Response spectrum matching ground motion generation method, system and terminal

Abstract

The present invention discloses a method, system and terminal for generating earthquake motion by matching response spectrum based on Fourier transform and S transform, the method comprising: calculating the Fourier coefficients and actual response spectrum of seed earthquake motion, performing S transform at the frequency point where amplitude adjustment is required, integrating the S transform coefficients after amplitude adjustment to obtain the adjusted Fourier coefficients, and finally performing inverse Fourier transform on the Fourier coefficients to obtain the target earthquake motion after response spectrum matching. The present invention combines the advantages of S transform and Fourier transform, greatly improves the calculation efficiency by using fast Fourier transform, uses S transform to perform sophisticated time-frequency localized adjustment on the signal, performs local S transform only at the frequency point where S transform coefficient amplitude adjustment is required, without performing S transform on the entire frequency domain, and realizes efficient, high-precision response spectrum matching that retains the non-stationary characteristics of the original earthquake motion time-frequency to the greatest extent.

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 earthquake motions with response spectrum matching based on Fourier transform and S transform. 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, especially the intensity non-stationary characteristics of 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] In frequency domain technology, the response spectrum matching algorithm based on Fourier transform is easy to destroy the intensity non-stationary characteristics of earthquake motion, because adjusting the Fourier coefficient of a certain frequency component is to modify all the frequency components of the entire earthquake motion duration. S transform is a time-frequency transform method similar to short-time Fourier transform. The response spectrum matching algorithm based on S transform iteratively adjusts the amplitude of S transform coefficient according to the time of occurrence of peak response under the natural vibration period of the structure and the ratio of response spectrum to standard response spectrum. The S transform is used to make fine time-frequency localized adjustment of seed earthquake motion, which can more accurately adjust the local earthquake motion and retain the non-stationary characteristics of seed earthquake motion to the greatest extent. However, the disadvantage of this algorithm is that each time the S transform coefficient is iteratively adjusted, the frequency points in the entire frequency domain must be S transformed to obtain the S transform coefficient, which greatly increases the calculation time and computing power requirements. S transform is essentially a combination of short-time Fourier transform and continuous wavelet transform. Therefore, S transform can be regarded as an extension of Fourier transform in time domain. The concepts of S transform and Fourier transform in frequency domain are consistent.

[0004] Therefore, the prior art still needs to be improved and developed. Summary of the invention

[0005] The main purpose of the present invention is to provide a method, system, terminal and computer-readable storage medium for generating response spectrum matching seismic motion based on Fourier transform and S transform, aiming to solve the problems that the response spectrum matching algorithm based on Fourier transform can easily destroy the intensity non-stationary characteristics of seismic motion and the response spectrum matching algorithm based on S transform has low computational efficiency.

[0006] To achieve the above-mentioned purpose, the present invention provides a method for generating earthquake motion by matching a response spectrum based on Fourier transform and S transform. The method for generating earthquake motion by matching a response spectrum based on Fourier transform and S transform comprises:

[0007] Acquire a seed earthquake motion and a target response spectrum, perform Fourier transform on the seed earthquake motion to obtain Fourier coefficients of the seed earthquake motion, and calculate an actual response spectrum of the seed earthquake motion;

[0008] Calculating an amplitude scaling function of an S transform coefficient according to the target response spectrum and the actual response spectrum, and determining whether an amplitude adjustment of the S transform coefficient is required according to the amplitude scaling function;

[0009] Performing an S transform on the seed earthquake motion at a frequency point where amplitude adjustment is required to obtain an S transform coefficient of the seed earthquake motion, performing amplitude adjustment on the S transform coefficient using the amplitude scaling function, and integrating the amplitude-adjusted S transform coefficient in the time domain to obtain an amplitude-adjusted Fourier coefficient;

[0010] The Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment are subjected to inverse Fourier transformation to obtain intermediate seismic motions, and error judgment is performed on the intermediate seismic motions, and the intermediate seismic motions that meet the error requirements are used as target seismic motions after response spectrum matching.

[0011] Optionally, the acquiring of the seed seismic motion and the target response spectrum, performing Fourier transform on the seed seismic motion to obtain the Fourier coefficients of the seed seismic motion, and calculating the actual response spectrum of the seed seismic motion specifically includes:

[0012] The obtained seed earthquake motion is recorded as , the target response spectrum is recorded as , s =1,…,Ns, where, express The corresponding sampling interval number, q=1,…N, where N is the length of the discrete seed ground motion signal; represents the sampling interval, 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, Ns represents the number of frequency points that need to be matched for the response spectrum;

[0013] Earthquake on the seeds Perform Fourier transform to obtain the Fourier coefficients of the seed earthquake motion ,in, express The corresponding frequency interval number, p=-N / 2+1,…,N / 2; represents the frequency interval, FT(·) represents the Fourier transform operator symbol;

[0014] According to the dynamic analysis response theory of single-degree-of-freedom linear elastic system, the actual response spectrum of the seed earthquake is calculated. , s = 1,…,Ns, for each frequency point , record the frequency point The time when the corresponding peak response occurs ,in, express The corresponding frequency interval number, express The corresponding sampling interval number.

[0015] Optionally, the calculating an amplitude scaling function of an S transform coefficient according to the target response spectrum and the actual response spectrum, and judging whether it is necessary to perform amplitude adjustment on the S transform coefficient according to the amplitude scaling function, specifically includes:

[0016] According to the target response spectrum and the actual response spectrum , calculate the scaling factor :

[0017] , s = 1,…,Ns;

[0018] According to the scaling factor , calculate the amplitude scaling function of the S transform coefficient :

[0019] ;

[0020] Among them, the scaling factor =

[0021] ;

[0022] 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;

[0023] 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 is the number of frequency points that need to be adjusted.

