Seismic oscillation stochastic simulation method considering uncertainty of evolution power spectrum parameters

Abstract

The invention discloses a seismic oscillation stochastic simulation method considering evolution power spectrum parameter uncertainty, and relates to the technical field of stochastic seismic oscillation simulation, comprising the following steps: determining a non-stationary seismic oscillation evolution power spectrum model and parameters thereof; selecting an actually measured seismic oscillation record from the seismic oscillation database; establishing an actual measurement seismic oscillation record evolution power spectrum estimation method; identifying an evolution power spectrum model parameter corresponding to each actually measured seismic oscillation record; determining an optimal probability distribution type of evolution power spectrum model parameters; establishing correlation among evolution power spectrum model parameters; generating random seismic oscillation representative samples with probability features in the same set; and comparing and verifying the effectiveness of the simulated random seismic oscillation sample and the engineering applicability. By adopting the seismic oscillation stochastic simulation method considering the uncertainty of the evolution power spectrum parameter, the defect of single engineering characteristic of a seismic oscillation sample caused by the traditional deterministic model parameter value is overcome.

Description

Technical Field

[0001] The invention relates to the technical field of random earthquake motion simulation, and in particular to a method for random earthquake motion simulation taking into account the uncertainty of evolving power spectrum parameters. Background Art

[0002] A large number of research results show that ground motion has obvious randomness and non-stationarity. Establishing a random ground motion model that can reasonably describe the characteristics of ground motion is the basis for conducting engineering structure analysis and reliability assessment. The evolutionary power spectrum model is based on characterizing the engineering characteristics of ground motion such as duration, amplitude, and spectrum, and has gradually become the most widely used random ground motion model in the field of earthquake engineering. For a given random ground motion model, the synthesis methods of ground motion mainly include spectral representation, intrinsic orthogonal decomposition, methods based on wavelet transform and its improved forms, and narrowband wave group superposition method.

[0003] At present, the deterministic values ​​obtained by fitting the code response spectrum are usually used as parameters of the seismic motion evolution power spectrum model. Although this is convenient for practical engineering applications, it ignores the uncertainty of magnitude, transmission path, and site mechanism, so that the randomness of the evolution power spectrum model parameters is ignored. The engineering characteristics of random seismic motion generated based on deterministic parameters are relatively simple and cannot reasonably reflect the natural variability of seismic motion.

[0004] In addition, the above-mentioned methods for synthesizing random seismic motions are essentially based on the Monte Carlo random sampling idea, which usually faces problems such as low efficiency in simulating high-dimensional random variables and incomplete sample probability information, making it difficult to achieve refined structural dynamic response analysis and reliability assessment at the probability level. Summary of the invention

[0005] The purpose of the present invention is to provide a random simulation method of seismic motion taking into account the uncertainty of evolving power spectrum parameters, to solve the problems raised in the above-mentioned background technology, and to overcome the defect of single engineering characteristics of seismic motion samples caused by traditional deterministic model parameter selection.

[0006] To achieve the above object, the present invention provides a random simulation method of ground motion considering the uncertainty of evolving power spectrum parameters, comprising the following steps:

[0007] Step 1: Determine the power spectrum model and parameters of non-stationary ground motion evolution;

[0008] Step 2: Select measured ground motion records from the ground motion database;

[0009] Step 3: Establish a power spectrum estimation method for the evolution of measured ground motion records based on wavelet packet transform (WPT);

[0010] Step 4: Based on frequency domain energy equality and genetic algorithm, the parameters of the evolving power spectrum model corresponding to each measured ground motion record are identified;

[0011] Step 5: Determine the optimal probability distribution type of the parameters of the evolution power spectrum model;

[0012] Step 6: Establish the correlation between the parameters of the evolving power spectrum model through the Copula function;

[0013] Step 7: Based on the spectral representation-random function theory, a representative sample of random ground motion with probability characteristics of the same set is efficiently generated;

[0014] Step 8: Comparative verification of the effectiveness and engineering applicability of simulated random seismic samples.

