Method, system and terminal for generating spatially varying multi-point ground motion based on response spectrum matching based on S transform

Abstract

The present invention discloses a method, system and terminal for generating multi-point earthquake motions based on response spectrum matching of S transform, the method comprising: using a single-point response spectrum matching earthquake motion algorithm to obtain the first intermediate earthquake motion after the seed earthquake motion response spectrum of each station is matched; combining the time-frequency power spectrum density of the first intermediate earthquake motion and the spatial coherence between the two stations, using a spectrum representation method to simulate and obtain the coherent earthquake motion of each station; using a single-point response spectrum matching earthquake motion algorithm to obtain the second intermediate earthquake motion after the coherent earthquake motion response spectrum of each station is matched; performing S transform on the coherent earthquake motion and the second intermediate earthquake motion to obtain the S transform coefficient, using the further calculated synchronous phase shuffling factor to perform phase update on the S transform coefficient of the second intermediate earthquake motion; obtaining the target earthquake motion of each station according to the S transform coefficient after the phase update. The present invention realizes the generation of multi-point response spectrum matching earthquake motions with high precision and maintaining earthquake motion coherence.

Description

Technical Field

[0001] The present invention relates to the technical field of earthquake-resistant design, and in particular to a method, system, terminal and computer-readable storage medium for generating spatially varying multi-point earthquake motions based on response spectrum matching based on S-transformation. Background Art

[0002] Matching the response spectrum according to the standard response spectrum (target response spectrum) in the seismic design code to obtain the seismic motion that fits the standard response spectrum within a certain accuracy is a hot research issue in the field of seismic design. The existing response spectrum matching technology can be mainly divided into two parts: frequency domain technology and time domain technology. The disadvantage of frequency domain technology is that it is easy to destroy the non-stationary characteristics of seed seismic motion. Compared with frequency domain technology, the disadvantage of time domain technology is that the calculation efficiency is lower and it takes longer.

[0003] When designing a large-span structure with multiple supports, such as a large-span bridge or dam, it is difficult to find earthquake records that meet the design site conditions from the real earthquake database. This is because the site conditions where the real earthquake records occur are often quite different from the actual design site conditions of the building, and the earthquake itself has spatial variation characteristics and coherence, which is particularly important for the time-history analysis of structures. However, historical real earthquake records are difficult to match the site distribution conditions of large-span structures. Therefore, it is necessary to develop an algorithm that can simulate or generate multi-point response spectrum matching earthquake motion. In the prior art, most of the research on the response spectrum matching multi-point earthquake motion method uses spectral representation to simulate multi-point earthquake motion, and the simulated earthquake motion response spectrum is not accurate enough relative to the target response spectrum. Summary of the invention

[0004] The main purpose of the present invention is to provide a method, system, terminal and computer-readable storage medium for generating spatially varying multi-point seismic motions based on response spectrum matching based on S transform, aiming to solve the problem that the spectral representation method is used to simulate multi-point seismic motions in the prior art, and the matching accuracy of the simulated seismic motion response spectrum relative to the target response spectrum is insufficient.

[0005] To achieve the above-mentioned object of the invention, the present invention provides a method for generating multi-point earthquake motions by matching spatial variations of response spectrum based on S transform, and the method for generating multi-point earthquake motions by matching spatial variations of response spectrum based on S transform comprises:

[0006] According to the obtained seed seismic motion and the target response spectrum of each site, a single-point response spectrum matching seismic motion algorithm is used to obtain the first intermediate seismic motion after the seed seismic motion of each site is matched with the response spectrum;

[0007] Calculating the time-frequency power spectrum density of the first intermediate seismic motion at each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate and obtain the coherent seismic motion of each station;

[0008] According to the coherent seismic motions of each site and the target response spectrum, a single-point response spectrum matching seismic motion algorithm is used to obtain the second intermediate seismic motion after the coherent seismic motions of each site are matched with the response spectrum;

[0009] Performing S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculating the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station;

[0010] The S transform coefficient of the second intermediate seismic motion of each station is phase updated by using the synchronous phase shuffling factor of each station, and the phase-updated S transform coefficient of each station is integrated in the time domain to obtain the phase-updated Fourier coefficient of each station;

[0011] The phase-updated Fourier coefficients of each station are subjected to inverse Fourier transform to obtain the third intermediate seismic motion of each station, and the error judgment is performed on the third intermediate seismic motion of each station, and the third intermediate seismic motion that meets the error requirement is used as the target seismic motion of the corresponding station.

[0012] Optionally, the step of obtaining the first intermediate seismic motion after response spectrum matching of the seed seismic motion of each station using a single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion and the target response spectrum of each station specifically includes:

[0013] Obtaining a seed earthquake motion and a target response spectrum of each site, performing Fourier transform on the seed earthquake motion to obtain Fourier coefficients of the seed earthquake motion, and calculating an actual response spectrum of the seed earthquake motion;

[0014] According to the target response spectrum of each site and the actual response spectrum of the seed earthquake motion, the first S transform coefficient amplitude scaling function of each site is calculated, and according to the first S transform coefficient amplitude scaling function of each site, it is determined whether the S transform coefficient needs to be adjusted in amplitude;

[0015] Performing S transformation on the seed seismic motion at the frequency point where amplitude adjustment is required at each site to obtain the S transformation coefficient of the seed seismic motion, performing amplitude adjustment on the S transformation coefficient of the seed seismic motion using the first S transformation coefficient amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient of the seed seismic motion in the time domain to obtain the Fourier coefficient of the amplitude-adjusted seed seismic motion at each site;

[0016] The Fourier coefficients of the seed seismic motion without amplitude adjustment at each site and the Fourier coefficients of the seed seismic motion after amplitude adjustment are subjected to inverse Fourier transformation to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion at each site.

[0017] Optionally, the calculating of the time-frequency power spectrum density of the first intermediate seismic motion of each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate the coherent seismic motion of each station specifically includes:

[0018] Perform an S transform on the first intermediate seismic motion of each station to obtain an S transform coefficient of the first intermediate seismic motion of each station:

[0019] ;

[0020] in, Indicates sites, , Indicates the number of sites; express The corresponding frequency interval number, , Indicates the signal length; Indicates the frequency interval; express The corresponding time interval number, ; Indicates a time interval; represents the S-transform coefficient of the first intermediate ground motion at the z-th station; Represents the symbol of the S-transform operator; represents the first intermediate ground motion at the z-th station; j Indicates the number of frequency intervals; express At the frequency point The Fourier coefficients at ; i Represents the imaginary number symbol;

[0021] The time-frequency power spectrum density of the first intermediate seismic motion at each station is calculated according to the S-transform coefficient of the first intermediate seismic motion at each station:

[0022] ;

[0023] in, represents the time-frequency power spectrum density of the first intermediate ground motion at the z-th station, represents the complex conjugate operation, is the parameter of the window function selected in the S transform;

[0024] Calculate the target coherence function matrix between two sites with a spatial distance of Δ, where the target coherence function matrix is ​​used to represent the spatial coherence between the two sites:

[0025] ;

[0026] ;

[0027] ;

[0028] in, represents the unbiased target coherence function matrix between two sites with a spatial distance of Δ, Represents the biased hysteresis coherence model between the ground motions of two stations with a spatial distance of Δ, , , , , , , are all model parameters;

[0029] Performing Cholesky decomposition on the target coherence function matrix to obtain a lower triangular matrix;

[0030] For each site, coherent seismic motion is simulated by superimposing sinusoidal waves of different frequency components, wherein the amplitude information of the sinusoidal wave of each frequency component is determined by the time-frequency power spectrum density, the lower triangular matrix and the sampling frequency of the seed seismic motion, and the phase information of the sinusoidal wave of each frequency component is determined by the lower triangular matrix.

