A baseline correction method applicable to fault ground motion

Abstract

This invention provides a baseline correction method applicable to fault ground motion, comprising the following steps: inputting the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data; randomly generating an initial population containing time parameters t1 (start time of the strong earthquake segment) and t2 (start time of the last segment of the velocity time history); performing baseline correction on each individual in the population: obtaining the velocity time history by subtracting the mean of the pre-earthquake acceleration based on t1 and integrating; obtaining the displacement time history by fitting the linear trend of the last segment of the velocity based on t2, subtracting the fitted acceleration component, and then integrating twice; using the absolute value of the residual between the corrected displacement end value and the GPS data as the objective function; updating the population through a differential evolution algorithm, wherein the mutation factor and crossover frequency can be dynamically adjusted according to the ground motion velocity time history, displacement residual, and number of iterations to balance global and local searches and avoid invalid solutions; iteratively optimizing until the residual is less than a threshold or the maximum number of iterations is reached; finally outputting the optimal t1, t2, and the corrected displacement time history.

Description

Technical Field

[0001] This invention relates to the field of earthquake engineering and ground motion data processing technology, specifically to a baseline correction method applicable to fault ground motion. Background Technology

[0002] Due to the significant impact of fault-slip thrust effects, permanent ground displacements may occur, often causing severe damage to structures near the fault, especially buildings. Therefore, selecting a suitable ground motion baseline correction method is crucial for accurately capturing permanent displacement information in seismic motions. Currently, some ground motion record baseline correction methods include permanent displacement data; however, the corrected permanent displacement values ​​exhibit significant differences. This means that baseline drift caused by surface uplift or tilting under strong earthquakes cannot be eliminated, resulting in inaccurate permanent displacement information. Therefore, it is necessary to study baseline correction methods that can accurately characterize permanent displacement. A reasonable baseline correction method can not only provide important basic data processing for the study of fault-slip thrust effects under strong earthquakes but also restore the original information in the ground motion to the greatest extent possible, thus promoting the development of seismic design for structures to a certain extent. Therefore, developing a baseline correction method that can efficiently and stably express the characteristics of permanent ground motion is particularly important.

[0003] The implementation process of "Prior Art 1" is as follows: Figure 1 As shown:

[0004] Step S1: Input the time history of the ground motion acceleration to be corrected;

[0005] Step S2: Subtract the average value of the pre-earthquake period (0-20s) from the original ground motion acceleration time history record, and obtain the velocity time history by integration;

[0006] Step S3: Use equation (a) to fit the end of the velocity time history, and use equation (b) to calculate the intersection point t2 of the fitted line and the time axis. Subtract 'a' from the end of the acceleration time history record. f The new acceleration time history is obtained:

[0007] Equation (a)

[0008] Equation (b)

[0009] In the formula:

[0010] This represents the velocity value at the end of the earthquake.

[0011] This represents the velocity value corresponding to the earthquake moment t2.

[0012] af This represents the acceleration value at the end of the earthquake.

[0013] t represents the time of the earthquake.

[0014] t2 is the time of the intersection of the fitting time and the time axis;

[0015] Step S4: Integrate to obtain the velocity time history;

[0016] Integrate the acceleration time history record obtained in step S3 to obtain the velocity time history.

[0017] Step S5: Initialize the speed time history;

[0018] Subtract the average value of the pre-earthquake period (0-20s) from the velocity time history record obtained in S4, and set the initial velocity to 0.

[0019] Step S6: Integrate to obtain the displacement time history;

[0020] Integrate the velocity time history obtained in step S5 to obtain the displacement time history.

[0021] Step S7: Output acceleration, velocity, and displacement time history.

[0022] The implementation process of "Prior Art 2" is as follows: Figure 2 As shown:

[0023] Step S1: Obtain raw ground motion acceleration data and preprocess the raw ground motion acceleration data to obtain ground motion acceleration data after eliminating accelerometer system bias;

[0024] Step S2: Determine T1-init and T3-init based on the ground motion acceleration data after eliminating accelerometer system bias, and obtain the value range of the three time parameters T1, T2, and T3 on the ground motion record time history after eliminating accelerometer system bias based on T1-init and T3-init;

[0025] Wherein, T1-init is the initial value of the time point at which the strong ground motion begins to produce permanent displacement, T3-init is the initial value of the time point at which baseline correction is introduced, T1 is the time point at which the strong ground motion begins to produce permanent displacement, T3 is the time point at which baseline correction is introduced, and T2 is any time point between T3 and the end time of the ground motion recording, Tend.

[0026] Step S3: Set the population size to N groups and the maximum number of generations to M. Use a genetic algorithm to obtain the optimal values ​​of T1, T2 and T3 for the individual, where M and N are non-zero natural numbers.

[0027] Step S4: Based on the optimal individual values ​​T1, T2 and T3, perform baseline correction on the ground motion.

[0028] Step S5: Output acceleration, velocity, and displacement time history.

[0029] The aforementioned "Prior Art 1" has the following disadvantages:

[0030] Disadvantage 1: The baseline correction results lack consistency and stability.

