A method for selecting earthquake record sets matching the probability distribution of multiple earthquake intensity indicators

Abstract

The present invention provides a method for selecting an earthquake record set that matches the probability distribution of multiple earthquake intensity indicators, including: according to different requirements of seismic time-history analysis of different structures, selecting the earthquake intensity indicator with the greatest impact on the structural response indicator as a conditional indicator. Perform a probabilistic earthquake hazard analysis on the engineering site where the structure to be analyzed is located, and set earthquake decoupling in two dimensions (magnitude-distance) or three dimensions (magnitude-longitude-latitude). Assuming that different earthquake intensity indicators satisfy a multivariate normal distribution, calculate the conditional probability distribution under the conditional earthquake intensity indicator. Calculate the earthquake intensity indicators of different records in the strong earthquake record database, and search for the earthquake record combination with the smallest difference from the target conditional probability distribution of the earthquake intensity indicator in the strong earthquake record database.

Description

Technical Field

[0001] The present invention belongs to a method for determining a combination of earthquake motion records for structural seismic time history analysis, and specifically relates to a method for constructing a probability distribution of target conditions for multiple earthquake motion intensity indicators and selecting records. Background Art

[0002] The current mainstream seismic motion record selection technology generally aims to achieve mean matching of the target response spectrum (such as the design response spectrum). In essence, it is to select seismic motion records one by one by judging the relative error between the earthquake record response spectrum and the target code response spectrum. However, the current diverse structural types and different structural response indicators require that seismic motion records should simultaneously control multiple seismic motion intensity indicators, rather than being limited to a single indicator such as the target response spectrum or peak acceleration. And with the maturity of structural seismic elastoplastic time-history analysis technology, it is often required to select a combination of multiple seismic motion records as the input of structural seismic analysis, so it is particularly important to simultaneously control the discreteness of multiple sets of seismic motion records. This is the main background for the construction of target probability distributions of multiple seismic motion intensity indicators and the proposal of an efficient record selection scheme in this study.

[0003] At present, the matching method for the target response spectrum mean is generally to determine the matching target periodic point (segment), and then measure the relative error by calculating the minimum sum of squares of the error based on the least squares idea. The differences among different scholars lie in the range of the periodic segment and the method of determining the amplitude modulation coefficient, such as the dual-band matching method, the full-period segment matching method, the adaptive record selection method proposed by Ji Kun and others, and the weighted seismic record selection method of Zhang Rui.

[0004] The core defect of the above method is that it cannot quantify and control the discreteness between the record selection results. It can only reduce the discreteness as much as possible. This ignores the uncertainty of the seismic motion itself and is only suitable for the mean estimation of the structural response index. It is not suitable for the selection of multiple records, and it is impossible to control multiple seismic intensity indicators at the same time. Studies have shown that the discreteness between records will greatly affect the results of the final structural seismic time-history analysis (Ji et al., 2022). Foreign scholars have verified that the influence of the discreteness between seismic records on the final results cannot be ignored under the requirements of New Zealand, the United States and Europe.

[0005] Liu Tingting proposed "A method for selecting seismic motion records based on cluster analysis, application number CN202111079292.9" and Hu Jinjun et al. proposed "An input seismic motion selection method for quantitative ranking of global seismic motion based on destructive intensity, application number CN202011564947.7". Neither of them involves the control of the mean and discreteness of the intensity index of the record selection intensity. The former is a screening and control method for earthquake information such as magnitude and site, and the latter is a screening based on the idea of ​​the most unfavorable seismic motion ranking. Both cannot select seismic motion records while simultaneously controlling the amplitude and discreteness of multiple seismic motion intensity indicators. Summary of the invention

[0006] The present invention provides a method for selecting earthquake record sets that matches the probability distribution of multiple earthquake intensity indicators for selecting earthquake input records in structural seismic time history analysis, and can simultaneously control the amplitudes and discreteness of multiple earthquake intensity indicators. The selection method comprises the following steps:

[0007] (1) According to the structural characteristics and the requirements of seismic time history analysis, based on the results of elastoplastic time history analysis, determine the combination of seismic intensity indices (IM) that have a high correlation with the response index of the structure to be analyzed, and determine the number of seismic records to be selected;

