A ground motion selection method considering spectral shape and duration parameters

Abstract

A method for selecting ground motions considering spectral shape and duration parameters includes the following steps: S1, performing probabilistic seismic hazard analysis on the target site to determine the target peak ground acceleration (PGA) value at a specified exceedance probability level; S2, extracting the spectral shape parameter vector and duration parameter for each actual ground motion record based on a selected candidate strong earthquake database; S3, constructing a conditional statistical distribution model; S4, determining the desired target parameter sample set; S5, linearly scaling the actual ground motion records in the candidate strong earthquake database to the PGA target value determined in S1, using each sample vector in the desired target parameter sample set determined in S4 as a matching target, selecting the actual ground motion record with the smallest mismatch, and forming a final ground motion set consistent with the target hazard level. This invention can more accurately evaluate the seismic performance of structures.

Description

Technical Field

[0001] This invention belongs to the field of earthquake engineering technology, specifically relating to a method for selecting ground motion records based on probabilistic seismic hazard analysis without the need for spectral analysis. Background Technology

[0002] my country is one of the countries most severely affected by continental earthquakes in the world. With the continuous improvement of seismic fortification requirements, performance-based seismic design has become an inevitable trend in earthquake engineering development. Nonlinear dynamic time history analysis is currently the most accurate and core calculation method for structural seismic performance assessment, vulnerability analysis, and life-cycle cost analysis. However, before conducting time history analysis, the reliability and accuracy of the structural response analysis results are directly determined by how to select natural ground motion records that match the characteristics of the target site from a massive database of strong earthquakes. In current engineering practice and scientific research, ground motion selection mainly relies on the response spectrum matching method. That is, a target response spectrum (such as the design spectrum or conditional spectrum CS) is constructed, and records with similar shapes to the target spectrum are searched in the database. The amplitude is adjusted linearly or nonlinearly to make it match the target spectrum at a specific period point or period segment. The core logic of this method is that the response spectrum, i.e., the peak response, determines the degree of structural damage.

[0003] However, with the deepening research into the nonlinear behavior of structures, researchers have discovered significant technical limitations in relying solely on response spectrum matching: 1. Neglecting the duration effect: Seismic motion duration is a key factor affecting the cumulative damage and collapse capacity of structures. Numerous studies have shown that, under the premise of the same response spectrum intensity, long-duration seismic motions lead to a significant increase in the cumulative energy dissipation of structures. Current response spectrum matching methods often only focus on amplitude characteristics, resulting in the selected seismic motion duration distribution potentially deviating significantly from the actual situation of the target site, thus leading to misjudgments of structural safety. 2. Lack of physical correlation: Even when considering duration, existing processing methods often involve simple screening or significant scaling of amplitude. This approach destroys the natural physical correlation between seismic motion intensity and duration. 3. Cumbersome calculation process and difficult engineering application: Although methods such as the generalized conditional intensity index attempt to introduce duration parameters, these methods usually require complex probabilistic seismic hazard decomposition to obtain the target distribution, resulting in extremely high computational barriers. In addition, conditional spectrum methods usually rely on specific conditional periods, making wave selection results highly sensitive to period selection and difficult to form a standardized and universal process.

[0004] Therefore, how to establish a seismic motion selection method that can accurately match the shape of the target response spectrum, explicitly consider duration characteristics, and maintain the real physical correlation between intensity and duration without increasing the complexity of probabilistic hazard decomposition calculations has become a key technical problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies, this invention provides a ground motion selection method that considers spectral shape and duration parameters. This method establishes a two-parameter target matching algorithm based on spectral shape and duration, without the need to predetermine the condition period or perform probabilistic seismic hazard decomposition. Using PGA as the condition parameter, it ensures that the selected ground motion retains the physical correlation between intensity and duration. Through dual matching with the target response spectrum and duration distribution, this invention can more accurately evaluate the seismic performance of the structure.

