Damage prediction method for base-isolated structure designed by direct displacement method

Abstract

The application provides a damage prediction method for a seismic isolation structure designed by a direct displacement-based design (DDBD) method. The application starts from the DDBD design idea of the seismic isolation structure, can calculate the parameters of the seismic isolation layer and the upper building structure by determining the target value, can equivalently obtain a 2DOF model, can extract 9 structure parameters and 13 seismic wave parameters of the seismic wave, can quickly predict the fragility curve based on the target value by using BO-XGBoost, can directly guide the DDBD design of the seismic isolation structure, and is a more rapid and efficient method, which is helpful to improve the DDBD idea of the seismic isolation structure. The prediction result is good, and in the open set case, the prediction accuracy is still good. The predicted fragility curve is close to the real data, and can be used as a reference for the DDBD structure design. It can be seen from the fragility curve that the DDBD design process can effectively make the seismic isolation structure achieve the expected target under the earthquake.

Description

Technical Field

[0001] This invention relates to the field of machine learning, and in particular to a method for predicting damage to seismic isolation structures designed using the direct displacement method. Background Technology

[0002] Seismic isolation structures, as an effective seismic design technique, can significantly reduce the impact of earthquakes on buildings, protecting structural integrity and operational safety. A seismic isolation structure consists of an isolation layer and the superstructure above it. The direct displacement design method can effectively design the design parameters of the isolation layer (such as a combination of lead-core rubber bearings (LRBs)) by setting target values ​​and the basic parameters of the superstructure. This performance-based design method enables the structure to meet design objectives under strong seismic loads, achieving good seismic resistance while reducing computational workload.

[0003] However, even with seismic isolation measures in place, earthquakes can still damage the isolated structures, especially during strong earthquakes. Therefore, timely and accurate assessment of the damage status of seismic isolation structures (through vulnerability analysis by predicting the maximum displacement of the entire isolation layer) is crucial for ensuring personnel safety and the functional restoration of the building. Furthermore, damage assessment helps in developing appropriate repair and reinforcement plans, reducing potential economic losses and social impacts, and ensuring efficient post-disaster recovery efforts.

[0004] Currently, 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 seismic response, which may lead to inaccurate damage assessment results. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting damage to seismic isolation structures designed using the direct displacement method.

[0006] To address the above problems, this invention provides a method for predicting damage to seismic isolation structures designed using the direct displacement method, comprising:

[0007] Step S1: Generate a preset sample seismic wave and establish the seismic wave parameters for each sample seismic wave;

[0008] Step S2: Based on the preset sample seismic waves, calculate and generate the structural parameters of the same number of sample isolation structures, and establish a one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure.

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

[0010] Step S4: Based on the seismic wave parameters of the sample seismic waves and the structural parameters of the corresponding sample isolation structure, as well as the maximum displacement D of the equivalent mass point of the corresponding superstructure. s The maximum displacement D of the isolation layer mass points b Furthermore, a predictive model for predicting the damage level of seismic isolation structures was trained by XGBoost model training and Bayesian hyperparameter optimization to obtain the trained predictive model.

[0011] Step S5: Design the seismic isolation structure using DDBD to obtain the generated test seismic isolation structure and its various structural parameters;

[0012] Step S6: Evaluate the trained prediction model to obtain a qualified prediction model.

[0013] Step S7: Input the actual structural parameters and seismic wave parameters of the seismic isolation structure to be evaluated into the qualified prediction model to obtain the prediction results.

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

[0015] Step S11: Seismic wave data is acquired, processed, and classified using the NGAWest2 seismic wave database in PEER; the first seismic wave is obtained, and seismic waves with a magnitude greater than 5 are selected as the second seismic wave; the 7274 selected second seismic waves are classified into 4 types based on the equivalent shear wave velocity of the soil layer and the thickness of the overlying soil layer; among them, the first type of site V s30 >550m / s, Vs30 for Class II sites is 265~550m / s, Vs30 for Class III sites s30 The speed range is 165–265 m / s, and the Class IV site V s30 <165m / s;

[0016] Step S12: Select seismic waves from the second seismic wave that represent sites of type I, II, and III as the third seismic wave. For each type of the selected third seismic wave, calculate the magnitude M and fault projection distance R of the seismic wave respectively. jbThe data were divided into four groups using the Gaussian mixture model distribution clustering method, resulting in a total of 12 groups of data from the first, second, and third types of sites in the third seismic wave.

[0017] Step S13: Filter the seismic waves for each of the 12 data sets using a grid filtering method: that is, filter the seismic waves in each of the 12 data sets based on magnitude M and fault projection distance R. jb为 The horizontal and vertical axes are divided into a 3×3 grid to obtain 9 magnitude M earthquakes and fault projection distances R. jb The range is defined as follows: using the grid outside the center grid in a 3×3 grid as the outer grid, two seismic waves are randomly selected from each of the outer grids, and a total of 16 seismic waves are obtained from the eight outer grids; four seismic waves are randomly selected from the center grid, so that 20 seismic waves are selected from each set of data, and a total of 240 seismic waves are selected from 12 sets of data for the three types of sites as the fourth seismic wave;

[0018] Step S13: The selected 240 fourth seismic waves are amplitude-modulated. The amplitude is adjusted according to the peak ground acceleration (PGA) range of 0.05 to 1.6g for each seismic wave, with a step size of 0.05g. The amplitude is adjusted 32 times to obtain 7680 sample seismic waves as excitation for structural calculations. The parameters of each seismic wave in 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 The magnitude M is used as the clustering parameter and normalized to obtain normalized data;

[0021] Step S122: Based on the normalized data for each field class, perform Gaussian mixture model clustering analysis on each field class. Evaluate the clustering effect of the Gaussian mixture model by setting different groups for each field class, 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; and L is the maximum likelihood estimate of the model.

[0023]

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

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

[0026] Duration of 5% to 95% of the acceleration time history: D S5-95 Peak ground acceleration: PGA; Peak ground velocity: PGV; Cumulative absolute velocity: CAV; Cumulative absolute displacement: CAD; Strength index: I a Root mean square acceleration: a rms Root mean square velocity: v rms Effective peak acceleration: EPA; Superior cycle: T s Average period: T avg ;T s Spectral acceleration per second: 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 two-DOF 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. According to the Latin hypercube and within the set range, randomly generate the structural parameters of 7680 sample isolation structures according to a normal distribution, corresponding to the number of sample seismic waves. Establish a one-to-one correspondence between the seismic wave parameters of one seismic wave and the structural parameters of a random isolation structure in the sample isolation structures. Based on the Bouc-Wen model parameters of the 2DOF system, extract the 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 For mass ratio, d ys α represents the yield displacement of the superstructure. s T represents the post-yield stiffness ratio of the superstructure. s For the basic period of the superstructure, ξ IS Let α be the structural damping ratio of the 2DOF model. b It is the yield stiffness ratio behind the seismic isolation layer, T b Let q be the natural period of the 2DOF model. D The yield-weight ratio of the isolation layer is defined as the failure stiffness k of the isolation layer. IS Total weight of the superstructure (m) T The ratio of ×g; where, in the generation of the Latin hypercube, M and γ are... m Correlation, that is, determining γ based on the value of M. m The range of values ​​for .

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

[0030] Step S31: An equivalent two-degree-of-freedom model is established using OpenSees finite element software. OpenSees uses the Bouc-Wen model, i.e., a bilinear model, to simulate both the superstructure and the isolation layer. Based on the one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure, and considering the acceleration and timing of the sample seismic waves, a nonlinear time history analysis is performed on the equivalent two-degree-of-freedom model to obtain the maximum displacement D of the equivalent mass point of the superstructure of the sample isolation structure. s The maximum displacement D of the isolation layer mass points b In 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, select 80% of the data from the sample seismic waves, and use the grid search method random_state to search within the range of 0 to 1000, and calculate the determination coefficient R of the currently selected 80% of the data. 2 ;

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

[0034] Step 43 involves first using a baseline model to conduct exploratory analysis of potential explanatory variables during the construction of the XGBoost prediction model, thereby selecting the hyperparameters that contribute the most to the model's predictive ability. Then, based on the training set and the selected hyperparameters that contribute the most, intelligent optimization methods are 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, ranging from [100:1000]; and the maximum depth, ranging from [3:100].

