Earthquake motion selection method and device based on main aftershock sequence double-condition response spectrum

Abstract

The application provides a kind of ground motion selection method and device based on main aftershock sequence double condition response spectrum, and the method comprises: determining mean and covariance matrix according to multiple groups of ground motion data selected in advance, and constructing the response spectrum of main aftershock sequence based on lognormal distribution assumption, wherein the covariance matrix is determined based on the correlation coefficient of two variables being two aftershock parameters;Random sampling is generated to multiple candidate target spectra for the constructed response spectrum, and a target spectrum set is determined according to the spectral variability of multiple candidate target spectra;Selecting several ground motion data with the highest matching degree with the target spectrum set in the ground motion database.The application constructs the response spectrum of main aftershock sequence, and then generates the target spectrum for selecting ground motion data in ground motion database by sampling the response spectrum, so that the determined target spectrum can better provide main aftershock sequence ground motion data support for nonlinear dynamic analysis of structure.

Description

Technical Field

[0001] This invention relates to the field of seismic design technology for buildings, and in particular to a method and apparatus for selecting seismic ground motions based on the dual-conditional response spectrum of the mainshock and aftershock sequence. Background Technology

[0002] Performance-based seismic design plays a crucial role in earthquake disaster prevention and mitigation, and in protecting life and property. Dynamic time-history analysis is commonly used to assess the seismic performance of major structures or infrastructure. The time-history sequence used as input for nonlinear dynamic analysis is typically selected from previously recorded ground motions. Since ground motion is one of the most significant factors influencing the uncertainty of the system response, selecting a suitable set of seismic records is a critical step in seismic design.

[0003] In recent years, scholars have developed many methods and tools for selecting ground motions. Among them, classical methods are usually used to select ground motions whose response spectrum values ​​match the target spectrum, such as the conditionally averaged spectrum and the design spectrum specified in modern design codes. Some more advanced ground motion selection methods select ground motions whose response spectrum matches the mean and variance of the target spectrum, or match the generalized spectrum composed of the response spectrum and non-spectral ground motion intensity parameters (IMs).

[0004] However, existing ground motion selection methods typically focus on selecting the ground motion of a single main shock, ignoring the impact of aftershocks on the structure. This makes it difficult for the selected ground motion data to accurately reflect the impact of the entire aftershock process on the building structure. Summary of the Invention

[0005] This invention provides a method and apparatus for selecting ground motions based on the dual-conditional response spectrum of the mainshock and aftershock sequence, which solves the problem that existing technologies are difficult to select ground motion data that reflect the complete aftershock process during seismic design, and realizes a more comprehensive method and apparatus for selecting ground motions based on the dual-conditional response spectrum of the mainshock and aftershock sequence.

[0006] This invention provides a method for selecting seismic motions based on the dual-conditional response spectrum of the mainshock and aftershock sequence, comprising: The mean and covariance matrix are determined based on a pre-selected set of ground motion data, and the response spectrum of the mainshock and aftershock sequence is constructed based on the log-normal distribution assumption. The covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters. Multiple candidate target spectra are generated by randomly sampling the constructed reaction spectrum, and a target spectrum set is determined based on the spectral variability of the multiple candidate target spectra; Several ground motion data points with the highest matching degree to the target spectrum set are selected from the ground motion database.

[0007] According to the present invention, a seismic motion selection method based on a dual-conditional response spectrum of a mainshock and aftershock sequence includes the following steps: randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining the target spectrum set based on the spectral variability of the multiple candidate target spectra. Multiple candidate target spectra are generated by randomly sampling the constructed reaction spectrum, and the multiple candidate target spectra generated at one time are used as a candidate spectrum set; Multiple candidate spectral sets are obtained through multiple sampling, and the spectral variability of each candidate spectral set is determined based on the residual between each candidate spectral set and the pre-selected multiple sets of ground motion data. The candidate spectrum set with the smallest spectral variability is selected as the target spectrum set.

[0008] According to the present invention, a method for selecting seismic motions based on the dual-conditional response spectrum of a mainshock sequence includes the following step: selecting several seismic motion data points with the highest matching degree to the target spectrum set from the seismic motion database. The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each seismic motion data in the seismic motion database. The ground motion data with the highest matching value are selected as the selected ground motion data.

[0009] According to the present invention, a method for selecting seismic motions based on the dual-conditional response spectrum of a mainshock sequence includes the following step: selecting several seismic motion data points with the highest matching degree to the target spectrum set from the seismic motion database. The seismic motion data in the seismic motion database is filtered based on preset constraints; The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each ground motion data obtained by screening in the ground motion database; The ground motion data with the highest matching value are selected as the selected ground motion data.

[0010] According to the present invention, a seismic motion selection method based on a dual-conditional response spectrum of a mainshock and aftershock sequence, prior to the steps of determining the mean and covariance matrices based on pre-selected multiple sets of seismic motion data and constructing the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, further includes: Multiple ground motion data are selected from the ground motion database, wherein each ground motion data includes records of the main shock and aftershocks; For each ground motion data point, calculate the correlation coefficient of aftershock spectral acceleration between any two periods; By taking any two periods from each ground motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, a two-aftershock autocorrelation coefficient prediction model is learned. The correlation coefficient between the two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model.

