A wave number-frequency spectrum representation based method for combined simulation of wind wave field loads

Abstract

The application belongs to the field of marine environment load simulation, and discloses a wind wave field load joint simulation method based on a wave number-frequency spectrum representation method, which comprises the following steps: constructing a two-dimensional double-variable space-time vector model of a wind-wave joint field; constructing self-wave number-frequency power spectrum densities of a wind speed field and a wave field respectively; constructing mutual wave number-frequency power spectrum densities based on a parameterized wind wave coherence function, and establishing a double-sided wave number-frequency power spectrum density matrix; realizing efficient dimension reduction decomposition of the wave number-frequency power spectrum density matrix by using coherence matrix factorization; constructing a harmonic superposition expression of the wind-wave field based on the decomposition result, and embedding a two-dimensional fast Fourier transform to realize fast generation of a space-time continuous wind-wave joint field; and synchronously simulating wind load and wave load satisfying a phase relationship. The application can effectively retain target spectrum characteristics and inherent coherence of wind-wave load, improve calculation efficiency, and provide a powerful tool for dynamic response analysis and reliability evaluation of structures such as sea-crossing bridges, offshore wind turbines and floating platforms.

Description

Technical Field

[0001] This invention relates to the field of marine environmental load simulation technology, specifically to a joint simulation method for wind and wave field loads based on wave number-frequency spectrum representation. Background Technology

[0002] Accurate and efficient co-simulation methods for stochastic wind-wave fields are crucial for the dynamic response and reliability analysis of marine engineering structures (such as floating platforms, offshore wind turbines, and cross-sea bridges) under the combined effects of wind and waves. Currently, the mainstream method for stochastic field simulation is the spectral representation method. In traditional wind-wave co-simulation, the spectral representation method is mostly based on a one-dimensional n-variable model, which decomposes the wind-wave field into scalar processes at multiple spatial points and achieves simulation through power spectral density matrix decomposition and point-by-point simulation.

[0003] However, existing technologies have the following limitations: 1. Computational efficiency bottleneck: When simulating large-scale wind and wave fields, the traditional one-dimensional n-variable spectrum representation becomes an n×n high-dimensional matrix as the number of spatial points increases. The PSD matrix needs to be repeatedly decomposed and simulated point by point. The computational burden increases exponentially with the number of spatial points, resulting in a serious efficiency bottleneck. 2. Lack of Physical Correlation: Strong winds are the core cause of wave generation, and there is a significant inherent physical correlation between the two. Existing technologies often use a simple superposition method after simulating wind and wave fields independently, without considering their correlation. This can easily overestimate the joint extreme response of marine engineering structures, leading to design redundancy or safety assessment bias. 3. Technology application gaps: WSRM has been widely used in wind engineering, but it has not yet been extended to the fields of joint modeling of wind-wave fields and synchronous simulation of associated loads.

[0004] Therefore, there is an urgent need for a co-simulation method for large-scale wind-wave fields and their associated loads that can accurately characterize the physical correlation between wind and waves and has high computational efficiency. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a joint simulation method for wind and wave field loads based on wavenumber-frequency spectrum representation. It innovatively treats the wind and wave field as a two-dimensional bivariate spatiotemporal vector field. By introducing a parameterized coherence model and approximating the wave dispersion relation using a Gaussian kernel function, an accurate wavenumber-frequency spectrum model is established. Utilizing the characteristics of coherence matrix decomposition and two-dimensional Fourier transform technology, efficient and synchronous simulation of large-scale wind and wave fields and their associated environmental loads is achieved. This invention effectively preserves the target spectral characteristics and inherent coherence of wind-wave loads, significantly improving computational efficiency. It provides a powerful tool for dynamic response analysis and reliability assessment of structures such as cross-sea bridges, offshore wind turbines, and floating platforms, solving the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a joint simulation method for wind and wave field loads based on the wavenumber-frequency spectral representation method (WSRM), comprising the following steps: S1. Construct a two-dimensional, two-variate (2D-2V) spatiotemporal vector model of the wind-wave joint field; S2. Construct the self-wave number-frequency power spectral density (Auto-WPSD) for the wind speed field and the wave field respectively. S3. Construct cross-wavenumber-frequency power spectral density (Cross-WPSD) based on parameterized wind-wave coherence function, and establish a two-sided wavenumber-frequency power spectral density matrix (Two-sided wavenumber-frequency PSD,WPSD). S4. Achieve efficient dimensionality reduction decomposition of the wavenumber-frequency power spectral density matrix using coherence matrix factorization; S5. Based on the decomposition results, construct the harmonic superposition expression of the wind and wave field, and embed the two-dimensional fast Fourier transform (2D-FFT) to realize the rapid generation of the spatiotemporal continuous wind and wave joint field. S6. Simulate wind and wave loads that satisfy phase relationships.

