A seismic motion simulation method matching long-period response spectra

Abstract

This application relates to a seismic motion simulation method that matches long-period response spectra. By extending the response spectrum analysis period to 20 seconds and constructing a low-frequency characteristic seismic motion database, high-precision characterization of seismic motion characteristics across the entire frequency band from 0.03 to 20 seconds is achieved. This method overcomes the limitation of traditional models that decay too quickly in the amplitude descent segment, providing a seismic motion input solution for the seismic design of long-period structures such as super high-rise buildings that combines broadband spectral matching accuracy with fidelity to the physical characteristics of the geological environment.

Description

Technical Field

[0001] This application relates to a seismic motion simulation method that matches long-period response spectra, applicable to the technical field of seismic engineering. Background Technology

[0002] In engineering practice, deep soft soil sites, super high-rise building structures, and long-span bridges place stringent requirements on the long-period spectral fidelity of input ground motions. Existing methods have significant limitations: seismic models based on physical mechanisms, such as the spectral element method, can simulate the entire wave propagation process, but their spectral matching accuracy is insufficient in the frequency bands of interest in engineering, such as 0.3-25Hz; while engineering methods based on statistical laws can improve computational efficiency, their empirical intensity envelopes are difficult to describe the low-frequency energy accumulation mechanism, resulting in spectral attenuation errors of up to 30% in long-period segments, for example, in the T>10s range.

[0003] Therefore, there is a need in the existing technology for a seismic motion simulation method that can meet the requirements of high accuracy in long-period spectrum matching in sensitive engineering frequency bands and can reasonably characterize the long-time amplitude attenuation characteristics, so that it can meet the accuracy and efficiency requirements of seismic design of structures. Summary of the Invention

[0004] This application provides a seismic motion simulation method that matches long-period response spectra. It integrates physical constraints and intelligent optimization algorithms, and is a method for generating seismic acceleration time histories that can match long-period response spectra. Targeting the long-period characteristics of deep soft soil sites and super high-rise buildings, by extending the response spectrum analysis period to 20 seconds and constructing a low-frequency characteristic seismic motion database, high-precision characterization of seismic motion characteristics across the entire frequency band from 0.03 to 20 seconds is achieved. This method overcomes the limitation of traditional models that decay too quickly in the amplitude descent segment, providing a seismic motion input solution for the seismic design of long-period structures such as super high-rise buildings that combines wideband spectral matching accuracy with fidelity to the physical characteristics of the geological environment.

[0005] This application relates to a method for simulating seismic motions that matches long-period response spectra, comprising the following steps:

[0006] (1) Based on the requirement of long-period response spectrum matching, a low-frequency characteristic ground motion database is constructed, and a systematic preprocessing process is implemented to obtain a long-period characteristic dataset with a unified format.

[0007] (2) Based on the seismic parameters implicit in the target response spectrum, multi-dimensional similarity matching is performed in the long-period characteristic dataset obtained above to construct a set of characteristic mother wave data reflecting the target characteristics;

[0008] (3) Based on the empirical inference of the time-frequency characteristics of the target response spectrum, the intensity envelope model is applied to the characteristic mother wave set to realize the reconstruction of non-stationary characteristics;

[0009] (4) Define the objective function to quantify the difference between the synthetic acceleration response spectrum and the target response spectrum. Based on the PSO algorithm, a random particle swarm is generated in the initialization stage, and each particle represents a set of weight coefficient vectors.

[0010] (5) Dynamic adjustments are made based on the iteration of the PSO algorithm, and a hard constraint mechanism is introduced to fit the target response spectrum to ensure that the relative fitting error of the spectrum in the whole period is controlled below 15%.

[0011] (6) Based on the objective function, the PSO algorithm obtains a set of optimal weight coefficients for the corresponding characteristic mother wave data set after several iterations of optimization, and then obtains the corresponding acceleration time history.

[0012] (7) Evaluate the error of the fitting results until the required seismic acceleration time history is obtained.

