Machine learning based method and system for predicting seismic residual displacement of a seismic mitigation bridge

Abstract

The present application relates to a machine learning-based seismic-induced residual displacement prediction method and system for a seismic mitigation bridge, and belongs to the technical field of bridge performance analysis. The present application solves the problems of high cost, slow speed and low accuracy of existing prediction methods. First, the basic information of the seismic mitigation bridge and the parameter information of the seismic mitigation device are obtained. A simulation model of the seismic mitigation bridge under seismic action is established. The Latin hypercube sampling method is used to sample the characteristic parameters, and feature processing and simulation model calculation are performed to construct a feature parameter-seismic-induced residual displacement sample set. A Stacking integrated model is trained based on the sample set. The trained Stacking integrated model is used to predict the seismic-induced residual displacement of the seismic mitigation bridge. The present application does not require the deployment of a large number of sensors, can quickly and accurately predict the bridge seismic-induced residual displacement under rare earthquakes, has the advantages of low cost, fast speed and high accuracy, and provides an effective technical means for bridge seismic resilience evaluation and post-disaster rapid identification.

Description

Technical Field

[0001] This invention relates to the field of bridge performance analysis technology, and in particular to a method and system for predicting seismic-induced residual displacement of seismic isolation bridges based on machine learning. Background Technology

[0002] my country has a large number of bridges, playing a vital role in land transportation infrastructure, especially small and medium-span bridges, which account for approximately 84% of the country's total bridges. However, with the increasing frequency of earthquakes, bridges face serious disaster risks, threatening not only people's lives but also causing huge economic losses. Therefore, improving the seismic toughness of bridge structures is crucial. Earthquakes cause irreversible deformation of bridge structures, i.e., residual displacement. Studies have shown that residual displacement indicators can effectively assess the damage state and safety of bridge structures after earthquakes. If the residual displacement of a bridge caused by an earthquake is too large, even if the structure does not collapse, it will lose part of its traffic capacity and cannot continue to be used normally. Therefore, rapid and accurate assessment of earthquake-induced residual displacement and reasonable control of earthquake-induced residual displacement are crucial aspects that cannot be ignored in modern bridge seismic design.

[0003] Accurate expression of the parameters characterizing the seismic-induced residual displacement of bridges is the basis for their prediction, and scholars at home and abroad have conducted research in this area.

[0004] For example, the paper "Analysis of Influencing Factors and Bayesian Estimation of Residual Displacement Index of RC Bridge Piers" published in the journal Vibration and Shock studied the statistical characteristics and main influencing factors of residual displacement index through the quasi-static numerical analysis results of 256 RC bridge piers. The results showed that among the four influencing factors of axial compression ratio, shear span ratio, longitudinal reinforcement ratio and stirrup ratio, axial compression ratio has the greatest impact on the residual displacement index of reinforced concrete bridge piers, and the mean value of residual displacement index decreases with the increase of axial compression ratio. The mean value of residual displacement index of reinforced concrete bridge piers increases with the increase of shear span ratio, longitudinal reinforcement ratio and stirrup ratio, but the overall increase is not large.

[0005] For example, the paper "Study on Residual Displacement of Reinforced Concrete Bridge Piers under Seismic Action" published in the journal Vibration and Shock shows that the influence coefficient of residual displacement of reinforced concrete bridge piers decreases with the increase of axial compression ratio, longitudinal reinforcement strength hardening coefficient, volumetric stirrup ratio, and slenderness ratio. The influence coefficient of residual displacement increases with the increase of longitudinal reinforcement ratio and longitudinal reinforcement to concrete strength ratio of bridge pier.

[0006] The existing methods mentioned above have obtained the characterization parameters of the seismic-induced residual displacement of the bridge structure system through numerical simulation analysis. However, the studies are all based on the pier model. In actual engineering applications, the influence of the main beam structure needs to be considered. Furthermore, the methods have not yet considered the clear expression of the characterization parameters of the residual displacement under the combined action of the device and the structure after the application of seismic isolation device to the seismic isolation bridge.

[0007] In the prediction of earthquake-induced residual displacement of bridges, some scholars have also conducted research and achieved certain results.

[0008] For example, in the Japanese Code for Seismic Design of Bridges, the formula for verifying residual displacement is expressed by the residual displacement ductility index. The formula uses the strength hardening coefficient of steel reinforcement, the displacement ductility coefficient of the pier, and the equivalent yield displacement of the pier as characteristic parameters of residual displacement.

[0009] For example, the master's thesis from Jilin University, "Rapid Assessment and Control Method of Residual Displacement of Small-Span Seismic Isolation Bridges under Seismic Action", constructs a proxy relationship model between seismic-induced residual displacement and various parameters based on the Marquardt-Global Optimization Algorithm, thus forming a rapid assessment method for post-earthquake residual displacement.

[0010] However, the residual displacement prediction method in Japanese standards is still designed for ordinary bridges and is not applicable to seismic isolation bridges. The Marquardt-Global Optimization algorithm used in the Jilin University paper is a point estimation algorithm that outputs a set of "optimal" parameters, but the reliability of these parameters cannot be determined. Furthermore, traditional seismic isolation bridge monitoring relies on the deployment of a large number of sensors, wired transmission, and dedicated data acquisition equipment. The costs of hardware procurement, installation, commissioning, and subsequent operation and maintenance are high, and it largely depends on manual inspection and offline analysis. The real-time data and coverage are insufficient, further increasing the cost of full life cycle monitoring and making it difficult to achieve large-scale promotion and application.