[0035] Learning rate, [0.001:0.1]; Minimum splitting loss, [5:10]; Regularization coefficient, [0.001:1];

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

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

[0038] Step S501: Determine the basic information regarding the component layout, materials, and cross-sectional properties of the superstructure. Based on the preliminary design, the superstructure is equivalent to a multi-degree-of-freedom shear structure model. The mass m of the i-th layer of the multi-degree-of-freedom shear structure model is then determined. i Horizontal lateral stiffness k i Damping coefficient c i and floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s D s,eq ; where D s,eq To maintain the equivalent displacement required for the superstructure;

[0039] Step S502: Under the design earthquake or rare earthquake, the superstructure must remain intact, and the main and non-structural components of the superstructure should not be damaged. The maximum inter-story drift angle is set as follows: The performance target of lead-core rubber seismic isolation bearings is the design displacement under design earthquakes or rare earthquakes.

[0040] Step S503: Based on the basic information of the component layout, material and cross-sectional properties of the superstructure and the performance targets of the lead-core rubber seismic isolation bearings, calculate the target displacement curves, D1 and D2, of the superstructure in the base-isolated structure. i These represent the deformations of the first and i-th floors of the superstructure, respectively; D i It is expressed as the following formula (1),

[0041]

[0042] In equation (1), Φ1 and Φ i Let R be the normalized function of the horizontal displacement of the first and i-th floors of the superstructure, given by the period ratio R. IS h i The parameters of the total height H of the superstructure are calculated, where R IS =T IS / T S TIS The fundamental period of a base isolation structure, T S The basic cycle of the superstructure;

[0043] Step S504: Establish a multi-degree-of-freedom shear structure model based on the target displacement curve of the superstructure in the base isolation structure. Calculate the target displacement D of the superstructure based on the DOF equivalent model. s,eq Equivalent mass m s,eq and equivalent height h s,eq ;

[0044] Step S505, calculate the new cycle ratio R IS In this process, the period ratio R in step S503 is increased. IS Assuming period ratio R IS Through the new cycle ratio R IS Until convergence, the new period is greater than R. IS It is calculated from the following display expression (2):

[0045] Display expression:

[0046] Among them, design displacement That is, D IS,eq ,

[0047] In equation (2), m T The total mass of the superstructure is m. IS The mass of the isolation layer; where m T Based on the basic information, m IS This is one of the basic information items;

[0048] Step S506: Based on the new period ratio R calculated in step S55 IS， Calculate the equivalent stiffness k of the base isolation structure IS And the equivalent damping ratio, where the equivalent stiffness k IS The equivalent stiffness k of a shear-type structural model of a multi-degree-of-freedom system IS,eq Equal; where the equivalent damping ratio ξ of the base isolation structure is equal. IS The damping ratio ξ of the first mode 1,eq The first-order modal damping ratio ξ is calculated to be... 1,eq Based on the design displacement spectrum, the first modal period T of the multi-degree-of-freedom system shear-type structural model is determined. 1,eq and Interpolation is performed; then the yield displacement d of the isolation layer is determined. yb According to k IS and ξ IS Calculate the characteristic strength Q and post-yield stiffness k of the seismic isolation layer. p ;

[0049] Step S507, Inelastic superstructure design, based on the base shear force V calculated using equivalent parameters. B Determine the seismic force of each floor of the superstructure, and then calculate the design seismic force F of each floor of the superstructure. ei The formula can be derived from the following equation (3):

[0050]

[0051] in, Δ i Let be the displacement of the upper structure of the i-th layer relative to the ground.

[0052] Step S508: Calculate the design shear force V of the superstructure on each floor. Si The actual yield bearing capacity F of the superstructure on each floor yi It is V Si The yield displacement u of each upper structure is obtained by multiplying by the super-strength coefficient Ω0, which is taken as 2.0 here. Then, the yield displacement u of each upper structure is calculated according to the initial stiffness of each upper structure in formula (4). yi This completes 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 =Ω0V Si

[0056] Step S509, initial stiffness k of the superstructure s =k s,eq Where, k s,eq It can be obtained from equation (5):

[0057]

[0058] Among them, T s,eq For the equivalent period of the superstructure, T s,eq =T s The equivalent method for the superstructure can be used to control displacement through pushover static analysis to obtain the top-floor displacement U. n and the bottom shear force V of the superstructure b The curve is simplified to a bilinear curve and then transformed into the spectral pseudo-acceleration A-spectral displacement D scheme (ADRS), i.e.:

[0059]

[0060] in, Φ is the equivalent mass of the superstructure derived from the first mode of vibration. n1 Φ is the first mode shape coefficient of the top layer, which is taken as 1 here; j1 Let D be the first mode shape coefficient of the j-th floor; take the inflection point of the bi-linear curve as D. y and A y Therefore, the formula is... Γ1 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 yield stiffness k behind the seismic isolation layer p pass: If we calculate the yield displacement d of the isolation layer, then... yb Determine the initial stiffness of the seismic isolation layer:

[0065]

[0066] Step S5111: Based on steps S51-S510 above, obtain the Bouc-Wen model parameters of the 2DOF system, and extract nine structural parameters of the base isolation structure based on the Bouc-Wen model parameters of the 2DOF system. Use the base isolation structure as the test isolation structure, and use the nine structural parameters of the base isolation structure as the nine structural parameters of the test isolation structure. The nine extracted structural parameters include:

[0067] M is the 2DOF model. With m IS The sum of; γ m For mass ratio, d ys d represents the yield displacement of the superstructure. ys =D y ;α s The ratio of the post-yield stiffness of the superstructure to the initial equivalent stiffness k of the superstructure is given by the post-yield stiffness. s,eq The ratio of T; s For the basic period of the superstructure, ξ IS The structural damping ratio of the 2DOF model is calculated using formula (8):

[0068]

[0069] Where, μeq and ε eq They are respectively:

[0070]

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

[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. The wave selection method is obtained from 19742 seismic waves obtained from the NGAWest2 database. Perform 32 peak ground acceleration amplitude modulations (PGA) at intervals of 0.05g from 0 to 1.6g, generating a total of 2560 seismic waves. Extract the seismic wave parameters from these 2560 seismic waves, and perform OpenSees finite element analysis based on 9 structural parameters of the test isolation structure to output the maximum displacement D of the equivalent mass point of the superstructure. s The maximum displacement D of the isolation layer mass points b ;

[0075] Step S62: Input the various 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 superstructure. s The maximum displacement D of the isolation layer mass points b , as the predicted output;

[0076] Step S63: Perform OpenSees finite element analysis on the various structural parameters of the test isolation structure and the corresponding seismic wave parameters of each test seismic wave to obtain the maximum displacement D of the equivalent mass point of the superstructure corresponding to the test isolation structure. s The maximum displacement D of the isolation layer mass points b , as the calculation result;

[0077] Step S64: Based on the preset evaluation method, the predicted output and the calculated output are evaluated and compared to obtain a qualified prediction model.

