Bridge prestressed steel post-tensioning method for predicting tensioning sequence based on machine learning

Abstract

The application discloses a bridge prestressed steel bar post-tensioning sequence prediction method based on machine learning, and belongs to the field of machine learning, which comprises the following steps: collecting basic information of a bridge structure, generating effective prestress data under different tensioning sequences through finite element simulation based on the basic information; determining an optimal tensioning sequence and constructing an original data set according to the effective prestress data; inputting the original data set into a machine learning model after pretreatment to train the model, and obtaining a prediction model for predicting the optimal tensioning sequence; and inputting the basic information of a bridge to be predicted into the prediction model to output the corresponding optimal tensioning sequence. The application can accurately predict the optimal tensioning sequence of the prestressed steel bar, thereby reducing the prestress loss in the tensioning of the prestressed steel bar, improving the bearing capacity of the bridge, improving the work efficiency and reducing the work cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of machine learning, and particularly relates to a bridge prestressed steel tendon post-tensioning sequence prediction method based on machine learning. BACKGROUND

[0002] There are multiple prestressed tendons in a prestressed concrete beam, and the structural system formed by the prestressed tendons and the beam body is similar to a multiple statically indeterminate structural system. Since the concrete will be elastically compressed when subjected to pressure, the effective length of the prestressed tendons is shortened, and the post-tensioning of the prestressed tendons will inevitably cause stress loss of the already tensioned prestressed tendons, thereby causing internal forces and deformations of the bridge after the bridge is completed, and reducing the crack resistance of the bridge components. Different tensioning sequences produce different prestress losses. To solve the above problems, it is necessary to explore an optimal prestressed tendon tensioning sequence to reduce the loss of prestress caused by elastic compression.

[0003] As shown in the paper "Post-tensioning sequence optimization of box girder considering the first batch of prestress loss" published in the Journal of Beijing University of Technology, the first batch of prestress loss of the prestressed tendons is simulated based on the minimum principle, and the influence of different tensioning schemes on the mechanical properties of the bridge is compared. The results show that for box girders with different construction techniques, the optimal tensioning sequence is different, and the tensioning sequence cannot be determined only by construction experience. For complex prestressed structures of bridges, the optimal tensioning sequence should be obtained through finite element simulation.

[0004] However, the optimal tensioning sequence considering only the first batch of prestress loss has certain limitations, and further research on the optimal tensioning sequence is still needed. As shown in the paper "Finite element analysis of post-tensioning prestressed concrete hollow slab beam tensioning" published in the Journal of Chongqing University of Architecture, the post-tensioning prestressed concrete hollow slab tensioning test was conducted, and the finite element was analyzed to explore the change law of the stress and deformation of the hollow slab beam under various tensioning sequences. The results show that the tensioning sequence of the prestressed tendons has a great influence on the prestress loss, stress, etc. of the slab beam. The current construction sequence of first down and then up, left-right symmetry is more reasonable than the clockwise tensioning sequence, and the prestress loss caused by tensioning is the smallest.

[0005] As shown in the paper "Research on prestressed tendon tensioning sequence of curved box girder bridge cross section" published in the Journal of Civil Engineering, the finite element was used to simulate the tensioning of the prestressed tendons of the Runyang Yangtze River Highway Bridge Interchange D Ramp Bridge, and the principles of the outer first and inner last, symmetric and balanced tensioning sequence for the prestressed tensioning construction of the curved box girder were given.

[0006] As a Chinese patent with publication number CN114790694A and the name of T-type beam tensioning method and tensioning sequence for large-span simply supported T-type beam, it proposes to arrange prestressed steel bars in the middle beam of the T-type beam, part of the prestressed steel bars have horizontal side bending, and a plurality of tensioning schemes are formulated. Simulation calculation is carried out in the tensioning simulation model to determine the optimal tensioning sequence.

[0007] The above methods can determine the optimal tensioning sequence of a certain beam, but require complex simulation, analysis of data, and low efficiency, which is not conducive to batch determination of tensioning sequence and has great limitations.

[0008] With the development of artificial intelligence technology, more and more artificial intelligence technology is applied to bridge engineering. Through machine learning and neural networks, input the data features that are easy to collect to achieve the goal of predicting complex data.