[0011] In summary, the research on methods for predicting seismic-induced residual displacement of seismically isolated bridges is still insufficient. Current research results cannot effectively combine the characteristic parameters of bridge structures and seismic isolation devices to predict seismic-induced residual displacement. Therefore, conducting research on the accurate expression of characteristic parameters of seismic-induced residual displacement and the prediction of residual displacement of seismically isolated bridges has important theoretical and practical application value for improving the seismic toughness of bridges. Summary of the Invention

[0012] To address the problems of high cost, slow speed, and low accuracy in existing earthquake-induced residual displacement prediction methods, this invention provides a machine learning-based method and system for predicting earthquake-induced residual displacement of seismically isolated bridges. This method and system utilizes an established numerical simulation model of the seismically isolated bridge, eliminating the need to deploy expensive sensors on the bridge structure. By using only basic information about the bridge and seismic isolation devices, the method can obtain the earthquake-induced residual displacement of the bridge under rare earthquakes, providing reliable data support for improving the seismic toughness of bridges and evaluating the structural performance of post-disaster relief.

[0013] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0014] A machine learning-based method for predicting seismic-induced residual displacement in seismically isolated and reduced-voltage bridges includes the following steps:

[0015] Step 100: Obtain the basic information of the seismic isolation bridge and the parameter information of the corresponding seismic isolation device;

[0016] Step 200: Based on the basic information and the parameter information, establish a simulation model of the seismic isolation bridge under seismic loading using OpenSees software;

[0017] Step 300: Using the Latin hypercube sampling method, multiple characterization parameters of the seismic-induced residual displacement are sampled to generate an original sample set. The original sample set is then subjected to feature processing, and the seismic-induced residual displacement corresponding to the sample parameters is calculated using the simulation model. Finally, a characteristic parameter-seismic-induced residual displacement sample set is constructed. The characterization parameters include span, shear span ratio, stiffness, damping coefficient, and velocity index.

[0018] Step 400: Based on the feature parameter - seismically induced residual displacement sample set, train the Stacking ensemble model to obtain the trained Stacking ensemble model;

[0019] Step 500: After feature processing of the characterization parameters of the seismic isolation bridge to be predicted, input them into the trained Stacking ensemble model, and output the seismic-induced residual displacement prediction results.

[0020] Accordingly, this invention also proposes a machine learning-based system for predicting seismic-induced residual displacement of seismically isolated bridges, comprising:

[0021] The acquisition module is used to acquire basic information about seismic isolation bridges and the parameter information of corresponding seismic isolation devices.

[0022] The model building module is used to build a simulation model of the seismic isolation bridge under seismic loading using OpenSees software based on the basic information and the parameter information.

[0023] The sample set construction module is used to sample multiple characterization parameters of seismic-induced residual displacement using the Latin hypercube sampling method to generate an original sample set. Then, the original sample set is subjected to feature processing, and the seismic-induced residual displacement corresponding to the sample parameters is calculated using the simulation model. Finally, the characteristic parameter-seismic-induced residual displacement sample set is constructed. The characterization parameters include span, shear span ratio, stiffness, damping coefficient, and velocity index.

[0024] The training module is used to train the Stacking ensemble model based on the feature parameter - the seismically induced residual displacement sample set, to obtain the trained Stacking ensemble model;

[0025] The prediction module is used to process the characterization parameters of the seismic isolation bridge to be predicted and input them into the trained Stacking ensemble model, and output the prediction results of seismic-induced residual displacement.

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] (1) This invention does not require the installation of expensive sensing equipment on the bridge piers, such as data acquisition equipment such as stress or strain sensors and displacement sensors used to monitor the bridge piers and main beams. It can predict the residual displacement caused by the earthquake of the bridge by simply acquiring the basic information of the seismic isolation bridge (such as shear span ratio, main beam cross-sectional dimensions, concrete strength, etc.) and the parameter information of the seismic isolation device (such as stiffness, damping coefficient and velocity index, etc.), which greatly reduces the cost of predicting the residual displacement caused by the earthquake of the bridge.

[0028] (2) This invention considers the key factors affecting the residual displacement of bridges caused by earthquakes. When using OpenSees for modeling, it fully considers the linear and nonlinear response characteristics of the main beam structure and pier structure under seismic loads. At the same time, it simplifies the characteristic parameters of commonly used passive seismic isolation devices to stiffness, damping and damping coefficient. It uses Elastomeric BearingPlasticity elements for accurate simulation. Compared with existing modeling methods, it does not require separate modeling of bridges with various passive seismic isolation devices. It only needs to match the device parameters and the three characteristic parameters to predict the residual displacement of bridges caused by earthquakes, which further improves the speed of predicting residual displacement caused by earthquakes.

[0029] (3) The present invention uses the Stacking ensemble model to fit the feature parameter - seismic residual displacement sample set, so that the prediction results are closer to the actual structural response and improve the prediction accuracy of seismic residual displacement of the seismic isolation bridge. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without exceeding the scope of protection claimed by the present invention.

[0031] Figure 1 This is a flowchart of the machine learning-based method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges according to an embodiment of the present invention.

[0032] Figure 2 A schematic diagram of the main beam cross-sectional dimensions for a seismic isolation bridge;

[0033] Figure 3A schematic diagram showing the cross-sectional dimensions and reinforcement of bridge piers for seismic isolation and vibration reduction;

[0034] Figure 4 The El Centro wave acceleration time history curve;

[0035] Figure 5 Here is the Northridge wave acceleration time history curve;

[0036] Figure 6 The Kobe wave acceleration time history curve;

[0037] Figure 7 These are the first 40 samples drawn using the Latin hypercube sampling method;

[0038] Figure 8 The last 30 samples were drawn using the Latin hypercube sampling method;

[0039] Figure 9 The results of seismic-induced residual displacement calculations are for 70 sets of samples extracted using the Latin hypercube sampling method.

