Buckling load prediction method and system for scour-damaged bridges based on machine learning

Abstract

The present invention relates to a method and system for predicting the buckling load of scour-damaged bridges based on machine learning, and belongs to the field of machine learning and structural engineering technology. The prediction method includes: raw data acquisition, raw data preprocessing, construction of a LightGBM machine learning model, and evaluation and verification of the constructed model using a variety of performance evaluation indicators. The present invention comprehensively considers key variables such as bridge structural parameters and foundation soil physical properties, constructs a large sample database covering a large number of scour combinations, and utilizes an energy-based buckling analysis method for the pier-cap-pile structure system after scour damage to accurately calculate the critical buckling load of the structure as the output target. Combined with an integrated learning algorithm, a multivariate nonlinear mapping relationship is established to replace traditional complex calculations. It has good engineering adaptability and universality, and can be applied to rapid prediction of buckling bearing capacity under different parameter bridges, different foundation forms and complex scour conditions.

Description

Technical Field

[0001] The present invention relates to the field of machine learning and structural engineering technology, and in particular 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 forms of failure in bridge structures. Once it occurs, it will pose a serious threat to the overall safety and stability of the bridge. Practice has shown that when a bridge foundation suffers severe scouring damage, the foundation's supporting capacity is greatly weakened, the overall structural stiffness is reduced, and the buckling risk is further exacerbated. In extreme cases, it will lead to sudden structural failure or total collapse, causing serious casualties and property losses. According to a survey, 80% of my country's active bridges cross water. Globally, approximately 60% of bridge water damage accidents are caused by scouring, and buckling of the substructure under scouring damage is a major factor leading to bridge collapse. Scouring causes soil loss around the bridge piers, which in turn causes structural instability. Therefore, research on the buckling safety evaluation of bridges under scouring is particularly important. How to quickly assess the safety of existing scouring-damaged bridges has become a key issue that needs to be addressed.

[0003] In the existing research on the buckling of bridge substructures, numerical calculation methods are widely used in the calculation of pile foundation buckling bearing capacity, among which the application of finite element method is particularly significant. For example, the paper "Geometrically nonlinear finite element analysis of pile buckling" published in the journal "Rock and Soil Mechanics" established a finite element model of spatial beam units with geometric nonlinear effects, and realized the full-process numerical simulation analysis of the problem of pile buckling instability under axial load. For example, the paper "Stability analysis of pile buckling taking into account shear deformation" published in the journal "Journal of Fuzhou University (Natural Science Edition)" combined the finite element principle to derive the column unit stiffness matrix expression considering shear deformation, established two types of buckling stability analysis equations suitable for different working conditions, and proposed a method taking into account the shear deformation and horizontal force. However, the above research method is still relatively complex and requires a lot of computing power and time.

[0004] Based on the principles of mechanics, it is particularly important to derive and study the structural buckling load formula and deeply analyze the structural failure mechanism. Among them, the energy method solves the structural buckling load by calculating the total energy of the system. It is easier to solve a variety of complex boundary conditions, making it widely used. For example, in the paper "Analysis of pile buckling stability considering the interaction of pile-soil coupling in multiple soil layers" published in the journal "Hunan Transportation Science and Technology", the following is analyzed: Law and The hyperbola method uses two pile-soil coupling models, and the energy method is used to derive the critical buckling load formula for multi-layer pile-soil systems. For example, the paper "Buckling Stability Analysis of Wedge-Shaped Piles in Slopes Based on the Energy Method" published in the Journal of Jiangsu University uses the Rayleigh-Ritz method, taking into account the side friction of the pile and the landslide thrust of the soil behind the pile, to establish the total potential energy equation of the pile-soil system and derive an analytical expression for the critical buckling load. For example, the Chinese patent application with publication number CN111382517A, entitled "Analytical Method for Analytical Solution of Critical Buckling Load of Pile Foundation Based on Dual-Parameter Foundation Model," proposes a method for analytical solution of critical buckling load of pile foundation based on the energy method, taking into account the reaction modulus and shear modulus of the foundation soil and the deadweight of the pile foundation to obtain an analytical solution for the critical buckling load of the pile foundation.

[0005] In recent years, research on the buckling stability of bridge substructures under varying scour depths has made some progress, but relatively few studies have been conducted. For example, a paper titled "Finite Element Calculation of Pier Structural Systems Under Scour" published in the Journal of Wuhan University (Engineering) constructed a three-dimensional finite element model of piers, abutments, piles, and soils using ANSYS finite element software. The piers were subjected to stress analysis considering varying scour depths, coupled with sediment scour and hydrodynamic pressure. Another paper, "Buckling Analysis of Pier Structural Systems Under Hydrodynamic Pressure and Scour Based on an Energy Method," published in the journal Hydropower Energy Science, derived a formula for calculating the buckling load of piers under the coupled effects of scour and hydrodynamic pressure using an energy method. The accuracy of the formula was verified by comparison with an equivalent single-column model and finite element simulations. For example, the paper "Calculation of Buckling Load of Pier Structural System under Scour Action" published in the journal "Journal of Wuhan University (Engineering Edition)" derived a calculation formula for buckling load considering the interaction between soil, piles and piers, the equivalent structural system of piers and pile groups, and the influence of sliding rubber bearings and abutments, and analyzed the effects of scour depth, pile-pier stiffness ratio, etc. on buckling load.

[0006] With the development of artificial intelligence and data-driven methods, machine learning has been widely applied to bridge structure and performance prediction. However, to date, no patents or papers have demonstrated the rapid assessment of bridge substructure buckling loads using data-driven methods.