[0013] Step (1) may also include the following steps: classifying earthquake events and regional seismic geological features in the NGA-West2 database using moment magnitude Mw, epicentral distance R, and site-average shear wave velocity Vs30 as classification dimensions; screening data with horizontal component frequencies below 0.1 Hz to construct a seismic ground motion database that retains long-period characteristics; preprocessing the grouped seismic ground motion data: optimizing the first arrival detection accuracy using the long-short time window energy ratio analysis method and eliminating invalid data segments; unifying the time history duration based on the piecewise exponential envelope function to ensure the comparability of time domain characteristics of multi-source data; and applying cubic spline interpolation to standardize the sampling rate to 200 Hz to eliminate the influence of sampling interval differences on frequency domain analysis.

[0014] Step (2) may also include the following steps: selecting similar data from a long-period characteristic database based on the magnitude, epicentral distance and site conditions of the target ground motion; constructing a set of ground motions that reflect the target characteristics through multidimensional parameter matching and data quality assessment; and further screening ground motion data with horizontal component frequencies all less than 0.05 Hz from the initially selected set of ground motions to form a set of characteristic mother waves.

[0015] In step (3), the intensity envelope model can be used to perform time history correction on the constructed characteristic mother wave data set using the three-segment intensity envelope model in the following formula:

[0016]

[0017] In the formula, t1 and t2 control the start and end times of the steady-state phase of a strong earthquake, respectively, t2-t1 represents the duration of the steady-state phase of the ground motion, and t d denoted by , represents the total duration of the ground motion, and c is the attenuation factor of the decreasing phase of the ground motion time history.

[0018] In step (4), the iterative formula for the particle's velocity v and position x can be:

[0019] v ij (t+1)=ωv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij(t) ]

[0020] x ij (t+1)=x ij (t)+v ij (t+1)

[0021] In the formula, ω represents the inertia weight; p ij (t) represents the optimal position of particle i in the t-th iteration; p gj (t) represents the global optimal position; c1 and c2 are learning factors, r1 and r2 are random numbers independently drawn from the interval [0,1], and j represents the j-th dimension of the solution vector.

[0022] This application presents a seismic motion simulation method based on matching long-period response spectra, addressing a key requirement of long-period response spectrum matching technology for structural seismic design. The method integrates physical mechanisms and intelligent optimization algorithms. This seismic motion simulation method provides a seismic motion input scheme for the seismic design of long-period structures such as super high-rise buildings, offering both broadband spectral matching accuracy and the ability to physically characterize the geological environment, significantly improving the reliability of seismic response analysis for long-period structures. Attached Figure Description

[0023] Figure 1 This is a flowchart of the seismic motion simulation method of this application.

[0024] Figure 2 This describes the basic process of synthesizing ground motion using the PSO algorithm in this application.

[0025] Figure 3 This is a schematic diagram of the target reaction spectrum and its fitting results in the embodiment.

[0026] Figure 4 This is a schematic diagram of the composite acceleration and its intensity envelope in the embodiment.

[0027] Figure 5 This is a schematic diagram of the main frequency curve in the embodiment. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in detail below with reference to the accompanying drawings. It should be noted that, unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

[0029] A seismic motion simulation method according to this application, which matches a long-period response spectrum, includes the following steps:

[0030] (1) Based on the requirement of long-period response spectrum matching, a low-frequency characteristic ground motion database is constructed, and a systematic preprocessing process is implemented to obtain a long-period characteristic dataset with a unified format.

[0031] (2) Based on the seismic parameters implicit in the target response spectrum, multi-dimensional similarity matching is performed in the long-period characteristic dataset obtained above to construct a set of characteristic mother wave data reflecting the target characteristics;

[0032] (3) Based on the empirical inference of the time-frequency characteristics of the target response spectrum, the intensity envelope model is applied to the characteristic mother wave set to realize the reconstruction of non-stationary characteristics;

[0033] (4) Define the objective function to quantify the difference between the synthetic acceleration response spectrum and the target response spectrum. Based on the PSO algorithm, a random particle swarm is generated in the initialization stage, and each particle represents a set of weight coefficient vectors.