[0009] As a Chinese patent with publication number CN119964334A and the name of bridge early warning method and system based on physical information neural network and machine vision, it proposes a warning method based on physical information neural network and machine vision. The real-time acquisition of dynamic response data is input into the trained physical information neural network model to evaluate the bridge operation state and check the abnormal information to generate a warning signal.

[0010] As a Chinese patent with publication number CN118999393A and the name of bridge deformation monitoring and system, it proposes a bridge deformation monitoring method and system. The neural network is trained by the sampling images and spatial state data obtained by the fixed sampling camera. The monitoring images of multiple sampling points obtained by the detection camera are input into the neural network model for analysis to realize the monitoring of the deformation of multiple detection points.

[0011] As a Chinese patent with publication number CN119067967A and the name of a bridge deflection intelligent precise measurement method based on artificial intelligence, it proposes to separate the bridge deflection feature by background modeling and mixed Gaussian model MOG2, extract the deflection feature based on the foreground segmentation network U-Net, and enhance the capture ability of the bridge dynamic behavior through ST-GCN combined with LSTM time and space modeling.

[0012] As a Chinese patent with publication number CN114036258A and the name of a bridge technical condition grade rapid identification method based on natural language processing, it proposes to input the bridge basic information arranged into text description as input and the bridge technical condition grade as output. Select the DT, SVM, RF, and XGB four machine learning algorithms to select the optimal model, input the bridge disease description, and get the bridge technical condition grade.

[0013] As the paper "Evaluation of the Technical Condition of Small and Medium-Span Bridges Based on Machine Learning" published in the Journal of Chang'an University proposes an intelligent evaluation method of the technical condition of bridges based on machine learning, and compares the evaluation performance of five machine learning algorithms, namely, decision tree (CART), support vector machine (SVM), random forest (RF), improved gradient boosting tree (XGBoost), and adaptive boosting (AdaBoost), the results show that the integrated algorithm is better than the single algorithm.

[0014] Currently, there are studies that have proven the excellent evaluation performance of machine learning algorithms, but there are fewer predictions of the bridge tensioning sequence, and the level of prediction of the tensioning sequence needs to be further improved. SUMMARY

[0015] To solve the problem of different prestress losses under different tensioning sequences caused by the elastic compression of concrete, the application provides a bridge prestressed steel post-tensioning method tensioning sequence prediction method based on machine learning, which realizes accurate prediction of the bridge prestressed steel tensioning sequence by analyzing the basic information of the bridge structure and using the extreme gradient boosting (XGBoost) machine learning algorithm, reduces the prestress loss, improves the mechanical properties of the bridge, and ensures the safe operation of the bridge in operation.

[0016] To achieve the above purpose, the application provides a bridge prestressed steel post-tensioning method tensioning sequence prediction method based on machine learning, which comprises:

[0017] Collecting the basic information of the bridge structure, generating effective prestress data under different tensioning sequences based on the basic information through finite element simulation;

[0018] Determining the optimal tensioning sequence and constructing an original data set according to the effective prestress data;

[0019] After preprocessing the original data set, input the machine learning model for training to obtain a prediction model for predicting the optimal tensioning sequence;

[0020] Inputting the basic information of the bridge to be predicted into the prediction model outputs the corresponding optimal tensioning sequence.

[0021] Preferably, the process of collecting the basic information of the bridge structure comprises:

[0022] Obtaining the parameters of the beam length, beam height, steel area, bending angle, cross-sectional area, cross-sectional moment of inertia, and steel eccentricity of the bridge.

[0023] Preferably, the process of generating effective prestress data under different tensioning sequences based on the basic information through finite element simulation comprises:

[0024] A finite element model of the bridge is established and material properties of the prestressed reinforcement and the concrete are defined;

[0025] An activation-kill unit technique is used to simulate the construction process of different tensioning sequences;

[0026] The weighted average effective tensioning stress of the prestressed reinforcement under each tensioning sequence is calculated.

[0027] Preferably, the process of determining the optimal tensioning sequence according to the effective prestress data comprises:

[0028] The weighted average effective tensioning stresses under different tensioning sequences are compared;

[0029] The tensioning sequence with the maximum weighted average effective tensioning stress is marked as the optimal tensioning sequence.