[0024] Optionally, performing S transformation on the seed seismic motion at the frequency point where amplitude adjustment is required to obtain S transformation coefficients of the seed seismic motion, performing amplitude adjustment on the S transformation coefficients using the amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficients in the time domain to obtain amplitude-adjusted Fourier coefficients, specifically includes:

[0025] At each frequency point where amplitude adjustment is required The seed earthquake motion is subjected to S transformation to obtain the S transformation coefficient of the seed earthquake motion. :

[0026] ;

[0027] Where ST(·) represents the symbol of the S-transform operator, express At the frequency point The Fourier coefficients at Interval number, i represents the imaginary number symbol;

[0028] The amplitude of the S transform coefficient is adjusted using the amplitude scaling function:

[0029] ;

[0030] in, represents the S transform coefficient after amplitude adjustment;

[0031] Integrate the amplitude-adjusted S transform coefficients in the time domain to obtain the amplitude-adjusted Fourier coefficients :

[0032] .

[0033] Optionally, the amplitude-adjusted S transform coefficients are integrated in the time domain to obtain the amplitude-adjusted Fourier coefficients. , and later:

[0034] According to the frequency conjugate symmetry of the Fourier transform of the real signal, the Fourier coefficient of the negative frequency is Equal to the Fourier coefficient of the positive frequency The conjugate of:

[0035] ;

[0036] in, Represents the conjugate operation.

[0037] Optionally, performing inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, performing error judgment on the intermediate seismic motion, and taking the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching specifically includes:

[0038] Performing inverse Fourier transformation on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain the intermediate ground motion;

[0039] Calculating the actual response spectrum of the intermediate ground motion and recording the time when the peak response corresponding to the frequency point occurs;

[0040] At all frequency points where response spectrum matching is required, it is determined whether the maximum relative error between the actual response spectrum value of the intermediate ground motion and the target response spectrum value is not greater than the set error tolerance value;

[0041] If yes, the intermediate ground motion is used as the target ground motion after response spectrum matching;

[0042] If not, the intermediate seismic motion is used as the seed seismic motion, and the calculation is repeated to obtain a new intermediate seismic motion until the maximum relative error between the actual response spectrum value of the intermediate seismic motion and the target response spectrum value is not greater than the set error tolerance value.

[0043] Optionally, the actual response spectrum includes an acceleration response spectrum;

[0044] The actual response spectrum of the seed earthquake is calculated according to the dynamic analysis response theory of the single-degree-of-freedom linear elastic system, specifically including:

[0045] For a single-degree-of-freedom linear elastic system, subjected to earthquake acceleration The equation of motion of the single-degree-of-freedom linear elastic system is expressed as:

[0046] ;

[0047] in, is the quality of the system, is the damping coefficient, ; is the stiffness, is the displacement response of the system, is the speed response of the system, is the acceleration response of the system, is the ground acceleration caused by the earthquake;

[0048] The motion equation is processed dimensionlessly to obtain the dimensionless motion equation:

[0049] ;

[0050] in, is the angular frequency of the system, It is a cycle;

[0051] The dimensionless motion equation is solved by numerical solution function to obtain the displacement response of the system at different periods. , take the maximum value to get the maximum displacement response :

[0052] ;

[0053] The maximum displacement response Multiply Get the maximum acceleration response , record the maximum acceleration response The actual response spectrum of the seed earthquake :

[0054] .

[0055] To achieve the above-mentioned purpose, the present invention further provides a response spectrum matching seismic motion generation system based on Fourier transform and S transform, and the response spectrum matching seismic motion generation system based on Fourier transform and S transform comprises:

[0056] Data acquisition and preprocessing module: used to acquire seed earthquake motion and target response spectrum, perform Fourier transform on the seed earthquake motion, obtain Fourier coefficients of the seed earthquake motion, and calculate the actual response spectrum of the seed earthquake motion;

[0057] Amplitude adjustment judgment module: used to calculate the amplitude scaling function of the S transform coefficient according to the target response spectrum and the actual response spectrum, and judge whether the amplitude of the S transform coefficient needs to be adjusted according to the amplitude scaling function;

[0058] Amplitude adjustment module: used to perform S transformation on the seed earthquake motion at the frequency point where amplitude adjustment is required to obtain the S transformation coefficient of the seed earthquake motion, use the amplitude scaling function to perform amplitude adjustment on the S transformation coefficient, and integrate the amplitude-adjusted S transformation coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient;

[0059] Target seismic motion generation module: used to perform inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, and perform error judgment on the intermediate seismic motion, and use the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching.

[0060] 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 seismic motion generation program based on Fourier transform and S transform stored in the memory and run on the processor, and when the response spectrum matching seismic motion generation program based on Fourier transform and S transform is executed by the processor, the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform as described above are implemented.

[0061] 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 seismic motion generation program based on Fourier transform and S transform, and when the response spectrum matching seismic motion generation program based on Fourier transform and S transform is executed by a processor, the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform as described above are implemented.

