Damage prediction method for seismic isolation structure designed through direct displacement method

Abstract

The invention provides a method for predicting the damage of a seismic isolation structure designed through a direct displacement method, and the method can be used for predicting the damage of the seismic isolation structure through the determination of a target value, the calculation of parameters of a seismic isolation layer and an upper building structure, the equivalence of a 2DOF model, and the extraction of 9 structure parameters and 13 seismic wave parameters of seismic waves from the design thought of the DDBD seismic isolation structure. According to the method, the vulnerability curve based on the target value can be quickly predicted through BO-XGBoost to intuitively guide the design of the seismic isolation structure of the DDBD, so that the method is quicker and more efficient, and is beneficial to perfecting the idea of the DDBD of the seismic isolation structure. The result shows that the prediction result is good, and good prediction precision can still be achieved under the condition of open set. A predicted vulnerability curve can be seen, and the predicted curve is close to real data and can be used as a reference for DDBD structure design. From a vulnerability curve, it can be seen that the DDBD design process can effectively enable the seismic isolation structure to reach an expected target under an earthquake.

Description

Technical Field

[0001] The present invention relates to the field of machine learning, and in particular to a damage prediction method for a seismic isolation structure designed by a direct displacement method. Background Art

[0002] As an effective seismic design technology, seismic isolation structure can significantly reduce the impact of earthquakes on buildings, protect the integrity of the structure and ensure its safety. Seismic isolation structure includes: seismic isolation layer and the upper building structure above the seismic isolation layer. The direct displacement design method can effectively design the design parameters of the seismic isolation layer (such as the combination of lead rubber bearings LRB) by setting target values ​​and basic parameters of the upper building structure. This performance-based design method can make the structure meet the design objectives under strong earthquakes, achieve better seismic resistance, and reduce the amount of calculation.

[0003] However, even with the use of seismic isolation measures, earthquakes may still cause damage to seismic isolation structures, especially in strong earthquake events. Therefore, timely and accurate assessment of the damage state of seismic isolation structures (by predicting the maximum displacement of the entire seismic isolation layer to perform vulnerability analysis) is crucial to ensure the safety of personnel and ensure the functional recovery of the building. In addition, damage assessment helps to formulate reasonable repair and reinforcement plans, reduce potential economic losses and social impacts, and ensure the efficient implementation of post-disaster recovery work.

[0004] There are still some challenges in the damage assessment of seismic isolation structures. For example, existing damage assessment methods are often computationally complex and time-consuming, and are not sensitive enough to the randomness of ground motion response, which may lead to inaccurate damage assessment results. Summary of the invention

[0005] The object of the present invention is to provide a damage prediction method for a seismic isolation structure designed by a direct displacement method.

[0006] In order to solve the above problems, the present invention provides a damage prediction method for a seismic isolation structure designed by a direct displacement method, comprising:

[0007] Step S1, generating preset sample seismic waves and establishing various seismic wave parameters of each sample seismic wave;

[0008] Step S2, based on the preset sample seismic waves, calculating and generating the structural parameters of the sample seismic isolation structures of the same corresponding number, and establishing a one-to-one correspondence between each sample seismic wave and a corresponding sample seismic isolation structure;

[0009] Step S3, based on the structural parameters of the isolation structure, the corresponding equivalent double-degree-of-freedom model is established using OpenSees finite element software; based on the equivalent double-degree-of-freedom model and the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, the maximum displacement D of the equivalent mass point of the upper building structure of the corresponding sample isolation structure is obtained. s The maximum displacement D of the particle with the seismic isolation layer b ;

[0010] Step S4: based on the seismic wave parameters of the sample seismic wave and the structural parameters of the corresponding sample seismic isolation structure, and the maximum displacement D of the equivalent mass point of the corresponding upper building structure, s The maximum displacement D of the particle with the seismic isolation layer b And through XGBoost model training and Bayesian hyperparameter optimization, a prediction model for predicting the damage degree of the seismic isolation structure is trained to obtain a trained prediction model;

[0011] Step S5, using DDBD to design a seismic isolation structure to obtain a generated test seismic isolation structure and its various structural parameters;

[0012] Step S6, evaluating the trained prediction model to obtain a prediction model that passes the evaluation;

[0013] Step S7, inputting the actual structural parameters and seismic wave parameters of the seismic isolation structure to be evaluated into the prediction model that has been evaluated to obtain the prediction result.

[0014] Furthermore, in the above method, step S1 includes:

[0015] Step S11, using the NGAWest2 seismic wave database in PEER to collect, organize and classify seismic wave data; obtain the first seismic wave, select the seismic wave with a magnitude greater than 5 in the first seismic wave as the second seismic wave; the 7274 second seismic waves selected can be divided into 4 categories according to the equivalent shear wave velocity of the soil layer and the thickness of the soil layer covering the site; among them, the first category site V s30 >550m / s, the second type of site Vs30 is 265~550m / s, the third type of site V s30 165~265m / s, the fourth type of site V s30 <165m / s;

[0016] Step S12: Select the seismic waves of the first, second and third types of sites from the second seismic wave as the third seismic wave, and for each type of the third seismic wave, respectively select the seismic waves according to the magnitude M and the fault projection distance R in the seismic wave. jb, and were divided into 4 groups of data by the Gaussian mixture model distribution clustering method, and a total of 12 groups of data were obtained from the first, second and third types of sites in the third seismic wave;

[0017] Step S13: Filter the seismic waves of each of the 12 data sets by using a grid screening method: that is, filter the seismic waves of each of the 12 data sets by magnitude M and fault projection distance R. jb为 The horizontal and vertical axes are divided into a 3×3 grid to obtain 9 magnitudes M and fault projection distances R jb range; the grids other than the central grid in the 3×3 grid are used as peripheral grids, 2 seismic waves are randomly selected from each grid in the peripheral grid, and 16 seismic waves are obtained from the 8 peripheral grids in total; 4 seismic waves are randomly selected from the middle grid, so that 20 seismic waves are selected from each group of data, and a total of 240 seismic waves are selected from 12 groups of three types of sites as the fourth seismic wave;

[0018] Step S13: The selected 240 fourth seismic waves are amplitude modulated, wherein the peak ground acceleration PGA of each seismic wave is in the range of 0.05 to 1.6 g, with a step length of 0.05 g, and a total of 32 amplitude modulations are performed to obtain 7680 sample seismic waves as excitation for structural calculation, and the seismic wave parameters of the 7680 sample seismic waves are extracted.

[0019] Furthermore, in the above method, step S12 includes:

[0020] Step S121, using the fault projection distance R in the seismic wave jb and magnitude M are clustering parameters and normalized to obtain normalized data;

[0021] Step S122, based on the normalized data of each type of venue, perform Gaussian mixture model cluster analysis on each type of venue, evaluate the clustering effect of the Gaussian mixture model by setting different groups for each type of venue, and use the Bayesian Information Criterion BIC to evaluate the Gaussian mixture model:

[0022] BIC = -2ln(L) + kln(n), where k is the number of model parameters; n is the number of samples; L is the maximum likelihood estimate of the model;

[0023]

[0024] Among them, K is the number of groups; D is the characteristic dimension, with magnitude M and fault projection distance R jb That is, take 2; cluster the number of groups K of the first, second and third types of sites according to 1 to 20, and perform cluster analysis respectively. According to the BIC value of cluster analysis, when K is four clusters, the BIC curve of the model becomes flat, so the category of each type of site in the model is further subdivided into four groups.

[0025] Furthermore, in the above method, various seismic wave parameters include:

[0026] Duration from 5% to 95% of the acceleration time: D S5-95 ; Peak ground acceleration: PGA; Peak ground velocity: PGV; Cumulative absolute velocity: CAV; Cumulative absolute displacement: CAD; Intensity index: I a ; Root mean square acceleration: a rms ; RMS velocity: v rms ; Effective peak acceleration: EPA; Excellent cycle: T s ; Average period: T avg ; T s Spectral acceleration in seconds: S a (T s ); Acceleration spectrum intensity: ASI.

[0027] Furthermore, in the above method, step S2 includes:

[0028] Step S21, calculate the structural parameters of the equivalent dual-degree-of-freedom model to be generated, there are a total of 9 structural characteristic parameters, set the values ​​of these 9 structural characteristic parameters within the corresponding range, randomly generate the structural parameters of 7680 sample isolation structures corresponding to the number of sample seismic waves according to the set range and normal distribution according to Latin hypercube, and establish a one-to-one correspondence between the seismic wave parameters of a seismic wave and the structural parameters of a random isolation structure in the sample isolation structure; according to the 2DOF system Bouc-Wen model parameters, extract 9 structural parameters, including: M is the sum of the upper mass of the 2DOF model and the mass of the isolation layer, γ m is the mass ratio, d ys is the yield displacement of the upper building structure, α s is the post-yield stiffness ratio of the upper building structure, T s is the basic period of the superstructure structure, ξ IS is the structural damping ratio of the 2DOF model, α b is the post-isolation layer yield stiffness ratio, T b is the natural oscillation period of the 2DOF model, q D is the yield-to-weight ratio of the seismic isolation layer, defined as the accident stiffness k of the seismic isolation layer IS Total weight of the superstructure m T ×g ratio; in Latin hypercube generation, M and γ m is associated, that is, γ is determined according to the value of M m The value range of .

