A method for simulating and generating long-period ground motion

Abstract

The present invention discloses a method for simulating and generating long-period ground motions, comprising the following steps: First, obtain actual long-period ground motion records that match the design ground motion parameters of the target site; then, separate the surface waves and body waves from the above-mentioned actual long-period ground motion records through the polarization characteristics of surface wave particles to obtain surface wave components and body wave components; secondly, perform multivariate empirical mode decomposition on the obtained body wave components to obtain intrinsic mode function components; finally, perform time-frequency parameter estimation on the surface wave components and the intrinsic mode function components, introduce random phase angles, and generate long-period ground motion simulation records after superposition and combination; the surface wave components refer to retrograde Rayleigh wave, prograde Rayleigh wave, and Love wave components; the time-frequency parameters are instantaneous frequency and instantaneous amplitude; the present invention solves the technical problem that the existing ground motion simulation methods are difficult to efficiently, conveniently, and accurately generate simulation records that conform to the fully non-stationary characteristics of long-period ground motions when applied to actual engineering.

Description

Technical Field

[0001] The present invention relates to the field of seismic resistance of engineering structures, and particularly to a method for simulating and generating long-period ground motions. Background Art

[0002] Long-period ground motions (low-frequency ground motions) are long-duration far-field ground motions with a relatively long dominant period in a basin, having significant secondary effects of surface waves, and often having the characteristics of a relatively large earthquake source, a relatively long period, a long duration, strong destructiveness, and a relatively long propagation distance. The vibration period of long-period ground motions is usually between 1 second and 10 seconds, and even longer up to one or two minutes, which makes the waveforms caused by them on the ground relatively flat but with strong energy. This makes the forces exerted on structures such as buildings uniform and of a certain intensity, making it easier to cause resonance and damage to structures such as buildings and bridges, and may lead to phenomena such as soil liquefaction. In addition, long-period seismic waves have little energy loss during propagation and can still affect structures such as buildings at places far from the earthquake source, resulting in more serious hazards.

[0003] Taking the evaluation of the seismic performance of high-rise buildings under long-period ground motions in engineering applications as an example, due to their relatively high height, high-rise buildings have a relatively long natural vibration period and are prone to being similar to the period of long-period ground motions, thus causing resonance and then obvious seismic damage. However, the existing records of real vibration data of long-period ground motions are limited, and it is difficult to evaluate the seismic performance of high-rise buildings under long-period ground motions only based on the existing records. Therefore, a method for simulating and generating long-period ground motions for engineering applications has important scientific research significance and engineering application value.

[0004] There are mainly three types of existing methods for simulating and generating ground motions, namely the physical-based finite difference method, the source-based statistical simulation method, and the empirical relationship method.

[0005] Specifically, the physical-based finite difference method performs refined modeling on the fault, propagation medium, and site, and generates seismic wave records. It is a method for simulating and generating ground motions that can accurately restore the seismic environment. In contrast, the source-based statistical simulation method starts from the statistical characteristics of the earthquake source and generates a large number of ground motion time histories through statistical models and a large number of parameter settings. The most commonly used is the empirical relationship method. This method is based on historical ground motion records, obtains the attenuation relationship of ground motion parameters, and then synthesizes the response spectrum of the target site through seismic hazard analysis, and further generates the ground motion time history.

[0006] However, for long-period ground motions, all of the above methods have obvious defects. Although the physics-based finite-difference method can reproduce the seismic environment, the modeling workload is huge, and it is difficult to comprehensively consider the uncertainties during the occurrence of ground motions; the parameter setting of the source-based statistical simulation method is too complex and not suitable for engineering applications; although the empirical relationship method can describe the spectral characteristics of ground motions well, it is difficult to consider the complete non-stationarity of ground motions. Moreover, the long-period ground motion simulation generation method for engineering applications not only needs to be highly efficient and convenient to use, but also needs to reflect the complete non-stationary characteristics such as the significant long-duration surface wave pulse family of long-period ground motions.

[0007] In summary, how to efficiently and accurately generate ground motion time histories that conform to the characteristics of long-period ground motions has become an urgent problem to be solved by those skilled in the art. Summary of the Invention

[0008] The object of the present invention is to provide a long-period ground motion simulation generation method to solve the technical problem that in the prior art, when the ground motion simulation method is applied to actual engineering, it is difficult to efficiently, conveniently, and accurately generate simulation records that conform to the complete non-stationary characteristics of long-period ground motions.

[0009] To solve the above technical problems, the present invention adopts the following technical solutions:

[0010] A long-period ground motion simulation generation method includes the following steps:

[0011] S1. Obtain actual long-period ground motion records that match the design ground motion parameters of the target site;

[0012] S2. Separate the surface waves and body waves from the actual long-period ground motion records in step S1 through the particle polarization characteristics of surface waves to obtain surface wave components and body wave components;

[0013] S3. Perform multivariate empirical mode decomposition on the body wave components obtained in step S2 to obtain intrinsic mode function components;

[0014] S4. Perform time-frequency parameter estimation on the surface wave components obtained in step S2 and the intrinsic mode function components obtained in step S3, introduce random phase angles, and generate long-period ground motion simulation records after superposition and combination;

[0015] The surface wave components refer to retrograde Rayleigh wave, prograde Rayleigh wave, and Love wave components; the time-frequency parameters refer to instantaneous frequency and instantaneous amplitude.

[0016] Further, in step S1, obtaining actual long-period ground motion records that match the design ground motion parameters of the target site includes three vibration components They are the vibration components observed in the north-south NS direction and east-west EW direction of the seismic wave in the horizontal direction, and the up-down UD direction in the vertical direction, where j ∈ (NS, EW, UD).

[0017] Furthermore, in step S2, three vibration components of the actual long-period ground motion in step S1 are separated through the particle polarization characteristics of surface waves into surface wave components in the NS, EW, and UD directions respectively according to the following formula:

[0018]

[0019] In the formula, is the total surface wave time history in the NS, EW, and UD directions, is the time history of the surface wave component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3);

[0020] Then, body wave components in the NS, EW, and UD directions are obtained respectively according to the following formula:

[0021]

[0022] In the formula, are the three vibration components of the actual long-period ground motion record, is the total surface wave time history in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3).

