Main shock and aftershock full-life vulnerability analysis method based on active learning

Abstract

The invention discloses a main shock and aftershock full-life vulnerability analysis method based on active learning, and belongs to the field of structural anti-seismic safety evaluation. The method solves the problems that an existing full-life analysis method needs high calculation cost and does not consider the influence of environmental factors and main shock and aftershock coupling effects on the initial damage of the structure. The agent model is constructed based on high-precision and low-precision data fusion, and a meta-learning mechanism is introduced to describe internal association among different degradation states, so that the sample utilization efficiency is improved; a generalized learning function is combined with a two-stage active learning strategy to dynamically select a training sample point with the most information amount, efficient refinement of a prediction model in each degradation scene is gradually realized, the calculation cost is further reduced, and the agent model prediction precision is improved. And finally, through a time-varying two-dimensional limit state equation, explicitly considering the correlation between the initial damage evolved along with time and the structure residual capacity, and effectively fusing the coupling effect of environmental degradation and the seismic sequence. The method can be applied to structure vulnerability analysis.

Description

Technical Field

[0001] The present invention belongs to the field of structural seismic safety assessment, and in particular relates to a mainshock and aftershock lifecycle vulnerability analysis method based on active learning. Background Art

[0002] During the service life of a structure, a large number of infrastructure facilities are inevitably subjected to the continuous effects of various environmental factors. For example, structures in coastal areas are susceptible to chloride ion corrosion, while structures in extremely cold regions frequently experience freeze-thaw cycles. These environmental factors will cause the material properties to continuously degrade, thereby reducing the seismic performance of the structure. At the same time, in many earthquake events, the main shock will be accompanied by multiple aftershocks. The continuous effects of multiple earthquakes will aggravate the cumulative damage to the structure, resulting in more serious earthquake losses. More importantly, long-term environmental degradation will also aggravate the adverse effects of earthquake sequences on the structure, significantly reducing the safety margin of the structure during its service life. Therefore, there is an urgent need to establish a full-life seismic safety assessment method for structures that can simultaneously consider the effects of long-term environmental degradation and earthquake sequences, so as to achieve more comprehensive and accurate risk identification and prevention.

[0003] Structural vulnerability analysis, a key method for assessing structural safety, has been widely used in seismic analysis of various engineering structures. However, when applied to the entire life cycle of a structure, traditional vulnerability analysis methods require extensive, repetitive analysis of the structure at different service stages, resulting in extremely high computational costs and difficulty meeting the efficiency requirements of engineering practice. Furthermore, existing vulnerability analysis methods typically assume that the seismic capacity of the structure remains unchanged. However, during the long-term service life of a structure, environmental effects will cause continuous material degradation, and earthquake sequences will also cause cumulative damage to the structure. Therefore, ignoring the impact of initial damage on the residual capacity of the structure will lead to an overestimation of the structural safety margin.

[0004] In recent years, active learning methods based on surrogate models have garnered widespread attention. These methods can significantly reduce computational costs while maintaining good computational accuracy for engineering probabilistic analysis. Therefore, active learning methods can provide strong support for efficient and reliable full-life vulnerability analysis. However, existing active learning methods primarily rely on Kriging models, which are limited in their model capabilities and scope of application and cannot meet the requirements of complex vulnerability analysis of structural systems. Furthermore, traditional active learning still requires a large amount of sampling, making full-life analysis computationally expensive. To construct a framework for full-life vulnerability analysis of structures under the coupled effects of long-term environments and main and aftershocks, it is imperative to extend active learning strategies to other efficient surrogate models and further improve sampling methods to enhance computational efficiency, thereby providing a more scientific and accurate basis for post-earthquake infrastructure condition assessment and emergency management decision-making. Summary of the Invention

[0005] The purpose of this invention is to solve the problems of high computational cost and failure to consider the influence of environmental factors and mainshock-aftershock coupling on the initial damage of the structure in existing life cycle analysis methods, and to propose a mainshock-aftershock life cycle vulnerability analysis method based on active learning.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a main shock and aftershock life cycle vulnerability analysis method based on active learning, the method specifically comprising the following steps:

[0007] Step 1: Set the concrete compressive strength f c Obeying the normal distribution with mean α1 and coefficient of variation β1, the yield strength of steel bar f y It obeys the lognormal distribution with mean α2 and coefficient of variation β2, and the damping ratio ξ R It obeys the log-normal distribution with a mean of α3 and a coefficient of variation of β3. The concrete cover thickness h obeys the normal distribution with a mean of α4 and a coefficient of variation of β4. The initial diffusion coefficient of chloride ions D0 obeys the normal distribution with a mean of α5 and a coefficient of variation of β5.

[0008] Compressive strength of concrete f c , steel bar yield strength f y , damping ratio ξ R , the concrete cover thickness h and the chloride ion initial diffusion coefficient D0 are randomly sampled, and a high-precision finite element model and a low-precision finite element model of the target structure are established based on the sampling results; the parameters of each group of sampling results are then adjusted according to the service time of the target structure, and high-precision finite element models and low-precision finite element models of the target structures with different service times are established based on the adjusted parameters of each group;

[0009] Then, nonlinear time history analysis is performed on all high-precision finite element models and low-precision finite element models of the target structure under the action of main shocks and aftershocks to obtain the displacement response of each finite element model under the action of main shocks and aftershocks.

[0010] Step 2: Meta-learn the proxy model using the structural parameters of the finite element models corresponding to different service years and the displacement response data of each finite element model under the main shock and aftershock;

[0011] Step 3: Establish the time-varying two-dimensional limit state equation of the target structure;

[0012] Step 4: According to the probability distribution of each parameter in step 1, the concrete compressive strength f c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h and chloride ion initial diffusion coefficient D0 are randomly sampled to obtain Q candidate samples;

[0013] Then, the parameters of the candidate samples are adjusted according to the service life of the structure to be predicted, and the learning function is used to select q local sampling centers from all the adjusted candidate samples;

[0014] And generate Q' candidate training samples in the local area of ​​each local sampling center, and then use the learning function to select q' local sampling centers from all candidate training samples;

[0015] A high-precision finite element model of the structure to be predicted is established based on the selected q' local sampling centers. The structural parameters and displacement responses of the high-precision finite element model of the structure to be predicted are used to actively learn the meta-learned proxy model to obtain the final trained proxy model.

[0016] Step 5: Use the finally trained proxy model and the time-varying two-dimensional limit state equation to obtain the fragility curve of the structure to be predicted.

[0017] The beneficial effects of the present invention are:

[0018] This method constructs a proxy model based on the fusion of high- and low-precision data and introduces a meta-learning mechanism to characterize the inherent correlations between different degradation states, thereby improving sample utilization efficiency and model generalization. A generalized learning function applicable to multiple types of proxy models is combined with a two-stage active learning strategy to dynamically select the most informative training sample points, gradually achieving efficient refinement of the prediction model under various degradation scenarios, further reducing computational costs and improving the proxy model's prediction accuracy. Finally, through a time-varying two-dimensional limit state equation, the correlation between the time-evolving initial damage and the structure's residual capacity is explicitly considered, comprehensively reflecting the evolution of the structure's seismic performance under multiple hazards. This method not only significantly reduces the computational cost of lifecycle vulnerability analysis but also effectively integrates the coupling effects of environmental degradation and earthquake sequences, overcoming the safety assessment bias caused by traditional methods that ignore the influence of initial damage. It is applicable to vulnerability analysis of any complex structure. By accurately assessing the residual seismic capacity and vulnerability evolution of structures at different service stages, it provides a more scientific and reliable basis for post-earthquake infrastructure safety assessment, maintenance strategy formulation, and resource optimization, thereby facilitating dynamic control and refined management of earthquake risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 This is a flow chart of a mainshock and aftershock lifecycle vulnerability analysis method based on active learning according to the present invention;