[0031] In "Prior Art 1", the first step in steps S2-S3 is to determine the start time (t1) and end time (t2) of the strong earthquake phase. The determination of this time parameter has a certain degree of subjectivity in human selection. Different selections of time parameters will lead to different correction results, making it impossible to form a unified baseline correction result.

[0032] Disadvantage 2: The results differ significantly from the actual GPS data.

[0033] "Prior Art 1" cannot accurately correlate ground motion records containing permanent displacements with d due to improper selection of time parameters. GPS Data matching issues led to significant differences between the calibration results and the actual GPS measurement data.

[0034] The aforementioned "Prior Art 2" has the following disadvantages:

[0035] Disadvantage 1: It is impossible to avoid the baseline correction result from being different from d. GPS The data has a large deviation.

[0036] In "Prior Art 2", steps S2-S3 are determined as T1-init when the cumulative acceleration energy ratio reaches 25% and T3-init when the cumulative acceleration energy ratio reaches 65%. However, strong background noise can distort the cumulative acceleration energy ratio curve and cause peak misalignment, which leads to errors in the initial time parameters. This initialization deviation will directly affect the subsequent correction results, making the difference between the permanent displacement and GPS data larger.

[0037] Disadvantage 2: It is not applicable to ground motions containing nonlinear permanent displacements.

[0038] Step S4 of "Prior Art 2" relies on the flatness index as a fitness function for baseline correction. However, the flatness index is designed to require that the displacement is linear and steady-state in the later stage. If this method is applied to the baseline correction of ground motion records with nonlinear permanent displacement characteristics caused by slip pulses, it will contradict the assumptions of the method, thus causing the method to fail.

[0039] Disadvantage 3: The mutation factor in the existing optimization algorithm is a fixed value, which can cause the baseline correction result to get stuck in a local optimum.

[0040] In "Prior Art 2", when performing population mutation and crossover operations in step S3, using fixed mutation factors and fixed crossover factors severely limits the search range and convergence efficiency of the optimization algorithm, ultimately affecting the accuracy of the baseline correction results. Summary of the Invention

[0041] To address the shortcomings and deficiencies of existing technologies, this invention provides a baseline correction method applicable to fault ground motion, aiming to solve problems such as reliance on manual experience in parameter selection, forced linearization of displacement time history leading to loss of nonlinear characteristics, and large correction residuals in traditional baseline correction methods.

[0042] This method generates an initial population containing time parameters t1 and t2 (t1 being the start time of the strong earthquake segment and t2 being the start time of the end segment of the velocity time history) by inputting the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data. Global parameter optimization is then achieved based on a differential evolution algorithm. During the correction process, the velocity time history is first obtained by subtracting the mean pre-earthquake acceleration from t1 and integrating, and the absolute value of the velocity difference between adjacent time points and the maximum value of the velocity time history are calculated. Then, the linear trend of the end segment of the velocity time history is fitted based on t2, and the fitted acceleration components are subtracted before obtaining the displacement time history through a second integration. The objective function is the absolute value of the residual between the corrected displacement time history end value and the GPS measured data. The population is iteratively updated through dynamic mutation, dynamic crossover, and selection operations until the residual is less than a minimum value close to 0 or the maximum number of iterations is reached. Finally, the optimal parameters and correction results are output.

[0043] The innovation of this invention lies in: using GPS measured data as the calibration benchmark, and automatically optimizing key time parameters through a differential evolution algorithm, avoiding the reliance on human experience in traditional methods; the dynamic mutation scaling factor and dynamic cross frequency in the differential evolution algorithm are dynamically adjusted based on the velocity characteristics of seismic waves, displacement residuals, and the number of iterations, making the optimization process deeply adapted to the nonlinear characteristics of fault ground motion; the initial population is randomly generated and covers a wide range of values, independent of the cumulative acceleration energy ratio, effectively avoiding local optima; the calibration process does not force the end of the displacement time history to be a linear steady state, which can preserve the nonlinear permanent displacement characteristics caused by the slip-thrust effect; and the combination of a residual threshold and a dual termination condition of the maximum number of iterations ensures both calibration accuracy and computational efficiency. This method significantly improves the accuracy and adaptability of fault ground motion baseline calibration, providing reliable data support for seismic analysis of structures under strong earthquakes.

[0044] The specific technical solution adopted by this invention to solve its technical problem is as follows:

[0045] A baseline correction method applicable to fault ground motion includes the following steps:

[0046] Input the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data;

[0047] Generate an initial population containing time parameters t1 and t2, where t1 is the start time of the strong earthquake segment and t2 is the start time of the last segment of the velocity time history.

[0048] Baseline correction was performed on each individual in the population:

[0049] Based on t1, the mean acceleration of the pre-earthquake phase is subtracted, and the velocity time history is obtained by integration; the absolute value of the velocity difference between adjacent time points and the maximum value of the velocity time history are calculated.

[0050] The displacement time history is obtained by double integration after subtracting the fitted acceleration component and fitting the linear trend of the velocity at the end of t2.

[0051] The population fitness was calculated using the absolute residual between the corrected end displacement value and the GPS data as the objective function.