[0030] Preferably, the process of preprocessing the original data set comprises:

[0031] Derived features are calculated based on the original features, including the ratio of the reinforcement area to the concrete area, the stiffness ratio of the prestressed reinforcement to the concrete section, and the total reinforcement area;

[0032] The data set is standardized and the training set and the test set are divided by stratified sampling.

[0033] Preferably, the process of standardizing the data set comprises:

[0034] The continuous type features are dimensionally unified using the Z-score standardization formula, wherein the feature values of the test set after standardization are calculated based on the mean and standard deviation of the training set.

[0035] Preferably, the process of inputting the machine learning model for training comprises:

[0036] A hybrid sampling strategy combining ADASYN and Tomek Links is used to balance the classes of the training set;

[0037] The balanced training set is trained using the XGBoost ensemble learning algorithm, and the hyperparameters are optimized through grid search and cross-validation.

[0038] Preferably, the hybrid sampling strategy comprises:

[0039] Synthetic samples of the minority class are adaptively generated by ADASYN;

[0040] The overlapping samples at the boundary of the majority class and the minority class are removed using the Tomek Links algorithm.

[0041] Preferably, the objective function of the machine learning model is a multi-classification logarithmic loss function, and the regularization term includes L1 and L2 regularization parameters for controlling the model complexity.

[0042] Preferably, the output corresponding optimal tensioning sequence includes:

[0043] The numerical label output by the prediction model is converted into the original tensioning sequence category through reverse mapping.

[0044] Compared with the prior art, the present application has the following advantages and technical effects:

[0045] (1) Improve the accuracy and stability of tensioning sequence prediction: The traditional tensioning sequence determination method needs to be simulated or simplified to determine the tensioning sequence. However, the simulation modeling is complex, the calculation cost is high, and the setting of some parameters needs to rely on experience, which cannot be batch calculated. The simplified calculation often has insufficient precision and limited scope of application. The pre-stressed tendon tensioning sequence prediction method based on machine learning adopted by the present application can accurately predict the optimal tensioning sequence of the bridge.

[0046] (2) Solve the difficulty of collecting original data: The cost of collecting parameters such as effective pre-stress of bridge pre-stressed reinforcement, bridge deflection and concrete stress during tensioning process through field post-tensioning test is high, the process is complex and the efficiency is low. The present application improves the efficiency of data collection, increases the number of original data samples and enhances the accuracy of the machine learning model by extracting the bridge length, beam height, reinforcement area, bending angle and effective pre-stress.

[0047] (3) Improve the generalization ability of the model: The present application adopts the XGBoost method of ensemble learning. The ensemble learning method has faster training speed on large-scale data sets, effectively prevents model overfitting through regularization parameters, performs well on various types of data sets and has good generalization ability. The ensemble learning provides rich super parameter settings: such as tree depth, learning rate, regularization penalty coefficient, sampling proportion, etc., which can improve the recognition ability of minority class samples and improve the accuracy of the model to the optimal tensioning sequence of pre-stressed reinforcement.

[0048] (4) Overcome the problem of imbalance of original data categories: The present application introduces the method of combining ADASYN and Tomek Links to balance the data. By generating samples and removing the overlapping area between the majority class and the minority class, the influence of noise data is reduced, and the influence of the imbalance of original data categories on the model's ability to identify minority class samples is overcome, thereby improving the accuracy of the optimal tensioning sequence prediction of pre-stressed reinforcement.

[0049] (5) Simplify the pre-processing of data: the application designs data pre-processing, calculates derived features, unifies dimensions, and divides training set and test set. The calculation of derived features generates new features through professional knowledge, which can improve the interaction performance of the model in capturing features, improve the interpretability, and improve the model performance.

