Method and system for predicting buckling load of scouring damaged bridge based on machine learning

Abstract

The invention relates to a machine learning-based scouring damage bridge buckling load prediction method and system, and belongs to the technical field of machine learning and structural engineering. The prediction method comprises the steps of obtaining original data, preprocessing the original data, constructing a LightGBM machine learning model, and evaluating and verifying the constructed model by adopting multiple performance evaluation indexes. According to the method, key variables such as bridge structure parameters and foundation soil physical property indexes are comprehensively considered, a large sample database covering a large number of scouring combinations is constructed, and the critical buckling load of the structure is accurately calculated as an output target by using a pier-bearing platform-pile structure system buckling analysis method after scouring damage based on an energy method. A multivariable nonlinear mapping relation is established in combination with an ensemble learning algorithm, traditional complex calculation is replaced, and the method has good engineering adaptability and universality and can be suitable for rapid prediction of the buckling bearing capacity under different parameter bridges, different foundation forms and complex scouring conditions.

Description

Technical Field

[0001] The present invention relates to the technical fields of machine learning and structural engineering, and particularly relates to a method and system for predicting the buckling load of a scour-damaged bridge based on machine learning. Background Art

[0002] Buckling instability is one of the main failure forms of bridge structures. Once it occurs, it will pose a serious threat to the overall safety and stability of the bridge. Practice shows that when the bridge foundation suffers severe scour damage, the foundation support capacity is greatly weakened, the overall stiffness of the structure is reduced, and the buckling risk is further aggravated. In extreme cases, it will lead to sudden structural failure or overall collapse, causing serious casualties and property losses. According to investigations, 80% of the existing bridges in China cross water surfaces. Globally, about 60% of bridge washout accidents are caused by scour, and buckling of the lower structure under scour damage is an important factor leading to bridge collapse. Scour causes soil loss around the bridge piers, which in turn leads to structural instability. Therefore, the research on the buckling safety evaluation of bridges under scour action is particularly important, and how to quickly evaluate the safety of existing scour-damaged bridges has become a key problem to be solved urgently.

[0003] In the existing research on the buckling of bridge lower structures, numerical calculation methods are widely used in the calculation of the buckling bearing capacity of pile foundations, and the finite element method is particularly prominent. For example, the paper "Geometrically Nonlinear Finite Element Analysis of Buckling of Foundation Piles" published in the journal "Rock and Soil Mechanics" established a spatial beam element finite element model considering geometric nonlinear effects, and realized the full-process numerical simulation analysis of the buckling instability problem of foundation piles under axial load. Another example is the paper "Buckling Stability Analysis of Foundation Piles Considering Shear Deformation" published in the journal "Journal of Fuzhou University (Natural Science Edition)", which derived the expression of the stiffness matrix of column elements considering shear deformation in combination with the finite element principle, established two types of buckling stability analysis equations applicable to different working conditions, and proposed a finite element analysis method for the buckling stability of foundation piles considering the shear deformation of horizontal forces and effects. However, the above research methods are still relatively complex and require a large amount of computing power and time.

[0004] Starting from the mechanical principle, it is particularly important to study the derivation of the structural buckling load formula and deeply analyze the structural failure mechanism. Among them, when the energy method calculates the total energy of the system to solve the structural buckling load, it is easier to solve for various complex boundary conditions, so it is widely used. For example, in the paper "Buckling Stability Analysis of Foundation Piles Considering the Coupling Effect of Multi-Layer Piles and Soils" published in the journal "Hunan Communication Science and Technology", the method and For the two pile-soil coupling models of the hyperbola method, the buckling critical load formula of the pile-soil system in multi-layer soil is derived based on the energy method. For example, the paper "Buckling Stability Analysis of Wedge-shaped Foundation Piles in Slopes Based on the Energy Method" published in the Journal of Jiangsu University uses the Rayleigh-Ritz method, considering the skin friction of the pile and the landslide thrust of the soil behind the pile, establishes the total potential energy equation of the pile-soil system, and derives the analytical expression of the buckling critical load. For example, the Chinese patent application with the publication number CN111382517A and the title "Analysis Method of Analytical Solution of Buckling Critical Load of Pile Foundation Based on Double-parameter Foundation Model" proposes an analytical solution method of the buckling critical load of pile foundation based on the energy method, considering the reaction modulus and shear modulus of the foundation soil and the self-weight of the pile foundation, and obtains the analytical solution of the buckling critical load of the pile foundation.

[0005] In recent years, certain progress has also been made in the research on the buckling stability of bridge substructures under the action of different scour depths, but there are relatively few related studies. For example, the paper "Finite Element Calculation of Pier Structure System under Scour" published in the Journal of Wuhan University (Engineering Science Edition) constructs a three-dimensional finite element model of pier-cap-pile-soil based on ANSYS finite element software, and conducts a stress analysis of the pier considering different scour depths, the coupling of sediment scour and hydrodynamic pressure. For example, the paper "Buckling Analysis of Pier Structure System under the Coupling Action of Scour and Hydrodynamic Pressure Based on the Energy Method" published in the Journal of Hydroelectric Energy Science derives the calculation formula of the buckling load of the pier considering the coupling action of scour and hydrodynamic pressure based on the energy method, and verifies the formula accuracy through comparison with the equivalent single-column model and finite element simulation. For example, the paper "Calculation of Buckling Load of Pier Structure System under Scour" published in the Journal of Wuhan University (Engineering Science Edition) derives the calculation formula of the buckling load considering the interaction of soil-pile-pier, the equivalent structural system of the pier and group piles, and the influence of sliding rubber bearings and pile caps, and analyzes the influence of scour depth, pile-pier stiffness ratio, etc. on the buckling load.

[0006] With the development of artificial intelligence and data-driven methods, machine learning has been widely applied in the field of bridge structure and performance prediction. However, up to now, no relevant patent literature and papers have used data-driven methods to achieve rapid assessment of the buckling load of bridge substructures.