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

[0079] Step S71: Obtain the superstructure DM. Based on the maximum horizontal displacement D of the superstructure and the maximum horizontal displacement D of the seismic isolation layer, find α and β in DM, and fit to obtain α and β. DM is the median of the maximum horizontal displacement of the superstructure under IM; DM = α(IM). s and the maximum horizontal displacement D of the seismic isolation layer b , find α and β in DM, fit to obtain α and β. DM is the median of the maximum horizontal displacement of the superstructure under IM; DM = α(IM). β , through 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, obtain 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 superstructure and the seismic isolation layer exceed the design index under the PGA of 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 superstructure and the seismic isolation layer are plotted. The above design index includes the target design value

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

[0086]

[0087] DO represents the target design value

[0088] Compared with existing technologies, this invention, starting from the design concept of seismic isolation structures in DDBD (Districted Seismic Breakdown) systems, proposes a machine learning-based design method. By determining target values, the parameters of the isolation layer and the superstructure are calculated, resulting in an equivalent 2DOF model. Nine structural parameters and thirteen seismic wave parameters are extracted, and BO-XGBoost can quickly predict the vulnerability curve based on the target values. This provides intuitive guidance for the design of seismic isolation structures in DDBD systems, offering a faster and more efficient method that helps improve the DDBD approach for seismic isolation structures. The results show good prediction accuracy, even in open-set conditions. The predicted vulnerability curve closely approximates the actual data and can serve as a reference for DDBD structural design. The vulnerability curve also demonstrates that the DDBD design process effectively enables the seismic isolation structure to achieve the expected goals under seismic conditions.

[0089] This 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 sustainable urban development. Attached Figure Description

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

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

[0092] Figure 3 This is a schematic diagram illustrating the principle steps of a direct displacement design method according to an embodiment of the present invention.

[0093] Figure 4 This is a schematic diagram of the DDBD design steps according to an embodiment of the present invention. Detailed Implementation

[0094] The present invention will now be described in further detail with reference to the accompanying drawings.

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

[0096] Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0097] Computer-readable media include both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, 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 technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include non-transitory computer-readable media, such as modulated data signals and carrier waves.

[0098] How to quickly and accurately predict the seismic performance of seismically isolated structures is a current research focus in this field. Machine learning prediction is a very convenient and effective method, and it has been widely and successfully applied in structural engineering, showing good generalization performance for data within the prediction database. However, research on prediction results is relatively limited when the parameters of the seismically isolated structure and the seismic parameters are relatively random and outside the training data range.

[0099] To address this, this application proposes a machine learning-based prediction model. Employing commonly used rubber bearings, it equates the isolation layer of the seismic isolation structure and the upper and lower parts of the superstructure to a two-degree-of-freedom (2DOF) system. Based on this 2DOF system, a predictive model for the damage level of the seismic isolation structure can be quickly established. Furthermore, the predictive range of the model can be expanded using the structural parameters of the 2DOF system, covering a wider range of earthquake magnitudes (M) and fault projection distances (R). jb Predictive models are trained over a wide range of structural parameters for two-degree-of-freedom (2DOF) systems. Furthermore, seismic performance of isolation structures designed using the Direct Displacement Design (DDBD) method is evaluated through the predictive model, and vulnerability analysis is employed to address the influence of seismic randomness. This method can quickly and accurately predict the seismic performance of DDBD-designed isolation structures under freely selected seismic excitation. Specifically, the magnitude M and fault projection distance R of the aforementioned seismic motion are used. 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 method for predicting damage to seismic isolation structures designed by the direct displacement method, the method comprising steps S1 to S7.

[0101] Step S1: Generate a preset sample seismic wave and establish the seismic wave parameters for each sample seismic wave;

[0102] Each seismic wave data point corresponds to a set of seismic wave parameters; this step generates the sets of seismic wave parameters used for training the prediction model to predict the damage level of the seismic isolation structure.

[0103] Preferably, step S1 includes:

[0104] Step S11, Seismic wave data acquisition. Seismic wave data was acquired, processed, and classified using the NGAWest2 seismic wave database from PEER (Pacific Earthquake Engineering Research Center). 19,742 first seismic waves were obtained. Seismic waves with a magnitude greater than 5 were selected from these 19,742 first seismic waves, resulting in 7,274 second seismic waves. These 7,274 second seismic waves were then classified into four site categories based on the equivalent shear wave velocity of the soil layer and the thickness of the overlying soil layer, according to the Chinese Code for Seismic Design of Buildings (GB50011.2010). Note that PEER's seismic ground motion records only provide magnitude V... s30 Based on the data, this application establishes the relationship between site type and V in the "Code for Seismic Design of Buildings". s30 Correspondence: Type I site V s30 >550m / s, Vs30 for Class II sites is 265~550m / s, Vs30 for Class III sites s30 The speed range is 165–265 m / s, and the Class IV site V s30 <165m / s;

[0105] Step S12: Select seismic waves from the 7274 second seismic waves representing sites of types I, II, and III as third seismic waves. For each type of selected third seismic wave, calculate the magnitude M and fault projection distance R of the seismic wave. jb The data were divided into four groups using the Gaussian Mixture Model (GMM) distribution clustering method. A total of 3×4=12 groups (clusters) of data were obtained from the first, second and third types of sites in the third seismic wave.

[0106] Preferably, in step S12, for each type of the selected third seismic wave, the magnitude M and fault projection distance R in the seismic wave are respectively calculated. jb (The characteristics that best reflect the intensity of seismic waves) were divided into 4 groups (clusters) using the Gaussian Mixture Model (GMM) distribution clustering method, including:

[0107] Step S121, using the fault projection distance R in the seismic wavejb The magnitude M is used as the clustering parameter and normalized to obtain normalized data; here, because R jb The order of magnitude is much larger than M, so we normalize these two data points to reduce R. jb Scale difference from M;

[0108] Step S122: Based on the normalized data for each field class, Gaussian Mixture Model (GMM) clustering analysis is performed on each field class. The clustering effect of Gaussian Mixture Model (GMM) is evaluated by setting different groups (clusters) for each field class. 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; and L is the maximum likelihood estimate of the model.

[0110]

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

[0112] A lower BIC value indicates better clustering, while also considering model complexity. kln(n) penalizes the number of model parameters, selecting a simpler model to avoid overfitting. Cluster analysis is performed on the number of groups (clusters) K for the first, second, and third site categories, ranging from 1 to 20. Based on the BIC values ​​from the cluster analysis, when K is four clusters, the model's BIC curve flattens out. Therefore, we further subdivide each site category into four groups. The purpose is to more precisely select representative seismic waves from each cluster to reduce computational load.

[0113] Gaussian Mixture Models (GMMs) are powerful probabilistic models used to represent complex datasets composed of multiple Gaussian distributions. Unlike hard clustering algorithms such as K-means, GMM soft clustering provides the probability that each seismic wave belongs to each group (cluster). This soft clustering method can describe uncertainties, especially when seismic wave features may have ambiguous boundaries or overlap. Each seismic wave data point is considered to originate from one of multiple Gaussian distributions, which represent different subgroups or clusters in the data. Clustering seismic waves into four groups using GMMs can clearly distinguish the differences in response spectrum characteristics among them.

[0114] Step S13: Filter the seismic waves for each of the 12 data clusters using a grid filtering method: that is, filter the seismic waves of each of the 12 data clusters based on magnitude M and fault projection distance R. jb为The horizontal and vertical axes are divided into a 3×3 grid to obtain 9 magnitude M earthquakes and fault projection distances R. jb The range is as follows: Using a 3×3 grid excluding the central grid as the outer grid, two seismic waves are randomly selected from each of the outer grids, resulting in a total of 16 seismic waves from the eight outer grids. Four seismic waves are randomly selected from the central grid, resulting in 20 seismic waves from each data set. A total of 20×4×3=240 seismic waves are selected from 12 groups (clusters) across the three site types as the fourth seismic wave. The parameters of each seismic wave are shown in Table 1 below.