[0052] The population is updated through dynamic mutation, dynamic crossover and selection operations of the differential evolution algorithm, and iterative optimization is performed until the residual is less than a predetermined threshold or the maximum number of iterations is reached.

[0053] Output the optimal time parameters t1 and t2, and the corrected displacement time history.

[0054] In the present invention, the mutation factor and crossover frequency of the differential evolution algorithm are dynamically adjusted according to the seismic velocity time history, displacement residual and number of iterations, so as to balance the global and local search and avoid invalid solutions.

[0055] Furthermore, the initial population is formed by randomly generating the values ​​of time parameters t1 and t2, the range of which covers the pre-earthquake stable period to the end of the strong earthquake in the earthquake motion record, and does not depend on the calculation of the cumulative acceleration energy ratio.

[0056] Furthermore, the pre-earthquake period is the time period from 0 to t1 before the earthquake occurs, during which the acceleration time history is in a stable state, which is used to eliminate the deviation of the accelerometer system.

[0057] Furthermore, the linear trend of the final segment of the velocity time history fitted based on t2 specifically means: fitting the velocity time history from t2 to the end of the earthquake motion record through a linear relationship, wherein the linear relationship is that the velocity value is equal to the sum of the product of the initial velocity at time t2 and the fitted acceleration component and time.

[0058] Furthermore, the subtraction of the fitted acceleration component specifically involves subtracting the fitted acceleration component from the acceleration time history from t2 to the end of the time period to eliminate the influence of the velocity time history baseline offset on the displacement calculation.

[0059] Furthermore, the dynamic mutation operation of the differential evolution algorithm is specifically as follows:

[0060] Three distinct individuals are randomly selected from the current population. Based on the absolute value of the velocity difference between adjacent time points, the maximum velocity time history, the current displacement residual, and the number of iterations, a dynamic mutation scaling factor is calculated. A mutation vector is generated by summing the product of the first individual, the dynamic mutation scaling factor, and the difference between the last two individuals. The value of the dynamic mutation scaling factor ranges from 0 to 2.

[0061] The dynamic crossover operation of the differential evolution algorithm is specifically as follows:

[0062] Based on the absolute value of the current displacement residual, the absolute value of the maximum displacement residual, the absolute value of the velocity difference between adjacent time moments, the maximum value of the velocity time history, and the number of iterations, the dynamic crossover frequency is calculated. The elements of the current population individual and the mutation vector are cross-combined. If the random number in the interval of 0 to 1 is less than or equal to the dynamic crossover frequency or is the element corresponding to the specified random integer, then the element of the mutation vector is used; otherwise, the element of the current population individual is retained. The value range of the dynamic crossover frequency is 0 to 1.

[0063] The selection operation specifically involves comparing the fitness values ​​of the crossover individuals with those of the current population, and retaining the individuals with the smaller fitness values ​​as members of the next generation population.

[0064] Furthermore, the dynamic variation scaling factor is calculated by combining the dynamic response factor, the ratio of the absolute value of the velocity difference between adjacent time moments to the maximum velocity time history value, and the external attenuation coefficient. The dynamic response factor is adjusted based on the displacement residual and the direction identifier, and the external attenuation coefficient decreases as the number of iterations increases.

[0065] The dynamic cross frequency is calculated as follows: the square root of the product of the attenuation term of the iteration number, the ratio of the absolute value of the current displacement residual to the absolute value of the maximum displacement residual, and the ratio of the absolute value of the velocity difference between adjacent moments to the maximum value of the velocity time history.

[0066] Furthermore, the predetermined threshold is a very small value close to 0, used to ensure that the residual between the corrected displacement time history end value and the GPS measured displacement data approaches 0.

[0067] Furthermore, the method is applicable to fault ground motion scenarios that include nonlinear permanent displacements. The correction process does not require the end of the displacement time history to be a linear steady state, so as to preserve the nonlinear displacement characteristics caused by the slip-thrust effect.

[0068] Furthermore, the population size is a preset non-zero natural number, and the number of individuals in the initial population is not less than 10 groups to ensure global coverage of the parameter search.

[0069] And, a baseline correction system for fault ground motion, comprising:

[0070] The data input module is used to input the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data;

[0071] The population generation module is used to generate an initial population containing time parameters t1 and t2, where t1 is the start time of the strong earthquake segment and t2 is the start time of the last segment of the velocity time history.

[0072] The correction operation module is used to perform baseline correction for each individual in the population, including: obtaining the velocity time history by subtracting the mean acceleration of the pre-earthquake segment based on t1 and integrating it; and obtaining the displacement time history by fitting the linear trend of the last segment of the velocity time history based on t2, subtracting the fitted acceleration components, and then performing a quadratic integration.

[0073] The fitness calculation module is used to calculate the population fitness using the absolute value of the residual between the corrected displacement time history end value and the GPS measured displacement data as the objective function.

[0074] The optimization iteration module is used to update the population through dynamic mutation, dynamic crossover and selection operations of the differential evolution algorithm, and iteratively optimize until the residual is less than a predetermined threshold or the maximum number of iterations is reached.