[0007] In summary, the existing analysis methods either calculate the buckling bearing capacity of pile foundations through complex numerical methods or derive and solve the critical buckling load under scour damage through mechanical principles. However, the research on the buckling stability evaluation method for the pier-cap-pile foundation structure system considering the structural self-weight is not sufficient, and the data-driven method has not been applied to the evaluation of the critical buckling load, resulting in the lack of integrity in safety evaluation. It is difficult to balance efficiency, accuracy, and adaptability, lacking a fusion mechanism between theoretical solution and data-driven prediction, and unable to conduct a rapid evaluation of the critical buckling load of existing damaged bridges. Therefore, there is an urgent need to develop a rapid prediction method for the critical buckling load of bridge scour damage based on machine learning to achieve the efficient quantification and intelligent evaluation of structural safety performance, improve the safety guarantee ability of bridge structures in complex hydrological environments, and provide theoretical support and engineering decision-making basis for disaster prevention and mitigation of bridges under scour effects. Summary of the Invention

[0008] The present invention aims to solve the technical problems in the prior art that the evaluation of the bridge structural performance of existing bridges under scour damage depends on a large number of finite element models and complex mechanical method calculations, with low prediction efficiency and poor engineering adaptability, and it is difficult to rapidly evaluate the stability limit of bridges, especially the change trend of the critical buckling load, which is not easy to quantify. The present invention provides a method and system for predicting the buckling load of scour-damaged bridges based on machine learning.

[0009] To solve the above technical problems, the technical solution of the present invention is specifically as follows: A method for predicting the buckling load of scour-damaged bridges based on machine learning, characterized by comprising the following steps: Step S101: Obtain original data, including bridge parameters, soil parameters, scour depth and the change rate of critical buckling load Obtain structural parameters; Bridge parameters include: slenderness ratio of pile , width of pier , height of pier , elastic modulus of pier , elastic modulus of pile ; The soil parameter is the proportional coefficient value of the soil foundation reaction coefficient ; Step S102: Preprocess the original data obtained in Step S101, including missing value filling, outlier removal, and feature standardization, to obtain the structural parameter input data set for the prediction task; Step S103: Use the bridge parameters, soil parameters, and scour depth in the data set obtained in Step S102 as input features, and use the change rate of critical buckling load Taking the critical buckling load change rate as the prediction target, a LightGBM machine learning model is constructed to establish a non-linear mapping relationship between the input features and the prediction target; During the training of the LightGBM machine learning model, the fitting ability to the high-dimensional structural feature space is improved by integrating multiple regression subtrees, and the k-fold cross-validation strategy is introduced to perform multiple rounds of partitioning and iterative training on the sample data of the data set, and the final regression model is obtained, which is used to realize the prediction of the critical buckling load change rate of the scoured damaged bridge; Step S104: Evaluate and verify the regression model obtained in step S103 using multiple performance evaluation indicators.

[0010] In the above technical solution, in step S101, the bridge parameters, soil parameters and scour depth are obtained by Latin hypercube sampling, and the sample data considering different scour depths are formed by combining at a certain scour depth interval; The critical buckling load change rate is obtained by using the buckling analysis method of the pier-cap-pile structural system after scour damage based on the energy method, and the accurate batch calculation of the sampling samples is realized by using MATLAB.

[0011] In the above technical solution, in step S101, the critical buckling load change rate is obtained by using the buckling analysis method of the pier-cap-pile structural system after scour damage based on the energy method, and the accurate batch calculation of the sampling samples is realized by using MATLAB, including the following steps: Establish the pier-cap-pile structural system. According to the principle of the energy method, the total potential energy function is , and the formula is as follows: ; Among them, is the bending strain energy of the system, is the pile-soil spring potential energy, is the work done by the axial force, is the work done by the body force; In the pier-cap-pile structural system, is the vertical position coordinate, is the deflection curve function of the system, and the bending strain energy is expressed as: ; Among them, is the pile length, is the total length of the pier-cap-pile structural system, is the pier stiffness, is the pile stiffness; is the second derivative of the deflection curve function of the system; The pile-soil interaction is considered by using the m method, and layers of soil are set. is the proportionality coefficient of the subgrade reaction coefficient of the soil, is the subgrade reaction force per unit length of the soil, and is expressed as: ; Among them, is the buried depth of the pile shaft, is the distance between the position of the pile cap and the soil, is the pile diameter, then the potential energy of the pile-soil spring is expressed as: ; Among them, is the vertical coordinate of the node of the layer soil element, , is the node spacing, is the vertical coordinate of the node of the layer soil element, is the value of the layer soil, represents the serial number of the soil layer, , , is the scour depth; The loads of the overall superstructure of the pier-pile are simplified to the axial forces acting on the top of the pier and the top of the pile. represents the axial force at the top of the pier, represents the axial force at the top of the pile, then the work done by the axial force is: ; , respectively represent the self-weight concentration of the pier and the pile, then the work done by the body force is: ; Among them, is the first derivative of the system deflection curve function; Assume that the pier-pile cap-pile-soil structure system follows the condition that the lower end of the pile is hinged and the upper end of the pier is free. Select the system deflection curve function of the overall lower structure of the pier-pile. The form of the system deflection curve function is: ; Among them, is the parameter to be determined; is the test function number; The total potential energy function Substitute into the potential energy stationary value condition, construct the buckling failure characteristic equation, and obtain the minimum eigenvalue by solving the eigenvalue Calculate the critical buckling load value , the critical buckling load value The formula is: ; Use MATLAB to solve and obtain the critical buckling load change rate , the formula is as follows: ; Among them, is the calculated value of the critical buckling load when the scour depth is , is the calculated value of the critical buckling load when the scour depth is 0.

