An improved method for time-domain non-stationarity of stochastic simulation of ground motion

Abstract

The present application relates to the field of seismology, especially to a kind of seismic motion random simulation time domain non-stationarity improvement method, comprising the following steps: (1) extracting characteristic ground motion;(2) calculate target Fourier amplitude spectrum;(3) calculate target waveform parameter;(4) generate target ground motion phase spectrum;(5) calculate final ground motion.The present application is based on random simulation method and ground motion waveform parameter statistical law, proposes a kind of ground motion random simulation time domain non-stationarity improvement method, establishes target function including ground motion waveform parameter, obtains more reasonable phase spectrum using multi-objective genetic algorithm, and the simulation result using the present application is more consistent with the waveform of real record.The present application can solve the defect that random simulation method is insufficient for expressing time domain non-stationarity of simulated ground motion.

Description

Technical Field

[0001] This invention relates to the field of seismology, and in particular to an improved method for time-domain nonstationarity in stochastic simulation of ground motion. Background Technology

[0002] Earthquake motions have a direct impact on the seismic response of structures, making them crucial for seismic hazard assessment, structural design, and risk analysis of urban building structures and infrastructure. Currently, the most direct method for obtaining earthquake motions for structural time-history response analysis is to select and amplitude-adjust existing earthquake motion databases. However, this method alters the relationship between earthquake motion characteristics and original physical conditions (such as magnitude, path, and site), potentially leading to significant differences between the characteristics of the selected earthquake motions and those observed in actual earthquake events. Therefore, conducting earthquake motion simulation is a more reasonable approach.

[0003] Stochastic seismic motion simulation combines seismological principles with stochastic processes, offering advantages such as ease of use and wide simulation bandwidth, and is widely applied in seismic motion simulation in practical engineering. Its basic principle is to generate an initial seismic motion waveform by windowing Gaussian white noise and then modulating its Fourier amplitude spectrum to obtain the final seismic motion. However, the shape parameter of the window function is usually fixed, resulting in highly similar time-domain waveforms in simulations under different seismic scenarios, which is insufficient for expressing the time-domain non-stationarity of seismic motion. Therefore, an improved method for addressing the time-domain non-stationarity of seismic motion stochastic simulation is proposed. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of stochastic simulation methods in expressing the time-domain non-stationarity of simulated ground motions, and to provide an improved method for stochastic simulation of ground motion time-domain non-stationarity.

[0005] This application provides an improved method for time-domain nonstationarity in stochastic seismic simulation, comprising the following steps:

[0006] (1) Extract characteristic ground motions;

[0007] (2) Calculate the target Fourier amplitude spectrum;

[0008] (3) Calculate the target waveform parameters;

[0009] (4) Generate the target ground motion phase spectrum;

[0010] (5) Calculate the final ground motion.

[0011] Furthermore, characteristic ground motions are extracted, and principal component analysis is used to reduce the dimensionality of the regional ground motion database, resulting in a set of orthogonal characteristic ground motions. These can be linearly superimposed to generate new ground motions using the following formula:

[0012]

[0013] Where t is time, a(t) is the new ground motion generated by the superposition of characteristic ground motions, N is the number of characteristic ground motions, and e i Let k represent the i-th characteristic ground motion. i This indicates the corresponding superposition coefficient.

[0014] Further, the target Fourier amplitude spectrum is calculated:

[0015]

[0016] In the above formula, Y(M0,R,f) represents the target Fourier amplitude spectrum, C represents the scaling factor, and f c Let M0 represent the corner frequency, f represent the seismic moment, R represent the distance, Z(R) represent the geometric diffusion coefficient, Q(f) represent the quality factor, A(f) represent the site amplification factor, β represent the shear wave velocity, and κ represent the high-frequency attenuation coefficient.

[0017] Furthermore, the target waveform parameters are calculated, using two parameters to control the waveform: the important duration D and the relative position P of the peak occurrence. The target important duration is calculated using the following formula:

[0018] ln(D) = 1.736 + f M,R -0.242ln(V S30 -0.007Z tor

[0019] Among them, V S30 Z represents the average shear wave velocity at 30m underground. tor f represents the fault burial depth. M,R Calculated using the following formula:

[0020]

[0021] In the formula M w For moment magnitude, R S R is the minimum value between the fault distance and 150 km. F This is the maximum value between the fault distance and 150 km;

[0022] For the waveform parameter P, since it has no obvious functional relationship with factors such as magnitude and distance, this invention establishes its random distribution model based on statistical data methods:

[0023]

[0024] Wherein, P follows an Exponweib distribution, and a, b, l, s are model parameters of this distribution. P is obtained by random sampling from this distribution model.

