A method for simulating sea ground motion suitable for seismic analysis of offshore wind power

Abstract

This invention relates to a marine seismic motion simulation method for seismic analysis of offshore wind power, comprising the following steps: Step S1: Calculate the seismic transfer function of the overlying seawater bedrock site; Step S2: Correct the design response spectrum based on the DMF model obtained by statistical regression, and then calculate the seismic power spectral density function; Step S3: Calculate the spatially varying seismic power spectral density matrix; Step S4: Simulate the seismic motion in the frequency domain, use inverse Fourier transform, and multiply by a shape function to obtain the non-stationary seismic acceleration time history; Step S5: Use the simulated seismic motion as input for seismic response analysis of the wind power structure. This invention addresses the shortcomings of using terrestrial seismic motion simulation methods for seismic analysis of offshore wind power structures due to the lack of marine seismic records, providing more accurate seismic motion input for seismic response analysis and seismic verification design of offshore wind power structures.

Description

Technical Field

[0001] The invention relates to a seismic motion simulation method, in particular to a sea area seismic motion simulation method suitable for offshore wind power seismic analysis. Background Art

[0002] Wind power generation has achieved rapid development in recent years due to its stability, practicality and environmental protection, especially in the coastal areas of my country where a large number of offshore wind farms have been built. Wind power structures (such as wind power towers) are slender and tall structures with large mass at the top and a relatively long basic period. Under different earthquake motions, they often present complex and changeable failure modes, so the seismic resistance of offshore wind power is particularly important.

[0003] Due to the lack of measured seabed seismic data and the lack of seismic design specifications specifically for offshore wind power structures, most of the current offshore wind power seismic analysis is calculated using onshore seismic records. However, many studies have shown that due to the influence of seawater layers, seabed soil layers, etc., there are significant differences between the characteristics of sea and land seismic motions. The traditional seismic performance analysis method for land wind power structures is not suitable for the study of seismic performance of offshore wind power structures. Therefore, conducting sea seismic motion simulation is an effective solution. When an offshore wind farm is subjected to an earthquake, due to the traveling wave effect caused by the different arrival times of seismic waves at different points of the seismic motion and the coherence effect caused by refraction and reflection during the propagation of seismic waves, there are relatively large differences between the seismic waves of wind towers at different locations. Therefore, the simulation of sea seismic motion needs to consider not only the influence of the seawater layer, but also its spatial effect. In order to consider the spatial effect of seismic motion, some scholars use traveling wave method, coherence function, spectral representation method, etc. to simulate spatially varying seismic motion, but these methods are obtained for land sites and have not yet considered the characteristics of sea seismic motion and the influence of seawater layers and seabed soil layers. Obviously, there is an urgent need to develop a seismic motion simulation method that is suitable for offshore wind power seismic analysis and can take into account spatial effects. Summary of the invention

[0004] The purpose of the present invention is to solve the defect of using land seismic motion simulation method to carry out seismic analysis of offshore wind power structures due to the lack of sea seismic motion records, and propose a sea seismic motion simulation method suitable for seismic analysis of offshore wind farms.

[0005] The technical solution adopted by the present invention is: a method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind farms, comprising the following steps:

[0006] Step S1: Calculate the dynamic stiffness matrix of the seawater layer and bedrock, and obtain the ground motion transfer function of the overlying seawater layer bedrock site based on the dynamic balance equation;

[0007] Step S2: Based on the seismic motion selection standard with the smallest deviation between the average response spectrum and the wind tower design spectrum, a DMF model for the quantile spectrum is established by statistical regression, the standard response spectrum with a damping ratio of 5% in the specification is corrected, and then the seismic motion power spectrum density function is determined according to the corrected seismic motion response spectrum;

[0008] Step S3: Calculating the spatially varying ground motion power spectrum density matrix based on the transfer function, the power spectrum density function, and the coherence loss function;

[0009] Step S4: Simulate the ground motion in the frequency domain, use inverse Fourier transform, and multiply by the shape function to obtain the non-stationary ground motion acceleration time history;

[0010] Step S5: Using the simulated earthquake motion as the input of wind power seismic resistance, and then conducting seismic response analysis of offshore wind power structures.

