Earthquake motion selection method and device based on dual-condition response spectrum of main shock sequence and aftershock sequence

Abstract

The invention provides a seismic oscillation selection method and device based on a dual-condition response spectrum of main and aftershock sequences, and the method comprises the steps: constructing a response spectrum of the main and aftershock sequences based on a logarithmic normal distribution hypothesis according to a mean value and a covariance matrix determined by a plurality of groups of seismic oscillation data selected in advance, the covariance matrix is determined based on a correlation coefficient with two variables being two aftershock parameters; randomly sampling the constructed response spectrum to generate a plurality of candidate target spectrums, and determining a target spectrum set according to the spectrum variability of the plurality of candidate target spectrums; and selecting a plurality of pieces of seismic oscillation data with the highest matching degree with the target spectrum set from the seismic oscillation database. According to the method, the response spectrums of the main and aftershock sequences are constructed, and the target spectrums used for selecting the seismic oscillation data in the seismic oscillation database are generated by sampling the response spectrums, so that the determined target spectrums can better provide main and aftershock sequence seismic oscillation data support for nonlinear dynamic analysis of the structure.

Description

Technical Field

[0001] The invention relates to the technical field of earthquake-resistant design of buildings, and in particular to a method and device for selecting earthquake motion based on a mainshock-aftershock sequence double-condition response spectrum. Background Art

[0002] Performance-based seismic design plays a very important role in earthquake disaster prevention and mitigation and in protecting life and property. Dynamic time history analysis is often used to evaluate the seismic performance of major structures or infrastructure. The time series used as input for nonlinear dynamic analysis is usually selected from previously recorded seismic motions. Since seismic motion is one of the most important factors affecting the uncertainty of system response, selecting a suitable set of seismic records becomes a key step in seismic design.

[0003] In recent years, scholars have developed many methods and tools for seismic motion selection. Among them, classical methods are usually used to select seismic motions whose response spectrum values ​​match the target spectrum, such as the conditional mean spectrum and the design spectrum specified in modern design specifications. Some more advanced seismic motion selection methods select seismic 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 seismic motion intensity parameters (IMs).

[0004] However, existing ground motion selection methods usually focus on the ground motion selection of a single main shock, ignoring the impact of aftershocks on structures, making it difficult for the selected ground motion data to accurately reflect the impact of the complete aftershock process on building structures. Summary of the invention

[0005] The present invention provides a method and device for selecting seismic motion based on the dual-condition response spectrum of a mainshock-aftershock sequence, so as to solve the defect of the prior art that it is difficult to select seismic motion data that reflects the complete aftershock process during seismic design, and realize a more comprehensive method and device for selecting seismic motion based on the dual-condition response spectrum of a mainshock-aftershock sequence.

[0006] The present invention provides a method for selecting earthquake motion based on a dual-condition response spectrum of a main shock and aftershock sequence, comprising: Constructing a response spectrum of a main-aftershock sequence based on a log-normal distribution assumption according to a mean and a covariance matrix determined from a plurality of pre-selected groups of earthquake motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters whose two variables are determined; Randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; A plurality of pieces of earthquake motion data with the highest matching degree with the target spectrum set are selected from the earthquake motion database.

[0007] According to a ground motion selection method based on a mainshock-aftershock sequence dual-condition response spectrum provided by the present invention, the step of randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set according to the spectral variability of the plurality of candidate target spectra specifically includes: Randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and using the multiple candidate target spectra generated at one time as a candidate spectrum set; Sampling multiple times to obtain a plurality of candidate spectrum sets, and determining the spectrum variability of each candidate spectrum set based on the residual between each candidate spectrum set and the pre-selected plurality of groups of ground motion data; The candidate spectrum set with the smallest spectrum variability is used as the target spectrum set.

[0008] According to a method for selecting ground motion based on a mainshock-aftershock sequence dual-condition response spectrum provided by the present invention, the step of selecting a plurality of ground motion data with the highest matching degree with the target spectrum set from the ground motion database specifically comprises: The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake data in the earthquake database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

[0009] According to a method for selecting ground motion based on a mainshock-aftershock sequence dual-condition response spectrum provided by the present invention, the step of selecting a plurality of ground motion data with the highest matching degree with the target spectrum set from the ground motion database specifically comprises: screening the seismic data in the seismic database based on preset restriction conditions; The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake motion data screened in the earthquake motion database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

[0010] According to a method for selecting earthquake motion based on a dual-condition response spectrum of a mainshock and aftershock sequence provided by the present invention, before the step of determining the mean and covariance matrix of a plurality of pre-selected groups of earthquake motion data and constructing the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, the method further includes: Selecting a plurality of earthquake motion data from the earthquake motion database, wherein each earthquake motion data includes recording data of a main shock and an aftershock; Calculate the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data; Taking any two cycles in each seismic data as input and the corresponding aftershock spectrum acceleration correlation coefficient as a label, a prediction model of two aftershock autocorrelation coefficients is learned; The correlation coefficient of two aftershock parameters of two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model.