[0040] Figure 10 This is a schematic diagram of the feature importance ranking results;

[0041] Figure 11 This is a schematic diagram of the feature correlation calculation results;

[0042] Figure 12 A comparison chart of predicted and actual values ​​for the entire dataset;

[0043] Figure 13 A comparison chart of predicted and actual values ​​for the test set;

[0044] Figure 14 A scatter plot for predicting accuracy. Detailed Implementation

[0045] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0046] like Figure 1 As shown, this embodiment provides a machine learning-based method for predicting seismically induced residual displacement in seismically isolated bridges. It belongs to the category of residual displacement analysis methods for simply supported beam bridges under seismic loading, specifically involving steps such as information acquisition, establishment of a nonlinear simulation model and characteristic parameter analysis, Latin hypercube sampling and analysis, and machine learning-based prediction of seismically induced residual displacement. The method specifically includes the following steps S100-S500.

[0047] Step S100: Obtain basic information about the seismic isolation bridge and parameter information of the seismic isolation device.

[0048] The basic information for seismic isolation and vibration reduction bridges includes bridge span, main girder cross-sectional dimensions, concrete strength, steel yield strength, pier cross-sectional dimensions, pier height, longitudinal reinforcement ratio, stirrup reinforcement ratio, number of supports, support friction coefficient, distance between the main girder and the pier, and specific parameters of the selected concrete and steel reinforcement materials. For example, the main girder cross-sectional dimensions of a seismic isolation and vibration reduction bridge obtained in this step are as follows: Figure 2 and Figure 3 As shown, Figure 2 The diagram shows the cross-sectional dimensions of the main beam, where the top plate has a width of 12.6m, a section height of 3.052m, a thickness of 0.285m, a bottom plate thickness of 0.28m, a web thickness of 0.45m, and a bottom plate width of 5.5m. Figure 3 The diagram shows the cross-sectional dimensions and reinforcement of the bridge pier. The total vertical height of the bridge pier is 3.28m, the length of the straight section in the middle is 4.32m, and the radius of the semi-circular sections at both ends is 1.64m.

[0049] Seismic isolation and damping devices are installed on bridges. The parameters of these devices include their stiffness, damping coefficient, and velocity index.

[0050] Step S200: Based on the basic information and parameter information obtained in step S100, a simulation model of the seismic isolation bridge under seismic loading is established using OpenSees software.

[0051] In this step, the concrete is simulated using the Concrete02 model, which fully considers the strength and stiffness degradation of concrete under cyclic loading. The reinforcing steel is simulated using the Steel02 model, which effectively describes the elastoplastic behavior of the steel during loading. The main beam structure is simulated using Elastic Beam Column Elements, the pier structure using Nonlinear Beam Column Elements, and ordinary supports using Zero Length Elements. The characteristic parameters of the passive seismic isolation device are simplified to stiffness, damping, and damping coefficient, and simulated using Elastomeric Bearing Plasticity elements. The pier base is consolidated using the `fix` command, and different components are connected using Rigid Link elements. When selecting seismic waves for the analysis, typical El Centro, Northridge, and Kobe waves are selected as seismic inputs, with the peak ground acceleration adjusted to 0.3g. The acceleration time history curves for each seismic wave are shown below. Figures 4-6 As shown, where Figure 4The El Centro wave acceleration time history curve, Figure 5 Here is the Northridge wave acceleration time history curve. Figure 6 This is the Kobe wave acceleration time history curve.

[0052] Step S300: Using the Latin hypercube sampling method, multiple characterization parameters of the seismic-induced residual displacement are sampled to generate an original sample set. The original sample set is then subjected to feature processing, and the seismic-induced residual displacement corresponding to the corresponding sample parameters is calculated using the simulation model established in step S200, thus constructing the feature parameter-seismic-induced residual displacement sample set.

[0053] Step S310: Using the Latin hypercube sampling method, multiple characterization parameters of the seismically induced residual displacement (span, shear span ratio, stiffness, damping coefficient, and velocity exponent) are sampled to generate the original sample set.

[0054] Step S320: Perform feature processing on the original sample set obtained in step S310, including feature screening, feature standardization, and feature sample skewness analysis and correction of the characterization parameters, and use the simulation model to calculate the seismic residual displacement corresponding to the corresponding sample parameters, and finally construct the feature parameter-seismic residual displacement sample set.

[0055] Specifically, step S321, feature selection: Based on the original five numerical features (span, shear-span ratio, stiffness, damping coefficient, and velocity exponent), corresponding derived features are generated using four methods: quadratic polynomial, interaction term, nonlinear transformation, and engineering empirical formula. These include quadratic polynomial features, key interaction features, nonlinear transformation features, and engineering significance features, with the total number of features controlled within 50. The derived features are then filtered through variance thresholding, F-test screening, Lasso regularization screening, and recursive feature elimination (RFE) screening processes, gradually eliminating low-value features and ultimately retaining the core features. In this embodiment, span, shear-span ratio, stiffness, damping coefficient, and velocity exponent are ultimately determined as the core features for training the Stacking ensemble model. For example, 70 samples are extracted using the Latin hypercube sampling method to form a feature parameter-seismic residual displacement sample set, as shown in the sampling results. Figure 4 and Figure 5 As shown, where Figure 4 These are the first 40 samples drawn using the Latin hypercube sampling method. Figure 5 These are the last 30 samples drawn using the Latin hypercube sampling method. The ranking of feature importance and the calculation results of feature correlation are as follows: Figure 10 and Figure 11 As shown.