[0050] (6) Possessing the universality and accuracy of engineering: the data of the application contains mainstream bridge types such as T-beam and box beam, and the data collection adopts parameters commonly owned by different types of bridges such as sectional moment of inertia, sectional area, and steel bar bending angle, and the model can adapt to the optimal tensioning sequence prediction of different types of bridges. Finite element simulation only needs to be run once in the data collection stage, and does not need to be repeatedly run, so that a large amount of data can be collected. In actual engineering application, it can quickly and accurately provide decision support and design guidance for construction. BRIEF DESCRIPTION OF DRAWINGS

[0051] The accompanying drawings, which form a part of this application, are included to provide a further understanding of the application and are incorporated in and constitute a part of this application. The embodiments of this application, and their

[0052] Figure 1 is a flowchart of the prestressed steel post-tensioning method tensioning sequence prediction method of the embodiment of the application;

[0053] Figure 2 is a flowchart of the original data acquisition process using finite element simulation technology of the embodiment of the application;

[0054] Figure 3 is a feature importance ranking result schematic diagram of the embodiment of the application;

[0055] Figure 4 is a confusion matrix schematic diagram of the embodiment of the application;

[0056] Figure 5 is a ROC curve schematic diagram of the embodiment of the application. DETAILED DESCRIPTION

[0057] It should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0058] It should be noted that the steps shown in the flowchart of the drawings can be executed in a computer system such as a group of computer executable instructions, and although the logical order is shown in the flowchart, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0059] Machine learning technology is suitable for different sizes of data sets, can continuously optimize the model with the input of new data, the model trained by the training set can be generalized to the test set, has strong generalization ability, and can accurately predict the optimal tensioning order of the bridge prestressed steel bar. Finite element simulation technology can accurately and efficiently analyze the effective tensioning stress of the prestressed steel bar, effectively reducing the cost of optimal tensioning order analysis. In addition, the correlation and importance of each feature are considered, and the generalization ability of the enhanced model is improved through balancing the unbalanced classes,

[0060] As shown in Figure 1 The embodiment provides a bridge prestressed steel bar post-tensioning method based on machine learning, which comprises the following steps:

[0061] Collecting the basic information of the bridge structure, generating effective prestress data under different tensioning sequences based on the basic information through finite element simulation;

[0062] Determining the optimal tensioning sequence according to the effective prestress data and constructing an original data set;

[0063] After preprocessing the original data set, input the machine learning model for training to obtain a prediction model for predicting the optimal tensioning sequence;

[0064] Inputting the basic information of the bridge to be predicted into the prediction model, and outputting the corresponding optimal tensioning sequence.

[0065] Further, the process of generating effective prestress data under different tensioning sequences based on basic information through finite element simulation comprises:

[0066] Establishing a bridge finite element model and defining the material properties of prestressed steel and concrete;

[0067] Using the activated killed element technology to simulate the construction process of different tensioning sequences;

[0068] Calculating the weighted average effective tensioning stress of the prestressed steel under each tensioning sequence.

[0069] Further, the process of determining the optimal tensioning sequence according to the effective prestress data comprises:

[0070] Comparing the weighted average effective tensioning stress under different tensioning sequences;

[0071] Marking the tensioning sequence with the maximum weighted average effective tensioning stress as the optimal tensioning sequence.

[0072] Further, the process of generating effective prestress data under different tensioning sequences based on basic information through finite element simulation comprises:

[0073] Based on the basic information of the bridge, finite element simulation is carried out, a simulation model of prestress loss of the bridge under different tension sequences is established, effective tension stress data of the prestressed reinforcement of different bridges are obtained, and the data are processed to obtain the optimal tension sequence of the prestressed reinforcement of different bridge structures;

[0074] Further, the process of preprocessing the original data set comprises:

[0075] Based on the original features, derivative features are calculated, including the ratio of steel area to concrete area, the stiffness ratio of prestressed reinforcement to concrete section, and the total area of steel reinforcement;

[0076] The data set is standardized and divided into training and test sets by stratified sampling.

[0077] Further, the process of standardizing the data set comprises:

[0078] The continuous features are standardized using the Z-score standardization formula, and the standardized feature values of the test set are calculated based on the mean and standard deviation of the training set.

[0079] Further, the process of inputting the machine learning model for training comprises:

[0080] The hybrid sampling strategy combining ADASYN and Tomek Links is used to balance the classes of the training set.

[0081] The balanced training set is trained using the XGBoost ensemble learning algorithm, and the hyperparameters are optimized through grid search and cross-validation.

[0082] Further, the hybrid sampling strategy comprises:

[0083] ADASYN is used to adaptively generate synthetic samples of minority classes;

[0084] Tomek Links algorithm is used to remove overlapping samples at the boundary between majority and minority classes.