[0011] According to a ground motion selection method based on a mainshock-aftershock sequence dual-condition response spectrum provided by the present invention, the step of calculating the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data specifically includes: Calculating the inter-event residual and the intra-event residual of each piece of ground motion data; Calculating the inter-event residual correlation coefficient and the intra-event residual correlation coefficient of each piece of seismic motion data according to the inter-event residual and the intra-event residual of each piece of seismic motion data; The aftershock spectral acceleration correlation coefficient of the arbitrary 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 seismic motion selection device based on a main shock and aftershock sequence dual condition response spectrum, comprising: A construction module, for constructing a response spectrum of a main shock and aftershock sequence based on a log-normal distribution assumption according to a mean and a covariance matrix determined by a plurality of pre-selected groups of earthquake motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters when two variables are selected; A determination module, configured to randomly sample the constructed response spectrum to generate a plurality of candidate target spectra, and determine a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; The selection module is used to select a number of earthquake motion data with the highest matching degree with the target spectrum set from the earthquake motion database.

[0013] The present invention also provides an electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the seismic motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence as described above is implemented.

[0014] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the method for selecting earthquake motion based on the dual-condition response spectrum of the mainshock and aftershock sequence as described in any one of the above is implemented.

[0015] The present invention also provides a computer program product, including a computer program, which, when executed by a processor, implements any of the above-mentioned methods for selecting earthquake motions based on the dual-condition response spectrum of a mainshock-aftershock sequence.

[0016] The present invention provides a method and device for selecting seismic motion based on a dual-conditional response spectrum of a mainshock-aftershock sequence. By determining the mean and covariance matrix of a plurality of pre-selected groups of seismic motion data, a response spectrum of the mainshock-aftershock sequence is constructed based on the log-normal distribution assumption. Then, a target spectrum for selecting seismic motion data in a seismic motion database is generated by sampling the response spectrum. The determined target spectrum can provide better support for seismic motion data of the mainshock-aftershock sequence for nonlinear dynamic analysis of the structure, making up for the deficiency that the traditional seismic motion selection method can only select a single mainshock seismic motion, and can be used for seismic motion selection in different mainshock-aftershock sequence scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0018] Picture 1 This is one of the flow diagrams of the method for selecting earthquake motion based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 2 It is a schematic diagram of the distribution of aftershock magnitudes and fault distances selected from an earthquake database in the earthquake motion selection method based on the main-aftershock sequence dual-condition response spectrum provided by the present invention; Picture 3 It is a schematic diagram of the standardized intra-event residuals for displaying aftershock spectral acceleration in the ground motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence provided by the present invention; Picture 4 (a) is the verification result of the QQ diagram when the period is 0.075S in the ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 4 (b) is the verification result of the QQ diagram when the period is 0.5S in the ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 4 (c) is the verification result of the QQ diagram when the period is 2S in the ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 4 (d) is the verification result of the QQ diagram when the period is 10S in the ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 5 It is a prediction flow chart of the autocorrelation coefficient prediction model in the ground motion selection method based on the main shock and aftershock sequence double condition response spectrum provided by the present invention; Picture 6 It is a partial period prediction value of the aftershock spectrum acceleration autocorrelation prediction model in the ground motion selection method based on the main-aftershock sequence dual-condition response spectrum provided by the present invention; Picture 7 It is the partial period prediction error of the aftershock spectrum acceleration autocorrelation prediction model in the ground motion selection method based on the mainshock and aftershock sequence dual condition response spectrum provided by the present invention; Picture 8 It is a curve diagram of the acceleration correlation coefficient of aftershock logarithmic spectrum of a part of the period in the ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 9 It is a hotspot diagram of the acceleration correlation coefficients of aftershock logarithmic spectra of different periods in the ground motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence provided by the present invention; Picture 10 This is the second flow chart of the method for selecting earthquake motion based on the dual-condition response spectrum of the main shock and aftershock sequence provided by the present invention; Picture 11 It is a schematic diagram of the acceleration spectrum of the main shock selected according to the set main aftershock sequence scenario in a specific implementation of the ground motion selection method based on the dual condition response spectrum of the main aftershock sequence provided by the present invention; Picture 12 It is a schematic diagram of aftershock spectrum acceleration selected according to a set main-aftershock sequence scenario in a specific implementation of the ground motion selection method based on the main-aftershock sequence dual-condition response spectrum provided by the present invention; Picture 13 It is a structural schematic diagram of a seismic motion selection device based on a main shock and aftershock sequence dual-condition response spectrum provided by the present invention; Picture 14 It is a structural schematic diagram of the electronic device provided by the present invention. DETAILED DESCRIPTION