[0012] In the above technical solution, in step S102: The missing value filling is: calculate the median of each structural parameter in the current dataset, and use this median to fill the missing position; The outlier removal is: calculate the standard score, set the standard deviation threshold, and remove the outlier samples whose absolute value of Z-score exceeds the standard deviation threshold in any parameter dimension. The formula is as follows: ; Among them, is the standard score, is the structural parameter value, and are respectively the mean and standard deviation of in the dataset; ; Among them, is the original structural parameter value after removing outliers, is the mean of in the dataset, is the standard deviation of

[0013] In the above technical solution, in step S103, The prediction function form of the LightGBM machine learning model is defined as follows: ; Among them, Indicates the prediction result for the input sample data , Indicates the output of the th regression subtree, Indicates the function space composed of regression subtrees, is the total number of multiple regression subtrees integrated in the LightGBM machine learning model, is the regression subtree number index; The LightGBM machine learning model uses the root mean square error as the optimization objective function, and the formula is as follows: ; Among them, is the number of samples, is the predicted value of the th sample, is the true value of the th sample, is the mean square error loss function value, is the sample number; The root mean square error RMSE is used as the evaluation index; the RMSE formula is as follows: ; The five-fold cross-validation strategy is adopted to perform multiple rounds of partitioning and training on the sample data; the average loss function of the five-fold cross-validation is defined as: ; Among them, is the average value of the losses of each fold in the five-fold cross-validation process, represents the loss value on the th fold validation set, is the fold index of the cross-validation.

[0014] In the above technical solution, in step S104, the performance evaluation indexes include: mean absolute error, root mean square error and determination coefficient.

[0015] A prediction system applicable to the machine learning-based scouring damage bridge buckling load prediction method described in the present invention includes: a data construction module for obtaining the original data of the data set, including bridge parameters, soil parameters, scouring depth and the change rate of the critical buckling load acquisition of structural parameters; A data preprocessing module for preprocessing the original data obtained by the data construction module, including missing value filling, outlier removal, and feature standardization, to obtain the structural parameter input data set for the prediction task, and providing a standardized data input interface for subsequent model calls; Model construction and buckling prediction module, which is used to construct a LightGBM machine learning model to achieve the prediction of the critical buckling load change rate of the scour-damaged bridge Prediction; Result analysis module, which is used to evaluate and verify the regression model obtained after training the constructed LightGBM machine learning model by using a variety of performance evaluation indexes.

[0016] The present invention has the following beneficial effects: The buckling load prediction method and system for scour-damaged bridges based on machine learning of the present invention comprehensively considers key variables such as bridge structure parameters and foundation soil physical property indexes, constructs a large sample database covering a large number of scour combinations, and uses the buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method to accurately calculate the critical buckling load of the structure as the output target. Combining with the ensemble learning algorithm, a multivariable nonlinear mapping relationship is established to replace the traditional complex calculation, and it has good engineering adaptability and universality, and can be applied to the rapid prediction of the buckling bearing capacity of bridges with different parameters, different foundation forms and under complex scour conditions.

[0017] The buckling load prediction method and system for scour-damaged bridges based on machine learning of the present invention significantly improves the buckling load evaluation efficiency. Specifically, the present invention takes machine learning as the core, optimizes the traditional finite element simulation and buckling analysis calculation process, and through steps such as feature extraction, model training and optimization, quickly completes the accurate prediction of the critical buckling load under the scour damage state of the bridge, and establishes a system with a complete process, avoiding a large amount of repetitive modeling and calculation work, greatly improving the structural performance evaluation efficiency, and having good engineering practical value.

[0018] The buckling load prediction method and system for scour-damaged bridges based on machine learning of the present invention effectively improves the prediction accuracy and stability. Specifically, the present invention adopts the buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method, comprehensively considers the overall structural effect, and is an accurate mechanical solution method; on this basis, multiple input parameters are set, and a LightGBM regression model based on gradient boosting decision tree (GBDT) is used to accurately capture the complex nonlinear relationship between the input parameters and the buckling load. At the same time, the fold cross-validation and early stopping mechanism are introduced to make full use of the training data and suppress the overfitting phenomenon, ensuring that the model can maintain a high prediction accuracy and robustness under different scour states.

[0019] The method and system for predicting the buckling load of a scour-damaged bridge based on machine learning of the present invention enhance the generalization and promotion ability of the model. Specifically, in the regression model constructed by the present invention, multiple groups of combinations of structural types and scour depths are introduced during the training process, and the optimal sub-model is selected as the final model through multiple rounds of verification. At the same time, the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) are used to comprehensively evaluate the model performance, verifying its good generalization ability on unseen samples, and it is applicable to the rapid analysis and early warning requirements of existing bridge structures.

[0020] Compared with traditional methods, the method and system for predicting the buckling load of a scour-damaged bridge based on machine learning of the present invention have both theoretical integrity, calculation accuracy, and engineering practicability, and are applicable to the anti-scour optimization in the bridge design stage, health monitoring during the operation period, and rapid assessment of bridge stability after floods, providing theoretical support and decision-making basis for disaster prevention and mitigation of bridges in a scour environment. Brief Description of the Drawings

[0021] The present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0022] Figure 1 is the flowchart of the method for predicting the buckling load of a scour-damaged bridge based on machine learning of the present invention; Figure 2 is the simplified model diagram of a single pier in the embodiment of the present invention; Figure 3 is the simplified mechanical model diagram in the embodiment of the present invention; Figure 4 is the prediction effect diagram of the LightGBM machine learning model in the embodiment of the present invention; Figure 5 is the residual distribution diagram of the results predicted by different models on the test set in the embodiment of the present invention (in the figure, the LightGBM machine learning model is abbreviated as LightGBM); Figure 6 is the structural schematic diagram of the prediction system applicable to the method for predicting the buckling load of a scour-damaged bridge based on machine learning of the present invention.