[0029] Furthermore, in the above method, step S3 includes:

[0030] Step S31, using OpenSees finite element software to establish an equivalent dual-degree-of-freedom model, wherein the OpenSees finite element software adopts the Bouc-Wen model, that is, a double-fold line model for modeling, and both the upper building structure and the isolation layer are simulated using the double-fold line model; based on the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, the acceleration and time sequence of the sample seismic wave, the equivalent dual-degree-of-freedom model is subjected to nonlinear time history analysis to obtain the maximum displacement D of the equivalent mass point of the upper building structure of the sample isolation structure. s The maximum displacement D of the particle with the seismic isolation layer b ; In the Bouc-Wen modeling, the parameters include: Post-yield stiffness ratio of linear hardening component is 0.05; Post-yield stiffness ratio of nonlinear hardening component is 0; Exponent of nonlinear hardening component is 1; Yielding exponent is 2; First hysteretic shape parameter is 0.5; Second hysteretic shape parameter is 0.5.

[0031] Furthermore, in the above method, step S4 includes:

[0032] Step 41, each time 80% of the data is selected from the sample seismic waves, and random_state is searched in the range of 0 to 1000 according to the grid search method, and the determination coefficient R of the currently selected 80% of the data is calculated. 2 ;

[0033] Step 42, determine the coefficient R 2 When the score is the highest, 80% of the data is selected as the training set, and the remaining 20% ​​of the data in the sample seismic wave is used as the validation set;

[0034] Step 43, when constructing the XGBoost prediction model, firstly, the benchmark model is used to perform an exploratory analysis on the potential explanatory variables, so as to screen out the hyperparameters that contribute most to the model prediction ability; then, based on the training set, on the basis of the screened out hyperparameters that contribute most, the intelligent optimization method is applied to fine-tune the hyperparameters of various machine learning algorithms; the hyperparameters that need to be adjusted in the XGBoost algorithm include: the number of decision trees, range: [100:1000]; the maximum depth, range: [3:100];

[0035] learning rate, [0.001:0.1]; minimum split loss, [5:10]; regularization coefficient, [0.001:1];

[0036] Step 44, during the model training phase, the validation set is divided into a plurality of subsets by random sampling, and a five-fold cross validation procedure is implemented to obtain a trained prediction model.

[0037] Furthermore, in the above method, step S5 includes:

[0038] Step S501, determining basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure, wherein, according to the preliminary design, the upper building structure is equivalent to a multi-degree-of-freedom system shear type structure model, and according to the mass m of the i-th layer of the multi-degree-of-freedom system shear type structure model i , horizontal lateral stiffness k i , damping coefficient c i And the floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s , D s,eq ; Among them, D s,eq The equivalent displacement required to maintain the superstructure;

[0039] Step S502: Under the design earthquake or rare earthquake, the upper building structure should remain intact, the main body and non-structural components of the upper building structure should not be damaged, and the maximum inter-story displacement angle is set to The performance target of the lead rubber isolation bearing is the design displacement under the design earthquake or rare earthquake.

[0040] Step S503, based on the basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure and the performance target of the lead rubber isolation bearing, calculate the target displacement curve of the upper building structure in the base isolation structure, D 1 and D i are the deformations of the first and i-th layers of the upper building structure respectively; D i It is expressed as the following formula (1):

[0041]

[0042] In formula (1), Φ 1 and Φ i is the normalized function of the horizontal displacement of the first and i-th floors of the upper building structure, which is determined by the period ratio R IS 、h i , the total height H of the upper building structure is calculated, where R IS =TIS / T S , T IS is the fundamental period of the base isolation structure, T S is the basic period of the superstructure structure;

[0043] Step S504: establish a multi-degree-of-freedom system shear type structure model according to the target displacement curve of the upper building structure in the base isolation structure, and calculate the target displacement D of the upper building structure based on the DOF equivalent model. s,eq , equivalent mass m s,eq and the equivalent height h s,eq ;

[0044] Step S505, calculate the new cycle ratio R IS , wherein the period ratio R in step S503 is IS Assuming the period ratio R IS , through the new cycle ratio R IS Until convergence, the new cycle is R IS It is calculated by the following explicit expression (2):

[0045] Display expressions:

[0046] The design displacement D IS,eq ,

[0047] In formula (2), m T is the total mass of the superstructure, m IS is the mass of the seismic isolation layer; where m T According to the basic information, m IS It is one of the basic information;

[0048] Step S506: Based on the new cycle ratio R calculated in step S55 IS， Calculate the equivalent stiffness k of the base-isolated structure IS and the equivalent damping ratio, where the equivalent stiffness k IS Equivalent stiffness k of shear-type structural model of multi-degree-of-freedom system IS,eq are equal; among them, the equivalent damping ratio ξ of the base isolation structure IS From the first-order modal damping ratio ξ 1,eq Calculated; the first-order modal damping ratio ξ 1,eq According to the designed displacement spectrum, the first modal period T of the shear structure model of the multi-degree-of-freedom system is 1,eq and Interpolation is then used to determine the yield displacement d of the seismic isolation layer. yb , according to k IS and ISCalculate the characteristic strength Q and post-yield stiffness k of the isolation layer p ;

[0049] Step S507, non-elastic upper building structure design, based on the base shear force V calculated by equivalent parameters B Determine the seismic force on each floor of the upper building structure, and thus calculate the design seismic force F on each floor of the upper building structure ei , the formula can be obtained from the following formula (3):

[0050]

[0051] in, Δ i is the displacement of the i-th layer superstructure relative to the ground;

[0052] Step S508, calculate the design shear force V of each layer of the upper structure Si , the actual yield bearing capacity of each layer of the superstructure F yi By V Si Multiply by the super strength factor Ω 0 The yield displacement u of each layer of the upper structure is calculated according to the initial stiffness of each layer of the upper structure according to formula (4). yi , thus completing the inelastic design of the superstructure.

[0053] u yi =F yi / k i (4)

[0054] in, F ei That is F ej ,

[0055] F yi =Ω 0 V Si

[0056] Step S509: initial stiffness k of the upper building structure s =k s,eq , where k s,eq It can be obtained from formula (5):

[0057]

[0058] Among them, T s,eq is the equivalent period of the upper building structure, T s,eq =T s The equivalent method of the upper building structure can control the displacement through Pushover static analysis and obtain the top floor displacement U n and the shear force V at the bottom of the upper building structure bThe curve is simplified into a double-broken line curve and converted into the spectral pseudo-acceleration A-spectral displacement D format (ADRS), that is:

[0059]

[0060] in, is the equivalent mass of the upper structure according to the first vibration mode, Φ n1 is the first mode coefficient of the top floor, which is taken as 1 here; Φ j1 is the first mode coefficient of the jth layer; the inflection point of the double-fold line is taken as D y and A y , so there is a formula Γ 1 and Formula (6) is as follows:

[0061]

[0062] Step S510: The characteristic strength Q of the seismic isolation layer is calculated by the following formula (7):

[0063]

[0064] Among them, the post-isolation layer yield stiffness k p pass: Calculate the yield displacement d of the isolation layer. yb Calculate the initial stiffness of the isolation layer:

[0065]

[0066] Step S5111, according to the above steps S51-S510, the 2DOF system Bouc-Wen model parameters are obtained, and 9 structural parameters of the base isolation structure are extracted based on the 2DOF system Bouc-Wen model parameters; the base isolation structure is used as the test isolation structure, and the 9 structural parameters of the base isolation structure are used as the 9 structural parameters of the test isolation structure, wherein the 9 structural parameters are extracted, including:

[0067] M is a 2DOF model With m IS The sum of γ m is the mass ratio, d ys is the yield displacement of the upper building structure, d ys =D y ; α s is the post-yield stiffness ratio of the upper structure, that is, the post-yield stiffness and the initial equivalent stiffness k of the upper structure s,eq The ratio of T s is the basic period of the superstructure structure, ξ ISis the structural damping ratio of the 2DOF model, which can be obtained according to formula (8):

[0068]

[0069] Among them, μ eq and ε eq They are:

[0070]

[0071] α b is the yield stiffness ratio of the isolation layer, k IS / k E ; T b is the natural vibration period of the 2DOF model, calculated according to the formula; q D is the yield-to-weight ratio of the seismic isolation layer, defined as k IS Total weight of the superstructure m T ×g ratio;

[0072]

[0073] Furthermore, in the above method, step S6 includes:

[0074] Step S61, select 80 seismic waves corresponding to the design site, with a magnitude greater than or equal to 5, and select the waves from 19742 seismic waves obtained from the NGAWest2 database; perform 32 peak acceleration amplitude modulations of 0 to 1.6g with an interval of 0.05g in the same way as step S13, and generate a total of 2560 seismic waves, extract seismic wave parameters from these 2560 seismic waves, and perform OpenSees finite element analysis based on the 9 structural parameters of the test isolation structure, and output the maximum displacement D of the equivalent mass point of the upper building structure s The maximum displacement D of the particle with the seismic isolation layer b ;

[0075] Step S62: Input the structural parameters of the test isolation structure and the corresponding seismic wave parameters of each test seismic wave into the prediction model to obtain the maximum displacement D of the equivalent mass point of the upper building structure. s The maximum displacement D of the particle with the seismic isolation layer b , as the prediction output;

[0076] Step S63, perform OpenSees finite element analysis on each structural parameter of the test isolation structure and each seismic wave parameter of each corresponding test seismic wave to obtain the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the test isolation structure. s The maximum displacement D of the particle with the seismic isolation layer b , as the calculation result;

[0077] Step S64: Based on a preset evaluation method, evaluate and compare the predicted output and the calculated output to obtain a prediction model that passes the evaluation.