[0019] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0020] Combine the following Picture 1 to Picture 12 The present invention introduces the ground motion selection method based on the double condition response spectrum of the main shock and aftershock sequence. Picture 1 As shown, including: Step 101, constructing a response spectrum of a main shock and aftershock sequence based on a log-normal distribution assumption according to means and covariance matrices determined from a plurality of pre-selected groups of earthquake motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters when two variables are selected; A large number of studies and earthquake damage records have shown that aftershocks often aggravate structural damage. Therefore, it is necessary to consider the combined effect of the mainshock and aftershock sequences on structures during earthquake-resistant design. Thanks to the improvement of seismic measurement technology, the aftershock data in the global ground motion database has gradually increased, which provides data support for the nonlinear dynamic analysis of structures under the action of mainshock and aftershock sequences. However, the problem of how to select appropriate mainshock and aftershock sequence ground motions from numerous earthquake events has not yet been solved. To this end, it is necessary to expand the existing ground motion selection method from the mainshock type to the mainaftershock sequence type.

[0021] Verification shows that the vast majority of seismic motion data of the mainshock and aftershock sequences conform to the lognormal distribution assumption. Therefore, on this basis, we can obtain multiple groups of seismic motion data that conform to the lognormal distribution through screening, calculate their means and standard deviations, and determine the covariance matrix based on the standard deviation. Through the mean and covariance matrix, the response spectrum of the mainshock and aftershock sequence can be expressed in the form of a normal distribution function.

[0022] The specific response spectrum is shown as follows: ; In the formula, Represents the 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 )]. Among them, [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 )] is the vector form of the response spectrum of multiple groups of pre-selected earthquake motion data, m represents the period number of the acceleration of the main shock response spectrum; n represents the period number of the acceleration of the aftershock response spectrum; subscript M represents the main shock, subscript A represents the aftershock. N represents the normal distribution function.

[0023] Right now, .

[0024] Represents the 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 )]: ; in: ; ; ; ; In the formula, σ represents the standard deviation, Represents the correlation coefficient.

[0025] Specifically, the correlation coefficient includes the correlation coefficient obtained when the two variables used in calculating the correlation coefficient are the main shock parameters, such as ; It also includes the correlation coefficient obtained by using the two variables used in calculating the correlation coefficient as the main aftershock parameters, such as ; and the correlation coefficient obtained when both variables used in calculating the correlation coefficient are aftershock parameters, such as .

[0026] Among them, the mean and the covariance matrix The standard deviations in σ It is calculated by pre-selecting multiple sets of seismic data. Through the above method, based on the log-normal distribution assumption, the vector mean and covariance matrix of the selected multiple sets of seismic data are calculated by the CB14 seismic attenuation formula, and the response spectrum is constructed.

[0027] In a specific embodiment, aftershock earthquake records are selected from the Global Earthquake Database (NGA-West2).

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

[0029] On the basis of satisfying the conditions, first select the appropriate aftershock data, then determine the mainshock data corresponding to the aftershock, and use the aftershock and the mainshock data corresponding to the aftershock as one seismic motion record data.

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

[0031] Since each selected seismic data has its applicable frequency range, it is assumed that is the lowest available frequency of earthquake motion. When the period T is greater than Based on this restriction, multiple cycles of data that meet the above restriction conditions are further selected from each selected seismic record data 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 earthquake motion record data that has passed the above-mentioned restriction conditions is verified to verify whether it conforms to the log-normal distribution assumption of the aftershock spectral acceleration and the joint log-normal distribution assumption of the main aftershock spectral acceleration.

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

[0034] Alternatively, if Picture 3 As shown, the difference between the within-event residuals and the within-event residual mean is calculated and then divided by the within-event residual standard deviation.

[0035] Then, the log-normal distribution hypothesis test of the aftershock spectral acceleration was performed on the selected seismic record data based on the standardized intra-event residuals.