[0023] Furthermore, before performing step S2, first, the three vibration components of the actual long-period ground motion record are preprocessed and then the actual long-period ground motion record in step S1 is separated into surface waves and body waves through the particle polarization characteristics of surface waves to obtain surface wave components and body wave components; specifically, it includes the following steps:

[0024] S201. Perform the S transform on the three vibration components of the actual long-period ground motion record according to the following formula, where j ∈ (NS, EW, UD), to obtain the transformation results of the three vibration components:

[0025]

[0026] where τ is the center position of the Gaussian window, f is the frequency (Hz), is the ground motion time history, t is the time, i is the imaginary unit, the square root of -1, that is, i 2 = -1, N, E, and U respectively represent the north, east, and vertically upward directions, and R and T respectively represent the radiation direction and transverse direction of surface wave propagation;

[0027] S202. Determine the angle of the main direction of the surface wave according to the equation listed below:

[0028]

[0029] where

[0030] θ I = θ r + π{1 - sign[sin(θ r )]} + π{1 - sign[cos(θ r )]}sign[sin(θ r )] / 2;

[0031]

[0032] where θ is the angle of the main direction of the surface wave, sign[·] is the functional function, x pr is the approximate azimuth of the seismic source, τ is the central position of the Gaussian window, and f is the frequency (Hz); is the complex value of the signal at the time interval τ and frequency f; Re[·] is the real part function, representing the difference in amplitude between the output signal and the input signal; Im[·] is the imaginary part function, indicating the phase shift of the signal after passing through the system; ^ represents the time domain conversion;

[0033] S203. Transform the three vibration components of the actual long-period ground motion record after the S transform into the surface wave propagation direction, that is, the radiation direction and the transverse direction, according to the following formula, to obtain the transformed results of the three vibration components of the actual long-period ground motion record after turning:

[0034]

[0035] where S(τ, f) is the complex value of the signal at the time interval τ and frequency f, R and T respectively represent the radiation direction and the transverse direction of the surface wave propagation, and N, E respectively represent the north direction and the east direction;

[0036] S204. Establish the NIP index of the ground motion record according to the surface wave particle polarization characteristics for Rayleigh waves and Love waves respectively. The Rayleigh waves include retrograde Rayleigh waves and prograde Rayleigh waves. The expression of the NIP index is as shown in the following formula:

[0037]

[0038] where S(τ, f) is the complex value of the signal at the time interval τ and frequency f, R and T respectively represent the radiation direction and the transverse direction of the surface wave propagation, N, E and U respectively represent the north direction, the east direction and the vertical upward direction, ^ represents the time domain conversion, A R (τ, f) is the amplitude of S R (τ, f), is The amplitude, Im[·] is the imaginary part function;

[0039] S205. Construct filters for extracting Rayleigh waves (including retrograde Rayleigh waves and prograde Rayleigh waves) and Love waves respectively, as shown in the following formula:

[0040]

[0041] where NIP is the non - linear exponent parameter, x represents the position at a certain moment in the input signal, γ represents the position of the center point of the cosine function, and Φ R (|NIP|) is the filter for Rayleigh waves, and Φ L (|NIP|) is the filter for Love waves;

[0042] S206. Use the filters described in step S205 and combine the NIP index obtained in step S204 and the angle of the main direction of the surface wave obtained in step S202 to filter the three vibration components of the long - period ground motion record, and separately isolate the surface wave components in the NS, EW, and UD directions according to the following formula:

[0043]

[0044] where is the total surface wave time history in the NS, EW, and UD directions, is the time history of the surface wave component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3);

[0045] Then, obtain the body wave components in the NS, EW, and UD directions respectively according to the following formula:

[0046]

[0047] where is the three vibration components of the actual long - period ground motion record, is the total surface wave time history in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3).

[0048] Furthermore, in step S3, perform multivariate empirical mode decomposition on the body wave components obtained in step S2 according to the following formula to obtain the intrinsic mode function components:

[0049]

[0050] where is the body wave component in the NS, EW, and UD directions, is the p - th order body wave intrinsic mode function component in the NS, EW, and UD directions, is the residual component after multi - experience mode decomposition, where p ∈ (1, 2, 3,... M), M is the maximum decomposition level of MEMD, and q ∈ (1, 2, 3).

[0051] Furthermore, step S4 specifically includes the following steps:

[0052] S401. For each of the surface wave components obtained in step S2 and the intrinsic mode function components obtained in step S3, use the AM - FM method to estimate the time - frequency parameters of the instantaneous frequency and instantaneous amplitude of each of the surface wave components and the body wave intrinsic mode function components as shown in the following formula:

[0053]

[0054] Where:

[0055] is the q - th order surface wave component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3), is the instantaneous amplitude of each of the surface wave components; is the time history of the surface wave component in the NS, EW, and UD directions of the instantaneous frequency;

[0056] is the p - th order body wave intrinsic mode function component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD), p ∈ (1, 2, 3,... M), M is the maximum decomposition level of MEMD, is the instantaneous amplitude of the body wave intrinsic mode function component, is the time history of the surface wave component in the NS, EW, and UD directions of the instantaneous frequency;

[0057] S402. On the basis of step S401, introduce a random phase angle uniformly distributed in the interval [0, 2π], combine the instantaneous amplitude, instantaneous frequency, and random phase angle, and generate a long - period ground motion simulation record according to the following formula after superposition and combination:

[0058]

[0059] Where:

[0060] is the simulated long - period ground motion simulation record, and Re[·] is the real - part function;

[0061] is the instantaneous amplitude of each of the surface wave components; refers to the instantaneous frequency of each of the said surface wave components, are the time histories of the surface wave components in the NS, EW, and UD directions of the instantaneous frequency, is the introduced random phase angle;

[0062] is the instantaneous amplitude of the body wave eigenmode function component, refers to the instantaneous frequency of the body wave eigenmode function component, are the time histories of the surface wave components in the NS, EW, and UD directions of the instantaneous frequency, is the introduced random phase angle;

[0063] is the residual component after multivariate empirical mode decomposition, where p ∈ (1, 2, 3,... M), M is the maximum decomposition level of MEMD, determined according to the user's tolerance limit for the residual component and generally, the larger M is, the smaller the residual component and the higher the simulation accuracy. j ∈ (NS, EW, UD), q ∈ (1, 2, 3).

[0064] The present invention has the following beneficial effects: Compared with the prior art, the present invention does not need to establish an empirical model of ground motion. Based on surface wave separation and modal decomposition, a large number of long-period ground motion time histories that conform to engineering practice are generated by adjusting the random phase information of actual ground motion records, effectively solving the problem of the lack of actual records of long-period ground motion, providing a reliable ground input technology for the seismic performance evaluation of high-rise structures in potential long-period ground motion occurrence areas, and thus having a wide application prospect in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] In order to make the objectives, technical solutions, and advantages of the invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings, where:

[0066] Figure 1 is a flowchart of the method for simulating and generating long-period ground motion of the present invention.

[0067] Figure 2 are the three vibration components of the long-period ground motion record with data number CHB022.

[0068] Figure 3 are the three vibration components of the long-period ground motion record with data number TKY015.

[0069] Figure 4 are the surface wave components separated from the long-period ground motion record with number CHB022 in the NS, EW, and UD directions respectively, as well as the total surface wave time history.

[0070] Figure 5 The surface wave components and the total surface wave time history separated from the long-period ground motion record numbered TKY015 in the NS, EW, and UD directions respectively.

