Method and device for synthesizing multi-point earthquake motion based on spatial cross-correlation of fitted response spectrum

Abstract

The present invention discloses a method and device for synthesizing spatially cross-correlated multi-point seismic motions for fitting a response spectrum. The method comprises: utilizing an influence matrix method to obtain a seismic acceleration time history that fits a target response spectrum with high precision, and calculating its Fourier amplitude spectrum and phase spectrum; considering the computational relationship between the power spectrum density function and the Fourier amplitude spectrum, using the power spectrum density function of the obtained time history as an initial value, utilizing random vibration theory and Cholesky decomposition to obtain a spatially cross-correlated multi-point seismic motion time history, further incorporating the phase spectrum of the seismic motion time history that fits the target response spectrum with high precision, and obtaining a spatially cross-correlated multi-point seismic motion for fitting a response spectrum through correction iteration. The present invention overcomes the shortcomings of current multi-point seismic motion time history synthesis technology, which is difficult to ensure the fitting effect with the target response spectrum and the non-stationarity of the synthesized seismic motion, and helps to improve the reliability of the dynamic response analysis results of large-scale engineering structures under the action of multi-point seismic motions.

Description

Technical Field

[0001] The present invention relates to the technical field of structural seismic design and analysis, and in particular to a method and device for synthesizing spatially cross-correlated multi-point earthquake motions using a fitted response spectrum. Background Art

[0002] Ground motion is a temporal process with spatial variations, involving both spatial and temporal components. Factors contributing to the spatial variation of ground motion primarily include site effects, coherence effects, traveling wave effects, and attenuation effects. During an earthquake, energy released from the earthquake source propagates to the ground in the form of waves, causing ground vibrations. Seismic waves received at different points on the ground travel through different paths, site conditions, and media, undergoing refraction and reflection. While the vibrations reflected on the surface are inevitably not identical, they do exhibit certain correlations. This correlation is determined by factors such as the earthquake source, propagation path, and site conditions.

[0003] The parametric changes of ground motion from one point to another can be described by the cross-power spectral density of the ground motion acceleration, and its normalization is called the coherence function. The coherence function is often used to represent the similarity of seismic motions at adjacent sites and can be used to analyze the seismic response of multi-support structures and long structures. When performing seismic analysis on long structures, seismic motion data needs to be input into the model. The first step in seismic analysis is to determine the input method of seismic motion, and considering seismic motion coherence is the basis for multi-point seismic motion input. Therefore, considering the synthetic spatial cross-correlation of multi-point seismic motion input is a more reasonable input mode for studying the seismic response of long structures.

[0004] Because seismic motion is non-repeatable and unpredictable, the damage it causes is both irreversible and extremely severe. Therefore, projects must be seismically designed in accordance with seismic fortification requirements and seismic design standards. Generally, the seismic motion time histories synthesized according to these requirements must consider their coherence effects and frequency domain nonstationarity. The method commonly used in the standards is to match the synthesized seismic motion response spectrum with the standard response spectrum or the site-specific response spectrum. However, seismic motion time histories generated using traditional random vibration theory cannot guarantee the nonstationarity of the synthesized cross-correlated seismic motion frequencies, and existing theories and technologies cannot meet the requirements for high-precision fitting of the synthesized multi-point seismic design response spectrum. Summary of the Invention

[0005] Purpose of the invention: In view of the shortcomings of the existing technology, the present invention provides a method for synthesizing spatial cross-correlated multi-point seismic motions for fitting response spectra. Based on the influence matrix method for high-precision fitting response spectra, the coherence effect of spatial seismic motions is taken into account, thereby establishing a spatial multi-point non-stationary seismic motion for fitting response spectra.