[0023] The reference numerals in the figures are represented as: 100 - Data construction module; 200 - Data preprocessing module; 300 - Model construction and buckling prediction module; 400 - Result analysis module. Specific Embodiments

[0024] The inventive concept of the present invention is as follows: The method for predicting the buckling load of a bridge damaged by scour based on machine learning of the present invention constructs a high-precision regression model by integrating multi-source feature information such as bridge scour depth, structural parameters, and soil mechanical properties, and realizes accurate and efficient prediction of the critical buckling load by means of a gradient boosting-based ensemble learning algorithm. It significantly improves the efficiency and reliability of structural safety assessment, and provides intelligent support for the operation management and disaster prevention and control of existing bridges.

[0025] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0026] As Figure 1 shown ( Figure 1 only the step summary of the prediction method of the present invention is shown), the method for predicting the buckling load of a bridge damaged by scour based on machine learning of the present invention includes the following steps: Step S101: Obtain original data, including bridge parameters, soil parameters, scour depth and the change rate of critical buckling load and obtain structural parameters; The bridge parameters include: slenderness ratio of pile , pier width , pier height , elastic modulus of pier , elastic modulus of pile ; The soil parameter is the proportional coefficient value of the subgrade reaction coefficient of the soil ; Among them, the bridge parameters, soil parameters and scour depth are obtained by Latin Hypercube Sampling (LHS), and a large number of sample data considering different scour depths are combined at a certain scour depth interval; the change rate of critical buckling load is obtained by using the buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method, and accurate batch calculation of the sampling samples is realized by using MATLAB software. Specifically: 1. Obtain bridge parameters, soil parameters and scour depth; Scour depth , the proportional coefficient value of the subgrade reaction coefficient of the soil , slenderness ratio of pile , pier width , pier height , elastic modulus of pier , elastic modulus of pile , if it is a group pile structure, according to the equivalent stiffness principle of group piles, it is equivalent to a single pile, and the equivalent pile structure parameters are obtained.

[0027] (1)Bridge parameter and soil parameter acquisition: To ensure the rationality and correctness of the calculation results of the critical buckling load of bridges damaged by scour, bridge parameters need to be evenly combined and cover most medium and small-span bridges. The Latin Hypercube Sampling (LHS) algorithm is used to sample the six-parameter combination of the proportional coefficient value of the soil foundation resistance coefficient, the slenderness ratio of the pile , the width of the bridge pier , the height of the bridge pier , the elastic modulus of the bridge pier , the elastic modulus of the pile . In this embodiment, according to relevant specifications such as the "Code for Design of Foundations of Highway Bridges and Culverts", and referring to the north approach bridge of the Sutong Bridge in the southeastern part of Jiangsu, the sampling ranges of each parameter are selected as follows: The width of the bridge pier will affect the flexural stiffness and overall stability of the bridge pier structure. The sampled bridge pier width is 0.8 - 1.3 times the width of the Sutong Bridge piers, that is, 5.20m - 8.45m; the height of the bridge pier will affect the failure mode and shear resistance of the bridge pier. In engineering, the shear span ratio (the ratio between the height of the bridge pier and the width of the bridge pier) is usually used to control the height of the bridge pier. The shear span ratio of medium and small-span bridge piers usually ranges from 5 to 10. Therefore, the sampled range of the bridge pier height is 26.0m - 84.5m; the slenderness ratio of the pile (the ratio of the pile length to the pile diameter) is directly related to the overall stability and bearing capacity of the pile. The pile length is controlled to be 90m and remains unchanged. The sampled range of the slenderness ratio of the pile is 15 - 25; the commonly used concrete materials for the lower structure of bridges are mainly C30 - C50 concrete. In this embodiment, referring to the Sutong Bridge, C40 concrete is used for the bridge pier and C30 concrete is used for the pile. Due to scour damage, the reduction range of the elastic modulus is taken as 0.6 - 1, that is, the sampled range of the elastic modulus of the bridge pier is 19.5GPa - 32.5GPa, and the elastic modulus of the pile is 18.0GPa - 30.0GPa; according to the specifications, the proportional coefficient value of the soil foundation resistance coefficient for soils such as clay, medium sand, coarse sand, and dense silt often ranges between 3000 - 30000 , so this is used as the sampling range. Compared with other parameters, the reduction of the concrete unit weight after scour has little obvious effect on the critical buckling load. Therefore, this parameter is not used as a parameter for the machine learning dataset in this example. According to the specifications, the unit weight of the bridge pier is set to , and the unit weight of the pile is set to . On this basis, to better conform to the actual situation, the lower limit of pier stiffness reduction is set to 0.5 times that of the piers of the basic bridge, and the lower limit of pile stiffness reduction is set to 0.28 times that of the piers of the basic bridge to limit the LHS sampling range. Subsequently, 300 groups of samples are taken for the above 6 bridge parameters and soil parameters for backup.

[0028] (2) Sample combined scour depth: To make the sampling results more universal, the scour depth of the present invention is a dimensionless parameter, that is, the percentage of the actual scour depth in the total buried depth of the pile foundation, and its formula is: ; where is the actual scour depth of the bridge, in meters, is the total buried depth of the pile foundation, in meters.

[0029] Since it is difficult for the actual scour depth of the bridge to exceed 80% of the pile length in actual engineering, the range is taken as 0% - 80%. In this embodiment, sampling is evenly carried out at intervals of 5% and combined with the sampling results of the above bridge parameters and soil parameters of 300 groups to form a final 5100 groups of sampling results as sample data.

