Seismic motion fitting method matched with multi-damping-ratio response spectrum

Abstract

The invention relates to a seismic oscillation fitting method matched with a multi-damping-ratio response spectrum. According to the seismic motion fitting method, the seismic geology environment of the region is classified and the feature mother wave set is constructed, so that the seismic geology features of the region can be fully considered, and the fitting result can better conform to the actual condition of the target region and is more targeted and accurate. Through combination of characteristic seismic oscillation mother wave optimization and a dynamic parameterized particle swarm optimization algorithm, aiming at nonlinear characteristics of multi-damping ratio spectrum coupling matching, an improved particle swarm optimization PSO algorithm with a self-adaptive inertia weight and a learning factor is designed, and while the multi-target response spectrum fitting precision is improved, the multi-target response spectrum fitting precision is improved. And the time-frequency non-stationary characteristic of original seismic oscillation is reserved.

Description

TECHNICAL FIELD

[0001] The application relates to a fitting method of ground motion matching multi-damping ratio response spectrum, and is suitable for the technical field of engineering anti-seismic. BACKGROUND

[0002] In structural anti-seismic design, reasonable ground motion input determines the reliability of the dynamic calculation result of the structure. For example, for the dynamic calculation of the safety shell and equipment of a nuclear power plant under the action of super design reference earthquake, the demand for artificial ground motion simulation matching multi-damping ratio response spectrum is proposed. The existing ground motion simulation method still has the following problems and defects in actual engineering application:

[0003] (1) While matching the multi-target response spectrum, the regional seismological characteristics are not considered; thus, the result of the anti-seismic design is not designed according to the regional seismological characteristics, so that the accuracy and practicability are greatly affected;

[0004] (2) The non-stationary characteristics of the intensity and frequency of the ground motion cannot be represented at the same time, so that the fitting accuracy and practicability are greatly affected. SUMMARY

[0005] According to the fitting method of ground motion matching multi-damping ratio response spectrum, the error control of the fitting ground motion on different damping ratio response spectrums can be realized, and the time-domain non-stationary characteristics and frequency-domain energy evolution law of the ground motion can be controlled.

[0006] The application relates to a fitting method of ground motion matching multi-damping ratio response spectrum, and comprises the following steps:

[0007] (1) Based on the matching demand of the multi-damping ratio response spectrum, an engineering adaptive ground motion data set is constructed, and the ground motion data is classified and pretreated;

[0008] (2) Based on the seismological parameters in the target response spectrum, multi-dimensional similarity matching is performed on the ground motion data set obtained in step (1), and a characteristic mother wave set reflecting the target characteristics is constructed; for the scene of the target of the acceleration time history data, based on the time-frequency characteristics of the target multi-damping ratio response spectrum, the parameters of the three-section intensity envelope model are determined according to experience;

[0009] (3) The obtained three-section intensity envelope model is applied to the characteristic mother wave set for duration constraint, so as to realize the reconstruction of the intensity non-stationary characteristics;

[0010] (4) Based on the PSO algorithm, a group of optimal weight coefficients corresponding to the characteristic mother wave set is obtained, so that the acceleration time history meeting the target response spectrum is obtained, and then the calculation response spectrum of the fitting ground motion is obtained;

[0011] (5) Perform error evaluation on the fitting results and iterate until the seismic acceleration time history that meets the target is obtained.

[0012] Wherein, in step (1), the following steps are included:

[0013] (1.1) Using moment magnitude Mw, epicentral distance R, and site average shear wave velocity Vs30 as classification dimensions, the records in the NGA-West2 database are grouped to form a general ground motion dataset (GAdataset) covering broadband ground motion characteristics in typical tectonic environments.

[0014] (1.2) To meet the requirements of near-fault ground motion pulse characteristics, multiple records with significant velocity pulse characteristics are extracted from the PEER database to construct a velocity pulse data set VAdataset; and a hierarchical screening criterion is established based on the pulse parameters;

[0015] (1.3) Based on regional seismic geological characteristics, different seismic regions are used as a framework, combined with the magnitude-distance attenuation relationship and engineering site classification standards, to form a regional characteristic dataset RAdataset containing multiple parameter combinations to characterize the soil response characteristics of different sites.