[0011] Furthermore, in step S1: assuming that seawater is an ideal fluid that cannot withstand shear stress and can only propagate compression waves (P waves) but not shear waves (S waves), the fluid mass conservation equation, Euler equation, and thermodynamic equation are used to express the motion under seismic excitation, and the partial differential equations are solved to obtain the displacement and stress expressions of the particles at the top and bottom of the seawater layer, and then the dynamic stiffness matrix and dynamic balance equation are obtained based on the relationship between displacement and load; the combined dynamic stiffness matrix and dynamic balance equation are solved to obtain the seismic transfer function of the bedrock site of the overlying seawater layer.

[0012] Further, in step S3, the power spectrum density function is solved based on the response spectrum obtained in step S2:

[0013] ;

[0014] In the formula, is the damping ratio, is the earthquake acceleration response spectrum, To hold the earthquake in time, is the probability of not exceeding the target response spectrum; ω represents the circular frequency;

[0015] The autopower spectral density function at site point a is:

[0016] ;

[0017] In the formula, Indicate point a The ground motion transfer function is represents the power spectral density function of the free surface ground motion of the bedrock; represents an imaginary unit;

[0018] point a and bThe mutual power spectral density function of the ground motion for:

[0019] ;

[0020] In the formula, the superscript * indicates complex conjugation; Indicate point a The ground motion transfer function at point a Changes in time; Indicate point b The complex conjugate of the seismic transfer function at is used to process the phase and amplitude relationship of the seismic signal in the frequency domain; represents the coherence loss function between bedrock points a and b;

[0021] So that you can get the venue n The power spectrum density function matrix of the ground motion at each point :

[0022] .

[0023] Further, in step S4, the ground motion power spectrum density function matrix obtained in step S3 is decomposed to obtain a complex lower triangular matrix and a Hermitian matrix :

[0024] ;

[0025] You can simulate the point in the frequency domain a Earthquake at:

[0026] ;

[0027] ;

[0028] ;

[0029] In the formula, is the amplitude of simulated earthquake motion, is the phase angle of simulated ground motion, is the frequency interval, For the matrix The frequency corresponding to and location 2. The elements of contain the amplitude and phase information of the earthquake motion, where a represents a specific point in space, m represents the corresponding frequency component; The interval is [0,2 ] is a random variable uniformly distributed in express The imaginary part; denominator express The real part of

[0030] right Use the inverse Fourier transform to get the time domain interior point a Steady ground acceleration at , multiplied by the intensity envelope function to obtain the final simulation point a Non-stationary ground acceleration time history.

[0031] Furthermore, in step S5, a finite element model of the wind turbine structure is established in the OpenSees software, and the simulated earthquake acceleration time history is used as input to calculate the structural responses of the wind turbine structure such as tower top displacement, tower top acceleration, tower bottom internal force, etc. under the action of the earthquake.

[0032] The present invention has the following advantages and effects:

[0033] The present invention proposes a method for simulating marine seismic motion suitable for seismic analysis of offshore wind power, which solves the problem of lack of marine seismic motion records and the defect of using land seismic motion simulation method to carry out seismic analysis of offshore wind power structures. The method takes into account the engineering characteristics of low damping ratio of wind power structures and reflects the spatial variability within wind farms, providing more accurate seismic motion input for seismic response analysis and seismic verification design of offshore wind power structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 is the earthquake motion (EW direction) simulated based on the method of the present invention;

[0035] Figure 2 is the earthquake motion (NS direction) simulated based on the method of the present invention;

[0036] Figure 3 is the earthquake motion (UD direction) simulated based on the method of the present invention;

[0037] Figure 4 To simulate the displacement of the top of a 1.5MW wind tower under earthquake motion, the solid line represents the EW direction and the dotted line represents the UD direction. DETAILED DESCRIPTION