[0025] Furthermore, to generate the target ground motion phase spectrum, an objective function (OF) incorporating the target waveform parameters is first established:

[0026] OF D =|D target -D a(t) |

[0027] OF P =|P target -P a(t) |

[0028] Among them, D target P target D represents the relative position of the target's important duration and the target's peak occurrence, respectively. a(t) With P a(t) The important duration and relative location of the peak occurrence of the new ground motion a(t) generated by the superposition of characteristic ground motions are respectively identified, and the superposition coefficient k is solved using a multi-objective genetic algorithm. i The ground motion a(t) that satisfies the target ground motion waveform parameters is obtained, and its phase spectrum is obtained by performing a Fourier transform on it.

[0029] Furthermore, the final ground motion is calculated, and the phase spectrum and amplitude spectrum are subjected to inverse Fourier transform to obtain the final ground motion time history, which is then compared with the results of the actual record and the current stochastic simulation method.

[0030] The beneficial effects of this invention are as follows: Based on stochastic simulation methods and the statistical laws of seismic motion waveform parameters, this invention proposes an improved method for the time-domain non-stationarity of stochastic seismic simulation. It establishes an objective function incorporating seismic motion waveform parameters, utilizes a multi-objective genetic algorithm to obtain a more reasonable phase spectrum, and the simulation results obtained using this invention better match the actually recorded waveforms. This invention can overcome the shortcomings of stochastic simulation methods in expressing the time-domain non-stationarity of simulated seismic motions. Attached Figure Description

[0031] Figure 1 Flowchart of the overall framework for an improved method to address the time-domain nonstationarity of stochastic seismic simulation;

[0032] Figure 2 This is a distribution map of the ground motion database for the target area in the example (green beach ball: epicenter; red triangle: ground motion station);

[0033] Figure 3 Here is a comparison chart of ground motion acceleration time histories at various stations in the example (red: actual records; blue line: results of this invention; black: results of the current stochastic simulation method. The numbers above the time histories represent ground motion amplitudes, and the numbers below represent important durations).

[0034] Figure 4A comparison of ground motion acceleration response spectra at various stations in the example (red: actual records; blue line: results of this invention; black: results of current stochastic simulation methods);

[0035] Figure 5 The average residual distribution of the acceleration response spectrum at each station is shown in the diagram. Detailed Implementation

[0036] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0037] like Figure 1-5 The method for improving the time-domain nonstationarity of random seismic simulation, as shown, includes the following steps:

[0038] (1) Extract characteristic ground motions;

[0039] (2) Calculate the target Fourier amplitude spectrum;

[0040] (3) Calculate the target waveform parameters;

[0041] (4) Generate the target ground motion phase spectrum;

[0042] (5) Calculate the final ground motion.

[0043] Specific Implementation Method 1: This specific implementation method for improving the time-domain non-stationarity of random seismic simulation is carried out according to the steps described above:

[0044] (1) Extracting characteristic ground motions:

[0045] Principal component analysis is used to reduce the dimensionality of the regional seismic ground motion database, resulting in a set of orthogonal characteristic ground motions, which can be linearly superimposed to generate new ground motions using the following formula:

[0046]

[0047] Where t is time, a(t) is the new ground motion generated by the superposition of characteristic ground motions, N is the number of characteristic ground motions, and e i Let k represent the i-th characteristic ground motion. i This indicates the corresponding superposition coefficient.

[0048] (2) Calculate the target Fourier amplitude spectrum:

[0049]

[0050] In the above formula, Y(M0,R,f) represents the target Fourier amplitude spectrum, C represents the scaling factor, and f c Let M0 represent the corner frequency, f represent the seismic moment, R represent the distance, Z(R) represent the geometric diffusion coefficient, Q(f) represent the quality factor, A(f) represent the site amplification factor, β represent the shear wave velocity, and κ represent the high-frequency attenuation coefficient.

[0051] (3) Calculate the target waveform parameters:

[0052] This invention uses two parameters to control the waveform: the important duration D and the relative position P of the peak occurrence. The target important duration is calculated using the following formula:

[0053] ln(D) = 1.736 + f M,R -0.242ln(V S30 -0.007Z tor

[0054] Among them, V S30 Z represents the average shear wave velocity at 30m underground. tor f represents the fault burial depth. M,R Calculated using the following formula:

[0055]

[0056] In the formula M w For moment magnitude, R S R is the minimum value between the fault distance and 150 km. F This is the maximum value between the fault distance and 150 km;

[0057] For the waveform parameter P, since it has no obvious functional relationship with factors such as magnitude and distance, this invention establishes its random distribution model based on statistical data methods:

[0058]

[0059] Wherein, P follows an Exponweib distribution, and a, b, l, s are model parameters of this distribution. P is obtained by random sampling from this distribution model.