[0015] Preferably, in step 1, based on the evolution spectrum theory, the evolution power spectrum of the non-stationary ground motion is expressed as:

[0016]

[0017] in, is the unilateral evolution power spectrum of non-stationary ground motion; A(t,ω) is the time-frequency modulation function; S(ω) is the unilateral power spectrum of stationary ground motion;

[0018] The frequency domain energy distribution function corresponding to the non-stationary ground motion evolution power spectrum model is expressed as:

[0019]

[0020] Wherein, a, b and c are parameters related to the attenuation of earthquake energy, and b=a+0.001; c=0.005; ω represents the frequency; t* represents the peak arrival time of each harmonic; λ represents the parameter vector.

[0021] Preferably, the measured seismic records selected in step 2 meet the following requirements:

[0022] (1) The distance to the fault is greater than 10 km, which reduces the number of near-fault ground motions;

[0023] (2) The magnitude of the measured earthquake record is greater than 5, excluding earthquake motions with minor impact on the structure.

[0024] Preferably, in step 3, based on wavelet packet transform WPT, the earthquake acceleration time history x(t) is decomposed into a series of wavelet packet coefficients of different times and frequencies, and the definition of wavelet packet coefficients is as follows:

[0025]

[0026] in, represents the wavelet packet coefficient of the i-th frequency band under the j scale and translation parameter k; is the wavelet basis function.

[0027] Preferably, step 4 specifically includes:

[0028] The frequency domain energy distribution function corresponding to the evolving power spectrum obtained by wavelet packet transform WPT is expressed as:

[0029]

[0030] Among them, S(ω i ,t) represents the evolving power spectrum of the sub-signal; ω i represents the frequency band of the sub-signal; t represents the time series of the signal;

[0031] A genetic algorithm is used to identify parameters in the evolving power spectrum model:

[0032]

[0033] Preferably, in step 5, the optimal probability distribution type of each evolution power spectrum model parameter is determined by KS test and AIC criterion:

[0034] AIC=2k+2lnL;

[0035] Where L is the maximum likelihood function and k is the number of parameters in the model.

[0036] Preferably, step 6 specifically includes:

[0037] Based on the Copula theory, the binary joint distribution function F can be obtained by the marginal cumulative distribution function F of the two variables. 1 (x 1 ) and F 2 (x 2 )express:

[0038] F(x 1 ,x 2 )=C(F 1 (x 1 ),F 2 (x 2 ));

[0039] Where C(·) represents the Copula cumulative distribution function;

[0040] Two-dimensional random variable x 1 and x 2 The joint probability density function is expressed as:

[0041] f(x 1 ,x 2 )=c 12 {F1 (x 1 ),F(x 2 )}·f 1 (x 1 )·f(x 2 );

[0042] When determining the conditional density c 12 When {·}, the correlation between the two variables is established according to the Copula model, and the marginal distribution under the relevant conditions is expressed as:

[0043]

[0044] For two random variables x 1 and x 2 , after determining their marginal distributions and Copula functions, by giving x 1 The value of the parameter x under relevant conditions is obtained 2 The value of .

[0045] Preferably, in step 7, for a non-stationary ground motion process with zero mean, the source spectrum is expressed as:

[0046]

[0047] Where N represents the number of truncation terms; ω k = kΔω and Δω is the frequency step size; X k and Y k is a set of standard orthogonal random vectors; k = 1, 2, 3, ....., N.

[0048] Therefore, the present invention adopts the above-mentioned random simulation method of seismic motion considering the uncertainty of the evolving power spectrum parameters, which has the following beneficial effects:

[0049] (1) Based on the measured seismic records, the parameters of the power spectrum model of non-stationary seismic motion evolution are statistically modeled, which overcomes the defect of the single engineering characteristics of seismic motion samples caused by the traditional deterministic model parameter selection.