[0071] Figure 6 The body wave components separated from the long-period ground motion record numbered CHB022 in the NS, EW, and UD directions respectively.

[0072] Figure 7 The body wave components separated from the long-period ground motion record numbered TKY015 in the NS, EW, and UD directions respectively.

[0073] Figure 8 The body wave IMF component of the long-period ground motion record numbered CHB022 in the NS direction.

[0074] Figure 9 The body wave IMF component of the long-period ground motion record numbered CHB022 in the EW direction.

[0075] Figure 10 The body wave IMF component of the long-period ground motion record numbered CHB022 in the UD direction.

[0076] Figure 11 The body wave IMF component of the long-period ground motion record numbered TKY015 in the NS direction.

[0077] Figure 12 The body wave IMF component of the long-period ground motion record numbered TKY015 in the EW direction.

[0078] Figure 13 The body wave IMF component of the long-period ground motion record numbered TKY015 in the UD direction.

[0079] Figure 14 The long-period ground motion simulation record generated from the long-period ground motion record numbered CHB022.

[0080] Figure 15 The long-period ground motion simulation record generated from the long-period ground motion record numbered TKY015.

[0081] Figure 16 The comparison diagram of the time-frequency distribution of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the NS direction.

[0082] Figure 17 The comparison diagram of the time-frequency distribution of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the EW direction.

[0083] Figure 18 It is a comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the UD direction.

[0084] Figure 19 It is a comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the NS direction.

[0085] Figure 20 It is a comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the EW direction.

[0086] Figure 21 It is a comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the UD direction. Specific implementation manners

[0087] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention.

[0088] It should be noted that similar reference numerals and letters indicate similar items in the following drawings. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings. In the description of the present invention, it should be noted that the orientation or positional relationship indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. is based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship in which the product of the invention is usually placed during use. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be construed as a limitation of the present invention. In addition, the terms "first", "second", "third", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance. In addition, the terms "horizontal", "vertical", etc. do not mean that the components are required to be absolutely horizontal or hanging, but can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined. In the description of the present invention, it should also be noted that unless otherwise clearly specified and limited, the terms "set", "installed", "connected", "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected or indirectly connected through an intermediate medium, and it can be the communication inside two components. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0089] The present invention can be applied to fields such as earthquake engineering, geotechnical engineering, structural engineering, and port and ocean engineering. For example: actual engineering scenarios such as subway and high-rise building structure design, dam safety assessment, geotechnical engineering, port and ocean engineering, etc., to help us predict and evaluate the possible damage degrees of different structural systems and environments during natural disasters.

[0090] The present invention solves the technical problem that the existing seismic ground motion simulation method is difficult to efficiently, conveniently and accurately generate a simulation record that conforms to the fully non-stationary characteristics of long-period seismic ground motion when applied to actual engineering.

[0091] As Figure 1 shown, based on the above solved technical problems, the present invention discloses a method for simulating and generating long-period seismic ground motion, including the following steps:

[0092] S1. Obtain an actual long-period seismic ground motion record that matches the design seismic ground motion parameters of the target site;

[0093] S2. Separate the surface waves and body waves from the actual long-period ground motion record in step S1 through the polarization characteristics of surface wave particles, obtaining the surface wave component and the body wave component;

[0094] S3. Perform multivariate empirical mode decomposition on the body wave component obtained in step S2 to obtain the intrinsic mode function components;

[0095] S4. Estimate the time-frequency parameters of the surface wave component obtained in step S2 and the intrinsic mode function components obtained in step S3, introduce random phase angles, and generate a long-period ground motion simulation record after superposition and combination;

[0096] Specifically, the surface wave component refers to the retrograde Rayleigh wave, prograde Rayleigh wave, and Love wave components; the time-frequency parameters refer to the instantaneous frequency and instantaneous amplitude.

[0097] Compared with the prior art, the present invention does not need to establish a ground motion empirical model. Based on surface wave separation and modal decomposition, a large number of long-period ground motion time histories that conform to engineering practice are generated by adjusting the random phase information of the actual ground motion record, effectively solving the problem of the lack of actual records of long-period ground motion, providing a reliable ground input technology for the seismic performance evaluation of high-rise structures in potential long-period ground motion occurrence areas, and thus having a wide application prospect in engineering practice. The highlight of the technical solution disclosed by the present invention is that it can directly generate a long-period ground motion simulation record according to the measured data, which better meets the actual needs of engineering.

[0098] Next, the above method will be elaborated in detail:

[0099] Specifically, in step S1, obtaining the actual long-period ground motion record that matches the design ground motion parameters of the target site includes three vibration components which are the vibration components observed in the north-south NS direction and east-west EW directions of the horizontal direction of the seismic wave, and the up-down UD direction of the vertical direction, where j ∈ (NS, EW, UD).

[0100] The NS (north-south) component refers to the vibration component of the seismic wave in the north-south direction. If the seismic wave propagates along the north direction, this vibration component will be along the north-south direction of the horizontal plane; the EW (east-west) component refers to the vibration component of the seismic wave in the east-west direction. If the seismic wave propagates along the east direction, this vibration component will be along the east-west direction of the horizontal plane; the UD (up-down) component refers to the vibration component of the seismic wave in the vertical direction, which represents the vibration vertically upward or downward from the ground.

[0101] Specifically, in step S2, through the polarization characteristics of surface wave particles from the three vibration components of the actual long-period ground motion record in step S1 In [it], the surface wave components in the NS, EW, and UD directions are separately separated according to Equation (1), and the body wave components in the NS, EW, and UD directions are obtained according to Equation (2):

[0102]

[0103] In Equations (1) and (2), are the three vibration components of the actual long-period ground motion record, is the total surface wave time history in the NS, EW, and UD directions, is the q-th order surface wave component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD) and q ∈ (1, 2, 3).

[0104] During the propagation of seismic waves, various waveforms will be generated, including body waves and surface waves, etc. Since body waves propagate along solids, their propagation speed is relatively fast, and they usually appear as waveforms with higher frequencies in seismic records.

[0105] The polarization characteristics of the surface wave particles used in Step S2 refer to that during the propagation of seismic waves, due to the non-uniformity of the ground structure, the seismic waves will be decomposed and reflected, and the components in different directions will have different polarization states. Using this characteristic, the surface wave components and body wave components in the seismic waves can be separated by decomposing and reconstructing the seismic waves.

[0106] Specifically, during the propagation of seismic waves, the surface wave particles move in an elliptical motion on the horizontal plane, while the body wave particles move in a straight line perpendicular to the ground direction. Then, during the propagation of seismic waves, by processing the seismic records in different directions, the waves propagating along the surface (also called surface waves) and the waves propagating along the volume (also called body waves) can be effectively separated.