[0060] (4) Generate the target ground motion phase spectrum:

[0061] First, establish the objective function (OF) that includes the target waveform parameters:

[0062] OF D =|D target -D a(t) |

[0063] OF P =|P target -Pa(t) |

[0064] Among them, D target P target D represents the relative position of the target's important duration and the target's peak occurrence, respectively. a(t) With P a(t) The important duration and relative location of the peak occurrence of the new ground motion a(t) generated by the superposition of characteristic ground motions are respectively identified, and the superposition coefficient k is solved using a multi-objective genetic algorithm. i The ground motion a(t) that satisfies the target ground motion waveform parameters is obtained, and its phase spectrum is obtained by performing a Fourier transform on it.

[0065] (5) Calculate the final ground motion:

[0066] The final ground motion time history is obtained by performing inverse Fourier transform on the phase spectrum and amplitude spectrum, and then compared with the results of real records and current stochastic simulation methods.

[0067] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that the formula for calculating the proportionality coefficient C in step two is as follows: in Here, V represents the frequency-dependent radiation factor, ρ represents the density, and F represents the free surface magnification factor.

[0068] Specific Implementation Method 3: This implementation method differs from Specific Implementation Method 1 or 2 in that the database used for data statistics in step 3 is derived from the NGA-West2 Global Shallow Crust Strong Ground Motion Database and is selected according to the following criteria: the horizontal two components of the ground motion are available; the ground motion originates from free surface stations; and the earthquake contains at least 4 ground motions.

[0069] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that the maximum number of rounds in the multi-objective genetic algorithm in step four is 100.

[0070] Example: The improved method for time-domain nonstationarity in random seismic simulation of earthquake motion in this example is implemented according to the following steps:

[0071] (1) Extracting characteristic ground motions:

[0072] The Iwate earthquake in Japan in 2008 was selected. Principal component analysis was used to reduce the dimensionality of the ground motion records in the region prior to 2008. In this example, the number of ground motion data points was 1160, resulting in a set of orthogonal characteristic ground motions. These can be linearly superimposed to generate new ground motions using the following formula:

[0073]

[0074] Where t represents time, a(t) is the new ground motion generated by the superposition of characteristic ground motions, N is the number of characteristic ground motions, which is 67 in this embodiment, and e i Let k represent the i-th characteristic ground motion. i This indicates the corresponding superposition coefficient.

[0075] (2) Calculate the target Fourier amplitude spectrum:

[0076]

[0077] In the above formula, Y(M0,R,f) represents the target Fourier amplitude spectrum, and f c M0 represents the corner frequency, and M0 represents the seismic moment, which is taken as 2.82 × 10⁻⁶ in this embodiment. 19 N·m, f represents frequency, R represents distance, Z(R) represents geometric diffusion coefficient, Q(f) represents quality factor, A(f) represents site amplification factor, β represents shear wave velocity, which is taken as 3.6 km / s in this embodiment, κ represents high-frequency attenuation coefficient, and C represents proportionality coefficient, calculated using the following formula: in The frequency-dependent radiation factor is given by V, which represents the horizontal component coefficient. In this embodiment, V is taken as 2.8 g / cm³. 3 ρ represents density, and in this embodiment, ρ is taken as 2.8 g / cm³. 3 F represents the free surface magnification factor, which is 2.0 in this embodiment.

[0078] (3) Calculate the target waveform parameters:

[0079] This invention uses two parameters to control the waveform: the important duration D and the relative position P of the peak occurrence. The target important duration is calculated using the following formula:

[0080] ln(D) = 1.736 + f M,R -0.242ln(V S30 -0.007Z tor

[0081] Among them, V S30 Z represents the average shear wave velocity at 30m underground. tor The fault depth is taken as 0.7 km in this embodiment, f M,R Calculated using the following formula:

[0082]

[0083] In the formula M w The moment magnitude is taken as 6.9 in this embodiment, R S R is the minimum value between the fault distance and 150 km. F It is the maximum value among fault distance and 150km.

[0084] For the waveform parameter P, since it has no obvious functional relationship with factors such as magnitude and distance, the NGA-West2 global shallow crustal strong ground motion database was first screened according to the following criteria: the horizontal two components of the ground motion are available; the ground motion originates from free surface stations; the earthquake contains at least 4 ground motions. A total of 14,209 ground motions were obtained, and their stochastic distribution model was established based on statistical methods.

[0085]

[0086] Wherein, P follows an Exponweib distribution, and a, b, l, s are model parameters of this distribution, which are 0.23109, 3.58482, 0.00025, and 0.54138, respectively. P is obtained by random sampling from this distribution model.

[0087] (4) Generate the target ground motion phase spectrum:

[0088] First, establish the objective function (OF) that includes the target waveform parameters:

[0089] OF D =|D target -D a(t) |

[0090] OF P =|P target -P a(t) |

[0091] Among them, D target P target D represents the relative position of the target's important duration and the target's peak occurrence, respectively. a(t) With P a(t) These represent the important duration and relative location of the peak value of the new ground motion a(t) generated by the superposition of characteristic ground motions. The superposition coefficient k is solved using a multi-objective genetic algorithm. i The maximum number of iterations in the multi-objective genetic algorithm is 100, which obtains the ground motion a(t) that satisfies the target ground motion waveform parameters, and performs a Fourier transform on it to obtain its phase spectrum.

