Method and apparatus for synthesizing spatially cross-correlated multi-point ground motions fitting response spectrum

Abstract

Disclosed in the present invention are a method and apparatus for synthesizing spatially cross-correlated multi-point ground motions fitting a response spectrum. The method comprises: using an influence matrix method to obtain ground motion acceleration time histories fitting a target reaction spectrum with high precision, and calculating a Fourier amplitude spectrum and a phase spectrum thereof; and considering a calculation relationship between a power spectral density function and the Fourier amplitude spectrum, taking the power spectral density function of the obtained time histories as an initial value, using a random vibration theory and Cholesky decomposition to obtain spatially cross-correlated multi-point ground motion time histories, further taking into account a phase spectrum of the ground motion time histories fitting the target reaction spectrum with high precision, and performing correction and iteration to obtain spatially cross-correlated multi-point ground motions fitting a response spectrum. The present invention overcomes the shortcomings in current multi-point ground motion time history synthesis techniques, such as the difficulty in ensuring good fitting to a target response spectrum and the non-stationarity of synthesized ground motions, helping to improve the reliability of dynamic response analysis results for large-scale engineering structures under the action of multi-point ground motions.

Description

A method and apparatus for synthesizing multi-point ground motions based on spatial cross-correlation of fitted response spectra Technical Field

[0001] This invention relates to the field of structural seismic design and analysis technology, and in particular to a method and apparatus for synthesizing multi-point ground motions by fitting response spectra through spatial cross-correlation. Background Technology

[0002] Earthquake ground motion is a spatially variable temporal process involving both spatial and temporal components. Factors contributing to this spatial variation primarily include site effects, coherence effects, traveling wave effects, and attenuation effects. When an earthquake occurs, the energy released from the hypocenter travels to the ground in the form of waves, causing ground vibrations. Seismic waves received at different points on the ground travel along different paths, under different site conditions, and undergo refraction and reflection in different media, resulting in vibrations on the Earth's surface that are not entirely identical, but a certain correlation exists. This correlation is determined by factors such as the hypocenter, propagation path, and site conditions.

[0003] The parameter variations of ground motion from one point to another can be described by the cross-power spectral density of ground motion acceleration; standardizing this density is called the coherence function. The coherence function is commonly used to represent the similarity of ground motions at neighboring points and can be used to analyze the seismic response of multi-braced and long structures. When performing seismic analysis on long structures, ground motion data needs to be input into the model. The first step in seismic analysis is to determine the input method for ground motions, and considering ground motion coherence is fundamental to multi-point ground motion input. Therefore, considering synthetic spatial cross-correlation multi-point ground motion input is a more reasonable input mode for studying the seismic response of long structures.

[0004] Because earthquakes are non-repeatable and unpredictable, the damage they cause is irreversible and the losses are severe. Therefore, engineering projects must be designed to withstand earthquakes according to seismic fortification requirements and seismic design codes. Generally, the synthesized earthquake time histories need to consider coherence effects and frequency domain non-stationarity. A common method in codes is to match the synthesized earthquake response spectrum with the code response spectrum or the site-specific response spectrum. However, earthquake time histories generated using traditional random vibration theory methods cannot guarantee the non-stationarity of the synthesized cross-correlated earthquake frequencies, and current theories and technologies cannot achieve high-precision fitting of the synthesized multi-point earthquake response spectrum to the seismic design response spectrum. Summary of the Invention

[0005] Purpose of the invention: To address the shortcomings of existing technologies, this invention provides a method for synthesizing spatially cross-correlated multi-point ground motions based on fitted response spectra. It is based on the influence matrix method for high-precision fitted response spectra and considers the coherence effect of spatial ground motions, thereby establishing spatially multi-point non-stationary ground motions with fitted response spectra.

[0006] Another object of the present invention is to provide a corresponding spatial cross-correlation multi-point ground motion synthesis device, computer equipment, and computer storage medium for fitting response spectra.