[0062] In the present invention, a seed seismic motion and a target response spectrum are obtained, a Fourier transform is performed on the seed seismic motion to obtain the Fourier coefficients of the seed seismic motion, and an actual response spectrum of the seed seismic motion is calculated; an amplitude scaling function of an S transform coefficient is calculated according to the target response spectrum and the actual response spectrum, and whether the S transform coefficient needs to be amplitude adjusted is determined according to the amplitude scaling function; an S transform is performed on the seed seismic motion at a frequency point where an amplitude adjustment is required to obtain the S transform coefficient of the seed seismic motion, the S transform coefficient is amplitude adjusted using the amplitude scaling function, and the amplitude-adjusted S transform coefficient is integrated in the time domain to obtain the amplitude-adjusted Fourier coefficient; an inverse Fourier transform is performed on the Fourier coefficients that have not been amplitude adjusted and the Fourier coefficients that have been amplitude adjusted to obtain an intermediate seismic motion, an error judgment is performed on the intermediate seismic motion, and the intermediate seismic motion that meets the error requirement is used as the target seismic motion after response spectrum matching. 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, performs the S transform only at the frequency point where the amplitude adjustment is required in each iteration process, obtains the adjusted Fourier coefficient by integrating the S transform coefficient after amplitude adjustment, and finally obtains the target seismic signal after response spectrum matching by inverse Fourier transforming the Fourier coefficient, greatly improves the calculation efficiency by utilizing the fast Fourier transform, utilizes the S transform to perform sophisticated time-frequency localized adjustment on the signal, performs local S transform only at the frequency point where the S transform coefficient amplitude adjustment is required, and there is no need to perform S transform on the entire frequency domain. Compared with the prior art, while retaining the time-frequency non-stationary characteristics of the seed seismic motion to the greatest extent, the calculation efficiency is greatly improved, and efficient, high-precision response spectrum matching that retains the time-frequency non-stationary characteristics of the original seismic motion to the greatest extent is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 It is a first flow chart of a preferred embodiment of the method for generating earthquake motion by matching response spectrum based on Fourier transform and S transform of the present invention;

[0064] Figure 2 is a second flow chart of a preferred embodiment of the method for generating earthquake motions by matching response spectrum based on Fourier transform and S transform of the present invention;

[0065] Figure 3 is a comparison diagram of the target response spectrum of the present invention and the response spectrum of the seed earthquake;

[0066] Figure 4 It is a comparison diagram of the properties of the target ground motion and the seed ground motion after the response spectrum matching of the present invention;

[0067] Figure 5 is a comparison diagram of the response spectrum of the target ground motion after the response spectrum matching of the present invention and the target response spectrum;

[0068] Figure 6 It is a time-frequency power spectrum density diagram of the target earthquake motion after the seed earthquake motion and the response spectrum are matched in the present invention;

[0069] Figure 7 It is a velocity time history comparison diagram of the target ground motion and the seed ground motion after the response spectrum matching of the present invention;

[0070] Figure 8 It is a displacement time history comparison diagram of the target ground motion and the seed ground motion after the response spectrum matching of the present invention;

[0071] Fig. 9 It is a summary diagram of the response spectrum matching results of the eleventh seed earthquake motion of the present invention;

[0072] Fig.10 is a third flow chart of a preferred embodiment of the method for generating earthquake motions by matching response spectrum based on Fourier transform and S transform of the present invention;

[0073] Fig.11 It is a structural diagram of a preferred embodiment of the response spectrum matching earthquake motion generation system based on Fourier transform and S transform of the present invention;

[0074] Fig.12 It is a structural diagram of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0075] 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.

[0076] Matching the response spectrum according to the code response spectrum (target response spectrum) in the seismic design code to obtain the seismic motion that fits the code 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. Frequency domain technology usually refers to Fourier transform (FT) of the selected seed seismic motion to obtain the Fourier coefficient of the seed seismic motion, and taking the ratio of the code response spectrum to the response spectrum of the seed seismic motion at a series of specific frequency points as the amplitude adjustment proportional factor, and then multiplying the Fourier coefficient of the initial seismic motion by the proportional factor. After iteratively adjusting the Fourier coefficient, the response spectrum of the seed seismic motion fits the code response spectrum, and the iteratively adjusted Fourier coefficient is inverse Fourier transform (IFT) to obtain the earthquake after the response spectrum is matched. The disadvantage of frequency domain technology is that it is easy to destroy the non-stationary characteristics of the seed seismic motion, especially the intensity non-stationary characteristics of the seismic motion. In order to solve this shortcoming, later researchers proposed a variety of time-frequency analysis tools for improvement, such as adjusting the wavelet transform coefficients or wavelet packet transform coefficients; adjusting the Hilbert-Huang transform coefficients and adjusting the S transform (ST) coefficients. Compared with the wavelet transform, the frequency in the S transform is equivalent to the frequency in the Fourier transform, which is an advantage that the wavelet transform does not have. In addition, the S transform can be regarded as an extension of the Fourier transform in the time domain, while the wavelet transform and the Hilbert-Huang transform do not have such characteristics. The response spectrum matching algorithm that adjusts the S transform coefficients iteratively adjusts the amplitude of the S transform coefficients based on the time when the peak response occurs under the natural vibration period of the structure and the ratio of the response spectrum to the standard response spectrum. However, the disadvantage of this algorithm is that the time required for calculation is quadratically increased with the length of the seismic signal. When the seismic duration considered is very long, the algorithm calculation will be very time-consuming. Another type of response spectrum matching technology is the time domain technology, such as iteratively superimposing the translated and scaled wavelet signal into the seed seismic signal to achieve the matching of the seismic response spectrum with the standard response spectrum. Some researchers have also decomposed the seed earthquake projection into a series of time functions, obtained the coefficients of these time functions and iteratively adjusted these coefficients. Compared with the frequency domain technology, the disadvantage of time domain technology is that it has lower computational efficiency and takes longer time.