[0030] II. Critical buckling load change rate Obtain; The critical buckling load of each sample is calculated by using the buckling stability evaluation method for the pier - cap - pile structural system after scour damage. This method is based on the energy method, different from the mechanical method only for the equivalent single - column model, considering the pier - cap - pile structural system, structural gravity, and setting multiple parameters to consider different characteristics of the structure, with high accuracy. The specific method process is as follows: (1) Construct a theoretical single - pier simplified model for buckling analysis of the pier - cap - pile structural system, as Figure 2 shown. In this embodiment, the pier type is a rectangular thin - wall pier, the pier height is , the pier width is (that is, the cross - section width of the pier is ), and the cross - section length is 4m. To facilitate the analysis of the buckling load of the bridge structure, according to the principle of equivalent stiffness of group piles, the group piles are simplified into single piles with the same bearing capacity, the pile diameter is , the pile length remains unchanged at 90m, the initial buried depth of the pile body is , is the distance between the cap position and the soil. The overall upper structure of the pier - pile is simplified into a vertical force (i.e., axial force) acting on the top of the pier, and according to the mass of the cap, it is simplified into a vertical force (i.e., axial force) applied to the top of the pile. Use to represent the axial force at the top of the pier, to represent the axial force at the top of the pile, , are the stiffness of the pier and the pile respectively. The bridge pile foundation is simplified to the buckling failure problem of an elastic foundation beam with an axial force acting on the top of the pier. The interaction between the pile and the soil is considered by the " m " method. Different soil types are set as different layers, with a total of layers, is the proportional coefficient of the soil foundation resistance coefficient. For example, the first layer m 1 、 The second layer m 2 、 The third layer m 3 … The N-1 layer m N-1 ， to calculate the soil foundation resistance of each layer. In this embodiment, only a single soil type is set.

[0031] Specifically, as shown in the simplified mechanical model diagram of the pier-cap-pile structure system Figure 3 , represent the coordinates of the first unit node to the N th unit node respectively. According to the principle of the energy method, including the bending strain energy of the system, the potential energy of the pile-soil spring, the work done by the axial force and the work done by the body force , the total potential energy function of the pier-cap-pile structure system is established, and the formula is as follows: ; Among them, is the bending strain energy of the system, is the potential energy of the pile-soil spring, is the work done by the axial force, is the work done by the body force; In the pier-cap-pile structure system, is the vertical position coordinate, is the deflection curve function of the system. The bending strain energy of the system is expressed as: ; Among them, is the pile length, is the total length of the pier-cap-pile structure system, that is , and are the stiffness of the pier and the pile respectively; is the second derivative of the deflection curve function of the system; The pile-soil interaction adoptsm Consider and set layers of soil mass is the proportionality coefficient of the soil foundation resistance coefficient is the soil reaction force per unit length, expressed as: ; Among them, is the buried depth of the pile shaft is the distance between the position of the bearing platform and the soil mass is the pile diameter, then the pile-soil spring potential energy is expressed as: ; Among them, is the vertical coordinate of the node of the th layer of soil mass element , is the node spacing is the vertical coordinate of the node of the th layer of soil mass element is the th layer of soil mass value of represents the serial number of the soil mass layer , , is the scour depth; Simplify the loads of the overall upper structure of the bridge pier-pile and the bearing platform into axial forces acting on the top of the bridge pier and the top of the pile, and use to represent the axial force at the top of the bridge pier, to represent the axial force at the top of the pile, then the work done by the axial force is: ; , respectively represent the self-weight concentration degrees of the bridge pier and the pile, then the work done by the body force is: ; Among them, is the first derivative of the system deflection curve function; (2) Assume that the bridge pier-bearing platform-pile-soil structure system obeys the condition that the lower end of the pile is hinged and the upper end of the bridge pier is free. Select the system deflection curve function of the overall lower structure of the bridge pier-pile. The form of the system deflection curve function is: ; Among them, is the undetermined parameter; is the test function number; Substitute it into the total potential energy function , according to the principle of stationary potential energy, the buckling failure characteristic equation is obtained and finally transformed into the problem of solving the minimum eigenvalue of the matrix. By solving the minimum eigenvalue, the critical buckling load value of the pier-cap-pile structural system is obtained. The formula is as follows: The problem is to solve the minimum eigenvalue. to obtain the critical buckling load value of the pier-cap-pile structural system. The formula is as follows: ; where, is the critical buckling load value, is the total length of the pier-cap-pile structural system (i.e., the sum of the pier length and the pile length), is the minimum eigenvalue.

[0032] (3) The above method is programmed by MATLAB software. In this embodiment, 5100 groups of sample data of LHS sampling are accurately calculated in batches, and the critical buckling load change rate is calculated on the basis of obtaining the critical buckling load. The formula is as follows: The formula is as follows: ; where, is the calculated value of the critical buckling load when the scour depth is , is the calculated value of the critical buckling load when the scour depth is 0.

[0033] Step S102: Preprocess the original data obtained in step S101, including missing value filling, outlier removal, and feature standardization, to obtain the structural parameter input data set for the prediction task; The original data are the structural parameters such as the bridge parameters, soil parameters, and scour depth obtained in step S101, specifically including the scour depth , the proportional coefficient of the soil foundation resistance coefficient, the slenderness ratio of the pile, the pier width , the pier height , the elastic modulus of the pier, the elastic modulus of the pile, and the critical buckling load change rate . .

[0034] (1) Missing value filling: The median filling method is selected for processing. Specifically, the median of each structural parameter in the current data set is calculated, and the missing positions of the corresponding fields are filled with the median.

[0035] (2) Outlier removal: The Z-score method is used to calculate the standard scores of each structural parameter. The specific steps are as follows: For each structural parameter value , calculate its mean in the data set.and standard deviation , and calculate accordingly. The standard score calculation formula is: ; in, is the standard score, is the structural parameter value, and They are The mean and standard deviation in the data set; In this embodiment, the Z-score determination threshold is set to 3.0. When the absolute value of the Z-score of any structural parameter sample in any parameter dimension exceeds the threshold, the sample is determined to be an abnormal sample and is removed.

[0036] (3) After the outliers are removed, the Z-score feature normalization process is performed on the retained structural parameter samples so that all structural parameters have the same scale distribution. The feature normalization process formula is the same as the aforementioned Z-score, that is: ; in, is the original structural parameter value after removing outliers, for The mean value in the data set, for The standard deviation in the data set, is the parameter value after standardization. Through this process, all structural parameter data are mapped to a standard normal distribution with a mean of 0 and a standard deviation of 1.