[0007] Technical solution: Firstly, a method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra, comprising the following steps:

[0008] (1) Select the natural ground motion time history A(t) based on the properties of the target response spectrum, and use the influence matrix method to adjust the selected natural ground motion response spectrum to a ground motion time history A that fits the target response spectrum with high accuracy. C (t), and the one-sided Fourier amplitude spectrum F(ω) and phase spectrum of this time history are calculated using Fourier transform.

[0009] (2) Based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the high-precision fitted target response spectrum is calculated. C The energy spectral density function P(ω) of (t) is used as the initial power spectral density function S(ω);

[0010] (3) Based on the power spectral density function S(ω), the coordinates of each seismic wave input point at the site, and the selected coherence function model, the autopower spectrum S at each point is calculated. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point indices;

[0011] (4) Based on the power spectrum matrix S(iω), the cross-correlation Fourier amplitudes and cross-correlation phase angles of different frequency components at different seismic wave input points are obtained by Cholesky decomposition. Using the uniformly distributed random phase, a stable multi-point ground motion time history is synthesized, and the phase spectrum of the ground motion time history of the high-precision fitted target response spectrum obtained in step (1) is included. Synthetic non-stationary multi-point ground motion time history;

[0012] (5) Calculate the relative error between the ground motion time history acceleration response spectrum and the target response spectrum at each input point. If the fitting accuracy does not meet the requirements, correct the input power spectral density function and repeat steps (3) to (5) until the fitting accuracy meets the requirements.

[0013] Furthermore, the selection of natural ground motion time histories based on the properties of the target response spectrum includes:

[0014] Select natural ground motion time histories with site type, source characteristics, and response spectrum shape similar to the target response spectrum.

[0015] Furthermore, based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the high-precision fitted target response spectrum is calculated. C The energy spectral density function P(ω) of (t) is calculated using the following formula:

[0016] Among them, t m =t 5-75 This is the duration of a strong earthquake required to increase the intensity from 5% to 75% of the Arias intensity.

[0017] Furthermore, the self-power spectrum S at each point jj (ω) and the cross-power spectrum S between points jk The formula for calculating (iω) is as follows:

[0018] In the formula, γ nm (iω k ) is the coherence function, |γ nm (iω k | is the hysteresis coherence function, used to describe the coherence effect of ground motion between two points; The phase angle between two ground motions is used to describe the traveling wave effect; d nm V represents the distance projected between two points along the direction of propagation. app This refers to the apparent wave velocity.

[0019] Furthermore, the input power spectral density function is modified using the following formula:

[0020] Where TRS is the target response spectrum and ARS is the ground motion acceleration response spectrum during the iterative calculation.

[0021] Secondly, a spatially cross-correlation multi-point ground motion synthesis device for fitting response spectra is provided, comprising:

[0022] The target response spectrum fitting module is used to select the natural ground motion time history A(t) based on the properties of the target response spectrum, and then use the influence matrix method to adjust the selected natural ground motion response spectrum to a ground motion time history A that fits the target response spectrum with high accuracy. C (t), and the one-sided Fourier amplitude spectrum F(ω) and phase spectrum of this time history are calculated using Fourier transform.

[0023] The power spectral density function calculation module is used to calculate the seismic time history A of the target response spectrum with high accuracy based on the obtained one-sided Fourier amplitude spectrum F(ω). C The energy spectral density function P(ω) of (t) is used as the initial power spectral density function S(ω);

[0024] The power spectrum matrix calculation module is used to calculate the autopower spectrum S at each point based on the power spectral density function S(ω), the coordinates of each seismic wave input point at the site, and the selected coherence function model. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point indices;

[0025] The multi-point ground motion synthesis module is used to obtain the cross-correlation Fourier amplitudes and cross-correlation phase angles of different frequency components at different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. Utilizing uniformly distributed random phases, it synthesizes stable multi-point ground motion time histories and incorporates the phase spectrum of the ground motion time histories obtained from the high-precision fitting of the target response spectrum by the target response spectrum fitting module. Synthetic non-stationary multi-point ground motion time history;

[0026] The iterative control module is used to calculate the relative error between the ground motion time history acceleration response spectrum at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectral density function is corrected, and the operations of the power spectrum matrix calculation module and the multi-point ground motion synthesis module are repeated until the fitting accuracy meets the requirements.