[0075] The output module is used to output the optimal time parameters t1 and t2, as well as the corrected displacement time history.

[0076] And a computer device including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method described above.

[0077] A non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described above.

[0078] Compared with existing technologies, this invention and its preferred solution use GPS measured displacement data as a correction benchmark and combine differential evolution algorithm to globally optimize key time parameters t1 and t2. This effectively solves the problems of inconsistent correction results and large deviations in permanent displacement values ​​caused by the reliance on human experience in parameter selection in traditional methods. It significantly reduces the residual between the corrected displacement time history end value and the actual displacement, and can more accurately characterize the permanent displacement characteristics of fault ground motion.

[0079] Meanwhile, the dynamic mutation scaling factor and dynamic crossover frequency in the differential evolution algorithm are adaptively adjusted based on unique parameters such as seismic wave velocity difference, maximum velocity, displacement residual, and iteration number, achieving precise control of population diversity. This avoids getting trapped in local optima and balances global search and local convergence efficiency, further improving correction accuracy and stability. The initial population is formed by randomly generating time parameter values ​​with a wide coverage range, and does not rely on the calculation of cumulative acceleration energy ratio, avoiding interference from background noise on parameter initialization. The correction process does not require the end of the displacement time history to be linear steady state, and can retain the nonlinear permanent displacement characteristics caused by the slip-thrust effect, making it suitable for fault ground motion scenarios containing nonlinear displacement. Combining the dual termination conditions of residual threshold and maximum iteration number, the algorithm ensures both correction accuracy and computational efficiency, providing more reliable basic data for the study of slip-thrust effect and seismic design of structures under strong earthquakes. Attached Figure Description

[0080] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0081] Figure 1 This is a flowchart illustrating the implementation of "Prior Art 1".

[0082] Figure 2 This is a flowchart illustrating the implementation of "Prior Art 2".

[0083] Figure 3 This is a flowchart illustrating the implementation of an embodiment of the present invention.

[0084] Figure 4 Here are the time histories of acceleration, velocity, and displacement for a given earthquake before and after correction using two existing technologies:

[0085] Wherein: (a) is the acceleration time history of prior art 1, (b) is the velocity time history of prior art 1, (c) is the displacement time history of prior art 1, (d) is the acceleration time history of prior art 2, (e) is the velocity time history of prior art 2, and (f) is the displacement time history of prior art 2;

[0086] Figure 5 The acceleration, velocity, and displacement time history diagrams of the AEW before and after correction using the technology of this invention are shown, where (d) is the acceleration time history, (e) is the velocity time history, and (f) is the displacement time history.

[0087] Figure 6 The following is a comparison of the acceleration, velocity, and displacement time histories of the AEW before and after correction by the prior art and the present invention, where (g) is the acceleration time history, (h) is the velocity time history, and (i) is the displacement time history.

[0088] Figure 7 The displacement and d after correction by the baseline correction method of this invention GPSData error analysis diagram, where: (j) is the automated baseline correction of the present invention, and (k) is the error change (differential evolution algorithm). Detailed Implementation

[0089] To make the features and advantages of the present invention more apparent and understandable, specific embodiments are described below in detail:

[0090] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used in this specification have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0091] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0092] To address the shortcomings and deficiencies of existing technologies, this invention proposes a baseline correction method suitable for fault ground motion, solving the problems of large deviations in permanent displacement values ​​and unstable correction results in existing baseline correction methods. The method includes the following steps: specifying the range of time parameters (t1 and t2) and using a differential evolution algorithm to calculate the optimal values ​​of time parameters (t1 and t2); then establishing an objective function and iteratively calculating the fitness value of the population; and comparing this fitness value with a selected threshold to determine whether the time parameters (t1 and t2) and the corrected displacement time history are optimal values. The baseline correction method according to this invention can effectively correct baseline drift of fault ground motion and reasonably characterize the permanent displacement of fault ground motion. By introducing GPS data, the residual at the end of the corrected displacement time history is made as close to zero as possible to the residual of the measured GPS data.

[0093] To achieve the objective of the invention, the specific implementation of baseline correction for raw seismic ground motion records in this embodiment includes the following steps, as detailed below:

[0094] Step S1: Input the earthquake acceleration time history file A(t) to be corrected;

[0095] Step S2: Generate N independent combinations of time parameters (t1, t2) based on equation (1), and combine them to obtain the initial population of generation t. Each group (t1, t2) is an independent population individual;

[0096] The initial population was selected from the type described in the literature {Rainer S. Differential evolution-A simple and efficient adaptive scheme for global optimization over continuous spaces[R]. Technical Report, TR 95-012, Berkeley, USA: University of California. International Computer Science Institute, 1995.}.

[0097] Equation (1)

[0098] in: , Each corresponds to a time parameter combination (t1, t2), where t1 is the start time of the strong earthquake segment and t2 is the start time of the last segment of the velocity time history.

[0099] Step S3: Generate the initial values ​​of time parameters t1 and t2 based on step S2.