[0006] The technical solution adopted by this invention to solve its technical problem is: A method for selecting seismic ground motions that considers spectral shape and duration parameters includes the following steps: S1. Determine the hazard level and condition parameters of the target site: Perform probabilistic seismic hazard analysis on the target site to determine the target value of peak ground acceleration (PGA) at a specified exceedance probability level (e.g., 2% exceedance probability in 50 years). This PGA value will be used as the sole condition parameter of the subsequent joint probability distribution model, without the need for PSHA de-aggregation. S2. Construct an unconditional distribution parameter set: Based on the selected candidate strong earthquake database (such as the NGA-West2 database), extract the spectral parameter vector and duration parameters for each actual ground motion record, where the spectral parameter vector is represented as [ T 0, T g , β max , γ ] T ,in T 0 characterizes the start and end periods of the spectral plateau segment. T g The characterization spectral plateau segment termination cutoff period, β max Characterizing the amplification factor of the spectral plateau segment, γ Characterize the decay exponent of the descent phase; calculate the unconditional mean vector of the spectral shape parameter vector and the logarithm of the duration parameter ( μ S ) and unconditional covariance matrix ( S SS ); S3. Construct a conditional statistical distribution model: Establish a joint probability distribution model among the spectral shape parameter vector, duration parameter, and intensity index (PGA). Based on the PGA target value determined in S1, use the conditional probability formula to calculate the conditional mean vector (μ) of the spectral shape parameter and duration parameter under a given PGA condition. S |PGA) and conditional covariance matrix (S S |PGA); S4. Determine the sample set of desired target parameters: Using the Monte Carlo simulation method, based on the conditional mean vector and conditional covariance matrix obtained in S3, randomly generate multiple sets of simulated sample sets containing spectral parameters and duration parameters; define the first mismatch function M1, calculate the mismatch between the sample mean and sample covariance of each simulated sample set and the conditional mean vector and conditional covariance matrix, and select the set with the smallest M1 value as the sample set of desired target parameters; S5. Screening ground motion records based on dual-parameter mismatch: The actual ground motion records in the candidate strong earthquake database are linearly scaled to the PGA target value determined in S1. Each sample vector in the expected target parameter sample set determined in S4 is used as the matching target. A second mismatch function M2 is defined. The mismatch between the parameters of each scaled actual ground motion record and the corresponding target sample vector is calculated. The actual ground motion record with the smallest M2 value is selected to form the final ground motion set consistent with the target hazard level.

[0007] The technical concept of this invention is to break through the limitations of traditional single-spectrum matching and to combine the duration parameter (preferably the cumulative absolute velocity) with the duration parameter. CAV This method combines spectral parameters with site PGA as a constraint parameter. It preserves the natural physical correlation between intensity and duration in real strong earthquake databases through a statistical model, which is used for screening ground motion records.

[0008] The beneficial effects of this invention are mainly reflected in: 1. Improve the reliability of structural vulnerability assessment: By explicitly introducing duration characteristics, the bias of traditional spectral method in systematically overestimating the probability of structural collapse caused by blindly selecting long-duration ground motions is effectively corrected.

[0009] 2. Greatly simplifies the engineering calculation process: It avoids the complex PSHA decomposition process, eliminates the need to obtain the target magnitude and fault distance, and removes the dependence on specific condition cycles, thus possessing extremely high engineering feasibility.

[0010] 3. Strong physical consistency: It ensures that the selected ground motion records, after scaling, can still naturally reflect the true ground motion intensity-duration joint distribution characteristics under the target hazard level. Attached Figure Description

[0011] Figure 1 This is a schematic flowchart of a ground motion selection method that considers spectral shape and duration parameters according to the present invention.

[0012] Figure 2 In the embodiments of the present invention, PGA and different duration parameters ( CAV , I A ,D S5_75 , D S5_95 A scatter plot showing the correlation between the two. Figure 3 This is a schematic diagram comparing the cumulative probability distribution of different duration parameters generated by the method of the present invention with the target distribution; Figure 4 To apply the method of this invention at different hazard levels, regardless of duration (a) PGA and considering different duration parameters (b) CAV (c) I A (d) D S5_75 (e) D S5_95 A schematic diagram of the selected natural seismic response spectrum; Figure 5 This is a comparison chart of structural seismic vulnerability curves obtained using the method of this invention and the traditional spectral matching method; Figure 6 This is a comparison chart of the distribution of seismic motion duration parameters selected in this invention and the distribution of actual strong earthquake database. Detailed Implementation

[0013] The present invention will now be further described with reference to the accompanying drawings.