[0115] Table 1 Seismic wave parameter extraction

[0116]

[0117] Step S13: The selected 240 fourth seismic waves are amplitude-modulated. The amplitude is adjusted by 0.05-1.6g of the PGA (Peak Ground Acceleration) of each seismic wave and a step size of 0.05g, for a total of 32 amplitude adjustments, resulting in 240*32=7680 sample seismic waves as excitation for structural calculation. The parameters (13 features) of each seismic wave in Table 1 of the 7680 sample seismic waves are extracted and can be used as part of the machine learning input for the prediction model.

[0118] Step S2: Based on the preset sample seismic waves, calculate and generate the structural parameters of the same number of sample isolation structures, and establish a one-to-one correspondence between each sample seismic wave and a corresponding sample isolation structure.

[0119] Each seismic isolation structure corresponds to a set of structural parameters;

[0120] Preferably, step S2 includes:

[0121] Step S21: Calculate the structural parameters of the equivalent two-degree-of-freedom (2DOF) model to be generated as input for subsequent prediction models. There are nine structural feature parameters as shown in Table 2. Set the values ​​of these nine structural feature parameters within the ranges described in Table 2. Based on the Latin Hypercube (LHS) and following the ranges in Table 2, randomly generate the structural parameters of 7680 sample isolation structures corresponding to the number of sample seismic waves according to a normal distribution. Establish a one-to-one correspondence between the seismic wave parameters of one seismic wave and the structural parameters of a random isolation structure in the sample isolation structures. In subsequent steps, a two-mass point (two-degree-of-freedom model) can be established by the 7680 seismic waves corresponding to S13 and the structural parameters. Preferably, based on the Bouc-Wen model parameters of the 2DOF system, nine features can be extracted for machine learning input, as shown in Table 2. Where M is the sum of the upper mass and the isolation layer mass of the 2DOF model, γ mThe mass ratio (the ratio of the mass of the superstructure to the total mass of the 2DOF), d ys α represents the yield displacement of the superstructure. s The ratio of the post-yield stiffness of the superstructure to the initial equivalent stiffness k of the superstructure. s,eq The ratio of T s For the basic period of the superstructure, ξ IS Let α be the structural damping ratio of the 2DOF model. b It is the yield stiffness ratio (k) after the seismic isolation layer. IS / k E ), T b Let q be the natural period of the 2DOF model. D The yield-weight ratio of the isolation layer is defined as the failure stiffness k of the isolation layer. IS Total weight of the superstructure (m) T The ratio of ×g.

[0122] Table 2 Structural Parameter Characteristics

[0123]

[0124] Preferably, it is important to note that in the Latin hypercube (LHS) generation, M is associated with γm, meaning the range of γm values ​​is determined based on the value of M. For example, if M is randomly generated between 300 and 400, then γm values ​​will be randomly generated within the range of [0.6, 0.65, 0.7]. This allows for the establishment of many different random isolation structures over a wider range, subsequently enabling the generation of equivalent two-degree-of-freedom (2DOF) models for 7680 random sample isolation structures.

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

[0126] Preferably, step S3 includes:

[0127] Step S31: An equivalent two-degree-of-freedom (2DOF) model is established using OpenSees finite element software. OpenSees uses the Bouc-Wen model, i.e., a bilinear model, to simulate both the superstructure and the isolation layer. Based on the one-to-one correspondence between each sample seismic wave and its corresponding isolation structure determined in step S2, along with the acceleration and timing of the sample seismic waves, a nonlinear time history analysis is performed on the equivalent two-DOF model to obtain the maximum displacement D of the equivalent mass point of the superstructure of the isolation structure. s The maximum displacement D of the isolation layer mass points b The data is then used as real-world data for training the prediction model. In this case, the OpenSees finite element software uses the Bouc-Wen model, specifically a bilinear model, to simulate both the superstructure and the isolation layer. The superstructure and isolation layer are connected using OpenSees' "Elastomeric Bearing (Bouc-Wen) Element," as higher-order modes have minimal impact on the superstructure, making this inelastic shear element a reasonable choice. The key parameters in the Bouc-Wen model are: Post-yield stiffness ratio of linear hardening component (0.05); Post-yield stiffness ratio of nonlinear hardening component (0); Exponent of nonlinear hardening component (1); Yielding exponent (sharpness of hysteresis loop corners) (2); First hysteretic shape parameter (0.5); Second hysteretic shape parameter (0.5).

[0128] Step S4: Based on the seismic wave parameters of the sample seismic waves and the structural parameters of the corresponding sample isolation structure, as well as the maximum displacement D of the equivalent mass point of the corresponding superstructure. s The maximum displacement D of the isolation layer mass points b Furthermore, a predictive model for predicting the damage level of seismic isolation structures was trained by XGBoost model training and Bayesian hyperparameter optimization to obtain the trained predictive model.

[0129] Preferably, step S4 includes:

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

[0131] Using the 13 seismic wave parameters (Table 1) and the corresponding 9 structural parameters (Table 2) of the sample seismic isolation structure as input, the maximum displacement D of the equivalent mass point of the superstructure is calculated. s The maximum displacement D of the isolation layer mass points b As the output target, a predictive model for predicting the damage level of seismic isolation structures is trained;

[0132] Here, the maximum displacement D of the equivalent mass point of the corresponding superstructure is established. s The maximum displacement D of the isolation layer mass points b Then, machine learning predictions can be performed based on this to quickly predict the structural response. First, the 13 seismic wave parameters in Table 1 and the 9 structural parameters in Table 2 are used as inputs, and the equivalent maximum displacement D of the superstructure is calculated. s With the maximum displacement D of the seismic isolation layer b As output, preferably, the training set R can be found by using a grid search method (random_state searches within the range of 0 to 1000, dividing the training set into 7680 proportions). 2 The segmentation method with the highest (coefficient of determination) score divides the database into 80% of the samples as the training set and 20% of the samples as the validation set, and uses Extreme Gradient Boosting (XGBoost) for machine learning prediction.

[0133] Step 41: Each time, select 80% of the data from the sample seismic waves, and use the grid search method random_state to search within the range of 0 to 1000, and calculate the determination coefficient R of the currently selected 80% of the data. 2 ;

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

[0135] Step 43 involves first using a benchmark model to conduct an exploratory analysis of potential explanatory variables (hyperparameters) to select the hyperparameters that contribute the most to the model's predictive ability. Then, based on the training set and the selected hyperparameters that contribute the most, intelligent optimization methods are applied to finely adjust the hyperparameters of various machine learning algorithms.

[0136] Step 44: During the model training phase, to improve the model's generalization ability, we randomly sample the validation set into multiple subsets and implement a five-fold cross-validation procedure to obtain the trained prediction model, ensuring the stability and reliability of the evaluation results. The evaluation criterion is based on the root mean square error (RMSE), which guides the hyperparameter optimization process, aiming to find the optimal hyperparameter configuration that balances fitting and generalization. This comprehensive approach aims to construct a machine learning model with high prediction accuracy and strong generalization ability.

[0137] In the field of machine learning, hyperparameter tuning is often considered a complex optimization challenge, resembling a "black box" problem. The choice of hyperparameters has a significant impact on the prediction accuracy of machine learning. Traditional gradient descent methods may not be applicable in this situation because the objective function may be non-differentiable or its derivative may be difficult to compute. Therefore, metaheuristic algorithms, due to their ability to explore the decision space without gradient information and their general applicability to a variety of problems, have become one of the preferred methods for handling such optimization problems.

[0138] These algorithms typically rely on simulations of natural or social behavioral strategies, rather than direct mathematical gradient methods, to search for globally optimal or near-optimal solutions among a wide range of potential solutions. A typical metaheuristic optimization algorithm is Bayesian optimization (BO): a probabilistic model that uses prior knowledge and data collected from the objective function to update posterior knowledge, thereby guiding sampling decisions during the search process to efficiently approximate the global optimum.