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

[0007] Technical solution: In the first aspect, a method for synthesizing spatially cross-correlated multi-point earthquake motions by fitting response spectra includes the following steps:

[0008] (1) Based on the properties of the target response spectrum, the natural earthquake time history A(t) is selected and the influence matrix method is used to adjust the selected natural earthquake response spectrum to a earthquake time history A(t) that fits the target response spectrum with high precision. C (t), and use Fourier transform to calculate the unilateral Fourier amplitude spectrum F(ω) and phase spectrum of the time course

[0009] (2) Based on the obtained unilateral Fourier amplitude spectrum F(ω), the earthquake time history A that fits the target response spectrum with high precision is calculated. C (t) energy spectral density function P(ω), and use P(ω) as the initial power spectral density function S(ω);

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

[0011] (4) Based on the power spectrum matrix S(iω), the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components of different seismic wave input points are obtained by Cholesky decomposition. The uniformly distributed random phase is used to synthesize a stable multi-point earthquake motion time history, which is included in the phase spectrum of the earthquake motion time history that fits the target response spectrum with high precision obtained in step (1). Synthesize non-stationary multi-point ground motion time history;

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

[0013] Furthermore, the natural ground motion time history is selected based on the properties of the target response spectrum, including:

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

[0015] Furthermore, based on the obtained unilateral Fourier amplitude spectrum F(ω), the earthquake time history A that fits the target response spectrum with high precision is calculated. C The energy spectral density function P(ω) of (t) is calculated as follows:

[0016]

[0017] Among them, t m =t 5-75 It is the duration of a strong earthquake required to increase from 5% to 75% of the Arias intensity.

[0018] Furthermore, the power spectrum S of each point jj (ω) and the cross power spectrum S between each point jk The calculation formula of (iω) is as follows:

[0019]

[0020] Where, γ nm (iω k ) is the coherence function, |γ nm (iω k )| is the hysteresis coherence function, which is used to describe the coherence effect of ground motion between two points; Represents the phase angle between the ground motions at two points, used to describe the traveling wave effect; d nm Represents the distance between two points projected along the propagation direction, V app is the apparent wave velocity.

[0021] Furthermore, the corrected input power spectrum density function uses the following formula:

[0022]

[0023] Among them, TRS is the target response spectrum, and ARS is the earthquake acceleration response spectrum in the iterative calculation process.

[0024] In a second aspect, a spatial cross-correlation multi-point seismic motion synthesis device for fitting a response spectrum is provided, comprising:

[0025] The target response spectrum fitting module is used to select the natural earthquake time history A(t) based on the properties of the target response spectrum, and adjust the selected natural earthquake response spectrum to the earthquake time history A(t) that fits the target response spectrum with high precision using the influence matrix method. C (t), and use Fourier transform to calculate the unilateral Fourier amplitude spectrum F(ω) and phase spectrum of the time course

[0026] The power spectrum density function calculation module is used to calculate the earthquake time history A of the target response spectrum with high precision based on the obtained unilateral Fourier amplitude spectrum F(ω). C(t) energy spectral density function P(ω), and use P(ω) as the initial power spectral density function S(ω);

[0027] The power spectrum matrix calculation module is used to calculate the power spectrum S of each point based on the power spectrum density function S(ω), the coordinates of each seismic wave input point on the site and the selected coherence function model. jj (ω) and the cross power spectrum S between each point jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, j and k are the serial numbers of the seismic wave input points;

[0028] The multi-point seismic motion synthesis module is used to obtain the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components of different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. It uses uniformly distributed random phases to synthesize a stable multi-point seismic motion time history and takes into account the phase spectrum of the seismic motion time history that fits the target response spectrum with high precision obtained by the target response spectrum fitting module. Synthesize non-stationary multi-point ground motion time history;

[0029] The iterative control module is used to calculate the relative error between the acceleration response spectrum of the earthquake time history at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectrum density function is corrected and the operations of the power spectrum matrix calculation module and the multi-point earthquake motion synthesis module are repeated until the fitting accuracy meets the requirements.

[0030] Furthermore, in the power spectrum density function calculation module, based on the obtained unilateral Fourier amplitude spectrum F(ω), the earthquake time history A that fits the target response spectrum with high precision is calculated. C The energy spectral density function P(ω) of (t) is calculated as follows:

[0031]

[0032] Among them, t m =t 5-75 It is the duration of a strong earthquake required to increase from 5% to 75% of the Arias intensity.