[0034] (5) Dynamic adjustments are made based on the iteration of the PSO algorithm, and a hard constraint mechanism is introduced to fit the target response spectrum to ensure that the relative fitting error of the spectrum in the whole period is controlled below 15%.

[0035] (6) Based on the objective function, the PSO algorithm obtains a set of optimal weight coefficients for the corresponding characteristic mother wave data set after several iterations of optimization, and then obtains the corresponding acceleration time history.

[0036] (7) Evaluate the error of the fitting results until the required seismic acceleration time history is obtained.

[0037] The seismic motion simulation method in this application adopts a triple adaptation mechanism:

[0038] 1) Based on source parameters such as magnitude, epicentral distance and site conditions, long-period characteristic mother waves are screened from the constructed database, while retaining low-frequency energy accumulation characteristics;

[0039] 2) Embed hard constraint functions in the particle swarm optimization (PSO) algorithm to force the maximum relative error of the entire period not to exceed 15%, and to focus on constraining the error of the long period sensitive region, such as T = 10-20s, to be less than 10%;

[0040] 3) By using segmented intensity envelope and time-frequency scaling techniques, the dynamic evolution of the amplitude of the synthesized time history and the non-stationary energy distribution dominated by low frequency are controlled to simulate the ground motion propagation effect in deep sites.

[0041] More specifically, adopting such Figure 1 The technical solution shown is used to perform acceleration time-history fitting of long-period response spectrum ground motions that integrates physical constraints and intelligent optimization. The specific steps are as follows:

[0042] (1) Classify and preprocess actual ground motion data.

[0043] Based on the requirement of long-period response spectrum matching, a low-frequency characteristic ground motion database is constructed, and a systematic preprocessing workflow is implemented, specifically including:

[0044] (1.1) The ground motion data of earthquake events and regional seismic geological characteristics in the NGA-West2 database are classified using moment magnitude Mw, epicentral distance R and site shear wave velocity Vs30 as classification dimensions.

[0045] (1.2) Filter the data with horizontal component frequencies of ground motion below 0.1 Hz to construct a ground motion database with long period characteristics;

[0046] (1.3) Preprocessing of grouped ground motion data: First arrival detection accuracy is optimized using long-short time window energy ratio analysis to eliminate invalid data segments; time duration is standardized based on piecewise exponential envelope function to ensure the comparability of time domain characteristics of multi-source data; cubic spline interpolation is applied to standardize the sampling rate to 200Hz to eliminate the influence of sampling interval differences on frequency domain analysis. After this preprocessing, a standardized ground motion dataset is obtained that can be directly applied to subsequent work.

[0047] (2) Selecting characteristic mother wave and determining intensity envelope function parameters

[0048] To achieve parameterized characterization of the intensity envelope driven by long-period response spectra, an empirical inference method for the envelope function based on the characteristics of the target response spectrum and a seismic motion database is proposed. The specific process is as follows:

[0049] (2.1) Target response spectrum correlation mother wave screening mechanism:

[0050] Based on the seismic parameters implicit in the target response spectrum, multi-dimensional similarity matching is performed on the obtained dataset to construct a set of characteristic parent wave data matrices reflecting the target characteristics. Based on the magnitude, epicentral distance, and site conditions of the target ground motion, similar data are selected from a long-period characteristic database. Then, through multi-dimensional parameter matching and data quality assessment, a set of ground motions reflecting the target characteristics is constructed. Finally, from the initially selected set of ground motions, ground motion data with horizontal component frequencies all less than 0.05 Hz are further selected to form a set of characteristic parent wave data {a1(t), a2(t), ..., a...}. n (t)}. In this application, the long period is defined to have a range of 0-20s.