[0007] Preferably, in the two-dimensional bivariate spatiotemporal vector model for constructing the wind-wave joint field, the random wind-wave field is represented as a two-dimensional bivariate 2D-2V spatiotemporal vector field according to the wavenumber-frequency spectrum representation (WSRM): ; Where η(x,t) is the spatiotemporal wavefront elevation component field, and V(x,t) is the spatiotemporal wind speed component field. The two components of the vector field correspond to the wavefront elevation and wind speed at the same spatial location and at the same time, respectively. x is the spatial coordinate, and t is the time coordinate. Two-dimensional (2D) refers to a two-dimensional spatiotemporal domain composed of space and time; bivariate (2V) refers to the two physical variables of wave elevation and wind speed.

[0008] Preferably, step S2 specifically includes the following: S21. Constructing the Auto-WPSD of the Wind Speed ​​Field: For the wind speed field, a two-sided Davenport spectrum is used as the single-point auto-WPSD. Combined with the Davenport spatial coherence model, the auto-WPSD of the wind speed field is obtained through integration, as follows: A two-sided Davenport spectrum is used as the single-point auto-WPSD of the wind speed field. V (ω), expressed as: ; In the formula, z is the calculation height of the wind speed field, U(z) is the average wind speed at height z, and u * For friction speed, satisfying k0 is the von Kármán constant, and z0 is the sea surface roughness; The lateral coherence of the wind field is considered using the Davenport coherence function γ. V (ξ,ω), expressed as: ; Where λ is the attenuation coefficient; The cross-wave number-frequency power spectral density (Cross-WPSD) is integrated as follows: ; The final form of the Auto-WPSD for obtaining the wind speed field is: ; In the formula, k is the wave number and ω is the frequency.

[0009] S V (k,ω) is a function symmetric about the quadrant, satisfying: , .

[0010] S22. Constructing the wave field's self-wave number-frequency power spectral density Auto-WPSD: Using the Jonswald spectrum as the wave's single-point self-power spectrum S η (ω), expressed as: ; , ; ; ; , , ; , ; Among them, H S For significant wave height; ω p T is the peak frequency; p For the spectral peak period; T z γ is the average crossing period; γ is the peak factor. Based on the dispersion relation ω 2 =gktanh(kd), constructs the initial form of the wave Auto-WPSD: Where δ(·) is the Dirac delta function; k(ω) is the implicit wavenumber function determined by the dispersion relation; g is the gravitational acceleration; d is the water depth; Sη (ω) represents the single-point self-power spectral density; S η (k,ω) is a function symmetric about the k-axis, satisfying: , ; Introducing the Gaussian kernel function to numerically approximate the Dirac delta function: ; Where ε is the bandwidth; The optimal bandwidth ε is solved based on the principle of minimizing the sum of the absolute errors between the approximate values ​​of the edge wavenumber spectrum and the edge frequency spectrum and the target value. * The optimization objective is: ; in, and These are the target values ​​for the marginal frequency spectrum and the marginal wavenumber spectrum, respectively. and These are approximate values ​​of the marginal frequency spectrum and the marginal wavenumber spectrum, respectively, obtained by applying S... η Integrating (k,ω) along the wavenumber and frequency dimensions yields: ; ; Based on optimal bandwidth ε * By using a Gaussian kernel function to achieve a high-precision approximation of the non-smooth Dirac delta function, the numerical wave field Auto-WPSD is obtained as follows: .

[0011] Preferably, in step S22, the algorithm for solving the optimal bandwidth ε* specifically includes the following: Step 1: Input the wave's single-point self-power spectral density S η (ω), cutoff wave number k u Cutoff frequency ω u ; Step 2: Convert the wavenumber domain [0, k] u Discretized into N k Wavenumber points, frequency domain [0, ω u Discretized into N ω One frequency point; Step 3: Assign an initial value to the bandwidth ε; Step 4: For each frequency component ω k Numerical approximation is performed in the wavenumber domain; Step 5: Calculate the sum of the absolute errors between the approximate values ​​of the marginal wavenumber spectrum and the marginal frequency spectrum and the target values; Step 6: Repeat the above steps by calling the optimization algorithm until the error and convergence are reached, and obtain the optimal bandwidth ε*.