[0100] Step S4: Perform baseline correction;

[0101] Step S4-1: Input d GPS Data, predetermined threshold [Q];

[0102] Step S4-2: Based on the initial value of the time parameter t1 generated in step S3, subtract the average value of the pre-earthquake portion (0-t1s) from the entire acceleration time history of the original ground motion record to obtain the new acceleration time history A1(t).

[0103] Step S4-3: Integrate the acceleration time history A1(t) obtained in S4-2 to calculate the corresponding velocity time history V1(t), and calculate the absolute value Δv of the velocity difference between adjacent time points;

[0104] Step S4-4: Based on the initial value of the time parameter t2 generated in step S3, use equation (2) to fit the last segment (t2-t) of the velocity time history. f s), using equation (3) to find the fitting line and the focus t on the time axis. m Then subtract a from the end of the acceleration time history record A1(t). f Thus, a new acceleration time history A2(t) is obtained.

[0105] Equation (2)

[0106] Equation (3)

[0107] In the formula:

[0108] This represents the velocity value at the end of the earthquake.

[0109] v0 is the velocity value corresponding to the earthquake motion at time t2;

[0110] a f To represent the acceleration value at the end of a seismic motion (a) f The value is the slope of the velocity time history baseline offset.

[0111] t represents the time of the earthquake.

[0112] t m This represents the time at the intersection of the fitted straight line and the time axis.

[0113] Step S4-5: Integrate the acceleration time history A2(t) generated in step S4-4 to obtain the velocity time history V2(t), and then subtract the average value of the pre-earthquake part (0-t1s) to obtain the new velocity time history V3(t);

[0114] Step S4-6: Initialize the velocity time history and set the initial velocity to 0, i.e. ;

[0115] Step S4-7: Integrate the velocity time history record V3(t) finally generated in step S4-5 to obtain the displacement time history record D3(t); obtain the displacement time history end value d.

[0116] As a preferred design in this embodiment, the displacement terminal value d of each individual in the population is generated independently based on its parameters (t1, t2) and updated iteratively.

[0117] Step S4-8: Calculate the permanent displacement values ​​d and d at the end of the displacement time history. GPS The residuals between them.

[0118] Step S5: Establish the objective function Q and set the maximum number of iterations [G] max ];

[0119] Based on the displacement values ​​d and d at the end of the corrected displacement time history record GPS The objective function is determined by the residuals between the data, as shown in equation (4).

[0120] Equation (4)

[0121] In the formula:

[0122] The fitness value of the objective function (referring to the error between the final displacement obtained after baseline correction and the measured GPS data);

[0123] d represents the final displacement value after seismic correction;

[0124] d GPS To represent the actual displacement values ​​observed by GPS in earthquake motion records;

[0125] Step S6: Calculate the initial population of generation t. fitness value;

[0126] The initial population of generation t is calculated according to equation (4). middle , , , fitness value .

[0127] Step S7: Determine the population calculated in steps S4-8 One of the groups error Is it less than a predetermined threshold [Q]? If yes, proceed to step S12 immediately; otherwise, proceed to step S8.

[0128] Step S8: First, determine the dynamic mutation scaling factor F. New Then, for the population Mutation operations are performed to form a new population. .

[0129] First, determine the dynamic mutation scaling factor according to formula (6-8), and then from the population... Extract 3 sets of vectors , , Then, the mutation vector is calculated according to equation (5). Generate a new population .

[0130] , Equation (5)

[0131] In the formula:

[0132] ;

[0133] Population size;

[0134] In this embodiment, F is the preferred design. NewF is the dynamic mutation scaling factor, an important parameter controlling population diversity and convergence speed, and is usually chosen within the range of [0,2]. New When the value is low, the population's diversity decreases, making it difficult for the evolutionary process to escape local optima, leading to premature population convergence. The mutation factor F... New A higher value can help the situation of escaping local extrema, but it will reduce the convergence speed.

[0135] To select a variation factor F suitable for seismic ground motion records with significant nonlinear displacement characteristics New This paper proposes a new method to calculate F. New The calculation formula is as follows:

[0136] Equation (6)

[0137] Equation (7)

[0138] Equation (8)

[0139] In the formula:

[0140] α is a dynamic response factor, and its value is calculated according to equation (7). The variation intensity can be adjusted according to the displacement residual.

[0141] Δv is the absolute value of the velocity difference between adjacent time points calculated in step S6. It changes dynamically with the individual population update. The initial value of Δv is the absolute value of the difference between the velocity at time t corresponding to the maximum abrupt change point in the velocity time history and the velocity at the previous time t-1. Where t-(t-1)=1 / fs, and fs is the sampling frequency of the seismic motion record.

[0142] v max This represents the maximum absolute velocity value in the earthquake motion record.

[0143] G represents the current iteration number;

[0144] The external decay coefficient is the coefficient that decreases with increasing iteration number G, causing the global search to weaken and tend towards a local search.

[0145] d represents the final value of the displacement time history output in step S10;

[0146] sgn is the direction identifier.

[0147] The Δv and d values ​​used in the mutation operation are taken from the output values ​​of the parent population individuals.