[0107] Among them, in surface waves, there are three important wave forms, namely retrograde Rayleigh waves, prograde Rayleigh waves, and Love waves; retrograde Rayleigh waves (P waves) are the fastest and farthest - traveling waves in seismic waves and are also the first to be recorded. When an earthquake occurs, seismic energy generates initial vibrations that spread out from the earthquake source in all directions. In a solid medium, retrograde Rayleigh waves propagate in the form of compressional waves, that is, the direction of displacement and vibration of the material is the same as the direction of wave propagation; prograde Rayleigh waves (S waves) are waves in seismic waves with a speed second only to retrograde Rayleigh waves and are a type of shear wave. When retrograde Rayleigh waves reach the boundary in the medium, phenomena such as refraction, reflection, and diffraction occur, forming prograde Rayleigh waves. Its propagation direction is perpendicular to the vibration direction, and the propagation speed of prograde Rayleigh waves in a solid medium is slower than that of retrograde Rayleigh waves; Love waves (L waves) are also a type of shear wave, which is a transverse body wave of the medium and only exists on the surface or interface of a half - space medium. It is formed by the reflection and refraction of retrograde Rayleigh waves on the surface of a half - space medium. Love waves have the characteristics of long wavelength, slow attenuation, and easy diffusion on the ground surface, and have important applications in engineering seismic exploration and earthquake disaster research.

[0108] Furthermore, in order to more accurately separate surface waves and body waves, before performing step S2 and using equations (1) and (2) to separate the surface - wave components and body - wave components in the NS, EW, and UD directions, first, signal pre - processing is performed on the three vibration components of the actual long - period ground motion records. Methods such as S - transform, determination of the main direction angle of surface waves, and filtering are used respectively. The S - transform is used to convert the traditional time - amplitude representation method into a frequency - amplitude representation method, which can improve the signal - to - noise ratio. In this domain, there is usually a clear difference between surface - wave components and body - wave components, which can facilitate their separation; determining the main direction angle of surface waves is to reduce problems such as different degrees of noise interference and other interference that may exist in different directions, in order to provide more accurate and practical information for the subsequent data processing; the filtering operation is to remove noise or information of non - interest within the frequency range, so as to extract as purely as possible the surface - wave components and body - wave components.

[0109] Then, the signal pre - processing of the three vibration components of the actual long - period ground motion records includes the following steps:

[0110] S201. For the three vibration components of the actual long - period ground motion records Perform S - transform according to the following formula, where j ∈ (NS, EW, UD), and obtain the transformation results of the three vibration components:

[0111]

[0112] In formula (3), τ is the central position of the Gaussian window, and f is the frequency (Hz). is the ground motion time history, t is time, i is the imaginary unit, the square root of -1, i.e., i 2 = -1, N, E, and U represent the north, east, and vertically upward directions respectively, and R and T represent the radiation direction and transverse direction of surface wave propagation respectively.

[0113] Specifically, performing the S transform on the three vibration components of the actual long-period ground motion record means performing the S transform on the three-direction components (east-west direction, north-south direction, vertical direction) of the long-period ground motion respectively, and the time-frequency distribution diagrams of the three-direction components can be obtained, which can more accurately describe the energy distribution of the long-period ground motion signal at different times and frequencies.

[0114] The radiation direction of the surface wave propagation refers to the direction perpendicular to the wavefront (i.e., the propagation direction), that is, starting from the seismic source, the direction corresponding to the maximum amplitude of this seismic wave that can be detected; the transverse direction of the surface wave propagation refers to the direction perpendicular to the radiation direction of the vibration range of the plasma or spatial medium, that is, the direction parallel to the ground surface, and the ground displacement it causes is perpendicular to the propagation direction and equal in magnitude.

[0115] Here, the meaning, basic idea, and advantages of the S transform are elaborated in detail. The S transform is a time-frequency analysis method that can decompose a signal into components at different frequencies and times, and at the same time provides high time and frequency resolutions, and can better describe the time-varying characteristics of the signal; the basic idea of the S transform is to perform window analysis on the signal, divide the signal into several segments, perform Fourier transform on the signal in each time period, and then translate and weight the Fourier transform results in different time periods in frequency to obtain the time-frequency distribution diagram of the signal.

[0116] Among them, the translation and weighting operations can be achieved by adjusting the kernel function of the S transform. The kernel function of the S transform is a set of complex sequences used to adjust the weighting and translation operations of the Fourier transform. Commonly used kernel functions include the Gabor function, Morlet function, Mexican Hat function, etc.

[0117] Compared with the traditional Fourier transform, the S transform has the following advantages: the S transform can provide high time and frequency resolutions, can more accurately describe the energy distribution of the signal at different times and frequencies, and is very useful for the analysis of time-varying signals; the S transform can adapt to the analysis of non-stationary signals, has stronger adaptability to non-stationary signals, while the Fourier transform can only be applied to the analysis of stationary signals, so in the analysis of time-varying signals, the S transform has more advantages; the S transform can provide information in both the time domain and the frequency domain at the same time, and can understand the characteristics of the signal more comprehensively.

[0118] S202. Determine the angle of the main direction of the surface wave according to the equations listed in the following formulas (4) to (7):

[0119]

[0120] Among them,

[0121] θ I = θ r + π{1 - sign[sin(θ r )]} + π{1 - sign[cos(θ r )]}sign[sin(θ r )] / 2 (5)

[0122]

[0123] In Equations (4) to (7), θ is the angle of the main direction of the surface wave, sign[·] is the functional function, x pr is the approximate azimuth of the seismic source, τ is the central position of the Gaussian window, and f is the frequency (Hz); is the complex value of the signal at the time interval τ and frequency f; Re[·] is the real - part function, representing the difference in amplitude between the output signal and the input signal; Im[·] is the imaginary - part function, indicating the phase shift of the signal after passing through the system; ^ represents the time - domain conversion, for example:

[0124]

[0125] S203. Transform the three vibration components of the actual long - period ground motion record after the S - transform into the surface - wave propagation direction, that is, the radiation direction and the transverse direction, according to the following formula, to obtain the transformed results of the three vibration components of the actual long - period ground motion record after turning:

[0126]

[0127] In Equation (8), S(τ, f) is the complex value of the signal at the time interval τ and frequency f, R and T respectively represent the radiation direction and the transverse direction of the surface - wave propagation, and N, E respectively represent the north direction and the east direction.

[0128] S204. Establish the NIP index of the ground - motion record according to the polarization characteristics of surface - wave particles for Rayleigh waves and Love waves respectively. The Rayleigh waves include retrograde Rayleigh waves and prograde Rayleigh waves. The expression of the NIP index is as shown in the following formula:

[0129]

[0130] In Equations (9) and (10), S(τ, f) is the complex value of the signal at the time interval τ and frequency f, R and T respectively represent the radiation direction and the transverse direction of the surface - wave propagation, N, E and U respectively represent the north direction, the east direction and the vertically upward direction, ^ represents the time - domain conversion, A R (τ, f) is S R(τ,f) amplitude, is amplitude, Im[·] is the imaginary part function.