[0031] Optionally, the step of obtaining the second intermediate seismic motion after response spectrum matching of the coherent seismic motion at each station using a single-point response spectrum matching seismic motion algorithm according to the coherent seismic motion at each station and the target response spectrum specifically includes:

[0032] Performing Fourier transform on the coherent seismic motion of each station to obtain the Fourier coefficient of the coherent seismic motion of each station, and calculating the actual response spectrum of the coherent seismic motion of each station;

[0033] According to the target response spectrum of each station and the actual response spectrum of the coherent ground motion, a second S transform coefficient amplitude scaling function of each station is calculated, and according to the second S transform coefficient amplitude scaling function of each station, it is determined whether the S transform coefficient needs to be adjusted in amplitude;

[0034] Performing S transformation on the coherent seismic motion at the frequency point where amplitude adjustment is required at each station to obtain the S transformation coefficient of the coherent seismic motion, performing amplitude adjustment on the S transformation coefficient of the coherent seismic motion using the second S transformation coefficient amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient of the coherent seismic motion in the time domain to obtain the Fourier coefficient of the amplitude-adjusted coherent seismic motion at each station;

[0035] The Fourier coefficients of the coherent seismic motion without amplitude adjustment at each site and the Fourier coefficients of the coherent seismic motion after amplitude adjustment are subjected to inverse Fourier transformation to obtain the second intermediate seismic motion after response spectrum matching of the coherent seismic motion at each site.

[0036] Optionally, performing S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculating the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, specifically includes:

[0037] Perform S transformation on the coherent seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion of each station:

[0038] ;

[0039] in, represents the S-transform coefficient of the coherent ground motion at the z-th station; represents the coherent ground motion at the z-th station; express At the frequency point The Fourier coefficients at ;

[0040] According to the S transform coefficient of the coherent seismic motion of each station, the phase of the S transform coefficient of the coherent seismic motion of each station is calculated:

[0041] ;

[0042] in, Indicates The phase of the S transform coefficient of the coherent ground motion at each station, Indicates The imaginary part of the S-transform coefficient of the coherent ground motion at each station, Indicates The real part of the S-transform coefficient of the coherent ground motion at each station;

[0043] Perform S transformation on the second intermediate seismic motion of each station to obtain the S transformation coefficient of the second intermediate seismic motion of each station:

[0044] ;

[0045] in, represents the S-transform coefficient of the second intermediate ground motion at the z-th station, represents the second intermediate ground motion at the z-th station; express At the frequency point The Fourier coefficients at ;

[0046] According to the S transformation coefficient of the second intermediate seismic motion of each station, the phase of the S transformation coefficient of the second intermediate seismic motion of each station is calculated:

[0047] ;

[0048] in, Indicates The phase of the S-transform coefficient of the second intermediate ground motion of each station, Indicates The imaginary part of the S-transform coefficient of the second intermediate ground motion of each station, Indicates The real part of the S-transform coefficient of the second intermediate ground motion of each station;

[0049] According to the phase of the coherent seismic motion at each station and the phase of the second intermediate seismic motion, the synchronous phase shuffling factor of each station is calculated:

[0050] ;

[0051] in, Indicates The synchronization phase shuffle factor for each site.

[0052] Optionally, the using the synchronous phase shuffling factor of each station to phase update the S transform coefficient of the second intermediate seismic motion of each station, and integrating the phase-updated S transform coefficient of each station in the time domain to obtain the phase-updated Fourier coefficient of each station specifically includes:

[0053] The S transform coefficient of the second intermediate seismic motion of each station is phase-updated by using the synchronous phase shuffling factor of each station to obtain the S transform coefficient of the second intermediate seismic motion of each station after phase update:

[0054] ;

[0055] in, Indicates The S transformation coefficient of the second intermediate ground motion after the phase update of each station;

[0056] The S transform coefficients of the second intermediate seismic motion after the phase of each station is updated are integrated in the time domain to obtain the Fourier coefficients of the second intermediate seismic motion after the phase of each station is updated:

[0057] ;

[0058] in, Indicates The Fourier coefficients of the second intermediate ground motion after phase update at each station;

[0059] According to the frequency symmetry of Fourier transform, let the Fourier coefficient of negative frequency Equal to the Fourier coefficient of the positive frequency :

[0060] .

[0061] Optionally, performing inverse Fourier transform on the phase-updated Fourier coefficients of each station to obtain a third intermediate seismic motion of each station, performing error judgment on the third intermediate seismic motion of each station, and taking the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding station specifically includes:

[0062] Performing inverse Fourier transformation on the Fourier coefficients of the second intermediate seismic motion after phase update at each station to obtain the third intermediate seismic motion at each station;

[0063] Calculate the actual response spectrum of the third intermediate earthquake motion at each station, and record the time when the peak response corresponding to the frequency point occurs;

[0064] For each site, at all frequency points where response spectrum matching is required, determining whether the maximum relative error between the actual response spectrum value of the third intermediate seismic motion and the target response spectrum value is not greater than a set error tolerance value;

[0065] If yes, taking the third intermediate seismic motion as the target seismic motion of the corresponding site;

[0066] If not, the third intermediate seismic motion is taken as the coherent seismic motion of the corresponding site, and the calculation is repeated to obtain a new third intermediate seismic motion until the maximum relative error between the actual response spectrum value of the third intermediate seismic motion and the target response spectrum value is no greater than the set error tolerance value.

[0067] To achieve the above-mentioned purpose, the present invention further provides a response spectrum matching spatial variation multi-point earthquake motion generation system based on S transform, the response spectrum matching spatial variation multi-point earthquake motion generation system based on S transform comprising:

[0068] The first intermediate seismic motion module is used to obtain the first intermediate seismic motion after the response spectrum matching of the seed seismic motion of each station by using the single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion and the target response spectrum of each station;

[0069] Coherent seismic motion module: used to calculate the time-frequency power spectrum density of the first intermediate seismic motion of each station, combine the time-frequency power spectrum density of each station and the spatial coherence between two stations, and use spectral representation method to simulate the coherent seismic motion of each station;

[0070] A second intermediate seismic motion module: configured to obtain, according to the coherent seismic motion of each site and the target response spectrum, a second intermediate seismic motion after response spectrum matching of the coherent seismic motion of each site by using a single-point response spectrum matching seismic motion algorithm;

[0071] Synchronous phase shuffling module: used to perform S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively, obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculate the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station;

[0072] Phase update module: used to update the phase of the S transform coefficient of the second intermediate seismic motion of each station by using the synchronous phase shuffling factor of each station, and integrate the S transform coefficient after the phase update of each station in the time domain to obtain the Fourier coefficient after the phase update of each station;

[0073] Target seismic motion module: used to perform inverse Fourier transform on the phase-updated Fourier coefficients of each site to obtain the third intermediate seismic motion of each site, perform error judgment on the third intermediate seismic motion of each site, and use the third intermediate seismic motion that meets the error requirements as the target seismic motion of the corresponding site.