[0078] Further, in the above method, step S7 includes:

[0079] Step S71: Obtain the upper building structure DM: Based on the horizontal maximum displacement D of the upper building structure s and the horizontal maximum displacement D of the seismic isolation layer b , find α and β in DM, and fit to find α and β. DM is the median of the maximum horizontal displacement of the upper building structure under IM; DM = α(IM) β , through the logarithmic regression of the following formula (9), a = lnα, b = β, IM is the PGA under different seismic wave amplitude modulations,

[0080] ln(DM) = a + bln(IM) (9);

[0081] Step S72: Based on DM, find the standard deviation σ of the maximum horizontal displacement of the structure in IM ln(DM|IM) , calculate through the following formula (10), where μ ln(DM|IM) is the median of the structure in IM (PGA under different seismic wave amplitude modulations),

[0082]

[0083] where N represents 80, that is, 80 seismic waves;

[0084] Step S73: Seismic performance evaluation result: Use the exceedance probability to represent the conditional probability that the upper building structure and the seismic isolation layer exceed the design index under the PGA under different seismic wave amplitude modulations, that is, the exceedance probability. The exceedance probability is represented by the following formula (11), and the vulnerability curves (seismic performance) of the upper building structure and the seismic isolation layer are drawn. The above design index includes the target design value

[0085] P(DM≥DO|IM) = 1 - P(DM<DO|IM). Through conversion (ln(DM) = a + bln(IM)), the above formula is written as:

[0086]

[0087] DO represents the target design value

[0088] Compared with the prior art, the present invention starts from the design idea of ​​DDBD seismic isolation structure and proposes a design method based on machine learning. By determining the target value, the parameters of the seismic isolation layer and the upper building structure are calculated, and the 2DOF model is equivalent to extracting 9 structural parameters and 13 seismic wave parameters of the seismic wave. The vulnerability curve based on the target value can be quickly predicted by BO-XGBoost to intuitively guide the seismic isolation structure design of DDBD. This is a faster and more efficient method, which helps to improve the DDBD idea of ​​seismic isolation structure. The results show that the prediction results are good, and in the case of open sets, good prediction accuracy can still be achieved. It can be seen from the predicted vulnerability curve that the predicted curve is close to the real data and can be used as a reference for DDBD structural design. It can also be seen from the vulnerability curve that the DDBD design process can effectively enable the seismic isolation structure to achieve the expected goals under earthquakes.

[0089] The present invention can quickly identify and quantify damage by analyzing historical earthquake data and structural response characteristics, providing engineers with real-time decision support, thereby improving the safety and resilience of buildings and promoting the sustainable development of cities. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 is a flow chart of a damage prediction method for a seismic isolation structure designed by a direct displacement method according to an embodiment of the present invention;

[0091] Figure 2 This is a flow chart of an XGBoost model training method according to an embodiment of the present invention;

[0092] Figure 3 Schematic diagram of the principle steps of a direct displacement design method according to an embodiment of the present invention;

[0093] Figure 4 FIG. 4 is a schematic diagram of DDBD design steps according to an embodiment of the present invention. DETAILED DESCRIPTION

[0094] The present invention is further described in detail below in conjunction with the accompanying drawings.

[0095] In a typical configuration of the present application, the terminal, the device of the service network and the trusted party all include one or more processors (CPU), input / output interfaces, network interfaces and memories.

[0096] The memory may include non-permanent storage in a computer-readable medium, random access memory (RAM) and / or non-volatile memory in the form of read-only memory (ROM) or flash RAM. The memory is an example of a computer-readable medium.

[0097] Computer readable media include permanent and non-permanent, removable and non-removable media that can be implemented by any method or technology to store information. Information can be computer readable instructions, data structures, program modules or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, magnetic tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device. As defined herein, computer readable media does not include non-transitory media such as modulated data signals and carrier waves.

[0098] How to quickly and accurately predict the seismic performance of seismic isolation structures is currently the focus of research in this field. Machine learning prediction is a very convenient and effective method that has been relatively maturely applied in the field of structural engineering and has good generalization performance for predicting data within the database range. However, when the parameters of the seismic isolation structure and the earthquake parameters are relatively random and are not within the range of the training data, there are relatively few studies on their prediction results.

[0099] To this end, the present application proposes a prediction model based on machine learning, which uses commonly used rubber bearings. By treating the seismic isolation layer and the upper and lower parts of the upper building structure of the seismic isolation structure as equivalent to a double degree of freedom (2DOF) system, a prediction model for predicting the damage degree of the seismic isolation structure can be quickly established based on the double degree of freedom (2DOF) system, and the prediction range of the prediction model can be expanded through the structural parameters of the double degree of freedom (2DOF) system, and the prediction range of the prediction model can be expanded in a wider range of earthquake magnitude M and fault projection distance R. jb The prediction model is trained within a wide range of structural parameters of the dual degree of freedom (2DOF) system. The seismic performance of the seismic isolation structure designed based on the direct displacement design method (DDBD) is evaluated through the prediction model, and the influence of the randomness of the ground motion is solved through vulnerability analysis. This method can quickly and accurately predict the seismic performance of the seismic isolation structure designed by DDBD under freely selected ground motion excitation. Specifically, the magnitude M of the ground motion and the fault projection distance R jb The two seismic wave characteristics can be used to select representative seismic waves.

[0100] like Figure 1 As shown, the present invention provides a damage prediction method for a seismic isolation structure designed by a direct displacement method, and the method includes: steps S1 to S7.

[0101] Step S1, generating preset sample seismic waves and establishing various seismic wave parameters of each sample seismic wave;

[0102] Each piece of seismic wave data corresponds to a set of seismic wave parameters; this step generates each set of seismic wave parameters for subsequent prediction model training of the damage degree of the seismic isolation structure;

[0103] Preferably, step S1 includes:

[0104] Step S11, seismic wave data collection. Use the NGAWest2 seismic wave database in the Pacific Earthquake Engineering Research Center (PEER) to collect, organize and classify seismic wave data; obtain 19742 first seismic waves, select seismic waves with a magnitude greater than 5 from the 19742 first seismic waves, and screen out a total of 7274 second seismic waves; divide the 7274 screened second seismic waves into 4 categories according to the equivalent shear wave velocity of the soil layer and the thickness of the site covering soil layer in accordance with China's "Code for Seismic Design of Buildings" (GB50011.2010). Among them, since the seismic motion records released by PEER only provide V s30 Therefore, this application establishes the site type and V s30 Corresponding relationship: First category site V s30 >550m / s, the second type of site Vs30 is 265~550m / s, the third type of site V s30 165~265m / s, the fourth type of site V s30 <165m / s;

[0105] Step S12: Select the seismic waves of the first, second and third types of sites from the 7274 second seismic waves as the third seismic waves, and for each type of the third seismic waves, respectively select the seismic waves according to the magnitude M and the fault projection distance R in the seismic wave. jb , and divided into 4 groups of data by Gaussian mixture model (GMM) distribution clustering method, from the first, second and third types of sites in the third seismic wave, a total of 3×4=12 groups (clusters) of data were obtained;

[0106] Preferably, in step S12, for each type of the selected third seismic wave, the magnitude M and the fault projection distance R in the seismic wave are respectively jb (the most representative feature of seismic wave intensity), and divided into 4 groups (clusters) of data by Gaussian mixture model (GMM) distribution clustering method, including:

[0107] Step S121, using the fault projection distance R in the seismic wavejb and magnitude M are clustering parameters and normalized to obtain normalized data; here, because R jb The order of magnitude is much larger than M, so these two data are normalized to reduce R jb The scale difference with M;

[0108] Step S122, based on the normalized data of each type of site, Gaussian mixture model (GMM) cluster analysis is performed on each type of site, and the Gaussian mixture model (GMM) clustering effect is evaluated by setting different groups (clusters) for each type of site, and the Bayesian information criterion BIC is used to evaluate the Gaussian mixture model (GMM):

[0109] BIC = -2ln(L) + kln(n), where k is the number of model parameters; n is the number of samples; L is the maximum likelihood estimate of the model;

[0110]

[0111] Among them, K is the number of groups (clusters) (i.e., the number of Gaussian distributions); D is the characteristic dimension, with magnitude M and fault projection distance R jb That is, take 2;

[0112] The lower the BIC value, the better the clustering effect, while taking into account the complexity of the model. kln(n) penalizes the number of model parameters, selects a simple model, and avoids overfitting; the number of groups (clusters) K of the first, second, and third types of sites are clustered according to 1 to 20. According to the BIC value of the cluster analysis, when K is four clusters, the model BIC curve appears flat, so we subdivide the category of each type of site in the model into four groups. The purpose is to more finely select the representative seismic waves in each cluster to reduce the amount of calculation.

