A method for selecting full-cycle natural ground motion records

Abstract

The present invention relates to the field of earthquake engineering technology, and in particular to a method for selecting full-cycle natural earthquake records, comprising the following steps: S100. Evaluating the intensity, design grouping, and site category of a proposed building site, and screening earthquake records according to the corresponding magnitude, epicenter distance, and equivalent shear wave velocity of the site; S200. Using the spectrum value of the standard response spectrum as the target mean and the standard deviation as the variable to generate a simulation spectrum, the uncertainty of the earthquake record is reflected by the uncertainty of the standard deviation, for each simulation spectrum, a record with a similar response spectrum is selected, the similarity between the earthquake response spectrum and the simulation spectrum is evaluated using the square sum of errors (SSE), and the first N records with the smallest SSE are selected; S300. The mean value and standard deviation of the simulation spectrum will approximately match the corresponding target value, and the record obtained in step S200 is improved by a greedy optimization method; S400. Determine the optimization variable and determine the range interval of each parameter; S500. Output the final optimization parameters and the selected record results.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake engineering, and in particular to a method for selecting full-cycle natural earthquake motion records. Background Art

[0002] Due to the complexity and diversity of earthquake motion, different natural earthquake motion records have different information and characteristics, and their impacts on structures are different, even huge. Therefore, the reasonable selection of natural earthquake motion records enables engineers to more accurately assess the possible impact of earthquakes on building structures, thereby ensuring the rationality of the structure.

[0003] Most of the current selection methods are local frequency band methods. The basic idea is to first determine the relevant natural vibration period of the structure and then match the response spectrum value within the period of interest. When selecting, only the difference between the record and the standard response spectrum is considered, ignoring the objective fact that the seismic record itself is discrete. At the same time, in actual engineering, these methods are largely controlled by structural engineers, and often ignore the unreasonable phenomenon of ignoring the earthquake scenario of the building site.

[0004] Therefore, those skilled in the art are committed to developing a method for selecting full-cycle natural earthquake records, so that the selection of earthquake records controlled by parameters can achieve relatively ideal results within the full cycle range. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for selecting natural earthquake records in a full cycle, so that the selection of earthquake records controlled by parameters can achieve relatively ideal results within the full cycle range.

[0006] The technical solution of the present invention to solve the above technical problems is as follows:

[0007] A method for selecting full-cycle natural earthquake records comprises the following steps:

[0008] S100. Evaluate the intensity, design grouping, and site category of the proposed building site, and screen the seismic records corresponding to the magnitude, epicenter distance, and equivalent shear wave velocity of the site;

[0009] S200. Generate a simulated spectrum with the spectrum value of the standard response spectrum as the target mean and the standard deviation as the variable. The uncertainty of the ground motion record is reflected by the uncertainty of the standard deviation. For each simulated spectrum, a record with a similar response spectrum is selected. The similarity between the ground motion response spectrum and the simulated spectrum is evaluated using the square error sum SSE, and the first N records with the smallest SSE are selected.

[0010] S300. The average value and standard deviation of the simulated spectrum will approximately match the corresponding target value, and the record obtained in step S200 is improved by a greedy optimization method;

[0011] S400. To make SSE N Minimum, at the same time, according to the spectral characteristics of the standard response spectrum, determine the optimization variables and the range of each parameter;

[0012] S500. Objective function SSE N After confirmation, Gaussian process is used as the probability proxy model, and PI (Probability of Improvement) is used as the acquisition function for Bayesian optimization. After setting the number of iterations, the final optimization parameters are output and the selected record results are recorded.

[0013] The beneficial effects of adopting the above scheme are: using Latin hypercube sampling to generate simulated spectra taking into account the discreteness of seismic motion spectrum acceleration, and then using the greedy optimization algorithm to further optimize the matching degree between the seismic motion record and the simulated spectrum. In the process of generating simulated spectra and greedy optimization, the sampling standard deviation, the period range corresponding to the sampling standard deviation, and the weights of different period ranges in the optimization process are set as variables. In this way, the above overall process can be regarded as a black box optimization process without a specific function form. Finally, Bayesian optimization is used to optimize the parameters so that the seismic motion record selection controlled by the parameters achieves a relatively ideal effect within the entire period range.

[0014] Based on the above technical solution, the present invention can also be improved as follows.