[0074] In order to achieve the above-mentioned purpose of the invention, the present invention also provides a terminal, which includes: a memory, a processor, and a response spectrum matching spatially varying multi-point seismic motion generation program based on S transform stored in the memory and run on the processor, and when the response spectrum matching spatially varying multi-point seismic motion generation program based on S transform is executed by the processor, the steps of the response spectrum matching spatially varying multi-point seismic motion generation method based on S transform as described above are implemented.

[0075] In order to achieve the above-mentioned purpose of the invention, the present invention also provides a computer-readable storage medium, which stores a response spectrum matching spatially varying multi-point seismic motion generation program based on S transform, and when the response spectrum matching spatially varying multi-point seismic motion generation program based on S transform is executed by a processor, the steps of the response spectrum matching spatially varying multi-point seismic motion generation method based on S transform as described above are implemented.

[0076] In the present invention, a single-point response spectrum matching seismic motion algorithm is used to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion of each station; the coherent seismic motion of each station is simulated by using the spectral representation method in combination with the time-frequency power spectrum density of the first intermediate seismic motion and the spatial coherence between the two stations; the single-point response spectrum matching seismic motion algorithm is used to obtain the second intermediate seismic motion after response spectrum matching of the coherent seismic motion of each station; the coherent seismic motion and the second intermediate seismic motion are S-transformed to obtain S-transformation coefficients, and the synchronous phase shuffling factors are obtained according to the phase calculation of the S-transformation coefficients, and the S-transformation coefficients of the second intermediate seismic motion are phase-updated using the synchronous phase shuffling factors; the phase-updated S-transformation coefficients of each station are integrated in the time domain to obtain the phase-updated Fourier coefficients of each station, the phase-updated Fourier coefficients of each station are inversely Fourier transformed, and error judgment is performed to obtain the target seismic motion of each station. The present invention enables the seismic motion after multi-point response spectrum matching to maintain the coherence of the seismic motion to the greatest extent while meeting the target response spectrum matching accuracy, thereby providing a reliable time-history analysis input for the seismic design of large-span structures; and realizes efficient, high-precision response spectrum matching that retains the time-frequency non-stationary characteristics of the original seismic motion to the greatest extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 It is a flow chart of a preferred embodiment of the method for generating multi-point earthquake motion based on response spectrum matching of S transform and spatial variation of the present invention;

[0078] Figure 2 It is another flow chart of a preferred embodiment of the method for generating spatially varying multi-point ground motions based on response spectrum matching of S transform according to the present invention;

[0079] Figure 3 is a diagram showing the matching results of the earthquake response spectra of site 1 and site 2 of the present invention;

[0080] Figure 4 is a schematic diagram of the coherence between site 1 and site 2 of the present invention;

[0081] Figure 5 It is a structural diagram of a preferred embodiment of the response spectrum matching spatial variation multi-point earthquake motion generation system based on S transform of the present invention;

[0082] Figure 6 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0083] In order to make the purpose, technical solution and advantages of the present invention clearer and more specific, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0084] When designing a large-span structure with multiple supports, such as a large-span bridge or dam, it is difficult to find earthquake records that meet the design site conditions from the real earthquake database. This is because the site conditions where the real earthquake records occur are often quite different from the actual design site conditions of the building, and the earthquake itself has spatial variation characteristics and coherence, which is particularly important for the time-history analysis of structures. However, historical real earthquake records are difficult to match the site distribution conditions of large-span structures. Therefore, it is necessary to develop an algorithm that can simulate or generate multi-point response spectrum matching earthquake motion. In the prior art, most of the research on the response spectrum matching multi-point earthquake motion method uses spectral representation to simulate multi-point earthquake motion, and the simulated earthquake motion response spectrum is not accurate enough relative to the target response spectrum.

[0085] In order to solve the above technical problems, the present invention provides a method for generating multi-point seismic motions by spatially varying response spectrum matching based on S transform, which adopts a single-point response spectrum matching seismic motion algorithm to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion of each station; combining the time-frequency power spectrum density of the first intermediate seismic motion and the spatial coherence between the two stations, a spectral representation method is used to simulate and obtain the coherent seismic motion of each station; a single-point response spectrum matching seismic motion algorithm is used to obtain the second intermediate seismic motion after response spectrum matching of the coherent seismic motion of each station; S transform is performed on the coherent seismic motion and the second intermediate seismic motion to obtain S transform coefficients, a synchronous phase shuffling factor is obtained according to the phase calculation of the S transform coefficients, and the S transform coefficient of the second intermediate seismic motion is updated in phase using the synchronous phase shuffling factor; the phase-updated S transform coefficients of each station are integrated in the time domain to obtain the phase-updated Fourier coefficients of each station, the phase-updated Fourier coefficients of each station are inversely Fourier transformed, and error judgment is performed to obtain the target seismic motion of each station. The present invention enables the seismic motion after multi-point response spectrum matching to satisfy the target response spectrum matching accuracy while retaining the coherent structure of the seismic motion to the greatest extent, and achieves simultaneous matching of the response spectra of multi-point seismic motions while maintaining the coherence of the seismic motion disturbed by adjusting the S-transform coefficient, thereby providing a reliable time-history analysis input for the seismic design of large-span structures; and achieves efficient, high-precision response spectrum matching that retains the time-frequency non-stationary characteristics of the original seismic motion to the greatest extent.

[0086] The application content is further explained below through the description of embodiments in conjunction with the accompanying drawings.

[0087] A preferred embodiment of the method for generating spatially varying multi-point ground motions based on response spectrum matching of S transform of the present invention is as follows: Figure 1 and Figure 2 As shown, specifically including:

[0088] S1: According to the obtained seed seismic motion and the target response spectrum of each site, a single-point response spectrum matching seismic motion algorithm is used to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion of each site.

[0089] In an implementation of this embodiment, the step of obtaining the first intermediate seismic motion after the seed seismic motion of each station is matched with the response spectrum by using a single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion and the target response spectrum of each station specifically includes:

[0090] S11: Get a seed earthquake and the target response spectrum of each site ，s = 1,…,Ns , perform Fourier transform on the seed earthquake motion, obtain the Fourier coefficient of the seed earthquake motion, and calculate the actual response spectrum of the seed earthquake motion ,s = 1,…,Ns , for each frequency point , record the frequency point The time when the corresponding peak response occurs , denoted as ,in, express The corresponding frequency interval number, express The corresponding number of sampling intervals;

[0091] in, Indicates the frequency points where response spectrum matching is required. Indicates the order of frequency points that need to be matched for response spectrum. represents the damping ratio, N Indicates the number of frequency points that need to be matched for response spectrum; Indicates frequency point The corresponding frequency interval number. It should be noted that the frequency points that need to be matched for response spectrum It is artificially determined. In the discrete Fourier transform and S transform, the positive frequency points used are , The value of is [0 N / 2], in fact, it is impossible to guarantee that every There is one Correspondingly, in practical applications, the program is used to ensure that each [ ] There is at most one (or possibly zero) frequency point in the interval that needs to be matched for the response spectrum ,distance The nearest frequency point or It is recorded as , The value is [0 N / 2]; in addition, the present invention only obtains one seed earthquake motion, so the seed earthquake motion of each station is the same;