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

[0037] Furthermore, based on the proof that the aftershock spectral acceleration of the selected earthquake motion record data obeys the log-normal distribution, the Henze-Zirkler method and the multivariate kurtosis method are used to test the joint log-normal distribution hypothesis of the mainshock and aftershock spectral acceleration.

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

[0039] Table 1 Joint logarithmic normality test of mainshock and aftershock spectral acceleration (Chi-Chi earthquake event)

[0040] Table 2 Joint logarithmic normality test of mainshock and aftershock spectral acceleration (three earthquake events)

[0041] In summary, the selected seismic record data are checked and confirmed to conform to the log-normal distribution hypothesis of the aftershock spectral acceleration and the joint log-normal distribution hypothesis of the main aftershock spectral acceleration. Therefore, the response spectrum can be constructed using the seismic record data selected in the above manner.

[0042] In the process of constructing the response spectrum, the CB14 earthquake motion attenuation formula is first used to calculate the mean and standard deviation of each earthquake motion record data. The expression of the CB14 earthquake motion attenuation formula is as follows: ; In the formula, is the natural logarithm of the spectral acceleration when the period is T; is the predicted median value of the logarithmic spectral acceleration when the period is T; M is the earthquake magnitude; R is the fault distance; Other parameters such as site conditions; is the inter-event residual (different earthquake events) in logarithmic space; are the within-event residuals (the same earthquake event) in logarithmic space.

[0043] Through the CB14 formula, the mean and standard deviation of each seismic motion data are calculated based on the magnitude, fault distance and other record values ​​of each seismic motion data, and then the covariance matrix is ​​constructed according to the standard deviation of each seismic motion data. 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 sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; The established response spectrum is randomly sampled to generate multiple target spectra, and the multiple target spectra generated by one sampling are regarded as a spectrum set.

[0045] Multiple spectrum sets are generated by random sampling multiple times, and one of the generated spectrum sets is selected as the target spectrum set.

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

[0047] Step 103: Select from the earthquake motion database a number of earthquake motion data with the highest matching degree with the target spectrum set.

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

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

[0050] The present invention determines the mean and covariance matrix of multiple groups of pre-selected seismic motion data, constructs a response spectrum of the mainshock-aftershock sequence based on the log-normal distribution assumption, and then generates a target spectrum for selecting seismic motion data in the seismic motion database by sampling the response spectrum, so that the determined target spectrum can better provide mainshock-aftershock sequence seismic motion data support for the nonlinear dynamic analysis of the structure, making up for the deficiency of the traditional seismic motion selection method that only a single mainshock seismic motion can be selected, and can be used for seismic motion selection in different mainshock-aftershock sequence scenarios.

[0051] In the ground motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence of the present invention, the step of randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and determining the target spectrum set according to the spectral variability of the multiple candidate target spectra specifically includes: Randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and using the multiple candidate target spectra generated at one time as a candidate spectrum set; Sampling multiple times to obtain a plurality of candidate spectrum sets, and determining the spectrum variability of each candidate spectrum set based on the residual between each candidate spectrum set and the pre-selected plurality of groups of ground motion data; The candidate spectrum set with the smallest spectrum variability is used as the target spectrum set.

[0052] Random sampling of constructed response spectra N candidate target spectra and generate them once N The candidate target spectra form a candidate spectrum set. Multiple rounds of sampling generate multiple candidate spectrum sets.

[0053] It is understandable that for the multiple candidate spectrum sets obtained by sampling, it is necessary to calculate the degree of variation between them and the constructed response spectrum, that is, 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 target spectrum for final use.

[0054] Therefore, the characteristics of the response spectrum can be characterized by the pre-selected multiple sets of earthquake motion data used in 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 multiple sets of earthquake motion data.

[0055] In a specific embodiment, the spectral variability of the candidate spectrum set is characterized by calculating the target residual, wherein the target residual is defined as the difference between the mean and standard deviation of the candidate spectrum set and the mean and standard deviation of multiple pre-selected groups of ground motion data, as shown below: ; ; In the formula, is the weight factor for different periods. Therefore, the total target residual Defined as: ; In the formula, a , b The mean residual and the standard deviation residual The weight coefficient of .

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

[0057] In the seismic motion selection method based on the mainshock-aftershock sequence dual-condition response spectrum of the present invention, the step of selecting a plurality of seismic motion data with the highest matching degree with the target spectrum set in the seismic motion database specifically includes: The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake data in the earthquake database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

[0058] After determining the target spectrum set to be used for matching, it is necessary to search for the seismic data with the highest matching degree with the target spectrum set in the seismic database.