[0015] Further, in step S200, the calculation formula of SSE is:

[0016]

[0017] Among them, lnS a (T i ) is the logarithmic acceleration response spectrum value of the earthquake recorded at period Ti;

[0018] is the uncertain simulated spectrum value;

[0019] m is the number of cycles considered, with 0.01 as the cycle interval.

[0020] The beneficial effect of adopting the above further scheme is: evaluating the similarity between the earthquake response spectrum and the simulation spectrum.

[0021] Further, in step S300, the greedy optimization method includes matching between the target and sample means and variances, and the deviation of the set mean and variance from the target mean and variance is estimated as follows:

[0022] SSE N =w1S1+w2S2 (12)

[0024]

[0025] Among them, SSE N is the sum of squared errors of N ground motion records;

[0026] w1 and w2 represent weight coefficients, both of which are 0.5;

[0027] S1 is the mean error sum of squares;

[0028] Represents the weight coefficient at period Ti;

[0029] Represents the record set at Ti ln S a (T i )’s mean;

[0030] Represents 1.2 times the code response spectrum value;

[0031] represents 0.8 times the code response spectrum value;

[0032] S2 is the standard error sum of squares;

[0033] Indicates that the record set is at Ti ln S a (T i )’s standard deviation;

[0034] is the target standard deviation, whose value is ln S a (T i ) in the earthquake attenuation relationship, the range is [0.20-0.32];

[0035] The mean and standard deviation of the record set are calculated as follows:

[0036]

[0037] in, represents the ln S of the jth record at period Ti a (T i ).

[0038] The beneficial effect of adopting the above further solution is that when the number of simulated spectra is small, it is necessary to further optimize the combination of the records.

[0039] Further, in step S300, the greedy optimization technique steps are as follows:

[0040] a. Set l = 1;

[0041] b. Set p = 1 and set the SSE of the ground motion record set obtained from the simulated spectrum N Designated as SSE N ,old.

[0042] c. If the pth record does not appear in the lth position in the set, replace it and calculate the SSE N ,i.

[0043] d. Increase p by 1 each time and repeat step c;

[0044] e. If the p value reaches the maximum number of databases, return to step c, otherwise the SSE calculated each time N ,i and SSE N ,old comparison, if SSE N ,i <SSE N ,old replaces the record at position l with the record p. If a replacement occurs, update SSE N ,old;

[0045] f. Add 1 to l. If l is less than the number of record sets N, return to step b; otherwise, terminate the algorithm.

[0046] The beneficial effect of adopting the above further scheme is: the rationality of the mean is captured more stably, so that the mean of the seismic motion set is better consistent with the standard response spectrum.

[0047] Further, in step S300, according to the sampling standard deviation of the initial simulation spectrum and Calculate SSE N

[0048] SSE N =F(σ S ,W) (17)

[0049] in Represents the sampling standard deviation of different period points;

[0050] Represents the weight of the sum of squared errors of different periods.

[0051] The beneficial effect of adopting the above further solution is: generating a black box function form of a specific expression.

[0052] Further, in step S400, the four-segment response spectrum is divided into seven segments. Except for the rising segment, the rest are divided into two segments. The number of each segment constitutes a vector V = [v1, v2, ... v7],

[0053] v i Represents the number of segments in each cycle, and the intervals are as follows:

[0054] vi =[0.5n,1.5n] (18)

[0055]

[0056] n stands for v i The number of periodic points in each segment of the four-segment standard response spectrum, n of v4, v5, v6, and v7 is half of the number of periodic points in the corresponding segment of the standard response spectrum;

[0057] Further modify Equation 7 to form the final objective function and optimization variables, and convert the period corresponding to V to σ S , W are combined, then

[0058] σ S =[σ1,σ2…v7];

[0059] W=[w1,w2…w7],

[0060] Formula (7) is finally expressed as:

[0061] SSE N =F(σ S ,W,V) (20)

[0062] The range of each parameter is as follows:

[0063] σ i =[0,0.23+0.2(i-1)] (21)

[0064]

[0065] Among them, w1-w4 is three to four times that of w5-w7.

[0066] The beneficial effect of adopting the above further scheme is to ensure the consistency with the manually calibrated standard spectrum.

[0067] Further, in step S500, the number of iterations is greater than or equal to 100.