[0007] In summary, the existing analysis methods mentioned above either calculate the buckling bearing capacity of pile foundations through complex numerical methods or derive the critical buckling load under scour damage based on mechanical principles. However, research on buckling stability assessment methods for pier-cap-pile foundation systems that consider the deadweight of the structure is insufficient, and data-driven methods have not been applied to critical buckling load assessment, resulting in a lack of complete safety assessment. This makes it difficult to balance efficiency, accuracy, and adaptability, and the lack of a mechanism to integrate theoretical solutions with data-driven predictions makes it impossible to rapidly assess the critical buckling load of existing damaged bridges. Therefore, there is an urgent need to develop a machine learning-based rapid prediction method for the critical buckling load of bridge scour damage to achieve efficient quantification and intelligent assessment of structural safety performance, enhance the safety assurance capabilities of bridge structures in complex hydrological environments, and provide theoretical support and engineering decision-making basis for bridge disaster prevention and mitigation 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 bridge structural performance under scour damage relies on a large amount of finite element modeling and complex mechanical method calculations, resulting in low prediction efficiency and poor engineering adaptability. It is difficult to quickly evaluate the stability limit of the bridge under various scour situations, especially the change trend of the critical buckling load is difficult to quantify. The present invention provides a method and system for predicting the buckling load of scour-damaged bridges based on machine learning.

[0009] In order to solve the above technical problems, the technical solutions of the present invention are as follows:

[0010] A method for predicting buckling load of scour-damaged bridges based on machine learning, characterized by comprising the following steps:

[0011] Step S101: Acquisition of original data, including bridge parameters, soil parameters, scour depth and the critical buckling load change rate Acquisition of structural parameters;

[0012] Bridge parameters include: pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus ;

[0013] Soil parameters are proportional coefficients of soil foundation resistance coefficients value;

[0014] Step S102: preprocessing the original data obtained in step S101, including filling missing values, removing outliers, and normalizing features, to obtain a structural parameter input data set for the prediction task;

[0015] Step S103: Using the bridge parameters, soil parameters and scour depth of the data set obtained in step S102 As the input characteristic, the critical buckling load change rate To predict the target, a LightGBM machine learning model is constructed to establish a nonlinear mapping relationship between input features and prediction targets;

[0016] 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 in multiple rounds using a fold-cross validation strategy to obtain the final regression model, which is used to predict the critical buckling load change rate of scour-damaged bridges.

[0017] Step S104: using a variety of performance evaluation indicators to evaluate and verify the regression model obtained in step S103.

[0018] In the above technical solution, in step S101, the bridge parameters, soil parameters and scour depth The Latin hypercube sampling is used to obtain the data, and the sample data of different scour depths are formed by combining them at intervals of a certain scour depth;

[0019] Critical buckling load change rate The buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method is adopted to obtain the data, and MATLAB is used to realize accurate batch calculation of sampling samples.

[0020] In the above technical solution, in step S101, the critical buckling load change rate The acquisition of the energy-based buckling analysis method for the pier-cap-pile structure after scour damage is carried out using MATLAB to achieve accurate batch calculation of sampling samples, which includes the following steps:

[0021] Establish a pier-cap-pile structure system. According to the energy method principle, the total potential energy function is: , the formula is as follows:

[0022] ;

[0023] in, is the bending strain energy of the system, is the pile-soil spring potential energy, is the work done by the axial force, To do work for physical strength;

[0024] In the pier-cap-pile structure system, is the vertical position coordinate, is the system deflection curve function, the system bending strain energy Expressed as:

[0025] ;

[0026] in, is the pile length, It is the full length of the pier-cap-pile structure system. is the pier stiffness, is the pile stiffness; is the second-order derivative of the system deflection curve function;

[0027] Pile soil effect m Consider and set layer of soil, is the proportional coefficient of the soil foundation resistance coefficient, is the foundation soil reaction force per unit length, expressed as:

[0028] ;

[0029] in, is the buried depth of the pile body, is the distance between the foundation and the soil, is the pile diameter, then the pile-soil spring potential energy Expressed as:

[0030] ;

[0031] in, For the Vertical coordinates of the soil unit nodes, , is the node spacing, For the Vertical coordinates of the soil unit nodes, For the layer of soil value, Represents the soil layer number, , , is the scour depth;

[0032] The pier-pile superstructure load and the cap are simplified to the axial force acting on the pier top and the pile top. Represents the top axial force of the pier, represents the axial force at the top of the pile, then the axial force does work for:

[0033] ;

[0034] 、 Represent the deadweight concentration of the pier and pile respectively, then the physical work for:

[0035] ;

[0036] in, is the first-order derivative of the system deflection curve function;

[0037] Assuming that the pier-cap-pile-soil structure system is hinged at the lower end of the pile and free at the top of the pier, the system deflection curve function of the pier-pile overall substructure is selected. , system deflection curve function The form is:

[0038] ;

[0039] in, is a parameter to be determined; Number the test function;

[0040] The total potential energy function Substitute the potential energy stationary condition to construct the buckling failure characteristic equation, and obtain the minimum eigenvalue by eigenvalue solution Calculation of critical buckling load values , critical buckling load value The formula is:

[0041] ;

[0042] Using MATLAB to solve the critical buckling load change rate , the formula is as follows:

[0043] ;

[0044] in, For the scouring depth The calculated value of the critical buckling load at is the calculated value of the critical buckling load when the scour depth is 0.