[0038] The present invention is described more completely and clearly below in conjunction with the accompanying drawings and specific embodiments. The described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] The present invention proposes a method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind farms. The specific method steps are as follows:

[0040] (1) Obtaining the ground motion transfer function of the bedrock site in the overlying seawater layer

[0041] Assuming that seawater is an ideal fluid that cannot withstand shear stress and can only propagate compression waves (P waves) but not shear waves (S waves), the fluid mass conservation equation, Euler equation, and thermodynamic equation are used to express the motion under seismic excitation. The partial differential equations are solved to obtain the displacement and stress expressions of the particles at the top and bottom of the seawater layer, and then the dynamic stiffness matrix and dynamic balance equation are obtained based on the relationship between displacement and load. The dynamic stiffness matrix and dynamic balance equation are combined to solve the seismic transfer function of the bedrock site overlying the seawater layer.

[0042] (2) Determine the ground motion power spectrum density function

[0043] Based on the seismic motion selection standard with the smallest deviation between the average response spectrum and the design spectrum of the wind turbine tower, a DMF model for the quantile spectrum is established by statistical regression, and the standard response spectrum with a damping ratio of 5% in the code is corrected. Then, the seismic motion power spectral density function is determined according to the corrected seismic motion response spectrum.

[0044] (3) Solving the spatially varying ground motion power spectrum density matrix

[0045] The spatially varying ground motion power spectral density matrix is ​​calculated based on the transfer function, power spectral density function, and coherence loss function.

[0046] Solve the power spectral density function based on the response spectrum obtained in step S2:

[0047] ;

[0048] In the formula, is the damping ratio, is the earthquake acceleration response spectrum, To hold the earthquake in time, The probability of not exceeding the target response spectrum is generally taken as 0.85; ω Represents circular frequency.

[0049] The auto-power spectral density function at a certain point a in the site is:

[0050] ;

[0051] In the formula, Indicate point a The ground motion transfer function is represents the power spectral density function of the free surface earthquake motion on bedrock, brIt is used to represent the relevant characteristics of bedrock. i represents the imaginary unit and is used to process the complex form of ground motion transfer function.

[0052] point a and b The mutual power spectral density function of the ground motion for:

[0053] ;

[0054] In the formula, the superscript * indicates complex conjugation; Indicate point a The ground motion transfer function at point a Changes in time; Indicate point b The complex conjugate of the seismic transfer function at is used to process the phase and amplitude relationship of the seismic signal in the frequency domain; Indicates bedrock point a and b The coherence loss function between them.

[0055] So that you can get the venue n The power spectrum density function matrix of the ground motion at each point :

[0056] .

[0057] (4) Simulating earthquake acceleration time history

[0058] Simulate the ground motion in the frequency domain, use the inverse Fourier transform, and multiply by the shape function to obtain the non-stationary ground motion acceleration time history. In step S3, the ground motion power spectrum density function matrix is ​​decomposed to obtain a complex lower triangular matrix and a Hermitian matrix :

[0059] ;

[0060] You can simulate a point in the frequency domain a Earthquake at:

[0061] ;

[0062] ;

[0063] ;

[0064] In the formula, is the amplitude of simulated earthquake motion, is the phase angle of simulated ground motion, is the frequency interval, For the matrix The frequency corresponding to and location 2. The elements of contain the amplitude and phase information of the earthquake motion, where a represents a specific point in space, m represents the corresponding frequency component; The interval is [0,2 ] is a random variable uniformly distributed in express The imaginary part; denominator express The real part of .

[0065] right Use the inverse Fourier transform to get the time domain interior point a Steady ground acceleration at , multiplied by the intensity envelope function to obtain the final simulation point a Non-stationary ground acceleration time history.

[0066] (5) Seismic response analysis of wind turbine towers

[0067] A finite element model of the wind turbine structure is established in the OpenSees software. The simulated earthquake acceleration time history is used as input to calculate the structural responses of the wind turbine structure such as tower top displacement, tower top acceleration, and tower bottom internal force under earthquake action.