[0016] Among them, in step (1), the preprocessing of seismic motion data includes: 1) optimizing the first arrival wave detection accuracy through the long-short time window energy ratio analysis method and eliminating invalid data segments; 2) unifying the time duration based on the piecewise exponential intensity envelope function to ensure the comparability of the time domain characteristics of multi-source data; 3) applying cubic spline interpolation to standardize the sampling rate to 200 Hz, eliminating the influence of sampling interval differences on frequency domain analysis, and obtaining a seismic motion data matrix with a unified format.

[0017] Among them, in step (2), the three-segment intensity envelope model in the following formula (1) is used to perform time history correction on the constructed characteristic mother wave set:

[0018]

[0019] Where t1 and t2 represent the start and end time of the strong earthquake steady phase, t2-t1 represents the duration of the steady phase of the earthquake; t d represents the total duration of the earthquake motion; c is a parameter that constrains the descent speed, which is used to control the attenuation speed of the descent intensity, and its value range is 0.1-2.0.

[0020] Wherein, in step (4), the following steps are included:

[0021] (4.1) Define the objective function to quantify the difference between the synthetic acceleration response spectrum and the target spectrum;

[0022] (4.2) Based on the PSO algorithm, a random particle swarm is generated in the initialization phase, and each particle represents a set of weight coefficient vectors;

[0023] (4.3) Based on the iteration of the PSO algorithm, its key parameters are dynamically adjusted to dynamically adjust the algorithm.

[0024] Preferably, in step (4.2), the update iterations of the particle velocity v and position x follow equations (3) and (4):

[0025] v ij (t+1)=ωv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij(t) ] (3)

[0026] x ij (t+1)=x ij (t)+v ij (t+1) (4)

[0027] Where ω represents the inertia weight; p ij (t) represents the individual optimal position of particle i at the tth iteration; p gj (t) represents the global optimal position; c1 and c2 are the individual learning factor and the social learning factor, respectively, c1 = c2 = 2.5; r1 and r2 are random numbers independently drawn from the interval [0,1]; j represents the jth dimension of the solution vector.

[0028] Preferably, in step (4.3), the dynamic adjustment of the algorithm includes time-varying expansion of the number of particles, nonlinear attenuation of inertia weights and anti-phase coupling of learning factors.

[0029] In particular, for the nonlinear attenuation of inertia weight, the hyperbolic tangent attenuation function is used to control the inertia weight, and its expression is:

[0030]

[0031] Among them, w max represents the maximum weight, w min represents the minimum weight, t max Indicates the maximum number of iterations.

[0032] In particular, the individual learning factor C1 and the social learning factor C2 are dynamically adjusted according to formula (7):

[0033]

[0034] Where, tmax Indicates the maximum number of iterations.

[0035] This application classifies the regional seismic geological environment and constructs a characteristic mother wave set, so that the seismic motion fitting method of this application can fully consider the seismic geological characteristics of the region, making the fitting results more consistent with the actual situation of the target area, more targeted and accurate. This application combines the characteristic seismic motion mother wave optimization with the dynamic parameterized particle swarm algorithm, and designs an improved particle swarm optimization (PSO) algorithm with adaptive inertia weights and learning factors for the nonlinear characteristics of multi-damping ratio spectrum coupling matching. While improving the fitting accuracy of the multi-damping ratio target response spectrum, it retains the time-frequency non-stationary characteristics of the original seismic motion. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the earthquake motion fitting method for matching multiple damping ratio response spectra in the present application.

[0037] Figure 2 This is the basic flow chart of the PSO algorithm for synthesizing earthquake motion in this application.

[0038] Figure 3 Schematic diagram of the target response spectrum and its fitting in the embodiment of the present application.

[0039] Figure 4 Schematic diagram of the synthetic acceleration and its intensity envelope in the embodiment of the present application.