[0077] The response spectrum matching algorithm based on Fourier transform is easy to destroy the intensity non-stationary characteristics of earthquake motion, because adjusting the Fourier coefficient of a certain frequency component is to modify all the frequency components of the entire earthquake motion duration. The response spectrum matching algorithm based on S transform uses S transform to make sophisticated time-frequency localized adjustments to the seed earthquake motion, which can more accurately adjust the earthquake motion locally and retain the non-stationary characteristics of the seed earthquake motion to the greatest extent. However, the disadvantage of this algorithm is that each time the S transform coefficient is iterated, the frequency points in the entire frequency domain must be S transformed to obtain the S transform coefficient, which greatly increases the calculation time and computing power requirements. The S transform is essentially a combination of short-time Fourier transform and continuous wavelet transform. Therefore, the S transform can be regarded as an extension of the Fourier transform in the time domain. The concepts of the S transform and the Fourier transform in the frequency domain are consistent.

[0078] In order to solve the above technical problems, the present invention provides a method for generating response spectrum matching seismic motion based on Fourier transform and S transform, which obtains seed seismic motion and target response spectrum, performs Fourier transform on the seed seismic motion to obtain Fourier coefficients of the seed seismic motion, and calculates the actual response spectrum of the seed seismic motion; calculates the amplitude scaling function of the S transform coefficient according to the target response spectrum and the actual response spectrum, and judges whether it is necessary to perform amplitude adjustment on the S transform coefficient according to the amplitude scaling function; performs S transform on the seed seismic motion at the frequency point where amplitude adjustment is required to obtain the S transform coefficient of the seed seismic motion, performs amplitude adjustment on the S transform coefficient using the amplitude scaling function, and integrates the amplitude-adjusted S transform coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient; performs inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, performs error judgment on the intermediate seismic motion, and uses the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching. 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, performs the S transform only at the frequency point where the amplitude adjustment is required in each iteration process, obtains the adjusted Fourier coefficient by integrating the S transform coefficient after amplitude adjustment, and finally obtains the target seismic signal after response spectrum matching by inverse Fourier transforming the Fourier coefficient, greatly improves the calculation efficiency by utilizing the fast Fourier transform, utilizes the S transform to perform sophisticated time-frequency localized adjustment on the signal, performs local S transform only at the frequency point where the S transform coefficient amplitude adjustment is required, and there is no need to perform S transform on the entire frequency domain. Compared with the prior art, while retaining the time-frequency non-stationary characteristics of the seed seismic motion to the greatest extent, the calculation efficiency is greatly improved, and efficient, high-precision response spectrum matching that retains the time-frequency non-stationary characteristics of the original seismic motion to the greatest extent is achieved.

[0079] The application content is further explained below through the description of embodiments in conjunction with the accompanying drawings.

[0080] A preferred embodiment of the method for generating earthquake motion based on response spectrum matching of Fourier transform and S transform of the present invention is as follows: Figure 1 and Figure 2 As shown, specifically including:

[0081] S1: Obtaining a seed seismic motion and a target response spectrum, performing Fourier transform on the seed seismic motion to obtain Fourier coefficients of the seed seismic motion, and calculating an actual response spectrum of the seed seismic motion.

[0082] In an implementation of this embodiment, the step of acquiring the seed seismic motion and the target response spectrum, performing Fourier transform on the seed seismic motion to obtain the Fourier coefficients of the seed seismic motion, and calculating the actual response spectrum of the seed seismic motion specifically includes:

[0083] S11: Record the obtained seed earthquake as , the target response spectrum is recorded as , s = 1,…,Ns, where, express The corresponding sampling interval number, q=1,…N, where N is the length of the discrete seed ground motion signal; represents the sampling interval, 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, Ns represents the number of frequency points that need to be matched for the response spectrum;

[0084] S12: Earthquake the seeds Perform Fourier transform to obtain the Fourier coefficients of the seed earthquake motion ,in, express The corresponding frequency interval number, p=-N / 2+1,…,N / 2; represents the frequency interval, FT(·) represents the Fourier transform operator symbol;

[0085] S13: Calculate the actual response spectrum of the seed earthquake according to the dynamic analysis response theory of the single-degree-of-freedom linear elastic system , 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 sampling interval number.

[0086] Specifically, the selected seed earthquake motion (original earthquake motion) is subjected to Fourier transform to obtain the Fourier amplitude spectrum, i.e., the Fourier coefficient. At the same time, the actual response spectrum, i.e., the acceleration response spectrum, of the seed earthquake motion is calculated according to the dynamic analysis response theory of the single degree of freedom linear elastic system (Single Degree of Freedom, SDOF). For each frequency point, the time when the maximum acceleration occurs is recorded.

[0087] S2: Calculate the amplitude scaling function of the S transform coefficient according to the target response spectrum and the actual response spectrum, and determine whether the amplitude of the S transform coefficient needs to be adjusted according to the amplitude scaling function.

[0088] In an implementation of this embodiment, the step of calculating an amplitude scaling function of an S transform coefficient according to the target response spectrum and the actual response spectrum, and determining whether the amplitude of the S transform coefficient needs to be adjusted according to the amplitude scaling function, specifically includes:

[0089] S21: According to the target response spectrum and the actual response spectrum , calculate the scaling factor :

[0090] , s = 1,…,Ns;

[0091] S22: According to the proportional factor , calculate the amplitude scaling function of the S transform coefficient :

[0092] ;

[0093] Among them, the scaling factor =

[0094] ;

[0095] 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, when When it is greater than 1 or less than 1, it controls the maximum and minimum values ​​of the scaling respectively;

[0096] S23: 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 is the number of frequency points that need to be adjusted.