[0045] In the above technical solution, in step S102:

[0046] Missing value filling is as follows: for each structural parameter, the median of the parameter in the current data set is calculated, and the missing position is filled using the median;

[0047] Outlier removal is as follows: calculate the standard score, set the standard deviation threshold, and remove abnormal samples whose Z-score absolute value exceeds the standard deviation threshold in any parameter dimension. The formula is as follows:

[0048] ;

[0049] in, is the standard score, is the structural parameter value, and They are The mean and standard deviation in the data set;

[0050] Feature standardization is to subtract the mean of each structural parameter and then divide it by its standard deviation so that all structural parameters are distributed within the same scale range; the formula is as follows:

[0051] ;

[0052] 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 normalized parameter value.

[0053] In the above technical solution, in step S103,

[0054] The prediction function form of the LightGBM machine learning model is defined as follows:

[0055] ;

[0056] in, Indicates the input sample data The prediction results, Indicates the The output of the regression subtree, represents the function space composed of regression subtrees, The total number of multiple regression subtrees integrated in the LightGBM machine learning model. Index the regression subtrees;

[0057] The LightGBM machine learning model uses the root mean square error as the optimization objective function. The formula is as follows:

[0058] ;

[0059] in, is the number of samples, For the The predicted value of the sample, For the The true value of the sample, is the mean square error loss function value, Number the sample;

[0060] The root mean square error (RMSE) is used as the evaluation indicator; the RMSE formula is as follows:

[0061] ;

[0062] A five-fold cross-validation strategy is used to perform multiple rounds of division and training on the sample data. The average loss function of the five-fold cross-validation is defined as:

[0063] ;

[0064] in, is the average loss of each fold during the five-fold cross validation process, Indicates the The loss value on the fold validation set, The index of the cross validation folds.

[0065] In the above technical solution, in step S104, the performance evaluation indicators include: mean absolute error, root mean square error and determination coefficient.

[0066] A prediction system suitable for the scour damaged bridge buckling load prediction method based on machine learning described in the present invention, comprising: a data construction module for constructing the original data acquisition of the data set, including bridge parameters, soil parameters, scour depth and the critical buckling load change rate Acquisition of structural parameters;

[0067] The data preprocessing module is used to preprocess the raw data obtained by the data construction module, including filling missing values, removing outliers, and standardizing features, to obtain the structural parameter input data set of the prediction task and provide a standardized data input interface for subsequent model calls;

[0068] Model building and buckling prediction module, used to build LightGBM machine learning model and realize the critical buckling load change rate of scour damaged bridges predict;

[0069] The result analysis module is used to evaluate and verify the regression model obtained after training the constructed LightGBM machine learning model using a variety of performance evaluation indicators.

[0070] The present invention has the following beneficial effects:

[0071] The machine learning-based buckling load prediction method and system for scour-damaged bridges of the present invention comprehensively consider key variables such as bridge structural parameters and foundation soil physical properties, construct a large sample database covering a large number of scour combinations, and utilize an energy-based buckling analysis method for the pier-cap-pile structure system after scour damage to accurately calculate the critical buckling load of the structure as the output target. Combined with an integrated learning algorithm, a multivariable nonlinear mapping relationship is established to replace traditional complex calculations. The system has good engineering adaptability and universality, and can be used for rapid prediction of buckling bearing capacity under bridges with different parameters, different foundation forms, and complex scour conditions.

[0072] The machine learning-based buckling load prediction method and system for scour-damaged bridges of the present invention significantly improve the efficiency of buckling load assessment. Specifically, the present invention uses machine learning as the core to optimize the traditional finite element simulation and buckling analysis calculation process. Through feature extraction, model training and optimization steps, it quickly completes the accurate prediction of the critical buckling load of the bridge under scour damage state, and establishes a complete process system, avoiding a large amount of repetitive modeling and calculation work, greatly improving the efficiency of structural performance assessment, and having good engineering practical value.

[0073] The machine learning-based buckling load prediction method and system for scour-damaged bridges of the present invention effectively improve the prediction accuracy and stability. Specifically, the present invention adopts an energy-based buckling analysis method for the pier-cap-pile structure system after scour damage, which comprehensively considers the overall effect of the structure and is an accurate mechanical solution method. On this basis, multiple input parameters are set, and a LightGBM regression model based on a gradient boosting decision tree (GBDT) is adopted to accurately capture the complex nonlinear relationship between the input parameters and the buckling load. At the same time, fold cross-validation and early stopping mechanisms are introduced to fully utilize the training data and suppress overfitting, ensuring that the model can maintain high prediction accuracy and robustness under different scour conditions.

[0074] The machine learning-based buckling load prediction method and system for scour-damaged bridges of the present invention enhance the model's generalization and scalability. Specifically, the regression model constructed by the present invention introduces multiple combinations of structural types and scour depths during the training process, selects the optimal sub-model as the final model through multiple rounds of verification, and uses the mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) to comprehensively evaluate the model's performance, verifying its good generalization ability on unseen samples. This makes it suitable for the rapid analysis and early warning needs of existing bridge structures.