[0056] Step S322, Feature Standardization: Use RobustScaler to standardize the core features. A significant advantage of using RobustScaler for feature standardization is its resistance to outlier interference, which avoids the influence of extreme values ​​on the standardization results, making it suitable for outlier samples that may exist in engineering data.

[0057] Specifically, when using RobustScaler for feature standardization, the core features obtained after screening are converted to the same scale through "median centering + interquartile range scaling", and the training set and test set are divided. The statistics of the training set (median, interquartile range) are used to process the training set and test set in a unified manner.

[0058] For example, from the obtained 70 sets of feature parameters - seismically induced residual displacement samples, 55 samples are selected as the training set and 15 samples as the test set. Let a certain feature... The samples in the training set are ,in The number of samples in the training set. Calculate the features in the training set. the median of Its value is the first ordered sample values ​​(if (For even numbers, take the average of the two middle samples). Calculate features. interquartile range The calculation formula is as follows:

[0059]

[0060] in, It is the 25th percentile (lower quartile). It is the 75th percentile (upper quartile).

[0061] Next, the feature samples in the training and test sets... All use the median of the training set. and interquartile range The transformation is performed, and the formula is as follows:

[0062]

[0063] in, Features The output feature values ​​after standardization These are the original input feature values ​​to be processed.

[0064] Step S323, Feature Sample Skewness Analysis and Correction: The skewness coefficient can be used to measure the degree of asymmetry in the data distribution. Its calculation formula is as follows:

[0065]

[0066] in:

[0067] The mean of the training set. Indicates the first training set A single true observation of a sample;

[0068] denoted as the standard deviation of the training set.

[0069] The criterion for skewness is: if the skewness coefficient If the skewness of the feature samples is strong right-skewed, then the skewness coefficient is... If the feature sample is skewed, then the skewness is strongly left-skewed.

[0070] To correct the skewed distribution of feature samples, three transformation methods were used: original transformation, log1p transformation, and Box-Cox transformation. The average coefficient of determination (i.e., average) of the Kernel Ridge model under 5-fold cross-validation (KFold) was then applied. Using as the evaluation indicator, the average was selected. The highest transformation method is selected as the optimal transformation method, and the skewness of the feature samples is corrected by using the selected optimal transformation method.

[0071] Among them, the average value of the Kernel Ridge model under 5-fold cross-validation The calculation formula is as follows:

[0072]

[0073] in, For the first The first fold verification set The value of a sample after processing by the current transformation method; For the KernelRidge model in the 1st On the folded verification set, for the first Predicted values ​​for each sample; For the first The average of all true values ​​in the validation set after being processed by the current transformation method.

[0074] The feature-processed sample parameters are used as input variables, and a pre-established simulation model is called to calculate the corresponding seismically induced residual displacements under the given sample parameters. The seismically induced residual displacements corresponding to the 70 sets of samples generated by the simulation model are shown below. Figure 9 As shown.

[0075] Thus, through Latin hypercube sampling, feature selection, feature standardization and skewness correction, and simulation model calculation, the entire process of constructing the feature parameter-seismic residual displacement sample set is completed, which can then be used for subsequent Stacking ensemble model training.

[0076] Step S400: Based on the feature parameter-seismic residual displacement sample set constructed in Step S300, train the Stacking ensemble model. Specifically, the feature parameter-seismic residual displacement sample set is divided into a training set and a test set. The training set is used to perform parameter fitting and hyperparameter optimization on the basic model layer and meta-model layer of the Stacking ensemble model to obtain the trained Stacking ensemble model. The test set is used to evaluate the accuracy of the trained Stacking ensemble model.

[0077] The Stacking ensemble model, as the core modeling architecture for residual displacement prediction, solves the problems of insufficient generalization ability and limited nonlinear fitting of single models through a two-level collaborative mechanism of "mining local feature patterns at the base model layer + fusing global prediction information at the meta-model layer". The construction process of the Stacking ensemble model in this step can be broken down into four core steps: architecture design, base model construction, meta-model adaptation, and hyperparameter optimization.

[0078] Step S410, Stacking Ensemble Model Architecture Design: The Stacking ensemble model adopts a "layered and progressive" architecture. Its core is to transform the prediction results of the base model into the input features of the meta-model, achieving an accuracy improvement through "local prediction → global fusion." The specific architecture and data flow are as follows:

[0079] Input layer: Receives the preprocessed core feature matrix, which consists of core features. The dimension is the number of samples × the number of features. That is, each row of the core feature matrix represents a sample, and each column represents a core feature (such as shear span ratio, stiffness, damping coefficient, etc.). All feature samples have been standardized by RobustScaler.

[0080] The base model layer consists of three heterogeneous models. It receives input layer features and outputs the model-level predicted value for each sample, forming a meta-feature matrix with the dimension of the number of samples × the number of base models.

[0081] Meta-model layer: Receives the meta-feature matrix and obtains the final predicted value, i.e., the predicted seismic residual displacement, through linear fusion.

[0082] Output layer: Outputs the final predicted value, the prediction results of the base model layer, and the coefficient of determination obtained after accuracy evaluation. and mean absolute percentage error .

[0083] Step S420, Basic Model Construction: The basic model is the core prediction unit of the Stacking ensemble model. It needs to be selected based on the principle of "covering different data patterns and complementary bias types" to ensure that the meta-feature matrix contains rich prediction information. In this embodiment, the Stacking ensemble model uses Bayesian ridge regression, kernel ridge regression, and gradient boosting regression as the basic models.