[0051] (2.2) Empirical modeling of the three-segment envelope function:

[0052] The envelope parameters are empirically inferred based on the time-frequency characteristics of the target response spectrum. Specifically, the three-segment intensity envelope model in the following formula is used to correct the time history of the constructed characteristic mother wave data set:

[0053]

[0054] In the formula, t1 and t2 control the start and end times of the steady-state phase of a strong earthquake, respectively, t2-t1 represents the duration of the steady-state phase of the ground motion, and t d The value represents the total duration of the ground motion, and c is the attenuation factor of the falling segment of the ground motion time history, which is used to control the attenuation rate of the falling segment. The value range can be 0.1-2.0, preferably 0.15.

[0055] (2.3) Mother wave duration constraint and adaptive adjustment:

[0056] The three-segment intensity envelope model obtained by equation (1) is applied to the characteristic mother wave set to reconstruct the amplitude non-stationary characteristics.

[0057] (3) Dynamically adjust the PSO algorithm parameters

[0058] This step utilizes a data-driven Particle Swarm Optimization (PSO) algorithm, guided by the target response spectrum, to achieve adaptive optimization of the weight coefficients. The specific steps are as follows:

[0059] (3.1) Define the objective function in equation (2) below to quantify the synthesis acceleration response spectrum S g (T i ) and target response spectrum The difference is expressed as:

[0060]

[0061] In the formula, For the target acceleration response spectrum, S g (Ti T represents the calculated response spectrum of the fitted ground motion. i is the i-th periodic point corresponding to the reaction spectrum; N is the total value of the reaction spectrum points.

[0062] (3.2) Based on the PSO algorithm, a random particle swarm is generated during the initialization phase, and each particle represents a set of weight coefficient vectors k. The iteration of the particle's velocity v and position x follows equations (3) and (4):

[0063] v ij (t+1)=ωv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij(t) (3)

[0064] x ij (t+1)=x ij (t)+v ij (t+1) (4)

[0065] In the formula, ω represents the inertia weight; p ij (t) represents the optimal position of particle i in the t-th iteration; p gj (t) represents the global optimal position; c1 and c2 are learning factors, while r1 and r2 are random numbers independently drawn from the interval [0,1], and j represents the j-th dimension of the solution vector. For example, if the optimization problem is D-dimensional (weight coefficient vector k = [k1,k2,…,k...), ... D If j∈{1,2,…,D}, then j∈{1,2,…,D}.

[0066] (3.3) Based on the iteration of the PSO algorithm, key parameters such as particle population, inertia weight, and learning factor are introduced for dynamic adjustment. The specific steps include:

[0067] (3.3.1) Time-varying expansion of particle population size

[0068] The initial number of particles is set to 1000, and it increases dynamically with the iteration number t according to equation (5):

[0069] N(t)=1000t (5)

[0070] In the formula, t is the number of iterations.

[0071] (3.3.2) Nonlinear decay of inertial weight

[0072] Design a hyperbolic tangent decay function to control the inertia weights:

[0073]

[0074] Where w max =0.9, w min =0, the function in the middle of the iteration (0.3t) max <t<0.7t max This exhibits a gradual change characteristic, preventing the algorithm from getting trapped in local optima too early. Where t... max This represents the maximum number of iterations.

[0075] (3.3.3) Learning factor anti-coupling

[0076] Individual learning factor C1 and social learning factor C2 are dynamically adjusted according to equation (7):

[0077]

[0078] The exponential learning factor is dynamically adjusted so that in the early stage of the algorithm, i.e., t→0, the focus is on the accumulation of individual experience, i.e., C1→2.0, C2→0; in the later stage, t→t max At that time, the focus shifts to collaborative collective intelligence, i.e., C1→0, C2→2.0.

[0079] (4) Introduce a hard constraint mechanism to fit the target response spectrum

[0080] In the above steps, the fitting accuracy for low-frequency components may be insufficient, and long-period ground motion is particularly sensitive to low-frequency components. To address this issue, this application introduces a hard constraint mechanism into the particle swarm optimization (PSO) algorithm to ensure that the relative spectral fitting error across the entire period is controlled below 15%. The hard constraint mechanism in this application refers to a management method that, under specific environmental conditions, strictly limits and regulates the behavior of individuals or organizations through clearly defined rules and regulations. Specifically, it is implemented through the following constraints:

[0081] g = ε max (T i )-ε threshold (T i (8)

[0082] In the formula, g represents the constraint function value, and ε max ε represents the maximum relative error at each period point. threshold This represents the maximum permissible error threshold for each period point, for example, it can be set to 15%, T i Indicates each period point.