[0027] Furthermore, in the power spectral density function calculation module, based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the high-precision fitted target response spectrum is calculated. C The energy spectral density function P(ω) of (t) is calculated using the following formula:

[0028] Among them, t m =t 5-75 This is the duration of a strong earthquake required to increase the intensity from 5% to 75% of the Arias intensity.

[0029] Furthermore, in the power spectrum matrix calculation module, the self-power spectrum S at each point... jj (ω) and the cross-power spectrum S between points jk The formula for calculating (iω) is as follows:

[0030] In the formula, γ nm (iω k ) is the coherence function, |γ nm (iω k | is the hysteresis coherence function, used to describe the coherence effect of ground motion between two points; The phase angle between two ground motions is used to describe the traveling wave effect; d nm V represents the distance projected between two points along the direction of propagation. app This refers to the apparent wave velocity.

[0031] Thirdly, a computer device is provided, comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra as described in the first aspect of the invention.

[0032] Fourthly, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra as described in the first aspect of the present invention.

[0033] Beneficial Effects: This invention provides a method and apparatus for synthesizing multi-point ground motions based on spatial cross-correlation of a fitted response spectrum. Utilizing the influence matrix method, it can adjust the selected natural ground motion time histories to achieve a high-precision fit to the target response spectrum across the entire frequency range. The energy spectral density function corresponding to the calculated time histories is used as the initial power spectral density function for synthesizing multi-point ground motions. Combined with the phase spectrum of the aforementioned time histories, a spatial multi-point cross-correlation non-stationary ground motion time histories fitting the target response spectrum are synthesized. This invention overcomes the difficulty in ensuring a good fit to the target response spectrum and the non-stationarity of the synthesized ground motions in current multi-point ground motion time history synthesis techniques, thus helping to improve the reliability of dynamic response analysis results for large engineering structures under multi-point ground motion. The iterative process of this invention is monotonic and convergent, meeting specification requirements and demonstrating strong practicality. Attached Figure Description

[0034] Figure 1 is a flowchart of a method for synthesizing multi-point ground motions by spatial cross-correlation of fitted response spectra according to an embodiment of the present invention.

[0035] Figure 2 shows the target response spectrum, the response spectrum of the natural ground motion time history, and the response spectrum of the ground motion time history obtained by using the influence matrix method to obtain a high-precision fit to the target response spectrum in an embodiment of the present invention.

[0036] Figure 3 is the response spectrum of the spatially cross-correlated multi-point ground motion acceleration time history calculated according to an embodiment of the present invention;

[0037] Figure 4 is the time history of spatially cross-correlated multi-point ground motion acceleration calculated according to an embodiment of the present invention. Detailed Implementation

[0038] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0039] In one embodiment, the RG1.60 design spectrum is selected as the target design response spectrum, and the method of the present invention is used to generate the spatially cross-correlated non-stationary multi-point ground motion input time histories that fit the target response spectrum. As shown in Figure 1, a method for synthesizing spatially cross-correlated multi-point ground motions that fit the response spectrum includes the following steps:

[0040] Step (1): Select the RG1.60 design spectrum as the target design response spectrum. The number of frequency points in the target response spectrum RG1.60 design spectrum is M = 301. The frequency points in the frequency range [0.1, 100] Hz are uniformly distributed in logarithmic coordinates.

[0041] Step (2): Select the natural ground motion time history with site type, source characteristics, and response spectrum shape similar to the target response spectrum. Use the influence matrix method to obtain the acceleration time history, velocity time history, and displacement time history of the target response spectrum TRS with high accuracy, and use Fourier transform to calculate the corresponding Fourier amplitude spectrum and phase spectrum of the obtained acceleration time history;

[0042] The specific implementation steps are as follows:

[0043] (2.1) In this embodiment, the acceleration time history of the Mammoth Lake earthquake recorded by the Long Valley station is selected as the original natural ground motion time history. The duration of the time history is T = 30s, and the time interval is dt = 0.005s.