[0020] Figure 2 is a schematic diagram of the target nuclear containment structure;

[0021] Figure 3 Provide a high-precision finite element model of the target nuclear containment structure;

[0022] Figure 4 A low-precision finite element model of the target nuclear containment structure;

[0023] Figure 5 This is the network architecture diagram of the proxy model;

[0024] Figure 6 It is a pseudo-static reciprocating loading scheme;

[0025] Figure 7 It is the time-varying two-dimensional limit state LS1;

[0026] Figure 8 It is the time-varying two-dimensional limit state LS2;

[0027] Figure 9 It is the time-varying two-dimensional limit state LS3;

[0028] Figure 10 It is the time-varying two-dimensional limit state LS4;

[0029] Figure 11 Schematic diagram of two-stage active learning;

[0030] Figure 12 is the vulnerability curve of the nuclear containment structure under three degradation scenarios of 0 years, 50 years and 100 years when the initial damage state is DS0;

[0031] Figure 13 is the vulnerability curve of the nuclear containment structure under three degradation scenarios of 0 years, 50 years and 100 years when the initial damage state is DS1;

[0032] Figure 14 is the vulnerability curve of the nuclear containment structure under three degradation scenarios of 0 years, 50 years and 100 years when the initial damage state is DS2;

[0033] Figure 15 is the vulnerability curve of the nuclear containment structure under three degradation scenarios of 0 years, 50 years and 100 years when the initial damage state is DS3;

[0034] Figure 16 The following is a comparison chart of vulnerability curves of different methods. DETAILED DESCRIPTION

[0035] Specific implementation method 1: Combination Figure 1 This embodiment describes a method for analyzing the vulnerability of main shocks and aftershocks throughout their life cycle based on active learning, which specifically includes the following steps:

[0036] Step 1: Set the concrete compressive strength f c Obeying the normal distribution with mean α1 and coefficient of variation β1, the yield strength of steel bar fy It obeys the lognormal distribution with mean α2 and coefficient of variation β2, and the damping ratio ξ R It obeys the log-normal distribution with a mean of α3 and a coefficient of variation of β3. The concrete cover thickness h obeys the normal distribution with a mean of α4 and a coefficient of variation of β4. The initial diffusion coefficient of chloride ions D0 obeys the normal distribution with a mean of α5 and a coefficient of variation of β5.

[0037] Compressive strength of concrete f c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h, and chloride ion initial diffusion coefficient D0 are randomly sampled, and a high-precision finite element model and a low-precision finite element model of the target structure are established based on the sampling results (other parameters including steel bar diameter are also required when establishing the finite element model, and the model established in this case uses the initial steel bar diameter); the parameters of each group of sampling results are then adjusted according to the service life of the target structure, and high-precision finite element models and low-precision finite element models of target structures with different service times are established based on the adjusted parameters of each group;

[0038] Then, nonlinear time history analysis is performed on all high-precision finite element models and low-precision finite element models of the target structure under the action of main shocks and aftershocks to obtain the displacement response of each finite element model under the action of main shocks and aftershocks.

[0039] Step 2: Meta-learning the proxy model using the structural parameters of the finite element models corresponding to different service years (concrete compressive strength, steel yield strength, damping ratio, steel diameter) and the displacement response data of each finite element model under the main shock and aftershock;

[0040] Step 3: Establish the time-varying two-dimensional limit state equation of the target structure;

[0041] Step 4: According to the probability distribution of each parameter in step 1, the concrete compressive strength f c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h and chloride ion initial diffusion coefficient D0 are randomly sampled to obtain Q candidate samples (at least one parameter value in each candidate sample is different);

[0042] Then, the parameters of the candidate samples are adjusted according to the service life of the structure to be predicted, and the learning function is used to select q local sampling centers from all the adjusted candidate samples;

[0043] And generate Q' candidate training samples in the local area of ​​each local sampling center, and then use the learning function to select q' local sampling centers from all candidate training samples (i.e., samples generated according to the local sampling centers);

[0044] A high-precision finite element model of the structure to be predicted is established based on the selected q' local sampling centers. The structural parameters and displacement responses of the high-precision finite element model of the structure to be predicted are used to actively learn the meta-learned proxy model to obtain the final trained proxy model.

[0045] Step 5: Use the finally trained proxy model and the time-varying two-dimensional limit state equation to obtain the fragility curve of the structure to be predicted.

[0046] Specific embodiment 2: This embodiment differs from specific embodiment 1 in that the high-precision finite element model of the target structure is established using Abaqus software, and the concrete and steel bars in the high-precision finite element model are solid units and truss units respectively;

[0047] The low-precision finite element model of the target structure is a multi-degree-of-freedom shear model, which adopts a trilinear skeleton curve and a single-parameter hysteresis model.

[0048] Other steps and parameters are the same as those in the first embodiment.

[0049] In a multi-precision data fusion framework, low-precision data can be used to reveal trends in actual data, while a small amount of high-precision data is used to correct systematic errors in the low-precision data. Therefore, the multi-precision data fusion strategy can effectively reduce computational costs while maintaining prediction accuracy.

[0050] Specific embodiment three: This embodiment differs from specific embodiments one or two in that the parameters of each group of sampling results are adjusted according to the service time of the target structure, specifically:

[0051] The service life of the target structure is recorded as N years. By dividing the entire service cycle into equal intervals (i.e., dividing N years into equal intervals), each equal-division point, 0, and N are respectively used as the service time corresponding to a training task;

[0052] For any training task, the parameters of each group of sampling results are adjusted according to the service time corresponding to the training task.

[0053] Other steps and parameters are the same as those in the first or second embodiment.

[0054] The initial random sampling result is taken as the target structure parameter when the service time is 0 years. With the increase of the service time, the reinforcement diameter, the reinforcement yield strength and the compressive strength of the concrete will change. Therefore, for each training task, the reinforcement diameter, the reinforcement yield strength and the compressive strength of the concrete can be calculated according to the service time corresponding to the training task, and then the adjusted parameters corresponding to each service time are obtained. According to the reinforcement diameter, the reinforcement yield strength and the compressive strength of the concrete corresponding to the service time, the high-precision finite element model and the low-precision finite element model of the target structure under the corresponding service time can be established, and finally the high-precision finite element model and the low-precision finite element model of the target structure corresponding to each training task are obtained.

[0055] Specific implementation four: different from one of the specific implementations one to three, when the target structure is a nuclear containment structure, the relationship between the compressive strength of the concrete and the reinforcement yield strength and the service time is obtained in the following manner:

[0056] Step 1, the chloride ion diffusion process in the concrete is:

[0057]

[0058] wherein C0 is the initial chloride ion concentration, C(x, t) represents the chloride ion concentration at x from the concrete surface when the service time is t years, D F is the corrected chloride ion diffusion coefficient; C s represents the chloride ion concentration of the concrete surface, erf(·) is the error function, η is the integral variable;

[0059] The structure service time T cr when the chloride ion concentration on the surface of the reinforcement reaches the critical threshold C i :

[0060]

[0061] wherein m is the aging factor, t0 is the initial diffusion time, D0 is the initial diffusion coefficient, h is the concrete protective layer thickness, Φ -1 (·) is the inverse function of the standard normal distribution;

[0062] Step 2, the diameter d(t i ) of the reinforcement when the service time is t years is calculated:

[0063] d(t i )=d0-0.0232t i ×i corr (t i ) (3)

[0064] Where d0 is the initial steel bar diameter; t i It indicates the time when steel bar corrosion damage occurs when the service time reaches t years (i.e. tT i );i corr (t i ) represents the corrosion rate of the steel bar when the service time reaches t years;

[0065]

[0066] Wherein, w / c is the water-cement ratio, w / c=27 / (f c +13.5), f c is the initial compressive strength of concrete;

[0067] Step 3: Calculate the yield strength f of the steel bar when the service time is t years. y (t i ):

[0068]

[0069] Among them, A0 represents the initial cross-sectional area of ​​the steel bar; A(t i ) represents the cross-sectional area of ​​the steel bar when the service time is t years; Indicates the initial yield strength of the steel bar;

[0070] Step 4: The compressive strength of concrete after freeze-thaw cycles is:

[0071]

[0072] in, represents the compressive strength of damaged concrete after freeze-thaw cycles, f c ' is the compressive strength at 28 days old, N d Indicates the number of freeze-thaw cycles.

