A method and system for selecting seismic motion records matching earthquake recurrence period

Abstract

The invention relates to the field of earthquake engineering technology, in particular to a method and system for selecting earthquake motion records matching an earthquake recurrence period; the method comprises the following steps: step one: generating a random earthquake event catalog; step two: calibrating the total earthquake occurrence rate; step three: determining a plurality of earthquake intensity indices related to an analysis structure; step four: determining the joint probability of a plurality of earthquake intensity indices; step five: obtaining a simulated spectrum through an error threshold of a Kendall recurrence period, and obtaining a target spectrum by calculating a mean and a standard deviation of the simulated spectrum; and step six: after the target spectrum distribution is known, selecting a set of records that meet the requirements from a target database; the invention constructs a target spectrum according to a multivariate Kendall recurrence period, which not only gets rid of the problem that a traditional wave selection scheme is greatly affected by the selection of a conditional earthquake motion intensity index, but also provides a mathematically rigorous scheme for constructing a wave selection target spectrum with an IM combined hazard level as a control index, thereby providing a more accurate earthquake demand estimation for earthquake motion records.

Description

Technical Field

[0001] The present invention relates to the field of earthquake engineering technology, and in particular to a method and system for selecting earthquake motion records that match an earthquake recurrence period. Background Art

[0002] With the implementation of urban renewal and new urbanization projects in my country, the seismic analysis of different types of engineering structures is developing in a diversified direction, and the requirements for engineering seismic input are also increasing. At present, the most commonly used method is to select strong vibration records that meet the target response spectrum for structural seismic analysis. The current mainstream wave selection target spectrum construction schemes are all based on the conditional spectrum framework theory. In essence, they all use a certain seismic intensity index as the "anchored" conditional strength index. Based on the correlation between other strength indicators and the conditional strength index, conditional probability distributions are constructed to constrain the probability hazard level of other strength indicators, and other vibration modes of the structure are not effectively considered. In addition, the seismic response of the structure in actual engineering may be related to multiple strength indicators such as response spectra at different period points, cumulative energy, and duration. Selecting different conditional strength indicators will cause non-negligible deviations in the results of the structural probabilistic seismic demand analysis.

[0003] Zhang Rui proposed the "Application No. CN202310123059.9, a method for selecting input seismic motion for seismic time-history analysis of structures based on joint target spectrum" and Li Bo et al. proposed the "Application No. CN202211507829.1, a method and device for selecting seismic motion records based on seismic hazard consistency". The former is essentially a segmented conditional spectrum, and the latter is essentially the selection of seismic motion records that are consistent with the seismic hazard of the target site. Neither of them has achieved the control of the joint hazard level of multiple seismic motion intensity indicators. Summary of the invention

[0004] The purpose of the present application is to provide a method and system for selecting seismic motion records that match the earthquake recurrence period, aiming to solve the problems in the prior art.

[0005] The present application provides a method for selecting seismic records matching an earthquake recurrence period, comprising the following steps:

[0006] Step 1: For the target site, random sampling is used to generate a random earthquake event catalog that can reflect the seismic activity characteristics of the site within a certain observation time span, and the generated random earthquake event catalog is simplified, and the simplified subset is used to represent the original event set;

[0007] Step 2: Use the minimum earthquake intensity index to set the earthquake decoupling invariance to calibrate the total occurrence rate of earthquake rupture events: In a certain earthquake rupture event rup i Next, the strength index IM i >x iThe conditional exceedance probability is as follows:

[0008]

[0009] Among them, λ(rup i ) indicates an earthquake rupture event rup i annual incidence rate.

[0010] From the above formula, we can know that when x i When it approaches the minimum value, it is equal to 1 for any earthquake event, then the intensity index IM i >x min The exceedance probability is equal to the sum of the occurrence rates of earthquake rupture events, that is:

[0011]

[0012] By using the minimum IM index to set the earthquake decoupling invariance to calibrate the total occurrence rate of earthquake rupture events, the error introduced by the approximate estimation is reduced and the stability of the final result is guaranteed.

