectral principal component process of a 2nV-1D random vector process W(t) can be expressed as Q(t) = [Q (1) (t) T Q (2) (t) T ] T Its elements Furthermore, the PSD matrix of Q(t) can be expressed as:

[0175]

[0176] The traditional method involves further feature decomposition of the PSD of Q(t). This invention will... Performing Cholesky decomposition yields... At this time, dZ Q (ω) can be expressed as:

[0177] dZ Q (ω)=H(ω)dZ R (ω) (12)

[0178] In the formula, R(t) = [R (1) (t) T R (2) (t) T ] T A 2nV⁻¹D random vector process with zero mean, whose elements dZ R (ω) satisfies I n×n This represents an n-order identity matrix.

[0179] Therefore, using equations (7) and (12), we obtain

[0180]

[0181] In the formula, H represents the lower triangular matrix (m) The p-th column of (ω); η(ω) represents a 2n×2n matrix, which is composed of 2n×n submatrices η. (m) It is a set of (ω)(m=1,2).

[0182] Substituting equation (13) into equation (5), W(t) can be approximately expressed as:

[0183]

[0184]

[0185] In the formula, Δω=ω u / N is the frequency step size, ω u X is the cutoff frequency, N is the frequency fraction; mpk and Y mpk An orthogonal random variable with zero mean satisfies the following condition:

[0186]

[0187] Because H (m) (ω) is a lower triangular matrix whose elements satisfy... so,

[0188]

[0189] Step 4: SRM representation of nV-1D stochastic vector processes

[0190] Based on the SRM method, the PSD matrix is ​​decomposed using Cholesky decomposition. Through derivation, the nV-1D stochastic vector process V(t) = [v1(t), v2(t), ..., v...]. n (t)] T It can be represented as:

[0191]

[0192] In the formula, H is a lower triangular matrix ν The elements in (ω), H ν (ω) is S v (ω) is the matrix obtained by Cholesky decomposition, i.e., S v (ω)=H ν (ω)H ν (ω) *T .

[0193] By combining equations (17) and (18), the stochastic turbulent wind field model of the present invention can be obtained.

[0194] Step 5: Simulation of stochastic turbulent wind field based on stochastic functions

[0195] By constructing a random function, the set of orthogonal random variables can be represented in the following form:

[0196]

[0197] In the formula: ω, r = 1, 2, 3; p, q = 1, 2, ..., n; k, l = 1, 2, ..., N; the basic random variables Θ = (Θ1, Θ2, Θ3) are independent of each other and all follow a uniform distribution on [0, 2π).

[0198] Substituting equation (19) into equations (17) and (18), we finally obtain the 2nV-1D random vector process W. i (t) and nV-1D random vector process v i The random function expression of (t):

[0199]

[0200]

[0201] A number-theoretic point selection method is used to select a representative set of 233 points within a three-dimensional unit cube, such as... Figure 2 As shown.

[0202] Step 6: Introduce the FFT algorithm

[0203] To further improve the computational efficiency of this invention, an FFT algorithm is introduced at the frequencies in equations (20) and (21). Here, we take equation (20) as an example and give the corresponding calculation formula:

[0204]

[0205]

[0206]

[0207] In the formula, Re[·] represents the real part; l = 0, 1, 2, ..., 2N-1; generally, ΔtΔω = π / N is taken.

[0208] The 50th wind speed sample at location P7 obtained by the simulation of this invention, as shown below. Figure 3 As shown; a comparison of the relative mean error and standard deviation error of the simulated sample at position P7 with the target value, as shown. Figures 4-5 As shown; a comparison between the simulated and target values ​​of the PSD functions for the longitudinal turbulence component u, the transverse turbulence component v, and the vertical turbulence component w at location P7, as shown. Figures 6-8 As shown; a comparison between the simulated and target values ​​of the PSD functions of the longitudinal turbulence component u and the vertical turbulence component w at location P7, as shown. Figure 9 As shown; a comparison between the simulated and target values ​​of the longitudinal turbulence component u at positions P4 and P7 using the PSD function, as shown. Figure 10 As shown; Figure 11 The simulation method provided by this invention is compared with the simulation efficiency of the traditional DPOD model, in which the construction of random functions and the use of the FFT algorithm are also performed.

[0209] First, the wind field is separated into two random vector processes, and Cholesky decomposition is used as much as possible to replace the eigenvalue decomposition in the traditional method. Then, random functions are constructed in the model of this invention to reduce the number of random variables. Finally, the simulation efficiency is further accelerated by introducing the FFT algorithm, generating a set of turbulent wind speed sample time histories, and obtaining the corresponding wind load time histories.