[0084] (1) Bayesian Ridge Regression Model: Based on the Bayesian framework, this model improves upon the traditional ridge regression model. The core of this improvement is to define the model parameters (coefficients). Noise variance Define the prior distribution:

[0085] The prior coefficients are: , The regularization strength parameter is... It is the identity matrix;

[0086] The noise variance prior is: , For shape parameters;

[0087] The parameters are updated by maximizing the logarithmic marginal likelihood function, thus balancing the fitting accuracy and the regularization strength.

[0088] This Bayesian ridge regression model provides coefficient interpretability, supports physical verification of feature importance, and avoids a disconnect between data-driven approaches and engineering experience.

[0089] (2) Kernel Ridge Regression Model: Kernel ridge regression is a combination of "kernel method + ridge regression". The core steps include:

[0090] Kernel mapping: via RBF kernel function This involves mapping low-dimensional features to a high-dimensional space to solve nonlinear fitting problems; among them, and The first The and the first One input feature vector, For RBF kernel width parameters, This represents the Euclidean norm.

[0091] Ridge regression fitting: Minimizing the loss function in a high-dimensional space using ridge regression, expressed by the following formula:

[0092]

[0093] in, For the kernel matrix, For kernel space coefficients, For regularization strength, This represents the number of training samples.

[0094] This kernel ridge regression model exhibits strong generalization ability with small samples. The kernel method does not require explicit construction of a high-dimensional space, thus avoiding the curse of dimensionality. It is suitable for 70 small samples and can solve the problem of limited sample size in the engineering field, which cannot support complex machine learning models.

[0095] (3) Gradient boosting regression model: Based on the ensemble idea of ​​"iterative fitting residuals", the core steps include:

[0096] Initialization: Use the mean of the target variable in the training set as the initial prediction value;

[0097] Iterative training: In each round, a decision tree is trained, fitting the residual from the previous round. ,in, For loss function, and The first The input feature vector and the true target value of each sample. For the front After the trees are merged, the first The predicted value for each sample, This represents the candidate regression trees to be selected during the optimization process. Indicates the candidate regression tree for the first... Output of each sample;

[0098] Result fusion: The prediction results of all trees are fused together using a learning rate weighting method. ,in, For learning rate, These are the initial predicted values ​​determined using the mean of the target variable in the training set.

[0099] This gradient boosting regression model has strong anti-overfitting ability. By using "residual correction + learning rate control", it avoids overfitting of a single tree and can still maintain stable generalization ability under small sample size.

[0100] The combination of Bayesian ridge regression model, kernel ridge regression model and gradient boosting regression model enables the meta-feature matrix to contain multi-dimensional information of "linear + nonlinear + piecewise", laying the foundation for meta-model optimization and fusion.

[0101] Step S430, Meta-model Adaptation: The meta-model takes the prediction results of the base model as input (i.e., the meta-feature matrix) and estimates the fusion coefficients using the least squares method, as follows:

[0102] The meta-feature matrix is: ,in, These are the predicted values ​​from the Bayesian ridge regression model. The predicted values ​​are from the kernel ridge regression model. To improve the predicted values ​​of the gradient boost regression model, It is the meta-feature matrix;

[0103] The linear fusion formula is:

[0104]

[0105] in, This is the final predicted value. For the intercept term, , , These are the weighting coefficients of the predicted values ​​for the Bayesian ridge regression model, the kernel ridge regression model, and the gradient boosting regression model, respectively.

[0106] Next, coefficient estimation is performed. The loss function is minimized using the least squares method. To obtain the optimal coefficient .in, This represents the true target value of the training set. This represents the vector of coefficients to be estimated in the linear fusion model. This represents the matrix transpose operation.

[0107] The base model has already captured complex patterns, so the meta-model only needs linear fusion (complex meta-models are prone to fitting meta-feature noise, especially in small sample scenarios), thus avoiding overfitting. At the same time, the contribution weights of the base model can be quantified through linear coefficients, resulting in strong interpretability.

[0108] Step S440, Hyperparameter Optimization: The default parameters of the basic model cannot be adapted to the specific data for predicting earthquake-induced residual displacement (such as the kernel space coefficients of the kernel ridge regression model). (The model needs to match the scale of stiffness characteristics), so it is necessary to find the optimal combination of hyperparameters through systematic parameter search to ensure that the model performance meets the target.

[0109] The effectiveness of hyperparameter optimization is reflected in three aspects: the accuracy of the basic model fitting, the balance of the basic model bias, and the achievement of engineering accuracy standards. Taking the kernel ridge regression model as an example, its kernel space coefficients... After optimization, the cross-validation determination coefficient of the nonlinear fitting is... The coefficient of determination (COP) was improved from 0.88 to 0.92. Simultaneously, the learning rate and tree depth of the gradient boosting regression model were optimized using grid search to prevent them from excessively dominating the fusion results, resulting in a more balanced contribution from the three base models. Based on these improvements, the average COP of the trained Stacking ensemble model after 5-fold cross-validation was [percentage missing]. The accuracy reaches above 0.95, meeting the actual requirements of structural engineering for the accuracy of residual displacement prediction.

[0110] The comparisons between predicted and actual values ​​for the entire dataset, the comparisons between predicted and actual values ​​for the test set, and the scatter plots of prediction accuracy calculated by the model are shown below. Figure 12, Figure 13 , Figure 14 As shown. By Figure 12 and Figure 13 As can be seen, the Stacking integrated model constructed in this embodiment can accurately predict the seismic-induced residual displacement of the seismic isolation bridge, and the prediction results are highly consistent with the actual values ​​of the finite element simulation, meeting the requirements of engineering applications for prediction accuracy. Figure 14 This further verified the concentration of prediction errors, with the prediction errors for the vast majority of samples being controlled within a small range.