[0139] The BO algorithm has been applied in many complex and multivariate optimization scenarios, including the selection and tuning of hyperparameters in machine learning models. It provides a powerful and flexible toolset for achieving effective hyperparameter optimization. Table 3 below shows the selection range of hyperparameters for XGBoost machine learning. To reduce computational costs and determine better hyperparameter configurations, this application implemented 100 rounds of hyperparameter optimization iterations on the training and test sets.

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

[0141]

[0142] Step S5: Design the seismic isolation structure using DDBD to obtain the 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 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 DDBD-based seismic isolation structure designs its horizontal mechanical performance parameters by determining the horizontal displacement performance of the isolation structure. The main idea is to treat the multi-story seismic isolation structure as equivalent to 2DOF, thereby calculating its seismic response to determine its horizontal mechanical performance parameters. Since the superstructure is assumed to be linearly elastic, an inelastic superstructure design is further implemented, and the designed seismic isolation superstructure is then equivalently transformed into a single-mass system with a bilinear mechanical model through a pushover approach.

[0145] Preferred, such as Figure 4 As shown, the DDBD design steps (designing a realistic test set):

[0146] Step S501: Determine the basic information regarding the component layout, materials, and cross-sectional properties of the superstructure. Based on the preliminary design, the superstructure can be equivalent to... Figure 3 The multi-degree-of-freedom shear structure model shown on the left, based on the mass m of the i-th layer of the multi-degree-of-freedom shear structure model... i Horizontal lateral stiffness k i Damping coefficient c i and floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s D s,eq ; where D s,eq To maintain the equivalent displacement required for the superstructure;

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

[0148] Step S503: Based on the basic information of the component layout, material and cross-sectional properties of the superstructure and the performance targets of the lead-core rubber seismic isolation bearings, calculate the target displacement curve of the superstructure in the base isolation structure, such as... Figure 3 As shown on the left, D1 and D i These represent the deformations of the first and i-th floors of the superstructure, respectively; D i It is expressed as the following formula (1),

[0149]

[0150] In equation (1), Φ1 and Φ i Let R be the normalized function of the horizontal displacement of the first and i-th floors of the superstructure, given by the period ratio R. IS h i The parameters of the total height H of the superstructure are calculated, where R IS =T IS / T S T IS The fundamental period of a base isolation structure, T S The basic cycle of the superstructure;

[0151] Step S504: Establish a multi-degree-of-freedom shear structure model based on the target displacement curve of the superstructure in the base isolation structure. Calculate the target displacement D of the superstructure based on the DOF equivalent model. s,eq Equivalent mass m s,eq and equivalent height h s,eq ;

[0152] Step S505, calculate the new cycle ratio R IS In this process, the period ratio R in step S503 is increased. IS Assuming period ratio R IS Through the new cycle ratio R IS Until convergence, the new period is greater than R. IS It is calculated from the following display expression (2):

[0153] Display expression:

[0154] Among them, design displacement That is, D IS,eq ,

[0155] In equation (2), m T The total mass of the superstructure is m. IS The mass of the isolation layer; where m T Based on the basic information, m IS This is one of the basic information items;

[0156] Step S506: Based on the new period ratio R calculated in step S55 IS， Calculate the equivalent stiffness k of the base isolation structure IS And the equivalent damping ratio, where the equivalent stiffness k IS The equivalent stiffness k of a shear-type structural model of a multi-degree-of-freedom system IS,eq Equal; where the equivalent damping ratio ξ of the base isolation structure is equal. IS The damping ratio ξ of the first mode 1,eqThe first-order modal damping ratio ξ is calculated to be... 1,eq Based on the design displacement spectrum, the first modal period T of the multi-degree-of-freedom system shear-type structural model is determined. 1,eq and Interpolation is performed; then the yield displacement d of the isolation layer is determined. yb According to k IS and ξ IS The characteristic strength Q of the seismic isolation layer (used in subsequent step S60) and the post-yield stiffness k are calculated. p (Used in subsequent step S60).

[0157] Step S507, Inelastic superstructure design, based on the base shear force V calculated using equivalent parameters. B Determine the seismic force of each floor of the superstructure, and then calculate the design seismic force F of each floor of the superstructure. ei The formula can be derived from the following equation (3):

[0158]

[0159] in, Δ i Let be the displacement of the upper structure of the i-th layer relative to the ground.

[0160] Step S508: Calculate the design shear force V of the superstructure on each floor. Si The actual yield bearing capacity F of the superstructure on each floor yi It is V Si The yield displacement u of each upper structure is obtained by multiplying by the super-strength coefficient Ω0, which is taken as 2.0 here. Then, the yield displacement u of each upper structure is calculated according to the initial stiffness of each upper structure in formula (4). yi This completes 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 =Ω0V Si

[0164] Steps S501 to S508 are for designing the parameters of the multi-degree-of-freedom mechanical model. In subsequent steps S509 to S511, nine model feature parameters can be derived from the parameters of the multi-degree-of-freedom mechanical model, which can be used as the real test set for the prediction model in the following steps.

[0165] The Bouc-Wen model employs a bilinear model, with both the superstructure and the isolation layer using bilinear stiffness. This necessitates converting the parameters calculated by DDBD. Because the DDBD program assumes the superstructure is linearly elastic, the inelastic superstructure needs to be further converted into a single-mass system of the bilinear mechanical model when establishing the database.

[0166] Step S509, initial stiffness k of the superstructure s =k s,eq Where, k s,eq It can be obtained from equation (5):

[0167]

[0168] Among them, T s,eq For the equivalent period of the superstructure, T s,eq =T s The equivalent method for the superstructure can be used to control displacement through pushover static analysis to obtain the top-floor displacement U. n and the bottom shear force V of the superstructure b The curve is simplified to a bilinear curve and then transformed into the spectral pseudo-acceleration A-spectral displacement D scheme (ADRS), i.e.:

[0169]

[0170] in, Φ is the equivalent mass of the superstructure derived from the first mode of vibration. n1 Φ is the first mode shape coefficient of the top layer, which is taken as 1 here. j1 Let D be the first mode shape coefficient of the j-th floor. The inflection point of the bilinear curve is taken as D. y and A y Therefore, the formula is... Γ1 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 yield stiffness k behind the seismic isolation layer p pass: If we calculate this, we can obtain the yield displacement d of the isolation layer. yb Determine the initial stiffness of the seismic isolation layer:

[0175]

[0176] Step S5111: Based on steps S51-S510 above, calculate the Bouc-Wen model parameters of the 2DOF system. Extract the nine structural parameters of the base isolation structure as shown in Table 2 based on the Bouc-Wen model parameters. Use the base isolation structure as the test isolation structure, and use the nine structural parameters of the base isolation structure as the nine structural parameters of the test isolation structure. These parameters can then be input into the trained prediction model for machine learning testing. The nine extracted structural parameters include:

[0177] M is the 2DOF model. With m IS The sum of; γ m For mass ratio, d ys d represents the yield displacement of the superstructure. ys =D y ;α s The ratio of the post-yield stiffness of the superstructure to the initial equivalent stiffness k of the superstructure is given by the post-yield stiffness. s,eq The ratio of T; s For the basic period of the superstructure, ξ IS The structural damping ratio of the 2DOF model is calculated using formula (8):

[0178]

[0179] Where, μ eq and ε eq They are respectively:

[0180]

[0181] α in Table 2 b It is the yield stiffness ratio behind the seismic isolation layer, k IS / k E ;T b The natural period of the 2DOF model is calculated using the formula; q D The yield-to-weight ratio of the seismic isolation layer is defined as k. IS Total weight of the superstructure (m) T The ratio of ×g;

[0182]