[0073] The other steps and parameters are the same as those in the first to third embodiments.

[0074] Specific embodiment 5: This embodiment differs from any one of specific embodiments 1 to 4 in that the modified chloride ion diffusion coefficient is:

[0075] D F =D·e 0.1072H (7)

[0076]

[0077] Among them, D Frepresents the corrected chloride ion diffusion coefficient, D represents the chloride ion diffusion coefficient without considering the effect of freeze-thaw cycles, H represents the degree of freeze-thaw damage, e represents the base of the natural logarithm, and S represents the number of equivalent freeze-thaw cycles indoors.

[0078] The other steps and parameters are the same as those in the first to fourth embodiments.

[0079] Specific embodiment 6: This embodiment differs from specific embodiments 1 to 5 in that the specific process of step 2 is as follows:

[0080] Step 21: Divide the low-precision finite element model structural parameters and displacement response data corresponding to each service time into two parts, that is, for each low-precision finite element model structural parameters and displacement response data corresponding to the service time, the low-precision finite element model structural parameters and displacement response data are divided into a support set and a query set;

[0081] The high-precision finite element model structural parameters and displacement response data corresponding to each service time are divided into two parts, that is, the high-precision finite element model structural parameters and displacement response data corresponding to each service time are divided into a support set and a query set;

[0082] Step 22: The data in the support set corresponding to each service time is used as training data for a training task;

[0083] The data in the query set corresponding to each service time is used as test data for a training task;

[0084] Step 2 and 3: Use the training data of each training task to meta-learn the proxy model until the loss function value of the proxy model on the test data of all training tasks converges, and stop learning to obtain the meta-learned proxy model.

[0085] The other steps and parameters are the same as those in the first to fifth embodiments.

[0086] Specific embodiment seven: This embodiment differs from any one of specific embodiments one to six in that the agent model includes a first submodule and a second submodule, wherein the first submodule is a first BP neural network, and the second submodule includes a second BP neural network, a third BP neural network, and a fully connected layer;

[0087] The input part of the training data (including concrete compressive strength, steel yield strength, damping ratio, steel diameter and ground peak acceleration) is used as the input of the first submodule, and the input part of the training data and the output of the first submodule are used as the input of the second submodule; the input of the second submodule passes through the second BP neural network and the third BP neural network respectively, and then the output of the second BP neural network and the third BP neural network are spliced, and the spliced ​​result is used as the input of the fully connected layer, and the output of the fully connected layer is used as the output of the proxy model;

[0088] The specific process of meta-learning of the agent model is as follows:

[0089] Step 231: Initialize the number of training tasks l = 1;

[0090] Step 232: Initialize the number of iterative training n=1;

[0091] Step 2, 3, 3. For any set of sampled parameters or any set of adjusted parameters of the first training task, the peak ground acceleration (PGA), concrete compressive strength, steel yield strength, damping ratio, steel diameter, and damage degree of the finite element model corresponding to the set of parameters are used as the input of the first submodule, and the displacement response of the finite element model is used as the training label of the first submodule;

[0092] The output of the first submodule and the peak ground acceleration (PGA), concrete compressive strength, steel yield strength, damping ratio, steel diameter, and damage degree of the finite element model corresponding to the set of parameters are used as the input of the second submodule. The output label of the proxy model is the displacement response of the finite element model corresponding to the set of parameters.

[0093] And traverse each set of parameters of the nth iteration training;

[0094] The loss function Loss used in the training process is:

[0095]

[0096] in, Indicates the number of training samples corresponding to the high-precision finite element model during the nth iteration training process; Indicates the number of training samples corresponding to the low-precision finite element model during the nth iteration training process, y i,L represents the label of the i-th training sample of the high-precision finite element model during the n-th iteration training process; y j,H Indicates the label of the jth training sample of the low-precision finite element model during the nth iteration training process, represents the predicted response to the i-th training sample of the high-precision finite element model, represents the predicted response to the jth training sample of the low-precision finite element model;

[0097] Use gradient descent method to update model parameters:

[0098]

[0099] Among them, θ n-1 represents the proxy model parameters after the n-1th iteration training, θ n represents the proxy model parameters after the nth iteration training, α1 represents the inner loop learning rate, Indicates that the training data for the nth iteration training is under the parameter θ n-1 The loss function on the surrogate model, express θ n-1 gradient;

[0100] Step 2, 3, 4: Determine whether n = L′, where L′ is the total number of iterative training times on the lth training task;

[0101] If n=L′, continue to execute steps 2, 3, and 5;

[0102] If n=L′ is not satisfied, set n=n+1 and return to step 233 to continue training the model after the nth iteration training;

[0103] Step 235: Determine whether l=L, where L represents the total number of training tasks;

[0104] If l=L, then execute steps 2, 3, and 6;

[0105] If l=L is not satisfied, set l=l+1 and return to step 232;

[0106] Step 236: Use the test data of all training tasks to test the trained proxy model and calculate the total loss of the test data of all training tasks on the trained proxy model

[0107]

[0108] in, Represents the loss of the test set data of the lth training task on the trained proxy model;

[0109] The Adam optimizer is used to update the proxy model parameters:

[0110]

[0111] Among them, α2 represents the learning rate of outer loop optimization, Indicates total loss Gradient of θ, θ′ represents the proxy model parameters after the total loss update, and θ represents the proxy model parameters before the total loss update;

[0112] Step 237: Determine the total loss Convergence:

[0113] If the total loss Convergence is achieved, and the meta-learned proxy model (also referred to as meta-model) is obtained;

[0114] If the total loss If it does not converge, return to step 2, 3, and 1.

[0115] The other steps and parameters are the same as those in the first to sixth embodiments.

[0116] Specific embodiment eight: This embodiment differs from any one of specific embodiments one to seven in that the specific process of step three is as follows:

[0117] Step 3.1 Displacement preloading stage (used to simulate initial damage under the main shock):

[0118] Apply different displacement loading to the target structure model to make the target structure reach various initial damage states;

[0119] Step 32: Displacement reciprocating loading stage (used to simulate aftershock effects):

[0120] The target structural models with various initial damage states are subjected to displacement reciprocating loading until each target structural model reaches the ultimate limit state, which includes the concrete cracking state LS1, the steel bar yielding state LS2, the concrete crushing state LS3 and the final structural failure state LS4;

[0121] Step 33: Perform steps 31 and 32 for the structure with a service life of t years, and then perform regression analysis on the target structural displacement in the preloading stage and the target structural displacement in each limit state to obtain the time-varying two-dimensional limit state equation for each limit state. The time-varying two-dimensional limit state equation for the ath limit state is recorded as:

[0122]

[0123] in, N represents the threshold value of the ath limit state when the service life of the target structure is t years; s,a (t) represents the correlation between the initial damage level of the structure and the residual seismic capacity when the service life of the target structure is t years; d MS represents the seismic response of the target structure under the main shock, d ASIt represents the seismic response of the target structure under aftershocks;

[0124]

[0125] Among them, k a,1 、k a,2 、k a,3 、k a,4 、k a,5 、k a,6 and k a,7 All are coefficients.

[0126] The other steps and parameters are the same as those in the first to seventh embodiments.