[0040] Figure 5 Schematic diagram of the main frequency curve in the embodiment of the present application. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical solutions and advantages of this application more clear, the following will describe the embodiments of this application in detail with reference to the accompanying drawings. It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of this application can be combined with each other in any way.

[0042] A method for fitting earthquake motions to match multiple damping ratio response spectra according to the present application includes the following steps:

[0043] (1) Based on the matching requirements of multiple damping ratio response spectra, a seismic motion dataset with engineering adaptability is constructed, and the seismic motion data is classified and preprocessed;

[0044] (2) Based on the seismological parameters in the target response spectrum, multi-dimensional similarity matching is performed on the seismic motion data set obtained in step (1) to construct a characteristic mother wave set reflecting the target characteristics; for the scenario without acceleration time history data, based on the time-frequency characteristics of the target multi-damping ratio response spectrum, the parameters of the three-segment intensity envelope function are empirically estimated;

[0045] (3) The obtained three-segment intensity envelope model is applied to the characteristic mother wave set to perform time constraints and realize the reconstruction of non-stationary characteristics;

[0046] (4) Based on the PSO algorithm, a set of optimal weight coefficients corresponding to the characteristic mother wave set is obtained, thereby obtaining the acceleration time history that meets the target response spectrum, and then obtaining the calculated response spectrum of the fitted ground motion;

[0047] (5) Perform error evaluation on the fitting results and iterate until the earthquake acceleration time history that meets the target is obtained.

[0048] like Figure 1 As shown, a seismic motion fitting method for matching multiple damping ratio response spectra according to the present application includes the following steps:

[0049] (1) Based on the matching requirements of multiple damping ratio response spectra, a seismic motion dataset with engineering adaptability is constructed, and the actual seismic motion data is classified and preprocessed.

[0050] First, we grouped the records in the Pacific Earthquake Engineering Center's NGA-West2 database using moment magnitude (Mw), epicentral distance (R), and site-average shear wave velocity (Vs30) as classification dimensions to form a general ground motion dataset (GAdataset), which covers broadband ground motion characteristics in typical tectonic environments.

[0051] Secondly, to meet the requirements of near-fault ground motion pulse characteristics, multiple records with significant velocity pulse characteristics were extracted from the PEER database to construct the velocity pulse ground motion dataset VAdataset. A grading and screening criterion was established based on pulse parameters such as pulse period and peak ratio and Vs30 site conditions.

[0052] Thirdly, based on the regional seismic geological characteristics, different seismic regions are used as the framework, combined with the magnitude-distance attenuation relationship and engineering site classification standards, a regional characteristic dataset RAdataset containing a multi-parameter combination is formed to characterize the soil response characteristics of different sites.

[0053] The grouped seismic data were then preprocessed, including: 1) optimizing first-arrival detection accuracy and eliminating invalid data segments using long- and short-time window energy ratio analysis; 2) unifying the time duration using a piecewise exponential intensity envelope model to ensure comparability of temporal characteristics across multiple data sources; and 3) applying cubic spline interpolation to standardize the sampling rate to 200 Hz, or a time interval of 0.005 seconds, to eliminate the impact of sampling interval variations on frequency-domain analysis. This processing yielded a uniformly formatted seismic data matrix suitable for subsequent processes.

[0054] (2) Select the characteristic mother wave and determine the parameters of the intensity envelope model

[0055] To achieve parameterized representation of the intensity envelope that reflects regional earthquake characteristics, an empirical inference method for the envelope function based on target spectral characteristics and a seismic motion database is proposed. The specific process is as follows:

[0056] (2.1) Based on the seismological parameters in the target response spectrum, multi-dimensional similarity matching is performed in the ground motion dataset obtained in step (1), that is, a mother wave screening mechanism associated with the target spectrum is set.

[0057] First, based on the magnitude, epicenter distance and site conditions of the target ground motion, the adapted datasets are selected from GAdataset, VAdataset and RAdataset. Secondly, RAdataset is preferred for regional feature simulation, while VAdataset is selected for near-site ground motion pulse characteristics. Finally, a characteristic mother wavelet set a is constructed to reflect the target characteristics through multi-dimensional parameter matching and data quality assessment. i (t)=(a1(t), a2(t),…,a n (t)).