[0033] Furthermore, in the power spectrum matrix calculation module, the power spectrum S of each point jj (ω) and the cross power spectrum S between each point jk The calculation formula of (iω) is as follows:

[0034]

[0035] Where, γ nm (iω k ) is the coherence function, |γ nm (iω k)| is the hysteresis coherence function, which is used to describe the coherence effect of ground motion between two points; Represents the phase angle between the ground motions at two points, used to describe the traveling wave effect; d nm Represents the distance between two points projected along the propagation direction, V app is the apparent wave velocity.

[0036] In a third aspect, 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the spatial cross-correlation multi-point seismic motion synthesis method for fitting the response spectrum as described in the first aspect of the present invention are implemented.

[0037] In a fourth aspect, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the steps of the spatial cross-correlation multi-point seismic motion synthesis method of fitting the response spectrum as described in the first aspect of the present invention are implemented.

[0038] Beneficial effects: The present invention provides a method and device for synthesizing spatially cross-correlated multi-point seismic motions based on a fitting response spectrum. The influence matrix method is used to adjust the selected natural seismic motion time history so that its response spectrum can fit the target response spectrum with high precision within the full frequency range. The energy spectrum density function corresponding to the obtained time history is calculated and used as the initial power spectrum density function for synthesizing multi-point seismic motions. Combined with the phase spectrum of the aforementioned time history, the spatially cross-correlated non-stationary seismic motion time history that fits the target response spectrum is synthesized. The present invention overcomes the difficulties in current multi-point seismic motion time history synthesis technology in ensuring the fitting effect with the target response spectrum and the non-stationarity of the synthesized seismic motion, and helps to improve the reliability of the dynamic response analysis results of large-scale engineering structures under the action of multi-point seismic motions. The iterative process of the present invention is monotonic and convergent, meets the requirements of the specification, and is highly practical. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is an overall flow chart of a method for synthesizing spatially cross-correlated multi-point earthquake motions based on a fitting response spectrum according to an embodiment of the present invention.

[0040] Figure 2 The target response spectrum of the embodiment of the present invention, the response spectrum of the natural earthquake time history, and the response spectrum of the earthquake time history obtained by using the influence matrix method to fit the target response spectrum with high precision;

[0041] Figure 3 is the response spectrum of the spatially cross-correlated multi-point earthquake acceleration time history calculated by an embodiment of the present invention;

[0042] Figure 4 It is the spatially cross-correlated multi-point earthquake acceleration time history calculated by the embodiment of the present invention. DETAILED DESCRIPTION

[0043] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0044] 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 a non-stationary multi-point earthquake input time history with spatial cross-correlation that fits the target response spectrum. Figure 1 As shown in FIG, a spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra includes the following steps:

[0045] Step (1): select the RG1.60 design spectrum as the target design response spectrum. The number of frequency points of the target response spectrum RG1.60 design spectrum is M = 301, and each frequency point in the frequency range [0.1, 100] Hz is evenly distributed on a logarithmic coordinate.

[0046] Step (2) selects a natural earthquake time history with a site type, source characteristics, and response spectrum shape similar to the target response spectrum. The influence matrix method is used to obtain the acceleration time history, velocity time history, and displacement time history that fit the target response spectrum TRS with high precision, and the Fourier transform is used to calculate the Fourier amplitude spectrum and phase spectrum corresponding to the obtained acceleration time history.

[0047] The specific implementation steps are as follows:

[0048] (2.1) In this example, the acceleration time history of the Mammoth Lake earthquake recorded at the Long Valley station is selected as the original natural ground motion time history. The time history duration is T = 30 s, and the time interval is dt = 0.005 s.