[0111] Furthermore, after step S400, an accuracy evaluation step is also included: the accuracy of the trained Stacking ensemble model is evaluated.

[0112] Accuracy assessment is a core step in validating the effectiveness of the Stacking ensemble model. It requires quantifying the consistency between predicted results and actual values ​​using multi-dimensional indicators, while also providing an interpretable error range tailored to engineering needs. This embodiment uses the coefficient of determination (COP). ) and mean absolute percentage error ( () is used as an evaluation metric for assessing the accuracy of the Stacking ensemble model.

[0113]

[0114]

[0115] in:

[0116] The number of samples in the test set;

[0117] For the first True residual displacement values ​​of each test sample (in mm).

[0118] For the first Predicted residual displacement values ​​(in mm) for each test sample.

[0119] This represents the mean of the actual residual displacement values ​​in the test set (in mm).

[0120] The determination coefficient of this Stacking ensemble model was calculated using the above evaluation steps. Mean absolute percentage error The results indicate that the Stacking ensemble model has a good fit, accurately predicts trends, and its prediction accuracy is within an acceptable range.

[0121] Step S500: Based on the Stacking ensemble model trained in step S400, the corresponding characterization parameters of the seismic isolation bridge to be predicted are processed and then input into the trained Stacking ensemble model to output the seismic-induced residual displacement prediction results.

[0122] After training and hyperparameter optimization of the Stacking ensemble model, the model enters the application prediction phase. For any seismic isolation bridge to be predicted, only its corresponding characterization parameters need to be obtained, including span, shear span ratio, stiffness, damping coefficient, and velocity exponent. These five characterization parameters are processed according to the same feature processing procedure as in step S320 (feature selection, feature standardization, and feature sample skewness analysis and correction) to form a core feature vector of the same dimension as in the training phase. This core feature vector is then input into the trained Stacking ensemble model.

[0123] In the trained Stacking ensemble model, the core feature vector is input from the input layer and outputs three independent predicted values ​​via the base model layer; subsequently, the meta-model layer calculates the predicted values ​​based on the weights determined during training. , , The earthquake-induced residual displacement prediction results of the seismic isolation bridge to be predicted are obtained by calculating according to the aforementioned linear fusion formula. The prediction results can be directly used to assess the damage status and traffic capacity of the seismic isolation bridge under rare earthquake action, and provide data support for rapid post-disaster identification and seismic toughness assessment.

[0124] The machine learning-based method for predicting seismically induced residual displacement in seismically isolated bridges proposed in this embodiment eliminates the need for expensive sensors on the bridge structure. It only requires acquiring basic structural information of the bridge and three key parameters of the seismic isolation device (stiffness, damping coefficient, and velocity exponent) to achieve rapid prediction of seismically induced residual displacement, significantly reducing hardware procurement and costs. When using OpenSees for modeling, the linear and nonlinear response characteristics of the main beam and pier structures under seismic loads are fully considered. The characteristic parameters of commonly used passive seismic isolation devices are simplified to stiffness, damping, and damping coefficient. Elastomeric Bearing Plasticity elements are used for accurate simulation. Compared with existing modeling methods, it eliminates the need for separate modeling of bridges with various passive seismic isolation devices. Matching the device parameters with the three characteristic parameters is sufficient to predict the seismically induced residual displacement, further improving the speed of prediction. Simultaneously, this method uses a Stacking ensemble model to fuse the prediction results of three heterogeneous models and combines 5-fold cross-validation to systematically optimize the model hyperparameters, significantly improving prediction accuracy. This provides an efficient and reliable technical means for assessing the seismic toughness of bridges and for rapid post-earthquake identification.

[0125] Corresponding to the above-mentioned machine learning-based method for predicting seismic-induced residual displacement of seismic-isolated bridges, this embodiment also provides a machine learning-based system for predicting seismic-induced residual displacement of seismic-isolated bridges. The system specifically includes an acquisition module, a model building module, a sample set construction module, a training module, and a prediction module. The functions of each module are as follows.

[0126] The acquisition module is used to acquire basic information about the seismic isolation bridge and the corresponding parameter information of the seismic isolation device. This module corresponds to step S100, and the specific content acquired includes the bridge span, main beam cross-sectional dimensions, concrete strength, steel yield strength, pier cross-sectional dimensions, pier cross-sectional height, longitudinal reinforcement ratio, stirrup reinforcement ratio, number of supports, support friction coefficient, distance between the main beam and the pier, and specific parameters of the selected concrete and steel materials, as well as the stiffness, damping coefficient, and velocity index of the seismic isolation device.

[0127] The model building module is used to build a simulation model of the seismic isolation bridge under seismic loading using OpenSees software based on the above basic information and parameter information. This module corresponds to step S200, and its specific modeling methods include: simulating concrete using the Concrete02 model and reinforcing steel using the Steel02 model; simulating the main beam structure using Elastic Beam Column Element; simulating the pier structure using Nonlinear Beam Column Element; simulating ordinary bearings using Zero Length Element; simulating the passive seismic isolation device using Elastomeric BearingPlasticity element; consolidating the pier base using the fix command and connecting different components using Rigid Link element; selecting El Centro wave, Northridge wave, and Kobe wave as the seismic waves, with the peak ground motion adjusted to 0.3g.

[0128] The sample set construction module is used to sample multiple characterization parameters of seismically induced residual displacement using the Latin hypercube sampling method to generate an original sample set. The original sample set is then subjected to feature processing, and the seismically induced residual displacement corresponding to the sample parameters is calculated using a simulation model. Finally, a characteristic parameter-seismically induced residual displacement sample set is constructed, where the characterization parameters include span, shear span ratio, stiffness, damping coefficient, and velocity exponent. This module corresponds to step S300.