[0044] (2.2) The selected natural ground motion records are adjusted to a ground motion time history that fits the target response spectrum with high precision using the influence matrix method. For specific steps of the influence matrix method, please refer to invention patent ZL201910011113.4 "An Influence Matrix Method for Adjusting Seismic Waves to Match the Target Response Spectrum with Precision" or ZL201910268756.7 "An Improved Influence Matrix Method for Alternating High and Low Frequency Bands to Match the Target Spectrum". This can obtain a natural ground motion time history that fits the target response spectrum with high precision. Figure 2 shows an example of a natural ground motion time history response spectrum and a target response spectrum.

[0045] (2.3) Based on the seismic acceleration time history of the target response spectrum with high precision fitting, the Fourier amplitude spectrum and phase spectrum of the time history are calculated by Fourier transform.

[0046] Step (3), the energy spectral density function P(ω) of the time history is calculated using the following formula:

[0047] Where |F(ω)| is calculated to obtain the one-sided Fourier amplitude spectrum, t m =t 5-75 This is the duration of a strong earthquake required to increase the intensity from 5% to 75% of the Arias intensity.

[0048] The obtained P(ω) is used as the initial power spectral density function S(ω).

[0049] Step (4): Based on the coordinates of each seismic wave input point at the site and the selected coherence function model, calculate the self-power spectrum S at each point. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point numbers.

[0050] The specific implementation steps are as follows:

[0051] (4.1) Select four points uniformly distributed on the horizontal surface of the site, namely P1, P2, P3 and P4, with the x-coordinates of the seismic wave input points being 0m, 80m, 160m and 180m respectively. Only horizontal ground motion is considered for each point.

[0052] (4.2) The Feng & Hu coherence function model is selected as follows:

[0053] Where: ρ1 and ρ2 are regression parameters, and ρ1 is taken as 1.5 * 10 -5 s / m, ρ2=4*10 -3 l / m, d jk Let j be the distance between points j and k.

[0054] (4.3) Calculate the self-power spectrum S at the four points using the following formula. jj (ω) and the cross-power spectrum S between the four points jk (iω), thus forming the power spectrum matrix S(iω), where j=1…4, k=1…4;

[0055] For ease of description, the subscript mn represents jj or jk. The power spectrum calculation formula is as follows:

[0056] Wherein: γ nm (iω k ) is the coherence function, |γ nm (iω k | is the hysteresis coherence function, used to describe the coherence effect of ground motion between two points; The phase angle between two ground motions is used to describe the traveling wave effect; d nm V represents the distance projected between two points along the direction of propagation. app This refers to the apparent wave velocity.

[0057] Step (5): Based on the power spectrum matrix S(iω), Cholesky decomposition is used to obtain the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components at different seismic wave input points. Using uniformly distributed random phases, a stationary multi-point ground motion time history is synthesized. Including the acceleration time history phase spectrum of the high-precision fitted target response spectrum obtained in step (2), a non-stationary multi-point ground motion time history is obtained. Figure 3 shows the response spectrum of the spatially cross-correlation multi-point ground motion acceleration time history calculated in the embodiment of the present invention, with a total of four points; Figure 4 shows the spatially cross-correlation multi-point ground motion acceleration time history calculated in the embodiment of the present invention.

[0058] Step (6): Calculate the relative error between the ground motion acceleration response spectrum (ARS) and the target response spectrum (TRS) obtained in step (5) at each input point. If the fitting accuracy does not meet the requirements, the input power spectral density function S(ω) is corrected using the following formula:

[0059] In this embodiment of the invention, the ARS is the average value of four horizontal ground motion response spectra; and steps (4) to (6) are repeated until the fitting accuracy meets the requirements.