[0059] Optionally, a weighted sum of squared errors (WSSE) is used to quantify the degree of match between the response spectrum of the earthquake data and the target spectrum. The smaller the WSSE, the more the response spectrum of the earthquake record matches the target spectrum. The WSSE is calculated by the following formula: ; In the formula, f is the linear scaling factor applied to the entire response spectrum in the earthquake record. By calculating and comparing the WSSE of the seismic data in the seismic database, the seismic data in the target spectrum are selected. N The entry spectrum that best matches N Scaling ground motion.

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

[0061] The details are as follows: ; ; The total recorded residual is calculated as follows: ; In the formula, a , b The mean residual and the standard deviation residual The weight coefficient of .

[0062] The calculation method and principle are the same as those for determining the spectral variability described above, and therefore will not be described in detail.

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

[0064] In the seismic motion selection method based on the mainshock-aftershock sequence dual-condition response spectrum of the present invention, the step of selecting a plurality of seismic motion data with the highest matching degree with the target spectrum set in the seismic motion database specifically includes: screening the seismic data in the seismic database based on preset restriction conditions; The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake motion data screened in the earthquake motion database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

[0065] Furthermore, in order to reduce the amount of calculation when matching with the target spectrum set, before matching the seismic data in the seismic data database, the seismic data may be pre-screened based on preset restriction conditions.

[0066] Among them, the preset restriction conditions are relevant conditions that characterize the characteristics of seismic data.

[0067] Optionally, the preset restriction condition may be at least one or more of earthquake magnitude range, earthquake fault type, distance range, and site Vs30 (average shear wave velocity within a soil layer of 30 meters in depth).

[0068] Determine the preset limit conditions according to the requirements of the seismic test.

[0069] The seismic data in the seismic database are pre-screened by preset restriction conditions, and the screened data are matched with the target spectrum set, thereby reducing the amount of calculation 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 earthquake motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence of the present invention, before the step of determining the mean and covariance matrix according to the pre-selected multiple groups of earthquake motion data and constructing the response spectrum of the mainshock and aftershock sequence based on the log-normal distribution assumption, the method further includes: Selecting a plurality of earthquake motion data from the earthquake motion database, wherein each earthquake motion data includes recording data of a main shock and an aftershock; It is not difficult to find that the covariance matrix of the response spectrum needs to use the correlation coefficient of two variables, namely two main shocks, two aftershocks, and one aftershock and one main shock. Among them, the correlation coefficient of two variables, namely two main shocks and one aftershock and one main shock, can be calculated by the existing method.

[0072] As for the correlation coefficient when the two variables are two aftershocks, it can be predicted in the following way.

[0073] First, multiple seismic data are selected from the seismic database. The selection method is the same as the method of pre-selecting multiple groups of seismic data when constructing the response spectrum, so it will not be repeated here.

[0074] Calculate the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data; Taking any two cycles in each seismic data as input and the corresponding aftershock spectrum acceleration correlation coefficient as a label, a prediction model of two aftershock autocorrelation coefficients is learned; Furthermore, the selected multiple seismic motion data are frequency screened to obtain seismic motion data of multiple periods. In this embodiment, seismic motion data of 21 periods (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) are selected.

[0075] The aftershock spectrum acceleration correlation coefficient of any two periods is calculated for each selected seismic motion data, so that the seismic motion data of any two periods can be used as input, and the aftershock spectrum acceleration correlation coefficient calculated based on it can be used as a label to construct and learn the two aftershock autocorrelation coefficient prediction model.

[0076] In a specific implementation, the obtained two aftershock autocorrelation coefficient prediction model is in the following form: ; ; ; ; ; In the formula, the period T ∈[0.01s, 10s]; and For any two period values ​​in this range, , .

[0077] The prediction process is as follows Picture 5 As shown: First, judge and The size of the first threshold is When it is less than or equal to the first threshold, the autocorrelation coefficient of the two aftershocks is calculated by C2; otherwise, Determine the size of the first threshold, If it is greater than the first threshold, the autocorrelation coefficient of the two aftershocks is calculated by C1; otherwise, continue to judge With the size of the second threshold, When it is greater than or equal to the second threshold, the autocorrelation coefficient of the two aftershocks is calculated by C3; otherwise, the smaller value of 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 implementation, the first threshold is 0.08 and the second threshold is 0.15. Picture 6 and Picture 7 The partial period prediction values ​​and prediction errors of the autocorrelation prediction model in this embodiment are shown in FIG.

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

[0080] On the basis of constructing and learning the autocorrelation coefficient prediction model, when constructing the response spectrum, by inputting multiple sets of pre-selected seismic motion data, the correlation coefficient of the two variables in the covariance matrix output by the model can be obtained as the two aftershock parameters.