[0068] The beneficial effect of adopting the above further solution is: further improving the optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 This is a flowchart of a specific embodiment of the present invention;

[0070] Figure 2 This is a single record of the second-class field in the seven-degree zone, the result mean and the target spectrum output diagram of the first embodiment of the present invention;

[0071] Figure 3 This is an output diagram of the mean error of the second-category field samples in the seven-degree area and the error limit value specified by the specification in the first embodiment of the present invention;

[0072] Figure 4 This is a logarithmic standard deviation output diagram of the second-category field samples in a seven-degree area according to the first embodiment of the present invention;

[0073] Figure 5 This is a single record of the second type of field in the octave area of ​​embodiment 1 of the present invention, the result mean and the target spectrum output diagram;

[0074] Figure 6 It is an output diagram of the mean error of the second type of field samples in the octave area and the error limit value specified by the specification in the first embodiment of the present invention;

[0075] Figure 7 This is a logarithmic standard deviation output diagram of the second type of field samples in the first octave region of the embodiment of the present invention. DETAILED DESCRIPTION

[0076] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples given are only used to explain the present invention and are not used to limit the scope of the present invention.

[0077] In the description of the present invention, it is necessary to understand that the terms "center", "length", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "inside", "outside", "peripheral", "circumferential" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the referred system or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the present invention.

[0078] In the description of the present invention, “plurality” means at least two, for example, two, three, etc., unless otherwise clearly and specifically defined.

[0079] In the present invention, unless otherwise clearly specified and limited, the terms "installed", "connected", "connected", "fixed" and the like 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 a direct connection or an indirect connection through an intermediate medium, it can be the internal connection of two elements or the interaction relationship between two elements, unless otherwise clearly defined. For ordinary technicians in this field, the specific meanings of the above terms in the present invention can be understood according to specific circumstances.

[0080] like Figure 1 As shown, a method for selecting full-cycle natural earthquake records includes the following steps:

[0081] S100. Evaluate the intensity, design grouping, and site category of the proposed building site, and screen the seismic records corresponding to the magnitude, epicenter distance, and equivalent shear wave velocity of the site.

[0082] S200. Generate simulated spectra with the spectral value of the standard response spectrum as the target mean and the standard deviation as the variable. The uncertainty of the ground motion record is reflected by the uncertainty of the standard deviation. For each simulated spectrum, a record with a similar response spectrum is selected. The similarity between the ground motion response spectrum and the simulated spectrum is evaluated using the square error sum SSE, and the first N records with the smallest SSE are selected.

[0083] Specifically, the calculation formula of SSE is:

[0084]

[0085] Among them, ln S a (T i ) is the logarithmic acceleration response spectrum value of the earthquake recorded at period Ti;

[0086] is the uncertain simulated spectrum value;

[0087] m is the number of cycles considered, with 0.01 as the cycle interval.

[0088] S300. The average value and standard deviation of the simulated spectrum will approximately match the corresponding target value, and the record obtained in step S200 is improved by a greedy optimization method;

[0089] Specifically, the greedy optimization method includes matching between the target and sample mean and variance, and the deviation of the set mean and variance from the target mean and variance is estimated as follows:

[0090] SSE N =w1S1+w2S2 (twenty three)

[0092]

[0093] Among them, SSE N is the sum of squared errors of N ground motion records;

[0094] w1 and w2 represent weight coefficients, both of which are 0.5;

[0095] S1 is the mean error sum of squares;

[0096] Represents the weight coefficient at period Ti;

[0097] Represents the record set at Ti ln S a (T i )’s mean;

[0098] Represents 1.2 times the code response spectrum value;

[0099] represents 0.8 times the code response spectrum value;

[0100] S2 is the standard error sum of squares;

[0101] Indicates that the record set is at Ti lnS a (T i )’s standard deviation;

[0102] is the target standard deviation, whose value is lnS a (T i ) in the earthquake attenuation relationship, the range is [0.20-0.32];

[0103] The mean and standard deviation of the record set are calculated as follows:

[0104]

[0105] in, represents the ln S of the jth record at period Ti a (T i ).

[0106] The steps of greedy optimization technology are as follows:

[0107] a. Set l = 1;

[0108] b. Set p = 1 and set the SSE of the ground motion record set obtained from the simulated spectrum N Designated as SSE N ,old.

[0109] c. If the pth record does not appear in the lth position in the set, replace it and calculate the SSE N ,i.