[0011] According to the present invention, a seismic motion selection method based on a dual-conditional response spectrum of a mainshock and aftershock sequence includes the step of calculating the correlation coefficient of aftershock spectral acceleration between any two periods for each seismic motion data point, specifically comprising: Calculate the inter-event residuals and intra-event residuals for each seismic motion data point; The correlation coefficients of the inter-event residuals and the correlation coefficients of the intra-event residuals for each ground motion data point are calculated based on the inter-event residuals and intra-event residuals for each ground motion data point. The aftershock spectrum acceleration correlation coefficient for any two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

[0012] The present invention also provides a ground motion selection device based on the dual-conditional response spectrum of the mainshock and aftershock sequence, comprising: The module is used to construct the response spectrum of the mainshock and aftershock sequence based on the mean and covariance matrix determined by multiple pre-selected sets of ground motion data and the log-normal distribution assumption. The covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters. The determination module is used to randomly sample the constructed response spectrum to generate multiple candidate target spectra, and determine the target spectrum set based on the spectral variability of the multiple candidate target spectra; The selection module is used to select several ground motion data that have the highest matching degree with the target spectrum set from the ground motion database.

[0013] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence as described above.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence as described above.

[0015] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence as described above.

[0016] The present invention provides a method and apparatus for selecting ground motions based on the dual-condition response spectrum of the mainshock and aftershock sequence. By determining the mean and covariance matrix of multiple pre-selected ground motion data, the response spectrum of the mainshock and aftershock sequence is constructed based on the log-normal distribution assumption. Then, by sampling the response spectrum, a target spectrum is generated for selecting ground motion data in the ground motion database. This allows the determined target spectrum to provide better support for the nonlinear dynamic analysis of the structure with ground motion data of the mainshock and aftershock sequence, which makes up for the deficiency of traditional ground motion selection methods that can only select a single mainshock ground motion. Moreover, it can be used for ground motion selection under different mainshock and aftershock sequence scenarios. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0018] Picture 1 This is one of the flowcharts of the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention; Picture 2 This is a schematic diagram of the distribution of aftershock magnitudes and fault distances selected from the earthquake database in the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention. Picture 3 This is a schematic diagram of the standardized intra-event residuals of aftershock spectrum acceleration used to illustrate the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention. Picture 4 (a) is the QQ diagram verification result of the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention when the period is 0.075S; Picture 4 (b) is the QQ diagram verification result of the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention when the period is 0.5S; Picture 4 (c) is the QQ diagram verification result with a period of 2S in the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention; Picture 4 (d) is the QQ diagram verification result with a period of 10S in the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention; Picture 5 This is a flowchart of the prediction process of the autocorrelation coefficient prediction model in the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention. Picture 6 These are partial periodic prediction values ​​of the autocorrelation prediction model of aftershock spectrum acceleration in the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by this invention. Picture 7 This refers to a partial periodic prediction error in the autocorrelation prediction model of aftershock spectrum acceleration in the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by this invention. Picture 8 This is a graph showing the correlation coefficient of logarithmic acceleration of aftershocks in a portion of the earthquake motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by this invention. Picture 9 This is a heatmap of the correlation coefficient of the logarithmic acceleration of aftershocks of different periods in the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention. Picture 10 This is the second flowchart of the seismic motion selection method based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention. Picture 11 This is a schematic diagram of the main shock spectrum acceleration selected according to the set main shock sequence scenario in a specific implementation of the seismic motion selection method based on the dual-condition response spectrum of the main shock sequence provided by the present invention. Picture 12 This is a schematic diagram of the aftershock spectrum acceleration selected according to the set mainshock sequence scenario in a specific implementation of the ground motion selection method based on the dual-condition response spectrum of the mainshock sequence provided by the present invention. Picture 13 This is a schematic diagram of the seismic motion selection device based on the dual-conditional response spectrum of the mainshock and aftershock sequence provided by the present invention. Picture 14 This is a schematic diagram of the structure of the electronic device provided by the present invention. Detailed Implementation

[0019] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0020] The following is combined with Picture 1 to Picture 12 This invention introduces a ground motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence, such as... Picture 1 As shown, it includes: Step 101: Based on the mean and covariance matrix determined by the pre-selected multiple sets of ground motion data, and based on the log-normal distribution assumption, construct the response spectrum of the mainshock and aftershock sequence, wherein the covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters; Numerous studies and earthquake damage records indicate that aftershocks often exacerbate structural damage; therefore, it is necessary to consider the combined effects of the mainshock and aftershock sequences on structures during seismic design. Thanks to advancements in seismic measurement technology, the amount of aftershock data in global seismic ground motion databases has gradually increased, providing data support for the nonlinear dynamic analysis of structures under the influence of mainshock and aftershock sequences. However, the problem of selecting suitable mainshock and aftershock sequences from numerous seismic events remains unsolved. Therefore, it is necessary to extend existing seismic ground motion selection methods from mainshock-type to mainshock-aftershock sequence-type methods.