[0127] Specific embodiment 9: This embodiment differs from any one of specific embodiments 1 to 8 in that the specific process of step 4 is as follows:

[0128] Step 4.1: Calculate the concrete compressive strength f according to the probability distribution of each parameter in step 1. c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h and chloride ion initial diffusion coefficient D0 are randomly sampled to obtain Q candidate samples;

[0129] Then, the parameters of the candidate samples are adjusted according to the service life of the structure to be predicted, and Q candidate samples after adjustment are obtained;

[0130] Step 42: Use the learning function to select q local sampling centers from the adjusted candidate samples; the specific selection method is:

[0131] For any candidate training sample x i :

[0132]

[0133] Among them, g(x i ) represents the response prediction value of the meta-learning agent model to the selected i-th candidate training sample, d min (g(x i )) represents the minimum Euclidean distance between the selected i-th candidate training sample and all the adjusted candidate training samples, x represents the selected q local sampling center sets, Z LS (g(x i )) represents the limit state equation (i.e. g(x i ) is brought into the limit state equation, the value on the left side of the formula), β represents the weight coefficient, Represents the agent model for candidate training samples x iThe prediction variance (the calculation method of the prediction variance is: randomly divide the Q candidate samples adjusted in step 4 into K data sets, and divide the divided samples x i The dataset where it is located is used as the validation set, and the other K-1 datasets are used as training sets. After training the proxy model after meta-learning with the K-1 training sets, the sample x is obtained. i The predicted value of the trained model; then the Q candidate samples adjusted in step 4-1 are randomly divided again to obtain K data sets, and then the divided samples x i The dataset is used as the validation set, and the other K-1 training sets obtained by division are still used to train the proxy model after meta-learning, and then the sample x is obtained. i The predicted value on the trained model; and so on, until the number of divisions reaches K times, the prediction variance is calculated based on the prediction results obtained by K divisions), GLF(x i ) represents the learning function value;

[0134] Calculate the learning function value GLF(x i ), select q candidate training samples with the largest learning function value as the selected local sampling centers;

[0135] Step 43: For each selected local sampling center, generate Q' candidate training samples in the local area of ​​the local sampling center;

[0136] Step 44: Use the learning function to select q' local sampling centers from the candidate training samples generated in step 43;

[0137] Step 4 and 5: Use the selected q' local sampling centers to establish high-precision finite element models of the structure to be predicted, and use the structural parameters and displacement responses of the high-precision finite element models of the structure to be predicted to actively learn the proxy model after meta-learning;

[0138] Calculate the relative error between the exceedance probability of the current trained model and the exceedance probability of the previous trained model (no judgment is required for the first iteration);

[0139] If the relative error is less than the preset threshold ξ or reaches the maximum number of training times, the final trained proxy model is obtained;

[0140] If the relative error is greater than or equal to the preset threshold ξ and the maximum number of training times has not been reached, the process returns to step 42 and continues to select candidate training samples from the candidate training samples that have not been selected in step 42.

[0141] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0142] This embodiment selects a meta-model based on multi-precision data fusion as the initial model, and uses a two-stage active learning method to improve the accuracy of the meta-learned proxy model in predicting the seismic response of specific degradation scenarios, which can further improve the accuracy of the proxy model in predicting the seismic response of different structural degradation scenarios.

[0143] Specific embodiment 10: This embodiment differs from specific embodiments 1 to 9 in that the specific process of step 5 is as follows:

[0144] Step 5.1. Use the Monte Carlo method to perform several simulations. According to the service life of the structure to be predicted, the structural parameters of the structure to be predicted are obtained for each simulation. (Because the structural parameters conform to the corresponding distribution, not every Monte Carlo simulation corresponds to the same parameter value. That is, the parameters of different simulations are slightly different within the distribution. Therefore, through multiple Monte Carlo simulations, the influence of sampling differences on the probability can be avoided.) Then, the finally trained proxy model is used to predict the displacement response of the structure under the main shock. The initial damage state of the structure is obtained based on the displacement response of the structure under the main shock.

[0145] Step 52: Under the initial damage state of the structure, the finally trained proxy model is used to predict the displacement response of the structure under aftershocks;

[0146] Step 5.3: Substitute the displacement response of the structure to be predicted under the main shock and aftershocks into the time-varying two-dimensional limit state equation:

[0147] If the calculation result If it is greater than 0, the structure to be predicted reaches the corresponding limit state;

[0148] If the calculation result If it is less than or equal to 0, the structure to be predicted has not reached the corresponding limit state;

[0149] When the time-varying two-dimensional limit state equation is used for calculation, if a certain limit state corresponds to and N s,a (t) make If it is greater than 0, the structure to be predicted has reached the target limit state;

[0150] The curves of the probability of exceeding various limit states of the structure to be predicted changing with the magnitude of aftershocks under different initial damage states are obtained, that is, the vulnerability curve of the structure to be predicted is obtained.

[0151] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0152] It should be noted that this embodiment is applicable to both vulnerability analysis of structures to be predicted that have been in service for several years and vulnerability analysis during the structural design phase. For structures to be predicted that have already been in service for several years, the structural parameters for the current phase can be determined based on the current service life of the structure to be predicted. The method of this embodiment can then be used to obtain the current vulnerability curve of the structure to be predicted. Of course, the vulnerability curve for the structure to be predicted at a specific future timeframe can also be obtained. For structures in the design phase, the structural parameters for several years of service can be determined based on the design parameters. The method of this embodiment can then be used to obtain vulnerability analysis results.

[0153] Example

[0154] In order to make the above-mentioned objects, features and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In this embodiment, the vulnerability analysis of the nuclear containment structure under the action of the main shock and aftershock is selected to illustrate the present invention. Figure 1 As shown, the specific implementation process is carried out in the following steps:

[0155] Target nuclear containment structure such as Figure 2 As shown in the figure, the cylinder is 1.1m thick, 44m high, and has an inner diameter of 18.9m. The heights of the dome and foundation are 19.65m and 6m respectively. The compressive strength of the concrete is 40MPa, and the yield strength of the steel bars is 350MPa. Figure 3 As shown in the figure, Abaqus software was used to establish a high-precision finite element model of the structure. Concrete and steel were respectively constructed using solid elements (C3D8R) and truss elements (T3D2). Concrete was constructed using plastic damage constitutive model, while steel was constructed using bilinear hardening model. Consolidation constraint was used at the bottom of the structure, and the damping ratio (ξ R ) is set to 5%. Since the containment structure exhibits shear deformation under earthquake action, the structure is simplified into a multi-degree-of-freedom (MDOF) shear model in the low-precision finite element model, such as Figure 4 As shown in Figure 2. In this model, concentrated masses at different heights are connected by shear springs. Each concentrated mass is equal to the structural mass within its height range, and all floor masses are assumed to be concentrated at its center of mass. Each concentrated mass considers only one horizontal degree of freedom, while rotational degrees of freedom are ignored. To more accurately simulate the nonlinear behavior and energy dissipation capacity of the structure, the MDOF model employs a trilinear skeleton curve and a single-parameter hysteretic model.

[0156] To ensure sufficient cooling water, nuclear power plants are typically built in coastal areas. Marine environments contain high concentrations of chloride ions, which adhere to structural surfaces and penetrate them, accelerating corrosion of steel reinforcement. The chloride ion diffusion process in concrete is often described using Fick's second law as follows:

[0157]

[0158] Where C0 is the initial chloride ion concentration, C(x,t) represents the chloride ion concentration at a distance x from the concrete surface after service time t years, and D F is the corrected chloride ion diffusion coefficient; C s represents the chloride ion concentration on the concrete surface, and erf(·) is the error function. i In 2016, the chloride ion concentration on the steel bar surface exceeded the critical threshold C cr , steel bars are corroded and damaged:

[0159]

[0160] Where m is the aging factor; D0 and t0 are the initial diffusion coefficient and the corresponding time respectively; h is the thickness of the concrete cover; Φ -1 Represents the inverse function of the standard normal distribution.