[0014] Reference Figures 1-6 A method for selecting seismic ground motions that considers spectral shape and duration parameters includes the following steps: S1. Determine the hazard level and condition parameters of the target site: Perform probabilistic seismic hazard analysis on the target site to determine the target value of peak ground acceleration (PGA) at a specified exceedance probability level (e.g., 2% exceedance probability in 50 years). This PGA value will be used as the sole condition parameter of the subsequent joint probability distribution model, without the need for PSHA de-aggregation. This embodiment uses the Los Angeles site (34º57'N, 118º56'W) as an example to demonstrate how to use the method of the present invention to select ground motions that take into account spectral shape and duration.

[0015] Probabilistic seismic hazard analysis (PSHA) was performed on the target site in Los Angeles. Taking a hazard level with a exceedance probability of 2% / 50 years as an example, the target peak ground acceleration (PGA) at this hazard level was obtained through PSHA: PGA = 0.7357g.

[0016] S2. Construct an unconditional distribution parameter set: Based on the selected candidate strong earthquake database (such as the NGA-West2 database), extract the spectral parameter vector and duration parameters for each actual ground motion record, where the spectral parameter vector is represented as [ T 0, Tg , β max , γ ] T ,in T 0 characterizes the start and end periods of the spectral plateau segment. T g The characterization spectral plateau segment termination cutoff period, β max Characterizing the amplification factor of the spectral plateau segment, γ Characterize the decay exponent of the descent phase; calculate the unconditional mean vector of the spectral shape parameter vector and the logarithm of the duration parameter ( μ S ) and unconditional covariance matrix ( S SS ); In this embodiment, 5136 unscaled actual ground motion records with PGA values ​​greater than 0.05g from the NGA-West2 database were selected. Four spectral parameters were extracted ( T 0, T g , β max , γ ) and duration parameters ( CAV , I A , D S5_75 , D S5_95 In this embodiment, correlation analysis (such as...) is used to... Figure 2 As shown), cumulative absolute velocity ( CAV The correlation coefficient between CAV and PGA is high (ρ=0.5119), and it also shows a strong correlation with structural engineering requirement parameters (such as peak inter-story drift angle PSDR), as shown in Table 1. Therefore, CAV is preferred as the duration parameter. The logarithmic unconditional mean vector of the above five parameters is calculated. μ S ) and unconditional covariance matrix ( S SS ), and the logarithmic mean of the conditional parameter PGA ( μ C ),variance( S CC ) and cross covariance ( S CS and S SC ).

[0017] Table 1 shows the correlation coefficients between duration parameters and peak inter-story drift angle;

[0018] S3. Construct a conditional statistical distribution model: Establish a joint probability distribution model among the spectral shape parameter vector, duration parameter, and intensity index (PGA). Based on the PGA target value determined in S1, use the conditional probability formula to calculate the conditional mean vector (μ) of the spectral shape parameter and duration parameter under a given PGA condition. S |PGA) and conditional covariance matrix (S S |PGA); In this embodiment, based on the joint log-normal distribution property, and using the PGA determined by S1 as a condition, the conditional mean μ of the spectral shape parameter and duration parameter under the given PGA condition is calculated according to the following formula. S |PGA and conditional covariance S S |PGA: ; ; ; ; S4. Determine the sample set of desired target parameters: Using the Monte Carlo simulation method, based on the conditional mean vector and conditional covariance matrix obtained in S3, randomly generate multiple sets of simulated sample sets containing spectral parameters and duration parameters; define the first mismatch function M1, calculate the mismatch between the sample mean and sample covariance of each simulated sample set and the conditional mean vector and conditional covariance matrix, and select the set with the smallest M1 value as the sample set of desired target parameters; In this embodiment, the Monte Carlo simulation method is used. Based on the conditional mean and conditional covariance obtained in step 3, 10,000 candidate parameter sample sets (each set containing, for example, 20 sample vectors) are randomly generated. A first mismatch function M1 is defined to measure the difference between the statistical characteristics of the sample set and the theoretical target value. ; In the formula, μ Mi and S Mij These are the mean and covariance of the simulated sample set, respectively; μ i and S ij These are the components corresponding to the conditional mean and conditional covariance calculated in step 3. Iterate through all generated candidate sets and select the set with the smallest M1 value as the desired target parameter sample set.