[0013] Step 3: According to the requirements of seismic time-history analysis and structural characteristics, multiple earthquake intensity indices with high correlation with the response index of the structure to be analyzed, namely, conditional IM index combination, are determined;

[0014] Step 4: Determine the joint probability distribution of multiple IM indicators according to the following formula; assuming that the logarithm of the multivariate IM indicator obeys the multivariate Gaussian distribution, the probability distribution of the multivariate IM can be expressed as:

[0015] (lnIM1,lnIM2,...,lnIM n )~N(μ,Σ)

[0016] Among them, the mean matrix μ and covariance matrix Σ of the multivariate Gaussian distribution are defined as follows:

[0017] μ=[μ1,μ2,...,μ n ]

[0018]

[0019] Among them, the mean (μ) and standard deviation (σ) can be obtained through the earthquake motion prediction equation; ρ ij represents the Pearson correlation coefficient between each IM; N(·) is the multivariate normal distribution;

[0020] For N rup random earthquake events, considering the weight of any earthquake rupture event, then in the earthquake rupture event rup i The joint probability density function of the multivariate IM index is:

[0021]

[0022] Step 5: Based on the multivariate Gaussian mixture distribution constructed in step 4, the Monte Carlo simulation method is used to approximate the quantile of the multivariate Gaussian mixture distribution; N random samplings are performed, and the specific formula is as follows:

[0023]

[0024] In the above formula, T KEN represents the return period determined based on the Kendall distribution function, and I(·) is the indicator function;

[0025] The error threshold of Kendall's return period is ±5%. The simulated spectrum that meets the conditions is screened through the allowable error range, and the mean and standard deviation of the simulated spectrum are calculated to obtain the target spectrum. The calculation method of the return period determined based on the Kendall distribution function is as follows:

[0026] Assume IM = [IM1, IM2, ..., IM n ] is an N-dimensional random variable. Combining the concept of Copula function, there is a unique Copula function such that:

[0027] P(IM1≤im1,IM2≤im2,...,IM n ≤im n )=C(u1,u2,...,u n )

[0028] Among them, u n For the variable IM n The marginal distribution function P(IM n <x); C(·) is the Copula function; Kendall exceedance probability is defined as the probability that the probability of the multivariate joint distribution is less than or equal to a certain probability level t(t∈(0,1)), that is: P(C(u1,u2...u n )≤t; the definition of the multivariate Kendall return period is as follows:

[0029]

[0030] Step 6: After the target spectrum distribution is known, select a set of records that meet the requirements from the target database.

[0031] Furthermore, the random earthquake event catalog generated in step 1 is based on the five generations of earthquake parameter zoning in my country. Figure 1 The three-level potential source division of earthquake motion and the relationship between the major and minor axis attenuation are shown in Figure 2.

[0032] Furthermore, the simplification of the generated earthquake rupture events in step 1 requires tolerance screening of the earthquake rupture events, using the screened sparse subset to represent the original event set within the tolerance range, and adjusting the weights of the subset events to ensure that the total occurrence rate remains unchanged.

[0033] Furthermore, in step three, the strength index combination includes one or more seismic intensity indexes, and the types of strength indexes may include but are not limited to: acceleration response spectrum value at the natural vibration period point of the structure, peak acceleration, peak velocity, and seismic intensity index of effective duration of seismic motion.

[0034] Furthermore, in step 4, according to the IM index type, the corresponding seismic motion prediction equation and intensity index correlation coefficient matrix can be used to extend the method to multiple seismic motion intensity indices including duration, peak ground velocity, and peak ground acceleration.

[0035] The present application also provides a system for selecting seismic records matching an earthquake recurrence period, the system comprising:

[0036] Acquisition module: used to generate a catalog of random earthquake events that can reflect the characteristics of the seismic activity of the target site, which is obtained by random sampling based on the target site using the seismic motion attenuation relationship that conforms to the characteristics of my country's seismic activity; the acquisition module is also used to simplify the catalog of random earthquake events to obtain a subset that can represent the original random earthquake events;

[0037] Calculation module: used to generate corresponding multivariate Gaussian mixture distribution according to multiple earthquake intensity indicators; the calculation module is also used to approximate the quantile of the multivariate Gaussian mixture distribution; the calculation module is also used to screen and obtain a simulated target spectrum according to the recurrence period of earthquake events;

[0038] Selection module: used to select a set of earthquake records that meet the requirements from the target earthquake database according to the target spectrum distribution.

[0039] The beneficial effects of the present invention are as follows: a wave selection target spectrum that can characterize the joint danger level of multiple earthquake intensity indices is constructed based on the multivariable Kendall return period, which can well solve the defect that the traditional conditional spectrum needs to artificially determine the anchoring conditional earthquake intensity index, and take into account the influence of other vibration modes when estimating the structural seismic response, so as to provide a more accurate earthquake demand estimation. Constructing the target spectrum based on the multivariable Kednall return period not only gets rid of the problem that the traditional wave selection scheme under the conditional spectrum theory framework is greatly affected by the selection of conditional earthquake intensity index, but also provides a mathematically rigorous scheme for constructing a wave selection target spectrum with the IM combined danger level as the control index. In addition, the present invention can be applied to different types of earthquake intensity indices, and only needs to replace the corresponding earthquake prediction equation and the intensity index correlation coefficient matrix. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 A method for selecting ground motions to match the return period of earthquake events and a system structure block diagram.