[0097] Specifically, Figure 3 As shown, Figure 3 It is a comparison chart of the target response spectrum and the response spectrum of the seed earthquake motion. The ratio of the target response spectrum to the response spectrum of the seed earthquake motion at a series of specific frequency points is used as the amplitude adjustment proportional factor (scaling factor), and the amplitude scaling function of the S transform coefficient is obtained according to the proportional factor. The amplitude scaling function is used to determine whether the relevant frequency points need to be adjusted in amplitude, and the S transform is performed at the frequency points where the amplitude adjustment is required. The present invention uses the S transform to perform sophisticated time-frequency localized adjustment of the seed earthquake motion, which can more accurately adjust the earthquake motion locally and retain the non-stationary characteristics of the seed earthquake motion to the greatest extent. It also solves the problem that the existing response spectrum matching algorithm based on the S transform needs to perform the S transform on the frequency points of the entire frequency domain to obtain the S transform coefficient each time the S transform coefficient is iteratively adjusted. The S transform is only performed at the frequency points where the S transform coefficient amplitude adjustment is required, and there is no need to perform the S transform on the entire frequency domain, which reduces the calculation time and the requirements for computing power.

[0098] S3: Perform an S transform on the seed seismic motion at the frequency point where amplitude adjustment is required to obtain the S transform coefficient of the seed seismic motion, use the amplitude scaling function to perform amplitude adjustment on the S transform coefficient, and integrate the amplitude-adjusted S transform coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient.

[0099] In an implementation of this embodiment, performing an S transform on the seed seismic motion at a frequency point where amplitude adjustment is required to obtain an S transform coefficient of the seed seismic motion, performing amplitude adjustment on the S transform coefficient using the amplitude scaling function, and integrating the amplitude-adjusted S transform coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient, specifically includes:

[0100] S31: At each frequency point where amplitude adjustment is required The seed earthquake motion is subjected to S transformation to obtain the S transformation coefficient of the seed earthquake motion. :

[0101] ;

[0102] Where ST(·) represents the symbol of the S-transform operator, express At the frequency point The Fourier coefficients at Interval number, i represents the imaginary number symbol;

[0103] S32: Using the amplitude scaling function to adjust the amplitude of the S transform coefficient:

[0104] ;

[0105] in, represents the S transform coefficient after amplitude adjustment;

[0106] S33: Integrate the amplitude-adjusted S transform coefficients in the time domain to obtain the amplitude-adjusted Fourier coefficients :

[0107] ;

[0108] S34: No amplitude adjustment is performed at the frequency point where the amplitude adjustment is not required, and the Fourier coefficients corresponding to the frequency point where the amplitude adjustment is not required are Fourier coefficients that have not been amplitude adjusted.

[0109] Specifically, the S transform is essentially a combination of the short-time Fourier transform and the continuous wavelet transform, so it can be regarded as an extension of the Fourier transform in the time domain. The concepts of the two transforms in the frequency domain are consistent. This feature allows us to combine the advantages of the two transforms, using the great improvement in computational efficiency of the fast Fourier transform and the S transform to provide sophisticated time-frequency localized adjustment of the signal. The S transform is only performed at the frequency points where the S transform coefficient amplitude adjustment is required to obtain the S transform coefficient, without the need to perform the S transform on the entire frequency domain. The amplitude of the S transform coefficient is then adjusted by multiplying the S transform coefficient by the amplitude scaling function, and the adjusted S transform coefficient is integrated in the time domain to obtain the adjusted Fourier coefficient. The new ground motion signal (target ground motion) after spectrum matching is then obtained by inverse Fourier transform, thereby achieving efficient, high-precision response spectrum matching that retains the time-frequency non-stationary characteristics of the original ground motion to the greatest extent.

[0110] In one implementation of this embodiment, the amplitude-adjusted S transform coefficients are integrated in the time domain to obtain the amplitude-adjusted Fourier coefficients. , and later:

[0111] S35: According to the frequency conjugate symmetry of the Fourier transform of the real signal, the Fourier coefficients of the negative frequency Equal to the Fourier coefficient of the positive frequency The conjugate of:

[0112] ;

[0113] in, Represents the conjugate operation.

[0114] Specifically, the frequency symmetry of the Fourier transform is utilized to assign the Fourier coefficients of the positive frequencies to the corresponding Fourier coefficients of the negative frequencies.

[0115] S4: performing inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, performing error judgment on the intermediate seismic motion, and taking the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching.

[0116] In an implementation of this embodiment, performing inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, performing error judgment on the intermediate seismic motion, and using the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching specifically includes:

[0117] S41: Perform inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain the intermediate ground motion ;

[0118] S42: Calculate the actual response spectrum of the intermediate ground motion , and record the frequency points The time when the corresponding peak response occurs ;

[0119] S43: At all frequency points where response spectrum matching is required, it is determined whether the maximum relative error between the actual response spectrum value of the intermediate ground motion and the target response spectrum value is not greater than a set error tolerance value;

[0120] S44: If yes, taking the intermediate ground motion as the target ground motion after response spectrum matching;

[0121] S45: If not, the intermediate seismic motion is used as a seed seismic motion, and the calculation is repeated to obtain a new intermediate seismic motion, until the maximum relative error between the actual response spectrum of the intermediate seismic motion and the target response spectrum value is not greater than the set error tolerance value.

[0122] Specifically, for the adjusted Fourier coefficients Perform inverse Fourier transform on the Fourier coefficients (including the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment) to obtain the new seismic signal (intermediate seismic signal) , (·) represents the symbol of the inverse Fourier transform operator. Calculate the response spectrum of the intermediate ground motion signal , and record the time when the peak response occurs .