[0092] (5) Calculate the final ground motion:

[0093] The final ground motion time history is obtained by performing inverse Fourier transform on the phase spectrum and amplitude spectrum, and then compared with the results of real records and current stochastic simulation methods.

[0094] This invention proposes an improved method for time-domain nonstationarity in stochastic seismic simulation based on stochastic simulation methods and statistical laws governing seismic motion waveform parameters. Based on this invention, seismic motion simulations of the 2008 Iwate earthquake in Japan were conducted. Figure 2 The example NGA-West2 strong ground motion database distribution map of Japan is shown. A total of 1,160 ground motion records from four earthquakes that occurred before 2008 were selected, with magnitudes ranging from 6.5 to 7 and fault distances ranging from 0.1 to 220 km. Figure 3 The paper presents a comparison between the simulated acceleration time histories from six stations, observed records, and existing methods. It shows that the amplitude of the acceleration time histories obtained in this invention is close to that of current methods, but the waveform, duration, and other time-domain characteristics are more consistent with actual records, indicating that the time-domain non-stationarity of the simulation results has been improved. Figure 4-5 It can be seen that the acceleration response spectrum simulation results, average residual distribution, and standard deviation interval width of the present invention at the six stations are basically consistent with the current method, indicating that the frequency domain characteristics of the simulation results have not shown obvious deviations, thus proving the reliability of the present invention.

[0095] It will be apparent to those skilled in the art that the present 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 its spirit or essential characteristics. Therefore, the embodiments should be considered in all respects as exemplary and non-limiting, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. An improved method for time-domain nonstationarity in random seismic simulation, characterized in that, Includes the following steps: (1) Extract characteristic ground motions; (2) Calculate the target Fourier amplitude spectrum; (3) Calculate the target waveform parameters; (4) Generate the target ground motion phase spectrum; (5) Calculate the final ground motion; Calculate the target waveform parameters, using two parameters to control the waveform: the important duration D and the relative position P of the peak occurrence. The target important duration is calculated using the following formula: in, V S30 The average shear wave velocity at 30m underground. Z tor The depth of the fault. f M,R Calculated using the following formula: In the formula M w For moment magnitude, R S R is the minimum value between the fault distance and 150 km. F This is the maximum value between the fault distance and 150 km; For the waveform parameter P, since it has no obvious functional relationship with factors such as magnitude and distance, this invention establishes its random distribution model based on statistical data methods: Wherein, P follows an Exponweib distribution, and a, b, l, s are model parameters of this distribution. P is obtained by random sampling from this distribution model. To generate the target ground motion phase spectrum, first establish an objective function OF that includes the target waveform parameters: Among them, D target P target D represents the relative position of the target's important duration and the target's peak occurrence, respectively. a(t) With P a(t) The important duration and relative location of the peak occurrence of the new ground motion a(t) generated by the superposition of characteristic ground motions are respectively identified, and the superposition coefficient k is solved using a multi-objective genetic algorithm. i The ground motion a(t) that satisfies the target ground motion waveform parameters is obtained, and its phase spectrum is obtained by performing a Fourier transform on it.

2. The method for improving the time-domain nonstationarity of random seismic simulation according to claim 1, characterized in that, Feature ground motions are extracted, and principal component analysis is used to reduce the dimensionality of the regional ground motion database, resulting in a set of orthogonal feature ground motions. These feature ground motions can be linearly superimposed to generate new ground motions using the following formula: Where t is time, a(t) is the new ground motion generated by the superposition of characteristic ground motions, and N is the number of characteristic ground motions. e i This represents the i-th characteristic ground motion. k i This indicates the corresponding superposition coefficient.

3. The improved method for time-domain nonstationarity in random seismic simulation according to claim 1, characterized in that, Calculate the target Fourier amplitude spectrum: In the above formula, Y(M0, R, f) represents the target Fourier amplitude spectrum, C represents the scaling factor, and f c Let M0 represent the corner frequency, f represent the seismic moment, R represent the distance, Z(R) represent the geometric diffusion coefficient, Q(f) represent the quality factor, and A(f) represent the site magnification factor. Indicates shear wave velocity. This represents the high-frequency attenuation coefficient.

4. The method for improving the time-domain nonstationarity of random seismic simulation according to claim 1, characterized in that, The final ground motion is calculated, and the phase spectrum and amplitude spectrum are subjected to inverse Fourier transform to obtain the final ground motion time history. The results are then compared with those obtained from real records and current stochastic simulation methods.

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