[0041] Figure 2 It is the distribution of earthquake surface source potential at the target site.

[0042] Figure 3 Distribution of random earthquake rupture events after tolerance screening.

[0043] Figure 4 The target spectrum is obtained by screening using the error threshold of the target recurrence period.

[0044] Figure 5 It is a set of ground motion records selected based on the wave selection target spectrum. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] Example 1

[0047] This embodiment provides a method for selecting ground motion records that match the recurrence period of an earthquake event, comprising the following steps:

[0048] Step 1: If Figure 2 As shown in the figure, based on the three-level potential source division of seismic motion and the relationship between the major and minor axis attenuation under the background of China's zoning, random sampling is used to generate a random earthquake event catalog for the target site and tolerance screening is performed to reduce the calculation burden. The distribution map after screening is shown in Figure 3 shown.

[0049] Step 2: Use the earthquake decoupling invariance of the minimum ground motion intensity index to calibrate the total incidence of earthquake rupture events, so as to avoid the problem of considering too many earthquake rupture events in the approximate estimation, thereby increasing the subsequent calculation burden.

[0050] Step 3: According to the requirements of seismic time-history analysis and structural characteristics, determine multiple seismic intensity indices that have a high correlation with the response indicators of the structure to be analyzed.

[0051] Step 4: Assuming that multiple seismic intensity indicators satisfy the multivariate normal distribution relationship, use the seismic prediction equation and the correlation coefficient matrix to calculate the mean and covariance of the target seismic intensity indicator, and construct a multivariate Gaussian mixture distribution based on the calculated mean matrix and covariance matrix.

[0052] Step 5: Monte Carlo simulation is used to estimate the quantile of the multivariate Gaussian mixture distribution. The constructed multivariate Gaussian mixture distribution is randomly sampled N times to generate N random simulation spectra that meet the site seismic activity characteristics and the ground motion prediction model. The target spectrum is obtained by screening using the error threshold of the target return period. The obtained target spectrum is as follows: Figure 4 shown.

[0053] Step 6: Select a set of ground motion records that meet the conditions from the target database based on the selected wave target spectrum, as shown in the schematic diagram Figure 5 shown.

[0054] like Figure 1 As shown, the seismic motion selection system for matching the recurrence period of earthquake events proposed in an embodiment of the present invention includes:

[0055] The acquisition module is used to generate a random earthquake event catalog that can reflect the seismic activity characteristics of the target site, which is obtained by random sampling based on the target site using the seismic motion attenuation relationship that conforms to the seismic activity characteristics of my country. The acquisition module is also used to simplify the random earthquake event catalog to obtain a subset that can represent the original random earthquake event.

[0056] The calculation module is used to calculate the mean matrix and the covariance matrix based on the earthquake prediction equation and the correlation coefficient matrix according to multiple earthquake intensity indicators, and generate the corresponding multivariate Gaussian mixture distribution. The calculation module is also used to approximate the quantile of the multivariate Gaussian mixture distribution. The calculation module is also used to screen and obtain the simulated target spectrum according to the recurrence period of the earthquake event.

[0057] The selection module is used to select a set of earthquake records that meet the requirements from a target earthquake database according to the target spectrum distribution.

[0058] Example 2

[0059] On the basis of Example 1, this embodiment uses a target spectrum construction scheme that characterizes the joint danger level of multiple seismic intensity indicators, including an acquisition module, a calculation module, and a selection module, which are used to execute the above-mentioned seismic record selection method that matches the recurrence period of an earthquake event. The specific steps include:

[0060] Step 1: Generate and screen the catalog of random earthquake rupture events at the site;

[0061] Adopting the surface source potential source division scheme corresponding to the earthquake zoning background of my country, random sampling is used to generate a random earthquake event catalog with an observation time span of 5000 years for the target site, of which there are 12123 earthquake rupture events, including 5635 non-repeated events. The earthquake rupture events are screened by tolerance, and the screened sparse subset is used to represent the original event set within the tolerance range to reduce the computational burden. At the same time, the weight of the subset event is adjusted to ensure that the total occurrence rate remains unchanged. After the site of this example is screened, the random earthquake event catalog is screened to 497.