[0021] Verification shows that the vast majority of mainshock and aftershock sequence ground motion data conform to the log-normal distribution assumption. Therefore, based on this, multiple sets of ground motion data conforming to the log-normal distribution can be obtained by screening, their mean and standard deviation can be calculated, and the covariance matrix can be determined based on the standard deviation. The response spectrum of the mainshock and aftershock sequence can be represented in the form of a normal distribution function using the mean and covariance matrix.

[0022] The specific reaction spectrum obtained is shown in the following formula: ; In the formula, Represents vector [ln Sa M ( T 1), ln Sa M ( T 2),…,ln Sa M ( T m ),ln Sa A ( T 1), ln Sa A ( T 2),…,ln Sa ( T n The mean of [ln]]. Sa M ( T 1), ln Sa M ( T 2),…,ln Sa M ( T m ),ln Sa A (T 1), ln Sa A ( T 2),…,ln Sa ( T n [] represents the vector form of the response spectrum of a pre-selected set of ground motion data, where m represents the number of periods of acceleration in the mainshock response spectrum; n represents the number of periods of acceleration in the aftershock response spectrum; subscript M indicates the mainshock, and subscript A indicates the aftershock. N represents the normal distribution function.

[0023] Right now, .

[0024] Represents vector [ln Sa M ( T 1), ln Sa M ( T 2),…,ln Sa M ( T m ),ln Sa A ( T 1), ln Sa A ( T 2),…,ln Sa ( T n The covariance matrix of ]: ; in: ; ; ; ; In the formula, σ Indicates standard deviation, This represents the correlation coefficient.

[0025] Specifically, the correlation coefficient includes the correlation coefficient obtained from the two main earthquake parameters used in calculating the correlation coefficient, for example... This also includes the correlation coefficient obtained from the two main aftershock parameters used in calculating the correlation coefficient, for example... ; and the correlation coefficient calculated using two variables that are both aftershock parameters, for example .

[0026] Among them, the mean Covariance Matrix Standard deviations in σ The response spectrum was calculated using a pre-selected set of ground motion data. Based on the log-normal distribution assumption, the vector mean and covariance matrix of the selected ground motion data were calculated using the CB14 ground motion attenuation formula, and the response spectrum was constructed.

[0027] In one specific implementation, aftershock ground motion records are selected from the global ground motion database (NGA-West2).

[0028] The selected seismic ground motion records must meet the following requirements: (1) the ground motion is caused by a shallow crustal fault; (2) the measured data comes from a free-field seismic station; (3) the mainshock and aftershock records of the same event should be measured data from the same station; (4) the seismic record information should be complete and the ground motion data should be filtered and corrected.

[0029] Based on the conditions, first select suitable aftershock data, then determine the main shock data corresponding to the aftershocks, and use the aftershocks and the corresponding main shock data as a ground motion record.

[0030] The aftershock ground motion records selected in this embodiment are as follows: Picture 2 As shown.

[0031] Since each selected seismic motion data point has its applicable frequency range, assuming If the minimum usable frequency for seismic motion is given, then when the period T is greater than... At that time, data for that period of the ground motion cannot be used to construct the response spectrum. Based on this limitation, data from multiple periods that meet the above limitation are further selected from each selected ground motion record to calculate the mean and standard deviation, and to construct the response spectrum of the mainshock and aftershock earthquake sequence.

[0032] Furthermore, in this embodiment, before constructing the response spectrum, each ground motion record data that has been screened through the above-mentioned constraints is verified to verify whether it conforms to the log-normal distribution assumption of aftershock spectrum acceleration and the joint log-normal distribution assumption of mainshock and aftershock spectrum acceleration.

[0033] The verification process first calculates the intra-event residuals of the selected seismic motion records using the CB14 seismic motion attenuation formula, and then standardizes the calculated intra-event residuals.

[0034] Optionally, such as Picture 3 As shown, the difference between the in-event residuals and the mean of the in-event residuals is calculated, and then the difference is divided by the standard deviation of the in-event residuals.

[0035] Then, the log-normal distribution hypothesis of aftershock spectral acceleration was tested on the selected ground motion record data based on the intra-event residuals after standardization.

[0036] Optionally, the QQ plot method can be used for testing. If the quantiles of the sample data plotted in the QQ plot are close to the quantiles of the standard normal distribution, then it is determined that the data follows a log-normal distribution. The QQ plot test results for some periods (T = 0.075s, 0.5s, 2s, 10s) are as follows: Picture 4 As shown.

[0037] Furthermore, based on the proof that the aftershock spectrum acceleration of the selected ground motion record data follows a log-normal distribution, the hypothesis that the main and aftershock spectrum accelerations are jointly log-normal is tested using the Henze-Zirkler method and the multivariate kurtosis method.

[0038] Specifically, if the calculated probability value or If the value is greater than 0.05, it is determined that it follows a joint log-normal distribution. The test results of the four earthquake events are shown in Table 1 and Table 2.

[0039] Table 1. Joint log-normal test of spectral acceleration of mainshocks and aftershocks (Chi-Chi earthquake events)

[0040] Table 2. Joint log-normal test of spectral acceleration of mainshocks and aftershocks (three earthquake events)

[0041] In summary, by verifying the selected ground motion record data, it was confirmed that they all conform to the log-normal distribution assumption of aftershock spectrum acceleration and the joint log-normal distribution assumption of mainshock and aftershock spectrum acceleration. Therefore, the ground motion record data selected in the above manner can be used to construct the response spectrum.