[0129] Specifically, the sample set construction module includes the following sub-modules:

[0130] The sampling module is used to sample five characterization parameters of earthquake-induced residual displacement—span, shear span ratio, stiffness, damping coefficient, and velocity exponent—using the Latin hypercube sampling method to generate an original sample set.

[0131] The feature processing submodule is used to perform feature processing on the original sample set generated by the sampling module. This feature processing submodule further includes:

[0132] The feature filtering unit is used to generate corresponding derived features based on the original five numerical features (span, shear span ratio, stiffness, damping coefficient, and velocity index) using four methods: quadratic polynomial, interaction term, nonlinear transformation, and engineering empirical formula. The total number of controlled features is kept within 50. The derived features are filtered through variance threshold filtering, F-test filtering, Lasso regularization filtering, and recursive feature elimination filtering processes to gradually eliminate low-value features and retain core features.

[0133] The standardization unit is used to standardize the core features using RobustScaler. This standardization is based on the median and interquartile range of the training set to uniformly process the training set and the test set. The transformation formula is described in the method implementation, and will not be repeated here.

[0134] The skewness correction unit is used to perform skewness analysis on feature samples and select the optimal transformation method from the original transformation, log1p transformation and Box-Cox transformation based on 5-fold cross-validation. The optimal transformation method is then used to correct the skewed distribution.

[0135] The simulation calculation submodule is used to substitute the sample parameters after feature processing into the simulation model established by the model building module to calculate the earthquake-induced residual displacement value under the corresponding sample parameters.

[0136] The training module is used to train the Stacking ensemble model based on the feature parameter-seismic residual displacement sample set, to obtain the trained Stacking ensemble model. This module corresponds to step S400.

[0137] The Stacking integration model includes:

[0138] The input layer receives the core feature matrix, where the number of rows represents the number of samples and the number of columns represents the number of core features.

[0139] The base model layer consists of three heterogeneous models: Bayesian Ridge Regression Model, Kernel Ridge Regression Model, and Gradient Boosting Regression Model. It receives input layer features and outputs model-level predicted values ​​for each sample, forming a meta-feature matrix. The number of rows in this matrix is ​​the number of samples, and the number of columns is the number of base models.

[0140] The meta-model layer is used to receive the meta-feature matrix and calculate the final predicted value, i.e., the seismically induced residual displacement, through a linear fusion formula.

[0141] The output layer is used to output the prediction results of the base model layer and the final prediction value of the meta-model layer.

[0142] The training module also includes a hyperparameter optimization submodule, used to optimize the bandwidth parameter of the RBF kernel function in the kernel ridge regression model. The learning rate and tree depth of the gradient boosting regression model are optimized using a grid search, with the average coefficient of determination under 5-fold cross-validation as the optimization objective, and the optimal combination of hyperparameters is selected.

[0143] Furthermore, the system also includes an accuracy evaluation module for evaluating the accuracy of the trained Stacking ensemble model, which uses the coefficient of determination (COP). ) and mean absolute percentage error ( () is used as an evaluation metric for assessing the accuracy of the Stacking ensemble model.

[0144] The prediction module is used to process the corresponding characterization parameters of the seismic isolation bridge to be predicted and input them into the trained Stacking ensemble model. The model outputs the earthquake-induced residual displacement prediction result. This module corresponds to step S500. Specifically, the prediction module obtains the span, shear span ratio, stiffness, damping coefficient, and velocity index of the bridge to be predicted. It performs feature processing according to the same feature selection, standardization, and skewness correction process as in the feature processing submodule to form a core feature vector, which is then input into the trained Stacking ensemble model. After calculation by the basic model layer and the meta-model layer, the earthquake-induced residual displacement prediction result is output.

[0145] The acquisition module, model building module, sample set construction module, training module, accuracy evaluation module, and prediction module are connected in sequence to realize the functions of data acquisition, model building, sample set construction, model training, accuracy evaluation, and earthquake-induced residual displacement prediction, respectively. For the specific implementation methods, please refer to the relevant descriptions of steps S100 to S500 above, which will not be repeated here.

[0146] The machine learning-based seismic isolation bridge seismic-induced residual displacement prediction system provided in this embodiment is based on the same inventive concept as the aforementioned method embodiment and can achieve the same technical effect. That is, it can quickly and accurately predict the seismic-induced residual displacement of bridges under rare earthquakes without the need to deploy a large number of sensors, using only the basic information of the bridge and seismic isolation devices. It has the advantages of low cost, high speed and high accuracy.

[0147] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0148] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these all fall within the protection scope of the present invention. Therefore, the protection scope of this invention patent should be determined by the appended claims.