[0012] Preferably, in step S3, the bilateral wavenumber-frequency power spectral density matrix S U The expression for (k,ω) is as follows: ; Among them, the diagonal element S η (k,ω) and S V (k,ω) represents the Auto-WPSD between η(x,t) and V(x,t), and the off-diagonal element S ηV (k,ω) represents the Cross-WPSD between the spatiotemporal wavefront elevation component field η(x,t) and the spatiotemporal wind speed component field V(x,t), and its expression is: , where γ ηV (ω) is a single-point coherence function of η(x,t) and V(x,t).

[0013] Preferably, in step S4, the efficient dimensionality reduction decomposition of the wavenumber-frequency power spectral density matrix using coherence matrix factorization specifically includes: For the two-sided wavenumber-frequency power spectral density matrix S U Factorize (k,ω): ; Wherein, the diagonal matrix D(k,ω) and the coherence matrix The expression for (ω) is: , ; Perform Chollisky decomposition on the non-negative definite Hermitian coherence matrix: ; Wherein, the superscript * denotes complex conjugate, the superscript T denotes matrix transpose, and B(ω) is a lower triangular matrix; The final decomposition form of the two-sided wavenumber-frequency power spectral density matrix is ​​obtained as follows: .

[0014] Preferably, in step S5, the construction of the harmonic superposition expression of the wind and wave field based on the decomposition results, and the embedding of a two-dimensional fast Fourier transform to achieve rapid generation of the spatiotemporal continuous wind and wave joint field, specifically includes: Based on the decomposition results, a harmonic superposition expression for the spatiotemporal wavefront elevation component field and the spatiotemporal wind speed component field is constructed: ; ; Among them, B 11B 21 B 22 These are the elements of the lower triangular matrix B(ω); Let N be an independent random phase angle uniformly distributed in the interval [0, 2π]; Δk is the wavenumber interval, Δω is the frequency interval, and N is the wavenumber interval. k N represents the number of wavenumber components. ω The number of frequency components; Discretize the spatial domain [0,L] and the time domain [0,T]: , , , ; , , , ; Where Δx is the spatial interval, Δt is the time interval, and N is the distance between the two points. x N is the number of discrete points in space. t This is the number of discrete time points, usually taken as a power of 2; To achieve rapid generation of the entire field, the harmonic superposition expression is rewritten in a 2D-FFT adapted form: ; .

[0015] Preferably, in step S6, the synchronous simulation of wind loads and wave loads that satisfy the phase relationship specifically includes: Wind pressure simulation: Assuming the pulsating wind pressure acting on the structure is in the same direction as the incoming wind speed and the characteristic dimensions of the structure are much smaller than the dominant vortex scale of the natural wind, the bridge deck wind pressure w(x,t) is calculated from the wind speed field: , ; Where, ρ a C is the density of air. p This refers to the wind pressure coefficient. Wave force simulation: Based on the Laplace equation and boundary conditions, the horizontal velocity u(x,t) and acceleration of wave particles at water depth z are obtained from the spatiotemporal wave surface elevation component field. : ; ; To facilitate the application of 2D-FFT, the following harmonic superposition method is adopted: ; ; Calculation of wave forces on bridge piers using Morrison's equations: ; Where, ρ w D is the density of seawater; D is the diameter of the bridge pier; A = πD 2 / 4 represents the cross-sectional area of ​​the bridge pier; C D C is the drag force coefficient. I It is the inertial force coefficient; by sharing random phase angles, the phase consistency between wave surface elevation, acceleration and wave force is ensured.