[0008] (2) According to the seismic motion intensity index (IM) combination, a scalar and / or vector probability seismic hazard analysis of the seismic motion intensity index in the seismic motion intensity index (IM) combination is performed on the site where the structure to be analyzed is located, and the amplitude level of the seismic motion intensity index under the target year exceedance probability is obtained, and then the decoupling results of the set earthquake events are obtained: magnitude-distance set earthquake events and / or magnitude-longitude-latitude set earthquake events; the magnitude-distance range and / or the magnitude-longitude-latitude range are obtained, and the contribution rate of the permutations and combinations of different set earthquake events within the magnitude-distance range and / or the magnitude-longitude-latitude range to the amplitude of the seismic motion intensity index under the target year exceedance probability level is obtained;

[0009] (3) Determine the probability distribution of the seismic intensity index in the seismic intensity index (IM) combination according to the following formula;

[0010] Assume that the amplitude of an earthquake intensity index IM1 under the target year exceedance probability level is x, and the other earthquake intensity index is IM2. Assuming that the combination of earthquake intensity indexes {lnIM1, lnIM2} conforms to the bivariate normal distribution under logarithm, the probability distribution of the combination of earthquake intensity indexes (IM) is defined as follows:

[0011]

[0012] Wherein, μ1 and μ2 are the logarithmic predicted medians of the seismic intensity index given by the seismic prediction equation or attenuation model of the province or seismic zone where the site is located, σ1 and σ2 are the logarithmic standard deviations of the seismic intensity index given by the seismic prediction equation or attenuation model; ρ is the Pearson correlation coefficient of IM1 and IM2; N{} is a bivariate normal distribution;

[0013] The probability distribution of IM2 is defined as follows: x represents the value of IM1;

[0014] IM2 Amplitude and standard deviation They are defined as:

[0015]

[0016] (4) obtaining the seismic intensity index of each record provided by the seismic record database, or calculating the seismic intensity index of each seismic record;

[0017] (5) Assuming that the structural seismic time history analysis requires n earthquake records as input, a random sampling without replacement is performed in the strong earthquake record database in (4), and m combinations of earthquake records are randomly selected, i.e., a total of m×n records, as the initial group; where the earthquake intensity index vector {IM1, IM2, IM m} as individuals in the initial population; each earthquake record combination contains n earthquake records; n and m are both positive integers, and the maximum number of iterations is set; through the genetic operator operations of selection, crossover, and mutation, the individual with the largest fitness function is taken as the optimal earthquake record combination. If the optimal solution is still not found after the maximum number of iterations, re-sampling is performed to determine a new initial population, and the above operations are repeated until the fluctuation value of the fitness function is lower than the set threshold or the specified maximum number of calculation steps is reached; the fitness function is defined as follows:

[0018]

[0019] Among them, w1 and w2 represent the weight coefficients of the mean and standard deviation; m is the number of groups of earthquake record combinations contained in the group, and n is the number of earthquake record items to be selected. and Determined based on the probability distribution of the target ground motion intensity index, see step (3);

[0020] (6) Perform a KS hypothesis test on the selected results of the seismic record combination in step (5) and determine the seismic intensity index vector {IM1, IM2, IM m}Whether it conforms to the target probability distribution; if the hypothesis test cannot be passed, that is, the IM distribution of the record selection result does not conform to the target probability distribution, repeat step (5), re-randomly determine the group, and select records until the final result meets the requirements, and take the n earthquake motion records that meet the requirements as the selection result.

[0021] Furthermore, in step (1), the seismic intensity index combination includes one or more seismic intensity indicators, including but not limited to: one or more of the acceleration response spectrum value (Sa(T1)) at the natural vibration period point of the structure, peak acceleration, peak velocity, and effective duration of seismic motion.

[0022] Furthermore, in step (2), the site includes but is not limited to a construction project site.

[0023] Furthermore, in step (4), the seismic record database is a domestic or foreign open source seismic record database, or a seismic record database built by the user.

[0024] Furthermore, in step (4), if the data source does not provide the calculation results of the intensity index of the seismic motion record, the IM index of different strong motion records should be calculated one by one. Before the calculation, the original seismic motion record is subjected to non-causal Butterworth filtering and polynomial baseline correction, and the low-pass filter cutoff frequency is determined by judging the residual displacement drift and signal-to-noise ratio and other indicators.

[0025] Furthermore, the value range of w1 and w2 is 0.1 to 1.0, and the default value is 0.5.

[0026] Furthermore, in step (5), the values ​​of w1 and w2 are manually set and can be adjusted according to the iteration results.

[0027] Furthermore, in step (5), the threshold is set to 5% per iteration step.