Claims

1. A machine learning-based method for predicting seismically induced residual displacement in seismically isolated and reduced-voltage bridges, characterized in that, Includes the following steps: Step 100: Obtain the basic information of the seismic isolation bridge and the parameter information of the corresponding seismic isolation device; Step 200: Based on the basic information and the parameter information, establish a simulation model of the seismic isolation bridge under seismic loading using OpenSees software; Step 300: Using the Latin hypercube sampling method, multiple characterization parameters of the seismic-induced residual displacement are sampled to generate an original sample set. The original sample set is then subjected to feature processing, and the seismic-induced residual displacement corresponding to the sample parameters is calculated using the simulation model. Finally, a characteristic parameter-seismic-induced residual displacement sample set is constructed. The characterization parameters include span, shear span ratio, stiffness, damping coefficient, and velocity index. Step 400: Based on the feature parameter - seismically induced residual displacement sample set, train the Stacking ensemble model to obtain the trained Stacking ensemble model; Step 500: After feature processing of the characterization parameters of the seismic isolation bridge to be predicted, input them into the trained Stacking ensemble model and output the seismic-induced residual displacement prediction results. The feature processing in step 300 includes feature selection, feature standardization, and feature sample skewness analysis and correction for the representation parameters. The specific process is as follows: Using the aforementioned characterization parameters as the original features, and based on these original features, corresponding derived features are generated using four methods: quadratic polynomial, interaction term, nonlinear transformation, and engineering empirical formula. These features include quadratic polynomial features, key interaction features, nonlinear transformation features, and engineering significance features. The derived features are filtered through variance thresholding, F-test screening, Lasso regularization screening, and recursive feature elimination screening processes to retain the core features. RobustScaler is used to standardize the core features; Skewness analysis is performed on the feature samples, and the optimal transformation method is selected from the original transformation, log1p transformation and Box-Cox transformation based on 5-fold cross-validation. The optimal transformation method is then used to correct the skewed distribution.

2. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 1, characterized in that, After step 400 and before step 500, the following steps are also included: The accuracy of the trained Stacking ensemble model is evaluated using the coefficient of determination and mean absolute percentage error as evaluation metrics.

3. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 1 or 2, characterized in that, The basic information includes bridge span, main beam cross-sectional dimensions, concrete strength, steel bar yield strength, pier cross-sectional dimensions, pier cross-sectional height, longitudinal reinforcement ratio, stirrup reinforcement ratio, number of supports, support friction coefficient, distance between the main beam and the pier, and specific parameters of concrete and steel reinforcement materials; the parameter information includes the stiffness, damping coefficient, and velocity index of the seismic isolation device.

4. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 1 or 2, characterized in that, In step 200, when establishing the simulation model of the seismic isolation bridge under seismic loading, the concrete is simulated using the Concrete02 model, and the steel reinforcement is simulated using the Steel02 model; the main beam structure is simulated using the Elastic Beam Column Element, the pier structure is simulated using the Nonlinear Beam Column Element, the ordinary bearing is simulated using the Zero Length Element, the passive seismic isolation device is simulated using the Elastomeric BearingPlasticity element, the pier base is fixed and constrained using the fix command, and different components are connected using the Rigid Link element. The seismic waves selected are El Centro wave, Northridge wave, and Kobe wave.

5. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 1 or 2, characterized in that, The Stacking integration model in step 400 includes: The input layer is used to receive the core feature matrix; The base model layer consists of three heterogeneous models, which receive input layer features and output model-level predictions for each sample, forming a meta-feature matrix with dimensions of number of samples × number of base models. The meta-model layer is used to receive the meta-feature matrix and obtain the final predicted value, i.e., the predicted seismic residual displacement, through linear fusion. The output layer is used to output the prediction results of the base model layer and the final prediction value of the meta-model layer.

6. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 5, characterized in that, The three heterogeneous models are the Bayesian ridge regression model, the kernel ridge regression model, and the gradient boosting regression model.

7. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 6, characterized in that, The linear fusion formula for the meta-model layer is: in, This is the final predicted value; , , These are the predicted values ​​for the Bayesian ridge regression model, the kernel ridge regression model, and the gradient boosting regression model, respectively. For the intercept term; , , These are the weighting coefficients of the predicted values ​​for the Bayesian ridge regression model, the kernel ridge regression model, and the gradient boosting regression model, respectively.

8. The method for predicting seismically induced residual displacement of seismically isolated and reduced-voltage bridges based on machine learning according to claim 1 or 2, characterized in that, The feature parameter - residual displacement sample set is divided into a training set and a test set. The training set is used for training and hyperparameter optimization of the Stacking ensemble model, and the test set is used for accuracy evaluation of the trained Stacking ensemble model.

9. A machine learning-based system for predicting seismic-induced residual displacement of seismically isolated bridges, characterized in that, include: The acquisition module is used to acquire basic information about seismic isolation bridges and the parameter information of corresponding seismic isolation devices. The model building module is used to build a simulation model of the seismic isolation bridge under seismic loading using OpenSees software based on the basic information and the parameter information. The sample set construction module is used to sample multiple characterization parameters of seismic-induced residual displacement using the Latin hypercube sampling method to generate an original sample set. Then, the original sample set is subjected to feature processing, and the seismic-induced residual displacement corresponding to the sample parameters is calculated using the simulation model. Finally, the characteristic parameter-seismic-induced residual displacement sample set is constructed. The characterization parameters include span, shear span ratio, stiffness, damping coefficient, and velocity index. The training module is used to train the Stacking ensemble model based on the feature parameter - the seismically induced residual displacement sample set, to obtain the trained Stacking ensemble model; The prediction module is used to process the characterization parameters of the seismic isolation bridge to be predicted and input them into the trained Stacking ensemble model, and output the prediction results of seismic-induced residual displacement. The sample set construction module includes a feature processing submodule, which includes: The feature filtering unit is used to take the characterization parameters as the original features and generate corresponding derived features based on the original features using four methods: quadratic polynomial, interaction term, nonlinear transformation and engineering empirical formula. These derived features include quadratic polynomial features, key interaction features, nonlinear transformation features and engineering significance features. The derived features are filtered through variance threshold filtering, F test filtering, Lasso regularization filtering and recursive feature elimination filtering processes to retain the core features. Standardization unit, used to standardize core features using RobustScaler; The skewness correction unit is used to perform skewness analysis on feature samples and select the optimal transformation method from the original transformation, log1p transformation and Box-Cox transformation based on 5-fold cross-validation, and use the optimal transformation method to correct the skewness distribution.

Images