[0050] (2) Based on the spectral representation-random function theory, the dimensionality reduction simulation of random seismic motion is realized. The generated random seismic motion has rich probabilistic characteristics and can be perfectly combined with reliability analysis methods, such as the probability density evolution method and the direct probability integration method, to carry out reliability assessment of engineering structures.

[0051] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1The implementation process of the non-stationary ground motion random simulation method considering the uncertainty of the evolving power spectrum parameters of the present invention;

[0053] Figure 2 This is a schematic diagram of fitting model parameters based on a genetic algorithm according to an embodiment of the present invention;

[0054] Figure 3 is the model parameter ω corresponding to the measured ground motion in the embodiment of the present invention g The optimal probability distribution fitting diagram of ;

[0055] Figure 4 is the model parameter ξ corresponding to the measured ground motion in the embodiment of the present invention g The optimal probability distribution fitting diagram of ;

[0056] Figure 5 is an optimal probability distribution fitting diagram of the model parameter a corresponding to the measured ground motion in an embodiment of the present invention;

[0057] Figure 6 Comparison between the representative values ​​of the model parameters simulated in the embodiments of the present invention and the parameters actually fitted;

[0058] Figure 7 A typical sample of a non-stationary ground motion randomly simulated in an embodiment of the present invention;

[0059] Figure 8 The comparison between the mean and standard deviation of the earthquake motion simulated based on the parameter mean in the embodiment of the present invention and the target value;

[0060] Fig. 9 The comparison between the mean and standard deviation of the earthquake motion simulated based on parameter randomness in the embodiment of the present invention and the target value;

[0061] Fig.10 The comparison between the mean and standard deviation of the earthquake motion simulated based on parameter uncertainty in the embodiment of the present invention and the target value;

[0062] Fig.11 A comparison of the mean values ​​of the response spectra between the randomly simulated ground motion and the measured ground motion in an embodiment of the present invention;

[0063] Fig.12 1 is a comparison of the standard deviation of the response spectra between the randomly simulated ground motion and the measured ground motion in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0065] Unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0066] Example

[0067] See also Figure 1-12 The present invention provides a random simulation method of earthquake motion considering the uncertainty of evolving power spectrum parameters, comprising the following steps:

[0068] Step 1: Determine the power spectrum model and parameters of non-stationary ground motion evolution;

[0069] Based on the evolution spectrum theory, the evolution power spectrum of non-stationary ground motion can be expressed as:

[0070]

[0071] in, is the unilateral evolving power spectrum of non-stationary ground motion; A(t,ω) is the time-frequency modulation function; S(ω) is the unilateral power spectrum of stationary ground motion.

[0072] In this embodiment, the power spectral density function adopts the Clough-Penzien spectrum, that is:

[0073]

[0074]

[0075] Among them, ξ g and ω g are the damping ratio and predominant circular frequency of the site soil respectively; ξ f and ω f are the damping ratio and predominant circular frequency of the bedrock, respectively; generally, ω f =0.1ω g ξ f =ξ g . S 0 is the spectral intensity factor; A maxis the mean of the peak acceleration; r is the peak factor, usually r=3; ω represents the frequency.

[0076] In this embodiment, the time-frequency modulation function is expressed as:

[0077]

[0078]

[0079] Wherein, a, b and c are parameters related to the attenuation of earthquake energy, and b=a+0.001; c=0.005, ω represents frequency; t* represents the peak arrival time of each harmonic; and t represents time.

[0080] Therefore, the parameters that need to be determined in the power spectrum model of non-stationary ground motion evolution are λ=(ω g ,ξ g ,a).

[0081] The frequency domain energy distribution function corresponding to the power spectrum model of non-stationary ground motion evolution can be expressed as:

[0082]

[0083] Where t* represents the peak arrival time of each harmonic.