[0148] Step S9: First, calculate the dynamic crossover frequency CR New Subsequently, the population and population Crossover operations are used to form new populations. ;

[0149] Calculate the dynamic crossover frequency according to formula (10), and then... individual vectors With variant populations individual vectors According to equation (9), cross-mixing is performed to obtain a new population. The specific crossover operation is as follows:

[0150] Equation (9)

[0151] In the formula:

[0152] ( ; ) refers to individual vectors The i-th element;

[0153] n is the total number of calibration parameters;

[0154] This refers to the random number generated for each element in the individual vector within the interval [0,1].

[0155] CR New The dynamic crossover frequency (CR) indicates the degree of participation of individual parameters in the crossover process, affecting the algorithm's global search capability and local search balance. Its value is generally between [0,1]. A lower CR... New A higher CR value reduces population diversity and can lead to premature convergence. New A high value can increase the convergence speed, but if it is too high, it may slow down the convergence due to excessive perturbation.

[0156] For A random integer within the specified interval.

[0157] To select a suitable dynamic crossover frequency, this embodiment proposes the following calculation formula:

[0158] Equation (10)

[0159] In the formula:

[0160] G represents the number of iterations;

[0161] This is the absolute value of the current displacement residual output in step S4-8;

[0162] This is the absolute value of the maximum displacement residual output in step S4-8;

[0163] Δv and v max The calculation method is described in step S8.

[0164] Step S10: Iterative calculation;

[0165] The initial population obtained according to equation (11) and new populations The individual vectors with smaller errors are used as the next generation population. The individual vectors in the calculation will participate in the next calculation.

[0166] Equation (11)

[0167] Step S11: Determine whether the fitness value of the individual vector in each group is less than the predetermined threshold [Q] or whether the number of iterations G has reached the maximum number of iterations [G]. max If yes, proceed to step S12. If no, obtain the next generation population. Proceed to step S6 and repeat the operation.

[0168] Step S12: Output the optimal solutions for the two time parameters t1 and t2 and the final baseline-corrected displacement time history.

[0169] The overall implementation flowchart of this invention embodiment is as follows: Figure 3 As shown.

[0170] The advantages of the solutions provided in the embodiments of the present invention include:

[0171] 1. It can eliminate inconsistencies in correction results caused by human intervention.

[0172] The present invention uses the differential evolution algorithm to globally search for the optimal solution through steps S7, S8, S9 and S10, which can accurately select the time parameter and avoid the problem of inconsistent baseline correction results caused by subjective selection of the time parameter.

[0173] 2. It can ensure that the final calibration result is consistent with the measured GPS data.

[0174] Steps S5-S11 of this invention construct a closed-loop optimization framework, while steps S4-S8 and S5 introduce d. GPS Data serves as a physical benchmark, i.e., by introducing d GPS The data makes the corrected permanent displacement and d GPS The optimization direction is to make the residuals of the data as close to 0 as possible. Through multiple iterative calculations, the corrected result can be made to approximate d. GPS The data match very closely.

[0175] 3. It can avoid the adverse effects of noise on baseline results.

[0176] In step S2 of this invention, N random values ​​are generated for the time parameter of each acceleration using equation (1), and combined to obtain the initial population X(t), which is the initial value of the time parameter; instead of being derived by calculating the cumulative energy ratio of acceleration, this effectively avoids noise affecting the final correction result.

[0177] 4. It can solve the problem of nonlinear permanent displacement correction failure.

[0178] In this invention, steps S4-8 and S5 use the residual between the end segment of the displacement time history and the GPS measured value as the objective function, and the differential evolution mechanism in steps S8-S10 uses absolute GPS measured data as the benchmark. It does not require the end of the displacement time history to be flat, and can effectively preserve the nonlinear displacement characteristics caused by the slippage effect.

[0179] 5. This invention determines the key parameters of the population optimization process based on the nonlinear characteristics of seismic motion, thus avoiding the baseline correction results from falling into local optima.

[0180] In step S8 of the present invention, during the mutation operation, the mutation factor F New Dynamic adjustments are made based on the nonlinear characteristics of the seismic signal and the number of iterations to achieve adaptive regulation of population diversity, effectively avoiding getting trapped in local optima; in step S9, during the population crossover operation, the crossover frequency CR New It also dynamically adjusts based on the nonlinear characteristics of the seismic signal and the number of iterations, so as to achieve a balance between global search and local search, which can effectively avoid generating invalid solutions that do not conform to physical properties.

[0181] The following specific test and verification example further demonstrates the above-mentioned solutions of the embodiments of the present invention:

[0182] 1. Baseline correction example:

[0183] The earthquake data used in this example is an earthquake in a certain area with a magnitude of 7.6. The selected ground motion station information is shown in Table 1, and the selected GPS station information and GPS measured earthquake displacement are shown in Table 2.

[0184] Table 1 Selected Seismic Ground Motion Monitoring Station Information

[0185] Earthquake ground station code A B C D E F

[0186] Table 2 shows the selected GPS station information and GPS-measured seismic displacement.