[0131] The NIP index refers to the non - linear index parameter, which is used to evaluate the degree of non - linear effect in ground motion records. It is calculated by analyzing the ratio of the high - order harmonic energy to the fundamental frequency energy of the seismic waveform. Specifically, after performing Fourier transform on the seismic waveform to obtain the spectrum, the NIP index calculates the proportion of the high - order harmonic energy in the total energy, thereby reflecting the non - linear degree of the seismic waveform. The value of the NIP index generally ranges from 0 to 1, where 0 represents complete linearity and 1 represents complete non - linearity.

[0132] S205. Construct filters for extracting Rayleigh waves (including retrograde Rayleigh waves and prograde Rayleigh waves) and Love waves respectively, as shown in the following formula:

[0133]

[0134]

[0135] In formula (11) and formula (12), NIP is the non - linear index parameter, x represents the position at a certain moment in the input signal, γ represents the position of the center point of the cosine function, Φ R (|NIP|) is the filter for Rayleigh waves, that is, Rayleigh waves, and Φ L (|NIP|) is the filter for Love waves, that is, Love waves.

[0136] [[ID=2,6]]S206. Use the filters described in step S205, combine with the NIP index obtained in step S204 and the angle of the main direction of the surface wave obtained in step S202 to filter the three vibration components of the long - period ground motion record, obtain the corresponding retrograde Rayleigh wave, prograde Rayleigh wave and Love wave surface wave components according to formula (1), and obtain the corresponding body wave components according to formula (2) based on the separated ground motion surface wave components.

[0137] Specifically, in step S3, perform multi - variable empirical mode decomposition on the body wave components obtained in step S2 according to the following formula to obtain the intrinsic mode function components:

[0138]

[0139] In formula (13), are the body wave components in the NS, EW, and UD directions, is the p - th order body wave intrinsic mode function component in the NS, EW, and UD directions, is the residual component after multivariate empirical mode decomposition, where p∈(1,2,3,...M), is the maximum decomposition level of MEMD, and q∈(1,2,3).

[0140] The Multivariate Empirical Mode Decomposition (MEMD) algorithm is an extension of the EMD (Empirical Mode Decomposition) algorithm from a single variable to any number of variables. Like the EMD, it suffers from the problem of modal mixing. The EMD method is considered to be a major breakthrough in linear and steady-state spectrum analysis based on Fourier transform since 2000. This method decomposes the signal based on the time scale characteristics of the data itself without presetting any basis functions. The purpose of performing EMD decomposition on the data signal is to obtain the Intrinsic Mode Functions (IMF). Simply put, the signal is composed of thousands of intrinsic mode functions, which overlap with each other to form a composite signal. The purpose of EMD decomposition is to decompose the intrinsic mode functions. It is precisely this characteristic that makes the EMD method theoretically applicable to the decomposition of any type of signal. Therefore, it has a very obvious advantage in processing non-stationary and nonlinear data. It is suitable for analyzing non-linear and non-stationary signal sequences and has a very high signal-to-noise ratio.

[0141] When analyzing seismic wave signals, the MEMD method adopted in the technical solution disclosed in the present invention can decompose nonlinear and non-stationary signals into a series of locally oscillating intrinsic mode function components (hereinafter referred to as IMF components). The frequency of each IMF function changes with time. The MEMD method can be used to decompose seismic wave signals into multiple IMF components, among which the body wave IMF component corresponds to the body wave propagating along the solid.

[0142] Specifically, the MEMD method can be used to analyze time series data and reveal its internal vibration characteristics. It can also adaptively decompose signals into fixed vibration modes, so it can process nonlinear and non-stationary signals while also well reflecting the vibration characteristics of the signal. In addition, the MEMD method is based on local feature decomposition, so it can well capture the local vibration characteristics in the signal. Using the MEMD method for data decomposition, various vibration modes can be extracted from the original data, such as natural frequency, damping ratio, mode shape, and other information. By analyzing the body wave IMF component, more accurate seismic wave spectrum information and propagation characteristics can be provided, thereby improving the accuracy and reliability of seismic motion analysis, thereby improving the results of earthquake hazard assessment and helping to formulate more scientific and reasonable earthquake response measures.

[0143] In specific implementation, the MEMD method can be implemented through various software, including Matlab, Python, etc. For example, the EMD function, CEEMDAN function, and EEMD function built in MATLAB, PyEMD, MEMD-Py, etc.

[0144] Specifically, step S4 is further elaborated in detail, and step S4 specifically includes the following steps:

[0145] S401. For each of the surface wave components obtained in step S2 and the intrinsic mode function components obtained in step S3, use the AM-FM method to estimate the time-frequency parameters of the instantaneous frequency and instantaneous amplitude of each of the surface wave components and the body wave intrinsic mode function components as shown in the following formula:

[0146]

[0147] In formulas (14) and (15):

[0148] is the q-th order surface wave component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD), q ∈ (1, 2, 3), is the instantaneous amplitude of each of the surface wave components; is the time history of the surface wave component in the NS, EW, and UD directions [[ID=Z7]]of the instantaneous frequency;

[0149] is the p-th order body wave intrinsic mode function component in the NS, EW, and UD directions, where j ∈ (NS, EW, UD), p ∈ (1, 2, 3,...M), and M is the maximum decomposition layer number of MEMD, is the instantaneous amplitude of the body wave intrinsic mode function component, is the time history of the surface wave component in the NS, EW, and UD directions of the instantaneous frequency.

[0150] Specifically, the AM-FM (Amplitude Modulation - Frequency Modulation) method is a signal decomposition technology aimed at decomposing a complex signal into its amplitude and frequency parts. This method can be applied to various fields, such as audio signal processing, image processing, biomedical signal processing, etc. The instantaneous amplitude refers to the amplitude size at a certain moment and can be used to analyze the instantaneous characteristics of seismic signals, such as studying the amplitude change of seismic signals in different time periods and extracting the instantaneous characteristic parameters of seismic signals.

[0151] S402. On the basis of step S401, a random phase angle uniformly distributed in the interval [0, 2π] is introduced. By combining the instantaneous amplitude, instantaneous frequency, and random phase angle and superimposing and combining them according to Equation (16), a long-period ground motion simulation record is generated:

[0152]

[0153] In Equation (16):

[0154] is the simulated long-period ground motion simulation record, and Re[·] is the real part function;

[0155] is the instantaneous amplitude of each of the surface wave components; refers to the instantaneous frequency of each of the surface wave components, is the time history of the surface wave component in the NS, EW, and UD directions of the instantaneous frequency, is the introduced random phase angle;

[0156] is the instantaneous amplitude of the body wave eigenmode function component, refers to the instantaneous frequency of the body wave eigenmode function component, is the time history of the surface wave component in the NS, EW, and UD directions of the instantaneous frequency, is the introduced random phase angle;

[0157] is the residual component after multivariate empirical mode decomposition; where p ∈ (1, 2, 3,... M), M is the maximum decomposition level of MEMD, which is determined according to the tolerance limit of the user for the residual component . Generally speaking, the larger M is, the smaller the residual component is, and the higher the simulation accuracy is; j ∈ (NS, EW, UD), q ∈ (1, 2, 3).