[0084] Step 2: Select measured ground motion records from the ground motion database;

[0085] The measured strong earthquake records were selected from the Pacific Earthquake Engineering Research Center (PEER) earthquake database, and the following principles were strictly followed:

[0086] (1) The distance between faults should be greater than 10 km to reduce the number of near-fault ground motions.

[0087] (2) The magnitude of the measured record is greater than 5 to exclude earthquake motions with lesser impact on the structure.

[0088] Through the above strict screening conditions, a total of 3003 measured ground motion records were selected. According to the average shear wave velocity (V s30 ), all selected measured seismic records were divided into 5 groups according to site conditions. Among the selected measured records, the magnitude range was 5 to 7.9, V s30 The range is 116.35m / s~1525.82m / s. Table 1 shows V s30 The range and number of measured strong earthquake records corresponding to different site conditions.

[0089] Table 1 Number of measured earthquake records under different site conditions

[0090]

[0091] Step 3: Establish a power spectrum estimation method for the evolution of measured ground motion records based on wavelet packet transform (WPT);

[0092] Based on WPT, the seismic acceleration time history x(t) can be decomposed into a series of wavelet packet coefficients with different times and frequencies. The definition of wavelet packet coefficients is as follows:

[0093]

[0094] in, represents the wavelet packet coefficient of the ith frequency band at j scale and translation parameter k (expressed in time); is a wavelet basis function, and Meyer wavelet is used in this embodiment.

[0095] The time interval between the centers of adjacent wavelet packet coefficients (dt ω ) and frequency interval (df ω ) can be defined as:

[0096]

[0097]

[0098] Where, dt represents the time interval of acceleration; f N represents the Nyquist sampling frequency. It is obvious from equations (8) and (9) that the frequency and time resolution cannot be improved at the same time. Considering the bandwidth and resolution comprehensively, when the number of decomposition levels is 7, the decomposition accuracy requirements of the non-stationary ground motion process can be met.

[0099] For the non-stationary ground acceleration time history x(t), it can be divided into 2j adjacent sub-bands based on WPT, and the frequency range of the i-th sub-band is between (i-1) / 2j)f and (i / 2j)f. The corresponding sub-signal can be expressed as follows after reconstruction:

[0100]

[0101] Based on the WPT theory and the definition of the evolving power spectrum, the relationship between the wavelet packet coefficients and the evolving power spectrum can be established from the energy perspective. For the non-stationary ground motion acceleration time history x(t), its energy E is calculated as follows:

[0102]

[0103] Based on formula (10) and the orthogonality of wavelet basis functions, the energy of the sub-signal corresponding to the sub-band can be expressed as:

[0104]

[0105] According to the definition of the evolving power spectrum, the energy of the sub-band signal can be expressed as:

[0106]

[0107] Where T is the duration of the non-stationary ground acceleration history; Δf i =f / 2 j .

[0108] Substituting formula (10) into formula (13), we get:

[0109]

[0110] Step 4: Based on frequency domain energy equality and genetic algorithm, the parameters of the evolving power spectrum model corresponding to each measured ground motion record are identified;

[0111] The frequency domain energy distribution function corresponding to the evolution power spectrum obtained by WPT can be expressed as:

[0112]

[0113] Among them, S(ω i ,t) represents the evolving power spectrum of the sub-signal; ω i represents the frequency band of the self-signal; t represents the time series;

[0114] If the frequency domain energy distributions obtained in step 2 and step 4 are the same, a genetic algorithm is used to identify the parameters in the evolving power spectrum model:

[0115]

[0116] Step 5: Determine the optimal probability distribution type of model parameters;

[0117] After identifying the model parameters corresponding to each measured seismic record, in order to establish an evolving power spectrum model with uncertain parameters, the gamma distribution (Gamma), generalized extreme value distribution (GEV), lognormal distribution (Lognormal), Weibull distribution (Weibull), and Gaussian distribution (Normal) are selected to fit the probability distribution of each parameter.

[0118] The KS test and AIC criterion are used to determine the optimal probability distribution type of each parameter of the evolution power spectrum model.