[0161] The degradation caused by steel bar corrosion is mainly manifested as a decrease in steel bar diameter and yield strength. This example uses a uniform corrosion degradation model to quantify the change in steel bar diameter over time, as follows:

[0162] d(t i )=d0-0.0232t i ×i corr (t i )

[0163] Where d0 is the initial steel bar diameter, t i Indicates the time from the appearance of corrosion damage, d(t i ) is the time after t i Steel bar diameter after 2018. Corrosion rate i corr (t i ) is expressed as:

[0164]

[0165] Among them, the water-cement ratio w / c=27 / (f c +13.5), f c Indicates the compressive strength of concrete. i The yield strength at moment is:

[0166]

[0167] in, is the initial yield strength; A0 and A(t i ) are the initial cross-sectional area of ​​the steel bar and t i Cross-sectional area at the moment.

[0168] Nuclear power plants located in extremely cold regions are exposed to extreme climatic conditions. In addition to chloride ion corrosion, their structures are also subject to freeze-thaw cycles (FTC). Freeze-thaw cycles significantly affect the mechanical properties of concrete. The compressive strength of concrete after FTC is:

[0169]

[0170] in, represents the compressive strength of damaged concrete after freeze-thaw cycles, f c ' is the compressive strength at 28 days old, N d Indicates the number of freeze-thaw cycles.

[0171] Under freeze-thaw cycle conditions, micro cracks appear in concrete, which promotes the diffusion of chloride ions and further accelerates the corrosion of steel bars. Considering the influence of freeze-thaw damage, the chloride ion diffusion coefficient in concrete can be corrected to:

[0172] D F =D·e 0.1072H

[0173]

[0174] Among them, H represents the degree of freeze-thaw damage, and S is the number of equivalent freeze-thaw cycles indoors.

[0175] Fragility analysis typically requires extensive finite element calculations, significantly increasing computational requirements. This issue is particularly acute in lifecycle fragility analysis, where repeated modeling and dynamic analysis are required for multiple stages of structural degradation. To balance computational efficiency and analytical accuracy, surrogate models can be constructed to replace finite element calculations in predicting structural seismic responses. However, constructing surrogate models typically relies on a large amount of high-precision data as training samples, thus still facing high computational costs. While high-precision data offers high accuracy, it is expensive to acquire and limited in quantity. In contrast, low-precision data is cheaper to acquire but has limited accuracy. In a multi-precision data fusion framework, low-precision data can be used to reveal trends in actual data, while a small amount of high-precision data is used to correct systematic errors in the low-precision data. Therefore, multi-precision data fusion strategies effectively reduce computational costs while maintaining prediction accuracy, making them an effective solution for efficiently constructing surrogate models.

[0176] In existing surrogate model-based structural safety assessments, a new surrogate model must be constructed for each new task. However, many engineering problems share certain similarities in nature. Transferring existing modeling experience between similar tasks can improve the efficiency of modeling for new tasks. Meta-learning aims to extract common modeling knowledge from multiple source tasks and use it to train a base model, enabling it to converge rapidly on new tasks with only a small number of samples and training iterations. The construction of the meta-model relies on a training dataset covering multiple tasks, which increases the workload of initial data collection. However, once trained, the meta-model can be retained and reused in subsequent tasks. When a large number of new tasks need to be analyzed, constructing a surrogate model using a pre-trained meta-model can significantly reduce the time required for data collection and model building. Lifecycle vulnerability analysis typically involves the assessment of multiple structural degradation conditions, and the inherent similarities between these conditions provide a theoretical basis for the application of meta-learning modeling methods in this analysis framework.

[0177] In order to reduce the computational cost of the whole-life vulnerability analysis, the present invention proposes a meta-model based on multi-precision data fusion as a proxy model for seismic response prediction. In order to establish a meta-model that can predict the seismic response of nuclear containment structures in different service periods, it is first necessary to establish different training tasks according to the degree of structural degradation. The service life of the nuclear power plant is set to 100 years, and a training task is set every 20 years, with a total of 6 tasks. The chloride ion concentration on the concrete surface is a fixed value, and the corrosion rate obeys a uniform distribution on the surface of the structure. Other parameters of the chloride ion diffusion process are as follows: C s =0.144%, C0=0%, C cr = 0.06%, m = 0.56. The average annual number of freeze-thaw cycles is 109, and S is 12.5. For each task, the degree of structural degradation is simulated by varying material properties. The variables listed in Table 1 are randomly sampled to obtain 100 high-precision models and 400 low-precision models. Specifically, a low-precision model is established for each set of parameters, and several sets are then selected to establish high-precision models. The number of low-precision models corresponding to each training task is approximately equal, and the number of high-precision models corresponding to each training task is also approximately equal.

[0178] Nonlinear time history analysis is performed on different high-precision and low-precision numerical models. Since the containment is a symmetrical structure, only a unidirectional horizontal earthquake action is applied to the structure. This embodiment considers four limit states of the containment: concrete cracking (LS1), steel yielding (LS2), concrete crushing (LS3) and final failure (LS4). i ,LS i+1 ]

[0179] Different structural damage states after the mainshock are defined (DS0 to DS3), with displacement ranges of [0, 1.090], (1.09, 4.52], (4.52, 6.99], and (6.99, 8.76], respectively, in cm. In the nonlinear time-history analysis, the target initial damage state is first simulated by amplitude modulating the mainshock record. The corresponding aftershocks are then applied to the damaged structure after the mainshock. The earthquake intensity level is measured by the peak ground acceleration (PGA), and the maximum vertex displacement of the structure is used to measure the structural seismic response under the mainshock and aftershocks. The aftershock intensity amplitude modulation range is 0.1g to 3.0g, with an amplitude modulation interval of 0.1g.

[0180] Table 1 Uncertainty of modeling parameters

[0181]

[0182]

[0183] Figure 5 The proxy model network architecture based on high and low precision data fusion adopted in this invention consists of two submodules: the first submodule (NN L ) is used to capture the relationship between input variables and low-precision earthquake responses. The second submodule (NN H ) is used to predict high-precision earthquake response. The first submodule contains six input nodes: peak ground acceleration (PGA), concrete compressive strength f c , steel bar yield strength f y , damping ratio ξ R , steel bar diameter and initial damage degree, these input parameters pass through four hidden layers in sequence, each layer contains 64 nodes. The second submodule contains two parallel hidden layer clusters: the upper hidden layer cluster is used to build a linear relationship between the input variables and the high-precision output, which contains three hidden layers and 32 nodes per layer; the lower hidden layer is used to capture the nonlinear relationship between the variables, which contains four hidden layers and 32 nodes per layer. The nonlinear layers in both subnetworks use the ReLU activation function, while the linear layers do not use the activation function. The learning rate of the first subnetwork of the model is set to 0.0005, the learning rate of the linear layer in the second part is set to 0.0002, and the learning rate of the nonlinear layer is set to 0.0001. In order to effectively process multiple precision data sets, high and low precision earthquake response prediction errors should be considered simultaneously during the model training process. Therefore, the loss function is:

[0184]

[0185] Among them, N yL and N yH Represent the number of training samples for high-precision model and low-precision model respectively, and and Represent the corresponding predicted responses.

[0186] In order to meta-train the proxy model based on multi-precision data fusion, the 500 data of each task are divided into a support set (60%) and a query set (40%). First, the support set is used for the parameter update process of the inner loop of the meta-training phase. The proxy model is trained separately using the support set of each training task, and the parameter is θ n-1 Metamodel Update to θ n :

[0187]

[0188] Among them, α1 is the inner loop learning rate.