[0060] Based on the same technical concept as the above-described method embodiments, in another embodiment, a spatially cross-correlated multi-point ground motion synthesis device for fitting response spectra is provided, comprising:

[0061] The target response spectrum fitting module is used to select the natural ground motion time history A(t) based on the properties of the target response spectrum, and then use the influence matrix method to adjust the selected natural ground motion response spectrum to a ground motion time history A that fits the target response spectrum with high accuracy. C (t), and the one-sided Fourier amplitude spectrum F(ω) and phase spectrum of this time history are calculated using Fourier transform.

[0062] The power spectral density function calculation module is used to calculate the seismic time history A of the target response spectrum with high accuracy based on the obtained one-sided Fourier amplitude spectrum F(ω). C The energy spectral density function P(ω) of (t) is used as the initial power spectral density function S(ω);

[0063] The power spectrum matrix calculation module is used to calculate the autopower spectrum S at each point based on the power spectral density function S(ω), the coordinates of each seismic wave input point at the site, and the selected coherence function model. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point indices;

[0064] The multi-point ground motion synthesis module is used to obtain the cross-correlation Fourier amplitudes and cross-correlation phase angles of different frequency components at different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. Utilizing uniformly distributed random phases, it synthesizes stable multi-point ground motion time histories and incorporates the phase spectrum of the ground motion time histories obtained from the high-precision fitting of the target response spectrum by the target response spectrum fitting module. Synthetic non-stationary multi-point ground motion time history;

[0065] The iterative control module is used to calculate the relative error between the ground motion time history acceleration response spectrum at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectral density function is corrected, and the operations of the power spectrum matrix calculation module and the multi-point ground motion synthesis module are repeated until the fitting accuracy meets the requirements.

[0066] It should be understood that the spatial cross-correlation multi-point ground motion synthesis device for fitting response spectra in the embodiments of the present invention can realize all the technical solutions in the above method embodiments. The functions of each functional module can be specifically implemented according to the methods in the above method embodiments. The specific implementation process can be referred to the relevant descriptions in the above embodiments, which will not be repeated here.

[0067] The present invention also provides a computer device comprising: one or more processors; a memory; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra as described above.

[0068] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra as described above.

[0069] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus (systems), computer devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0070] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations of steps in the flowchart can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in one or more steps of the flowchart.

[0071] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more processes of a flowchart.

[0072] These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more processes in the flowchart.

Claims

1. A method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra, characterized in that, Includes the following steps: (1) Select the natural ground motion time history A(t) based on the properties of the target response spectrum, and use the influence matrix method to adjust the selected natural ground motion response spectrum to a ground motion time history A that fits the target response spectrum with high accuracy. C (t), and the one-sided Fourier amplitude spectrum F(ω) and phase spectrum of this time history are calculated using Fourier transform. (2) Based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the high-precision fitted target response spectrum is calculated. C The energy spectral density function P(ω) of (t) is used as the initial power spectral density function S(ω); (3) Based on the power spectral density function S(ω), the coordinates of each seismic wave input point at the site, and the selected coherence function model, the autopower spectrum S at each point is calculated. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point indices; (4) Based on the power spectrum matrix S(iω), the cross-correlation Fourier amplitudes and cross-correlation phase angles of different frequency components at different seismic wave input points are obtained by Cholesky decomposition. Using the uniformly distributed random phase, a stable multi-point ground motion time history is synthesized, and the phase spectrum of the ground motion time history of the high-precision fitted target response spectrum obtained in step (1) is included. Synthetic non-stationary multi-point ground motion time history; (5) Calculate the relative error between the ground motion time history acceleration response spectrum and the target response spectrum at each input point. If the fitting accuracy does not meet the requirements, correct the input power spectral density function and repeat steps (3) to (5) until the fitting accuracy meets the requirements.

2. The method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra according to claim 1, characterized in that, The selection of natural ground motion time histories based on the properties of the target response spectrum includes: Select natural ground motion time histories with site type, source characteristics, and response spectrum shape similar to the target response spectrum.