[0016] The beneficial effects of this invention are as follows: The method fully utilizes the powerful capabilities of WSRM for modeling multidimensional spatiotemporal continuous random fields and the high efficiency of WSRM adapted to 2D-FFT. It transforms the complex mode of traditional independent simulation and point-by-point calculation of physically correlated wind-wave joint fields into a global synchronous simulation of 2D-2V spatiotemporal vector fields, achieving rapid solution through frequency domain-wavenumber domain dimensionality reduction. This invention fully leverages the advantages of WSRM in characterizing the joint statistical properties of multiple fields and combines it with classical spectral models in wind engineering and marine engineering, as well as engineering load calculation theories. This achieves accurate modeling of wind-wave joint random fields, synchronous simulation of associated environmental loads, and functional extension of traditional spectral representation methods in marine engineering joint load simulation scenarios. This invention can be widely applied to various structural analysis problems in the field of marine engineering. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the joint simulation method for wind and wave field loads based on wavenumber-frequency spectrum representation in an embodiment of the present invention; Figure 2 This is a schematic diagram of the cross-sea cable-stayed bridge structure used in the embodiments of the present invention; Figure 3 The following is a schematic diagram of the spatiotemporal distribution of wavefront elevation field and wind speed field generated by simulation in the embodiment of the present invention. (a) is the wavefront elevation at z=0m, and (b) is the wind speed at z=50m. Figure 4 The above is a schematic diagram of the spatiotemporal distribution of wave force field and wind pressure field generated synchronously in an embodiment of the present invention. (a) is the wave force at -10m, and (b) is the wind pressure at z=50m. Figure 5 This is a schematic diagram of wind speed time history sample curves at typical spatial locations in an embodiment of the present invention; Figure 6 This is a schematic diagram of wind pressure time history sample curves at typical spatial locations in an embodiment of the present invention; Figure 7 This is a schematic diagram of wavefront elevation time history sample curves at typical spatial locations in an embodiment of the present invention; Figure 8This is a schematic diagram of the time history sample curve of wave force at a typical spatial location in an embodiment of the present invention; Figure 9 This is a schematic diagram showing the verification comparison between the estimated value of the self-spectrum / cross-power spectrum of wavefront elevation and the target value in an embodiment of the present invention. (a) is the self-spectrum at x=0m, (b) is the cross-spectrum between x=0m and 50m, (c) is the self-spectrum at x=50m, (d) is the cross-spectrum between x=50m and 100m, (e) is the self-spectrum at x=100m, and (f) is the cross-spectrum between x=0m and 100m. Figure 10 This is a schematic diagram showing the verification comparison between the estimated value of the wind speed's autospectrum / cross-power spectrum and the target value in an embodiment of the present invention. (a) is the autospectrum at x=0m, (b) is the cross-spectrum between x=0m and 50m, (c) is the autospectrum at x=50m, (d) is the cross-spectrum between x=50m and 100m, (e) is the autospectrum at x=100m, and (f) is the cross-spectrum between x=0m and 100m. Figure 11 This is a schematic diagram showing the verification comparison between the estimated value and the target value of the cross spectrum of wind speed and wave surface elevation in an embodiment of the present invention. (a) represents η(x=0,t) and V(x=0,t), (b) represents η(x=0,t) and V(x=50,t), (c) represents η(x=50,t) and V(x=50,t), (d) represents η(x=50,t) and V(x=100,t), (e) represents η(x=50,t) and V(x=50,t), and (f) represents η(x=50,t) and V(x=100,t). Detailed Implementation

[0018] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] This invention provides a technical solution: a joint simulation method for wind and wave field loads based on wavenumber-frequency spectrum representation, the steps of which are as follows: Figure 1 As shown in the figure, this embodiment adopts a cross-sea cable-stayed bridge structure, and the model schematic diagram is as follows. Figure 2 As shown, a long-span cable-stayed bridge with a total length of 2000m, a main span of 1000m, a tower height of 200m, and a bridge deck height of 50m is used as the simulation object. Eight piers are located on each side of the bridge, spaced 50m apart. Including the piers below the towers, a total of 18 piers bear wave forces in deep-water conditions. The simulation method for the stochastic wind-wave combined field and its environmental loads in this embodiment specifically includes the following steps: S1. Construct a two-dimensional, two-variate (2D-2V) spatiotemporal vector model of the wind-wave joint field. In the construction of the two-dimensional, two-variate spatiotemporal vector model of the wind-wave joint field, according to the wavenumber-frequency spectrum representation (WSRM), the random wind-wave field is represented as a two-dimensional, two-variable (2D-2V) spatiotemporal vector field: ; Where η(x,t) is the spatiotemporal wavefront elevation component field, and V(x,t) is the spatiotemporal wind speed component field. The two components of the vector field correspond to the wavefront elevation and wind speed at the same spatial location and at the same time, respectively. x is the spatial coordinate, and t is the time coordinate. Two-dimensional (2D) refers to a two-dimensional spatiotemporal domain composed of space and time; bivariate (2V) refers to the two physical variables of wave elevation and wind speed.

[0020] S2. Construct the self-wavenumber-frequency power spectral density (Auto-WPSD) for the wind speed field and wave field, respectively. This includes the following: S21. Constructing the Auto-WPSD of the Wind Speed ​​Field: For the wind speed field, the Davenport spectrum is used as the single-point auto-WPSD. Combined with the Davenport spatial coherence model, the auto-WPSD of the wind speed field is obtained through integration, as follows: The bilateral Davenport spectrum is used as the single-point auto-WPSD of the wind speed. V (ω), the core parameter settings are shown in Table 1.