[0058] (2.2) Three-segment envelope function empirical modeling:

[0059] For scenarios without acceleration time history data, the envelope parameters are empirically estimated based on the time-frequency characteristics of the target multi-damping ratio response spectrum. That is, the following three-segment strength envelope model can be used to perform time history correction on the constructed characteristic mother wave set, as shown in formula (1).

[0060]

[0061] Where t1 and t2 represent the start and end time of the strong earthquake steady phase, respectively; t2-t1 represents the duration of the steady phase of the earthquake motion; t d represents the total duration of the earthquake motion; c is a parameter for constraining the descent speed, which is used to control the attenuation speed of the descent section intensity. The value range can be 0.1-2.0, and is preferably 0.15.

[0062] (2.3) Mother wave duration constraint and adaptive adjustment:

[0063] The three-segment intensity envelope model obtained by formula (1) is applied to the characteristic mother wave set for duration constraint to achieve the reconstruction of intensity non-stationary characteristics.

[0064] (3) Fitting target response spectrum based on PSO algorithm

[0065] First, define the objective function shown in formula (2) to quantify the synthetic acceleration response spectrum S g (T i ) and target spectrum The difference is expressed as:

[0066]

[0067] Where, is the target acceleration response spectrum, S g (T i ) is the calculated response spectrum of the fitted earthquake motion, T i is the i-th period point corresponding to the response spectrum; N is the total value of the response spectrum points.

[0068] Then, based on the PSO algorithm, a random particle swarm is generated in the initialization phase, where each particle represents a set of weight coefficient vectors k. The update iterations of the particle velocity v and position x follow equations (3) and (4):

[0069] v ij (t+1)=ωv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij(t) ] (3)

[0070] x ij (t+1)=x ij (t)+v ij (t+1) (4)

[0071] Where ω represents the inertia weight; p ij (t) represents the individual optimal position of particle i at the tth iteration; p gj (t) represents the global optimal position; c1 and c2 are learning factors, which can be set to c1 = c2 = 2.5; r1 and r2 are random numbers independently drawn from the interval [0,1]; j represents the jth dimension of the solution vector. For example, if the optimization problem is D-dimensional, the weight coefficient vector k = [k1, k2, ..., k D ], then j∈{1,2,…,D}.

[0072] Based on the iteration of the PSO algorithm, key parameters such as the number of particles, inertia weight, and learning factors, including individual learning factors and social learning factors, are dynamically adjusted to dynamically adjust the algorithm. Specifically, this may include:

[0073] (1) The time-varying expansion of the particle population size, i.e., the number of particles

[0074] The initial number of particles is set to 1000, and the number of particles N(t) increases dynamically with the number of iterations t according to the following formula:

[0075] N(t)=1000t (5)

[0076] Where t is the number of iterations.

[0077] (2) Nonlinear attenuation of inertia weight

[0078] A hyperbolic tangent decay function is proposed to control the inertia weight, which is expressed as

[0079]

[0080] Among them, w max =0.9, w min = 0, the function is in the middle of the iteration (0.3t max <t<0.7t max ) presents a slow-changing characteristic, which prevents the algorithm from falling into the local optimum too early. max Indicates the maximum number of iterations.

[0081] (3) Anti-phase coupling of learning factors

[0082] The individual learning factor C1 and the social learning factor C2 are dynamically adjusted according to formula (7):

[0083]

[0084] The exponential learning factor is dynamically adjusted so that the algorithm focuses on individual experience accumulation in the early stage, i.e., C1→2.0, C2→0; in the later stage, t→t max When , it turns to collective intelligence collaboration, that is, C1→0, C2→2.0.

[0085] Finally, based on the objective function, the PSO algorithm obtains a set of optimal weight coefficients k corresponding to the characteristic mother wave set after several iterative optimizations, and then obtains the acceleration time history ü that meets the target response spectrum. g (t).

[0086]

[0087] Where a i (t) represents a characteristic acceleration waveform. The basic process is as follows Figure 2 shown.