[0092] S12: Calculate the first S transform coefficient amplitude scaling function of each site according to the target response spectrum of each site and the actual response spectrum of the seed earthquake motion. , and judging whether it is necessary to adjust the amplitude of the S transform coefficient according to the first S transform coefficient amplitude scaling function of each site;

[0093] ;

[0094] Scale Factor :

[0095] ;

[0096] Scale Factor ,s = 1,…,Ns ;

[0097] in, Indicates frequency, Indicates time, and Respectively expressed as and The local time-frequency domain centered on and is the scaled half bandwidth, and To control the parameters of the zoom window, is the scale factor;

[0098] For each frequency point ,like , indicating that the actual response spectrum is at the frequency point The value at the frequency point is consistent with the target response spectrum If the values ​​at are not equal, then the frequency point is the frequency point that needs amplitude adjustment, and the frequency point that needs amplitude adjustment is recorded as ,in, for The corresponding frequency interval number, M The number of frequency points that need to be adjusted in amplitude;

[0099] S13: Frequency points where amplitude adjustment is required at each station The seed earthquake motion is subjected to S transformation to obtain the S transformation coefficient of the seed earthquake motion. , using the first S transform coefficient amplitude scaling function to adjust the amplitude of the S transform coefficient of the seed earthquake motion, and converting the amplitude-adjusted S transform coefficient of the seed earthquake motion into Integrating in the time domain to obtain the Fourier coefficients of the seed earthquake motion after the amplitude adjustment of each station;

[0100] ;

[0101] It should be noted that the amplitude scaling function of the first S transform coefficient of each station is different, resulting in different frequency points that need to be adjusted for amplitude. Therefore, the S transform coefficients of the seed ground motion obtained at each station are different.

[0102] S14: Perform inverse Fourier transformation on the Fourier coefficients of the seed seismic motion without amplitude adjustment at each site and the Fourier coefficients of the seed seismic motion after amplitude adjustment to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion at each site .

[0103] The single-point response spectrum matching seismic motion algorithm of the present invention utilizes the characteristic that the S transform can be regarded as an extension of the Fourier transform in the time domain, combines the advantages of the S transform and the Fourier transform, utilizes the fast Fourier transform to greatly improve the calculation efficiency, utilizes the S transform to perform sophisticated time-frequency localized adjustment of the signal, and only performs the S transform at the frequency point where the S transform coefficient amplitude adjustment is required, without the need to perform the S transform on the entire frequency domain, thereby achieving efficient, high-precision response spectrum matching that retains the original seismic motion time-frequency non-stationary characteristics to the greatest extent.

[0104] S2: Calculate the time-frequency power spectrum density of the first intermediate seismic motion of each station, combine the time-frequency power spectrum density of each station and the spatial coherence between two stations, and use spectral representation to simulate and obtain the coherent seismic motion of each station.

[0105] In an implementation of this embodiment, the calculating of the time-frequency power spectrum density of the first intermediate seismic motion of each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate the coherent seismic motion of each station specifically includes:

[0106] S21: Perform an S transformation on the first intermediate seismic motion of each station to obtain an S transformation coefficient of the first intermediate seismic motion of each station:

[0107] ;

[0108] in, Indicates sites, , Indicates the number of sites; express The corresponding frequency interval number, , Indicates the signal length; Indicates the frequency interval; express The corresponding time interval number, ; Indicates a time interval; represents the S-transform coefficient of the first intermediate ground motion at the z-th station; Represents the symbol of the S-transform operator; represents the first intermediate ground motion at the z-th station; j Indicates the number of frequency intervals; express At the frequency point The Fourier coefficients at ; i Represents the imaginary number symbol;

[0109] S22: Calculate the time-frequency power spectrum density of the first intermediate seismic motion at each station according to the S transformation coefficient of the first intermediate seismic motion at each station:

[0110] ;

[0111] in, represents the time-frequency power spectrum density of the first intermediate ground motion at the z-th station, represents the complex conjugate operation, is the parameter of the window function selected in the S transform, usually taken as 1;

[0112] S23: Calculate the target coherence function matrix between two sites with a spatial distance of Δ, where the target coherence function matrix is ​​used to represent the spatial coherence between the two sites:

[0113] ;

[0114] ;

[0115] ;

[0116] in, represents the unbiased target coherence function matrix between two sites with a spatial distance of Δ, Represents the biased hysteresis coherence model between the ground motions of two stations with a spatial distance of Δ, , , , , , , are all model parameters; in this embodiment, =0.2, , , , =5.7, ;

[0117] S24: performing Cholesky decomposition on the target coherence function matrix to obtain a lower triangular matrix;

[0118] S25: For each station, the coherent ground motion is simulated by superimposing sine waves with different frequency components. , wherein the amplitude information of the sine wave of each frequency component is determined by the time-frequency power spectrum density, the lower triangular matrix and the sampling frequency of the seed seismic motion, and the phase information of the sine wave of each frequency component is determined by the lower triangular matrix.

[0119] The spectral representation method is based on the evolution power spectral density model of ground motion, which describes the energy distribution of ground motion at different frequencies and times. The specific principle of using the spectral representation method to generate simulation samples consistent with the target coherence function is as follows:

[0120] 1) Determine the evolution power spectrum density and the target coherence function matrix between sites: The evolution power spectrum density is the key input of the earthquake simulation, which describes the energy distribution of the earthquake at different frequencies and times. The target coherence function matrix between sites describes the coherence of the earthquake between different sites. In the present invention, the input evolution power spectrum density is the time-frequency power spectrum density TFPSD obtained based on S transform, and the target coherence function matrix is ;

[0121] 2) Perform Cholesky decomposition: Perform Cholesky decomposition on the target coherence function matrix to obtain a lower triangular matrix, which contains the random phase angle and amplitude information required to generate simulated ground motion;

[0122] 3) Simulated seismic records: For each simulated seismic sample, a random phase angle is generated by the lower triangular matrix obtained by Cholesky decomposition; for each station, the seismic motion is simulated by superimposing sine waves with different frequency components, where the amplitude information of each frequency component is obtained by the evolution power spectral density and the lower triangular matrix as well as the sampling frequency of the seismic motion. Together, the phase information is determined by the random phase angle mentioned above.

[0123] S3: According to the coherent seismic motions of each site and the target response spectrum, a single-point response spectrum matching seismic motion algorithm is used to obtain a second intermediate seismic motion after response spectrum matching of the coherent seismic motions of each site.