[0075] Compared with traditional methods, the machine learning-based scour-damaged bridge buckling load prediction method and system of the present invention combines theoretical integrity, computational accuracy and engineering practicality. It is suitable for scour resistance optimization in the bridge design stage, health monitoring during operation, and rapid assessment of bridge stability after floods, providing theoretical support and decision-making basis for bridge disaster prevention and mitigation in scour environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0077] Figure 1 Flowchart of the buckling load prediction method for scour-damaged bridges based on machine learning of the present invention;

[0078] Figure 2 This is a simplified model diagram of a single pier in an embodiment of the present invention;

[0079] Figure 3 A simplified mechanical model diagram in an embodiment of the present invention;

[0080] Figure 4 This is a diagram showing the prediction effect of the LightGBM machine learning model in an embodiment of the present invention;

[0081] Figure 5 This is a distribution diagram of the residual errors of the prediction results of different models on the test set in an embodiment of the present invention (the LightGBM machine learning model is referred to as LightGBM in the figure);

[0082] Figure 6 Schematic diagram of the structure of the prediction system of the scour damaged bridge buckling load prediction method based on machine learning applicable to the present invention.

[0083] The reference numerals in the figures indicate:

[0084] 100-Data construction module; 200-Data preprocessing module; 300-Model construction and buckling prediction module; 400-Result analysis module. DETAILED DESCRIPTION

[0085] The inventive concept of this invention is this: This machine learning-based method for predicting the buckling load of scour-damaged bridges integrates multi-source characteristic information, such as bridge scour depth, structural parameters, and soil mechanical properties, to construct a high-precision regression model. This method, using a gradient boosting-based ensemble learning algorithm, enables accurate and efficient prediction of the critical buckling load. This significantly improves the efficiency and reliability of structural safety assessments, providing intelligent support for the operational management and disaster prevention of existing bridges.

[0086] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0087] like Figure 1 As shown ( Figure 1 (Only the steps of the prediction method of the present invention are summarized) The method for predicting the buckling load of scour-damaged bridges based on machine learning of the present invention comprises the following steps:

[0088] Step S101: Acquisition of original data, including bridge parameters, soil parameters, scour depth and the critical buckling load change rate Acquisition of structural parameters;

[0089] Bridge parameters include: pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus ;

[0090] Soil parameters are proportional coefficients of soil foundation resistance coefficients value;

[0091] Among them, bridge parameters, soil parameters and scour depth The Latin hypercube sampling (LHS) is used to obtain the data, and a large number of sample data considering different scour depths are formed at intervals of a certain scour depth; the critical buckling load change rate The acquisition adopts the energy-based buckling analysis method of the pier-cap-pile structure system after scour damage, and uses MATLAB software to achieve accurate batch calculation of sampling samples. Specifically:

[0092] 1. Obtain bridge parameters, soil parameters and scour depth;

[0093] Scour depth , proportional coefficient of soil foundation resistance coefficient Value, pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus If it is a pile group structure, it is equivalent to a single pile according to the principle of equivalent stiffness of pile groups, and the equivalent pile structure parameters are obtained.

[0094] (1) Obtaining bridge and soil parameters: To ensure the rationality and correctness of the calculation results of the critical buckling load of scour-damaged bridges, the bridge parameters need to be evenly combined and cover most small and medium span bridges. The Latin hypercube sampling (LHS) algorithm is used to calculate the proportional coefficient of the soil foundation resistance coefficient. Value, pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus These six parameter combinations are sampled. This embodiment selects the sampling range of each parameter based on the "Highway Bridge and Culvert Foundation and Subgrade Design Specifications" and other relevant specifications, with reference to the north approach bridge of the Sutong Bridge in southeastern Jiangsu. The specific ranges are as follows:

[0095] The width of the bridge pier will affect the bending stiffness and overall stability of the bridge pier structure. It is 0.8~1.3 times the width of the Sutong Bridge pier, that is, 5.20m-8.45m. The pier height will affect the failure mode and shear resistance of the pier. The shear span ratio (the ratio between the pier height and the pier width) is often used in engineering to control the pier height. The shear span ratio of the piers of small and medium span bridges is usually in the range of 5-10. Therefore, the pier height is taken as The sampling range is 26.0m-84.5m; the pile slenderness ratio (the ratio of pile length to pile diameter) is directly related to the overall stability and bearing capacity of the pile. The pile length is controlled to be 90m and the pile slenderness ratio is kept constant. The sampling range is 15-25; the concrete materials commonly used in bridge substructures are mainly C30~C50 concrete. This example refers to the Sutong Bridge, where the piers are made of C40 concrete and the piles are made of C30 concrete. Due to scouring damage, the elastic modulus reduction range is 0.6-1, that is, the elastic modulus of the sampled piers is The range is 19.5GPa-32.5GPa, the pile elastic modulus 18.0GPa-30.0GPa; According to the specification, the proportional coefficient of the foundation resistance coefficient of clay, medium sand, coarse sand, dense silt and other soils is Values are usually between 3000-30000 Compared with other parameters, the reduction of concrete bulk density after scouring has no obvious effect on the critical buckling load, so this example does not use it as a machine learning dataset parameter. According to the specification, the pier bulk density Set to , pile density Set to On this basis, to better reflect actual conditions, the lower limit for the reduction of pier stiffness was set at 0.5 times the base bridge pier, and the lower limit for the reduction of pile stiffness was set at 0.28 times the base bridge pier, to limit the LHS sampling range. Subsequently, 300 sets of samples were collected for the above six bridge and soil parameters for future use.

[0096] (2) Sample combination scouring depth: In order to make the sampling results more universal, the scouring depth of the present invention It is a dimensionless parameter, that is, the percentage of the actual scouring depth to the total buried depth of the pile foundation. Its formula is:

[0097] ;

[0098] in, is the actual scouring depth of the bridge, in meters. It is the total buried depth of pile foundation in meters.