[0088] (4) Evaluate the fitting results and iterate until the earthquake acceleration time history that meets the target is obtained.

[0089] The relative fitting error between the synthetic spectrum and the target spectrum in the full cycle is calculated using Equation (2). If the error is higher than the allowable threshold, the number of iterations of the PSO algorithm, the maximum value of the inertia weight, and the starting value of the learning factor in step 3 are readjusted and the iteration is repeated until the predetermined target is met.

[0090] According to a seismic motion fitting method for matching multiple damping ratio response spectra in the present application, a large number of earthquake acceleration records are first used as initial seismic motions, and a characteristic mother wave set is constructed by classifying the regional seismic geological environment; then, the particle swarm optimization algorithm is improved to break through the nonlinear convergence problem of collaborative optimization of multiple target parameters such as multiple damping ratio response spectra, duration, and non-stationary envelope, so that the artificially fitted seismic motion can achieve matching of multiple targets. By integrating data-driven and physical constraints, the present application not only overcomes the dependence of statistical models on the completeness of training data, but also breaks through the limitations of the physical mechanism model on the matching accuracy of multiple damping ratio response spectra in the frequency band of engineering interest, providing seismic motion input with both spectrum matching accuracy and reasonable time-frequency characteristics for areas where strong earthquake data is scarce.

[0091] Example

[0092] Taking the seismic analysis of a certain project as an example, the target response spectra of different damping ratios are as follows: Figure 3 As shown, the horizontal axis represents the time period in seconds, and the vertical axis represents the acceleration in g. Based on the earthquake information reflected by the target response spectrum, when constructing the characteristic seismic motion dataset in the GAdataset database, 100 acceleration records with magnitude Mw of 5.5-6.0, epicenter distance of 20-40km, and Class II site conditions were selected as basic data. Then, the three-segment intensity envelope parameters of the target spectrum were calculated using formula (1), and the rising segment cutoff time t1=2s, the plateau segment end time t2=15s, the attenuation factor c=0.15, and the total duration t d =50s.

[0093] After the characteristic mother wave is modified based on the above envelope function, the particle swarm optimization (PSO) algorithm is introduced to iteratively optimize the mother wave weight coefficient with the multi-damping ratio target response spectrum as the convergence standard, and finally the synthetic acceleration time history matching the target spectrum is obtained. Figure 3 As shown in the figure, the maximum relative fitting error of the 2% damping ratio response spectrum is 13.46%, the maximum relative fitting error of the 5% damping ratio response spectrum is 8.7%, and the maximum relative fitting error of the 7% damping ratio response spectrum is 12.2%. The relative fitting errors of the full period segment are all less than 15%. The synthetic acceleration and its intensity envelope are shown in the figure. Figure 4 As shown, the main frequency curve is as follows Figure 5 As shown. Figures 4-5 In the figure, the horizontal axis represents the time period in seconds, and the vertical axis represents the acceleration in g and the frequency in Hz, respectively. The seismic response spectrum, acceleration duration, intensity, and frequency nonstationary characteristics all meet the requirements.

Claims

1. A seismic motion fitting method for matching multiple damping ratio response spectra, characterized in that: The following steps are involved: (1) Based on the matching requirements of multiple damping ratio response spectra, a seismic motion dataset with engineering adaptability is constructed, and the seismic motion data is classified and preprocessed; (2) Based on the seismological parameters in the target response spectrum, multi-dimensional similarity matching is performed on the seismic motion data set obtained in step (1) to construct a characteristic mother wave set reflecting the target characteristics; for scenarios without acceleration time history data, the parameters of the three-stage strength envelope model are empirically estimated based on the spectral characteristics of the target multi-damping ratio response spectrum; (3) The obtained three-segment intensity envelope model is applied to the characteristic mother wave set to perform time constraints and realize the reconstruction of the intensity non-stationary characteristics; (4) Based on the PSO algorithm, a set of optimal weight coefficients corresponding to the characteristic mother wave set is obtained, thereby obtaining the acceleration time history that meets the target response spectrum, and then obtaining the fitted target response spectrum; (5) Perform error evaluation on the fitting results and iterate until the seismic acceleration time history that meets the target is obtained.