[0124] In an implementation of this embodiment, the obtaining, according to the coherent seismic motions at each site and the target response spectrum, of the second intermediate seismic motions after the coherent seismic motions at each site are matched with the response spectrum using a single-point response spectrum matching seismic motion algorithm specifically includes:

[0125] S31: The relevant earthquake motions at each site Performing Fourier transform to obtain the Fourier coefficients of the coherent seismic motion at each station, and calculating the actual response spectrum of the coherent seismic motion at each station;

[0126] S32: calculating a second S transform coefficient amplitude scaling function of each site according to the target response spectrum of each site and the actual response spectrum of the coherent ground motion, and judging whether it is necessary to adjust the amplitude of the S transform coefficient according to the second S transform coefficient amplitude scaling function of each site;

[0127] S33: performing S transformation on the coherent seismic motion at the frequency point where amplitude adjustment is required at each station to obtain the S transformation coefficient of the coherent seismic motion, performing amplitude adjustment on the S transformation coefficient of the coherent seismic motion using the second S transformation coefficient amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient of the coherent seismic motion in the time domain to obtain the Fourier coefficient of the amplitude-adjusted coherent seismic motion at each station;

[0128] S34: performing inverse Fourier transformation on the Fourier coefficients of the coherent seismic motions of each station without amplitude adjustment and the Fourier coefficients of the coherent seismic motions after amplitude adjustment, to obtain the second intermediate seismic motions of the coherent seismic motions of each station after response spectrum matching. .

[0129] It should be noted that the specific process of step S3 is similar to that of step S1, and the two only process different objects, which will not be described again here. It should be noted that the processing object of step S1 is the seed ground motion, and the processing object of step S3 is the coherent ground motion.

[0130] S4: Perform S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculate the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station.

[0131] In an implementation of this embodiment, the coherent seismic motion and the second intermediate seismic motion of each station are respectively subjected to S transformation to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and the synchronous phase shuffling factor of each station is calculated according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, which specifically includes:

[0132] S41: Performing S transformation on the coherent seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion of each station:

[0133] ;

[0134] in, represents the S-transform coefficient of the coherent ground motion at the z-th station; represents the coherent ground motion at the z-th station; express At the frequency point Fourier coefficients at the point where the coherent ground motion is transformed by S. S transformation is performed at the frequency point where amplitude adjustment is required, which is different from step S33. Perform S transformation at

[0135] S42: Calculate the phase of the S transform coefficient of the coherent seismic motion at each station according to the S transform coefficient of the coherent seismic motion at each station:

[0136] ;

[0137] in, Indicates The phase of the S transform coefficient of the coherent ground motion at each station, Indicates The imaginary part of the S-transform coefficient of the coherent ground motion at each station, Indicates The real part of the S-transform coefficient of the coherent ground motion at each station;

[0138] S43: Performing S transformation on the second intermediate seismic motion of each station to obtain an S transformation coefficient of the second intermediate seismic motion of each station:

[0139] ;

[0140] in, represents the S-transform coefficient of the second intermediate ground motion at the z-th station, represents the second intermediate ground motion at the z-th station; express At the frequency point The Fourier coefficients at ;

[0141] S44: Calculate the phase of the S transform coefficient of the second intermediate seismic motion at each station according to the S transform coefficient of the second intermediate seismic motion at each station:

[0142] ;

[0143] in, Indicates The phase of the S-transform coefficient of the second intermediate ground motion of each station, Indicates The imaginary part of the S-transform coefficient of the second intermediate ground motion of each station, Indicates The real part of the S-transform coefficient of the second intermediate ground motion of each station;

[0144] S45: Calculate the synchronous phase shuffling factor of each site according to the phase of the coherent seismic motion of each site and the phase of the second intermediate seismic motion:

[0145] ;

[0146] in, Indicates The synchronization phase shuffle factor for each site.

[0147] S5: Use the synchronous phase shuffling factor of each site to update the phase of the S transform coefficient of the second intermediate seismic motion of each site, and integrate the phase-updated S transform coefficient of each site in the time domain to obtain the phase-updated Fourier coefficient of each site.

[0148] In an implementation of this embodiment, the phase of the S transform coefficient of the second intermediate seismic motion of each station is updated by using the synchronous phase shuffling factor of each station, and the phase-updated S transform coefficient of each station is integrated in the time domain to obtain the phase-updated Fourier coefficient of each station, which specifically includes:

[0149] S51: using the synchronous phase shuffling factor of each station to perform phase update on the S transformation coefficient of the second intermediate seismic motion of each station, to obtain the S transformation coefficient of the second intermediate seismic motion of each station after phase update:

[0150] ;

[0151] in, Indicates The S transformation coefficient of the second intermediate ground motion after the phase update of each station;

[0152] S52: Integrate the S transform coefficients of the second intermediate seismic motion after the phase of each site is updated in the time domain to obtain the Fourier coefficients of the second intermediate seismic motion after the phase of each site is updated:

[0153] ;

[0154] in, Indicates The Fourier coefficients of the second intermediate ground motion after phase update at each station;

[0155] S53: According to the frequency symmetry of Fourier transform, let the Fourier coefficients of negative frequencies Equal to the Fourier coefficient of the positive frequency :

[0156] .

[0157] A key to generating spatially varying multi-point response spectrum matching ground motions is to maintain the coherence of ground motions during the iterative process of response spectrum matching. In order to maintain coherence in each iteration, the present invention adopts a concept called "synchronous phase shuffling" to restore coherence.

[0158] S6: Perform inverse Fourier transform on the phase-updated Fourier coefficients of each site to obtain the third intermediate seismic motion of each site, perform error judgment on the third intermediate seismic motion of each site, and use the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding site.

[0159] In an implementation of this embodiment, performing inverse Fourier transform on the phase-updated Fourier coefficients of each station to obtain the third intermediate seismic motion of each station, performing error judgment on the third intermediate seismic motion of each station, and taking the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding station specifically includes:

[0160] S61: performing inverse Fourier transform on the Fourier coefficients of the second intermediate seismic motion of each station after phase update to obtain the third intermediate seismic motion of each station;

[0161] S62: Calculate the actual response spectrum of the third intermediate earthquake motion at each station, and record the time when the peak response corresponding to the frequency point occurs;

[0162] S63: for each site, at all frequency points where response spectrum matching is required, determining whether the maximum relative error between the actual response spectrum value of the third intermediate ground motion and the target response spectrum value is not greater than a set error tolerance value (5%);

[0163] S64: If yes, taking the third intermediate ground motion as the target ground motion of the corresponding station;

[0164] S65: If not, the third intermediate seismic motion is used as the coherent seismic motion of the corresponding site, and the calculation is repeated to obtain a new third intermediate seismic motion until the actual response spectrum value of the third intermediate seismic motion is With the target response spectrum value The maximum relative error is not greater than the set error tolerance;

[0165] That is, to judge the following inequality:

[0166] ,s=1,2,…,Ns ;

[0167] in, is the set error tolerance. If the inequality holds, the response spectrum matching result has not converged, and the third intermediate seismic motion is used as the coherent seismic motion of the corresponding station, and the above steps S3 to S6 are repeated until the response spectrum matching result converges. When the response spectrum matching result converges, the final seismic motion signal is the target seismic motion signal that maintains coherence after the response spectrum matching of the corresponding station.