[0037] Step S103: Using the bridge parameters, soil parameters and scour depth of the data set obtained in step S102 The input characteristics are expressed as the critical buckling load change rate To predict the target, a LightGBM machine learning model based on the gradient boosted decision tree (GBDT) framework was constructed to establish a nonlinear mapping relationship between input features and prediction targets; During training, the LightGBM machine learning model improves the fitting ability of high-dimensional structural feature space by integrating multiple regression subtrees. The sample data of the dataset is divided and iteratively trained for multiple rounds using the fold cross-validation strategy to obtain the LightGBM machine learning model with the best generalization performance, i.e., the final regression model, which is used to quickly predict the critical buckling load change rate of scour-damaged bridges. The adopted LightGBM machine learning model belongs to the gradient boosting decision tree model in the ensemble learning framework. Its basic idea is to iteratively integrate multiple weak learners (decision trees) to gradually optimize the overall prediction performance. The prediction function form of the LightGBM machine learning model is defined as follows: ; Among them, represents the prediction result of the input sample data . represents the output of the th regression subtree, represents the function space composed of regression subtrees, is the total number of regression subtrees integrated in the LightGBM machine learning model, is the regression subtree number index.

[0038] The LightGBM machine learning model uses the root mean square error RMSE as the optimization objective function, and the formula is as follows: ; Among them, is the number of samples, is the predicted value of the rd sample, is the true value of the th sample, is the mean square error loss function value, is the sample number; The root mean square error RMSE is used as the evaluation index; the RMSE formula is as follows: ; Among them, the parameter meanings are the same as above.

[0039] To evaluate the stability and generalization ability of the LightGBM machine learning model under different data partitions, a -fold cross-validation strategy is introduced to perform multiple rounds of partitioning and iterative training on the sample data. In this embodiment, a five-fold cross-validation (5-Fold Cross Validation) strategy is used to perform multiple rounds of partitioning and training on the training data (i.e., sample data). Specifically, all the training data is evenly divided into five subsets. In each round, four of these subsets are selected for training the LightGBM machine learning model, and the remaining one subset is used as the validation set. This process is repeated five times to ensure that each subset serves as the validation set once. The average loss function of the five-fold cross-validation is defined as: ; Among them, is the average value of the losses of each fold in the five-fold cross-validation process, represents the The loss value (RMSE) on the fold validation set, is the index of the number of folds for cross-validation.

[0040] During the training process, to prevent the LightGBM machine learning model from overfitting on the training set and to control the number of iterations, an early stopping mechanism is introduced. In this embodiment, the LightGBM machine learning model is trained for at most 1000 rounds. If the root mean square error of the performance metric on the validation set does not show significant optimization in 50 consecutive iterations, the training process is automatically terminated.

[0041] Step S104: Evaluate and validate the regression model obtained in step S103 using multiple performance evaluation metrics.

[0042] Among them, the performance evaluation metrics include but are not limited to: mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²).

[0043] The above three performance evaluation metrics evaluate the prediction performance of the LightGBM machine learning model from different dimensions. MAE measures the average error size, RMSE emphasizes the penalty ability for large errors, and R² reflects the fitting degree of the LightGBM machine learning model to the overall trend. In this embodiment, the overall prediction results of five-fold cross-validation are used to calculate the above metrics to obtain the comprehensive performance of the LightGBM machine learning model under different data partitions.

[0044] The prediction results of the LightGBM machine learning model of this embodiment on each evaluation metric are: the mean absolute error is 0.0036, the root mean square error is 0.0026, and the coefficient of determination is 0.9998, all indicating that this LightGBM machine learning model has high accuracy. Further, comparing the test set with the actual values, the prediction results are as Figure 4 shown. It can be observed that the predicted values fit well with the actual values and the error is small, verifying again that this LightGBM machine learning model can accurately calculate the critical buckling load change rate .

[0045] On this basis, to prove the superiority of the LightGBM machine learning model in this example, it is compared with three typical machine learning regression models: KNN (K-Nearest Neighbors Regressor), Shallow Decision Tree Regressor, and Random Forest Regressor. Among them, the output of the Shallow Decision Tree Regressor presents as discrete piecewise constants, while the outputs of KNN (K-Nearest Neighbors Regressor) and Random Forest Regressor and the LightGBM machine learning model used in the invention (the LightGBM machine learning model represented by LightGBM in Table 1 and Figure 5 the LightGBM machine learning model represented by LightGBM used in

[0046] Table 1 Comparison results of the prediction effects of each algorithm

[0047] To more intuitively compare the prediction effects, calculate the residuals between the prediction results and the actual results of the four models in the table, and plot them as violin plots, as Figure 5 shown. Among them, the LightGBM machine learning model has the smallest residuals and a concentrated distribution, which once again proves the accuracy and superiority of the LightGBM machine learning model of the present invention.

[0048] As Figure 6 shown, another embodiment of the present invention provides a prediction system applicable to the above-mentioned machine learning-based prediction method for the buckling load of scoured bridges. The system includes a data construction module 100, a data preprocessing module 200, a model construction and buckling prediction module 300, and a result analysis module 400.