[0183] Step S6: Evaluate the trained prediction model to obtain a qualified prediction model: Generate each test seismic wave corresponding to the test isolation structure; Based on each structural parameter of the test isolation structure and each seismic wave parameter of the corresponding test seismic waves, perform OpenSees finite element analysis to obtain the maximum displacement D of the equivalent mass point of the superstructure corresponding to the test isolation structure. s The maximum displacement D of the isolation layer mass pointsb As the calculation result; based on the structural parameters of the second isolation structure and the corresponding seismic wave parameters of each second seismic wave, as well as the maximum displacement D of the equivalent mass point of the superstructure. s The maximum displacement D of the isolation layer mass points b The trained prediction model is evaluated 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 with a magnitude greater than or equal to 5 are selected for the site corresponding to the design. The wave selection method is based on the code response spectrum in the Chinese "Code for Seismic Design of Buildings" (GB50011.2010), and is selected from 19742 seismic waves obtained from the NGAWest2 database. Following the same method as in step S13, 32 peak ground acceleration amplitude modulations are performed from 0 to 1.6g with intervals of 0.05g, generating a total of 2560 seismic waves. Seismic wave parameters are extracted from these 2560 seismic waves, and OpenSees finite element analysis is performed based on the 9 structural parameters of the test isolation structure obtained in step S5 to output the maximum displacement D of the equivalent mass point of the superstructure. s The maximum displacement D of the isolation layer mass points b This can then be used for machine learning evaluation. Subsequently, the structural parameters of the test isolation structure and the characteristic values ​​of the seismic wave parameters of each corresponding test seismic wave can be input into the machine learning model trained by S6, resulting in 2560 sets of machine learning response predictions.

[0186] Step S62: Input the various 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 superstructure. s The maximum displacement D of the isolation layer mass points b , as the predicted output;

[0187] Step S63: Perform OpenSees finite element analysis on the various structural parameters of the test isolation structure and the corresponding seismic wave parameters of each test seismic wave to obtain the maximum displacement D of the equivalent mass point of the superstructure corresponding to the test isolation structure. s The maximum displacement D of the isolation layer mass points b , as the calculation result;

[0188] Here, features can be extracted from these 2560 seismic waves, and OpenSees finite element analysis can be performed using the nine structural parameters of the derived 2DOF model to output the maximum displacement D of the equivalent mass point of the superstructure. sThe maximum displacement D of the isolation layer mass points b , as the calculation result;

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

[0190] Here, the hyperparameter-tuned model 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 structural parameters (9) and seismic wave parameters (13) of the actual seismic isolation structure to be evaluated into the qualified prediction model to obtain the maximum displacement D of the equivalent mass point of the superstructure corresponding to the actual seismic isolation structure to be evaluated. s The maximum displacement D of the isolation layer mass points b The maximum displacement D of the equivalent mass point of the superstructure corresponding to the actual seismic isolation structure to be evaluated. s The maximum displacement D of the isolation layer mass points b The vulnerability analysis and prediction of the actual seismic isolation structure to be evaluated are carried out to complete the seismic performance evaluation of the actual seismic isolation structure to be evaluated.

[0192] Specifically, incremental dynamic analysis (IDA) observes the degree of damage to a structure by applying progressively increasing seismic intensity. Commonly used seismic intensity indices (IMs) include peak ground acceleration (PGA) or peak ground velocity (PGV). This paper uses PGA amplitude-modulated seismic waves as the intensity index.

[0193] Probabilistic earthquake demand analysis (PSDA) is a method for assessing the structural response demand of a structure under seismic loading. It comprehensively considers both seismic intensity (IM) and structural damage index (DM, in this application, the maximum horizontal displacement D of the superstructure). s The maximum horizontal displacement D of the seismic isolation layer b The correlation between seismic motion and structural performance under different earthquake intensity (IM) conditions. This application aims to demonstrate that the structure exceeds the design objective (the target design value proposed in this paper) under different earthquake intensity (IM) conditions. The conditional probability of the structure is obtained by using regression analysis, and then the transcendence probability of the structure is obtained.

[0194] Step S71: Calculate the superstructure DM. Based on the horizontal maximum displacement D of the superstructure and the horizontal maximum displacement D of the isolation layer, find α and β in DM, and fit to obtain α and β. DM is the median of the maximum horizontal displacement of the superstructure under IM; DM = α(IM). s and the horizontal maximum displacement D of the isolation layer b , find α and β in DM, fit to obtain α and β. DM is the median of the maximum horizontal displacement of the superstructure under IM; DM = α(IM). β , through logarithmic regression of the following formula (9), a = lnα, b = β, IM is the PGA under different earthquake wave amplitude modulations

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

[0196] Here, 2560 earthquake waves are obtained by scaling 80 earthquake waves. Based on the 2560 earthquake waves, the two - mass horizontal structural responses of the original structure's 2DOF model can be calculated. Input the earthquake wave parameters of the 2560 earthquake waves into the trained prediction model to obtain the horizontal structural responses predicted by BO - XGBoost, and obtain the predicted responses under different PGA amplitude modulations. Take the logarithm of the median of the maximum displacement under each earthquake wave amplitude modulation and fit it with ln(PGA) to obtain the fitting curve, as well as the corresponding curve equation and fitting score R 2 .

[0197] Step S72: Based on DM, calculate 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 earthquake wave amplitude modulations)

[0198]

[0199] where N represents 80, that is, 80 earthquake waves

[0200] Step S73: Seismic performance evaluation result: Use the probability of exceedance to represent the conditional probability that the superstructure and the isolation layer exceed the design index under the PGA under different earthquake wave amplitude modulations, that is, the probability of exceedance. The probability of exceedance is represented by the following formula (11), and the vulnerability curves (seismic performance) of the superstructure and the isolation layer are drawn. The above - mentioned design index includes the target design value

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

[0202]

[0203] DO represents the target design value

[0204] In this invention, by inputting seismic wave parameters and structural parameters extracted from a two-degree-of-freedom (2DOF) system to a predictive model for predicting the damage level of a seismic isolation structure, the maximum horizontal displacement of the upper and lower structures of the two-degree-of-freedom (2DOF) system can be output.

[0205] This invention can provide construction engineers with new ideas for judging the seismic performance of seismic isolation structures and further provide a reference for evaluating the health status of seismic isolation structures.

[0206] In vulnerability analysis, the determination of the damage index DM affects the evaluation results. The damage index used 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 mass point of the superstructure. s Maximum displacement D of the seismic isolation layer b .

[0207] The beneficial effects of this invention are:

[0208] This invention, starting from the design concept of seismic isolation structures in Direct Seismic Diversion (DDBD), proposes a machine learning-based design method. By determining target values, the parameters of the isolation layer and the superstructure are calculated, resulting in an equivalent 2DOF model. Nine structural parameters and thirteen seismic wave parameters are extracted, and BO-XGBoost is used to quickly predict the vulnerability curve based on the target values. This provides intuitive guidance for the design of seismic isolation structures in DDBD, offering a faster and more efficient method that helps improve the DDBD approach for seismic isolation structures. The results show good prediction accuracy, even in open-set conditions. The predicted vulnerability curve closely approximates the actual data and can serve as a reference for DDBD structural design. The vulnerability curve also demonstrates that the DDBD design process effectively enables the seismic isolation structure to achieve the expected goals under seismic conditions.

[0209] This 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 sustainable urban development.

[0210] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such 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, 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 associated data structures) can be stored in a computer-readable recording medium, such as RAM memory, a magnetic or optical drive, a floppy disk, or similar devices. Furthermore, some steps or functions of the present invention can be implemented in hardware, for example, as circuitry that works with a processor to perform the various steps or functions.