[0062] Step 2: Calculate the total incidence of earthquake rupture events;

[0063] Since there are multiple potential sources at the site, it is impossible to directly estimate the annual occurrence rate of a given earthquake event through the seismic activity parameters of the potential sources. Using the total number of events in the earthquake event catalog / observation time (year) to approximate the annual occurrence rate of a given earthquake event does not guarantee the stability of the final result. i Next, λ(rup i ) is the incidence rate of the event, IM i >x i The conditional exceedance probability is as follows:

[0064]

[0065] From the above formula, we can see that when x i When it approaches the minimum value, it is equal to 1 for any earthquake event, then IM i >x min The exceedance probability is equal to the sum of the occurrence rates of earthquake rupture events, that is:

[0066]

[0067] The total occurrence rate of earthquake rupture events is calibrated by setting the earthquake decoupling invariance using the minimum IM index, which reduces the error introduced by the approximate estimation and ensures the stability of the final result.

[0068] Step 3: Determine the earthquake intensity index to be selected;

[0069] It is assumed that the structure to be subjected to seismic time history analysis is a multi-degree-of-freedom layer shear system with a natural vibration period of 1.0s. Taking the inter-layer displacement angle as the structural response index, the study shows 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 (1.0s). Therefore, the conditional intensity index used to construct the target spectrum is the spectrum acceleration value at 0.5s, 1.0s, and 2.0 periods. It should be noted that the present invention can be applied to different types of seismic intensity index types, and only the corresponding seismic prediction equation and the intensity index correlation coefficient matrix need to be replaced.

[0070] In order to estimate the structural seismic response more comprehensively and reduce the uncertainty in the selection process, the number of seismic motion records to be selected is selected as 50.

[0071] Step 4: Multivariate Gaussian mixture distribution expression of target spectrum;

[0072] Based on the assumption of multivariate normal distribution of earthquake intensity index, the target spectrum S a (T1,T2,..T n ) can be expressed as:

[0073] lnSa(T 1，2...n )~N(μ,Σ)

[0074] Among them, the mean matrix μ and covariance matrix Σ of the multivariate Gaussian distribution are defined as follows:

[0075]

[0076] Among them, the mean (μ) and standard deviation (σ) can be obtained through the earthquake prediction equation. ij represents the Pearson correlation coefficient between each IM. random earthquake events, considering the weight of any earthquake rupture event, then in the earthquake rupture event rup i The joint probability density function of the multivariate IM index is:

[0077]

[0078] Step 5: Generate random simulation spectrum and construct target spectrum of multivariate Kendall return period;

[0079] Known earthquake intensity index combination:

[0080] Sa={Sa1,Sa2,Sa3}={Sa(0.5s),Sa(1s),Sa(2s)}, combined with the concept of Copula function, we can get:

[0081] P(Sa1≤x1,Sa2≤x2,Sa3≤x3)=C(u1,u2,u3)(u n =P(Sa n ≤x n ))

[0082] According to the above definition of Kendall's exceedance probability, we can get:

[0083]

[0084] The Monte Carlo simulation method is used for approximate estimation. Based on the constructed multivariate Gaussian mixture distribution, 10 5 The random sampling was repeated 16 times to generate 1.6 million random simulation spectra that conform to the site seismic activity characteristics and the ground motion prediction model. The combination of the target period points of the response spectrum that need to be considered is {T1, T2, …, T m}, the simulated spectrum set that meets the conditions can be screened through the tolerance range (±5%) of the target return period of 475 years / 2475 years. Kendall return period T KEN The simulated spectrum expression is:

[0085]

[0086] I(·) is a nominal variable, which takes the value of 1 if the condition is met, otherwise it takes the value of 0. The construction of the target spectrum can be completed by calculating the mean and standard deviation of the above simulated spectrum set.

[0087] Step 6: Select a set of earthquake records that meet the conditions from the target database based on the constructed wave selection target spectrum.