[0113] Among them, GMM is a powerful probabilistic model used to represent complex data sets composed of multiple Gaussian distributions. Unlike hard clustering algorithms such as K-means, the GMM soft clustering algorithm provides the probability of each seismic wave belonging to each group (cluster). This soft clustering method can describe uncertainty, especially when the seismic wave characteristics may have fuzzy boundaries or overlap. Each seismic wave data is regarded as originating from one of multiple Gaussian distributions, which represent different subgroups or clusters in the data. The seismic waves are divided into four groups through GMM clustering, and the differences in the response spectrum characteristics can be clearly distinguished.

[0114] Step S13: Filter the seismic waves of each of the 12 groups (clusters) of data by using a grid screening method: that is, filter the seismic waves of each of the 12 groups (clusters) of data by using the magnitude M and the fault projection distance R. jb为The horizontal and vertical axes are divided into a 3×3 grid to obtain 9 magnitudes M and fault projection distances R jb range; the grids other than the central grid in the 3×3 grid are used as peripheral grids, 2 seismic waves are randomly selected from each grid in the peripheral grid, and 16 seismic waves are obtained from 8 peripheral grids; 4 seismic waves are randomly selected from the middle grid, so that 20 seismic waves are selected from each group of data, and a total of 20×4×3=240 seismic waves are selected from 12 groups (clusters) of three types of sites as the fourth seismic wave. Here, the parameters of each seismic wave are as shown in Table 1:

[0115] Table 1 Seismic wave parameter extraction

[0116]

[0117] Step S13: The selected 240 fourth seismic waves are amplitude modulated, wherein the PGA (peak ground acceleration) of each seismic wave is 0.05~1.6g, the step length is 0.05g, and the amplitude modulation is performed 32 times in total, and 240*32=7680 sample seismic waves are obtained as excitation for structural calculation, and the seismic wave parameters (13 features) in Table 1 of the 7680 sample seismic waves are extracted, which can be used as part of the machine learning input of the prediction model later.

[0118] Step S2, based on the preset sample seismic waves, calculating and generating the structural parameters of the sample seismic isolation structures of the same corresponding number, and establishing a one-to-one correspondence between each sample seismic wave and a corresponding sample seismic isolation structure;

[0119] Among them, each isolation structure corresponds to a set of structural parameters;

[0120] Preferably, step S2 comprises:

[0121] Step S21, calculate the structural parameters of the equivalent dual-degree-of-freedom model (2DOF model) to be generated as the input of the subsequent prediction model. There are a total of nine structural characteristic parameters as shown in Table 2. The values ​​of these nine structural characteristic parameters are set within the range described in Table 2. According to the Latin hypercube (LHS) and the range taken in Table 2, the structural parameters of 7680 sample isolation structures corresponding to the number of sample seismic waves are randomly generated according to the normal distribution, and a one-to-one correspondence between the seismic wave parameters of a seismic wave and the structural parameters of a random isolation structure in the sample isolation structure is established. In the subsequent steps, a double mass (dual-degree-of-freedom model) formed by the 7680 seismic waves corresponding to S13 and the structural parameters can be established; preferably, according to the Bouc-Wen model parameters of the 2DOF system, 9 features can be extracted and input into machine learning, as shown in Table 2. Wherein, M is the sum of the upper mass of the 2DOF model and the mass of the isolation layer, γ mis the mass ratio (the ratio of the upper building structure mass to the total mass of 2DOF), d ys is the yield displacement of the upper building structure, α s is the post-yield stiffness ratio of the upper structure (post-yield stiffness divided by the initial equivalent stiffness k of the upper structure). s,eq ratio), T s is the basic period of the superstructure structure, ξ IS is the structural damping ratio of the 2DOF model, α b is the yield stiffness ratio of the isolation layer (k IS / k E ), T b is the natural oscillation period of the 2DOF model, q D is the yield-to-weight ratio of the seismic isolation layer, defined as the accident stiffness k of the seismic isolation layer IS Total weight of the superstructure m T ×g ratio.

[0122] Table 2 Structural parameter characteristics

[0123]

[0124] Preferably, it should be noted that in the Latin hypercube (LHS) generation, M is associated with γm, that is, the value range of γm is determined according to the value of M. For example, when M is randomly generated between 300 and 400, the value of γm is randomly generated in the range of [0.6, 0.65, 0.7]. In this way, many different random seismic isolation structures are established, and the range is wider. Subsequently, the equivalent two-degree-of-freedom models (2DOF models) of 7680 random sample seismic isolation structures can be generated.

[0125] Step S3, based on the structural parameters of the isolation structure, the corresponding equivalent double degree of freedom model (2DOF model) is established using OpenSees finite element software; based on the equivalent double degree of freedom model (2DOF model) and the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, the maximum displacement D of the equivalent mass point of the upper building structure of the corresponding sample isolation structure is obtained. s The maximum displacement D of the particle with the seismic isolation layer b , can be stored in a database;

[0126] Preferably, step S3 includes:

[0127] Step S31, using OpenSees finite element software to establish an equivalent two-degree-of-freedom model (2DOF model), wherein the OpenSees finite element software adopts the Bouc-Wen model, that is, a double-fold line model for modeling, and both the upper building structure and the isolation layer are simulated by the double-fold line model; based on the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure determined in step S2, the acceleration and time series of the sample seismic wave, the equivalent two-degree-of-freedom model is subjected to nonlinear time history analysis to obtain the maximum displacement D of the equivalent mass point of the upper building structure of the sample isolation structure s The maximum displacement D of the particle with the seismic isolation layer b , as the subsequent real data for the training of the prediction model; here, the OpenSees finite element software uses the Bouc-Wen model, that is, the double-fold line model for modeling, and the upper building structure and the isolation layer are simulated by the double-fold line model. Among them, the upper building structure and the isolation layer are connected by OpenSees's "Elastomeric Bearing (Bouc-Wen) Element". Because the high-order mode has little effect on the upper building structure, it is reasonable to use this inelastic shear element. In the Bouc-Wen modeling, its main parameters: Post-yield stiffness ratio of linear hardening component is 0.05; Post-yield stiffness ratio of nonlinear hardening component is 0; Exponent of nonlinear hardening component is 1; Yielding exponent (sharpness of hysteresis loop corners) is 2; Firsthysteretic shape parameter is 0.5; Second hysteretic shape parameter is 0.5.

[0128] Step S4: based on the seismic wave parameters of the sample seismic wave and the structural parameters of the corresponding sample seismic isolation structure, and the maximum displacement D of the equivalent mass point of the corresponding upper building structure, s The maximum displacement D of the particle with the seismic isolation layer b And through XGBoost model training and Bayesian hyperparameter optimization, a prediction model for predicting the damage degree of the seismic isolation structure is trained to obtain a trained prediction model;

[0129] Preferably, step S4 comprises:

[0130] XGBoost model training and Bayesian hyperparameter optimization. The steps for training the prediction model are as follows: Figure 2 As shown;

[0131] The 13 seismic wave parameters of the sample seismic wave as shown in Table 1 and the 9 structural parameters of the corresponding sample seismic isolation structure as shown in Table 2 are used as input, and the maximum displacement D of the equivalent mass point of the corresponding upper building structure is s The maximum displacement D of the particle with the seismic isolation layer b As the output target, a prediction model for predicting the damage degree of the seismic isolation structure is trained;

[0132] Here, the corresponding maximum displacement D of the equivalent mass point of the upper building structure is established. s The maximum displacement D of the particle with the seismic isolation layer b After that, machine learning prediction can be performed based on this, so that the structural response can be predicted quickly. First, the 13 seismic wave parameters in Table 1 and the 9 structural parameters in Table 2 are used as input, and the maximum displacement D of the equivalent upper building structure is calculated. s The maximum displacement of the isolation layer D b As output. Preferably, the training set R can be found by using the grid search method (random_state is searched in the range of 0 to 1000, and the proportion of the training set is divided into 7680). 2 The segmentation method with the highest (coefficient of determination) score divided the database into 80% of the samples as the training set and 20% of the samples as the validation set, and extreme gradient boosting (XGBoost) was used for machine learning prediction.

[0133] Step 41, each time 80% of the data is selected from the sample seismic waves, and random_state is searched in the range of 0 to 1000 according to the grid search method, and the determination coefficient R of the currently selected 80% of the data is calculated. 2 ;

[0134] Step 42, determine the coefficient R 2 When the score is the highest, 80% of the data is selected as the training set, and the remaining 20% ​​of the data in the sample seismic wave is used as the validation set;

[0135] Step 43, when constructing the XGBoost prediction model, firstly, the benchmark model is used to perform an exploratory analysis on the potential explanatory variables (hyperparameters), so as to screen out the hyperparameters that contribute most to the model prediction ability; then, based on the training set, on the basis of the screened out hyperparameters that contribute most, the intelligent optimization method is applied to fine-tune the hyperparameters of various machine learning algorithms;

[0136] Step 44, in the model training stage, in order to improve the generalization ability of the model, we divide the validation set into multiple subsets by random sampling, and implement a five-fold cross-validation procedure to obtain a trained prediction model to ensure the stability and reliability of the evaluation results. Among them, the evaluation standard is based on the root mean square error (RMSE) to guide the optimization process of hyperparameters, aiming to find the hyperparameter configuration with the best balance between fitting and generalization. Through this comprehensive method, it is intended to build a machine learning model with high prediction accuracy and strong generalization ability.