[0110] d. Increase p by 1 each time and repeat step c;

[0111] e. If the p value reaches the maximum number of databases, return to step c, otherwise the SSE calculated each time N ,i and SSE N ,old comparison, if SSE N ,i <SSE N ,old replaces the record at position l with the record p. If a replacement occurs, update SSE N ,old;

[0112] f. Add 1 to l. If l is less than the number of record sets N, return to step b; otherwise, terminate the algorithm.

[0113] According to the sampling standard deviation of the initial simulation spectrum and Calculate SSE N

[0114] SSE N =F(σ S ,W) (28)

[0115] in Represents the sampling standard deviation of different period points;

[0116] Represents the weight of the sum of squared errors of different periods.

[0117] S400. To make SSE N At the same time, according to the spectral characteristics of the standard response spectrum, the optimization variables and the range of each parameter are determined. Specifically, the four-segment response spectrum is divided into seven segments. Except for the rising segment, the rest are divided into two segments. The number of each segment constitutes a vector V = [v1, v2, ... v7],

[0118] v i Represents the number of segments in each cycle, and the intervals are as follows:

[0119] v i =[0.5n,1.5n] (29)

[0120]

[0121] n stands for v i The number of periodic points in each segment of the four-segment standard response spectrum, n of v4, v5, v6, and v7 is half of the number of periodic points in the corresponding segment of the standard response spectrum;

[0122] Further modify Equation 7 to form the final objective function and optimization variables, and convert the period corresponding to V to σ S , W are combined, then

[0123] σ S =[σ1,σ2…σ7];

[0124] W=[w1,w2…w7],

[0125] Formula (7) is finally expressed as:

[0126] SSE N =F(σ S ,W,V) (31)

[0127] The range of each parameter is as follows:

[0128] σ i =[0,0.23+0.2(i-1)] (32)

[0129]

[0130] Among them, w1-w4 is three to four times that of w5-w7.

[0131] S500. Objective function SSE N After confirmation, the Gaussian process is used as the probability proxy model, and PI (Probability of Improvement) is used as the acquisition function for Bayesian optimization. After setting the number of iterations, the number of iterations is greater than or equal to 100, and the final optimization parameters are output and the selected record results are recorded.

[0132] Embodiment 1

[0133] like Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 7 As shown, a method for selecting full-period natural ground motion records based on a Bayesian-greedy optimization algorithm includes:

[0134] 1. Preliminary selection of earthquake records:

[0135] Before the formal selection, the intensity, design grouping and site category of the proposed building site are evaluated, and the seismic records are screened according to the corresponding magnitude, epicentral distance and equivalent shear wave velocity of the site to ensure the rationality of the record source.

[0136] 2. Setting of objective function

[0137] Step 1: Generate simulated spectrum and select initial records using Latin hypercube sampling:

[0138] The spectral value of the standard response spectrum is taken as the target mean and the standard deviation is used as the variable to generate the simulated spectrum. The uncertainty of the ground motion record is reflected by the uncertainty of the standard deviation. For each simulated spectrum, a record with a similar response spectrum is selected. The similarity between the ground motion response spectrum and the simulated spectrum is evaluated using the sum of squared errors (SSE):

[0139]

[0140] where ln S a (T i ) is the logarithmic acceleration response spectrum value of the earthquake recorded at period Ti,

[0141] is the uncertain simulated spectrum value, whose value is affected by the standard deviation.

[0142] m is the number of cycles to be considered, and 0.01 is generally considered as the cycle interval.

[0143] The SSE of all preliminary selected records is calculated by formula (1), and the first N records with the smallest SSE are selected.

[0144] Step 2: Use the greedy optimization algorithm to optimize the record combination:

[0145] The mean and standard deviation of the simulated spectra will approximately match the corresponding target values ​​because they are sampled from the expected distribution. If the number of simulated spectra is large, the overall mean and standard deviation will match exactly, but the project generally requires only a few seismic records, so when the number of simulated spectra is small, it is necessary to further optimize the records. The greedy optimization technique is used to further improve the records obtained in step 1.

[0146] In this approach, each previously selected ground motion is replaced one at a time by the ground motions in the database, which results in the best improvement in the match between the target and sample means and variances.

[0147] The estimates of the deviations of the ensemble mean and variance from the target mean and variance are as follows:

[0148] SSE N =w1S1+w2S2 (35)

[0150]

[0151] Among them SSE N is the sum of squared errors of N earthquake records, which should be as small as possible in practice.