[0123] At all frequency points where response spectrum matching is required, determine whether the maximum relative error between the intermediate earthquake acceleration response spectrum value and the target response spectrum value is less than the set error tolerance (5%), that is, determine the following inequality:

[0124] , for s=1,2,…,Ns;

[0125] Where ε is the set error tolerance. If this inequality holds, the response spectrum matching result has not converged, and the intermediate ground motion signal is recorded as for Repeat the above steps S1 to S4 until the response spectrum matching result converges. When the response spectrum matching result converges, the final seismic signal That is the target ground motion signal after response spectrum matching.

[0126] like Figure 3-Figure 9 As shown, Figure 3 This is a comparison chart between the target response spectrum and the response spectrum of the seed earthquake. Figure 4 This is a comparison chart of the characteristics of the target ground motion and the seed ground motion after response spectrum matching. Figure 5 This is a comparison chart between the response spectrum of the target earthquake after response spectrum matching and the target response spectrum. Figure 6 (a) is the time-frequency power spectrum density diagram of the seed earthquake. Figure 6 (b) in the figure is the time-frequency power spectrum density diagram of the target ground motion after response spectrum matching. Figure 7 It is a velocity time history comparison diagram of the target ground motion and the seed ground motion after response spectrum matching. Figure 8 This is a comparison diagram of the displacement time history of the target ground motion and the seed ground motion after response spectrum matching. Fig. 9 The result of response spectrum matching of eleven seed earthquake motions is summarized in FIG. Among them, the response spectrum comparison diagram refers to the response spectrum acceleration comparison diagram. It can be seen that the present invention realizes the response spectrum matching with high efficiency and high precision and retains the time-frequency non-stationary characteristics of the original earthquake motion to the greatest extent.

[0127] In an implementation of this embodiment, the actual response spectrum includes an acceleration response spectrum;

[0128] The actual response spectrum of the seed earthquake is calculated according to the dynamic analysis response theory of the single-degree-of-freedom linear elastic system, specifically including:

[0129] S131: For a single-degree-of-freedom linear elastic system, under the action of earthquake acceleration, the motion equation of the single-degree-of-freedom linear elastic system is expressed as:

[0130] ;

[0131] in, is the quality of the system, is the damping coefficient, ; is the stiffness, is the displacement response of the system, is the speed response of the system, is the acceleration response of the system, is the ground acceleration caused by the earthquake (seismic acceleration);

[0132] S132: Perform dimensionless processing on the motion equation to obtain the dimensionless motion equation:

[0133] ;

[0134] in, is the angular frequency of the system, It is a cycle;

[0135] S133: Solve the dimensionless motion equation by numerical solution function to obtain the displacement response of the system at different periods , take the maximum value to get the maximum displacement response :

[0136] ;

[0137] S134: Maximum displacement response Multiply Get the maximum acceleration response , record the maximum acceleration response The actual response spectrum of the seed earthquake :

[0138] .

[0139] Specifically, for a single-degree-of-freedom vibration system, the motion equation is obtained under the action of earthquake acceleration, which is divided by m and the natural angular frequency of the system is introduced. and damping ratio , we can get the dimensionless motion equation; solve the above motion equation by numerical solution function, get the displacement response of the system at different periods, then take the maximum value to get the maximum displacement response, the maximum acceleration response is obtained by multiplying the maximum displacement response by The maximum acceleration response is obtained and is recorded as the acceleration response spectrum of the earthquake motion.

[0140] like Fig.10 As shown, the idea of ​​the present invention is: select a seed earthquake motion, perform Fourier transform on it to obtain its Fourier amplitude spectrum and phase spectrum, perform S transform on the frequency point where amplitude adjustment is required to obtain its S transform coefficient, iteratively adjust the S transform coefficient amplitude spectrum in such a time-frequency localized area, then integrate the adjusted S transform coefficient amplitude spectrum in the time domain back to the Fourier amplitude spectrum, and finally obtain the earthquake motion signal after response spectrum matching, i.e., the adjusted seed earthquake motion, through inverse Fourier transform.

[0141] In addition, based on the above-mentioned response spectrum matching seismic motion generation method based on Fourier transform and S transform, the present invention also provides a response spectrum matching seismic motion generation system based on Fourier transform and S transform. The preferred embodiment of the response spectrum matching seismic motion generation system based on Fourier transform and S transform is as follows: Fig.11 As shown, including:

[0142] Data acquisition and preprocessing module 01: used to acquire seed seismic motion and target response spectrum, perform Fourier transform on the seed seismic motion to obtain Fourier coefficients of the seed seismic motion, and calculate the actual response spectrum of the seed seismic motion;

[0143] Amplitude adjustment judgment module 02: used to calculate the amplitude scaling function of the S transform coefficient according to the target response spectrum and the actual response spectrum, and judge whether the amplitude of the S transform coefficient needs to be adjusted according to the amplitude scaling function;

[0144] Amplitude adjustment module 03: used to perform S transformation on the seed earthquake motion at the frequency point where amplitude adjustment is required to obtain the S transformation coefficient of the seed earthquake motion, use the amplitude scaling function to perform amplitude adjustment on the S transformation coefficient, integrate the amplitude-adjusted S transformation coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient; no amplitude adjustment is performed at the frequency point where amplitude adjustment is not required;

[0145] Target seismic motion generation module 04: used to perform inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, and perform error judgment on the intermediate seismic motion, and use the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching.