[0099] Since the actual scouring depth of a bridge is unlikely to exceed 80% of the pile length in actual engineering, the range is 0%-80%. In this embodiment, 300 groups of sampling results are uniformly sampled at intervals of 5% and combined with the above-mentioned bridge parameters and soil parameters to form a final 5100 groups of sampling results as sample data.

[0100] 2. Critical Buckling Load Change Rate Get;

[0101] The critical buckling load for each sample was calculated using a method for assessing the buckling stability of a pier-cap-pile structure after scour damage. This method, based on an energy approach, differs from mechanical methods that only target an equivalent single-column model. It considers the pier-cap-pile structure, structural gravity, and multiple parameters to account for varying structural characteristics, resulting in high accuracy. The specific method steps are as follows:

[0102] (1) Construct a simplified single pier model for the buckling analysis of the pier-cap-pile structure system, such as Figure 2 In this embodiment, the pier type is a rectangular thin-walled pier, and the pier height is The width of the bridge pier is (i.e. the width of the pier section is ), the cross-section length is 4m. In order to facilitate the analysis of the buckling load of the bridge structure, the pile group is simplified into a single pile with the same bearing capacity according to the principle of equivalent stiffness of the pile group. The pile diameter is , pile length The initial pile burial depth is , is the distance between the cap and the soil. The pier-pile superstructure is simplified to the vertical force (i.e. axial force) acting on the top of the pier. , and simplified it into the vertical force (i.e. axial force) applied to the top of the pile according to the mass of the pile cap ,use Represents the top axial force of the pier, represents the axial force at the pile top, 、 are the stiffness of the pier and pile respectively. The bridge pile foundation is simplified to the problem of elastic foundation beam buckling failure under axial force on the top of the pier. The interaction between pile and soil is adopted m "Method is considered, different soil types are set as different layers, layer, is the proportional coefficient of the soil foundation resistance coefficient, such as the first layer m 1 、Layer 2 m 2 、 Layer 3 m 3 … No. N-1 layer m N-1 ， In order to calculate the foundation resistance of each layer of soil, this embodiment only sets the single-layer soil type.

[0103] Specifically, if Figure 3 The simplified mechanical model diagram of the pier-cap-pile structure system is shown in the figure. Represents the first unit node to the N The coordinates of each unit node, according to the principle of energy method, include the bending strain energy of the system , pile-soil spring potential energy , axial force work Work with physical strength , establish the total potential energy function of the pier-cap-pile structure system , the formula is as follows:

[0104] ;

[0105] in, is the bending strain energy of the system, is the pile-soil spring potential energy, is the work done by the axial force, To do work for physical strength;

[0106] In the pier-cap-pile structure system, is the vertical position coordinate, is the system deflection curve function, the system bending strain energy Expressed as:

[0107] ;

[0108] in, is the pile length, is the full length of the pier-cap-pile structure system, i.e. , and are the stiffness of piers and piles respectively; is the second-order derivative of the system deflection curve function;

[0109] Pile soil effect m Consider and set layer of soil, is the proportional coefficient of the soil foundation resistance coefficient, is the foundation soil reaction force per unit length, expressed as:

[0110] ;

[0111] in, is the buried depth of the pile body, is the distance between the foundation and the soil, is the pile diameter, then the pile-soil spring potential energy Expressed as:

[0112] ;

[0113] in, For the Vertical coordinates of the soil unit nodes, , is the node spacing, For the Vertical coordinates of the soil unit nodes, For the layer of soil value, Represents the soil layer number, , , is the scour depth;

[0114] The pier-pile superstructure load and the cap are simplified to the axial force acting on the pier top and the pile top. Represents the top axial force of the pier, represents the axial force at the top of the pile, then the axial force does work for:

[0115] ;

[0116] 、 Represent the deadweight concentration of the pier and pile respectively, then the physical work for:

[0117] ;

[0118] in, is the first-order derivative of the system deflection curve function;

[0119] (2) Assuming that the pier-cap-pile-soil structure system is hinged at the lower end of the pile and free at the top of the pier, the system deflection curve function of the pier-pile overall substructure is selected. , system deflection curve function The form is:

[0120] ;

[0121] in, is a parameter to be determined; Number the trial function; substitute into the total potential energy function , according to the principle of potential energy stationary value, the characteristic equation of buckling failure is obtained, and finally converted into solving the minimum eigenvalue of the matrix problem, by solving the minimum eigenvalue , the critical buckling load value of the pier-cap-pile structure system is obtained The formula is as follows:

[0122] ;

[0123] in, is the critical buckling load value, is the total length of the pier-cap-pile structure system (i.e. the sum of the pier length and the pile length), is the minimum eigenvalue.

[0124] (3) The above method is programmed by MATLAB software. This embodiment performs accurate batch calculations on 5100 sets of sample data from LHS sampling, and calculates the critical buckling load change rate based on the critical buckling load. , the formula is as follows:

[0125] ;

[0126] in, For the scouring depth The calculated value of the critical buckling load at is the calculated value of the critical buckling load when the scour depth is 0.

[0127] Step S102: preprocessing the original data obtained in step S101, including filling missing values, removing outliers, and normalizing features, to obtain a structural parameter input data set for the prediction task;

[0128] The original data are the bridge parameters, soil parameters, scour depth, and Structural parameters such as scour depth , proportional coefficient of soil foundation resistance coefficient Value, pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus and the critical buckling load change rate .