[0152] w1 and w2 represent weight coefficients. In order to make the mean and standard deviation ideal at the same time, they are both taken as 0.5;

[0153] S1 is the mean error sum of squares, represents the weight coefficient at period Ti,

[0154] Represents the record set at Ti ln S a (T i ),

[0155] represents 1.2 times the code response spectrum value,

[0156] represents 0.8 times the code response spectrum value,

[0157] This setting is to capture the rationality of the mean more stably, so that the mean of the earthquake motion set is better consistent with the standard response spectrum.

[0158] S2 is the standard error sum of squares, Indicates that the record set is at Ti ln S a (T i ),

[0159] is the target standard deviation, whose value is ln S a (T i ) in the earthquake attenuation relationship, the range is [0.20-0.32].

[0160] The mean and standard deviation of the record set are calculated as follows:

[0161]

[0162]

[0163] in represents the ln S of the jth record at period Ti a (T i ).

[0164] The steps of greedy optimization technology are as follows:

[0165] a. Set l = 1;

[0166] b. Set p = 1 and set the SSE of the ground motion record set obtained from the simulated spectrum N Designated as SSE N ,old;

[0167] c. If the pth record does not appear in the lth position in the set, replace it and calculate the SSE N ,I;

[0168] d. Increase p by 1 each time and repeat step c;

[0169] If the p value reaches the maximum number of databases, return to step c, otherwise the SSE calculated each time N ,i and SSE N ,old comparison, if SSE N ,i <SSE N ,old replaces the record at position l with the record p. If a replacement occurs, update SSE N ,old;

[0170] f. Add 1 to l. If l is less than the number of record sets N, return to step b; otherwise, terminate the algorithm.

[0171] In the above description, it is not difficult to find that the final N ground motion records are generated by SSE N Determined, and SSE N The result is the sampling standard deviation of the initial simulation spectrum and It can be expressed as the following function:

[0172] SSE N =F(σ S ,W) (40)

[0173] in Represents the sampling standard deviation of different period points,

[0174] Represents the weight of the sum of squared errors of different periods.

[0175] The objective function for seismic record selection is shown in equation (7), which is a black box function without a specific expression.

[0176] 3. Bayesian Optimization

[0177] Step 1: Determine the optimization variables and their intervals

[0178] To make SSE N At the same time, according to the spectral characteristics of the standard response spectrum, the four-segment response spectrum is divided into seven segments. Except for the rising segment, the rest are divided into two segments. The number of each segment constitutes a vector V = [v1, v2, ... v7], v i Represents the number of segments in each cycle, and the intervals are as follows:

[0179] v i =[0.5n,1.5n] (41)

[0180]

[0181] n stands for v i Corresponding to the number of periodic points in each section of the four-section standard response spectrum, since the periodic range of the last two sections of the standard spectrum is larger, the n of v4, v5, v6, and v7 is half of the number of periodic points in the corresponding section of the standard spectrum.

[0182] Therefore, we further modify equation (7) to form the final objective function and optimization variables. We transform the period corresponding to V and σ S , W for combination,

[0183] Then σ S =[σ1,σ2…σ7], W = [w1,w2…w7], and the final expression of Formula 7 is:

[0184] SSE N=F(σ S ,W,V) (43)

[0185] The range of each parameter is as follows:

[0186] σ i =[0,0.23+0.2(i-1)] (44)

[0187]

[0188] where w 1-4 Can be set to w 5-7 to ensure consistency with the manually calibrated standard spectrum.

[0189] Step 2: Bayesian optimization and result output

[0190] Objective function SSE N After confirmation, Gaussian process is used as the probability proxy model, PI (Probability of Improvement) is used as the acquisition function for Bayesian optimization, the number of iterations is set to 100, and the final optimization parameters and selected record results are output.

[0191] In the description of this specification, the description with reference to the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described may be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art may combine and combine the different embodiments or examples described in this specification and the features of the different embodiments or examples, without contradiction.