[0158] In signal processing, time-frequency parameter estimation is used to analyze the changes of a signal in time and frequency. When performing time-frequency parameter estimation on a signal, the signal is decomposed into some components, each component corresponding to a signal component within a specific time and frequency range, and the time-frequency characteristics of the component can be extracted. Introducing a random phase angle is to randomize the phase angle of the signal, making it no longer have the original phase information, making the analysis more objective and comprehensive, and reducing subjective interference.

[0159] Since the frequency and amplitude of seismic signals can vary over time, this time-variability is very important in seismic analysis. By performing the operations in step S4, performing time-frequency analysis on each component, and introducing a random phase angle, it is possible to more realistically simulate the waveform characteristics of seismic waves, more accurately describe the time-varying characteristics of seismic signals, improve the accuracy of seismic wave synthesis, provide a more refined input for subsequent seismic analysis, improve the results of seismic hazard prediction and engineering design, and enhance the accuracy and reliability of tasks such as seismic wave synthesis and seismic hazard prediction.

[0160] Adopting a long-period ground motion simulation generation method disclosed by the present invention has the following technical effects: The present invention solves the technical problem that existing ground motion simulation methods are difficult to efficiently, conveniently, and accurately generate simulation records that conform to the fully non-stationary characteristics of long-period ground motion when applied to practical engineering. Compared with the prior art, the present invention does not require establishing a ground motion empirical model. Based on surface wave separation and modal decomposition, a large number of long-period ground motion time histories that conform to engineering practice are generated by adjusting the random phase information of actual ground motion records, effectively solving the problem of the lack of actual records of long-period ground motion, providing a reliable ground input technology for the seismic performance assessment of high-rise structures in potential long-period ground motion occurrence areas, and thus having a wide application prospect in engineering practice. The highlight of the technical solution disclosed by the present invention is that it can directly generate long-period ground motion simulation records based on a single set of measured long-period ground motion record data, which is more in line with engineering actual needs and has greater application value. At the same time, due to the introduction of the surface wave separation method, the ground motion simulation records generated by the present invention can better retain the fully non-stationary characteristics of long-period ground motion compared with traditional methods.

[0161] In order to further elaborate in detail on the long-period ground motion simulation generation method of the present invention, as well as the effects and advantages brought by the method, the present invention discloses the following preferred embodiments.

[0162] Embodiment

[0163] This embodiment solves the technical problem that existing ground motion simulation methods are difficult to efficiently, conveniently, and accurately generate simulation records that conform to the fully non-stationary characteristics of long-period ground motion when applied to practical engineering.

[0164] As Figures 2 to 21 shown, based on the above technical problems to be solved, this embodiment discloses a long-period ground motion simulation generation method, including the following steps:

[0165] S1. Obtain actual long-period ground motion records that match the design ground motion parameters of the target site; the actual long-period ground motion records include three vibration components, which are the vibration components observed in the horizontal direction (north-south NS and east-west EW) and the vertical direction (up-down UD) of the seismic wave, and the expression is Where j∈(NS,EW,UD).

[0166] like Figure 2 and Figure 3 As shown, two sets of different types of long-period earthquake motion records (data numbers CHB022 and TKY015) with three vibration components (NS, EW, UD) are taken as the actual long-period earthquake motion records of the target site design earthquake motion parameters described in step S1. Figure 2 and Figure 3 In the figure, the vertical axis is Acc, which represents acceleration in cm / s. 2 The horizontal axis is time t, the unit is s. The larger the Acc value is, the stronger the ground vibration when the surface earthquake occurs.

[0167] in, Figure 2 The three vibration components of the long-period ground motion record with data number CHB022 are shown; Figure 3 The three vibration components of the long-period ground motion record with data number TKY015 are shown. Figure 2 and Figure 3 It can be seen that the events in which the two sets of data have stronger vibrations are different, and in the EW direction, the long-period seismic motion record numbered CHB022 has stronger vibrations, while in the UD direction, the long-period seismic motion record numbered TKY015 has more persistent and stronger vibrations. The two sets of long-period seismic motion records represent different types of vibrations.

[0168] S2. Record three vibration components of actual long-period earthquake motion After preprocessing the signal, the actual long-period ground motion recorded in step S1 is separated into surface waves and body waves by using the surface wave particle polarization characteristics to obtain surface wave components and body wave components;

[0169] Specifically, the surface wave components refer to the reverse Rayleigh wave, the forward Rayleigh wave and the Love wave components;

[0170] Specifically, the three vibration components of actual long-period ground motion records are first preprocessed using S-transformation, determination of the main direction angle of the surface roll, and filtering. The S-transform is used to convert the traditional time-amplitude representation into a frequency-amplitude representation, which can improve the signal-to-noise ratio. In this domain, there is usually a clear difference between the surface roll component and the body roll component, which can be easily separated. The main direction angle of the surface roll is determined to reduce the varying degrees of noise interference and other problems caused by different directions, so as to provide more accurate and practical information for subsequent data processing. The filtering operation removes noise or non-interesting information within the frequency range, thereby extracting the purest surface roll and body roll components as much as possible.

[0171] The specific steps are as follows:

[0172] S201. Perform S-transform on the three vibration components of two groups of different types of actual long-period ground motion records according to the aforementioned formula (3), where j ∈ (NS, EW, UD), to obtain the transformation results of the three vibration components;

[0173] S202. Determine the angle θ of the main direction of the surface wave according to the equations listed in the aforementioned formulas (4) to (7);

[0174] S203. Transform the three vibration components of the actual long-period ground motion record after S-transform to the surface wave propagation direction, i.e., the radiation direction and the transverse direction, according to the aforementioned formula (8), to obtain the transformation results of the three vibration components of the actual long-period ground motion record after turning;

[0175] S204. Establish the NIP index of the ground motion record for Rayleigh waves (including retrograde Rayleigh waves and prograde Rayleigh waves) and Love waves respectively according to the aforementioned formulas (9) and (10) based on the polarization characteristics of surface wave particles;

[0176] S205. Construct filters for extracting Rayleigh waves (including retrograde Rayleigh waves and prograde Rayleigh waves) and Love waves respectively, as shown in the aforementioned formulas (11) and (12);

[0177] S206. Use the filters described in step S205 and combine with the NIP index obtained in step S204 and the angle of the main direction of the surface wave obtained in step S202 to filter the three vibration components of the long-period ground motion record, and obtain the corresponding retrograde Rayleigh wave (Rayleigh-retro), prograde Rayleigh wave (Rayleigh-pro) and Love wave surface wave components according to the aforementioned formula (1), and obtain the corresponding body wave components according to the aforementioned formula (2) based on the separated surface wave components of the ground motion.