[0129] (1) Missing value filling: The median filling method is used for processing. Specifically, the median of each structural parameter in the current data set is calculated, and the missing position of the corresponding field is filled with the median.

[0130] (2) Outlier elimination: The Z-score method is used to calculate the standard score of each structural parameter. The specific steps are: , calculate its mean in the data set and standard deviation , and calculate accordingly. The standard score calculation formula is:

[0131] ;

[0132] in, is the standard score, is the structural parameter value, and They are The mean and standard deviation in the data set;

[0133] In this embodiment, the Z-score 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 eliminated.

[0134] (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:

[0135] ;

[0136] 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 normalized parameter value. 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.

[0137] Step S103: Using the bridge parameters, soil parameters and scour depth of the data set obtained in step S102 As the input characteristic, 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;

[0138] 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 was divided and iteratively trained multiple times using a fold-cross validation strategy to obtain the LightGBM machine learning model with the best generalization performance, i.e., the final regression model. This regression model is used to quickly predict the critical buckling load change rate of scour-damaged bridges.

[0139] The LightGBM machine learning model used is a 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:

[0140] ;

[0141] in, Indicates the input sample data The prediction results, Indicates the The output of the regression subtree, represents the function space composed of regression subtrees, The total number of multiple regression subtrees integrated in the LightGBM machine learning model. Index the regression subtrees.

[0142] The LightGBM machine learning model uses the root mean square error (RMSE) as the optimization objective function. The formula is as follows:

[0143] ;

[0144] in, is the number of samples, For the The predicted value of the sample, For the The true value of the sample, is the mean square error loss function value, Number the sample;

[0145] The root mean square error (RMSE) is used as the evaluation indicator; the RMSE formula is as follows:

[0146] ;

[0147] The meanings of the parameters are the same as above.

[0148] In order to evaluate the stability and generalization ability of the LightGBM machine learning model under different data partitions, we introduce The five-fold cross validation strategy performs multiple rounds of partitioning and iterative training on the sample data. This example uses the 5-fold cross validation strategy to perform multiple rounds of partitioning and training on the training data (i.e., sample data). Specifically, all training data is evenly divided into five subsets. Four subsets are selected in each round for LightGBM machine learning model training, and the remaining subset is used as a validation set. This process is repeated five times to ensure that each subset is used as a validation set. The average loss function of the five-fold cross validation is defined as:

[0149] ;

[0150] in, is the average loss of each fold during the five-fold cross validation process, Indicates the The loss value (RMSE) on the fold validation set, The index of the cross validation folds.

[0151] During the training process, an early stopping mechanism is introduced to prevent the LightGBM machine learning model from overfitting on the training set and to control the number of iterations. In this embodiment, the LightGBM machine learning model is trained for a maximum of 1000 rounds. If the root mean square error performance indicator on the validation set does not show significant improvement in 50 consecutive iterations, the training process is automatically terminated.

[0152] Step S104: using a variety of performance evaluation indicators to evaluate and verify the regression model obtained in step S103.

[0153] Among them, performance evaluation indicators include but are not limited to: mean absolute error (MAE), root mean square error (RMSE) and coefficient of determination (R²).

[0154] The above three performance evaluation indicators evaluate the prediction performance of the LightGBM machine learning model from different dimensions. MAE measures the average error, RMSE emphasizes the penalty for large errors, and R² reflects the degree of fit of the LightGBM machine learning model to the overall trend. In this embodiment, the overall prediction results of the five-fold cross-validation are used to calculate the above indicators to obtain the comprehensive performance of the LightGBM machine learning model under different data partitions.

[0155] The prediction results of the LightGBM machine learning model in this embodiment for each evaluation index are: mean absolute error is 0.0036, root mean square error is 0.0026, and determination coefficient is 0.9998, all of which indicate that this LightGBM machine learning model has high accuracy. Further, the test set is compared with the actual value, and the prediction results are as follows Figure 4 As shown. It can be observed that the predicted value is in good agreement with the actual value, with a small error, which once again verifies that this LightGBM machine learning model can accurately calculate the critical buckling load change rate. .

[0156] On this basis, in order 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. The output of Shallow Decision Tree Regressor is a discrete piecewise constant type, while KNN (K-Nearest Neighbors Regressor), Random Forest Regressor and the LightGBM machine learning model adopted by the invention (Table 1 and Figure 5 The LightGBM machine learning model (represented by LightGBM in the example) outputs continuous values. As shown in Table 1, the results show that the LightGBM machine learning model outperforms the other three models in terms of the evaluation indicators mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²).

[0157] Table 1 Comparison of prediction effects of various algorithms

[0158]

[0159] In order to compare the prediction results more intuitively, the residuals between the prediction results of the four models in the table and the actual results are calculated and plotted as violin plots, as shown in the following example: Figure 5 Among them, the LightGBM machine learning model has the smallest residual and a concentrated distribution, which once again proves the accuracy and superiority of the LightGBM machine learning model of the present invention.

[0160] like Figure 6 As shown, another embodiment of the present invention provides a prediction system suitable for the above-mentioned scour-damaged bridge buckling load prediction method based on machine learning, which 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.