[0168] The idea adopted by the present invention is to first use the single-point response spectrum matching seismic motion algorithm to match a selected seed seismic motion with the target response spectrum at each site, and obtain the first intermediate seismic motion after the response spectrum matching at each site, and then calculate the time-frequency power spectral density (Time-Frequency Power Spectral Density, TFPSD) of these first intermediate seismic motions, and use TFPSD and the spatial coherence between two points to simulate coherent multi-point coherent seismic motions with coherence using spectral representation. The simulated multi-point coherent seismic motions are used as seed seismic motions of each site. At this time, the response spectrum of the seed seismic motion of each site will no longer fit with its corresponding target response spectrum, and it is necessary to combine it with the concept of "synchronous phase shuffling" by performing "synchronous phase shuffling" on the phase of the S transform coefficient in the iterative process of adjusting the amplitude of the S transform coefficient. Figure 3 and Figure 4 As shown, Figure 3 (a) in the figure indicates that the seismic response spectrum matching result of station 1 has converged. Figure 3 (b) in the figure shows that the seismic response spectrum matching result of station 2 has converged. Figure 4 It indicates that the coherence between site 1 and site 2 is still maintained after the response spectrum matching. The present invention enables the seismic motion after multi-point response spectrum matching to maintain the coherence of the seismic motion to the greatest extent while satisfying the matching accuracy of the target response spectrum, wherein the spectral acceleration of the seismic motion sample after matching refers to the actual response spectrum of the target seismic motion, the target spectral acceleration refers to the target response spectrum, the seismic motion sample generated by the spectral representation method refers to the coherent seismic motion, and the seismic motion after the response spectrum matching refers to the target seismic motion.

[0169] In addition, based on the above-mentioned S-transform-based response spectrum matching spatial variation multi-point seismic motion generation method, the present invention also provides a S-transform-based response spectrum matching spatial variation multi-point seismic motion generation system, and a preferred embodiment of the S-transform-based response spectrum matching spatial variation multi-point seismic motion generation system is as follows: Figure 5 As shown, specifically including:

[0170] The first intermediate seismic motion module 01 is used to obtain the first intermediate seismic motion of each station after the seed seismic motion of each station is matched with the response spectrum by using the single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion of each station and the target response spectrum;

[0171] Coherent seismic motion module 02: used to calculate the time-frequency power spectrum density of the first intermediate seismic motion of each station, and combine the time-frequency power spectrum density of each station and the spatial coherence between two stations to simulate the coherent seismic motion of each station using spectral representation method;

[0172] The second intermediate seismic motion module 03 is used to obtain the second intermediate seismic motion of each site after the response spectrum matching of the coherent seismic motion of each site by using a single-point response spectrum matching seismic motion algorithm according to the coherent seismic motion of each site and the target response spectrum;

[0173] Synchronous phase shuffling module 04: used to perform S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively, obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculate the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station;

[0174] Phase updating module 05: used to update the phase of the S transform coefficient of the second intermediate seismic motion of each station by using the synchronous phase shuffling factor of each station, and integrate the S transform coefficient after the phase update of each station in the time domain to obtain the Fourier coefficient after the phase update of each station;

[0175] Target seismic motion module 06: used to perform inverse Fourier transform on the phase-updated Fourier coefficients of each station to obtain the third intermediate seismic motion of each station, perform error judgment on the third intermediate seismic motion of each station, and use the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding station.

[0176] In addition, based on the above-mentioned S-transform-based response spectrum matching spatial variation multi-point ground motion generation method and system, the present invention also provides a terminal accordingly, wherein a preferred embodiment of the terminal is as follows: Figure 6 As shown, it specifically includes a processor 10, a memory 20 and a display 30. Figure 6Only some components of the terminal are shown, but it should be understood that it is not required to implement all the components shown, and more or fewer components may be implemented instead. In one embodiment, the memory 20 stores a response spectrum matching spatial variation multi-point ground motion generation program 40 based on S transform, and the response spectrum matching spatial variation multi-point ground motion generation program 40 based on S transform can be executed by the processor 10, thereby implementing the steps of the response spectrum matching spatial variation multi-point ground motion generation method based on S transform in the present application.

[0177] The present invention also provides a computer-readable storage medium accordingly, wherein the computer-readable storage medium stores a response spectrum matching spatially varying multi-point seismic motion generation program based on S transform, and when the response spectrum matching spatially varying multi-point seismic motion generation program based on S transform is executed by a processor, the steps of the response spectrum matching spatially varying multi-point seismic motion generation method based on S transform as described above are implemented.

[0178] It should be understood that the application of the present invention is not limited to the above examples. For ordinary technicians in this field, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for generating multi-point ground motions based on response spectrum matching with spatial variation based on S transform, characterized in that: The S-transform-based response spectrum matching spatial variation multi-point ground motion generation method comprises: According to the obtained seed seismic motion and the target response spectrum of each site, a single-point response spectrum matching seismic motion algorithm is used to obtain the first intermediate seismic motion after the seed seismic motion of each site is matched with the response spectrum; Calculating the time-frequency power spectrum density of the first intermediate seismic motion at each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate and obtain the coherent seismic motion of each station; According to the coherent seismic motions of each site and the target response spectrum, a single-point response spectrum matching seismic motion algorithm is used to obtain the second intermediate seismic motion after the coherent seismic motions of each site are matched with the response spectrum; Performing S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculating the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station; The S transform coefficient of the second intermediate seismic motion of each station is phase updated by using the synchronous phase shuffling factor of each station, and the phase-updated S transform coefficient of each station is integrated in the time domain to obtain the phase-updated Fourier coefficient of each station; Performing inverse Fourier transform on the phase-updated Fourier coefficients of each station to obtain the third intermediate seismic motion of each station, performing error judgment on the third intermediate seismic motion of each station, and taking the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding station; The calculating of the time-frequency power spectrum density of the first intermediate seismic motion of each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate and obtain the coherent seismic motion of each station, specifically includes: Perform an S transform on the first intermediate seismic motion of each station to obtain an S transform coefficient of the first intermediate seismic motion of each station: Where z represents the zth site, z = 1,…,n, n represents the number of sites; p represents pΔ f The corresponding frequency interval number, p = -N / 2+1, ..., N / 2, N represents the signal length; Δ f represents the frequency interval; q represents qΔ t The corresponding number of time intervals, q = 1, ..., N; Δ t Indicates the time interval; x s,new1,z (pΔ f ,qΔ t ) represents the S-transform coefficient of the first intermediate ground motion of the z-th station; ST(·) represents the symbol of the S-transform operator; x new1,z (qΔ t ) represents the first intermediate ground motion of the zth station; j represents the frequency interval number; Represents x new1,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficient at ; i represents the imaginary number sign; The time-frequency power spectrum density of the first intermediate seismic motion at each station is calculated according to the S-transform coefficient of the first intermediate seismic motion at each station: Among them, TFPSD z represents the time-frequency power spectrum density of the first intermediate ground motion at the z-th station, * represents the complex conjugate operation, and κ′ is the parameter of the window function selected in the S transform; Calculate the target coherence function matrix between two sites with a spatial distance of Δ, where the target coherence function matrix is ​​used to represent the spatial coherence between the two sites: |C(pΔ f ,Δ)|=tanh(tanh -1 (|C Bias (pΔ f ,D)|-e)); θ(pΔ f )=κ″(1+(pΔ f / f0′) B ) -1 / 2 ; Among them, |Γ(pΔ f ,Δ)| represents the unbiased target coherence function matrix between two sites with a spatial distance of Δ, |Γ Biαs (pΔ f ,Δ)| represents the biased hysteresis coherence model between the ground motions of two stations with a spatial distance of Δ, θ(pΔ f ), ε, A, α0, κ″, B, f0′ are all model parameters; Performing Cholesky decomposition on the target coherence function matrix to obtain a lower triangular matrix; For each site, coherent ground motion is obtained by superimposing sine waves of different frequency components, wherein the amplitude information of the sine wave of each frequency component is determined by the time-frequency power spectrum density, the lower triangular matrix and the sampling frequency of the seed ground motion, and the phase information of the sine wave of each frequency component is determined by the lower triangular matrix; The step of performing S transformation on the coherent seismic motion and the second intermediate seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculating the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, specifically includes: Perform S transformation on the coherent seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion of each station: Among them, x s,old2,z (pΔ f ,qΔ t ) represents the S transform coefficient of the coherent ground motion at the z-th station; x old2,z (qΔ t ) represents the coherent ground motion at the z-th station; Represents x old2,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficients at ; According to the S transform coefficient of the coherent seismic motion of each station, the phase of the S transform coefficient of the coherent seismic motion of each station is calculated: Among them, θ z (pΔ f ,qΔ t ) represents the phase of the S transform coefficient of the coherent ground motion at the z-th station, represents the imaginary part of the S-transform coefficient of the coherent ground motion at the z-th station, represents the real part of the S-transform coefficient of the coherent ground motion at the z-th station; Perform S transformation on the second intermediate seismic motion of each station to obtain the S transformation coefficient of the second intermediate seismic motion of each station: Among them, x s,new2,z (pΔ f ,qΔ t ) represents the S transformation coefficient of the second intermediate ground motion at the zth station, x new2,z (qΔ t ) represents the second intermediate earthquake motion at the z-th station; Represents x new2,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficients at ; According to the S transformation coefficient of the second intermediate seismic motion of each station, the phase of the S transformation coefficient of the second intermediate seismic motion of each station is calculated: Among them, φ z (pΔ f ,qΔ t ) represents the phase of the S transform coefficient of the second intermediate ground motion at the z-th station, represents the imaginary part of the S-transform coefficient of the second intermediate ground motion at the z-th station, represents the real part of the S-transform coefficient of the second intermediate ground motion at the z-th station; According to the phase of the coherent seismic motion at each station and the phase of the second intermediate seismic motion, the synchronous phase shuffling factor of each station is calculated: Among them, α(pΔ f ,qΔ t ) represents the synchronization phase shuffling factor of the zth site.