[0192] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for selecting full-cycle natural ground motion records, characterized in that: The following steps are involved: S100. Evaluate the intensity, design grouping, and site category of the proposed building site, and screen the seismic records corresponding to the magnitude, epicenter distance, and equivalent shear wave velocity of the site; S200. Generate a simulated spectrum with the spectrum value of the standard response spectrum as the target mean and the standard deviation as the variable. The uncertainty of the ground motion record is reflected by the uncertainty of the standard deviation. For each simulated spectrum, a record with a similar response spectrum is selected. The similarity between the ground motion response spectrum and the simulated spectrum is evaluated using the square error sum SSE, and the first N records with the smallest SSE are selected. S300. The average value and standard deviation of the simulated spectrum will approximately match the corresponding target value, and the record obtained in step S200 is improved by a greedy optimization method; S400. To make SSE N Minimum, at the same time, according to the spectral characteristics of the standard response spectrum, determine the optimization variables and the range of each parameter; S500. Objective function SSE N After confirmation, Gaussian process is used as the probability proxy model, PI is used as the acquisition function for Bayesian optimization, and after setting the number of iterations, the final optimization parameters are output and the selected record results are recorded.

2. The method for selecting full-cycle natural earthquake records according to claim 1, characterized in that , In step S200, the calculation formula of SSE is: Among them, ln S a (T i ) is the logarithmic acceleration response spectrum value of the earthquake recorded at period Ti; is the uncertain simulated spectrum value; m is the number of cycles considered, with 0.01 as the cycle interval.

3. The method for selecting full-cycle natural earthquake records according to claim 1, characterized in that , In step S300, the greedy optimization method includes matching between the target and sample means and variances, and the deviation of the set mean and variance from the target mean and variance is estimated as follows: SSE N =w1S1+w2S2 (1) Among them, SSE N is the sum of squared errors of N ground motion records; w1 and w2 represent weight coefficients, both of which are 0.5; S1 is the mean error sum of squares; Represents the weight coefficient at period Ti; Represents the record set at Ti ln S a (T i )’s mean; Represents 1.2 times the code response spectrum value; represents 0.8 times the code response spectrum value; S2 is the standard error sum of squares; Indicates that the record set is at Ti ln S a (T i )’s standard deviation; is the target standard deviation, whose value is ln S a (T i ) in the earthquake attenuation relationship, the range is [0.20-0.32]; The mean and standard deviation of the record set are calculated as follows: in, represents the ln S of the jth record at period Ti a (T i ).

4. The method for selecting full-cycle natural earthquake records according to claim 3, characterized in that: In step S300, the greedy optimization technique steps are as follows: a. Set l = 1; b. Set p = 1 and set the SSE of the ground motion record set obtained from the simulated spectrum N Designated as SSE N ,old; c. If the pth record does not appear in the lth position in the set, replace it and calculate the SSE N ,i; d. Increase p by 1 each time and repeat step c; e. If the p value reaches the maximum number of databases, return to step c, otherwise the SSE calculated each time N ,i and SSE N ,old comparison, if SSE N ,i <SSE N ,old replaces the record at position l with the record p. If a replacement occurs, update SSE N ,old; f. Add 1 to l. If l is less than the number of record sets N, return to step b; otherwise, terminate the algorithm.

5. The method for selecting full-cycle natural earthquake records according to claim 4, characterized in that: In step S300, according to the sampling standard deviation of the initial simulation spectrum and Calculate SSE N SSE N =F(σ S ,W) (6) in Represents the sampling standard deviation of different period points; Represents the weight of the sum of squared errors of different periods.

6. The method for selecting full-cycle natural earthquake records according to claim 1, characterized in that , In step S400, the four-segment response spectrum is divided into seven segments. Except for the rising segment, the rest are divided into two segments. The number of each segment constitutes a vector V = [v1, v2, ... v7], v i Represents the number of segments in each cycle, and the intervals are as follows: v i =[0.5n,1.5n] (7) n stands for v i The number of periodic points in each segment of the four-segment standard response spectrum, n of v4, v5, v6, and v7 is half of the number of periodic points in the corresponding segment of the standard response spectrum; Further modify Equation 7 to form the final objective function and optimization variables, and convert the period corresponding to V to σ S , W are combined, then s S =[σ1,σ2…σ7]; W=[w1,w2…w7], Formula (7) is finally expressed as: SSE N =F(σ S (9) The range of each parameter is as follows: s i =[0,0.23+0.2(i-1)] (10) Among them, w1-w4 is three to four times that of w5-w7.

7. The method for selecting full-cycle natural earthquake records according to claim 1, characterized in that , In step S500, the number of iterations is greater than or equal to 100.

Images