[0042] In constructing the response spectrum, the mean and standard deviation of each ground motion record are first calculated using the CB14 ground motion attenuation formula. The CB14 ground motion attenuation formula is expressed as follows: ; In the formula, Let T be the natural logarithm of the spectral acceleration with period T. The predicted median of the logarithmic spectral acceleration with period T; M The magnitude of the earthquake; R This is the fault distance; Other parameters, such as site conditions; For the residuals between events in logarithmic space (different earthquake events); For the intra-event residuals (for the same earthquake event) in logarithmic space.

[0043] Using the CB14 formula, the mean and standard deviation of each ground motion record are calculated based on the recorded values ​​such as magnitude and fault distance. Then, a covariance matrix is ​​constructed based on the standard deviation of each ground motion record. Finally, the response spectrum of the mainshock and aftershock earthquake sequence is constructed in the form of a normal distribution function based on the mean and covariance matrix.

[0044] Step 102: Randomly sample the constructed reaction spectrum to generate multiple candidate target spectra, and determine the target spectrum set based on the spectral variability of the multiple candidate target spectra; The established reaction spectrum is randomly sampled to generate multiple target spectra, and the multiple target spectra generated in one sampling are combined into a spectrum set.

[0045] Multiple spectra are generated through random sampling, and one of these spectra is selected as the target spectra.

[0046] Optionally, the spectral variability between each spectral set and the specified spectral set is calculated, and the spectral set with the smallest spectral variability is determined as the final target spectral set. The specified spectral set is the spectral set used when constructing the response spectrum.

[0047] Step 103: Select several ground motion data that have the highest matching degree with the target spectrum set from the ground motion database.

[0048] The seismic ground motion database is a database that records seismic ground motion data. Optionally, the seismic ground motion database used for matching can be the same as or different from the seismic ground motion database used for constructing the response spectrum. In this embodiment, the global seismic ground motion database (NGA-West2) is used.

[0049] Optionally, the ground motion data in the ground motion database is matched with the target spectrum set, the matching degree of each ground motion data is calculated, and the data with the highest matching degree are used as the ground motion data for seismic design tests.

[0050] This invention determines the mean and covariance matrix of multiple pre-selected sets of ground motion data, constructs the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, and then generates a target spectrum for selecting ground motion data from the ground motion database by sampling the response spectrum. This allows the determined target spectrum to provide better support for the nonlinear dynamic analysis of the structure with ground motion data of the mainshock and aftershock sequence, making up for the deficiency of traditional ground motion selection methods that can only select a single mainshock ground motion, and can be used for ground motion selection under different mainshock and aftershock sequence scenarios.

[0051] In the seismic motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence of this invention, the step of randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining the target spectrum set based on the spectral variability of the multiple candidate target spectra, specifically includes: Multiple candidate target spectra are generated by randomly sampling the constructed reaction spectrum, and the multiple candidate target spectra generated at one time are used as a candidate spectrum set; Multiple candidate spectral sets are obtained through multiple sampling, and the spectral variability of each candidate spectral set is determined based on the residual between each candidate spectral set and the pre-selected multiple sets of ground motion data. The candidate spectrum set with the smallest spectral variability is selected as the target spectrum set.

[0052] Random sampling of the constructed reaction spectrum generates N 1 candidate target spectrum, and generate 1 at a time N Each candidate target spectrum is composed of a candidate spectrum set. Multiple rounds of sampling generate multiple candidate spectrum sets.

[0053] Understandably, for multiple candidate spectrum sets obtained through sampling, it is necessary to calculate the degree of variation between them and the constructed response spectrum, that is, to calculate the spectral variability between them and the response spectrum, so as to select the candidate spectrum set with the smallest spectral variability as the final target spectrum.

[0054] Therefore, the characteristics of the response spectrum can be characterized by a pre-selected set of ground motion data used when constructing the response spectrum, and the spectral variability of the candidate spectrum set with respect to the response spectrum can be characterized by the residual between the candidate spectrum set and the pre-selected set of ground motion data.

[0055] In one specific implementation, the spectral variability of the candidate spectral set is characterized by calculating the target residual, where the target residual is defined as the difference between the mean and standard deviation of the candidate spectral set and the mean and standard deviation of a pre-selected set of ground motion data, as shown below: ; ; In the formula, These are weighting factors for different periods. Therefore, the total objective residual... Defined as: ; In the formula, a , b These are the mean residuals and standard deviation residuals The weighting coefficients.

[0056] The candidate spectrum set with the smallest total target residual in each generated candidate spectrum set is calculated and determined. This candidate spectrum set is considered to have the smallest spectral variability and is used as the target spectrum set.

[0057] In the seismic motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence of this invention, the step of selecting several seismic motion data with the highest matching degree with the target spectrum set from the seismic motion database specifically includes: The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each seismic motion data in the seismic motion database. The ground motion data with the highest matching value are selected as the selected ground motion data.