[0189] The query set is then used to update the outer loop of meta-learning, first calculating the loss of the meta-model on the query set of different training tasks The meta-loss is defined as the cumulative loss of all training tasks and can be expressed as:

[0190]

[0191] The goal of the meta-learning outer loop is to minimize the total loss of all tasks, thereby improving the meta-model's ability to capture general knowledge. The outer loop training uses the Adam optimizer to update the proxy model parameters:

[0192]

[0193] Among them, α2 is the learning rate of the outer loop optimization.

[0194] Repeat the above meta-learning process until the loss function convergence.

[0195] Currently, in the vulnerability analysis of structures under main and aftershocks, it is usually assumed that the structural limit state threshold is a fixed value. However, the cumulative damage to the structure under an earthquake sequence will cause the continuous degradation of the structural seismic resistance, and the long-term environmental effects will also aggravate the impact of the initial earthquake damage on the residual seismic resistance of the structure. Ignoring the influence of multiple degradation mechanisms will lead to an overestimation of the safety margin of the structure. Therefore, it is necessary to consider the coupling effect of long-term environmental exposure and sudden earthquake sequences in the calculation of vulnerability exceedance probability. In the vulnerability analysis framework proposed in the present invention, a time-varying two-dimensional limit state equation is introduced to characterize the dependence between different degradation mechanisms and residual seismic resistance.

[0196] In this paper, in order to consider the long-term environmental effects and capture the impact of main shock-induced damage on the residual seismic capacity of the structure, a time-varying two-dimensional limit state equation is used to describe the performance level of the containment structure:

[0197]

[0198] where d LS (·) and N s (·) are functions of service time t. d LS (t) represents the limit state threshold of the structure at different service periods, while N s (t) reflects the correlation between the initial damage level and the residual seismic capacity at different service periods. d MS and d AS represent the seismic responses of the structure under the main shock and aftershock, respectively.

[0199] To obtain the time-dependent two-dimensional limit state equation of the structure, pseudo-static cyclic loading analysis was performed on the nuclear containment structure at different service periods (at 10-year intervals). As shown in Fig. Figure 6 , the loading scheme adopted displacement-controlled loading and was divided into two stages:

[0200] (a) preloading stage, gradually loading until the structure reached the target initial damage state;

[0201] (b) regular cyclic loading stage, continuing to load the damaged structure until it reached the limit state.

[0202] The maximum displacement of preloading was increased by 0.5 cm to simulate various initial damage levels. Once the structure reached the target limit state, the maximum displacement of the preloading stage and the corresponding displacement in the subsequent cyclic loading process were recorded. Regression analysis was performed on the displacement values corresponding to each service period of the structure to determine the key parameters of the limit state equation. Figures 7 to 10 For the time-dependent two-dimensional limit state of the nuclear containment structure, Table 2 shows the related parameters of the limit state equation.

[0203] In Fig. Figures 7 to 10 , the horizontal coordinate represents the structure damage level after the main shock and the structure service period, while the vertical coordinate is the residual seismic capacity of the structure, measured by the top displacement. As shown in Fig. Figures 7 to 10 , as the damage level corresponding to the limit state increases, the parameter N s shows a downward trend, indicating that the influence of initial damage on the residual capacity of the structure is increasingly significant. At the same time, as the service time of the structure increases, its limit state threshold gradually decreases, and the dependence between the initial damage level and the residual capacity at each limit state significantly increases.

[0204] Table 2 Key parameters of the time-dependent two-dimensional limit state equation

[0205]

[0206] Active learning algorithms are adaptive and can identify the most informative samples, thereby building a proxy model with accurate predictions using as few training samples as possible. In traditional active learning methods, a large number of random candidate samples are generated through Monte Carlo simulation, and the optimal training samples are selected from them using a learning function, and the initial proxy model is updated. However, as the problem dimension and the total sample size increase, the candidate sample screening process becomes increasingly time-consuming. To further improve the efficiency of active learning, the present invention proposes a two-stage active learning strategy, which includes two active learning stages: global and local.

[0207] In order to further improve the accuracy of the proxy model in predicting the seismic response of different structural degradation scenarios, a meta-model based on multi-precision data fusion is selected as the initial model, and a two-stage active learning method is used to improve the accuracy of the meta-model in predicting the seismic response of specific degradation scenarios. The global loop is designed to determine the sampling center. Figure 11 As shown, first, 300 low-difference samples are generated in the entire variable space, and the optimal sampling center x is selected using the learning function. global , marked as "+". Then enter the local loop stage, global 200 candidate samples are generated in the local area centered on the . Local active learning also uses the learning function to select the most informative sample points and calculates the seismic response corresponding to the sample using a high-precision numerical model; then the selected sample-response pairs are added to the training set and used to train the meta-model again. In each iteration, the updated proxy model is used to calculate the exceedance probability P f Convergence is determined by the relative error in exceedance probabilities between two consecutive iterations. If the relative error is less than a preset threshold ξ (0.01) or the maximum number of iterations, 1000, is reached, the iteration cycle ends. Otherwise, the selected sample points and their corresponding seismic responses are added to the training set, and the metamodel is optimized using the updated training set.

[0208] In order to improve the applicability of active learning methods to different proxy models, this paper proposes a general learning function GLF(·) to evaluate the quality of candidate sample points based on two key indicators: distance and variance:

[0209]

[0210] Among them, g(x i ) represents the response prediction value of the surrogate model to the i-th candidate sample point; d min represents the minimum Euclidean distance between the candidate sample and the existing training samples; Z LS represents the limit state equation, σ 2is the predicted variance of the proxy model. The weight coefficient β is used to balance the contribution of the distance and variance indicators to the learning function. In this embodiment, β is set to 2.0. In the general learning function, the candidate points close to the limit state are selected by f D (·) is rewarded, while points with smaller prediction variance are rewarded by f V (·) is penalized. Therefore, in each round of active learning iteration, the candidate point that maximizes the GLF value is selected to update the training set.

[0211] Based on the trained proxy model, combined with the time-varying two-dimensional limit state equation, the structural vulnerability curves of different service periods can be solved. Since the current explicit mathematical calculation formula of exceedance probability cannot take into account the correlation between the initial damage level and the residual seismic capacity, the present invention adopts a simple Monte Carlo simulation method and calculates the number of failure samples (i.e., Z LS (d MS ,d AS )≥0) to the total number of simulations as the exceedance probability. For each earthquake intensity level, 1×10 5 The vulnerability curves were obtained by performing a sampling simulation and fitting the exceedance probabilities at different intensities with a log-normal distribution. Finally, the vulnerability curves of the nuclear containment under the full life cycle of the mainshock and aftershock sequence were obtained using proxy models with different service years.

[0212] Figures 12 to 15 The vulnerability curves for the nuclear containment structure are presented under three degradation scenarios: 0, 50, and 100 years. At 0 years, after the structure experienced DS3, the median LS4 intensity (i.e., the earthquake intensity corresponding to a 50% probability of exceedance) decreased by 24.3% compared to LS4|DS0. At 100 years, the impact of DS3 on the median LS4 intensity was even more significant, decreasing by 42.0% compared to the intact structure. These results further demonstrate that long-term environmental effects and sudden mainshock and aftershock sequences significantly reduce structural safety margins, emphasizing the urgent need to consider multi-hazard coupling in structural seismic safety assessments.