[0088] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. A method for selecting seismic records matching the earthquake recurrence period, characterized in that: The following steps are involved: Step 1: For the target site, a random seismic event catalogue that can reflect the seismic activity characteristics of the site within a certain observation time span is generated by random sampling. At the same time, the generated seismic rupture events are simplified and the simplified subset is used to represent the original event set; Step 2: Use the minimum earthquake intensity index to set the earthquake decoupling invariance to calibrate the total occurrence rate of earthquake rupture events: In a certain earthquake rupture event rup i Next, the strength index IM i >x i The conditional exceedance probability is as follows: Among them, λ(rup i ) indicates an earthquake rupture event rup i The annual incidence rate From the above formula, we can know that when x i When it approaches the minimum value, it is equal to 1 for any earthquake event, then the intensity index IM i >x min The exceedance probability is equal to the sum of the occurrence rates of earthquake rupture events, that is: By using the minimum IM index to set the earthquake decoupling invariance to calibrate the total occurrence rate of earthquake rupture events, the error introduced by the approximate estimation is reduced and the stability of the final result is guaranteed. Step 3: According to the requirements of seismic time-history analysis and structural characteristics, multiple earthquake intensity indices with high correlation with the response index of the structure to be analyzed, namely, conditional IM index combination, are determined; Step 4: Determine the joint probability distribution of multiple IM indicators according to the following formula; assuming that the logarithm of the multivariate IM indicator obeys the multivariate Gaussian distribution, the probability distribution of the multivariate IM can be expressed as: (lnIM1,lnIM2,...,lnIM n )~N(μ,Σ) Among them, the mean matrix μ and covariance matrix Σ of the multivariate Gaussian distribution are defined as follows: μ=[μ1,μ2,...,μ n ] Among them, the mean (μ) and standard deviation (σ) can be obtained through the earthquake motion prediction equation; ρ ij represents the Pearson correlation coefficient between each IM; N(·) is the multivariate normal distribution; For N rup random earthquake events, considering the weight of any earthquake rupture event, then in the earthquake rupture event rup i The joint probability density function of the multivariate IM index is: Step 5: Based on the multivariate Gaussian mixture distribution constructed in step 4, the Monte Carlo simulation method is used to approximate the quantile of the multivariate Gaussian mixture distribution; N random samplings are performed, and the specific formula is as follows: In the above formula, T KEN is the return period determined based on the Kendall distribution function, I(·) is the indicator function; The error threshold of Kendall's return period is ±5%. The simulated spectrum that meets the conditions is screened through the allowable error range, and the mean and standard deviation of the simulated spectrum are calculated to obtain the target spectrum. The calculation method of the return period determined based on the Kendall distribution function is as follows: Assume IM = [IM1, IM2, ..., IM n ] is an N-dimensional random variable. Combining the concept of Copula function, there is a unique Copula function such that: P(IM1≤im1,IM2≤im2,...,IM n ≤im n )=C(u1,u2,...,u n ) Among them, u n For the variable IM n The marginal distribution function P(IM n <x); C(·) is the Copula function; Kendall exceedance probability is defined as the probability that the probability of the multivariate joint distribution is less than or equal to a certain probability level t(t∈(0,1)), that is: P(C(u1,u2...u n )≤t); the definition of the multivariate Kendall return period is as follows: Step 6: After the target spectrum distribution is known, select a set of records that meet the requirements from the target database.

2. The method for selecting seismic records matching the earthquake recurrence period according to claim 1, characterized in that: The random earthquake event catalog generated in step 1 is based on the three-level potential source division of earthquake motion and the major and minor axis attenuation relationship consistent with the five-generation earthquake parameter zoning map of my country.

3. The method for selecting seismic records matching the earthquake recurrence period according to claim 1, characterized in that: The specific operation of simplifying the generated earthquake rupture events in the step 1 is to perform tolerance screening on the earthquake rupture events, use the screened sparse subset to represent the original event set within the tolerance range, and adjust the weight of the subset event to ensure that the total occurrence rate remains unchanged.

4. The method for selecting seismic records matching the earthquake recurrence period according to claim 1, characterized in that: In step three, the strength index combination includes one or more seismic intensity indexes, and the types of strength indexes may include but are not limited to: acceleration response spectrum value at the natural vibration period point of the structure, peak acceleration, peak velocity, and seismic effective duration seismic intensity index.

5. The method for selecting seismic records matching the earthquake recurrence period according to claim 1, characterized in that: In step 4, according to the IM index type, the corresponding earthquake motion prediction equation and intensity index correlation coefficient matrix are used to extend the method to multiple earthquake motion intensity indicators including duration, peak ground velocity, and peak ground acceleration.

6. A seismic record selection system for matching earthquake recurrence period constructed based on the seismic record selection method according to any one of claims 1 to 5, characterized in that: The system comprises: Acquisition module: used to generate a catalog of random earthquake events that can reflect the characteristics of the seismic activity of the target site, which is obtained by random sampling based on the target site using the seismic motion attenuation relationship that conforms to the characteristics of my country's seismic activity; the acquisition module is also used to simplify the catalog of random earthquake events to obtain a subset that can represent the original random earthquake events; Calculation module: used to generate corresponding multivariate Gaussian mixture distribution according to multiple earthquake intensity indicators; the calculation module is also used to approximate the quantile of the multivariate Gaussian mixture distribution; the calculation module is also used to screen and obtain a simulated target spectrum according to the recurrence period of earthquake events; Selection module: used to select a set of earthquake records that meet the requirements from the target earthquake database according to the target spectrum distribution.

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