3. The method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra according to claim 1, characterized in that, Based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the high-precision fitted target response spectrum is calculated. C The energy spectral density function P(ω) of (t) is calculated using the following formula: Among them, t m =t 5-75 This is the duration of a strong earthquake required to increase the intensity from 5% to 75% of the Arias intensity.

4. The method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra according to claim 1, characterized in that, Self-power spectrum at each point S jj (ω) and the cross-power spectrum S between points jk The formula for calculating (iω) is as follows: In the formula, γ nm (iω k ) is the coherence function, |γ nm (iω k | is the hysteresis coherence function, used to describe the coherence effect of ground motion between two points; The phase angle between two ground motions is used to describe the traveling wave effect; d nm V represents the distance projected between two points along the direction of propagation. app This refers to the apparent wave velocity.

5. The method for synthesizing multi-point ground motion data based on spatial cross-correlation of fitted response spectra according to claim 1, characterized in that, The input power spectral density function is corrected using the following formula: Where TRS is the target response spectrum and ARS is the ground motion acceleration response spectrum during the iterative calculation.

6. A spatially cross-correlation multi-point ground motion synthesis device for fitting response spectra, characterized in that, include: The target response spectrum fitting module is used to select the natural ground motion time history A(t) based on the properties of the target response spectrum, and then use the influence matrix method to adjust the selected natural ground motion response spectrum to a ground motion time history A that fits the target response spectrum with high accuracy. C (t), and the one-sided Fourier amplitude spectrum F(ω) and phase spectrum of this time history are calculated using Fourier transform. The power spectral density function calculation module is used to calculate the seismic time history A of the target response spectrum with high accuracy based on the obtained one-sided Fourier amplitude spectrum F(ω). C The energy spectral density function P(ω) of (t) is used as the initial power spectral density function S(ω); The power spectrum matrix calculation module is used to calculate the autopower spectrum S at each point based on the power spectral density function S(ω), the coordinates of each seismic wave input point at the site, and the selected coherence function model. jj (ω) and the cross-power spectrum S between points jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, and j and k are the seismic wave input point indices; The multi-point ground motion synthesis module is used to obtain the cross-correlation Fourier amplitudes and cross-correlation phase angles of different frequency components at different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. Utilizing uniformly distributed random phases, it synthesizes stable multi-point ground motion time histories and incorporates the phase spectrum of the ground motion time histories obtained from the high-precision fitting of the target response spectrum by the target response spectrum fitting module. Synthetic non-stationary multi-point ground motion time history; The iterative control module is used to calculate the relative error between the ground motion time history acceleration response spectrum at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectral density function is corrected, and the operations of the power spectrum matrix calculation module and the multi-point ground motion synthesis module are repeated until the fitting accuracy meets the requirements.

7. The spatial cross-correlation multi-point ground motion synthesis device for fitting response spectra according to claim 6, characterized in that, In the power spectral density function calculation module, based on the obtained one-sided Fourier amplitude spectrum F(ω), the seismic time history A of the target response spectrum with high precision is calculated. C The energy spectral density function P(ω) of (t) is calculated using the following formula: Among them, t m =t 5-75 This is the duration of a strong earthquake required to increase the intensity from 5% to 75% of the Arias intensity.

8. The spatial cross-correlation multi-point ground motion synthesis device for fitting response spectra according to claim 6, characterized in that, In the power spectrum matrix calculation module, the self-power spectrum S at each point jj (ω) and the cross-power spectrum S between points jk The formula for calculating (iω) is as follows: In the formula, γ nm (iω k ) is the coherence function, |γ nm (iω k | is the hysteresis coherence function, used to describe the coherence effect of ground motion between two points; The phase angle between two ground motions is used to describe the traveling wave effect; d nm V represents the distance projected between two points along the direction of propagation. app This refers to the apparent wave velocity.

9. A computer device, characterized in that, include: One or more processors; Memory; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra as described in any one of claims 1 to 5.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the spatial cross-correlation multi-point ground motion synthesis method for the fitted response spectrum as described in any one of claims 1 to 5.

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