[0081] In the ground motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence of the present invention, the step of calculating the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data specifically includes: Calculating the inter-event residual and the intra-event residual of each piece of ground motion data; Calculating the inter-event residual correlation coefficient and the intra-event residual correlation coefficient of each piece of seismic motion data according to the inter-event residual and the intra-event residual of each piece of seismic motion data; Specifically, in order to calculate the correlation coefficient of the two aftershock parameters, the inter-event residual is calculated using the CB14 seismic attenuation formula for each of the selected multiple seismic data. and the within-event residual .

[0082] The inter-event residuals calculated above are and the within-event residual As sample data, the Pearson correlation coefficient is calculated and recorded as and ,in, is the residual correlation coefficient between events, is the residual correlation coefficient within the event. The calculation formula is as follows: ; In the formula, is the Pearson correlation coefficient; is a variable; , are the means of the variables when the periods are T1 and T2 respectively.

[0083] It is understandable that in order to calculate the aftershock autocorrelation coefficient, is an aftershock. When calculating other correlation coefficients, The definition of is adjusted accordingly.

[0084] In this embodiment, the above formula is used to calculate and .

[0085] The aftershock spectral acceleration correlation coefficient of the arbitrary two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

[0086] Further, based on and Calculate the correlation coefficient of aftershock spectral acceleration between any two periods: ; Where, is the correlation coefficient of aftershock spectrum acceleration between any two periods; and are the aftershock spectrum acceleration between any two periods; is the standard deviation between events; is the standard deviation within an event; is the total standard deviation. The calculated results are as follows: Picture 8 and Picture 9 shown.

[0087] like Picture 10 As shown, a specific implementation method is introduced below according to the steps of data set preparation, autocorrelation prediction model construction and ground motion selection method development.

[0088] In the process of data set preparation, a large amount of aftershock data and main shock data corresponding to the aftershocks are first selected from the seismic motion database in the manner described above as the seismic motion record data of a seismic event.

[0089] The CB14 earthquake attenuation formula is used to calculate the aftershock spectral acceleration residuals in the logarithmic space for each earthquake record data, including the 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 seismic motion selection method, we first select seismic motion record data of multiple periods through frequency restriction, and based on the standardized intra-event residual data, we verify the normal distribution hypothesis of the aftershock spectral acceleration through the QQ plot method, and test the joint log-normal distribution hypothesis of the mainshock and aftershock spectral acceleration through the Henze-Zirkler method and the multivariate kurtosis method.

[0091] When the above test results are all in line with the log-normal distribution assumption, the seismic motion record data of multiple selected periods can be used to construct an autocorrelation prediction model and complete the development of the seismic motion selection method.

[0092] Specifically, in the process of constructing the autocorrelation prediction model, the inter-event residual correlation coefficient is calculated based on the calculated intra-event residual and inter-event residual. and the intra-event residual correlation coefficient The acceleration correlation coefficient of aftershock spectrum between any two periods is further calculated. .

[0093] On this basis, taking any two cycles in each seismic motion data as input and the corresponding aftershock spectrum acceleration correlation coefficient as label, the prediction model of two aftershock autocorrelation coefficients is learned.

[0094] After the two aftershock autocorrelation coefficient prediction models are built, the mean and standard deviation of the seismic record data of multiple cycles selected by frequency restriction are calculated to construct the response spectrum: ; in, The correlation coefficient obtained by using both variables as aftershock parameters , obtained using the two aftershock autocorrelation coefficient prediction model constructed using the above steps.

[0095] The correlation coefficient between the two variables is the main shock parameters. The calculation formula is as follows: ; ; ; ; .

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

[0097] The construction of the dual-condition response spectrum of the mainshock and aftershock sequence is completed in the above manner. By randomly selecting and generating from the constructed response spectrum and determining the target spectrum set, the required seismic motion data can be matched in the seismic motion database through the target spectrum set. The seismic motion data obtained at this time can better reflect the impact of the combined action of the mainshock and aftershocks on the structure in the seismic design.

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

[0099] The seismic motion selection device based on the dual-condition response spectrum of the mainshock-aftershock sequence provided by the present invention is described below. The seismic motion selection device based on the dual-condition response spectrum of the mainshock-aftershock sequence described below and the seismic motion selection method based on the dual-condition response spectrum of the mainshock-aftershock sequence described above can be referenced to each other.