[0021] Table 1 Modeling parameters for random wind speed fields

[0022] The bilateral Davenport spectrum expression is: ; In the formula, z is the calculation height of the wind speed field, U(z) is the average wind speed at height z, and u * For friction speed, satisfying k0 is the von Kármán constant, and z0 is the sea surface roughness; The lateral coherence of the wind field is considered using the Davenport coherence function γ. V (ξ,ω), expressed as: ; Where λ is the attenuation coefficient; The cross-wave number-frequency power spectral density (Cross-WPSD) is integrated as follows: ; The final form of the Auto-WPSD for obtaining the wind speed field is: ; In the formula, k is the wave number and ω is the frequency.

[0023] S V (k,ω) is a function symmetric about the quadrant, satisfying: , .

[0024] S22. Constructing the wave field's self-wave number-frequency power spectral density Auto-WPSD: Using the Jonswald spectrum as the wave's single-point self-power spectrum S η (ω), the core parameter settings are shown in Table 2: Table 2 Modeling parameters for random wave fields

[0025] The expression is: ; , ; ; ; , , ; , ; Among them, H S For significant wave height; ω p T is the peak frequency; p For the spectral peak period; T z γ is the average crossing period; γ is the peak factor. Based on the dispersion relation ω 2 =gktanh(kd), constructs the initial form of the wave Auto-WPSD: Where δ(·) is the Dirac delta function; k(ω) is the implicit wavenumber function determined by the dispersion relation; g is the gravitational acceleration; d is the water depth; S η (ω) represents the single-point self-power spectral density; S η (k,ω) is a function symmetric about the k-axis, satisfying: , ; Introducing the Gaussian kernel function to numerically approximate the Dirac delta function: ; Where ε is the bandwidth; The optimal bandwidth ε is solved based on the principle of minimizing the sum of the absolute errors between the approximate values ​​of the edge wavenumber spectrum and the edge frequency spectrum and the target value. *The optimization objective is: ; in, and These are the target values ​​for the marginal frequency spectrum and the marginal wavenumber spectrum, respectively. and These are approximate values ​​of the marginal frequency spectrum and the marginal wavenumber spectrum, respectively, obtained by applying S... η Integrating (k,ω) along the wavenumber and frequency dimensions yields: ; ; Based on optimal bandwidth ε * By using a Gaussian kernel function to achieve a high-precision approximation of the non-smooth Dirac delta function, the numerical wave field Auto-WPSD is obtained as follows: .

[0026] Solving for the optimal bandwidth ε * The relevant parameter settings are shown in Table 3: Table 3 Simulation parameters of random wind and wave fields

[0027] The algorithm for solving the optimal bandwidth ε* includes the following: Step 1: Input the wave's single-point self-power spectral density S η (ω), cutoff wave number k u Cutoff frequency ω u ; Step 2: Convert the wavenumber domain [0, k] u Discretized into N k Wavenumber points, frequency domain [0, ω u Discretized into N ω One frequency point; Step 3: Assign an initial value to the bandwidth ε; Step 4: For each frequency component ω k Numerical approximation is performed in the wavenumber domain; Step 5: Calculate the sum of the absolute errors between the approximate values ​​of the marginal wavenumber spectrum and the marginal frequency spectrum and the target values; Step 6: Repeat the above steps by calling the optimization algorithm until the error and convergence are reached, and obtain the optimal bandwidth ε*.

[0028] S3. Construct the cross-wavenumber-frequency power spectral density (Cross-WPSD) based on the parameterized wind-wave coherence function, and establish the two-sided wavenumber-frequency power spectral density matrix (WPSD). The two-sided wavenumber-frequency power spectral density matrix S UThe expression for (k,ω) is as follows: ; Among them, the diagonal element S η (k,ω) and S V (k,ω) represents the Auto-WPSD between η(x,t) and V(x,t), and the off-diagonal element S ηV (k,ω) represents the Cross-WPSD between the spatiotemporal wavefront elevation component field η(x,t) and the spatiotemporal wind speed component field V(x,t), and its expression is: , where γ ηV (ω) is a single-point coherence function of η(x,t) and V(x,t).

[0029] This embodiment uses the following parameterized coherence function model, and the relevant parameters are shown in Table 4: Table 4 Wind and Wave Coherence Parameters

[0030] The coherence function expression is: .