[0119] AIC=2k+2lnL (17)

[0120] Among them, L is the maximum likelihood function; k is the number of parameters in the model. Generally speaking, the model corresponding to the minimum AIC value is finally selected. The optimal probability distribution types of model parameters corresponding to ground motions under different site conditions are shown in Table 2.

[0121] Table 2 Optimal probability distribution type of parameters

[0122]

[0123]

[0124] When the probability model is Gaussian distribution and lognormal distribution, Par 1 and Par 2 Represents the mean and standard deviation respectively. When the probability model is Gamma and Weibull distribution, Par 1 and Par 2 are parameters about shape and scale respectively. When the probability model is GEV distribution, Par 1 、Par 2 and Par 3 represent shape parameter, scale parameter and location parameter respectively.

[0125] Step 6: Establish the correlation between model parameters through Copula function;

[0126] In general, the randomness and correlation of model parameters have a significant impact on the natural variability of random ground motion. The correlation between parameters can be established through Copula functions.

[0127] Based on the Copula theory, the binary joint distribution function F can be obtained by the marginal cumulative distribution function F of the two variables. 1 (x 1 ) and F 2 (x 2 )express:

[0128] F(x 1 ,x 2 )=C(F 1 (x 1 ),F 2 (x 2 )) (18)

[0129] Where C(·) represents the Copula cumulative distribution function. A two-dimensional random variable x 1 and x 2 The joint probability density function can be expressed as:

[0130] f(x 1 ,x 2 )=c 12 {F 1 (x 1 ),F(x 2 )}·f 1 (x 1)·f(x 2 ) (19)

[0131] When determining the conditional density c 12 When {·}, the correlation between the two variables can be established according to the Copula model. The marginal distribution under the correlation condition can be expressed as:

[0132]

[0133] Therefore, for two random variables x 1 and x 2 , after determining their marginal distributions and Copula functions, we can give x 1 The value of the parameter x under relevant conditions is obtained 2 The value of .

[0134] Establishing the correlation between variables depends on knowing the Copula distribution function and density function between the variables. This embodiment uses eight Copula distribution functions, namely Gaussian, Plackett, Frank, Clayton, Rotated Clayton, Gumbel, and RotatedGumbel, to establish the correlation between parameters.

[0135] The optimal Copula distribution function type between the parameters is determined by the AIC and BIC criteria. Usually, the smallest AIC and BIC values ​​correspond to the optimal Copula function type. The optimal Copula distribution function type obtained in this embodiment is shown in Table 3.

[0136] Table 3 Optimal Copula distribution function types and corresponding coefficients

[0137]

[0138]

[0139] Step 7: Based on the spectral representation-random function theory, a representative sample of random ground motion with probability characteristics of the same set is efficiently generated;

[0140] For a zero-mean non-stationary ground motion process, the source spectrum can be expressed as:

[0141]

[0142] Where N represents the number of truncation terms; ω k =kΔω, Δω is the frequency step; X k and Y k is a set of orthonormal random vectors.

[0143] The random function is introduced to convert the standard orthogonal random vector {X k ,Y k} is defined as an orthogonal function of the basic random vector:

[0144]

[0145]

[0146] Where, k=1,2,3,....,N; cas(x)=sin(x)+cos(x); Θ 1 and θ 2 are elementary random variables, which are independent of each other and uniformly distributed in the interval [0,2π). The "randperm" function in Matlab can convert Mapping to {X k ,Y k}, so that the orthogonal random variables in formula (21) can be uniquely determined.

[0147] Combined with the random variables in the evolving power spectrum model, the spectral representation-random function simulation of earthquake motion contains a total of 5 basic random variables

[0148] Initial representative point set θ 1,l ~θ 3,l They are used to generate the parameters ω in the evolution power spectrum model g , g and a. First, based on the parameter ω g The optimal probability distribution type is obtained by using the representative point generation method based on generalized F deviation and inverse probability transformation to obtain a set of random numbers, such as Figure 6 As shown, the representative values ​​of the simulated parameters are in good agreement with the parameters obtained by actual fitting.