[0178] As Figures 4 to 7 shown, Figure 4 shows the surface wave components separated in the NS, EW, and UD directions respectively and the total surface wave time history of the long-period ground motion record numbered CHB022; Figure 5 shows the surface wave components separated in the NS, EW, and UD directions respectively and the total surface wave time history (Extracted surface wave) of the long-period ground motion record numbered TKY015; Figure 6 shows the body wave components separated in the NS, EW, and UD directions respectively of the long-period ground motion record numbered CHB022; Figure 7Shows the body wave components separated from the long-period ground motion record numbered TKY015 in the NS, EW, and UD directions respectively; from Figures 4 to 7 As can be seen from the results shown in, the long-period ground motion simulation generation method adopted in this embodiment can effectively identify the surface wave components (including retrograde Rayleigh waves, prograde Rayleigh waves, and Love waves) and body wave components, and obtain the surface wave part and body wave part through separation, and the separation result is good.

[0179] S3. Perform multivariate empirical mode decomposition on the body wave components obtained in step S2 to obtain intrinsic mode function components; specifically, perform multivariate empirical mode decomposition on the body wave components obtained in step S2 according to the aforementioned formula (13) to obtain intrinsic mode function components. In this embodiment, the MEMD method is implemented using Matlab software, and the maximum decomposition layer M of MEMD is 8 layers.

[0180] As Figures 8 to 13 shown, the multivariate empirical mode decomposition results, that is, IMF components, obtained after step S3 for the body wave part are given. Figure 8 Shows the body wave IMF components of the long-period ground motion record numbered CHB022 in the NS direction; Figure 9 Shows the body wave IMF components of the long-period ground motion record numbered CHB022 in the EW direction; Figure 10 Shows the body wave IMF components of the long-period ground motion record numbered CHB022 in the UD direction; Figure 11 Shows the body wave IMF components of the long-period ground motion record numbered TKY015 in the NS direction; Figure 12 Shows the body wave IMF components of the long-period ground motion record numbered TKY015 in the EW direction; Figure 13 Shows the body wave IMF components of the long-period ground motion record numbered TKY015 in the UD direction.

[0181] S4. Perform time-frequency parameter estimation on the surface wave components obtained in step S2 and the intrinsic mode function components obtained in step S3, introduce a random phase angle, and generate a long-period ground motion simulation record after superposition and combination; the time-frequency parameters refer to the instantaneous frequency and instantaneous amplitude; specifically, it includes the following steps:

[0182] S401. Use the AM-FM method for each of the surface wave components obtained in step S2 and the intrinsic mode function components obtained in step S3 to Figure 4 and Figure 5 shown for each of the surface wave components and body wave intrinsic mode function components to perform time-frequency parameter estimation on the instantaneous frequency and instantaneous amplitude according to the aforementioned formulas (14) and (15);

[0183] S402. On the basis of step S401, a random phase angle uniformly distributed in the interval [0, 2π] is introduced. By combining the instantaneous amplitude, instantaneous frequency, and the random phase angle, a long-period ground motion simulation record is generated according to the aforementioned formula (16) through superposition and combination, as Figure 14 and [[ID= shown.

[0184] ​ shows the long-period ground motion simulation record generated from the long-period ground motion record numbered CHB022; ​ shows the long-period ground motion simulation record generated from the long-period ground motion record numbered TKY015.

[0185] To verify the rationality of the generation results, ​ time-frequency distribution diagrams of two groups of original long-period ground motion records and the long-period ground motion simulation records automatically generated by the present invention are respectively given.

[0186] ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the NS direction; ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the EW direction; ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered CHB022 and the generated long-period ground motion simulation record in the UD direction.

[0187] ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the NS direction; ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the EW direction; ​ shows the comparison diagram of the time-frequency distributions of the original long-period ground motion record numbered TKY015 and the generated long-period ground motion simulation record in the UD direction.

[0188] From ​It can be seen that the long-period ground motion simulation records generated by the present invention are consistent with the original records in terms of amplitude and time-frequency non-stationary characteristics, and at the same time exhibit certain randomness. Therefore, the present invention can directly generate long-period ground motion simulation records based on a single set of measured long-period ground motion record data, which better meets the actual engineering requirements and has greater application value. At the same time, due to the introduction of the surface wave separation method, the ground motion simulation records generated by the present invention can better retain the complete non-stationary characteristics of long-period ground motion compared with traditional methods.

[0189] The long-period ground motion simulation generation method disclosed in this embodiment has the following technical effects: Compared with the prior art, the present invention does not need to establish a ground motion empirical model. Based on surface wave separation and modal decomposition, a large number of long-period ground motion time histories that meet the actual engineering requirements are generated by adjusting the random phase information of the actual ground motion records, effectively solving the problem of lack of actual long-period ground motion records, providing a reliable ground input technology for the seismic performance evaluation of high-rise structures in potential long-period ground motion occurrence areas, and thus having a wide application prospect in engineering practice. The highlight of the technical solution disclosed in the present invention is that it can directly generate long-period ground motion simulation records based on measured data, which better meets the actual engineering requirements.

[0190] It can be understood that the present invention is described through some embodiments. Those skilled in the art know that without departing from the spirit and scope of the present invention, various changes or equivalent substitutions can be made to these features and embodiments. Under the teaching of the present invention, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of the present invention. The embodiments described in the present invention are some embodiments of the present invention, rather than all embodiments. Usually, the components of the embodiments of the present invention described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed present invention, but merely represents the selected embodiments of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

Claims

1. A method for simulating and generating long-period earthquake motion, characterized in that: The following steps are involved: S1. Obtaining actual long-period seismic records that match the design seismic parameters of the target site; S2. Separating the actual long-period ground motion recorded in step S1 into surface waves and body waves by using the surface wave particle polarization characteristics to obtain surface wave components and body wave components; S3, performing multivariate empirical mode decomposition on the body wave components obtained in step S2 to obtain intrinsic mode function components; S4, performing time-frequency parameter estimation on the surface roll component obtained in step S2 and the intrinsic mode function component obtained in step S3, introducing a random phase angle, and superimposing and combining them to generate a long-period ground motion simulation record; The surface wave components refer to the backward Rayleigh wave, the forward Rayleigh wave and the Love wave components; the time-frequency parameters refer to the instantaneous frequency and the instantaneous amplitude.

2. The long-period earthquake motion simulation generation method according to claim 1, characterized in that: In step S1, the actual long-period earthquake record matching the design earthquake parameters of the target site is obtained, which includes three vibration components: are the vibration components of the seismic wave observed in the north-south NS direction and east-west EW direction in the horizontal direction, and the up-down UD direction in the vertical direction, where j∈(NS,EW,UD).