[0100] like Picture 13 As shown, the earthquake motion selection device based on the dual-condition response spectrum of the main shock and aftershock sequence includes a construction module 1301, a determination module 1302 and a selection module 1303: A construction module 1301 is used to construct a response spectrum of a main shock and aftershock sequence based on a log-normal distribution assumption according to a mean and a covariance matrix determined by a plurality of pre-selected groups of ground motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters when two variables are selected; Verification shows that the vast majority of seismic motion data of the mainshock and aftershock sequences conform to the lognormal distribution assumption. Therefore, on this basis, we can obtain multiple groups of seismic motion data that conform to the lognormal distribution through screening, calculate their means and standard deviations, and determine the covariance matrix based on the standard deviation. Through the mean and covariance matrix, the response spectrum of the mainshock and aftershock sequence can be expressed in the form of a normal distribution function.

[0101] The specific response spectrum is shown as follows: ; In the formula, Represents the 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 )]. Among them, [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 )] is the vector form of the response spectrum of multiple groups of pre-selected earthquake motion data, m represents the period number of the acceleration of the main shock response spectrum; n represents the period number of the acceleration of the aftershock response spectrum; subscript M represents the main shock, subscript A represents the aftershock. N represents the normal distribution function.

[0102] A determination module 1302 is used to randomly sample the constructed response spectrum to generate a plurality of candidate target spectra, and determine a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; The established response spectrum is randomly sampled to generate multiple target spectra, and the multiple target spectra generated by one sampling are regarded as a spectrum set.

[0103] Multiple spectrum sets are generated by random sampling multiple times, and one of the generated spectrum sets is selected as the target spectrum set.

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

[0105] The selection module 1303 is used to select a number of earthquake motion data with the highest matching degree with the target spectrum set from the earthquake motion database.

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

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

[0108] The present invention determines the mean and covariance matrix of multiple groups of pre-selected seismic motion data, constructs a response spectrum of the mainshock-aftershock sequence based on the log-normal distribution assumption, and then generates a target spectrum for selecting seismic motion data in the seismic motion database by sampling the response spectrum, so that the determined target spectrum can better provide mainshock-aftershock sequence seismic motion data support for the nonlinear dynamic analysis of the structure, making up for the deficiency of the traditional seismic motion selection method that only a single mainshock seismic motion can be selected, and can be used for seismic motion selection in different mainshock-aftershock sequence scenarios.

[0109] Picture 14 An example of a physical structure diagram of an electronic device is shown in FIG. 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 through the communication bus 1440. The processor 1410 may call the logic instructions in the memory 1430 to execute the ground motion selection method of the dual-condition response spectrum of the main-aftershock sequence, the method comprising: constructing the response spectrum of the main-aftershock sequence based on the mean and covariance matrix determined by a plurality of pre-selected groups of ground motion data and based on the log-normal distribution assumption, wherein the covariance matrix is ​​determined based on the correlation coefficient of two variables being two aftershock parameters; randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining the target spectrum set based on the spectrum variability of the plurality of candidate target spectra; and selecting a plurality of ground motion data with the highest matching degree with the target spectrum set from the ground motion database.

[0110] In addition, the logic instructions in the above-mentioned memory 1430 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when it is sold or used as an independent product. Based on such an understanding, the technical solution of the present invention can be essentially or partly embodied in the form of a software product that contributes to the prior art. The computer software product is stored in a storage medium, including several instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, etc. Various media that can store program codes.

[0111] On the other hand, the present invention also provides a computer program product, which includes a computer program, which 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 seismic motion selection method for the dual-conditional response spectrum of the mainshock sequence provided by the above-mentioned methods, the method including: constructing the response spectrum of the mainshock sequence based on the log-normal distribution assumption according to the mean and covariance matrix determined by multiple groups of pre-selected seismic motion data, wherein the covariance matrix is ​​determined based on the correlation coefficient of two aftershock parameters based on two variables; 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; and selecting from the seismic motion database a number of seismic motion data with the highest matching degree with the target spectrum set.

[0112] On the other hand, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to execute the seismic motion selection method for the dual-conditional response spectrum of the mainshock sequence provided by the above-mentioned methods, the method comprising: constructing a response spectrum of the mainshock sequence based on the log-normal distribution assumption according to the mean and covariance matrix determined according to a plurality of pre-selected groups of seismic motion data, wherein the covariance matrix is ​​determined based on the correlation coefficient of two aftershock parameters based on two variables; randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set based on the spectral variability of the plurality of candidate target spectra; and selecting from the seismic motion database a plurality of seismic motion data with the highest matching degree with the target spectrum set.