[0058] After determining the target spectral set for matching, it is necessary to find the ground motion data with the highest matching degree in the ground motion database.

[0059] Optionally, the weighted sum of squared errors (WSSE) can be used to quantify the degree of matching between the response spectrum and the target spectrum of the seismic motion data. The smaller the WSSE, the better the match between the response spectrum of the earthquake record and the target spectrum. WSSE is calculated using the following formula: ; In the formula, f This is the linear scaling factor applied to the entire response spectrum in the seismic record. By calculating and comparing the WSSE of ground motion data in the ground motion database, factors corresponding to the target spectrum are selected. N The most matching target spectrum N A scaling earthquake.

[0060] Furthermore, for the N scaled ground motion data selected here, their data quality can be evaluated by calculating the total record residuals between them and the constructed response spectrum.

[0061] Specifically as follows: ; ; The total recorded residuals are calculated as follows: ; In the formula, a , b These are the mean residuals and standard deviation residuals The weighting coefficients.

[0062] The calculation method and principle are the same as those used to determine spectral variability as described above, so they will not be repeated here.

[0063] The smaller the residual of the total record spectrum, the higher the quality of the selected ground motion dataset.

[0064] In the seismic motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence of this invention, the step of selecting several seismic motion data with the highest matching degree with the target spectrum set from the seismic motion database specifically includes: The seismic motion data in the seismic motion database is filtered based on preset constraints; The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each ground motion data obtained by screening in the ground motion database; The ground motion data with the highest matching value are selected as the selected ground motion data.

[0065] Furthermore, in order to reduce the computational burden when matching with the target spectral set, the seismic ground motion data in the seismic ground motion database can be pre-screened based on preset constraints before matching.

[0066] The preset constraints are relevant conditions that characterize the features of seismic data.

[0067] Optionally, the preset constraints can be at least one or more of the following: earthquake magnitude range, earthquake fault type, distance range, and site Vs30 (average shear wave velocity within a 30-meter depth of the soil layer).

[0068] Determine the preset constraints based on the requirements of the seismic test.

[0069] By pre-screening ground motion data in the ground motion database with preset constraints, the selected data is matched with the target spectrum set, thereby reducing the amount of computation required for the matching process.

[0070] The subsequent matching process is the same as the matching process described above, so it will not be repeated here.

[0071] In the seismic motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence of the present invention, before the steps of determining the mean and covariance matrix based on pre-selected multiple sets of seismic motion data and constructing the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, the method further includes: Multiple ground motion data are selected from the ground motion database, wherein each ground motion data includes records of the main shock and aftershocks; It is not difficult to see that the covariance matrix of the response spectrum requires correlation coefficients for two variables: the two main shocks, the two aftershocks, and the one aftershock and one main shock. The correlation coefficients for the two main shocks and the one aftershock and one main shock can be calculated using existing methods.

[0072] The correlation coefficient for the case where the two variables are two aftershocks can be predicted in the following way.

[0073] First, multiple ground motion data are selected from the ground motion database. The selection method is the same as the method of pre-selecting multiple sets of ground motion data when constructing the response spectrum, so it will not be described in detail.

[0074] For each ground motion data point, calculate the correlation coefficient of aftershock spectral acceleration between any two periods; By taking any two periods from each ground motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, a two-aftershock autocorrelation coefficient prediction model is learned. Furthermore, the selected ground motion data are frequency-filtered to obtain ground motion data with multiple periods. In this embodiment, a total of 21 periods of ground motion data (0.01s, 0.02s, 0.03s, 0.05s, 0.075s, 0.1s, 0.15s, 0.2s, 0.25s, 0.3s, 0.4s, 0.5s, 0.75s, 1s, 1.5s, 2s, 3s, 4s, 5s, 7.5s, 10s) were selected.

[0075] For each selected ground motion data, the correlation coefficient of aftershock spectral acceleration between any two periods is calculated. Thus, ground motion data of any two periods can be used as input, and the correlation coefficient of aftershock spectral acceleration calculated based on it can be used as a label to construct and learn a prediction model of the autocorrelation coefficient between two aftershocks.

[0076] In one specific implementation, the resulting prediction model for the autocorrelation coefficients of two aftershocks takes the following form: ; ; ; ; ; In the formula, the period T ∈[0.01s, 10s]; and For any two periodic values ​​within this range, , .

[0077] Its prediction process is as follows: Picture 5 As shown: First, determine the relationship with The size of the first threshold, in If the autocorrelation coefficients of the two aftershocks are less than or equal to the first threshold, the autocorrelation coefficients are calculated using C2; otherwise, Determine the magnitude of the value relative to the first threshold. If the values ​​are greater than the first threshold, the autocorrelation coefficients of the two aftershocks are calculated using C1; otherwise, further judgment is made. With respect to the size of the second threshold, in If the value is greater than or equal to the second threshold, the autocorrelation coefficient of the two aftershocks is calculated using C3; otherwise, the smaller value between C2 and C3 is determined as the autocorrelation coefficient of the two aftershocks.