[0210] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0211] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. An efficient simulation method for large-scale structural stochastic turbulent wind fields, characterized in that, The efficient simulation method includes the following steps: Step 1: Separate the 3nV-1D random turbulent wind field into two random vectors, 2nV-1D and nV-1D. Based on the assumption that the forward and vertical turbulence components are uncorrelated with the transverse turbulence component, its bilateral-power spectral density matrix is ​​expressed as: In the formula, S v (ω) represents an nV⁻¹D random vector process V(t) = [v₁(t), v₂(t), ..., vₙ]. n (t)] T The power spectral density (PSD) matrix; S uw (ω) is a 2nV⁻¹D random vector process. W i (t)=[u i (t),w i (t)] T PSD matrix; Among them, W i The power spectral density matrix of (t) is: In the formula, For the turbulent component u i (t) and w i The coherence function of (t); Step 2: POD-SRM hybrid representation of 2nV-1D stochastic vector processes. According to spectral analysis theory: In the formula, complex-valued orthogonal incremental process It satisfies zero mean, and its increment Existing spectral eigentransform forms: in, Also a complex-valued orthogonal incremental process; spectral principal component process PSD matrix Its elements and They are respectively eigenvalues ​​and eigenvector matrices; If the spectral eigenvalue transformation is applied to the j-th point, then and The following relationship exists: Taking the expectation of both sides of equation (5), we obtain the PSD matrix of any two-point vector process: In the formula, For the principal component process Q i (t) and Q j The PSD matrix of (t); Step 3: SRM representation of an nV-1D random vector process. According to the SRM method, the PSD matrix is ​​decomposed by Cholesky, and the nV-1D stochastic vector process V(t) = [v1(t), v2(t), ..., v n (t)] T Represented as: In the formula, H is a lower triangular matrix ν The elements in (ω), H ν (ω) is S v (ω) is the matrix obtained by Cholesky decomposition, i.e., S v (ω)=H ν (ω)H ν (ω) *T ; Step 4: Simulation of stochastic turbulent wind field based on stochastic functions. By constructing a random function, the set of orthogonal random variables can be represented in the following form: In the formula: m, r = 1, 2, 3; p, q = 1, 2, ..., n; k, l = 1, 2, ..., N; the basic random variables Θ = (Θ1, Θ2, Θ3) are independent of each other and all follow a uniform distribution on [0, 2π). Substituting equation (15) into equations (13) and (14), we finally obtain the 2nV-1D random vector process W. i (t) and nV-1D random vector process v i The random function expression of (t): Step 5: Introduce the FFT algorithm. The FFT algorithm is introduced at the frequencies in equations (16) and (17).

2. The efficient simulation method according to claim 1, characterized in that: In step one, for the random turbulent wind field, a 3nV-1D random vector process is selected. To represent; Among them, U i (t)=[u i (t),v i (t),w i (t)] T (i=1,2,…,n), and u i (t), v i (t), w i (t) represents the forward, lateral, and vertical turbulence components at a single point, respectively.

3. The efficient simulation method according to claim 2, characterized in that: In step one, based on the assumption that the vertical turbulence component is uncorrelated with both longitudinal and transverse turbulence components in the measured wind field, the 3nV-1D stochastic turbulent wind field is represented as a combination of two stochastic vector processes. At the same time, Cholesky decomposition is used to replace the eigenvalue decomposition in the traditional DPOD model.

4. The efficient simulation method according to claim 3, characterized in that: In step two, based on the single-point spectral principal component process Q i The definition of (t) is similar, and the spectral principal component process of the 2nV-1D random vector process W(t) is expressed as Q(t)=[Q (1) (t) T Q (2) (t) T ] T ; Its elements Furthermore, the PSD matrix of Q(t) can be expressed as: Will Performing Cholesky decomposition yields... At this time, dZ Q (ω) is represented as: dZ Q (ω)=H(ω)dZ R (oh) (8) In the formula, R(t) = [R (1) (t) T ,R (2) (t) T ] T A 2nV⁻¹D random vector process with zero mean, whose elements dZ R (ω) satisfies I n×n Represents an n-order identity matrix; Therefore, by using equations (5) and (8), we obtain In the formula, Represents the lower triangular matrix H (m) The p-th column of (ω); η(ω) represents a 2n×2n matrix, which is composed of 2n×n submatrices η. (m) The set is composed of (ω)(m=1,2); Substituting equation (9) into equation (3), W(t) is approximately expressed as: In the formula, Δω=ω u / N is the frequency step size, ω u X is the cutoff frequency, N is the frequency fraction; mpk and Y mpk For an orthogonal random variable with zero mean, the following conditions must be met:

5. The efficient simulation method according to claim 4, characterized in that: The H (m) (ω) is a lower triangular matrix whose elements satisfy... so, 6. The efficient simulation method according to claim 5, characterized in that: In step five, taking equation (16) as an example, the corresponding calculation formula is given: In the formula, Re[·] represents the real part; l = 0, 1, 2, ..., 2N-1; and ΔtΔω = π / N.

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