[0213] To further verify the accuracy and effectiveness of the proposed method, a comparative analysis was conducted between the proposed method and traditional methods. ANN (Artificial Neural Network)-MCS is a widely used vulnerability analysis method based on surrogate models and has been shown to have good robustness. Figure 16The vulnerability curves corresponding to different methods under the 100-year LS4|DS3 condition are compared, and the sample size of the proxy model ANN is 300, 600, 900 and 1200. It can be seen that when the training sample is 900, the vulnerability corresponding to ANN-MCS tends to be stable, and the method proposed in the application can reach a similar median intensity with about 650 high-precision samples (600 samples for meta-training, and 50 samples selected by active learning). The total calculation time mainly comes from the construction of the proxy model and the Monte Carlo simulation for probability estimation. It is worth noting that 1x10 5 times of simulation are performed under each seismic intensity, so the time of random simulation is almost the same in all analysis cases, about 6.8 hours. However, the construction time of the proxy model differs greatly. In the traditional ANN-MCS method, since the proxy model needs to be re-established for each service period, a total of 2700 high-precision samples (3x900) are required for the three aging stages of 0 years, 50 years and 100 years, and the calculation time of each high-precision sample is about 7 hours. In contrast, the framework proposed in the application requires a total of about 3150 samples (of which 750 are high-precision samples and 2400 are low-precision samples), of which 3000 are used for training of the initial meta-model, and about 50 samples are selected for each degradation scenario to optimize the proxy model through the active learning method. The calculation time of each sample of the low-precision finite element model is only about 3 minutes. Therefore, the method of the application not only can realize accurate estimation of the exceedance probability, but also can compress the total calculation time to 28.4% of the ANN-MCS method. It is worth emphasizing that once the initial meta-model is trained, only a small number of additional samples are required to obtain high-precision proxy models for each aging stage through the two-stage active learning method. Therefore, the more degradation scenarios that need to be analyzed, the more significant the total calculation time saved, making the method of the application particularly suitable for efficient solution of the full-life vulnerability problem.

[0214] The above examples of the application are only to illustrate the calculation model and calculation process of the application, and are not a limitation on the embodiments of the application. Based on the above description, other different forms of changes or variations can be made by those skilled in the art, and it is impossible to enumerate all the embodiments here. Any obvious changes or variations derived from the technical solutions of the application still fall within the protection scope of the application.

Claims

1. A main shock and aftershock life cycle vulnerability analysis method based on active learning, characterized by: The method specifically comprises the following steps: Step 1: Set the concrete compressive strength f c Obeying the normal distribution with mean α1 and coefficient of variation β1, the yield strength of steel bar f y It obeys the lognormal distribution with mean α2 and coefficient of variation β2, and the damping ratio ξ R It obeys the log-normal distribution with a mean of α3 and a coefficient of variation of β3. The concrete cover thickness h obeys the normal distribution with a mean of α4 and a coefficient of variation of β4. The initial diffusion coefficient of chloride ions D0 obeys the normal distribution with a mean of α5 and a coefficient of variation of β5. Compressive strength of concrete f c , steel bar yield strength f y , damping ratio ξ R , the concrete cover thickness h and the chloride ion initial diffusion coefficient D0 are randomly sampled, and a high-precision finite element model and a low-precision finite element model of the target structure are established based on the sampling results; the parameters of each group of sampling results are then adjusted according to the service time of the target structure, and high-precision finite element models and low-precision finite element models of the target structures with different service times are established based on the adjusted parameters of each group; Then, nonlinear time history analysis is performed on all high-precision finite element models and low-precision finite element models of the target structure under the action of main shocks and aftershocks to obtain the displacement response of each finite element model under the action of main shocks and aftershocks. Step 2: Meta-learn the proxy model using the structural parameters of the finite element models corresponding to different service years and the displacement response data of each finite element model under the main shock and aftershock; Step 3: Establish the time-varying two-dimensional limit state equation of the target structure; Step 4: According to the probability distribution of each parameter in step 1, the concrete compressive strength f c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h and chloride ion initial diffusion coefficient D0 are randomly sampled to obtain Q candidate samples; Then, the parameters of the candidate samples are adjusted according to the service life of the structure to be predicted, and the learning function is used to select q local sampling centers from all the adjusted candidate samples; And generate Q' candidate training samples in the local area of ​​each local sampling center, and then use the learning function to select q' local sampling centers from all candidate training samples; A high-precision finite element model of the structure to be predicted is established based on the selected q' local sampling centers. The structural parameters and displacement responses of the high-precision finite element model of the structure to be predicted are used to actively learn the meta-learned proxy model to obtain the final trained proxy model. Step 5: Use the finally trained proxy model and the time-varying two-dimensional limit state equation to obtain the fragility curve of the structure to be predicted.

2. The method for life-cycle vulnerability analysis of main shocks and aftershocks based on active learning according to claim 1, characterized in that: The high-precision finite element model of the target structure is established using Abaqus software, and the concrete and steel bars in the high-precision finite element model are respectively solid elements and truss elements; The low-precision finite element model of the target structure is a multi-degree-of-freedom shear model, which adopts a trilinear skeleton curve and a single-parameter hysteresis model.

3. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 2 is characterized in that: The parameters of each group of sampling results are adjusted according to the service time of the target structure, specifically: The service life of the target structure is recorded as N years. By dividing the entire service cycle into equal intervals, each equal-division point, 0 and N, is used as the service time corresponding to a training task; For any training task, the parameters of each group of sampling results are adjusted according to the service time corresponding to the training task.

4. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 3 is characterized in that: When the target structure is a nuclear containment structure, the relationship between the concrete compressive strength and the steel yield strength and the service time is obtained as follows: Step 1: The chloride ion diffusion process in concrete is: Where C0 is the initial chloride ion concentration, C(x,t) represents the chloride ion concentration at a distance x from the concrete surface when the service time is t years, and D F is the corrected chloride ion diffusion coefficient; C s represents the chloride ion concentration on the concrete surface, erf(·) is the error function, η is the integration variable; Calculate the chloride ion concentration on the steel bar surface to reach the critical threshold C cr The structural service time T i : Where m is the aging factor, t0 is the initial diffusion time, D0 is the initial diffusion coefficient, h is the thickness of the concrete cover, Φ -1 (·) is the inverse function of the standard normal distribution; Step 2: Calculate the diameter d(t i ): d(t i )=d0-0.0232t i ×i corr (t i ) (3) Where d0 is the initial steel bar diameter; t i Indicates the time when steel bar corrosion damage has occurred when the service time reaches t years; i corr (t i ) represents the corrosion rate of the steel bar when the service time reaches t years; Wherein, w / c is the water-cement ratio, w / c=27 / (f c +13.5), f c is the initial compressive strength of concrete; Step 3: Calculate the yield strength f of the steel bar when the service time is t years. y (t i ): Among them, A0 represents the initial cross-sectional area of ​​the steel bar; A(t i ) represents the cross-sectional area of ​​the steel bar when the service time is t years; Indicates the initial yield strength of the steel bar; Step 4: The compressive strength of concrete after freeze-thaw cycles is: in, represents the compressive strength of damaged concrete after freeze-thaw cycles, f c ' is the compressive strength at 28 days old, N d Indicates the number of freeze-thaw cycles.

5. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 4 is characterized in that: The corrected chloride ion diffusion coefficient is: D F =D·e 0.1072H (7) Among them, D F represents the corrected chloride ion diffusion coefficient, D represents the chloride ion diffusion coefficient without considering the effect of freeze-thaw cycles, H represents the degree of freeze-thaw damage, e represents the base of the natural logarithm, and S represents the number of equivalent freeze-thaw cycles indoors.

6. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 5, characterized in that: The specific process of step 2 is as follows: Step 21: Divide the low-precision finite element model structural parameters and displacement response data corresponding to each service time into two parts, that is, for each low-precision finite element model structural parameters and displacement response data corresponding to the service time, the low-precision finite element model structural parameters and displacement response data are divided into a support set and a query set; The high-precision finite element model structural parameters and displacement response data corresponding to each service time are divided into two parts, that is, the high-precision finite element model structural parameters and displacement response data corresponding to each service time are divided into a support set and a query set; Step 22: The data in the support set corresponding to each service time is used as training data for a training task; The data in the query set corresponding to each service time is used as test data for a training task; Step 2 and 3: Use the training data of each training task to meta-learn the proxy model until the loss function value of the proxy model on the test data of all training tasks converges, and stop learning to obtain the meta-learned proxy model.