[0078] The first threshold and the second threshold are values ​​obtained through machine learning. In this embodiment, the first threshold is 0.08 and the second threshold is 0.15. Picture 6 and Picture 7 The figure shows some periodic prediction values ​​and prediction errors of the autocorrelation prediction model in this embodiment.

[0079] The correlation coefficient between the two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model.

[0080] Based on the autocorrelation coefficient prediction model that has been constructed and learned, when constructing the response spectrum, by inputting multiple pre-selected sets of ground motion data, the correlation coefficients of the two variables in the covariance matrix output by the model can be obtained as the parameters of the two aftershocks.

[0081] In the seismic motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence of this invention, the step of calculating the correlation coefficient of aftershock spectral acceleration between any two periods for each seismic motion data specifically includes: Calculate the inter-event residuals and intra-event residuals for each seismic motion data point; The correlation coefficients of the inter-event residuals and the correlation coefficients of the intra-event residuals for each ground motion data point are calculated based on the inter-event residuals and intra-event residuals for each ground motion data point. Specifically, in order to calculate the correlation coefficient between the two aftershock parameters, the inter-event residuals were calculated for each selected seismic motion data point using the CB14 seismic motion attenuation formula. and the residual within the event .

[0082] The inter-event residuals obtained from the above calculations and intra-event residuals The Pearson correlation coefficient was calculated using the sample data, denoted as . and ,in, The correlation coefficient of residuals between events. This is the correlation coefficient of the residuals within the event. The calculation formula is as follows: ; In the formula, The Pearson correlation coefficient; As a variable; , These are the mean values ​​of the variables for periods T1 and T2, respectively.

[0083] Understandably, this is necessary to calculate the autocorrelation coefficient of aftershocks. This is an aftershock. When calculating other correlation coefficients, The definition should be adjusted accordingly.

[0084] In this embodiment, the calculation is based on the above formula. and .

[0085] The aftershock spectrum acceleration correlation coefficient for any two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

[0086] Furthermore, based on and Calculate the correlation coefficient of aftershock spectral acceleration between any two periods: ; In the formula, is the correlation coefficient of aftershock spectral acceleration between any two periods; and are the aftershock spectral accelerations of any two periods, respectively; is the standard deviation between events; is the standard deviation within events; and is the total standard deviation. The calculated results are as follows: Picture 8 and Picture 9 As shown.

[0087] like Picture 10 As shown, the following describes a specific implementation method following the steps of dataset preparation, construction of autocorrelation prediction model and development of ground motion selection method.

[0088] During the preparation of the dataset, a large amount of aftershock data and the corresponding mainshock data of the aftershocks were selected from the ground motion database in the manner described above, as a ground motion record data of an earthquake event.

[0089] For each ground motion record, the CB14 ground motion attenuation formula is used to calculate the aftershock spectrum acceleration residual in logarithmic space, specifically including intra-event residuals and inter-event residuals, and the intra-event residuals are standardized.

[0090] Furthermore, in order to construct an autocorrelation prediction model and develop a ground motion selection method, ground motion records of multiple periods were first selected by frequency limitation. Based on the standardized intra-event residual data, the normal distribution hypothesis of aftershock spectrum acceleration was verified by the QQ plot method, and the joint log-normal distribution hypothesis of mainshock and aftershock spectrum acceleration was tested by the Henze-Zirkler method and the multivariate kurtosis method.

[0091] If the above test results all conform to the log-normal distribution assumption, then the selected seismic ground motion record data from multiple periods can be used to construct an autocorrelation prediction model and complete the development of the seismic ground motion selection method.

[0092] Specifically, in the process of constructing the autocorrelation prediction model, the correlation coefficient between event residuals is calculated based on the already calculated within-event residuals and between-event residuals. Correlation coefficient with intra-event residuals Furthermore, the correlation coefficient of aftershock spectral acceleration between any two cycles was calculated. .

[0093] Based on this, using any two periods from each ground motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, a two-aftershock autocorrelation coefficient prediction model is learned.

[0094] After the autocorrelation coefficient prediction model for two aftershocks was constructed, the mean and standard deviation of ground motion records from multiple periods were calculated using frequency constraints to construct the response spectrum. ; in, The correlation coefficients were obtained by considering both variables as aftershock parameters. The two aftershock autocorrelation coefficient prediction model constructed using the above steps is obtained.

[0095] In the middle, the correlation coefficients obtained from the two variables, the main earthquake parameters, are... The calculation formula is as follows: ; ; ; ; .

[0096] exist In the middle, the correlation coefficient is obtained by taking the parameters of the main shock and the aftershock as the two variables. The calculation formula is as follows: ; ; .

[0097] The construction of the dual-condition response spectrum of the main shock and aftershock sequence is completed in the above manner. By randomly selecting and determining the target spectrum set from the completed response spectrum, the required ground motion data can be obtained by matching the target spectrum set in the ground motion database. The ground motion data obtained at this time can better reflect the combined effect of the main shock and aftershock on the structure in seismic design.

[0098] In this embodiment, the mainshock and aftershock sequence scenario is set as follows: mainshock magnitude 8.00, aftershock magnitude 7.46; fault distance between mainshock and aftershock is 53 km; Vs30 of the mainshock and aftershock site is 760 m / s, belonging to a rocky site. The spectral acceleration of the selected mainshock and aftershock sequence is as follows: Picture 11 and Picture 12 As shown.