[0031] S4. Utilize coherence matrix factorization to achieve efficient dimensionality reduction decomposition of the wavenumber-frequency power spectral density matrix. Specifically, this includes: Taking advantage of the fact that the wind-wave coherence function is only frequency-dependent, the bilateral wavenumber-frequency power spectral density matrix S is analyzed. U Factorize (k,ω): ; Wherein, the diagonal matrix D(k,ω) and the coherence matrix The expression for (ω) is: , ; Perform Cholliski decomposition on a 2×2 nonnegative definite Hermitian coherence matrix that is only related to frequency: ; Wherein, the superscript * denotes complex conjugate, the superscript T denotes matrix transpose, and B(ω) is a lower triangular matrix; The final decomposition form of the two-sided wavenumber-frequency power spectral density matrix is ​​obtained as follows: .

[0032] The final dimensionality reduction decomposition of the spectral matrix is ​​achieved by performing second-order matrix decomposition in only 1024 frequency steps, without performing high-dimensional matrix decomposition in the full wavenumber-frequency dimension, reducing the computational cost by more than 99%.

[0033] S5. Based on the decomposition results, construct the harmonic superposition expression of the wind and wave field, and embed a two-dimensional fast Fourier transform (2D-FFT) to achieve rapid generation of the spatiotemporal continuous wind and wave joint field. Specifically, this includes: Based on the decomposition results, a harmonic superposition expression for the spatiotemporal wavefront elevation component field and the spatiotemporal wind speed component field is constructed: ; ; Among them, B 11 B 21 B 22 These are the elements of the lower triangular matrix B(ω); Let N be an independent random phase angle uniformly distributed in the interval [0, 2π]; Δk is the wavenumber interval, Δω is the frequency interval, and N is the wavenumber interval. k N represents the number of wavenumber components. ω The number of frequency components; Discretize the spatial domain [0,L] and the time domain [0,T]: , , , ; , , , ; Where Δx is the spatial interval, Δt is the time interval, and N is the distance between the two points. x N is the number of discrete points in space. t This is the number of discrete time points, usually taken as a power of 2; To achieve rapid generation of the entire field, the harmonic superposition expression is rewritten in a 2D-FFT adapted form: ; .

[0034] Wavefront elevation and wind speed fields in the entire space and time domains can be rapidly generated using 2D-FFT. Representative samples are shown below. Figure 3 As shown, the time history curves at typical locations are as follows: Figure 5 , Figure 7 As shown.

[0035] S6. Simulate wind and wave loads that satisfy phase relationships. Specifically, this includes: Wind pressure simulation: Assuming the pulsating wind pressure acting on the structure is in the same direction as the incoming wind speed and the characteristic dimensions of the structure are much smaller than the dominant vortex scale of the natural wind, the bridge deck wind pressure w(x,t) is calculated from the wind speed field: , ; Where, ρ a C is the density of air. p The wind pressure coefficient; representative samples of the wind pressure field are as follows: Figure 4 As shown, the time history curves at typical locations are as follows: Figure 6 As shown.

[0036] Wave force simulation: Based on the Laplace equation and boundary conditions, the horizontal velocity u(x,t) and acceleration of wave particles at water depth z are obtained from the spatiotemporal wave surface elevation component field by sharing a random phase. To ensure phase consistency: ; ; To facilitate the application of 2D-FFT, the following harmonic superposition method is adopted: ; ; Calculation of wave forces on bridge piers using Morrison's equations: ; Where, ρ w D is the density of seawater; D is the diameter of the bridge pier; A = πD 2 / 4 represents the cross-sectional area of ​​the bridge pier; C D C is the drag force coefficient. I This represents the inertial force coefficient; by sharing random phase angles, phase consistency between wave surface elevation, acceleration, and wave force is ensured. Representative samples of the wave force field are shown below. Figure 4 As shown, the time history curves at typical locations are as follows: Figure 8 As shown.

[0037] This embodiment is based on 1000 sets of simulation samples and is evaluated by achieving three core indicators: spectral characteristics, coherence, and computational efficiency. Figure 9 , Figure 10 As shown, the estimated values ​​of wavefront elevation and wind speed at different horizontal positions, including the self-spectrum and cross-power spectrum, are highly consistent with the target values, with an average relative error of less than 2%, accurately reproducing the target spectral characteristics. Figure 11As shown, the cross-spectral estimates of wind speed and wave surface elevation at the same / different horizontal locations exhibit excellent consistency with the target values, and the wind-wave coherence retention rate is greater than 98%, fully preserving the physical correlation between the two. In the embodiment, generating 1000 sets of wind-wave field and load samples across the entire bridge range took only 11.7 minutes, which is more than 200 times more efficient than the traditional one-dimensional n-variable spectrum representation method, breaking through the computational bottleneck in large-scale scenarios. In summary, the method proposed in this invention can efficiently and accurately complete the joint simulation of large-scale wind-wave fields and their associated loads, and can be seamlessly applied to the dynamic response analysis and reliability assessment of various marine engineering structures, possessing both extremely high computational efficiency, simulation accuracy, and engineering practical value.