[0028] In addition, the present invention also provides a seismic record set selection system for matching the probability distribution of multiple seismic intensity indicators, including a calculation module for executing the above-mentioned seismic record set selection method for matching the probability distribution of multiple seismic intensity indicators.

[0029] The beneficial effects of the present invention include: when selecting a combination of multiple seismic records as input for structural seismic analysis, the discreteness of multiple sets of seismic records can be controlled simultaneously. The present invention can set a quantitative target discreteness before selecting seismic records, and actively select seismic records according to the set discreteness, thereby overcoming the shortcomings of the traditional seismic record selection method that can only calculate the discreteness after selecting the seismic record, and cannot quantify and control the discreteness between seismic records in advance. In addition, the present invention fully considers the uncertainty of the seismic intensity index in the seismic record, thereby ensuring that the results of the subsequent structural seismic force history analysis are representative. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 Flowchart of the strong motion record combination selection method for simultaneously controlling the amplitude and discreteness of multiple seismic intensity indicators.

[0031] Figure 2 It is a schematic diagram of the result of setting earthquake decoupling in the site probabilistic seismic hazard analysis of the embodiment.

[0032] Figure 3 Comparison chart of the IM mean and target mean for the selected seismic record.

[0033] Figure 4 Comparison chart of IM cumulative probability distribution and target probability distribution for earthquake motion record selection results. DETAILED DESCRIPTION

[0034] In order to make the purpose, technical scheme and advantages of the present invention clearer, the technical scheme of the present invention will be described in detail below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other implementation methods obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0035] Example 1

[0036] refer to Figure 1 As shown, this embodiment provides a method for selecting a combination of strong earthquake records that can simultaneously control the amplitude and discreteness of multiple earthquake intensity indicators, including the following steps:

[0037] Step S1: Figure 1 As shown, the earthquake intensity index with a high correlation with the structural response index concerned in the seismic time-history analysis of the target structure and the number of records that need to be selected are determined.

[0038] Step S2: Figure 1As shown, a scalar (vector) probability seismic hazard analysis of a single or multiple seismic intensity index is performed on the engineering site where the structure is located. The amplitude level of the seismic intensity index under the target year exceedance probability is obtained, and decoupled to obtain a two-dimensional (magnitude-distance) or three-dimensional (magnitude-longitude-latitude) set earthquake event.

[0039] Step S3: Figure 1 As shown, assuming that different earthquake intensity indicators satisfy the multivariate normal distribution relationship, the multivariate probability distribution of the target earthquake intensity indicator is determined through conditional probability, and then the mean and standard deviation of the earthquake intensity indicator are determined.

[0040] Step S4: Calculate the seismic intensity index of each seismic record through open source strong earthquake record databases at home and abroad or user-built strong earthquake record databases. If it is an unprocessed original record, non-causal filtering and baseline correction should be performed.

[0041] Step S5: Using a genetic algorithm, efficiently search for a combination of earthquake records with the smallest difference between the earthquake intensity index vector and the mean and standard deviation obtained in step S3.

[0042] Step S6: Through the KS hypothesis test, verify whether the seismic intensity index of the strong motion record combination selected in step S5 is consistent with the target probability distribution within the confidence interval.

[0043] Example 2

[0044] On the basis of Example 1, this embodiment uses a seismic record set selection system that matches the probability distribution of multiple seismic intensity indicators, including a calculation module, executes a seismic record set selection method that matches the probability distribution of multiple seismic intensity indicators, and applies the method to a high-rise concrete frame-shear structure. The specific steps include:

[0045] (1) Determine the earthquake intensity index and number of records to be selected

[0046] Assume that the structure to be subjected to seismic time history analysis is a high-rise concrete frame-shear structure with a natural vibration period of 3.0s. The target structural response index is the maximum inter-story displacement angle. Studies have shown that the seismic intensity index with a strong correlation with it is the seismic acceleration response spectrum value at the natural vibration period, that is, Sa(3.0s). In addition to this conditional index, the seismic intensity indexes considered in this example include:

[0047] Acceleration response spectrum at T = 0.05, 0.1, 0.2, 0.3, 0.5, 1.0, 2.0, 5.0, 10.0s, peak acceleration PGA, peak velocity PGV, spectral acceleration intensity ASI, Hausner spectral intensity SI, displacement spectral intensity DSI, cumulative spectral intensity CAV, significant duration Ds575, and significant duration Ds595

[0048] The number of records to be selected is generally 10 to 30, 30 are selected here, and in some embodiments, 20 or 15 are selected.