[0137] Here, in the field of machine learning, hyperparameter tuning is often regarded as a complex optimization challenge, which is similar in nature to a "black box" problem. The choice of hyperparameters has a great impact on the prediction accuracy of machine learning. Traditional gradient descent methods may not be applicable in this case because the objective function may not be differentiable or the derivative is difficult to calculate. Therefore, metaheuristic algorithms have become one of the preferred methods for dealing with such optimization problems because they can explore the decision space without gradient information and are generally applicable to a variety of problems.

[0138] These algorithms usually rely on simulations of natural or social behavior strategies rather than direct mathematical gradient methods to search for the global optimum or near-optimal solution among a wide range of potential solutions. A typical meta-heuristic optimization algorithm is Bayesian Optimization (BO): a probabilistic model that updates posterior knowledge using prior knowledge and data collected from the objective function, and then guides sampling decisions during the search process to effectively approximate the global optimal solution.

[0139] The BO algorithm has been applied in many complex and multivariable optimization scenarios, including the selection and adjustment of hyperparameters in machine learning models. It provides a powerful and flexible toolset for effective hyperparameter optimization. Table 3 below shows the selection range of XGBoost machine learning hyperparameters. In order to reduce the computational cost and determine a better hyperparameter configuration, this application implemented 100 rounds of hyperparameter optimization iterations on the training set and test set.

[0140] Table 3: Hyperparameters that need to be adjusted in the XGBoost algorithm

[0141]

[0142] Step S5, using DDBD to design a seismic isolation structure to obtain a generated test seismic isolation structure and its various structural parameters;

[0143] Here, DDBD is used to design and test the seismic isolation structure to determine the basic information and performance targets. Pushover analysis is performed on the designed seismic isolation structure, which is equivalent to a 2DOF bilinear model, to extract the structural characteristic parameters of the test seismic isolation structure;

[0144] The isolation structure based on DDBD is designed by determining the horizontal displacement performance of the isolation structure to design the horizontal mechanical performance parameters of the isolation structure. The main idea is to equate the multi-layer isolation structure to 2DOF, so as to calculate its seismic response to determine its horizontal mechanical performance parameters. Since the upper building structure is assumed to be linear elastic, based on this, the inelastic upper design is further carried out, and the designed isolation upper building structure is equivalent to a single-particle system with a double-broken line mechanical model through Pushover.

[0145] Preferably, Figure 4 As shown, the DDBD design steps (designing a real test set):

[0146] Step S501, determine the basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure, wherein, according to the preliminary design, the upper building structure can be equivalent to Figure 3 The multi-degree-of-freedom system shear-type structure model shown on the left is based on the mass m of the i-th layer of the multi-degree-of-freedom system shear-type structure model. i , horizontal lateral stiffness k i , damping coefficient c i And the floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s , D s,eq ; Among them, D s,eq The equivalent displacement required to maintain the superstructure;

[0147] Step S502, clarify the performance objectives of the base isolation structure: under the design earthquake or rare earthquake, the upper building structure must remain intact, the main body and non-structural components of the upper building structure should not be damaged, and the maximum inter-story displacement angle is set to The performance target of the lead rubber isolation bearing is the design displacement under the design earthquake or rare earthquake.

[0148] Step S503, based on the basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure and the performance target of the lead rubber isolation bearing, calculate the target displacement curve of the upper building structure in the base isolation structure, such as Figure 3 As shown on the left, D 1 and D i are the deformations of the first and i-th layers of the upper building structure respectively; D i It is expressed as the following formula (1):

[0149]

[0150] In formula (1), Φ 1 and Φ i is the normalized function of the horizontal displacement of the first and i-th floors of the upper building structure, which is determined by the period ratio R IS 、h i , the total height H of the upper building structure is calculated, where R IS =T IS / T S , T IS is the fundamental period of the base isolation structure, T S is the basic period of the superstructure structure;

[0151] Step S504: establish a multi-degree-of-freedom system shear type structure model according to the target displacement curve of the upper building structure in the base isolation structure, and calculate the target displacement D of the upper building structure based on the DOF equivalent model. s,eq , equivalent mass m s,eq and the equivalent height h s,eq ;

[0152] Step S505, calculate the new cycle ratio R IS , wherein the period ratio R in step S503 is IS Assuming the period ratio R IS , through the new cycle ratio R IS Until convergence, the new cycle is R IS It is calculated by the following explicit expression (2):

[0153] Display expressions:

[0154] The design displacement D IS,eq ,

[0155] In formula (2), m T is the total mass of the superstructure, m IS is the mass of the seismic isolation layer; where m T According to the basic information, m IS It is one of the basic information;

[0156] Step S506: Based on the new cycle ratio R calculated in step S55 IS， Calculate the equivalent stiffness k of the base-isolated structure IS and the equivalent damping ratio, where the equivalent stiffness k IS Equivalent stiffness k of shear-type structural model of multi-degree-of-freedom system IS,eq are equal; among them, the equivalent damping ratio ξ of the base isolation structure ISFrom the first-order modal damping ratio ξ 1,eq Calculated; the first-order modal damping ratio ξ 1,eq According to the designed displacement spectrum, the first modal period T of the shear structure model of the multi-degree-of-freedom system is 1,eq and Interpolation is then used to determine the yield displacement d of the seismic isolation layer. yb , according to k IS and IS Calculate the characteristic strength Q of the seismic isolation layer (used in the subsequent step S60) and the post-yield stiffness k p (Used in the subsequent step S60).

[0157] Step S507, non-elastic upper building structure design, based on the base shear force V calculated by equivalent parameters B Determine the seismic force on each floor of the upper building structure, and thus calculate the design seismic force F on each floor of the upper building structure ei , the formula can be obtained from the following formula (3):

[0158]

[0159] in, Δ i is the displacement of the i-th layer superstructure relative to the ground;

[0160] Step S508, calculate the design shear force V of each layer of the upper structure Si , the actual yield bearing capacity of each layer of the superstructure F yi By V Si Multiply by the super strength factor Ω 0 The yield displacement u of each layer of the upper structure is calculated according to the initial stiffness of each layer of the upper structure according to formula (4). yi , thus completing the inelastic design of the superstructure.

[0161] u yi =F yi / k i (4)

[0162] in, F ei That is F ej ,

[0163] F yi =Ω 0 V Si

[0164] Steps S501 to S508 are for designing multi-degree-of-freedom mechanical model parameters, and subsequent steps S509 to S511 can be used to deduce 9 model characteristic parameters based on the parameters of the multi-degree-of-freedom mechanical model parameters, which serve as a real test set for the subsequent prediction model;

[0165] The Bouc-Wen model uses a double-fold line model, and the upper building structure and the isolation layer both use double-fold line stiffness. The parameters calculated by DDBD need to be converted. Because the DDBD program assumes that the upper building structure is in a linear elastic state, when establishing the database, it is necessary to further equate the inelastic upper building structure to a single-particle system of the double-fold line mechanical model.

[0166] Step S509: initial stiffness k of the upper building structure s =k s,eq , where k s,eq It can be obtained from formula (5):

[0167]

[0168] Among them, T s,eq is the equivalent period of the upper building structure, T s,eq =T s The equivalent method of the upper building structure can control the displacement through Pushover static analysis and obtain the top floor displacement U n and the shear force V at the bottom of the upper building structure b The curve is simplified into a double-broken line curve and converted into the spectral pseudo-acceleration A-spectral displacement D format (ADRS), that is:

[0169]

[0170] in, is the equivalent mass of the upper structure based on the first vibration mode. n1 is the coefficient of the first vibration mode of the top layer, which is taken as 1 here. Φ j1 is the first mode coefficient of the jth layer. The inflection point of the double-fold line is D y and A y , so there is a formula Γ 1 and Formula (6) is as follows:

[0171]

[0172] Step S510: The characteristic strength Q of the seismic isolation layer is calculated by the following formula (7):

[0173]

[0174] Among them, the post-isolation layer yield stiffness kp pass: Then, the yield displacement d of the seismic isolation layer can be obtained. yb Calculate the initial stiffness of the isolation layer:

[0175]

[0176] Step S5111, according to the above steps S51-S510, the 2DOF system Bouc-Wen model parameters are obtained, and the 9 structural parameters of the base isolation structure as shown in Table 2 are extracted based on the 2DOF system Bouc-Wen model parameters; the base isolation structure is used as the test isolation structure, and the 9 structural parameters of the base isolation structure are used as the 9 structural parameters of the test isolation structure. The trained prediction model can be input for machine learning test later, wherein the 9 structural parameters are extracted, including:

[0177] M is a 2DOF model With m IS The sum of γ m is the mass ratio, d ys is the yield displacement of the upper building structure, d ys =D y ; α s is the post-yield stiffness ratio of the upper structure, that is, the post-yield stiffness and the initial equivalent stiffness k of the upper structure s,eq The ratio of T s is the basic period of the superstructure structure, ξ IS is the structural damping ratio of the 2DOF model, which can be obtained according to formula (8):

[0178]

[0179] Among them, μ eq and ε eq They are:

[0180]

[0181] Table 2 b is the yield stiffness ratio of the isolation layer, k IS / k E ; T b is the natural vibration period of the 2DOF model, calculated according to the formula; q D is the yield-to-weight ratio of the seismic isolation layer, defined as k IS Total weight of the superstructure m T ×g ratio;

[0182]

[0183] Step S6, evaluating the trained prediction model to obtain a qualified prediction model: generating each test seismic wave corresponding to the test seismic isolation structure; performing OpenSees finite element analysis based on each structural parameter of the test seismic isolation structure and each seismic wave parameter of each corresponding test seismic wave, and obtaining the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the test seismic isolation structure. s The maximum displacement D of the particle with the seismic isolation layer b , as the calculation result; based on the various structural parameters of the second seismic isolation structure and the corresponding various seismic wave parameters of the corresponding second seismic waves, and the corresponding maximum displacement D of the equivalent mass point of the upper building structure s The maximum displacement D of the particle with the seismic isolation layer b , evaluate the trained prediction model to obtain a qualified prediction model;

[0184] Preferably, step S6 includes: seismic wave selection and structural BO-XGBoost response prediction;

[0185] Specifically, in step S61, 80 seismic waves corresponding to the design site are selected, and the magnitude is greater than or equal to 5. The wave selection method is based on the standard response spectrum in China's "Code for Seismic Design of Buildings" (GB50011.2010), and is selected from 19742 seismic waves obtained from the NGAWest2 database; according to the same method as step S13, 32 peak acceleration amplitude modulations of 0 to 1.6g and an interval of 0.05g are performed to generate a total of 2560 seismic waves, and seismic wave parameters are extracted from these 2560 seismic waves. Based on the 9 structural parameters of the test isolation structure obtained in step S5, OpenSees finite element analysis is performed to output the maximum displacement D of the equivalent mass point of the upper building structure. s The maximum displacement D of the particle with the seismic isolation layer b , which can be used as a machine learning evaluation later. Subsequently, the various structural parameters of the test isolation structure and the corresponding characteristic values ​​of the seismic wave parameters of each test shock wave can be input into the machine learning model trained by S6, and 2560 sets of machine learning response predictions can be obtained.

[0186] Step S62: Input the structural parameters of the test isolation structure and the corresponding seismic wave parameters of each test seismic wave into the prediction model to obtain the maximum displacement D of the equivalent mass point of the upper building structure. s The maximum displacement D of the particle with the seismic isolation layer b , as the prediction output;

[0187] Step S63, perform OpenSees finite element analysis on each structural parameter of the test isolation structure and each seismic wave parameter of each corresponding test seismic wave to obtain the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the test isolation structure.s The maximum displacement D of the particle with the seismic isolation layer b , as the calculation result;

[0188] Here, the features of these 2560 seismic waves can be extracted, and the 9 structural parameters of the 2DOF model can be combined to perform OpenSees finite element analysis to output the maximum displacement D of the equivalent mass point of the upper building structure. s The maximum displacement D of the particle with the seismic isolation layer b , as the calculation result;

[0189] Step S64, based on a preset evaluation method, the predicted output and the calculated output are evaluated and compared to obtain a qualified prediction model.

[0190] Here, the model after hyperparameter tuning can be evaluated on the aforementioned validation set and the test set generated by the 2DOF model calculated by the DDBD program. The evaluation methods include: Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MARE).

[0191] Step S7: Input the actual structural parameters (9) and seismic wave parameters (13) of the seismic isolation structure to be evaluated into the qualified prediction model to obtain the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the actual seismic isolation structure to be evaluated. s The maximum displacement D of the particle with the seismic isolation layer b ; Based on the actual maximum displacement D of the equivalent mass point of the upper building structure corresponding to the seismic isolation structure to be evaluated s The maximum displacement D of the particle with the seismic isolation layer b , conduct vulnerability analysis and prediction on the actual seismic isolation structure to be evaluated, thereby completing the seismic performance evaluation of the actual seismic isolation structure to be evaluated.

[0192] Specifically, incremental dynamic analysis (IDA) is to observe the damage degree of the structure by applying gradually increasing earthquake intensity to the structure. The earthquake intensity index (IM) usually used is peak ground acceleration (PGA) or peak ground velocity (PGV). This paper uses PGA amplitude modulated seismic waves as the intensity index.

[0193] Probabilistic seismic demand analysis (PSDA) is a method used to evaluate the structural response requirements of a structure under earthquake action, which comprehensively considers the seismic intensity (IM) and the structural damage index (DM, which is the maximum horizontal displacement D of the upper building structure in this application).s , maximum horizontal displacement of the isolation layer D b This application hopes to show that the structure exceeds the design objective (Design Objective, which is the target design value proposed in this paper) under different IM. ), and then use regression analysis to obtain the exceedance probability of the structure.

[0194] Step S71, calculate the upper building structure DM: based on the maximum horizontal displacement D of the upper building structure s and the maximum horizontal displacement D of the isolation layer b , find out α and β in DM, and find out α and β by fitting. DM is the median value of the maximum horizontal displacement of the upper building structure under IM; DM = α (IM) β , through the logarithmic regression of the following formula (9), a = lnα, b = β, IM is the PGA under different seismic wave amplitude modulation,

[0195] ln(DM)=a+bln(IM) (9)

[0196] Here, 2560 seismic waves are obtained by scaling 80 seismic waves. Based on the 2560 seismic waves, the horizontal structural response of the two-particle 2DOF model of the original structure can be calculated. The seismic wave parameters of the extracted 2560 seismic waves are input into the trained prediction model to obtain the horizontal structural response predicted by BO-XGBoost and the predicted response under different PGA amplitude modulations. The logarithm of the median maximum displacement under each seismic wave amplitude modulation is taken and fitted with ln(PGA) to obtain the fitting curve, the corresponding curve equation and the fitting score R 2 .

[0197] Step S72: Based on DM, find the standard deviation σ of the maximum horizontal displacement of the structure in IM ln(DM|IM) , calculated by the following formula (10), where μ ln(DM|IM) is the median value of the structure in IM (PGA under different seismic wave amplitude modulation),

[0198]

[0199] Among them, N represents 80, that is, 80 seismic waves;

[0200] Step S73, seismic performance evaluation results: The exceedance probability is used to represent the conditional probability that the upper building structure and the seismic isolation layer exceed the design index under the PGA under different seismic wave amplitude modulation, that is, the exceedance probability. The exceedance probability is expressed by the following formula (11), which can be used to draw the vulnerability curve (seismic performance) of the upper building structure and the seismic isolation layer. The above design indicators include the target design value

[0201] P(DM≥DO|IM) = 1 - P(DM < DO|IM). Through transformation (ln(DM) = a + bln(IM)), the above equation can be written as:

[0202]

[0203] DO represents the target design value

[0204] In the present invention, by inputting the seismic wave parameters and the structural parameters extracted from a two-degree-of-freedom (2DOF) system into a prediction model for predicting the damage degree of a base-isolated structure, the maximum horizontal displacements of the upper and lower structures of the two-degree-of-freedom (2DOF) system can be output.

[0205] The present invention can provide new ideas for construction engineers to judge the seismic performance of base-isolated structures and further provide a reference for evaluating the health status of base-isolated structures.

[0206] In vulnerability analysis, the determination of the damage index DM will affect the evaluation results. The damage index adopted in this patent is the target design value proposed during the design process Equivalent to a two-degree-of-freedom system, the maximum horizontal displacement D of the upper building structure mass point s , the maximum displacement D of the isolation layer b .

[0207] The beneficial effects of the present invention are as follows:

[0208] Starting from the design idea of the base-isolated structure of DDBD, the present invention proposes a design method based on machine learning. By determining the target value, the parameters of the isolation layer and the upper building structure can be calculated, and a 2DOF model can be equivalent. Nine structural parameters and thirteen seismic wave parameters of the seismic wave can be extracted, and then the vulnerability curve based on the target value can be quickly predicted by BO-XGBoost to intuitively guide the design of the base-isolated structure of DDBD. This is a more rapid and efficient method, which helps to improve the DDBD idea of the base-isolated structure. The results show that the prediction results are good, and even in the case of an open set, a relatively good prediction accuracy can still be achieved. From the predicted vulnerability curve, it can be seen that the predicted curve is close to the real data and can be used as a reference for the design of the DDBD structure. It can also be seen from the vulnerability curve that the DDBD design process can effectively enable the base-isolated structure to achieve the expected goal under earthquakes.

[0209] The present invention can quickly identify and quantify damage by analyzing historical earthquake data and structural response characteristics, provide real-time decision support for engineers, and thus improve the safety and resilience of buildings and promote the sustainable development of cities.