[0019] S5. Screening ground motion records based on dual-parameter mismatch: The actual ground motion records in the candidate strong earthquake database are linearly scaled to the PGA target value determined in S1. Each sample vector in the expected target parameter sample set determined in S4 is used as the matching target. A second mismatch function M2 is defined. The mismatch between the parameters of each scaled actual ground motion record and the corresponding target sample vector is calculated. The actual ground motion record with the smallest M2 value is selected to form the final ground motion set consistent with the target hazard level.

[0020] In this embodiment, the records in the candidate database are linearly scaled to the target PGA (the scaling factor is limited to between 1 / 3 and 3). Each vector in the desired target parameter sample set determined in step 4 is used as a matching object, and a second mismatch function M2 is defined: ; In the formula, T 0, T g , β max , γ And D represents the spectral shape and duration parameters of the scaled records in the database; variables with subscripts M represent the corresponding parameters in the desired target samples; for each desired sample, the record with the smallest M² is selected, ultimately forming a target ground motion set containing 20 records, such as... Figure 4 As shown, the selected ground motions closely match the target distribution in terms of duration. Figure 5 The vulnerability analysis shown demonstrates that this method more accurately reflects the performance state of the structure than traditional methods that do not consider duration.

[0021] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit the present invention. For example, the duration parameter is not limited to... CAV Arias strength can also be used ( IA The number of groups and the number of waveforms generated in the Monte Carlo simulation can be adjusted according to actual needs. For those skilled in the art, any equivalent substitutions or adjustments made without departing from the concept of this invention should fall within the protection scope of this invention.

Claims

1. A method for selecting seismic ground motions considering spectral shape and duration parameters, characterized in that, The method includes the following steps: S1. Determine the hazard level and condition parameters of the target site: Perform probabilistic seismic hazard analysis on the target site and determine the peak ground acceleration (PGA) target value under the specified exceedance probability level; S2. Construct an unconditional distribution parameter set: Based on the selected candidate strong earthquake database, extract the spectral parameter vector and duration parameters of each actual ground motion record; S3. Construct a conditional statistical distribution model: Establish a joint probability distribution model among the spectral parameter vector, duration parameter, and intensity index PGA. Based on the PGA target value determined in S1, use the conditional probability formula to obtain the conditional mean vector and conditional covariance matrix of the spectral parameter and duration parameter under the given PGA condition. S4. Determine the sample set of desired target parameters: Using the Monte Carlo simulation method, based on the conditional mean vector and conditional covariance matrix obtained in S3, randomly generate multiple sets of simulation sample sets containing spectral parameters and duration parameters; select the set with the smallest mismatch as the sample set of desired target parameters. S5. Screening ground motion records based on dual-parameter mismatch: The actual ground motion records in the candidate strong earthquake database are linearly scaled to the PGA target value determined in S1. Each sample vector in the expected target parameter sample set determined in S4 is used as the matching target. The actual ground motion record with the smallest mismatch is selected to form the final ground motion set consistent with the target hazard level.

2. The method for selecting seismic motion considering spectral shape and duration parameters as described in claim 1, characterized in that, In S2, the spectral shape parameter vector is represented as [ T 0, T g , β max , γ ] T ,in T 0 characterizes the start and end periods of the spectral plateau segment. T g The characterization spectral plateau segment termination cutoff period, β max Characterizing the amplification factor of the spectral plateau segment, γ The decay exponent characterizes the descent phase, and the unconditional mean vector of the spectral shape parameter vector and the logarithm of the duration parameter is calculated. μ S and unconditional covariance matrix S SS .

3. A method for selecting seismic motion considering spectral shape and duration parameters as described in claim 1 or 2, characterized in that, In step S4, a first mismatch function M1 is defined, and the mismatch degree between the sample mean and sample covariance of each simulated sample set and the conditional mean vector and conditional covariance matrix is ​​calculated. The set with the smallest M1 value is selected as the desired target parameter sample set.

4. The method for selecting seismic motion considering spectral shape and duration parameters as described in claim 3, characterized in that, In step S5, a second mismatch function M2 is defined to calculate the mismatch between the parameters of each scaled actual ground motion record and the corresponding target sample vector. The actual ground motion record with the smallest M2 value is selected to form the final ground motion set consistent with the target hazard level.

Images