[0083] Finally, based on the objective function, the PSO algorithm, after several iterations of optimization, obtains a set of optimal weight coefficients k for the corresponding characteristic mother wave data set, and then obtains the corresponding acceleration time history. Right now

[0084]

[0085] In the formula, a i (t) represents a characteristic acceleration waveform.

[0086] (5) Evaluate the error of the fitting results until the required seismic acceleration time history is obtained.

[0087] The relative fitting error between the synthetic spectrum and the target response spectrum over the entire period is calculated using equation (2). If it exceeds the allowable threshold, the number of iterations, the maximum value of the inertial weight, the initial value of the learning factor, and the hard constraint threshold of the PSO algorithm in step three are readjusted. For example, the threshold can be relaxed to 20% for iterative operation until the predetermined target is met, thereby obtaining the seismic acceleration time history that meets the target.

[0088] Example

[0089] Taking a long-period reaction spectroscopy analysis as an example, the target reaction spectrum is as follows: Figure 3 The black line shows the period on the horizontal axis, which is in seconds; the vertical axis is the target acceleration response spectrum, which is in g. Based on the seismic information reflected by the target response spectrum, this application selects 108 acceleration records with magnitude Mw≥7.0, epicentral distance≥100km, site shear wave velocity Vs30>500m / s, and horizontal component frequencies all below 0.05HZ as basic data when constructing a characteristic ground motion dataset in the long-period characteristic database. Furthermore, the approximate three-segment intensity envelope parameters of the target response spectrum are calculated using equation (1), and its rising segment cutoff time t1=47s, stationary segment termination time t2=110s, attenuation factor c=0.15, and total duration td=300s are determined.

[0090] After time-based correction of the characteristic mother wave based on the aforementioned envelope function, a particle swarm optimization (PSO) algorithm is introduced to iteratively optimize the mother wave weight coefficients using the target response spectrum as the convergence criterion (see details in the flowchart). Figure 2 Ultimately, the synthesis acceleration time history matching the target response spectrum was obtained. The maximum relative fitting error in the long-period critical range T = 10–20 s was controlled below 10%, the error in the medium-short period range T = 0.1–1 s was below 15%, and the maximum error in the structurally sensitive period range T = 1–10 s did not exceed 15%. The errors across the entire periodic domain met the engineering design threshold requirements. Figure 3 As shown. The resultant acceleration and its intensity envelope are as follows. Figure 4 As shown, the horizontal axis represents the period in seconds, and the vertical axis represents the acceleration in g. The dominant frequency curve is shown below. Figure 5 As shown, the horizontal axis represents the period in seconds, and the vertical axis represents the dominant frequency in Hz. The seismic response spectrum, acceleration duration, intensity, and frequency non-stationary characteristics all meet the objectives.

[0091] In summary, this application establishes a three-order progressive optimization system:

[0092] (1) Construction of low-frequency characteristic mother wave dataset: A seismic motion database with different characteristics was established, and seismic records that conform to the characteristics of deep target sites and target response spectra were systematically screened from the corresponding database to construct a characteristic mother wave dataset. In this seismic motion database, the horizontal component frequencies of the data are all below 0.1Hz to ensure that they have significant long-period characteristics.

[0093] (2) Characteristic mother wave reconstruction technology: The long-period characteristic mother waves selected from the constructed database are reconstructed over time using a three-segment intensity envelope function physical model.

[0094] (3) Spectrum-time domain decoupling constraint: In the PSO algorithm, a dual-path optimization objective is set—the key parameters are dynamically adjusted, requiring the particle swarm to continuously adjust its own state to find the optimal solution; in the frequency domain, a hard constraint is adopted to force the full-cycle error of 0.03-20s to not exceed 15%.