[0049] (2.2) Using the influence matrix method, the selected natural ground motion records are adjusted to ground motion time histories that accurately fit the target response spectrum. For the specific steps of the influence matrix method, please refer to invention patents ZL201910011113.4, "An influence matrix method for adjusting seismic waves to accurately match target response spectra," or ZL201910268756.7, "An improved influence matrix method for alternating high and low frequency bands to match target spectra." This method can obtain natural ground motion time histories that accurately fit the target response spectrum. Figure 2 Shown are examples of natural ground motion time history response spectra and target response spectra;

[0050] (2.3) Based on the high-precision fitting of the earthquake acceleration time history of the target response spectrum, the Fourier transform is used to calculate the corresponding Fourier amplitude spectrum and phase spectrum of the time history.

[0051] Step (3): Calculate the energy spectrum density function P(ω) of the time course using the following formula:

[0052]

[0053] Among them, |F(ω)| calculates the one-sided Fourier amplitude spectrum, t m =t 5-75 It is the duration of a strong earthquake required to increase from 5% to 75% of the Arias intensity.

[0054] The obtained P(ω) is used as the initial power spectral density function S(ω).

[0055] Step (4): Based on the coordinates of each seismic wave input point in the site and the selected coherence function model, the autopower spectrum S of each point is calculated. jj (ω) and the cross power spectrum S between each point jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, j and k are the serial numbers of the seismic wave input points.

[0056] The specific implementation steps are as follows:

[0057] (4.1) Select four points evenly distributed on the horizontal surface of the site, namely P1, P2, P3, and P4, with the x-coordinates of the seismic input points being 0 m, 80 m, 160 m, and 180 m, respectively. For each point, only horizontal seismic motion is considered.

[0058] (4.2) Select the Feng&Hu coherence function model as shown below:

[0059]

[0060] Among them: ρ1, ρ2 are regression parameters, take ρ1=1.5*10 -5 s / m,ρ2=4*10 -3 l / m,d jk is the distance between the jth point and the kth point;

[0061] (4.3) Use the following formula to calculate the four points' autopower spectrum S 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;

[0062] For the convenience of description, the subscript mn represents jj or jk, and the power spectrum calculation formula is as follows:

[0063]

[0064] Where: γ nm (iω k ) is the coherence function, |γ nm (iω k)| is the hysteresis coherence function, which is used to describe the coherence effect of ground motion between two points; Represents the phase angle between the ground motions at two points, used to describe the traveling wave effect; d nm Represents the distance between two points projected along the propagation direction, V app is the apparent wave velocity.

[0065] In step (5), based on the power spectrum matrix S(iω), the 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. The uniformly distributed random phase is used to synthesize the stationary multi-point earthquake motion time history. The acceleration time history phase spectrum of the high-precision fitting target response spectrum obtained in step (2) is taken into account to obtain the non-stationary multi-point earthquake motion time history. Figure 3 The response spectrum of the spatially cross-correlated multi-point earthquake acceleration time history calculated by the embodiment of the present invention, with a total of four points; Figure 4 It is the spatially cross-correlated multi-point earthquake acceleration time history calculated by the embodiment of the present invention.

[0066] Step (6) calculates the relative error between the response spectrum ARS of the earthquake acceleration at each input point obtained in step (5) and the target response spectrum TRS. If the fitting accuracy does not meet the requirements, the input power spectrum density function S(ω) is corrected using the following formula:

[0067]

[0068] In the embodiment of the present invention, the ARS takes the average value of the four horizontal earthquake response spectra; and repeats steps (4) to (6) until the fitting accuracy meets the requirements.

[0069] Based on the same technical concept as the above method embodiment, in another embodiment, a spatial cross-correlation multi-point ground motion synthesis device for fitting response spectra is provided, comprising:

[0070] The target response spectrum fitting module is used to select the natural earthquake time history A(t) based on the properties of the target response spectrum, and adjust the selected natural earthquake response spectrum to the earthquake time history A(t) that fits the target response spectrum with high precision using the influence matrix method. C (t), and use Fourier transform to calculate the unilateral Fourier amplitude spectrum F(ω) and phase spectrum of the time course

[0071] The power spectrum density function calculation module is used to calculate the earthquake time history A of the target response spectrum with high precision based on the obtained unilateral Fourier amplitude spectrum F(ω). C (t) energy spectral density function P(ω), and use P(ω) as the initial power spectral density function S(ω);