[0049] (2) Site probabilistic seismic hazard analysis and earthquake decoupling

[0050] A scalar probability earthquake hazard analysis is conducted on the engineering site where the structure is located, and the amplitudes of different seismic intensity indicators are obtained when the target earthquake hazard level is an annual exceedance probability of 2%, where Sa(3.0s)=0.14g.

[0051] Then, two-dimensional earthquake decoupling is performed to obtain different earthquake settings (magnitude-distance combinations). The decoupling results of some earthquake intensity indicators, that is, the contribution rate bar chart of magnitude-distance combinations, are shown in the figure below.

[0052] (3) Obtaining the multivariate probability distribution of different earthquake intensity indicators

[0053] Estimate the conditional probability distribution of different earthquake intensity indices under Sa(3.0s) = 0.14g. The mean (amplitude index) of any earthquake intensity index IM2 is and standard deviation (dispersion indicator) Defined as:

[0054]

[0055] in, is the logarithmic predicted median of the seismic intensity index given by the seismic prediction equation of the province or seismic zone where the site is located. The seismic prediction equation here adopts the attenuation relationship used in the fifth generation seismic parameter zoning map of my country. The predicted median is and σ2 are the logarithmic standard deviations of the seismic intensity index Sa(3.0s) and IM2 given by the seismic prediction equation or attenuation model. ρ is the Pearson correlation coefficient between Sa(3.0s) and IM2, and the value of this coefficient can be obtained from the literature. (e.g. Ji et al., 2020; 2021) and The results are listed in Table 1.

[0056] Table 1

[0057]

[0058] (4) Calculate the seismic intensity index of the seismic records in the strong motion record database.

[0059] Sixth-order multiple baseline correction and non-causal Butterworth filtering were performed on 7183 earthquake records in the NSMONS database of China from 2007 to 2015, which have relatively complete earthquake information and all three components of ground motion acceleration. The filtering frequency band is 0.2 Hz to 20 Hz. Multiple ground motion intensity indicators considered in this example were calculated.

[0060] (5) Selection of seismic records matching target probability distribution based on genetic algorithm

[0061] The genetic algorithm parameters used are as follows:

[0062] Group size: 600

[0063] Crossover rate: 0.6

[0064] Mutation rate: 0.01

[0065] Maximum number of iterations: 1000

[0066] Fitness function change threshold: 5% / step

[0067] Random sampling without replacement is performed in the strong earthquake record database in (3), and 600×30 seismic record combinations are randomly selected as the group, where the intensity index vector {Sa, PGA, PGV, ASI, SI, Ds595} of each seismic record combination is used as an individual. The maximum number of iterations is set to 1000. Through the genetic operator operations of selection, crossover and mutation, the individual with the largest fitness function is taken as the optimal strong earthquake record combination. If the optimal solution is still not found after exceeding the maximum number of iterations, re-sampling is performed to determine a new initial group, and the above operation is repeated until the fitness function fluctuation value is lower than the threshold.

[0068]

[0069] in, and Obtained in step (3), see Table 1.

[0070] Finally, the comparison results of the mean and standard deviation of the selected results and the target probability distribution are recorded as follows: Figure 3 shown.

[0071] (6) Verify whether the record selection results meet the target probability distribution.

[0072] Through the KS hypothesis test, draw a 5% confidence interval, such as Figure 4 By comparing the cumulative probability distribution curve (CDF) of the seismic intensity index of the strong motion record combination selected in the previous step with the confidence boundary, it is shown that multiple seismic intensity indexes fall within the confidence interval, and it can be considered that the record selection result is consistent with the target probability distribution.