[0149]

[0150] Where l = 1, 2, 3, .... n sel ; Representative parameter ω g The inverse function of the optimal probability distribution function.

[0151] Subsequently, based on the correlation between the parameters of the evolving power spectrum model constructed by Copula theory, the inverse probability transformation method was used to obtain other model parameters in turn.

[0152]

[0153]

[0154] For the initial representative point set θ4l and θ 4l , which are used to generate random variables {X k ,Y k In this way, the basic set of random variables for simulating random seismic motion is obtained. Therefore, based on formula (21), the random simulation of non-stationary seismic motion considering the uncertainty of the evolving power spectrum parameters can be realized. This method considers the randomness and correlation of the evolving power spectrum model parameters at the same time.

[0155] At the same time, this embodiment also simulates two groups of non-stationary seismic motion samples based on the mean and randomness of the evolved power spectrum model parameters, respectively. Through comparative analysis, the advanced nature of the non-stationary seismic motion random simulation method considering the uncertainty of the evolved power spectrum model parameters in the embodiment of the present invention is reflected.

[0156] The simulation error of the non-stationary ground motion random process can be expressed as:

[0157]

[0158] Among them, ω u =NΔω is the cutoff frequency of the non-stationary ground motion process; T is the duration of the ground motion.

[0159] It should be noted that among the basic parameters required by formula (21), the number of frequency truncation terms N = 1600; frequency step Δω = 0.15 rad / s; frequency step dt = 0.15 rad / s; time step Δt = 0.01 s; simulated non-stationary ground motion duration T = 30 s; the number of ground motion samples n sel = 300. Typical samples of random simulated earthquake motions are as follows: Figure 7 As shown, it has obvious non-stationary and random characteristics.

[0160] Step 8: Comparative verification of the effectiveness and engineering applicability of the simulated random ground motion samples;

[0161] In order to demonstrate the correctness of the random simulation method for non-stationary ground motion in the embodiment of the present invention, the mean and standard deviation of the generated random ground motion acceleration time history are compared with the target value. Figure 8 , 9 It can be seen from 10 that the simulated value and the target value have a good fitting effect, which reflects the effectiveness of the earthquake motion dimension reduction simulation method in this embodiment.

[0162] In order to further illustrate the engineering applicability of the random simulation method in the embodiment of the present invention, the mean and standard deviation of the response spectrum of the randomly simulated earthquake motion samples are compared with the measured earthquake motion.

[0163] like Fig.10 and 11As shown in the figure, the difference between the mean values ​​of the response spectra of the random simulated ground motion and the measured ground motion is small, but the standard deviation shows a significant difference. The random ground motion simulated by coupling the randomness and correlation of the parameters of the evolving power spectrum model can more reasonably represent the natural variability of ground motion.

[0164] Therefore, the present invention adopts the above-mentioned random simulation method of seismic motion taking into account the uncertainty of the evolution power spectrum parameters, and statistically models the parameters of the non-stationary seismic motion evolution power spectrum model based on the measured seismic motion records, thereby overcoming the defect of the single engineering characteristics of the seismic motion samples caused by the traditional deterministic model parameter selection.

[0165] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A random simulation method of ground motion considering the uncertainty of evolving power spectrum parameters, characterized in that: The following steps are involved: Step 1: Determine the power spectrum model and parameters of non-stationary ground motion evolution; Step 2: Select measured ground motion records from the ground motion database; Step 3: Establish a power spectrum estimation method for the evolution of measured ground motion records based on wavelet packet transform (WPT); Step 4: Based on frequency domain energy equality and genetic algorithm, the parameters of the evolving power spectrum model corresponding to each measured ground motion record are identified; Step 5: Determine the optimal probability distribution type of the parameters of the evolution power spectrum model; Step 6: Establish the correlation between the parameters of the evolving power spectrum model through the Copula function; Step 7: Based on the spectral representation-random function theory, a representative sample of random ground motion with probability characteristics of the same set is efficiently generated; Step 8: Comparative verification of the effectiveness and engineering applicability of simulated random seismic samples.