[0187] GPS station code EW(m) NS(m) UD(m) M324 -3.4230 -8.4510 -3.9720 AF26 0.5580 -0.3830 -0.0670 G104 -2.7310 6.5220 2.9980 HTZS -1.8770 1.2840 -0.6030 M408 -1.3720 0.8320 -0.1630 M509 -1.5190 0.7550 -0.0310

[0188] The GPS station codes selected in Table 2 correspond one-to-one with the ground motion station codes selected in Table 1. For example, the triaxial (EW, NS, UD) displacement of ground motion A corresponds to the triaxial (EW, NS, UD) displacement of ground motion A measured by M324.

[0189] 2. Fitting results of existing technologies

[0190] Following steps S1-S6 of prior art 1 and steps S1-S5 of prior art 2, taking the EW of station A as an example, the comparison chart of the results before and after correction is as follows. Figure 4 As shown.

[0191] 3. Fitting results of the present invention

[0192] Following steps S1-S12 of this invention, taking station A as an example, a comparison diagram of the results before and after correction is obtained as follows. Figure 5 As shown.

[0193] 4. Comparison of the effects of the present invention and the prior art is as follows: Figure 6 As shown.

[0194] Figure 7 This further demonstrates the difference between the baseline-corrected permanent displacement value and the true d. GPS The error fitness value Q between the data demonstrates that the baseline correction method proposed in this invention can accurately match the real d. GPS It provides data, and is efficient and easy to operate.

[0195] Table 3 shows the optimal time parameters and permanent ground motion displacements obtained by the baseline correction method proposed in this example for each station. It can be observed that the permanent ground motion displacements obtained by this method are consistent with d... GPS The data are basically consistent.

[0196] Table 3 shows the baseline correction results for this example.

[0197] Earthquake Records <![CDATA[t1(s)]]> <![CDATA[t2(s)]]> Permanent displacement due to seismic motion (m) GPS displacement (m) AEW 10.0047 72.3173 -3.4230 -3.4230 ANS 30.5852 63.8249 8.4552 8.4510 AUD 30.7378 41.7985 3.9720 3.9720 BEW 10.1487 40.0000 0.5580 0.5580 BNS 35.0000 42.6937 -0.3829 -0.3830 BUD 15.6790 72.7785 -0.0670 -0.0670 CEW 34.1628 72.8200 -2.7314 -2.7310 CNS 29.0943 67.3993 6.5220 6.5220 CUD 34.2873 46.8133 2.9980 2.9980 DEW 11.3589 76.5678 -1.8770 -1.8770 DNS 10.7905 46.8290 0.0000 1.2840 DUD 30.2717 51.0862 -0.6030 -0.6030 EEW 18.6475 52.4595 -1.3720 -1.3720 ENS 12.7206 73.0234 0.8319 0.8320 EUD 25.8851 66.6881 -0.1629 -0.1630 FEW 10.0000 56.6273 -1.5190 -1.5190 FNS 16.7103 80.0000 0.7550 0.7550 FUD 26.0813 57.3297 -0.0310 -0.0310

[0198] Table 4 shows the permanent displacement results after correction using different baseline correction methods and their comparison with d. GPS The data comparison results show that the result corrected by this method is closer to d than the result obtained by existing methods. GPS The data is better, and the method has smaller errors and is superior.

[0199] Table 4 shows the permanent displacement results of baseline correction using different methods and d. GPS Data Comparison

[0200]

[0201] Note that 0.0000 in the table does not represent an error of 0, but rather that the data in this example retains four significant digits.

[0202] Based on the same inventive concept, this invention also provides a computer device, comprising: one or more processors, and a memory for storing one or more computer programs; the programs include program instructions, and the processor executes the program instructions stored in the memory. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, used to implement one or more instructions, specifically for loading and executing one or more instructions stored in a computer storage medium to implement the above-described method.

[0203] It should be further explained that, based on the same inventive concept, the present invention also provides a computer storage medium storing a computer program, which, when executed by a processor, performs the above-described method. This storage medium can be any combination of one or more computer-readable media. A computer-readable medium can be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0204] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0205] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

[0206] This invention is not limited to the preferred embodiment described above. Anyone inspired by this invention can derive other various forms of baseline correction methods applicable to fault ground motion. All equivalent variations and modifications made within the scope of the claims of this invention shall fall within the scope of this invention.

Claims

1. A baseline correction method applicable to fault ground motion, characterized in that, Includes the following steps: Input the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data; Generate an initial population containing time parameters t1 and t2, where t1 is the start time of the strong earthquake segment and t2 is the start time of the last segment of the velocity time history. Baseline correction was performed on each individual in the population: Based on t1, the mean acceleration of the pre-earthquake phase is subtracted, and the velocity time history is obtained by integration; the absolute value of the velocity difference between adjacent time points and the maximum value of the velocity time history are calculated. The displacement time history is obtained by double integration after subtracting the fitted acceleration component and fitting the linear trend of the velocity at the end of t2. The population fitness was calculated using the absolute residual between the corrected end displacement value and the GPS data as the objective function. The population is updated through dynamic mutation, dynamic crossover and selection operations of the differential evolution algorithm, and iterative optimization is performed until the residual is less than a predetermined threshold or the maximum number of iterations is reached. Output the optimal time parameters t1 and t2, and the corrected displacement time history.