[0161] Data construction module 100, which is used to construct the original data of the data set, obtain bridge parameters, soil parameters, scour depth and the critical buckling load change rate Structural parameters. The structural parameters obtained include scour depth , proportional coefficient of soil foundation resistance coefficient Value, pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus , critical buckling load change rate . In the case that the bridge is a pile group foundation structure, the pile group equivalent stiffness principle is adopted to transform the pile group structure into a single pile structure model, and the relevant parameters of the equivalent pile are extracted. The Latin hypercube sampling algorithm is adopted for sampling. This embodiment generates 300 sets of structure and foundation parameter combination samples in the above parameter space. In order to fully cover the structural response under different scouring effects, this embodiment combines and expands each set of parameter samples at intervals of 5% scouring depth to construct a sample data set containing multiple scouring levels. Obtain the critical buckling load change rate The buckling stability assessment method for the pier-cap-pile structure after scour damage is adopted. This method considers the overall structural effect, that is, the overall structural system of the pier-cap-pile-soil, and considers the different structural characteristics and body forces of the pier and pile foundation, as well as the gravity of the cap. The total potential energy function of the pier-cap-pile structure system is established based on the principle of energy method. , assuming the system deflection curve function under the hinge-free boundary condition Form (i.e., assuming that the pier-cap-pile-soil structure system is hinged at the lower end of the pile and free at the top of the pier, the system deflection curve function of the pier-pile overall substructure is selected ), the total potential energy function Substitute the potential energy stationary value condition, construct the characteristic equation, and obtain the minimum eigenvalue by solving the eigenvalue Calculate the critical buckling load value. The above method uses MATLAB software programming to achieve accurate batch calculation of sample sets and obtain a complete data set.

[0162] The data preprocessing module 200 is used to preprocess the original data obtained by the data construction module 100, including filling missing values, eliminating outliers, and standardizing features, to obtain the structural parameter input data set of 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 to fill missing values; using the Z-score method to calculate the standard score, setting the standard deviation threshold to 3.0, and eliminating abnormal samples that exceed the threshold in any parameter dimension; using the Z-score standardization to normalize the feature quantity to eliminate the influence of different dimensions.

[0163] Model building and buckling prediction module 300, used to build LightGBM machine learning models to achieve the critical buckling load change rate of scour damaged bridges Quick prediction. The pre-processed data sets are used to collect bridge parameters, soil parameters and scour depth. As an input feature, the critical buckling load rate of change As the prediction target, a LightGBM machine learning model is constructed. In the training of the LightGBM machine learning model, multiple regression subtrees are integrated to improve the fitting ability of the high-dimensional structural feature space. This embodiment introduces a five-fold cross-validation strategy to perform multiple rounds of division and iterative training on the sample data. An early termination mechanism (Early Stopping) based on the validation set loss function is introduced in each fold verification. 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 in the validation set is selected as the representative model for each fold, and finally the model with the best comprehensive performance from all folds is selected as the final LightGBM machine learning model, that is, the final regression model, which can achieve the critical buckling load change rate. Quick predictions.

[0164] Results analysis module 400 is used to evaluate and validate the regression model obtained after training the constructed LightGBM machine learning model using multiple performance evaluation metrics. This module evaluates the performance of the LightGBM machine learning model's prediction results to improve the engineering interpretability of the prediction results. The system uses mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²) regression performance metrics to quantitatively evaluate the performance of the LightGBM machine learning model on the test set.

[0165] In summary, this paper provides a machine learning-based method for predicting the buckling load of scour-damaged bridges. Combining precise theoretical calculations with machine learning algorithms, this method establishes a nonlinear mapping relationship between bridge, soil, and scour parameters and the rate of change of the critical buckling load through parameter sampling, buckling analysis, data preprocessing, and regression model training. This method can efficiently and accurately predict the evolution of the critical buckling capacity of bridge piers under various scour scenarios, providing technical support for scour damage assessment and bridge structural safety analysis.

[0166] This method uses the LightGBM machine learning model, a lightweight and high-precision machine learning framework, to train the final regression model. This method, while fully incorporating a data-driven approach based on theoretical mechanics, offers advantages such as high model training accuracy, rapid speed, and strong adaptability. Compared with traditional analytical and numerical methods, this method significantly improves computational efficiency and significantly reduces reliance on specialized computing resources. It is suitable for rapid buckling load screening and risk warning for a wide range of small- and medium-span bridges with existing scour damage.

[0167] Overall, the present invention has good engineering practicality and promotion value in predicting the buckling performance of small and medium-span bridges with existing scour damage. It helps to improve the intelligence and data level of maintenance and management of existing scour-damaged bridges, enhance the safety assurance capability 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.

[0168] Obviously, the above embodiments are merely examples for clarity of explanation and are not intended to limit the implementation methods. Those skilled in the art will readily appreciate that other variations or modifications based on the above descriptions are possible. It is not necessary and impossible to enumerate all implementation methods here. Obvious variations or modifications arising therefrom remain within the scope of protection of the present invention.

Claims

1. A method for predicting buckling load of scour-damaged bridges based on machine learning, characterized in that: The following steps are involved: Step S101: Acquisition of original data, including bridge parameters, soil parameters, scour depth and the critical buckling load change rate Acquisition of structural parameters; Bridge parameters include: pile slenderness ratio , pier width , pier height , elastic modulus of pier , pile elastic modulus ; Soil parameters are proportional coefficients of soil foundation resistance coefficients value; Step S102: preprocessing the original data obtained in step S101, including filling missing values, removing outliers, and normalizing features, to obtain a structural parameter input data set for the prediction task; Step S103: Using the bridge parameters, soil parameters and scour depth of the data set obtained in step S102 As the input characteristic, the critical buckling load change rate To predict the target, a LightGBM machine learning model is 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 in multiple rounds using a fold-cross validation strategy to obtain the final regression model, which is used to predict the critical buckling load change rate of scour-damaged bridges. Step S104: using a variety of performance evaluation indicators to evaluate and verify the regression model obtained in step S103.