[0038] This invention can effectively preserve the target spectrum characteristics and inherent coherence of wind-wave loads, significantly improve computational efficiency, and provide a powerful tool for dynamic response analysis and reliability assessment of structures such as cross-sea bridges, offshore wind turbines, and floating platforms.

[0039] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0040] The terminology used in the embodiments of this invention is for the purpose of describing particular embodiments only and is not intended to limit the invention. The singular forms “a,” “the,” and “the” as used in the embodiments of this invention and the appended claims are also intended to include the plural forms unless the context clearly indicates otherwise.

[0041] It should be understood that the term "and / or" used in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this article generally indicates that the preceding and following related objects have an "or" relationship.

[0042] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0043] The terms "first" and "second" used in the embodiments are merely to distinguish similar objects and do not represent a specific ordering of objects. It is understood that "first" and "second" can be interchanged in a specific order or sequence where permitted. It should be understood that the objects distinguished by "first" and "second" can be interchanged where appropriate so that the embodiments described herein can be implemented in an order other than those illustrated or described herein.

[0044] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation, characterized in that, Includes the following steps: S1. Construct a two-dimensional bivariate spatiotemporal vector model of the wind-wave joint field; S2. Construct the self-wave number-frequency power spectral density of the wind speed field and the wave field respectively; S3. Construct cross-wave number-frequency power spectral density based on parameterized wind-wave coherence function, and establish a two-sided wave number-frequency power spectral density matrix; S4. Achieve efficient dimensionality reduction decomposition of the wavenumber-frequency power spectral density matrix using coherence matrix factorization; S5. Based on the decomposition results, construct the harmonic superposition expression of the wind and wave field, and embed the two-dimensional fast Fourier transform to realize the rapid generation of the spatiotemporal continuous wind and wave joint field. S6. Simulate wind and wave loads that satisfy phase relationships.

2. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: In the two-dimensional bivariate spatiotemporal vector model for constructing the wind-wave joint field, the random wind-wave field is represented as a two-dimensional bivariate 2D-2V spatiotemporal vector field according to the wavenumber-frequency spectrum representation (WSRM): ； Where η(x,t) is the spatiotemporal wavefront elevation component field, V(x,t) is the spatiotemporal wind speed component field, x is the spatial coordinate, and t is the time coordinate.

3. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: Step S2 specifically includes the following: S21. Constructing the self-wavenumber-frequency power spectral density (Auto-WPSD) of the wind speed field: Using a two-sided Davenport spectrum as the single-point self-power spectral density of wind speed (S). V (ω), expressed as: ； In the formula, z is the calculation height of the wind speed field, U(z) is the average wind speed at height z, and u * For friction speed, satisfying k0 is the von Kármán constant, and z0 is the sea surface roughness; The lateral coherence of the wind field is considered using the Davenport coherence function γ. V (ξ,ω), expressed as: ； Where λ is the attenuation coefficient; The cross-wave number-frequency power spectral density (Cross-WPSD) is integrated as follows: ； The final form of the Auto-WPSD for obtaining the wind speed field is: ； In the formula, k is the wave number and ω is the frequency; S V (k,ω) is a function symmetric about the quadrant, satisfying: , ； S22. Constructing the wave field's self-wave number-frequency power spectral density Auto-WPSD: Using the Jonswald spectrum as the wave's single-point self-power spectrum S η (ω), expressed as: ； ， ； ； ； , , ； , ； Based on the dispersion relation ω 2 =gktanh(kd), constructs the initial form of the wave Auto-WPSD: ; S η (k,ω) is a function symmetric about the k-axis, satisfying: , ； Introducing the Gaussian kernel function to numerically approximate the Dirac delta function: ； The optimal bandwidth ε is solved based on the principle of minimizing the sum of the absolute errors between the approximate values ​​of the edge wavenumber spectrum and the edge frequency spectrum and the target value. * The optimization objective is: ； in, and These are the target values ​​for the marginal frequency spectrum and the marginal wavenumber spectrum, respectively. and These are approximate values ​​of the marginal frequency spectrum and the marginal wavenumber spectrum, respectively, obtained by applying S... η Integrating (k,ω) along the wavenumber and frequency dimensions yields: ； ； Based on optimal bandwidth ε * By using a Gaussian kernel function to achieve a high-precision approximation of the non-smooth Dirac delta function, the numerical wave field Auto-WPSD is obtained as follows: .

4. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 3, characterized in that: In step S22, the algorithm for solving the optimal bandwidth ε* specifically includes the following: Step 1: Input the wave's single-point self-power spectral density S η (ω), cutoff wave number k u Cutoff frequency ω u ; Step 2: Convert the wavenumber domain [0, k] u Discretized into N k Wavenumber points, frequency domain [0, ω u Discretized into N ω One frequency point; Step 3: Assign an initial value to the bandwidth ε; Step 4: For each frequency component ω k Perform numerical approximation in the wavenumber domain; Step 5: Calculate the sum of the absolute errors between the approximate values ​​of the marginal wavenumber spectrum and the marginal frequency spectrum and the target values; Step 6: Repeat the above steps by calling the optimization algorithm until the error and convergence are reached, and obtain the optimal bandwidth ε*.

5. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: In step S3, the bilateral wavenumber-frequency power spectral density matrix S U The expression for (k,ω) is as follows: ； Among them, the diagonal element S η (k,ω) and S V (k,ω) represents the Auto-WPSD between η(x,t) and V(x,t), and the off-diagonal element S ηV (k,ω) represents the Cross-WPSD between the spatiotemporal wavefront elevation component field η(x,t) and the spatiotemporal wind speed component field V(x,t), and its expression is: , where γ ηV (ω) is a single-point coherence function of η(x,t) and V(x,t).

6. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: In step S4, the efficient dimensionality reduction decomposition of the wavenumber-frequency power spectral density matrix using coherence matrix factorization specifically includes: For the two-sided wavenumber-frequency power spectral density matrix S U Factorize (k,ω): ； Wherein, the diagonal matrix D(k,ω) and the coherence matrix The expression for (ω) is: ， ； Perform Chollisky decomposition on the non-negative definite Hermitian coherence matrix: ； Wherein, the superscript * denotes complex conjugate, the superscript T denotes matrix transpose, and B(ω) is a lower triangular matrix; The final decomposition form of the two-sided wavenumber-frequency power spectral density matrix is ​​obtained as follows: 。 7. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: In step S5, the construction of a harmonic superposition expression for the wind and wave field based on the decomposition results, and the embedding of a two-dimensional fast Fourier transform to achieve rapid generation of the spatiotemporal continuous wind and wave joint field, specifically includes: Based on the decomposition results, a harmonic superposition expression for the spatiotemporal wavefront elevation component field and the spatiotemporal wind speed component field is constructed: ； ； Among them, B 11 B 21 B 22 These are the elements of the lower triangular matrix B(ω); Let N be an independent random phase angle uniformly distributed in the interval [0, 2π]; Δk is the wavenumber interval, Δω is the frequency interval, and N is the wavenumber interval. k N represents the number of wavenumber components. ω The number of frequency components; Discretize the spatial domain [0,L] and the time domain [0,T]: , , , ； , , , ； Where Δx is the spatial interval, Δt is the time interval, and N is the distance between the two points. x N is the number of discrete points in space. t The number of discrete points in time; Rewrite the harmonic superposition expression in a 2D-FFT adapted form: ； 。 8. The method for joint simulation of wind and wave field loads based on wavenumber-frequency spectrum representation according to claim 1, characterized in that: In step S6, the synchronous simulation of wind loads and wave loads that satisfy the phase relationship specifically includes: Wind pressure simulation: Assuming the pulsating wind pressure acting on the structure is in the same direction as the incoming wind speed and the characteristic dimensions of the structure are much smaller than the dominant vortex scale of the natural wind, the bridge deck wind pressure w(x,t) is calculated from the wind speed field: , ； Where, ρ a C is the density of air. p This refers to the wind pressure coefficient. Wave force simulation: Based on the Laplace equation and boundary conditions, the horizontal velocity u(x,t) and acceleration of wave particles at water depth z are obtained from the spatiotemporal wave surface elevation component field. : ； ； To facilitate the application of 2D-FFT, the following harmonic superposition method is adopted: ； ； Calculation of wave forces on bridge piers using Morrison's equations: ； Where, ρ w D is the density of seawater; D is the diameter of the bridge pier; A = πD 2 / 4 represents the cross-sectional area of ​​the bridge pier; C D C is the drag force coefficient. I It is the inertial force coefficient; by sharing random phase angles, the phase consistency between wave surface elevation, acceleration and wave force is ensured.

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