2. The method for generating multi-point earthquake motions by matching spatially varying response spectra based on S transform according to claim 1 is characterized in that: The step of obtaining the first intermediate seismic motion after the seed seismic motion of each station is matched with the response spectrum by using a single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion and the target response spectrum of each station specifically includes: Obtaining a seed earthquake motion and a target response spectrum of each site, performing Fourier transform on the seed earthquake motion to obtain Fourier coefficients of the seed earthquake motion, and calculating an actual response spectrum of the seed earthquake motion; According to the target response spectrum of each site and the actual response spectrum of the seed earthquake motion, the first S transform coefficient amplitude scaling function of each site is calculated, and according to the first S transform coefficient amplitude scaling function of each site, it is determined whether the S transform coefficient needs to be adjusted in amplitude; Performing S transformation on the seed seismic motion at the frequency point where amplitude adjustment is required at each site to obtain the S transformation coefficient of the seed seismic motion, performing amplitude adjustment on the S transformation coefficient of the seed seismic motion using the first S transformation coefficient amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient of the seed seismic motion in the time domain to obtain the Fourier coefficient of the amplitude-adjusted seed seismic motion at each site; The Fourier coefficients of the seed seismic motion without amplitude adjustment at each site and the Fourier coefficients of the seed seismic motion after amplitude adjustment are subjected to inverse Fourier transformation to obtain the first intermediate seismic motion after response spectrum matching of the seed seismic motion at each site.

3. The method for generating multi-point ground motion based on response spectrum matching with spatial variation based on S transform according to claim 2 is characterized in that: The step of obtaining the second intermediate seismic motion after response spectrum matching of the coherent seismic motion at each station by using a single-point response spectrum matching seismic motion algorithm according to the coherent seismic motion at each station and the target response spectrum specifically includes: Performing Fourier transform on the coherent seismic motion of each station to obtain the Fourier coefficient of the coherent seismic motion of each station, and calculating the actual response spectrum of the coherent seismic motion of each station; According to the target response spectrum of each station and the actual response spectrum of the coherent ground motion, a second S transform coefficient amplitude scaling function of each station is calculated, and according to the second S transform coefficient amplitude scaling function of each station, it is determined whether the S transform coefficient needs to be adjusted in amplitude; Performing S transformation on the coherent seismic motion at the frequency point where amplitude adjustment is required at each station to obtain the S transformation coefficient of the coherent seismic motion, performing amplitude adjustment on the S transformation coefficient of the coherent seismic motion using the second S transformation coefficient amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient of the coherent seismic motion in the time domain to obtain the Fourier coefficient of the amplitude-adjusted coherent seismic motion at each station; The Fourier coefficients of the coherent seismic motion without amplitude adjustment at each site and the Fourier coefficients of the coherent seismic motion after amplitude adjustment are subjected to inverse Fourier transformation to obtain the second intermediate seismic motion after response spectrum matching of the coherent seismic motion at each site.

4. The method for generating multi-point ground motion based on response spectrum matching and spatial variation based on S transform according to claim 1 is characterized in that: The method of updating the phase of the S transform coefficient of the second intermediate seismic motion of each station by using the synchronous phase shuffling factor of each station, and integrating the phase-updated S transform coefficient of each station in the time domain to obtain the phase-updated Fourier coefficient of each station specifically includes: The S transform coefficient of the second intermediate seismic motion of each station is phase-updated by using the synchronous phase shuffling factor of each station to obtain the S transform coefficient of the second intermediate seismic motion of each station after phase update: Among them, x s,new2,z ′(pΔ f ,qΔ t ) represents the S transformation coefficient of the second intermediate ground motion after the phase update of the z-th station; The S transform coefficients of the second intermediate seismic motion after the phase of each station is updated are integrated in the time domain to obtain the Fourier coefficients of the second intermediate seismic motion after the phase of each station is updated: in, represents the Fourier coefficient of the second intermediate ground motion after phase update at the z-th station; According to the frequency symmetry of Fourier transform, let the Fourier coefficient of negative frequency Equal to the Fourier coefficient of the positive frequency 5. The method for generating multi-point ground motion based on response spectrum matching and spatial variation based on S transform according to claim 1 is characterized in that: The inverse Fourier transform is performed on the phase-updated Fourier coefficients of each station to obtain the third intermediate seismic motion of each station, the error judgment is performed on the third intermediate seismic motion of each station, and the third intermediate seismic motion that meets the error requirement is used as the target seismic motion of the corresponding station, specifically including: Performing inverse Fourier transformation on the Fourier coefficients of the second intermediate seismic motion after phase update at each station to obtain the third intermediate seismic motion at each station; Calculate the actual response spectrum of the third intermediate earthquake motion at each station, and record the time when the peak response corresponding to the frequency point occurs; For each site, at all frequency points where response spectrum matching is required, determining whether the maximum relative error between the actual response spectrum value of the third intermediate seismic motion and the target response spectrum value is not greater than a set error tolerance value; If yes, taking the third intermediate seismic motion as the target seismic motion of the corresponding site; If not, the third intermediate seismic motion is taken as the coherent seismic motion of the corresponding site, and the calculation is repeated to obtain a new third intermediate seismic motion until the maximum relative error between the actual response spectrum value of the third intermediate seismic motion and the target response spectrum value is no greater than the set error tolerance value.