[0146] In addition, based on the above-mentioned response spectrum matching ground motion generation method and system based on Fourier transform and S transform, the present invention also provides a terminal accordingly, wherein a preferred embodiment of the terminal is as follows: Fig.12 As shown, it specifically includes a processor 10, a memory 20 and a display 30. Fig.12 Only some components of the terminal are shown, but it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0147] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 20 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, and a flash card (Flash Card) equipped on the terminal. Further, the memory 20 may also include both an internal storage unit of the terminal and an external storage device. The memory 20 is used to store application software and various types of data installed in the terminal, such as program codes of the storage terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In one embodiment, a response spectrum matching seismic motion generation program 40 based on Fourier transform and S transform is stored on the memory 20, and the response spectrum matching seismic motion generation program 40 based on Fourier transform and S transform can be executed by the processor 10, thereby realizing the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform in the present application.

[0148] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor or other data processing chip, and is used to run program codes or process data stored in the memory 20, such as executing a response spectrum matching seismic motion generation program 40 based on Fourier transform and S transform.

[0149] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, etc. The display 30 is used to display information on the terminal and to display a visual user interface. The components of the terminal communicate with each other through a system bus.

[0150] In one embodiment, when the processor 10 executes the response spectrum matching earthquake motion generation program 40 based on Fourier transform and S transform in the memory 20, the steps of the response spectrum matching earthquake motion generation method based on Fourier transform and S transform as described above are implemented.

[0151] The present invention also provides a computer-readable storage medium accordingly, wherein the computer-readable storage medium stores a response spectrum matching seismic motion generation program based on Fourier transform and S transform, and when the response spectrum matching seismic motion generation program based on Fourier transform and S transform is executed by a processor, the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform as described above are implemented.

[0152] 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 earthquake motion by matching response spectrum based on Fourier transform and S transform, characterized in that: The response spectrum matching ground motion generation method based on Fourier transform and S transform includes: Acquire a seed earthquake motion and a target response spectrum, perform Fourier transform on the seed earthquake motion to obtain Fourier coefficients of the seed earthquake motion, and calculate an actual response spectrum of the seed earthquake motion; Calculating an amplitude scaling function of an S transform coefficient according to the target response spectrum and the actual response spectrum, and determining whether an amplitude adjustment of the S transform coefficient is required according to the amplitude scaling function; Performing an S transform on the seed earthquake motion at a frequency point where amplitude adjustment is required to obtain an S transform coefficient of the seed earthquake motion, performing amplitude adjustment on the S transform coefficient using the amplitude scaling function, and integrating the amplitude-adjusted S transform coefficient in the time domain to obtain an amplitude-adjusted Fourier coefficient; Performing inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, performing error judgment on the intermediate seismic motion, and taking the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching; The step of acquiring the seed earthquake motion and the target response spectrum, performing Fourier transform on the seed earthquake motion to obtain the Fourier coefficient of the seed earthquake motion, and calculating the actual response spectrum of the seed earthquake motion specifically includes: The obtained seed earthquake motion is recorded as , the target response spectrum is recorded as , s = 1,…,Ns, where, express The corresponding sampling interval number, q=1,…N, where N is the length of the discrete seed ground motion signal; represents the sampling interval, 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, Ns represents the number of frequency points that need to be matched for the response spectrum; Earthquake on the seeds Perform Fourier transform to obtain the Fourier coefficients of the seed earthquake motion ,in, express The corresponding frequency interval number, p=-N / 2+1,…,N / 2; represents the frequency interval, FT(·) represents the Fourier transform operator symbol; According to the dynamic analysis response theory of single-degree-of-freedom linear elastic system, the actual response spectrum of the seed earthquake is calculated. , s = 1,…,Ns, for each frequency point , record the frequency points The time when the corresponding peak response occurs ,in, express The corresponding frequency interval number, express The corresponding sampling interval number.

2. The method for generating earthquake motion by matching response spectrum based on Fourier transform and S transform according to claim 1, characterized in that: The step of calculating an amplitude scaling function of an S transform coefficient according to the target response spectrum and the actual response spectrum, and judging whether it is necessary to adjust the amplitude of the S transform coefficient according to the amplitude scaling function, specifically includes: According to the target response spectrum and the actual response spectrum , calculate the scaling factor : ,s = 1,…,Ns; According to the scaling factor , calculate the amplitude scaling function of the S transform coefficient : ； Among them, the scaling factor ； 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; 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 is the number of frequency points that need to be adjusted.

3. The method for generating earthquake motion based on response spectrum matching of Fourier transform and S transform according to claim 2 is characterized in that: The step of performing S transformation on the seed earthquake motion at the frequency point where amplitude adjustment is required to obtain the S transformation coefficient of the seed earthquake motion, performing amplitude adjustment on the S transformation coefficient using the amplitude scaling function, and integrating the amplitude-adjusted S transformation coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient specifically includes: At each frequency point where amplitude adjustment is required The seed earthquake motion is subjected to S transformation to obtain the S transformation coefficient of the seed earthquake motion. : ； Where ST(·) represents the symbol of the S-transform operator, express At the frequency point The Fourier coefficient at , j represents the frequency interval number, i represents the imaginary number sign; The amplitude of the S transform coefficient is adjusted using the amplitude scaling function: ； in, represents the S transform coefficient after amplitude adjustment; Integrate the amplitude-adjusted S transform coefficients in the time domain to obtain the amplitude-adjusted Fourier coefficients : 。 4. The method for generating earthquake motion by matching response spectrum based on Fourier transform and S transform according to claim 3 is characterized in that: The amplitude-adjusted S transform coefficients are integrated in the time domain to obtain the amplitude-adjusted Fourier coefficients , and later: According to the frequency conjugate symmetry of the Fourier transform of the real signal, the Fourier coefficient of the negative frequency is Equal to the Fourier coefficient of the positive frequency The conjugate of: ； in, Represents the conjugate operation.