[0072] The power spectrum matrix calculation module is used to calculate the power spectrum S of each point based on the power spectrum density function S(ω), the coordinates of each seismic wave input point on the site and the selected coherence function model. jj (ω) and the cross power spectrum S between each point jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, j and k are the serial numbers of the seismic wave input points;

[0073] The multi-point seismic motion synthesis module is used to obtain the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components of different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. It uses uniformly distributed random phases to synthesize a stable multi-point seismic motion time history and takes into account the phase spectrum of the seismic motion time history that fits the target response spectrum with high precision obtained by the target response spectrum fitting module. Synthesize non-stationary multi-point ground motion time history;

[0074] The iterative control module is used to calculate the relative error between the acceleration response spectrum of the earthquake time history at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectrum density function is corrected and the operations of the power spectrum matrix calculation module and the multi-point earthquake motion synthesis module are repeated until the fitting accuracy meets the requirements.

[0075] It should be understood that the spatial cross-correlation multi-point seismic motion synthesis device for fitting response spectra in the embodiment of the present invention can implement all the technical solutions in the above-mentioned method embodiment, and the functions of its various functional modules can be specifically implemented according to the methods in the above-mentioned method embodiment. The specific implementation process can refer to the relevant description in the above-mentioned embodiment, which will not be repeated here.

[0076] 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the spatial cross-correlation multi-point seismic motion synthesis method of fitting the response spectrum as described above are implemented.

[0077] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the spatial cross-correlation multi-point seismic motion synthesis method of fitting response spectra as described above.

[0078] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, apparatus (systems), computer devices, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0079] The present invention is described with reference to flowcharts of methods according to embodiments of the present invention. It should be understood that each process in the flowcharts and combinations of processes in the flowcharts can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts. Figure 1 A device that specifies functions in a process or multiple processes.

[0080] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A function specified in a process or multiple processes.

[0081] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 The steps of a specified function in a process or multiple processes.

Claims

1. A spatial cross-correlation multi-point earthquake motion synthesis method for fitting response spectra, characterized in that: The steps include: (1) Based on the properties of the target response spectrum, the natural earthquake time history A(t) is selected and the influence matrix method is used to adjust the selected natural earthquake response spectrum to a earthquake time history A(t) that fits the target response spectrum with high precision. C (t), and use Fourier transform to calculate the unilateral Fourier amplitude spectrum F(ω) and phase spectrum of the time course (2) Based on the obtained unilateral Fourier amplitude spectrum F(ω), the earthquake time history A that fits the target response spectrum with high precision is calculated. C (t) energy spectral density function P(ω), and use P(ω) as the initial power spectral density function S(ω); (3) Based on the power spectrum density function S(ω), the coordinates of each seismic wave input point on the site and the selected coherence function model, the auto-power spectrum S of each point is calculated respectively. jj (ω) and the cross power spectrum S between each point jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, j and k are the serial numbers of the seismic wave input points; (4) Based on the power spectrum matrix S(iω), the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components of different seismic wave input points are obtained by Cholesky decomposition. The uniformly distributed random phase is used to synthesize a stable multi-point earthquake motion time history, which is included in the phase spectrum of the earthquake motion time history that fits the target response spectrum with high precision obtained in step (1). Synthesize non-stationary multi-point ground motion time history; (5) Calculate the relative error between the acceleration response spectrum of the earthquake time history at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, correct the input power spectrum density function and repeat steps (3) to (5) until the fitting accuracy meets the requirements.

2. The spatial cross-correlation multi-point earthquake motion synthesis method of the fitted response spectrum according to claim 1 is characterized in that: The natural ground motion time history selected based on the properties of the target response spectrum includes: Select natural ground motion time histories whose site type, source characteristics, and response spectrum shape are similar to the target response spectrum.