[0095] The seismic motion simulation method of this application can provide a seismic motion input scheme that combines broadband spectrum matching accuracy and physical characterization of the geological environment for the seismic design of long-period structures such as super high-rise buildings, significantly improving the reliability of seismic response analysis of long-period structures.

[0096] Although the embodiments disclosed in this application are as described above, the content is merely for the purpose of facilitating understanding of this application and is not intended to limit this application. Any person skilled in the art to which this application pertains may make any modifications and changes in the form and details of the implementation without departing from the spirit and scope disclosed in this application; however, the scope of patent protection of this application shall still be determined by the scope defined in the appended claims.

Claims

1. A method of simulating ground motion matching long-period response spectra, characterized by, The method comprises the following steps: (1) Based on the long-period response spectrum matching requirements, a low-frequency characteristic ground motion database is constructed, and a systematic preprocessing procedure is implemented to obtain a long-period characteristic data set with uniform format; (2) Based on the seismological parameters implied by the target response spectrum, multi-dimensional similarity matching is performed in the long-period characteristic data set obtained above to construct a characteristic mother wave data set reflecting the target characteristics; (3) Based on the empirical inference of the target response spectrum time-frequency characteristic envelope parameters, the strength envelope model is applied to the characteristic mother wave set to realize the reconstruction of non-stationary characteristics; (4) A target function is defined to quantify the difference between the synthesized acceleration response spectrum and the target response spectrum, and a random particle swarm is generated in the initialization stage based on the PSO algorithm, and each particle represents a set of weight coefficient vectors; (5) Based on the iteration of the PSO algorithm, dynamic adjustment is performed, and a hard constraint mechanism is introduced to fit the target response spectrum, so that the relative fitting error in the whole period range is controlled to be less than 15%; (6) Based on the target function, the PSO algorithm obtains a set of optimal weight coefficients corresponding to the characteristic mother wave data set after several iterations, and then obtains the corresponding acceleration time history; (7) The fitting result is error evaluated until the required ground motion acceleration time history is obtained.

2. The seismic motion simulation method according to claim 1, characterized by, In step (1), the following steps are included: (1.1) The seismic events and seismic ground motion data of regional seismic geological characteristics in the NGA-West2 database are classified according to the classification dimensions of moment magnitude Mw, epicentral distance R and site shear wave velocity Vs30; (1.2) The data with horizontal component frequency lower than 0.1HZ is selected to construct the ground motion database preserving long-period characteristics; (1.3) The grouped ground motion data is preprocessed: the first arrival wave detection accuracy is optimized by long-short time window energy ratio analysis method to eliminate invalid data segments; the time duration is unified based on piecewise exponential envelope function to ensure the comparability of time domain characteristics of multi-source data; the sampling rate is standardized to 200Hz by using cubic spline interpolation to eliminate the influence of sampling interval difference on frequency domain analysis.

3. The seismic motion simulation method according to claim 1, characterized by, In step (2), the following steps are included: Based on the magnitude, epicentral distance and site condition of the target ground motion, similar data is selected from the long-period characteristic database; Through multi-dimensional parameter matching and data quality evaluation, a ground motion set reflecting the target characteristics is constructed; The horizontal component frequency of the ground motion data in the preliminary selected ground motion set is less than 0.05HZ to form a characteristic mother wave data set.

4. The seismic motion simulation method according to any one of claims 1 to 3, characterized by, In step (3), the strength envelope model is a three-section strength envelope model in the following formula: ； wherein, , respectively control the start and end time of the strong motion stationary segment, denotes the duration of the stationary segment of the ground motion, represents the total duration of the ground motion, and c is the decay factor of the ground motion time history descending segment.

5. The seismic motion simulation method according to any one of claims 1 to 3, characterized by, In step (4), the iteration formula of the velocity v and position x of the particle is: ； ； wherein represents the inertia weight; represents the particle the individual optimal position at the tth iteration; represents the global optimal position; and is the learning factor, and is a random number independently drawn from the interval [0, 1], represents the jth dimension of the solution vector. represents the jth dimension of the solution vector.

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