[0212] Furthermore, a portion of this invention can be applied as a computer program product, such as computer program instructions, which, when executed by a computer, can invoke or provide the methods and / or technical solutions according to the invention through the operation of the computer. The program instructions invoking the methods of the invention may be stored in a fixed or removable recording medium, and / or transmitted via a data stream in a broadcast or other signal-carrying medium, and / or stored in the working memory of a computer device operating according to the program instructions. Here, an embodiment of the invention includes an apparatus comprising a memory for storing computer program instructions and a processor for executing the program instructions, wherein, when the computer program instructions are executed by the processor, the apparatus is triggered to operate the methods and / or technical solutions based on the foregoing embodiments of the invention.

[0213] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be embraced within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims. Furthermore, it is clear that the word "comprising" does not exclude other units or steps, and the singular does not exclude the plural. Multiple units or devices recited in the apparatus claims may also be implemented by a single unit or device in software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any particular order.

Claims

1. A method of predicting damage to a seismic isolation structure designed by a direct displacement method, characterized by, Comprise: Step S1, generate a preset sample seismic wave, establish each seismic wave parameter of each sample seismic wave; Step S2, based on the preset sample seismic wave, calculate the generated structure parameters of the same corresponding number of sample isolation structures, and establish a one-to-one corresponding relationship between each sample seismic wave and a sample isolation structure; Step S3, based on the structure parameters of the isolation structure, and using OpenSees finite element software to establish the corresponding equivalent double freedom model; based on the one-to-one correspondence between each sample earthquake wave and the 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 isolation layer mass point b ; Step S4, based on the seismic wave parameters of the sample seismic wave and the structure parameters of the corresponding sample base-isolated structure, and the maximum displacement D of the corresponding upper building structure equivalent particle s With the maximum displacement D of the base-isolation layer particle b And through XGBoost model training and Bayesian hyperparameter optimization, train the prediction model for predicting the damage degree of the base-isolated structure to obtain the trained prediction model. Step S5, using DDBD to design the isolation structure to obtain the generated test isolation structure and its various structure parameters; Step S6, evaluate the trained prediction model to obtain an evaluation qualified prediction model; Step S7, input the actual structure parameters and seismic wave parameters of the isolation structure to be evaluated into the evaluation qualified prediction model to obtain a prediction result.

2. The damage prediction method for a seismic isolation structure designed by the direct displacement method according to claim 1, wherein In step S1, comprising: Step S11, using the NGAWest2 seismic wave database in PEER to collect, arrange and classify the seismic wave data; obtaining the first seismic wave, selecting the seismic wave with magnitude greater than 5 in the first seismic wave as the second seismic wave; according to the equivalent shear wave velocity of soil layer and the thickness of site covering soil layer, the site of the second seismic wave can be divided into four categories; wherein, the first category V s30 >550m / s, the second category Vs30 is 265-550m / s, the third category V s30 is 165-265m / s, and the fourth category V s30 <165m / s; Step S12: selecting the seismic waves of the first, second and third types of sites from the second seismic waves as third seismic waves, for each type of the selected third seismic waves, respectively according to the magnitude M and the fault projection distance R in the seismic waves jb and by the method of Gaussian mixture model distribution clustering, the first, second and third types of sites in the third seismic waves are divided into 4 groups of data respectively, and a total of 12 groups of data are obtained; Step S13: screening the seismic waves in each of the 12 groups of data by the method of grid screening: that is, screening the seismic waves in each of the 12 groups of data by magnitude M and fault projection distance R jb为 Horizontal and vertical coordinates, divided into a 3x3 grid to obtain 9 ranges of magnitude M and fault projection distance R jb ; taking the grids other than the center grid in the 3x3 grid as peripheral grids, randomly screening 2 seismic waves from each of the peripheral grids, and obtaining a total of 16 seismic waves from the 8 peripheral grids; randomly screening 4 seismic waves from the center grid, so that 20 seismic waves are screened from each group of data, and a total of 240 seismic waves are screened from the 12 groups of data in the three types of sites as the fourth seismic waves; Step S13: the selected 240 fourth seismic waves are amplitude modulated, wherein the peak ground acceleration PGA range of each seismic wave is 0.05-1.6g, and the step length is 0.05g. Amplitude modulation is performed 32 times to obtain 7680 sample seismic waves as excitation for structure calculation, and each seismic wave parameter of the 7680 sample seismic waves is extracted.

3. The damage prediction method for a seismic isolation structure designed by the direct displacement method according to claim 2, wherein Step S12, comprising: Step S121, projecting the fault in the seismic wave by the distance R jb and magnitude M as clustering parameters and normalizing to obtain normalized data; Step S122, based on the normalized data of each type of site, Gaussian mixture model clustering analysis is performed on each type of site, the Gaussian mixture model clustering effect is evaluated by setting different groups for each type of site, and the Bayesian information criterion BIC is used to evaluate the Gaussian mixture model: BIC = -2ln(L) + kln(n), wherein k is the number of model parameters; n is the number of samples; L is the maximum likelihood estimate of the model; Where K is the number of groups; D is the feature dimension, with magnitude M and fault projection distance R jb That is, take 2; the number of groups K of the first, second and third types of sites is respectively clustered according to 1-20, and according to the BIC value of the cluster analysis, when K is four clusters, the model BIC curve appears flat, so the category of each type of site of the model is further subdivided into four groups.

4. The damage prediction method for a seismic isolation structure designed by the direct displacement method according to claim 1, wherein Each seismic wave parameter, including: Duration of the acceleration time history from 5% to 95%: D S5-95 ; peak ground acceleration: PGA; peak ground velocity: PGV; cumulative absolute velocity: CAV; cumulative absolute displacement: CAD; intensity measure: I a ; root mean square acceleration: a rms ; root mean square velocity: v rms ; effective peak acceleration: EPA; predominant period: T s ; mean period: T avg ; T s spectral acceleration at 1 second: S a (T s ); acceleration spectrum intensity: ASI.

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

6. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to Claim 1, wherein Step S3, comprising: In step S31, an equivalent double-freedom model is established using the OpenSees finite element software, wherein the OpenSees finite element software adopts a Bouc-Wen model, i.e., a double-fold line model, and 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 the corresponding sample isolated structure, the acceleration and time sequence of the sample seismic wave are used to perform nonlinear time history analysis on the equivalent double-freedom model, so as to obtain the maximum displacement D s of the upper building structure equivalent mass point of the sample isolated structure b ; in the Bouc-Wen modeling, the parameters include: the post-yield stiffness ratio of the linear hardening component is 0.05; the post-yield stiffness ratio of the nonlinear hardening component is 0; the exponent of the nonlinear hardening component is 1; the yielding exponent is 2; the first hysteretic shape parameter is 0.5; and the second hysteretic shape parameter is 0.

5.