6. A response spectrum matching spatial variation multi-point earthquake motion generation system based on S transform, characterized in that: The response spectrum matching spatial variation multi-point earthquake motion generation system based on S transform includes: The first intermediate seismic motion module is used to obtain the first intermediate seismic motion after the response spectrum matching of the seed seismic motion of each station by using the single-point response spectrum matching seismic motion algorithm according to the obtained seed seismic motion and the target response spectrum of each station; Coherent seismic motion module: used to calculate the time-frequency power spectrum density of the first intermediate seismic motion of each station, combine the time-frequency power spectrum density of each station and the spatial coherence between two stations, and use spectral representation method to simulate the coherent seismic motion of each station; A second intermediate seismic motion module: configured to obtain, according to the coherent seismic motion of each site and the target response spectrum, a second intermediate seismic motion after response spectrum matching of the coherent seismic motion of each site by using a single-point response spectrum matching seismic motion algorithm; Synchronous phase shuffling module: used to perform S transformation on the coherent seismic motion and the second intermediate seismic motion of each station respectively, obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculate the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station; Phase update module: used to update the phase of the S transform coefficient of the second intermediate seismic motion of each station by using the synchronous phase shuffling factor of each station, and integrate the S transform coefficient after the phase update of each station in the time domain to obtain the Fourier coefficient after the phase update of each station; Target seismic motion module: used to perform inverse Fourier transform on the Fourier coefficients of each station after phase update to obtain the third intermediate seismic motion of each station, perform error judgment on the third intermediate seismic motion of each station, and use the third intermediate seismic motion that meets the error requirement as the target seismic motion of the corresponding station; The calculating of the time-frequency power spectrum density of the first intermediate seismic motion of each station, combining the time-frequency power spectrum density of each station and the spatial coherence between two stations, and using a spectral representation method to simulate and obtain the coherent seismic motion of each station, specifically includes: Perform an S transform on the first intermediate seismic motion of each station to obtain an S transform coefficient of the first intermediate seismic motion of each station: Where z represents the zth site, z = 1,…,n, n represents the number of sites; p represents pΔ f The corresponding frequency interval number, p = -N / 2+1, ..., N / 2, N represents the signal length; Δ f represents the frequency interval; q represents qΔ t The corresponding number of time intervals, q = 1, ..., N; Δ t Indicates the time interval; x s,new1,z (pΔ f ,qΔ t ) represents the S-transform coefficient of the first intermediate ground motion of the z-th station; ST(·) represents the symbol of the S-transform operator; x new1,z (qΔ t ) represents the first intermediate ground motion of the zth station; j represents the frequency interval number; Represents x new1,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficient at ; i represents the imaginary number sign; The time-frequency power spectrum density of the first intermediate seismic motion at each station is calculated according to the S-transform coefficient of the first intermediate seismic motion at each station: Among them, TFPSD z represents the time-frequency power spectrum density of the first intermediate ground motion at the z-th station, * represents the complex conjugate operation, and κ′ is the parameter of the window function selected in the S transform; Calculate the target coherence function matrix between two sites with a spatial distance of Δ, where the target coherence function matrix is ​​used to represent the spatial coherence between the two sites: |C(pΔ f ,Δ)|=tanh(tanh -1 (|C Bias (pΔ f ,D)|-e)); θ(pΔ f )=κ″(1+(pΔ f / f0′) B ) -1 / 2 ; Among them, |Γ(pΔ f ,Δ)| represents the unbiased target coherence function matrix between two sites with a spatial distance of Δ, |Γ Biαs (pΔ f ,Δ)| represents the biased hysteresis coherence model between the ground motions of two stations with a spatial distance of Δ, θ(pΔ f ), ε, A, α0, κ″, B, f0′ are all model parameters; Performing Cholesky decomposition on the target coherence function matrix to obtain a lower triangular matrix; For each site, coherent ground motion is obtained by superimposing sine waves of different frequency components, wherein the amplitude information of the sine wave of each frequency component is determined by the time-frequency power spectrum density, the lower triangular matrix and the sampling frequency of the seed ground motion, and the phase information of the sine wave of each frequency component is determined by the lower triangular matrix; The step of performing S transformation on the coherent seismic motion and the second intermediate seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, and calculating the synchronous phase shuffling factor of each station according to the S transformation coefficient of the coherent seismic motion and the S transformation coefficient of the second intermediate seismic motion of each station, specifically includes: Perform S transformation on the coherent seismic motion of each station to obtain the S transformation coefficient of the coherent seismic motion of each station: Among them, x s,old2,z (pΔ f ,qΔ t ) represents the S transform coefficient of the coherent ground motion at the z-th station; x old2,z (qΔ t ) represents the coherent ground motion at the z-th station; Represents x old2,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficients at ; According to the S transform coefficient of the coherent seismic motion of each station, the phase of the S transform coefficient of the coherent seismic motion of each station is calculated: Among them, θ z (pΔ f ,qΔ t ) represents the phase of the S transform coefficient of the coherent ground motion at the z-th station, represents the imaginary part of the S-transform coefficient of the coherent ground motion at the z-th station, represents the real part of the S-transform coefficient of the coherent ground motion at the z-th station; Perform S transformation on the second intermediate seismic motion of each station to obtain the S transformation coefficient of the second intermediate seismic motion of each station: Among them, x s,new2,z (pΔ f ,qΔ t ) represents the S transformation coefficient of the second intermediate ground motion at the zth station, x new2,z (qΔ t ) represents the second intermediate earthquake motion at the z-th station; Represents x new2,z (qΔ t ) at the frequency point (j+p)Δ f The Fourier coefficients at ; According to the S transformation coefficient of the second intermediate seismic motion of each station, the phase of the S transformation coefficient of the second intermediate seismic motion of each station is calculated: Among them, φ z (pΔ f ,qΔ t ) represents the phase of the S transform coefficient of the second intermediate ground motion at the z-th station, represents the imaginary part of the S-transform coefficient of the second intermediate ground motion at the z-th station, represents the real part of the S-transform coefficient of the second intermediate ground motion at the z-th station; According to the phase of the coherent seismic motion at each station and the phase of the second intermediate seismic motion, the synchronous phase shuffling factor of each station is calculated: Among them, α(pΔ f ,qΔ t ) represents the synchronization phase shuffling factor of the zth site.

7. A terminal, characterized in that: The terminal includes: a memory, a processor, and a response spectrum matching spatial variation multi-point seismic motion generation program based on S transform stored in the memory and executable on the processor. When the response spectrum matching spatial variation multi-point seismic motion generation program based on S transform is executed by the processor, the steps of the response spectrum matching spatial variation multi-point seismic motion generation method based on S transform as described in any one of claims 1 to 5 are implemented.

8. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a response spectrum matching spatially varying multi-point seismic motion generation program based on S transform, and when the response spectrum matching spatially varying multi-point seismic motion generation program based on S transform is executed by a processor, the steps of the response spectrum matching spatially varying multi-point seismic motion generation method based on S transform as described in any one of claims 1 to 5 are implemented.

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