5. The method for generating earthquake motion by matching response spectrum based on Fourier transform and S transform according to claim 4, characterized in that: The inverse Fourier transform is performed on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain the intermediate seismic motion, and the error judgment is performed on the intermediate seismic motion, and the intermediate seismic motion that meets the error requirement is used as the target seismic motion after response spectrum matching, specifically including: Performing inverse Fourier transformation on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain the intermediate ground motion; Calculating the actual response spectrum of the intermediate ground motion and recording the time when the peak response corresponding to the frequency point occurs; At all frequency points where response spectrum matching is required, it is determined whether the maximum relative error between the actual response spectrum value of the intermediate ground motion and the target response spectrum value is not greater than the set error tolerance value; If yes, the intermediate ground motion is used as the target ground motion after response spectrum matching; If not, the intermediate seismic motion is used as the seed seismic motion, and the calculation is repeated to obtain a new intermediate seismic motion until the maximum relative error between the actual response spectrum value of the intermediate seismic motion and the target response spectrum value is not greater than the set error tolerance value.

6. The method for generating earthquake motion based on response spectrum matching of Fourier transform and S transform according to claim 1, characterized in that: The actual response spectrum includes an acceleration response spectrum; The actual response spectrum of the seed earthquake is calculated according to the dynamic analysis response theory of the single-degree-of-freedom linear elastic system, specifically including: For a single-degree-of-freedom linear elastic system, under the action of earthquake acceleration, the motion equation of the single-degree-of-freedom linear elastic system is expressed as: ； in, is the quality of the system, is the damping coefficient, ; is the stiffness, is the displacement response of the system, is the speed response of the system, is the acceleration response of the system, is the ground acceleration caused by the earthquake; The motion equation is processed dimensionlessly to obtain the dimensionless motion equation: ； in, is the angular frequency of the system, It is a cycle; The dimensionless motion equation is solved by numerical solution function to obtain the displacement response of the system at different periods. , take the maximum value to get the maximum displacement response : ； The maximum displacement response Multiply Get the maximum acceleration response , record the maximum acceleration response The actual response spectrum of the seed earthquake : 。 7. A response spectrum matching earthquake motion generation system based on Fourier transform and S transform, characterized in that: The response spectrum matching earthquake motion generation system based on Fourier transform and S transform comprises: Data acquisition and preprocessing module: used to acquire seed earthquake motion and target response spectrum, perform Fourier transform on the seed earthquake motion, obtain Fourier coefficients of the seed earthquake motion, and calculate the actual response spectrum of the seed earthquake motion; Amplitude adjustment judgment module: used to calculate the amplitude scaling function of the S transform coefficient according to the target response spectrum and the actual response spectrum, and judge whether the amplitude of the S transform coefficient needs to be adjusted according to the amplitude scaling function; Amplitude adjustment module: used to perform S transformation on the seed earthquake motion at the frequency point where amplitude adjustment is required to obtain the S transformation coefficient of the seed earthquake motion, use the amplitude scaling function to perform amplitude adjustment on the S transformation coefficient, and integrate the amplitude-adjusted S transformation coefficient in the time domain to obtain the amplitude-adjusted Fourier coefficient; Target seismic motion generation module: used for performing inverse Fourier transform on the Fourier coefficients without amplitude adjustment and the Fourier coefficients after amplitude adjustment to obtain intermediate seismic motion, and performing error judgment on the intermediate seismic motion, and taking the intermediate seismic motion that meets the error requirement as the target seismic motion after response spectrum matching; The step of acquiring the seed earthquake motion and the target response spectrum, performing Fourier transform on the seed earthquake motion to obtain the Fourier coefficient of the seed earthquake motion, and calculating the actual response spectrum of the seed earthquake motion specifically includes: The obtained seed earthquake motion is recorded as , the target response spectrum is recorded as , s = 1,…,Ns, where, express The corresponding sampling interval number, q=1,…N, where N is the length of the discrete seed ground motion signal; represents the sampling interval, 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, Ns represents the number of frequency points that need to be matched for the response spectrum; Earthquake on the seeds Perform Fourier transform to obtain the Fourier coefficients of the seed earthquake motion ,in, express The corresponding frequency interval number, p=-N / 2+1,…,N / 2; represents the frequency interval, FT(·) represents the Fourier transform operator symbol; According to the dynamic analysis response theory of single-degree-of-freedom linear elastic system, the actual response spectrum of the seed earthquake is calculated. , s = 1,…,Ns, for each frequency point , record the frequency points The time when the corresponding peak response occurs ,in, express The corresponding frequency interval number, express The corresponding sampling interval number.

8. A computer terminal, characterized in that: The computer terminal includes: a memory, a processor, and a response spectrum matching seismic motion generation program based on Fourier transform and S transform stored in the memory and executable on the processor. When the response spectrum matching seismic motion generation program based on Fourier transform and S transform is executed by the processor, the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform as described in any one of claims 1 to 6 are implemented.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a response spectrum matching seismic motion generation program based on Fourier transform and S transform, and when the response spectrum matching seismic motion generation program based on Fourier transform and S transform is executed by a processor, the steps of the response spectrum matching seismic motion generation method based on Fourier transform and S transform as described in any one of claims 1 to 6 are implemented.

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