[0099] The ground motion selection device based on the dual-conditional response spectrum of the mainshock sequence provided by the present invention will be described below. The ground motion selection device based on the dual-conditional response spectrum of the mainshock sequence described below can be referred to in correspondence with the ground motion selection method based on the dual-conditional response spectrum of the mainshock sequence described above.

[0100] like Picture 13 As shown, the seismic motion selection device based on the dual-conditional response spectrum of the mainshock and aftershock sequence includes a construction module 1301, a determination module 1302, and a selection module 1303: The construction module 1301 is used to construct the response spectrum of the mainshock and aftershock sequence based on the mean and covariance matrix determined by multiple pre-selected sets of ground motion data and the log-normal distribution assumption. The covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters. Verification shows that the vast majority of mainshock and aftershock sequence ground motion data conform to the log-normal distribution assumption. Therefore, based on this, multiple sets of ground motion data conforming to the log-normal distribution can be obtained by screening, their mean and standard deviation can be calculated, and the covariance matrix can be determined based on the standard deviation. The response spectrum of the mainshock and aftershock sequence can be represented in the form of a normal distribution function using the mean and covariance matrix.

[0101] The specific reaction spectrum obtained is shown in the following formula: ; In the formula, Represents vector [ln Sa M ( T 1), ln Sa M ( T 2),…,ln Sa M ( T m ),ln Sa A ( T 1), ln Sa A ( T 2),…,ln Sa ( T n The mean of [ln]]. Sa M ( T 1), ln Sa M ( T 2),…,ln Sa M ( T m ),ln SaA ( T 1), ln Sa A ( T 2),…,ln Sa ( T n [] represents the vector form of the response spectrum of a pre-selected set of ground motion data, where m represents the number of periods of acceleration in the mainshock response spectrum; n represents the number of periods of acceleration in the aftershock response spectrum; subscript M indicates the mainshock, and subscript A indicates the aftershock. N represents the normal distribution function.

[0102] The determination module 1302 is used to randomly sample the constructed reaction spectrum to generate multiple candidate target spectra, and determine the target spectrum set based on the spectral variability of the multiple candidate target spectra; The established reaction spectrum is randomly sampled to generate multiple target spectra, and the multiple target spectra generated in one sampling are combined into a spectrum set.

[0103] Multiple spectra are generated through random sampling, and one of these spectra is selected as the target spectra.

[0104] Optionally, the spectral variability between each spectral set and the specified spectral set is calculated, and the spectral set with the smallest spectral variability is determined as the final target spectral set. The specified spectral set is the spectral set used when constructing the response spectrum.

[0105] The selection module 1303 is used to select several ground motion data that have the highest matching degree with the target spectrum set from the ground motion database.

[0106] The seismic ground motion database is a database that records seismic ground motion data. Optionally, the seismic ground motion database used for matching can be the same as or different from the seismic ground motion database used for constructing the response spectrum. In this embodiment, the global seismic ground motion database (NGA-West2) is used.

[0107] Optionally, the ground motion data in the ground motion database is matched with the target spectrum set, the matching degree of each ground motion data is calculated, and the data with the highest matching degree are used as the ground motion data for seismic design tests.

[0108] This invention determines the mean and covariance matrix of multiple pre-selected sets of ground motion data, constructs the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, and then generates a target spectrum for selecting ground motion data from the ground motion database by sampling the response spectrum. This allows the determined target spectrum to provide better support for the nonlinear dynamic analysis of the structure with ground motion data of the mainshock and aftershock sequence, making up for the deficiency of traditional ground motion selection methods that can only select a single mainshock ground motion, and can be used for ground motion selection under different mainshock and aftershock sequence scenarios.

[0109] Picture 14 An example is a schematic diagram of the physical structure of an electronic device, such as... Picture 14 As shown, the electronic device may include a processor 1410, a communication interface 1420, a memory 1430, and a communication bus 1440, wherein the processor 1410, the communication interface 1420, and the memory 1430 communicate with each other via the communication bus 1440. The processor 1410 can call logical instructions in the memory 1430 to execute a seismic motion selection method for the dual-conditional response spectrum of the mainshock and aftershock sequence. This method includes: determining the mean and covariance matrix based on a pre-selected set of seismic motion data; constructing the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, wherein the covariance matrix is ​​determined based on the correlation coefficient of the two variables being two aftershock parameters; randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining a target spectrum set based on the spectral variability of the multiple candidate target spectra; and selecting several seismic motion data with the highest matching degree with the target spectrum set from the seismic motion database.

[0110] Furthermore, the logical instructions in the aforementioned memory 1430 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0111] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the ground motion selection method for the dual-conditional response spectrum of the mainshock and aftershock sequence provided by the above methods. The method includes: constructing the response spectrum of the mainshock and aftershock sequence based on the mean and covariance matrix determined by a pre-selected set of ground motion data and the log-normal distribution assumption, wherein the covariance matrix is ​​determined based on the correlation coefficient of the two variables being two aftershock parameters; randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining a target spectrum set based on the spectral variability of the multiple candidate target spectra; and selecting several ground motion data with the highest matching degree with the target spectrum set from the ground motion database.