[0210] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

[0211] It should be noted that the present invention can be implemented in software and / or a combination of software and hardware, for example, can be implemented using an application specific integrated circuit (ASIC), a general purpose computer or any other similar hardware device. In one embodiment, the software program of the present invention can be executed by a processor to implement the steps or functions described above. Similarly, the software program of the present invention (including related data structures) can be stored in a computer readable recording medium, for example, a RAM memory, a magnetic or optical drive or a floppy disk and the like. In addition, some steps or functions of the present invention can be implemented using hardware, for example, as a circuit that cooperates with a processor to perform each step or function.

[0212] In addition, a part of the present invention may be applied as a computer program product, such as a computer program instruction, which, when executed by a computer, can call or provide the method and / or technical solution according to the present invention through the operation of the computer. The program instruction for calling the method of the present invention may be stored in a fixed or removable recording medium, and / or transmitted through a data stream in a broadcast or other signal-bearing medium, and / or stored in a working memory of a computer device that runs according to the program instruction. Here, according to an embodiment of the present invention, a device is included, the device including a memory for storing computer program instructions and a processor for executing program instructions, wherein, when the computer program instruction is executed by the processor, the device is triggered to run the method and / or technical solution based on the aforementioned multiple embodiments of the present invention.

[0213] It is obvious to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive, and the scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved. In addition, it is obvious that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices stated in the device claim can also be implemented by one unit or device through software or hardware. The words first, second, etc. are used to indicate names, and do not indicate any particular order.

Claims

1. A damage prediction method for a seismic isolation structure designed by a direct displacement method, characterized in that: include: Step S1, generating preset sample seismic waves and establishing various seismic wave parameters of each sample seismic wave; Step S2, based on the preset sample seismic waves, calculating and generating the structural parameters of the sample seismic isolation structures of the same corresponding number, and establishing a one-to-one correspondence between each sample seismic wave and a corresponding sample seismic isolation structure; Step S3, based on the structural parameters of the isolation structure, the corresponding equivalent double-degree-of-freedom model is established using OpenSees finite element software; based on the equivalent double-degree-of-freedom model and the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, the maximum displacement D of the equivalent mass point of the upper building structure of the corresponding sample isolation structure is obtained. s The maximum displacement D of the particle in the isolation layer b ; Step S4: based on the seismic wave parameters of the sample seismic wave and the structural parameters of the corresponding sample seismic isolation structure, and the maximum displacement D of the equivalent mass point of the corresponding upper building structure, s The maximum displacement D of the particle with the seismic isolation layer b And through XGBoost model training and Bayesian hyperparameter optimization, a prediction model for predicting the damage degree of the seismic isolation structure is trained to obtain a trained prediction model; Step S5, using DDBD to design a seismic isolation structure to obtain a generated test seismic isolation structure and its various structural parameters; Step S6, evaluating the trained prediction model to obtain a prediction model that passes the evaluation; Step S7, inputting the actual structural parameters and seismic wave parameters of the seismic isolation structure to be evaluated into the prediction model that has been evaluated to obtain the prediction result.

2. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S1 includes: Step S11, using the NGAWest2 seismic wave database in PEER to collect, organize and classify seismic wave data; obtain the first seismic wave, select the seismic wave with a magnitude greater than 5 in the first seismic wave as the second seismic wave; the 7274 second seismic waves selected can be divided into 4 categories according to the equivalent shear wave velocity of the soil layer and the thickness of the soil layer covering the site; among them, the first category site V s30 >550m / s, the second type of site Vs30 is 265~550m / s, the third type of site V s30 165~265m / s, the fourth type of site V s30 <165m / s; Step S12: Select the seismic waves of the first, second and third types of sites from the second seismic wave as the third seismic wave, and for each type of the third seismic wave, respectively select the seismic waves according to the magnitude M and the fault projection distance R in the seismic wave. jb , and were divided into 4 groups of data by the Gaussian mixture model distribution clustering method, and a total of 12 groups of data were obtained from the first, second and third types of sites in the third seismic wave; Step S13: Filter the seismic waves of each of the 12 data sets by using a grid screening method: that is, filter the seismic waves of each of the 12 data sets by magnitude M and fault projection distance R. jb为 The horizontal and vertical axes are divided into a 3×3 grid to obtain 9 magnitudes M and fault projection distances R jb range; the grids other than the central grid in the 3×3 grid are used as peripheral grids, 2 seismic waves are randomly selected from each grid in the peripheral grid, and 16 seismic waves are obtained from the 8 peripheral grids in total; 4 seismic waves are randomly selected from the middle grid, so that 20 seismic waves are selected from each group of data, and a total of 240 seismic waves are selected from 12 groups of three types of sites as the fourth seismic wave; Step S13: The selected 240 fourth seismic waves are amplitude modulated, wherein the peak ground acceleration PGA of each seismic wave is in the range of 0.05 to 1.6 g, with a step length of 0.05 g, and a total of 32 amplitude modulations are performed to obtain 7680 sample seismic waves as excitation for structural calculation, and the seismic wave parameters of the 7680 sample seismic waves are extracted.

3. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 2, characterized in that: Step S12 includes: Step S121, using the fault projection distance R in the seismic wave jb and magnitude M are clustering parameters and normalized to obtain normalized data; Step S122, based on the normalized data of each type of venue, perform Gaussian mixture model cluster analysis on each type of venue, evaluate the clustering effect of the Gaussian mixture model by setting different groups for each type of venue, and use the Bayesian Information Criterion BIC to evaluate the Gaussian mixture model: BIC = -2ln(L) + kln(n), where k is the number of model parameters; n is the number of samples; L is the maximum likelihood estimate of the model; Among them, K is the number of groups; D is the characteristic dimension, with magnitude M and fault projection distance R jb That is, take 2; cluster the number of groups K of the first, second and third types of sites according to 1 to 20, and perform cluster analysis respectively. According to the BIC value of cluster analysis, when K is four clusters, the BIC curve of the model becomes flat, so the category of each type of site in the model is further subdivided into four groups.

4. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Various seismic wave parameters, including: Duration from 5% to 95% of the acceleration time: D S5-95 ; Peak ground acceleration: PGA; Peak ground velocity: PGV; Cumulative absolute velocity: CAV; Cumulative absolute displacement: CAD; Intensity index: I a ; Root mean square acceleration: a rms ; RMS velocity: v rms ; Effective peak acceleration: EPA; Excellent cycle: T s ; Average period: T avg ; T s Spectral acceleration in seconds: S a (T s ); Acceleration spectrum intensity: ASI.

5. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S2 comprises: Step S21, calculate the structural parameters of the equivalent dual-degree-of-freedom model to be generated, there are a total of 9 structural characteristic parameters, set the values ​​of these 9 structural characteristic parameters within the corresponding range, randomly generate the structural parameters of 7680 sample isolation structures corresponding to the number of sample seismic waves according to the set range and normal distribution according to Latin hypercube, and establish a one-to-one correspondence between the seismic wave parameters of a seismic wave and the structural parameters of a random isolation structure in the sample isolation structure; according to the 2DOF system Bouc-Wen model parameters, extract 9 structural parameters, including: M is the sum of the upper mass of the 2DOF model and the mass of the isolation layer, γ m is the mass ratio, d ys is the yield displacement of the upper building structure, α s is the post-yield stiffness ratio of the upper building structure, T s is the basic period of the superstructure structure, ξ IS is the structural damping ratio of the 2DOF model, α b is the post-isolation layer yield stiffness ratio, T b is the natural oscillation period of the 2DOF model, q D is the yield-to-weight ratio of the seismic isolation layer, defined as the accident stiffness k of the seismic isolation layer IS Total weight of the superstructure m T ×g ratio; in Latin hypercube generation, M and γ m is associated, that is, γ is determined according to the value of M m The value range of .

6. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S3 includes: Step S31, using OpenSees finite element software to establish an equivalent dual-degree-of-freedom model, wherein the OpenSees finite element software adopts the Bouc-Wen model, that is, a double-fold line model for modeling, and both the upper building structure and the isolation layer are simulated using the double-fold line model; based on the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, the acceleration and time sequence of the sample seismic wave, the equivalent dual-degree-of-freedom model is subjected to nonlinear time history analysis to obtain the maximum displacement D of the equivalent mass point of the upper building structure of the sample isolation structure. s The maximum displacement D of the particle in the isolation layer b ; In the Bouc-Wen modeling, the parameters include: Post-yield stiffness ratio of linear hardening component is 0.05; Post-yield stiffness ratio of nonlinear hardening component is 0; Exponent of nonlinear hardening component is 1; Yielding exponent is 2; First hysteretic shape parameter is 0.5; Second hysteretic shape parameter is 0.

5.

7. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S4 comprises: Step 41, each time 80% of the data is selected from the sample seismic waves, and random_state is searched in the range of 0 to 1000 according to the grid search method, and the determination coefficient R of the currently selected 80% of the data is calculated. 2 ; Step 42, determine the coefficient R 2 When the score is the highest, 80% of the data is selected as the training set, and the remaining 20% ​​of the data in the sample seismic wave is used as the validation set; Step 43, when constructing the XGBoost prediction model, firstly, the benchmark model is used to perform an exploratory analysis on the potential explanatory variables, so as to screen out the hyperparameters that contribute most to the model prediction ability; then, based on the training set, on the basis of the screened out hyperparameters that contribute most, the intelligent optimization method is applied to fine-tune the hyperparameters of various machine learning algorithms; the hyperparameters that need to be adjusted in the XGBoost algorithm include: the number of decision trees, range: [100:1000]; the maximum depth, range: [3:100]; learning rate, [0.001:0.1]; minimum split loss, [5:10]; regularization coefficient, [0.001:1]; Step 44, during the model training phase, the validation set is divided into a plurality of subsets by random sampling, and a five-fold cross validation procedure is implemented to obtain a trained prediction model.

8. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S5 includes: Step S501, determining basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure, wherein, according to the preliminary design, the upper building structure is equivalent to a multi-degree-of-freedom system shear type structure model, and according to the mass m of the i-th layer of the multi-degree-of-freedom system shear type structure model i , horizontal lateral stiffness k i , damping coefficient c i And the floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s , D s,eq ; Among them, D s,eq The equivalent displacement required to maintain the superstructure; Step S502: Under the design earthquake or rare earthquake, the upper building structure should remain intact, the main body and non-structural components of the upper building structure should not be damaged, and the maximum inter-story displacement angle is set to The performance target of the lead rubber isolation bearing is the design displacement under the design earthquake or rare earthquake. Step S503, based on the basic information of the component arrangement, material and cross-sectional characteristics of the upper building structure and the performance target of the lead rubber isolation bearing, calculate the target displacement curve of the upper building structure in the base isolation structure, D1 and D i are the deformations of the first and i-th layers of the upper building structure respectively; D i It is expressed as the following formula (1): In formula (1), Φ1 and Φ i is the normalized function of the horizontal displacement of the first and i-th floors of the upper building structure, which is determined by the period ratio R IS 、h i , the total height H of the upper building structure is calculated, where R IS =T IS / T S , T IS is the fundamental period of the base isolation structure, T S is the basic period of the superstructure structure; Step S504: establish a multi-degree-of-freedom system shear type structure model according to the target displacement curve of the upper building structure in the base isolation structure, and calculate the target displacement D of the upper building structure based on the DOF equivalent model. s,eq , equivalent mass m s,eq and the equivalent height h s,eq ; Step S505, calculate the new cycle ratio R IS , wherein the period ratio R in step S503 is IS Assuming the period ratio R IS , through the new cycle ratio R IS Until convergence, the new cycle is R IS It is calculated by the following explicit expression (2): Display expressions: The design displacement D IS,eq , In formula (2), m T is the total mass of the superstructure, m IS is the mass of the seismic isolation layer; where m T According to the basic information, m IS It is one of the basic information; Step S506: Based on the new cycle ratio R calculated in step S55 IS， Calculate the equivalent stiffness k of the base-isolated structure IS and the equivalent damping ratio, where the equivalent stiffness k IS Equivalent stiffness k of shear-type structural model of multi-degree-of-freedom system IS,eq are equal; among them, the equivalent damping ratio ξ of the base isolation structure IS From the first-order modal damping ratio ξ 1,eq Calculated; the first-order modal damping ratio ξ 1,eq According to the designed displacement spectrum, the first modal period T of the shear structure model of the multi-degree-of-freedom system is 1,eq and Interpolation is then used to determine the yield displacement d of the seismic isolation layer. yb , according to k IS and IS Calculate the characteristic strength Q and post-yield stiffness k of the isolation layer p ; Step S507, non-elastic upper building structure design, based on the base shear force V calculated by equivalent parameters B Determine the seismic force on each floor of the upper building structure, and thus calculate the design seismic force F on each floor of the upper building structure ei , the formula can be obtained from the following formula (3): in, Δ i is the displacement of the i-th layer superstructure relative to the ground; Step S508, calculate the design shear force V of each layer of the upper structure Si , the actual yield bearing capacity of each layer of the superstructure F yi By V Si The yield displacement u of each layer of the upper structure is calculated by multiplying the super strength coefficient Ω0, which is 2.0 here. Then, the initial stiffness of each layer of the upper structure is calculated according to formula (4): yi , thus completing the inelastic design of the superstructure. u yi =F yi / k i (4) in, F ei That is F ej , F yi =Ω0V Si Step S509: initial stiffness k of the upper building structure s =k s,eq , where k s,eq It can be obtained from formula (5): Among them, T s,eq is the equivalent period of the upper building structure, T s,eq =T s The equivalent method of the upper building structure controls the displacement through Pushover static analysis and obtains the top floor displacement U n and the shear force V at the bottom of the upper building structure b The curve is simplified into a double-broken line curve and converted into the spectral pseudo-acceleration A-spectral displacement D format, that is: in, is the equivalent mass of the upper structure according to the first vibration mode, Φ n1 is the first mode coefficient of the top floor, which is taken as 1 here; Φ j1 is the first mode coefficient of the jth layer; the inflection point of the double-fold line is taken as D y and A y , so there is a formula Γ1 and Formula (6) is as follows: Step S510: The characteristic strength Q of the seismic isolation layer is calculated by the following formula (7): Among them, the post-isolation layer yield stiffness k p pass: Calculate the yield displacement d of the isolation layer. yb Calculate the initial stiffness of the isolation layer: Step S5111: According to the above steps S51 - S510, calculate the Bouc - Wen model parameters of the 2DOF system, and extract 9 structural parameters of the base - isolated structure based on the Bouc - Wen model parameters of the 2DOF system; Take the base - isolated structure as the test isolated structure, and take the 9 structural parameters of the base - isolated structure as the 9 structural parameters of the test isolated structure. Among them, the extraction of 9 structural parameters includes: M is a 2DOF model With m IS The sum of γ m is the mass ratio, d ys is the yield displacement of the upper building structure, d ys =D y ; α s is the post-yield stiffness ratio of the upper structure, that is, the post-yield stiffness and the initial equivalent stiffness k of the upper structure s,eq The ratio of s is the basic period of the superstructure structure, ξ IS is the structural damping ratio of the 2DOF model, which can be obtained according to formula (8): Among them, μ eq and ε eq They are: α b is the yield stiffness ratio of the isolation layer, k IS / k E ; T b is the natural vibration period of the 2DOF model, calculated according to the formula; q D is the yield-to-weight ratio of the seismic isolation layer, defined as k IS Total weight of the superstructure m T ×g ratio; 9. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to claim 1, characterized in that: Step S6 includes: Step S61, select 80 seismic waves corresponding to the design site, with a magnitude greater than or equal to 5, and select the waves from 19742 seismic waves obtained from the NGAWest2 database; perform 32 peak acceleration amplitude modulations of 0.05 to 1.6g with an interval of 0.05g in the same way as step S13, and generate a total of 2560 seismic waves, extract seismic wave parameters from these 2560 seismic waves, and perform OpenSees finite element analysis based on the 9 structural parameters of the test isolation structure, and output the maximum displacement D of the equivalent mass point of the upper building structure s The maximum displacement D of the particle with the seismic isolation layer b ; Step S62: Input the structural parameters of the test isolation structure and the corresponding seismic wave parameters of each test seismic wave into the prediction model to obtain the maximum displacement D of the equivalent mass point of the upper building structure. s The maximum displacement D of the particle in the isolation layer b , as the prediction output; Step S63, perform OpenSees finite element analysis on each structural parameter of the test isolation structure and each seismic wave parameter of each corresponding test seismic wave to obtain the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the test isolation structure. s The maximum displacement D of the particle in the isolation layer b , as the calculation result; Step S64: Based on a preset evaluation method, evaluate and compare the predicted output and the calculated output to obtain a qualified prediction model.

10. The damage prediction method for a seismic isolation structure designed by direct displacement method according to claim 1, characterized in that: Step S7 includes: Step S71, calculate the upper building structure DM: based on the maximum horizontal displacement D of the upper building structure s and the maximum horizontal displacement D of the isolation layer b , find out α and β in DM, and find out α and β by fitting. DM is the median value of the maximum horizontal displacement of the upper building structure under IM; DM = α (IM) β , through the logarithmic regression of the following formula (9), a = lnα, b = β, IM is the PGA under different seismic wave amplitude modulation, ln(DM) = a + bln(IM) (9); Step S72: Based on DM, find the standard deviation σ of the maximum horizontal displacement of the structure in IM ln(DM|IM) , calculated by the following formula (10), where μ ln(DM|IM) is the median value of the structure in IM, Where, N represents 80, that is, 80 seismic waves; Step S73, seismic performance evaluation results: The exceedance probability is used to represent the conditional probability that the upper building structure and the seismic isolation layer exceed the design index under the PGA under different seismic wave amplitude modulation, that is, the exceedance probability. The exceedance probability is expressed by the following formula (11), which can be used to draw the vulnerability curves of the upper building structure and the seismic isolation layer. The design index includes the target design value P(DM≥DO|IM) = 1 - P(DM<DO|IM). Through transformation (ln(DM) = a + bln(IM)), the above formula can be written as: DO stands for target design value

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