3. The spatial cross-correlation multi-point earthquake motion synthesis method of the fitted response spectrum according to claim 1 is characterized in that: Based on the obtained unilateral Fourier amplitude spectrum F(ω), the earthquake time history A that fits the target response spectrum with high precision is calculated. C The energy spectral density function P(ω) of (t) is calculated as follows: Among them, t m =t 5-75 It is the duration of a strong earthquake required to increase from 5% to 75% of the Arias intensity.

4. The spatial cross-correlation multi-point earthquake motion synthesis method of the fitted response spectrum according to claim 1 is characterized in that: Autopower spectrum S of each point jj (ω) and the cross power spectrum S between each point jk The calculation formula of (iω) is as follows: Where, γ nm (iω k ) is the coherence function, |γ nm (iω k )| is the hysteresis coherence function, which is used to describe the coherence effect of ground motion between two points; Represents the phase angle between the ground motions at two points, used to describe the traveling wave effect; d nm Represents the distance between two points projected along the propagation direction, V app is the apparent wave velocity.

5. The spatial cross-correlation multi-point earthquake motion synthesis method of fitting response spectrum according to claim 1 is characterized in that: The corrected input power spectral density function uses the following formula: Among them, TRS is the target response spectrum, and ARS is the earthquake acceleration response spectrum in the iterative calculation process.

6. A spatial cross-correlation multi-point earthquake motion synthesis device for fitting response spectrum, characterized in that: include: The target response spectrum fitting module is used to select the natural earthquake time history A(t) based on the properties of the target response spectrum, and adjust the selected natural earthquake response spectrum to the earthquake time history A(t) that fits the target response spectrum with high precision using the influence matrix method. C (t), and use Fourier transform to calculate the unilateral Fourier amplitude spectrum F(ω) and phase spectrum of the time course The power spectrum density function calculation module is used to calculate the earthquake time history A of the target response spectrum with high precision based on the obtained unilateral Fourier amplitude spectrum F(ω). C (t) energy spectral density function P(ω), and use P(ω) as the initial power spectral density function S(ω); The power spectrum matrix calculation module is used to calculate the power spectrum S of each point based on the power spectrum density function S(ω), the coordinates of each seismic wave input point on the site and the selected coherence function model. jj (ω) and the cross power spectrum S between each point jk (iω), thus forming the power spectrum matrix S(iω), where i is the imaginary unit, j and k are the serial numbers of the seismic wave input points; The multi-point seismic motion synthesis module is used to obtain the cross-correlation Fourier amplitude and cross-correlation phase angle of different frequency components of different seismic wave input points based on the power spectrum matrix S(iω) through Cholesky decomposition. It uses uniformly distributed random phases to synthesize a stable multi-point seismic motion time history and takes into account the phase spectrum of the seismic motion time history that fits the target response spectrum with high precision obtained by the target response spectrum fitting module. Synthesize non-stationary multi-point ground motion time history; The iterative control module is used to calculate the relative error between the acceleration response spectrum of the earthquake time history at each input point and the target response spectrum. If the fitting accuracy does not meet the requirements, the input power spectrum density function is corrected and the operations of the power spectrum matrix calculation module and the multi-point earthquake motion synthesis module are repeated until the fitting accuracy meets the requirements.

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

8. The spatial cross-correlation multi-point earthquake motion synthesis device for fitting response spectrum according to claim 6, characterized in that: In the power spectrum matrix calculation module, the power spectrum S of each point jj (ω) and the cross power spectrum S between each point jk The calculation formula of (iω) is as follows: Where, γ nm (iω k ) is the coherence function, |γ nm (iω k )| is the hysteresis coherence function, which is used to describe the coherence effect of ground motion between two points; Represents the phase angle between the ground motions at two points, used to describe the traveling wave effect; d nm Represents the distance between two points projected along the propagation direction, V app is 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 are configured to be executed by the one or more processors, and when the programs are executed by the processors, the steps of the spatial cross-correlation multi-point seismic motion synthesis method for fitting the response spectrum as described in any one of claims 1 to 5 are implemented.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the spatial cross-correlation multi-point ground motion synthesis method for fitting response spectra according to any one of claims 1 to 5 are implemented.

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