7. The damage prediction method for a seismic isolation structure designed by the direct displacement method according to Claim 1, wherein Step S4, comprising: Step 41, 80% of the data is selected from the sample seismic wave each time, and the grid search method is used to search the random state in the range of 0-1000 to calculate the determination coefficient R of the current selected 80% of the data 2 ; Step 42, the decision coefficient R 2 When the score is the highest, the selected 80% of the data is taken as the training set, and the remaining 20% of the data in the sample seismic wave is taken as the verification set. Step 43, when constructing the XGBoost prediction model, first, a baseline model is used to perform exploratory analysis on potential explanatory variables, thereby screening out the super parameter that contributes most to the model prediction ability; then, based on the training set, the super parameter that contributes most is screened out, and an intelligent optimization method is applied to finely adjust the super parameters of various machine learning algorithms; the super parameters that need to be adjusted in the XGBoost algorithm include: the number of trees of the decision tree, the range is [100:1000]; the maximum depth, the range is [3:100]; The learning rate is [0.001:0.1]; the minimum split loss is [5:10]; the regularization coefficient is [0.001:1]; Step 44, in the model training stage, the verification set is divided into multiple subsets by random sampling, and a five-fold cross-validation program 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, wherein Step S5, comprising: Step S501: Determine the basic information regarding the component layout, materials, and cross-sectional properties of the superstructure. Based on the preliminary design, the superstructure is equivalent to a multi-degree-of-freedom shear structure model. The mass m of the i-th layer of the multi-degree-of-freedom shear structure model is then determined. i Horizontal lateral stiffness k i Damping coefficient c i and floor height h i Determine the natural vibration period T of the superstructure s and damping ratio β s D s,eq ; where D s,eq To maintain the equivalent displacement required for the superstructure; Step S502, under the fortification earthquake or rare earthquake, the upper building structure needs to remain intact, the main body and non-structural components of the upper building structure should not be damaged, and the maximum story drift angle is set to The performance target of the lead rubber bearing is the design displacement under the fortification earthquake or rare earthquake Step S503, according to the basic information of the component arrangement, material and cross-section characteristics of the upper building structure and the performance target of the lead rubber isolation bearing, the target displacement curve of the upper building structure in the base isolation structure is calculated, D1 and D i respectively represent the deformation of the first layer and the i-th layer of the upper building structure; D i is expressed as the following formula (1), In formula (1), Φ1 and Φ i are the normalized functions of horizontal displacement of the first and i-th floors of the upper building structure, which are calculated by the period ratio R IS , h i , and the total height H of the upper building structure, wherein R IS = T IS / T S , T IS is the fundamental period of the base isolation structure, and T S is the fundamental period of the upper building structure; Step S504, a multi-degree-of-freedom system shear type structure model is established according to the target displacement curve of the upper building structure in the base isolation structure, and the target displacement D of the upper building structure is calculated based on the DOF equivalent model s,eq , the equivalent mass m s,eq , and the equivalent height h s,eq ; Step S505, calculate the new period ratio R IS where the new period ratio R IS As the assumed period ratio R IS The new period ratio R IS Until convergence, the new period ratio R IS is calculated from the following display expression (2): Display expression: wherein the design displacement i.e. D IS,eq , m in formula (2) T m is the total mass of the upper building structure IS m is the mass of the isolation layer; wherein T According to the basic information, m IS m is one of the basic information Step S506, based on the step S55 calculated new period ratio R IS， The equivalent stiffness k of the base-isolated structure is calculated IS And the equivalent damping ratio, wherein the equivalent stiffness k IS Of the base-isolated structure is equal to the equivalent stiffness k of the multi-degree-of-freedom system shear type structure model IS,eq ; wherein the equivalent damping ratio ξ of the base-isolated structure is equal to the first modal damping ratio ξ IS Of the multi-degree-of-freedom system shear type structure model 1,eq ; the first modal damping ratio ξ 1,eq Is calculated; the first modal damping ratio ξ 1,eq Is calculated according to the design displacement spectrum, the first modal period T of the multi-degree-of-freedom system shear type structure model yb And Interpolation is obtained; then the yield displacement d of the isolation layer is determined IS , the characteristic strength Q and the post-yield stiffness k IS Of the isolation layer are calculated according to k p And ξ Step S507, non-elastic upper building structure design, the base shear V calculated according to the equivalent parameter B The seismic force of each floor of the upper building structure is determined, so as to calculate the design seismic force F of each floor of the upper building structure ei The formula can be derived from the following formula (3): wherein Δ i is the displacement of the superstructure on the i-th layer relative to the ground; Step S508, calculating the design shear V of each story superstructure Si , the actual yield load F of each story superstructure yi is obtained by multiplying V Si by the super-strength coefficient Ω0, which is taken as 2.0, and then the yield displacement u of each story superstructure is calculated according to formula (4) based on the initial stiffness of each story superstructure yi , thereby completing the inelastic design of the superstructure, u yi = F yi / k i (4) wherein F ei i.e. F ej , F yi = Ω0V Si Step S509, initial stiffness k of upper building structure s = k s,eq , where k s,eq may be obtained from equation (5): where T s,eq is the equivalent period of the superstructure, T s,eq = T s The equivalent method of the superstructure controls the displacement by Pushover static analysis to obtain the top displacement U n and the bottom shear V b of the superstructure, and the curve is simplified into a double broken line curve and converted into the spectrum pseudo-acceleration A-spectrum displacement D format, i.e. wherein, Meff is the equivalent mass of the upper building structure according to the first mode shape; and n1 Φ is the first mode shape coefficient of the top floor, which is taken as 1; and j1 Φ is the first mode shape coefficient of the jth floor; and the inflection point of the double-folded line is taken as D y and A y so that the formula Γ1 and The formula (6) is as follows: Step S510, the isolation layer characteristic strength Q is obtained from formula (7): Wherein, the post-yield stiffness k of the isolation layer p By: The yield displacement d of the isolation layer is obtained yb The initial stiffness of the isolation layer is obtained 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 taken as a test isolation structure, and the 9 structural parameters of the base isolation structure are taken as the 9 structural parameters of the test isolation structure, wherein the 9 structural parameters are extracted, including: M is a 2DOF model with m IS ; γ m is the mass ratio, d ys is the yield displacement of the superstructure, d ys = D y ; α s is the post-yield stiffness ratio of the superstructure, i.e., the ratio of the post-yield stiffness to the initial equivalent stiffness k s,eq of the superstructure; T s is the fundamental period of the superstructure, ξ IS is the structural damping ratio of the 2DOF model, which is calculated according to equation (8): where μ eq and ε eq are respectively: α b is the post-yield stiffness ratio of the isolation layer, k IS / k E ; T b is the natural period of the 2DOF model, calculated according to the formula; q D is the yield weight ratio of the isolation layer, defined as k IS and the total weight of the upper building structure m T ×g.

9. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to Claim 1, wherein Step S6, comprising: Step S61, select 80 seismic waves corresponding to the design site 80, magnitude greater than or equal to 5, and the wave selection method is selected from 19742 seismic waves obtained from the NGAWest2 database; 32 peak acceleration amplitudes of 0.05-1.6g with an interval of 0.05g are generated according to the same method of step S13, a total of 2560 seismic waves, the seismic wave parameters of the 2560 seismic waves are extracted, and OpenSees finite element analysis is carried out based on the 9 structural parameters of the test isolation structure, and the maximum displacement D of the equivalent particle of the upper building structure is output s The maximum displacement D of the isolation layer particle b ; Step S62, input each structure parameter of the test isolation structure and each seismic wave parameter 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 and the maximum displacement D of the mass point of the isolation layer b as the prediction output; Step S63, on the basis of the various structural parameters of the test isolated structure and the various seismic wave parameters of the corresponding various test seismic waves, OpenSees finite element analysis is performed to obtain the maximum displacement D of the equivalent mass point of the upper building structure corresponding to the test isolated structure s and the maximum displacement D of the mass point of the isolation layer b as the calculation result; Step S64, based on the preset evaluation method, the predicted output and the calculated output are evaluated and compared to obtain an evaluation-qualified prediction model.

10. The damage prediction method for a seismic isolation structure designed by a direct displacement method according to Claim 1, wherein Step S7, comprising: Step S71, obtaining 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 isolation layer b , obtaining α and β in DM, fitting to obtain α and β, DM is the median value of the maximum horizontal displacement of the upper building structure under IM; DM = α (IM) β , through logarithmic regression of the following formula (9), a = lnα, b = β, IM is the PGA under different seismic wave 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 of the structure in IM, Wherein N represents 80, that is, 80 seismic waves; Step S73, anti-seismic performance evaluation result: using the exceeding probability to express the conditional probability of the upper building structure and the isolation layer exceeding the design index under the PGA of different seismic wave amplitude modulation, i.e. the exceeding probability, the exceeding probability is expressed by the following formula (11), both the vulnerability curves of the upper building structure and the isolation layer are drawn, and the design index includes the target design value P(DM≥DO|IM)=1-P(DM<DO|IM) by conversion (ln(DM)=a+bln(IM)), the above formula is written as: DO represents the target design value

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