2. The seismic motion fitting method according to claim 1, wherein: In step (1), the following steps are included: (1.1) Using moment magnitude Mw, epicentral distance R, and site average shear wave velocity Vs30 as classification dimensions, the records in the NGA-West2 database are grouped to form a general ground motion dataset (GAdataset) covering broadband ground motion characteristics in typical tectonic environments. (1.2) To meet the requirements of near-fault ground motion pulse characteristics, multiple records with significant velocity pulse characteristics were extracted from the PEER database to construct a velocity pulse ground motion dataset VAdataset; and a hierarchical screening criterion was established based on the pulse parameters. (1.3) Based on regional seismic geological characteristics, different seismic regions are used as a framework, combined with the magnitude-distance attenuation relationship and engineering site classification standards, to form a regional characteristic dataset RAdataset containing multiple parameter combinations to characterize the soil response characteristics of different sites.

3. The ground motion fitting method according to claim 1, wherein: In step (1), the seismic data are preprocessed, including: 1) optimizing the first arrival wave detection accuracy by the long-short time window energy ratio analysis method and eliminating invalid data segments; 2) unifying the time duration based on the piecewise exponential intensity envelope function to ensure the comparability of the time domain characteristics of multi-source data; 3) applying cubic spline interpolation to standardize the sampling rate to 200 Hz, eliminating the influence of sampling interval differences on frequency domain analysis, and obtaining a seismic data matrix with a unified format.

4. The ground motion fitting method according to any one of claims 1 to 3, characterized in that: In step (2), the three-segment intensity envelope model in the following formula (1) is used to perform time history correction on the constructed characteristic mother wave set: Where t1 and t2 represent the start and end time of the strong earthquake steady phase, respectively, and t2-t1 represents the duration of the steady phase of the earthquake motion. t d represents the total duration of the earthquake motion; c is a parameter that constrains the descent speed and is used to control the decay speed of the descent intensity. Its value range is 0.1-2.

0.

5. The ground motion fitting method according to any one of claims 1 to 3, characterized in that: In step (4), the following steps are included: (4.1) Define the objective function to quantify the difference between the synthetic acceleration response spectrum and the target spectrum; (4.2) Based on the PSO algorithm, a random particle swarm is generated in the initialization phase, and each particle represents a set of weight coefficient vectors; (4.3) Based on the iteration of the PSO algorithm, its key parameters are dynamically adjusted to dynamically adjust the algorithm.

6. The ground motion fitting method according to claim 5, characterized in that: In step (4.2), the update iteration of particle velocity v and position x follows equations (3) and (4): v ij (t+1)=ωv ij (t)+c1r1(t)[p ij (t)-x ij (t)]+c2r2(t)[p gj (t)-x ij(t) ] (3) x ij (t+1)=x ij (t)+v ij (t+1) (4) Where ω represents the inertia weight; p ij (t) represents the individual optimal position of particle i at the tth iteration; p gj (t) represents the global optimal position; c1 and c2 are the individual learning factor and the social learning factor, respectively, c1 = c2 = 2.5; r1 and r2 are random numbers independently drawn from the interval [0,1]; j represents the jth dimension of the solution vector.

7. The ground motion fitting method according to claim 5, characterized in that: In step (4.3), the dynamic adjustment of the algorithm includes the time-varying expansion of the number of particles, the nonlinear decay of the inertia weight and the anti-phase coupling of the learning factor.

8. The ground motion fitting method according to claim 7, characterized in that: For the nonlinear attenuation of inertia weight, the hyperbolic tangent attenuation function is used to control the inertia weight, and its expression is: Among them, w max represents the maximum weight, w min represents the minimum weight, t max Indicates the maximum number of iterations.

9. The ground motion fitting method according to claim 7, wherein: The individual learning factor C1 and the social learning factor C2 are dynamically adjusted according to formula (7): Where, t max Indicates the maximum number of iterations.

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