2. The baseline correction method for fault ground motion according to claim 1, characterized in that: The initial population is formed by randomly generating time parameters t1 and t2, the range of which covers the pre-earthquake stable period to the end of the strong earthquake in the ground motion record, and does not depend on the cumulative energy ratio of acceleration.

3. The baseline correction method for fault ground motion according to claim 1, characterized in that: The pre-earthquake period is the time interval from 0 to t1 before the earthquake occurs. During this period, the acceleration time history is in a stable state, which is used to eliminate the deviation of the accelerometer system.

4. The baseline correction method for fault ground motion according to claim 1, characterized in that: The linear trend of the final segment of the velocity time history fitted based on t2 is specifically: the velocity time history from t2 to the end of the earthquake motion record is fitted by a linear relationship, wherein the linear relationship is that the velocity value is equal to the sum of the product of the initial velocity at time t2 and the fitted acceleration component and time.

5. A baseline correction method for fault ground motion according to claim 1, characterized in that: The deduction of the fitted acceleration component specifically involves subtracting the fitted acceleration component from the acceleration time history from t2 to the end of the time period, in order to eliminate the influence of the velocity time history baseline offset on the displacement calculation.

6. The baseline correction method for fault ground motion according to claim 1, characterized in that: The dynamic mutation operation of the differential evolution algorithm is specifically as follows: Three distinct individuals are randomly selected from the current population. Based on the absolute value of the velocity difference between adjacent time points, the maximum velocity time history, the current displacement residual, and the number of iterations, a dynamic mutation scaling factor is calculated. A mutation vector is generated by summing the product of the first individual, the dynamic mutation scaling factor, and the difference between the last two individuals. The value of the dynamic mutation scaling factor ranges from 0 to 2. The dynamic crossover operation of the differential evolution algorithm is specifically as follows: Based on the absolute value of the current displacement residual, the absolute value of the maximum displacement residual, the absolute value of the velocity difference between adjacent time moments, the maximum value of the velocity time history, and the number of iterations, the dynamic crossover frequency is calculated. The elements of the current population individual and the mutation vector are cross-combined. If the random number in the interval of 0 to 1 is less than or equal to the dynamic crossover frequency or is the element corresponding to the specified random integer, then the element of the mutation vector is used; otherwise, the element of the current population individual is retained. The value range of the dynamic crossover frequency is 0 to 1. The selection operation specifically involves comparing the fitness values ​​of the crossover individuals with those of the current population, and retaining the individuals with the smaller fitness values ​​as members of the next generation population.

7. A baseline correction method for fault ground motion according to claim 6, characterized in that: The dynamic variation scaling factor is calculated by combining the dynamic response factor, the ratio of the absolute value of the velocity difference between adjacent time moments to the maximum value of the velocity time history, and the external attenuation coefficient. The dynamic response factor is adjusted based on the displacement residual and the direction identifier, and the external attenuation coefficient decreases as the number of iterations increases. The dynamic cross frequency is calculated as follows: the square root of the product of the attenuation term of the iteration number, the ratio of the absolute value of the current displacement residual to the absolute value of the maximum displacement residual, and the ratio of the absolute value of the velocity difference between adjacent moments to the maximum value of the velocity time history.

8. A baseline correction method for fault ground motion according to claim 1, characterized in that: The predetermined threshold is a very small value close to 0, used to ensure that the residual between the corrected displacement time history end value and the GPS measured displacement data approaches 0.

9. A baseline correction method for fault ground motion according to claim 1, characterized in that: The method is applicable to fault ground motion scenarios that include nonlinear permanent displacement. The correction process does not require the end of the displacement time history to be a linear steady state, so as to preserve the nonlinear displacement characteristics caused by the slip-thrust effect.

10. A baseline correction system suitable for fault ground motion, characterized in that, include: The data input module is used to input the earthquake acceleration time history to be corrected and the corresponding GPS measured displacement data; The population generation module is used to generate an initial population containing time parameters t1 and t2, where t1 is the start time of the strong earthquake segment and t2 is the start time of the last segment of the velocity time history. The correction operation module is used to perform baseline correction for each individual in the population, including: obtaining the velocity time history by subtracting the mean acceleration of the pre-earthquake segment based on t1 and integrating, and calculating the absolute value of the velocity difference between adjacent time points and the maximum value of the velocity time history; obtaining the displacement time history by fitting the linear trend of the last segment of the velocity time history based on t2, subtracting the fitted acceleration components, and then performing a quadratic integration. The fitness calculation module is used to calculate the population fitness using the absolute value of the residual between the corrected displacement time history end value and the GPS measured displacement data as the objective function. The optimization iteration module is used to update the population through dynamic mutation, dynamic crossover and selection operations of the differential evolution algorithm, and iteratively optimize until the residual is less than a predetermined threshold or the maximum number of iterations is reached. The output module is used to output the optimal time parameters t1 and t2, as well as the corrected displacement time history.

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