[0049] The data construction module 100 is used to construct the acquisition of the original data of the data set, and obtain bridge parameters, soil parameters, scour depth and the change rate of the critical buckling load structural parameters. The obtained structural parameters specifically include the scour depth , the proportional coefficient of the soil foundation resistance coefficient , the slenderness ratio of the pile , the width of the bridge pier , the height of the bridge pier , the elastic modulus of the bridge pier , pile elastic modulus , critical buckling load change rate . In the case where the bridge has a group pile foundation structure, the group pile equivalent stiffness principle is used to convert the group pile structure into a single pile structure model, and the relevant parameters of the equivalent pile are extracted. The Latin hypercube sampling algorithm is used for sampling. In this embodiment, 300 groups of structural and foundation parameter combination samples are generated within the above parameter space. In order to comprehensively cover the structural responses under different scour effects, in this embodiment, each group of parameter samples is combined and extended at intervals of 5% scour depth to construct a sample data set containing various scour levels. Obtain the critical buckling load change rate Adopt the buckling stability evaluation method for the pier-cap-pile structure system after scour damage. The method considers the overall structural effect, that is, the overall structural system of the pier-cap-pile-soil, considering the different structural characteristics and physical forces of the pier and pile foundation, as well as the gravity of the cap. Establish the total potential energy function of the pier-cap-pile structure system according to the principle of energy method , assume the deflection curve function of the system under the hinged-free boundary condition form (that is, assume that the pier-cap-pile-soil structure system obeys the hinge at the lower end of the pile and the free upper end of the pier, and select the deflection curve function of the overall lower structure of the pier-pile ), substitute the total potential energy function into the stationary value condition of the potential energy, construct the characteristic equation, and obtain the minimum eigenvalue by solving the eigenvalue Calculate the critical buckling load value. The above method is programmed using MATLAB software to achieve batch and accurate calculation of the sample set and obtain a complete data set

[0050] The data preprocessing module 200 is used to preprocess the original data obtained by the data construction module 100, including missing value filling, outlier removal, and feature standardization, to obtain the structural parameter input data set for the prediction task, and provide a standardized data input interface for subsequent model (LightGBM machine learning model) calls; this embodiment specifically includes: using the median filling method for missing value filling; calculating the standard score using the Z-score method, setting the standard deviation threshold to 3.0, and removing the outlier samples that exceed this threshold in any parameter dimension; using the Z-score standardization to process the feature quantities for normalization to eliminate the influence brought by different dimensions

[0051] The model construction and buckling prediction module 300 is used to construct a LightGBM machine learning model to realize the rapid prediction of the critical buckling load change rate of the bridge damaged by scour . Use the bridge parameters, soil parameters, and scour depth in the preprocessed data set as input features, and the critical buckling load change rate As a prediction target, a LightGBM machine learning model is constructed. During the training of the LightGBM machine learning model, multiple regression subtrees are integrated to improve the fitting ability for the high-dimensional structural feature space. In this embodiment, a five-fold cross-validation strategy is introduced to perform multiple rounds of partitioning and iterative training on the sample data. An early stopping mechanism (Early Stopping) based on the validation set loss function is introduced in each fold of validation. In this embodiment, when the root mean square error (RMSE) on the validation set does not show a significant decrease within 50 consecutive iterations, the model improvement process is automatically stopped. The sub-model with the smallest RMSE on the validation set is selected as the representative model for each fold, and finally the model with the optimal comprehensive performance from all folds is used as the final LightGBM machine learning model, that is, the final regression model, thus realizing the critical buckling load change rate Fast prediction.

[0052] The result analysis module 400 is used to evaluate and verify the regression model obtained after training the constructed LightGBM machine learning model by using a variety of performance evaluation indicators. The performance of the prediction results of the LightGBM machine learning model is evaluated to improve the engineering interpretability of the prediction results. The system uses regression performance indicators such as the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) to quantitatively evaluate the performance of the LightGBM machine learning model on the test set.

[0053] In summary, the present invention provides a method for predicting the buckling load of a scour-damaged bridge based on machine learning, which combines accurate theoretical calculations with machine learning algorithms. Through steps such as parameter sampling, buckling analysis, data preprocessing, and regression model training, a non-linear mapping relationship between bridge, soil, and scour parameters and the critical buckling load change rate is established. This method can efficiently and accurately predict the evolution law of the critical buckling capacity of bridge piers under various scour scenarios, providing technical support for scour damage assessment and bridge structure safety analysis.

[0054] The final regression model obtained after training the LightGBM machine learning model of the lightweight and high-precision machine learning framework adopted by the present invention fully integrates the data-driven method on the basis of fully considering the mechanical theory, and has the advantages of high model training accuracy, fast speed, and strong adaptability. Compared with traditional analytical methods and numerical calculation methods, the present invention greatly improves the calculation efficiency, significantly reduces the dependence on professional computing resources, and is applicable to the rapid screening and risk warning of the buckling load of medium and small-span bridges with existing scour damage in a large range.

[0055] Overall, the present invention has good engineering practicability and popularization value in predicting the buckling performance of medium and small-span bridges with existing scour damage, which helps to improve the intelligent and data-based level of the maintenance management of bridges with existing scour damage, enhance the safety guarantee ability of bridge structures in complex hydrological environments, and provide theoretical support and engineering decision-making basis for disaster prevention and reduction of bridges under the action of scour.

[0056] Obviously, the above-mentioned embodiments are merely examples for clear illustration and not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for predicting the buckling load of a scour-damaged bridge based on machine learning, characterized in that, It includes the following steps: Step S101: Obtain original data, including bridge parameters, soil parameters, scour depth and the change rate of critical buckling load Obtain structural parameters; Bridge parameters include: pile slenderness ratio , pier width , pier height , pier elastic modulus , pile elastic modulus ; The soil parameters are the proportionality coefficients of the subgrade reaction coefficient of the soil mass value; Step S102: Preprocess the original data obtained in Step S101, including missing value filling, outlier removal, and feature standardization, to obtain the input data set of structural parameters for the prediction task; Step S103: Using the bridge parameters, soil parameters, and scour depth of the data set obtained in Step S102 as input features, and using the critical buckling load change rate as the prediction target, construct a LightGBM machine learning model to establish a non-linear mapping relationship between the input features and the prediction target; During the training of the LightGBM machine learning model, the fitting ability for the high-dimensional structural feature space is improved by integrating multiple regression subtrees, and the k-fold cross-validation strategy is introduced to perform multiple rounds of partitioning and iterative training on the sample data of the dataset, and finally a regression model is obtained. This regression model is used to predict the change rate of the critical buckling load of the scoured damaged bridge. Step S104: Evaluate and verify the regression model obtained in Step S103 using multiple performance evaluation metrics.