[0068] The earthquake motion (EW direction) simulated by the method of the present invention is as follows: Figure 1 As shown in the figure, the simulated ground motion (NS direction) is as follows Figure 2 As shown in the figure, the simulated ground motion (UD direction) is as follows Figure 3 shown. Figure 4 The displacement of the top of a 1.5MW wind tower under simulated earthquake motion.

Claims

1. A method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind power, characterized in that: The following steps are involved: Step S1: Calculate the dynamic stiffness matrix of the seawater layer and bedrock, and obtain the ground motion transfer function of the bedrock site overlying the seawater layer based on the dynamic balance equation; Step S2: Based on the seismic motion selection standard with the smallest deviation between the average response spectrum and the wind tower design spectrum, a DMF model for the quantile spectrum is established by statistical regression, the standard response spectrum with a damping ratio of 5% in the specification is corrected, and then the seismic motion power spectrum density function is determined according to the corrected seismic motion response spectrum; Step S3: Calculating the spatially varying ground motion power spectrum density matrix based on the transfer function, the power spectrum density function, and the coherence loss function; Step S4: Simulate the ground motion in the frequency domain, use inverse Fourier transform, and multiply by the shape function to obtain the non-stationary ground motion acceleration time history; Decompose the ground motion power spectrum density function matrix obtained in step S3 to obtain a complex lower triangular matrix and a Hermitian matrix : ； You can simulate the point in the frequency domain a Earthquake at: ； ； ； In the formula, is the amplitude of simulated earthquake motion, is the phase angle of simulated ground motion, is the frequency interval, For the matrix The frequency corresponding to and location 2. The elements of contain the amplitude and phase information of the earthquake motion, where a represents a specific point in space, m represents the corresponding frequency component; The interval is [0,2 ] is a random variable uniformly distributed in express The imaginary part; denominator express The real part of right Use the inverse Fourier transform to get the time domain interior point a Steady ground acceleration at , multiplied by the intensity envelope function to obtain the final simulation point a Non-stationary ground acceleration time history at ; Step S5: Using the simulated earthquake motion as the input of wind power seismic resistance, and then conducting seismic response analysis of offshore wind power structures.

2. The method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind power according to claim 1, characterized in that: In step S1: seawater is assumed to be an ideal fluid that cannot withstand shear stress and can only transmit compression waves but not shear waves. The fluid mass conservation equation, Euler equation, and thermodynamic equation are used to express the motion under seismic excitation. The partial differential equations are solved to obtain the displacement and stress expressions of the particles at the top and bottom of the seawater layer. Based on the relationship between displacement and load, the dynamic stiffness matrix and dynamic balance equation are obtained. The combined dynamic stiffness matrix and dynamic balance equation are solved to obtain the seismic transfer function of the bedrock site of the overlying seawater layer.

3. The method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind power according to claim 1, characterized in that: In step S3, the power spectral density function is solved based on the response spectrum obtained in step S2: ； In the formula, is the damping ratio, is the earthquake acceleration response spectrum, To hold the earthquake in time, is the probability of not exceeding the target response spectrum; ω represents the circular frequency; The autopower spectral density function at site point a is: ； In the formula, Indicate point a The ground motion transfer function is represents the power spectral density function of the free surface ground motion of the bedrock; represents an imaginary unit; point a and b The mutual power spectral density function of the ground motion for: ； In the formula, the superscript * indicates complex conjugation; Indicate point a The ground motion transfer function at point a Changes in time; Indicate point b The complex conjugate of the seismic transfer function at is used to process the phase and amplitude relationship of the seismic signal in the frequency domain; represents the coherence loss function between bedrock points a and b; So that you can get the venue n The power spectrum density function matrix of the ground motion at each point : 。 4. The method for simulating sea-area earthquake motion suitable for seismic analysis of offshore wind power according to claim 1, characterized in that: In step S5, a finite element model of the wind turbine structure is established in the OpenSees software, and the simulated earthquake acceleration time history is used as input to calculate the tower top displacement, tower top acceleration, and tower bottom internal force of the wind turbine structure under the action of an earthquake.

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