2. The method for predicting buckling load of scour-damaged bridges based on machine learning according to claim 1 is characterized in that: In step S101, bridge parameters, soil parameters and scour depth The Latin hypercube sampling is used to obtain the data, and the sample data of different scour depths are formed by combining them at intervals of a certain scour depth; Critical buckling load change rate The buckling analysis method of the pier-cap-pile structure system after scour damage based on the energy method is adopted to obtain the data, and MATLAB is used to realize accurate batch calculation of sampling samples.

3. The method for predicting buckling load of scour-damaged bridges based on machine learning according to claim 2 is characterized in that: In step S101, the critical buckling load change rate The acquisition of the energy-based buckling analysis method for the pier-cap-pile structure after scour damage is carried out using MATLAB to achieve accurate batch calculation of sampling samples, which includes the following steps: Establish a pier-cap-pile structure system. According to the energy method principle, the total potential energy function is: , the formula is as follows: ； in, is the bending strain energy of the system, is the pile-soil spring potential energy, is the work done by the axial force, To do work for physical strength; In the pier-cap-pile structure system, is the vertical position coordinate, is the system deflection curve function, the system bending strain energy Expressed as: ； in, is the pile length, It is the full length of the pier-cap-pile structure system. is the pier stiffness, is the pile stiffness; is the second-order derivative of the system deflection curve function; Pile soil effect m Consider and set layer of soil, is the proportional coefficient of the soil foundation resistance coefficient, is the foundation soil reaction force per unit length, expressed as: ； in, is the buried depth of the pile body, is the distance between the foundation and the soil, is the pile diameter, then the pile-soil spring potential energy Expressed as: ； in, For the Vertical coordinates of the soil unit nodes, , is the node spacing, For the Vertical coordinates of the soil unit nodes, For the layer of soil value, Represents the soil layer number, , , is the scour depth; The pier-pile superstructure load and the cap are simplified to the axial force acting on the pier top and the pile top. Represents the axial force at the top of the pier, represents the axial force at the top of the pile, then the axial force does work for: ； 、 Represent the deadweight concentration of the pier and pile respectively, then the physical work for: ； in, is the first-order derivative of the system deflection curve function; Assuming that the pier-cap-pile-soil structure system is hinged at the lower end of the pile and free at the top of the pier, the system deflection curve function of the pier-pile overall substructure is selected. , system deflection curve function The form is: ； in, is a parameter to be determined; Number the test function; The total potential energy function Substitute the potential energy stationary condition to construct the buckling failure characteristic equation, and obtain the minimum eigenvalue by eigenvalue solution Calculation of critical buckling load values , critical buckling load value The formula is: ； Using MATLAB to solve the critical buckling load change rate , the formula is as follows: ； in, For the scouring depth The calculated value of the critical buckling load at is the calculated value of the critical buckling load when the scour depth is 0.

4. The method for predicting buckling load of scour-damaged bridges based on machine learning according to claim 1 is characterized in that: In step S102: Missing value filling is as follows: for each structural parameter, the median of the parameter in the current data set is calculated, and the missing position is filled using the median; Outlier removal is as follows: calculate the standard score, set the standard deviation threshold, and remove abnormal samples whose Z-score absolute value exceeds the standard deviation threshold in any parameter dimension. The formula is as follows: ； in, is the standard score, is the structural parameter value, and They are The mean and standard deviation in the data set; Feature standardization is to subtract the mean of each structural parameter and then divide it by its standard deviation so that all structural parameters are distributed within the same scale range; the formula is as follows: ； 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 normalized parameter value.

5. The method for predicting buckling load of scour-damaged bridges based on machine learning according to claim 1 is characterized in that: In step S103, The prediction function form of the LightGBM machine learning model is defined as follows: ； in, Indicates the input sample data The prediction results, Indicates the The output of the regression subtree, represents the function space composed of regression subtrees, The total number of multiple regression subtrees integrated in the LightGBM machine learning model. Number the index for the regression subtree; The LightGBM machine learning model uses the root mean square error as the optimization objective function. The formula is as follows: ； in, is the number of samples, For the The predicted value of the sample, For the The true value of the sample, is the mean square error loss function value, Number the sample; The root mean square error (RMSE) is used as the evaluation indicator; the RMSE formula is as follows: ； A five-fold cross-validation strategy is used to perform multiple rounds of division and training on the sample data. The average loss function of the five-fold cross-validation is defined as: ； in, is the average loss of each fold during the five-fold cross validation process, Indicates the The loss value on the fold validation set, The index of the cross validation folds.

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

7. A prediction system applicable to the method for predicting buckling load of scour-damaged bridges based on machine learning according to any one of claims 1 to 6, characterized in that: include: Data construction module (100) is used to obtain the original data of the data set, including bridge parameters, soil parameters, scour depth and the critical buckling load change rate Acquisition of structural parameters; The data preprocessing module (200) is used to preprocess the raw data obtained by the data construction module (100), including filling missing values, removing outliers, and standardizing features, to obtain a structural parameter input data set for the prediction task, and to provide a standardized data input interface for subsequent model calls; Model building and buckling prediction module (300), used to build LightGBM machine learning model to realize the critical buckling load change rate of scour damaged bridges predict; The result analysis module (400) is used to evaluate and verify the regression model obtained after training the constructed LightGBM machine learning model using multiple performance evaluation indicators.

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