[0112] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements a method for selecting seismic motions of a mainshock-aftershock sequence with a dual-conditional response spectrum provided by the methods described above. The method includes: constructing a response spectrum of the mainshock-aftershock sequence based on the mean and covariance matrix determined from a pre-selected set of seismic motion data, and based on the log-normal distribution assumption, wherein the covariance matrix is ​​determined based on the correlation coefficient of two variables as two aftershock parameters; randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining a target spectrum set based on the spectral variability of the multiple candidate target spectra; and selecting several seismic motion data with the highest matching degree with the target spectrum set from a seismic motion database.

[0113] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0114] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for selecting ground motion based on a master aftershock sequence bi-conditioned response spectrum, characterized by, include: Multiple ground motion data points were selected from the ground motion database, with each data point including records of the main shock and aftershocks; For each ground motion data point, calculate the correlation coefficient of aftershock spectral acceleration between any two periods; By taking any two periods from each ground motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, a two-aftershock autocorrelation coefficient prediction model is learned. The correlation coefficient between the two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model, which represents the two aftershock parameters. The mean and covariance matrix are determined based on a pre-selected set of ground motion data, and the response spectrum of the mainshock and aftershock sequence is constructed based on the log-normal distribution assumption. The covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters. Multiple candidate target spectra are generated by randomly sampling the constructed reaction spectrum, and a target spectrum set is determined based on the spectral variability of the multiple candidate target spectra; Select several ground motion data points from the ground motion database that have the highest matching degree with the target spectrum set; The step of calculating the correlation coefficient of aftershock spectral acceleration between any two periods for each seismic motion data specifically includes: Calculate the inter-event residuals and intra-event residuals for each seismic motion data point; The correlation coefficients of the inter-event residuals and the correlation coefficients of the intra-event residuals for each ground motion data point are calculated based on the inter-event residuals and intra-event residuals for each ground motion data point. The aftershock spectrum acceleration correlation coefficient for any two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

2. The ground motion selection method based on the main aftershock sequence double conditional response spectrum according to claim 1, characterized in that, The step of randomly sampling the constructed reaction spectrum to generate multiple candidate target spectra, and determining the target spectrum set based on the spectral variability of the multiple candidate target spectra, specifically includes: Multiple candidate target spectra are generated by randomly sampling the constructed reaction spectrum, and the multiple candidate target spectra generated at one time are used as a candidate spectrum set; Multiple candidate spectral sets are obtained through multiple sampling, and the spectral variability of each candidate spectral set is determined based on the residual between each candidate spectral set and the pre-selected multiple sets of ground motion data. The candidate spectrum set with the smallest spectral variability is selected as the target spectrum set.

3. The ground motion selection method based on the main aftershock sequence double conditional response spectrum according to claim 1, characterized in that, The step of selecting several ground motion data points with the highest matching degree to the target spectral set from the ground motion database specifically includes: The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each seismic motion data in the seismic motion database. The ground motion data with the highest matching value are selected as the selected ground motion data.

4. The ground motion selection method based on the main aftershock sequence double conditional response spectrum according to claim 1, characterized in that, The step of selecting several ground motion data points with the highest matching degree to the target spectral set from the ground motion database specifically includes: The seismic motion data in the seismic motion database is filtered based on preset constraints; The weighted sum of squared errors method is used to calculate the matching value between the target spectrum set and the response spectrum of each ground motion data obtained by screening in the ground motion database; The ground motion data with the highest matching value are selected as the selected ground motion data.

5. A seismic motion selection device based on the dual-conditional response spectrum of the mainshock and aftershock sequence, characterized in that, include: The module is used to construct the response spectrum of the mainshock and aftershock sequence based on the mean and covariance matrix determined by multiple pre-selected sets of ground motion data and the log-normal distribution assumption. The covariance matrix is ​​determined based on the correlation coefficient of the two variables as two aftershock parameters. The determination module is used to randomly sample the constructed response spectrum to generate multiple candidate target spectra, and determine the target spectrum set based on the spectral variability of the multiple candidate target spectra; The selection module is used to select several ground motion data that have the highest matching degree with the target spectrum set from the ground motion database. The construction module is also used to select multiple ground motion data from the ground motion database, wherein each ground motion data includes records of the main shock and aftershocks; For each ground motion data point, calculate the correlation coefficient of aftershock spectral acceleration between any two periods; By taking any two periods from each ground motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, a two-aftershock autocorrelation coefficient prediction model is learned. The correlation coefficient between the two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model, which represents the correlation coefficient between the two aftershock parameters. The construction module is specifically used to calculate the inter-event residuals and intra-event residuals for each seismic motion data. The correlation coefficients of the inter-event residuals and the correlation coefficients of the intra-event residuals for each ground motion data point are calculated based on the inter-event residuals and intra-event residuals for each ground motion data point. The aftershock spectrum acceleration correlation coefficient for any two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the ground motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the ground motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence as described in any one of claims 1 to 4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the ground motion selection method based on the dual-conditional response spectrum of the mainshock and aftershock sequence as described in any one of claims 1 to 4.

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