2. A random simulation method for earthquake motion considering uncertainty of evolving power spectrum parameters according to claim 1, characterized in that: In step 1, based on the evolution spectrum theory, the evolution power spectrum of non-stationary ground motion is expressed as: in, is the unilateral evolution power spectrum of non-stationary ground motion; A(t,ω) is the time-frequency modulation function; S(ω) is the unilateral power spectrum of stationary ground motion; The frequency domain energy distribution function corresponding to the non-stationary ground motion evolution power spectrum model is expressed as: Wherein, a, b and c are parameters related to the attenuation of earthquake energy, and b=a+0.001; c=0.005; ω represents the frequency; t* represents the peak arrival time of each harmonic; λ represents the parameter vector.

3. A random simulation method for earthquake motion considering the uncertainty of evolving power spectrum parameters according to claim 2, characterized in that: In step 2, the measured earthquake records are selected to meet the following requirements: (1) The distance to the fault is greater than 10 km, which reduces the number of near-fault ground motions; (2) The magnitude of the measured earthquake record is greater than 5, excluding earthquake motions with minor impact on the structure.

4. A random simulation method for earthquake motion considering the uncertainty of evolving power spectrum parameters according to claim 3, characterized in that: In step 3, based on wavelet packet transform WPT, the ground motion acceleration time history x(t) is decomposed into a series of wavelet packet coefficients of different time and frequency. The definition of wavelet packet coefficients is as follows: in, represents the wavelet packet coefficient of the i-th frequency band under the j scale and translation parameter k; is the wavelet basis function.

5. The method for random simulation of ground motion considering the uncertainty of evolving power spectrum parameters according to claim 4, characterized in that: Step 4 specifically includes: The frequency domain energy distribution function corresponding to the evolving power spectrum obtained by wavelet packet transform WPT is expressed as: Among them, S(ω i ,t) represents the evolving power spectrum of the sub-signal; ω i represents the frequency band of the sub-signal; t represents the time series of the signal; A genetic algorithm is used to identify parameters in the evolving power spectrum model:

6. A random simulation method for earthquake motion considering the uncertainty of evolving power spectrum parameters according to claim 5, characterized in that: In step 5, the KS test and AIC criterion are used to determine the optimal probability distribution type of each evolution power spectrum model parameter: AIC=2k+2lnL; Where L is the maximum likelihood function and k is the number of parameters in the model.

7. A random simulation method for earthquake motion considering the uncertainty of evolving power spectrum parameters according to claim 6, characterized in that: Step 6 specifically includes: Based on the Copula theory, the binary joint distribution function F can be represented by the marginal cumulative distribution functions F1(x1) and F2(x2) of the two variables: F(x1,x2)=C(F1(x1),F2(x2)); Where C(·) represents the Copula cumulative distribution function; The joint probability density function of two-dimensional random variables x1 and x2 is expressed as: f(x1,x2)=c 12 {F1(x1),F(x2)}·f1(x1)·f(x2); When determining the conditional density c 12 When {·}, the correlation between the two variables is established according to the Copula model, and the marginal distribution under the relevant conditions is expressed as: For two random variables x1 and x2, after determining their marginal distributions and Copula functions, the value of parameter x2 under relevant conditions is obtained by giving the value of x1.

8. The method for random simulation of ground motion considering the uncertainty of evolving power spectrum parameters according to claim 7, characterized in that: In step 7, for the zero-mean non-stationary ground motion process, the source spectrum is expressed as: Where N represents the number of truncation terms; ω k = kΔω and Δω is the frequency step size; X k and Y k is a set of standard orthogonal random vectors; k = 1, 2, 3, ....., N.

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