Claims

1. A method for selecting an earthquake record set that matches the probability distribution of multiple earthquake intensity indicators, characterized in that: The steps include: (1) According to the structural characteristics and the requirements of seismic time history analysis, based on the results of elastoplastic time history analysis, determine the combination of seismic intensity indices (IM) that have a high correlation with the response index of the structure to be analyzed, and determine the number of seismic records to be selected; (2) According to the IM combination, the scalar and / or vector probability seismic hazard analysis of the IM combination is performed on the site where the structure to be analyzed is located, and the amplitude level of the IM under the exceedance probability of the target year is obtained, and then the decoupling results of the set earthquake events are obtained: magnitude-distance set earthquake events and / or magnitude-longitude-latitude set earthquake events; Obtaining a magnitude-distance range and / or a magnitude-longitude-latitude range, and obtaining contribution rates of permutations and combinations of different set earthquake events within the magnitude-distance range and / or the magnitude-longitude-latitude range to the amplitude of the seismic intensity index under the target year exceedance probability level; (3) Determine the probability distribution of the seismic intensity index in the seismic intensity index (IM) combination according to the following formula; Assume that the amplitude of an earthquake intensity index IM1 under the target year exceedance probability level is x, and the other earthquake intensity index is IM2. Assuming that the combination of earthquake intensity indexes {lnIM1, lnIM2} conforms to the bivariate normal distribution under logarithm, the probability distribution of the combination of earthquake intensity indexes (IM) is defined as follows: Wherein, μ1 and μ2 are the logarithmic predicted medians of the seismic intensity index given by the seismic prediction equation or attenuation model of the province or seismic zone where the site is located, σ1 and σ2 are the logarithmic standard deviations of the seismic intensity index given by the seismic prediction equation or attenuation model; ρ is the Pearson correlation coefficient of IM1 and IM2; N{} is a bivariate normal distribution; The probability distribution of IM2 is defined as follows: x represents the value of IM1; IM2 Amplitude and standard deviation They are defined as: (4) obtaining the seismic intensity index of each record provided by the seismic record database, or calculating the seismic intensity index of each seismic record; (5) Assuming that the structural seismic time history analysis requires n earthquake records as input, a random sampling without replacement is performed in the strong earthquake record database in (4), and m combinations of earthquake records are randomly selected, i.e., a total of m×n records, as the initial group; where the earthquake intensity index vector {IM1, IM2, IM m } as individuals in the initial population; each earthquake record combination contains n earthquake records; n and m are both positive integers, and the maximum number of iterations is set; through the genetic operator operations of selection, crossover, and mutation, the individual with the largest fitness function is taken as the optimal earthquake record combination. If the optimal solution is still not found after the maximum number of iterations, re-sampling is performed to determine a new initial population, and the above operations are repeated until the fluctuation value of the fitness function is lower than the set threshold or the specified maximum number of calculation steps is reached; the fitness function is defined as follows: Among them, w1 and w2 represent the weight coefficients of the mean and standard deviation; m is the number of groups of earthquake record combinations contained in the group, and n is the number of earthquake record items to be selected. and Determined based on the probability distribution of the target ground motion intensity index, see step (3); (6) Perform a KS hypothesis test on the selected results of the seismic record combination in step (5) and determine the seismic intensity index vector of the selected n seismic record data under a 5% confidence interval. {IM1,IM2,IM m }Whether it conforms to the target probability distribution; if the hypothesis test cannot be passed, that is, the IM distribution of the record selection result does not conform to the target probability distribution, repeat step (5), re-randomly determine the group, and select records until the final result meets the requirements, and take the n earthquake motion records that meet the requirements as the selection result.

2. The selection method according to claim 1, characterized in that: In step (1), the seismic intensity index combination includes one or more seismic intensity indicators, including but not limited to: one or more of the acceleration response spectrum value (Sa(T1)) at the natural vibration period point of the structure, peak acceleration, peak velocity, and effective duration of seismic motion.

3. The selection method according to claim 1, characterized in that: In step (2), the site includes but is not limited to a construction project site.

4. The selection method according to claim 1, characterized in that: In step (4), the seismic record database is a domestic or foreign open source seismic record database, or a seismic record database built by the user.

5. The selection method according to claim 1, characterized in that: In step (4), if the data source does not provide the calculation results of the intensity index of the seismic motion record, the IM index of different strong motion records should be calculated one by one. Before calculation, the original seismic motion record is subjected to non-causal Butterworth filtering and polynomial baseline correction, and the low-pass filter cutoff frequency is determined by judging the residual displacement drift and the signal-to-noise ratio.

6. The selection method according to claim 1, characterized in that: In step (5), the value range of w1 and w2 is 0.1 to 1.0, and the default value is 0.

5.

7. The selection method according to claim 1, characterized in that: In step (5), the values ​​of w1 and w2 are set manually and can be adjusted according to the iteration results.

8. The selection method according to claim 1, characterized in that: In step (5), the threshold is set to 5% per iteration step.

9. A seismic record set selection system matching the probability distribution of multiple seismic intensity indicators, characterized in that: It includes a calculation module for executing the earthquake record set selection method for matching the probability distribution of multiple earthquake intensity indicators as described in any one of claims 1-8.

Images