3. The long-period earthquake motion simulation generation method according to claim 2, characterized in that: In step S2, three vibration components are recorded from the actual long-period ground motion in step S1 through the surface wave particle polarization characteristics. In the equation, the surface wave components in the NS, EW, and UD directions are separated according to the following formula: Where, is the total surface wave time in the NS, EW, and UD directions, is the time history of the surface wave component in the NS, EW, and UD directions, where j∈(NS,EW,UD) and q∈(1,2,3); Then, the body wave components in the NS, EW, and UD directions are obtained according to the following formulas: Where, These are the three vibration components of the actual long-period earthquake record. is the total surface wave time in the NS, EW, and UD directions, where j∈(NS,EW,UD) and q∈(1,2,3).

4. The long-period earthquake motion simulation generation method according to claim 2, characterized in that: Before proceeding to step S2, first record the three vibration components of the actual long-period earthquake After signal preprocessing, the actual long-period ground motion recorded in step S1 is separated into surface waves and body waves by using the surface wave particle polarization characteristics to obtain surface wave components and body wave components. The specific steps include: S201. Record three vibration components of actual long-period earthquake motion Perform S transformation according to the following formula, where j∈(NS,EW,UD), and obtain the transformation results of the three vibration components: Where τ is the center position of the Gaussian window, f is the frequency (Hz), is the earthquake time history, t is time, i is the imaginary unit, the square root of -1, that is, i 2 = -1, N, E and U represent the north, east and vertical upward directions respectively, R and T represent the radial and lateral directions of surface wave propagation respectively; S202. Determine the angle of the main direction of the surface wave according to the following equation: in, i I =θ r +π{1-sign[sin(θ r )]}+π{1-sign[cos(θ r )]}sign[sin(θ r )] / 2; where θ is the angle of the main direction of the surface wave, sign[·] is the power function, and x pr is the approximate azimuth of the earthquake source, τ is the center position of the Gaussian window, and f is the frequency (Hz); is the complex value of the signal at time interval τ and frequency f; Re[·] is the real part function, representing the difference in amplitude between the output signal and the input signal; Im[·] is the imaginary part function, representing the phase offset after the signal passes through the system; ^ represents the time domain conversion; S203. The three vibration components of the actual long-period ground motion record that have undergone S-transformation are transformed to the surface wave propagation direction, i.e., the radial direction and the lateral direction, according to the following formula, to obtain the transformed results of the three vibration components of the actual long-period ground motion record after being turned: Where S(τ,f) is the complex value of the signal at time interval τ and frequency f, R and T represent the radial and lateral directions of surface wave propagation, respectively, and N and E represent the north and east directions, respectively. S204. Establish NIP indices for the earthquake records for Rayleigh waves and Love waves respectively based on the surface wave particle polarization characteristics. The Rayleigh waves include backward Rayleigh waves and forward Rayleigh waves. The expression of the NIP indices is as follows: Where S(τ,f) is the complex value of the signal at time interval τ and frequency f, R and T represent the radial direction and lateral direction of surface wave propagation, N, E and U represent the north, east and vertical upward directions, ^ represents the time domain conversion, A R (τ,f) is S R The magnitude of (τ,f), yes The amplitude of , Im[·] is the imaginary part function; S205. Construct filters for extracting Rayleigh waves and Love waves, respectively, as shown in the following equations: Among them, NIP is the nonlinear exponential parameter, x represents the position of the input signal at a certain moment, γ represents the position of the center point of the cosine function, Φ R (|NIP|) is the filter for Rayleigh waves, Φ L (|NIP|) is the filter of Love waves; S206. Filter the three vibration components of the long-period ground motion record using the filter in step S205 in combination with the NIP index obtained in step S204 and the angle of the main surface roll direction obtained in step S202, and separate the surface roll components in the NS, EW, and UD directions according to the following formulas: in, is the total surface wave time in the NS, EW, and UD directions, is the time history of the surface wave component in the NS, EW, and UD directions, where j∈(NS,EW,UD) and q∈(1,2,3); Then, the body wave components in the NS, EW, and UD directions are obtained according to the following formulas: in, These are the three vibration components of the actual long-period earthquake record. is the total surface wave time in the NS, EW, and UD directions, where j∈(NS,EW,UD) and q∈(1,2,3).

5. The long-period earthquake simulation generation method according to any one of claims 1 to 4, characterized in that: In step S3, multivariate empirical mode decomposition is performed on the body wave components obtained in step S2 according to the following formula to obtain intrinsic mode function components: in, is the body wave component in the NS, EW, and UD directions, is the p-th order body wave eigenmode function component in the NS, EW, and UD directions, is the residual component after multivariate empirical mode decomposition, where p∈(1,2,3,...M), is the maximum decomposition level of MEMD, and q∈(1,2,3).

6. The long-period earthquake motion simulation generation method according to claim 5, characterized in that: Step S4 specifically includes the following steps: S401, using the AM-FM method to perform the surface roll component obtained in step S2 and the intrinsic mode function component obtained in step S3 on each surface roll component. and body wave eigenmode function components The instantaneous frequency and instantaneous amplitude of are used to estimate the time-frequency parameters, as shown in the following formula: in: is the qth order surface wave component in the NS, EW, and UD directions, where j∈(NS,EW,UD), q∈(1,2,3), is the instantaneous amplitude of each of said surface roll components; is the time history of the surface wave component in the NS, EW, and UD directions The instantaneous frequency of is the p-th order body wave eigenmode function component in the NS, EW, and UD directions, where j∈(NS,EW,UD), p∈(1,2,3,...M), is the maximum decomposition level of MEMD, is the instantaneous amplitude of the body wave eigenmode function component, is the time history of the surface wave component in the NS, EW, and UD directions The instantaneous frequency of S402: Based on step S401, a random phase angle uniformly distributed in the interval [0, 2π] is introduced, and the instantaneous amplitude, instantaneous frequency, and random phase angle are combined and superimposed according to the following formula to generate a long-period ground motion simulation record: in: is the simulated long-period ground motion record generated by simulation, Re[·] is the real part function; is the instantaneous amplitude of each of said surface roll components; is the instantaneous frequency of each of the surface roll components, is the time history of the surface wave component in the NS, EW, and UD directions The instantaneous frequency, is the introduced random phase angle; is the instantaneous amplitude of the body wave eigenmode function component, is the instantaneous frequency of the body wave eigenmode function component, is the time history of the surface wave component in the NS, EW, and UD directions The instantaneous frequency, is the introduced random phase angle; is the residual component after multivariate empirical mode decomposition, where p∈(1,2,3,...M), M is the maximum decomposition level of MEMD, j∈(NS,EW,UD), and q∈(1,2,3).

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