[0113] The device embodiments described above are merely illustrative, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0114] Through the description of the above implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, can also be implemented by hardware. Based on this understanding, the above technical solution is essentially or the part that contributes to the prior art can be embodied in the form of a software product, and the computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment 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, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions 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 the double-condition response spectrum of mainshock and aftershock sequences, characterized in that: include: Constructing a response spectrum of a main-aftershock sequence based on a log-normal distribution assumption according to a mean and a covariance matrix determined from a plurality of pre-selected groups of earthquake motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters whose two variables are determined; Randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; A plurality of seismic motion data with the highest matching degree with the target spectrum set are selected from the seismic motion database.

2. The ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence according to claim 1 is characterized in that: The step of randomly sampling the constructed response spectrum to generate a plurality of candidate target spectra, and determining a target spectrum set according to the spectrum variability of the plurality of candidate target spectra specifically includes: Randomly sampling the constructed response spectrum to generate multiple candidate target spectra, and using the multiple candidate target spectra generated at one time as a candidate spectrum set; Sampling multiple times to obtain a plurality of candidate spectrum sets, and determining the spectrum variability of each candidate spectrum set based on the residual between each candidate spectrum set and the pre-selected plurality of groups of ground motion data; The candidate spectrum set with the smallest spectrum variability is used as the target spectrum set.

3. The ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence according to claim 1 is characterized in that: The step of selecting a plurality of pieces of seismic motion data with the highest matching degree with the target spectrum set from the seismic motion database specifically includes: The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake data in the earthquake database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

4. The ground motion selection method based on the dual-condition response spectrum of the main shock and aftershock sequence according to claim 1 is characterized in that: The step of selecting a plurality of pieces of seismic motion data with the highest matching degree with the target spectrum set from the seismic motion database specifically includes: screening the seismic data in the seismic database based on preset restriction conditions; The weighted error square sum method is used to calculate the matching value between the target spectrum set and the response spectrum of each earthquake motion data screened in the earthquake motion database; The plurality of pieces of seismic motion data having the highest matching values ​​are determined as the selected plurality of pieces of seismic motion data.

5. The method for selecting ground motion based on the dual-condition response spectrum of mainshock and aftershock sequences according to any one of claims 1 to 4, characterized in that: Before the step of determining the mean and covariance matrix of the pre-selected multiple groups of earthquake motion data and constructing the response spectrum of the main shock and aftershock sequence based on the log-normal distribution assumption, the method further includes: Selecting a plurality of earthquake motion data from the earthquake motion database, wherein each earthquake motion data includes recording data of a main shock and an aftershock; Calculate the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data; Taking any two cycles in each seismic data as input and the corresponding aftershock spectrum acceleration correlation coefficient as a label, a prediction model of two aftershock autocorrelation coefficients is learned; The correlation coefficient of two aftershock parameters of two variables in the covariance matrix is ​​determined by the autocorrelation coefficient prediction model.

6. The method for selecting ground motion based on the dual-condition response spectrum of mainshock and aftershock sequences according to claim 5 is characterized in that: The step of calculating the aftershock spectrum acceleration correlation coefficient of any two cycles for each ground motion data specifically includes: Calculating the inter-event residual and the intra-event residual of each piece of ground motion data; Calculating the inter-event residual correlation coefficient and the intra-event residual correlation coefficient of each piece of seismic motion data according to the inter-event residual and the intra-event residual of each piece of seismic motion data; The aftershock spectral acceleration correlation coefficient of the arbitrary two periods is calculated based on the inter-event residual correlation coefficient and the intra-event residual correlation coefficient.

7. A seismic motion selection device based on the dual-condition response spectrum of the main shock and aftershock sequence, characterized in that: include: A construction module, for constructing a response spectrum of a main shock and aftershock sequence based on a log-normal distribution assumption according to a mean and a covariance matrix determined by a plurality of pre-selected groups of ground motion data, wherein the covariance matrix is ​​determined based on a correlation coefficient of two aftershock parameters based on two variables; A determination module, configured to randomly sample the constructed response spectrum to generate a plurality of candidate target spectra, and determine a target spectrum set according to the spectrum variability of the plurality of candidate target spectra; The selection module is used to select a number of earthquake motion data with the highest matching degree with the target spectrum set from the earthquake motion database.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the ground motion selection method based on the dual-condition response spectrum of the mainshock and aftershock sequence as described in any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for selecting earthquake motion based on the dual-condition response spectrum of a mainshock-aftershock sequence as claimed in any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method for selecting earthquake motion based on the dual-condition response spectrum of a mainshock-aftershock sequence as claimed in any one of claims 1 to 6 is implemented.

Images