2. The method for predicting the buckling load of a scour-damaged bridge based on machine learning according to claim 1, wherein In step S101, the bridge parameters, soil parameters, and scour depth are obtained by Latin hypercube sampling and combined at a certain interval of scour depth to form sample data considering different scour depths; Critical buckling load change rate is obtained by using the buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method, and the accurate batch calculation of sampling samples is realized by using MATLAB.

3. The method for predicting the buckling load of a scour-damaged bridge based on machine learning according to claim 2, wherein In step S101, the critical buckling load change rate is obtained by using the buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method, and MATLAB is used to achieve accurate batch calculation of sampling samples, including the following steps: A pier-cap-pile structural system is established. According to the principle of energy method, the total potential energy function is , and the formula is as follows: ； Among them, is the system bending strain energy, is the pile-soil spring potential energy, is the work done by the axial force, is the work done by the body force; In the pier-cap-pile structural system, is the vertical position coordinate, is the deflection curve function of the system, and the bending strain energy of the system is expressed as: ； Wherein, is the pile length, is the total length of the pier-cap-pile structural system, is the pier stiffness, is the pile stiffness; is the second derivative of the system deflection curve function; The pile-soil interaction is considered by using m method, and layers of soil are set. is the proportionality coefficient of the subgrade reaction coefficient of the soil, is the subgrade reaction force per unit length of the soil, expressed as: ； Among them, is the buried depth of the pile body, is the distance between the position of the pile cap and the soil mass, is the pile diameter, then the pile-soil spring potential energy is expressed as: ； Among them, is the vertical coordinate of the node of the -th layer of soil element, , is the node spacing, is the vertical coordinate of the node of the -th layer of soil element, is the value of the -th layer of soil, represents the serial number of the soil layer, , , is the scour depth; The loads of the pier-pile integral superstructure and the pile cap are simplified as axial forces acting on the top of the pier and the top of the pile. Using to represent the axial force at the top of the pier, to represent the axial force at the top of the pile, then the work done by the axial force is: ； , represent the self-weight per unit volume of the pier and the pile respectively. Then the work done by the body force is as follows: ； Among them, is the first derivative of the system deflection curve function; Assume that the pier-cap-pile-soil structural system follows the conditions of hinged lower end of the pile and free upper end of the pier top, and select the system deflection curve function of the overall lower structure of the pier-pile , the system deflection curve function is in the form of: ； Among them, is a parameter to be determined; is the trial function number; Substitute the total potential energy function into the stationary value condition of potential energy, construct the buckling failure characteristic equation, and obtain the minimum eigenvalue by solving the eigenvalue Calculate the critical buckling load value , the formula for the critical buckling load value is as follows: ； The critical buckling load change rate is obtained by solving with MATLAB , and the formula is as follows: ； Among them, is the calculated value of the critical buckling load when the scour depth is , and is the calculated value of the critical buckling load when the scour depth is 0.

4. The method for predicting the buckling load of a scour-damaged bridge based on machine learning according to claim 1, characterized in that In Step S102: Missing value filling: Calculate the median of each structural parameter in the current data set and use the median to fill the missing positions; Outlier removal: Calculate the standard score, set the standard deviation threshold, and remove the outlier samples whose absolute value of Z-score exceeds the standard deviation threshold in any parameter dimension. The formula is as follows: ； Among them, is the standard score, is the structural parameter value, and are respectively the mean and standard deviation in the dataset; Feature standardization: Subtract the mean of each structural parameter and then divide it by its standard deviation to make all structural parameters distributed within the same scale range. The formula is as follows: ； Among them, is the original structural parameter value after removing outliers, is the mean value in the dataset, is the standard deviation in the dataset, is the parameter value after standardization.

5. The method for predicting the buckling load of a scour-damaged bridge based on machine learning according to claim 1, characterized in that In Step S103, The prediction function form of the LightGBM machine learning model is defined as follows: ； Among them, represents the prediction result of the input sample data ; represents the output of the th regression subtree; represents the function space composed of regression subtrees; is the total number of multiple regression subtrees integrated in the LightGBM machine learning model; is the regression subtree number index; The LightGBM machine learning model uses the root mean square error as the optimization objective function. The formula is as follows: ； Among them, is the number of samples, is the predicted value of the -th sample, is the true value of the -th sample, is the value of the mean squared error loss function, is the sample number; Use the root mean square error RMSE as the evaluation metric; The RMSE formula is as follows: ； Adopt a five-fold cross-validation strategy to divide and train the sample data in multiple rounds; The average loss function of five-fold cross-validation is defined as: ； Among them, is the average of the losses of each fold in the five-fold cross-validation process, represents the loss value on the fold validation set, is the fold index of cross-validation.

6. The method for predicting the buckling load of a scour-damaged bridge based on machine learning according to claim 1, characterized in that, In Step S104, the performance evaluation metrics include: mean absolute error, root mean square error, and coefficient of determination.

7. A prediction system applicable to the prediction method for the buckling load of a scour-damaged bridge based on machine learning according to any one of claims 1-6, characterized in that, It includes: The data construction module (100) is used to obtain the original data for constructing the data set, including bridge parameters, soil parameters, and scour depth and the change rate of the critical buckling load Obtaining of structural parameters; A data preprocessing module (200) for preprocessing the original data obtained by the data construction module (100), including missing value filling, outlier removal, and feature standardization, to obtain the input data set of structural parameters for the prediction task and provide a standardized data input interface for subsequent model calls; Model construction and buckling prediction module (300), which is used to construct a LightGBM machine learning model to achieve the prediction of the change rate of the critical buckling load of a scour-damaged bridge Prediction; A result analysis module (400) for evaluating and verifying the regression model obtained after training the constructed LightGBM machine learning model using multiple performance evaluation metrics.

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