7. The active learning-based full-life vulnerability analysis method for main shocks and aftershocks according to claim 6 is characterized in that: The proxy model includes a first submodule and a second submodule, wherein the first submodule is a first BP neural network, and the second submodule includes a second BP neural network, a third BP neural network and a fully connected layer; The input part of the training data is used as the input of the first submodule, and the input part of the training data and the output of the first submodule are used as the input of the second submodule; the input of the second submodule passes through the second BP neural network and the third BP neural network respectively, and then the outputs of the second BP neural network and the third BP neural network are spliced, and the spliced ​​result is used as the input of the fully connected layer, and the output of the fully connected layer is used as the output of the proxy model; The specific process of meta-learning of the agent model is as follows: Step 231: Initialize the number of training tasks l = 1; Step 232: Initialize the number of iterative training n=1; Step 233: For any set of sampled parameters or any set of adjusted parameters of the first training task, use the ground peak acceleration, concrete compressive strength, steel yield strength, damping ratio, steel diameter, and damage degree of the finite element model corresponding to the set of parameters as the input of the first submodule, and use the displacement response of the finite element model as the training label of the first submodule; The output of the first submodule and the ground peak acceleration, concrete compressive strength, steel yield strength, damping ratio, steel diameter, and damage degree of the finite element model corresponding to the set of parameters are used as the input of the second submodule. The output label of the proxy model is the displacement response of the finite element model corresponding to the set of parameters. And traverse each set of parameters of the nth iteration training; The loss function Loss used in the training process is: in, Indicates the number of training samples corresponding to the high-precision finite element model during the nth iteration training process; Indicates the number of training samples corresponding to the low-precision finite element model during the nth iteration training process, y i,L represents the label of the i-th training sample of the high-precision finite element model during the n-th iteration training process; y j,H Indicates the label of the jth training sample of the low-precision finite element model during the nth iteration training process, represents the predicted response to the i-th training sample of the high-precision finite element model, represents the predicted response to the jth training sample of the low-precision finite element model; Use gradient descent method to update model parameters: Among them, θ n-1 represents the proxy model parameters after the n-1th iteration training, θ n represents the proxy model parameters after the nth iteration training, α1 represents the inner loop learning rate, Indicates that the training data for the nth iteration training is under the parameter θ n-1 The loss function on the surrogate model, express θ n-1 gradient; Step 2, 3, 4: Determine whether n = L′, where L′ is the total number of iterative training times on the lth training task; If n=L′, continue to execute steps 2, 3, and 5; If n=L′ is not satisfied, set n=n+1 and return to step 233 to continue training the model after the nth iteration training; Step 235: Determine whether l=L, where L represents the total number of training tasks; If l=L, then execute steps 2, 3, and 6; If l=L is not satisfied, set l=l+1 and return to step 232; Step 236: Use the test data of all training tasks to test the trained proxy model and calculate the total loss of the test data of all training tasks on the trained proxy model in, Represents the loss of the test set data of the lth training task on the trained proxy model; The Adam optimizer is used to update the proxy model parameters: Among them, α2 represents the learning rate of outer loop optimization, Indicates total loss Gradient of θ, θ′ represents the proxy model parameters after the total loss update, and θ represents the proxy model parameters before the total loss update; Step 237: Determine the total loss Convergence: If the total loss Convergence, then the meta-learned proxy model is obtained; If the total loss If it does not converge, return to step 2, 3, and 1.

8. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 7, characterized in that: The specific process of step three is: Step 31: Displacement preloading stage: Apply different displacement loading to the target structure model to make the target structure reach various initial damage states; Step 32: Displacement reciprocating loading stage: The target structural models with various initial damage states are subjected to displacement reciprocating loading until each target structural model reaches the ultimate limit state, which includes the concrete cracking state LS1, the steel bar yielding state LS2, the concrete crushing state LS3 and the final structural failure state LS4; Step 33: Perform steps 31 and 32 for the structure with a service life of t years, and then perform regression analysis on the target structural displacement in the preloading stage and the target structural displacement in each limit state to obtain the time-varying two-dimensional limit state equation for each limit state. The time-varying two-dimensional limit state equation for the ath limit state is recorded as: in, N represents the threshold value of the ath limit state when the service life of the target structure is t years; s,a (t) represents the correlation between the initial damage level of the structure and the residual seismic capacity when the service life of the target structure is t years; d MS represents the seismic response of the target structure under the main shock, d AS It represents the seismic response of the target structure under aftershocks; Among them, k a,1 、k a,2 、k a,3 、k a,4 、k a,5 、k a,6 and k a,7 All are coefficients.

9. The active learning-based vulnerability analysis method for main shock and aftershock life cycle according to claim 8, characterized in that: The specific process of step 4 is as follows: Step 4.1: Calculate the concrete compressive strength f according to the probability distribution of each parameter in step 1. c , steel bar yield strength f y , damping ratio ξ R , concrete cover thickness h and chloride ion initial diffusion coefficient D0 are randomly sampled to obtain Q candidate samples; Then, the parameters of the candidate samples are adjusted according to the service life of the structure to be predicted, and Q candidate samples after adjustment are obtained; Step 42: Use the learning function to select q local sampling centers from the adjusted candidate samples; the specific selection method is: For any candidate training sample x i : Among them, g(x i ) represents the response prediction value of the meta-learning agent model to the selected i-th candidate training sample, d min (g(x i )) represents the minimum Euclidean distance between the selected i-th candidate training sample and all the adjusted candidate training samples, x represents the selected q local sampling center sets, Z LS (g(x i )) represents the limit state equation, β represents the weight coefficient, Represents the agent model for candidate training samples x i The prediction variance, GLF(x i ) represents the learning function value; Calculate the learning function value GLF(x i ), select q candidate training samples with the largest learning function value as the selected local sampling centers; Step 43: For each selected local sampling center, generate Q' candidate training samples in the local area of ​​the local sampling center; Step 44: Use the learning function to select q' local sampling centers from the candidate training samples generated in step 43; Step 4 and 5: Use the selected q' local sampling centers to establish high-precision finite element models of the structure to be predicted, and use the structural parameters and displacement responses of the high-precision finite element models of the structure to be predicted to actively learn the proxy model after meta-learning; Calculate the relative error between the exceedance probability of the current training model and the exceedance probability of the previous training model; If the relative error is less than the preset threshold ξ or reaches the maximum number of training times, the final trained proxy model is obtained; If the relative error is greater than or equal to the preset threshold ξ and the maximum number of training times has not been reached, the process returns to step 42 and continues to select candidate training samples from the candidate training samples that have not been selected in step 42.

10. The active learning-based full-life vulnerability analysis method for main shocks and aftershocks according to claim 9, characterized in that: The specific process of step five is: Step 51: Use the Monte Carlo method to perform several simulations, obtain the structural parameters of the structure to be predicted in each simulation based on the service life of the structure to be predicted, and then use the finally trained proxy model to predict the displacement response of the structure under the main shock, and obtain the initial damage state of the structure based on the displacement response of the structure under the main shock; Step 52: Under the initial damage state of the structure, use the finally trained proxy model to predict the displacement response of the structure under aftershocks; Step 5.3: Substitute the displacement response of the structure to be predicted under the main shock and aftershocks into the time-varying two-dimensional limit state equation: If the calculation result If it is greater than 0, the structure to be predicted reaches the corresponding limit state; If the calculation result If it is less than or equal to 0, the structure to be predicted has not reached the corresponding limit state; The curves of the probability of exceeding various limit states of the structure to be predicted changing with the magnitude of aftershocks under different initial damage states are obtained, that is, the vulnerability curve of the structure to be predicted is obtained.

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