[0085] Further, the sampling method combining ADASYN and Tomek Links is used to sample the training set, adaptively generate new samples according to the difficulty of classification, remove classification boundary noise, and balance the number of samples of each class;

[0086] Based on the balanced training set, the performance of different hyperparameter combinations is evaluated through grid search and 5-fold cross-validation, and the best hyperparameters are used to train a gradient boosting model with multiple decision trees on the entire training set to obtain the final ensemble learning model.

[0087] Further, the objective function of the machine learning model is a multi-classification logarithmic loss function, and the regularization term includes L1 and L2 regularization parameters for controlling the model complexity.

[0088] Further, the output corresponding optimal tensioning sequence includes:

[0089] The numerical label output by the prediction model is converted into the original tensioning sequence category through reverse mapping.

[0090] The method of the embodiment effectively solves the problem that the tensioning sequence is not easy to determine due to the prestress loss caused by the compression of concrete in the prestressed steel tensioning project. The method provides a scheme combining finite element simulation technology and machine learning algorithm, generates an original data set through finite element simulation, pre-processes the original data, uses the ADASYN and Tomek Links mixed sampling strategy to sample the training set, increases the number of minority class samples, and eliminates boundary noise; through grid search combined with 5-fold cross-validation method, the optimal super parameter combination is selected, the balanced training set is used to train the model, the objective function is optimized, and the final ensemble learning model is obtained. The present application can accurately predict the optimal tensioning sequence of the prestressed steel, thereby reducing the prestress loss in the tensioning of the prestressed steel, improving the carrying capacity of the bridge, improving the work efficiency, and reducing the work cost. Specifically, the method includes the following steps S101 to S105.

[0091] Step S101: data acquisition. According to the standard construction drawings of the bridge, the basic information of various T-beams and box beams such as beam length, beam height, steel area, bending angle, cross-sectional area, cross-sectional moment of inertia, and steel eccentric distance is collected.

[0092] The data of the embodiment is collected according to the standard construction drawings of the bridge, and is supplemented according to the original data of the bridge construction drawings to increase the data. The necessary bridge structure parameters required for finite element analysis are extracted, and the data of two mainstream bridge types of T-beams and box beams is collected.

[0093] Step S102: obtaining the optimal tensioning sequence through finite element simulation. Based on the bridge basic information, finite element simulation is performed, and through finite element simulation, different structure bridges are established, the numerical calculation of different tensioning sequences for each structure bridge is performed, the effective tensioning stress of the prestressed steel under different tensioning sequences is calculated, and based on the principle of maximum effective tensioning stress, the optimal tensioning sequence of the prestressed steel of different structure bridges is obtained.

[0094] Prestress loss in post-tensioning method: loss caused by friction between prestressed steel and pipe , loss caused by deformation of anchorage device, steel retraction and joint compression , loss caused by elastic compression of concrete Under the influence of different tensioning sequences, the prestress loss caused by different concrete compressions in bridges is analyzed.

[0095] Losses caused by friction between prestressed steel bars and ducts during the tensioning of post-tensioned members The calculation formula is as follows:

[0096] ;

[0097] in, This indicates the control stress for tensioning prestressed steel bars under the anchor. This represents the coefficient of friction between the prestressed steel bars and the pipe. This represents the sum of the angles between the tensioning end and the tangents of the curved pipe section at the calculated cross-section; This represents the coefficient that indicates the influence of local deviation per meter of pipeline on the friction coefficient. This indicates the length of the pipe from the tensioning end to the calculated cross section.

[0098] Losses during post-tensioning of members caused by anchor deformation, rebar retraction, and joint compression. The calculation formula is as follows:

[0099] ;

[0100] in This represents the values ​​for anchorage deformation at the tensioning end, rebar retraction, and joint compression. This indicates the distance between the tensioning end and the anchorage section; This indicates the elastic modulus of prestressed steel bars.

[0101] In the finite element simulation, the equivalent temperature change method is used to apply prestress, and the temperature load formula is expressed as follows:

[0102] ;

[0103] Where T represents the temperature applied to the unit; Indicates the coefficient of linear expansion of the reinforcing steel; This indicates the elastic modulus of prestressed steel bars; This indicates the control stress for tensioning prestressed steel bars under the anchor. This indicates the loss caused by friction between prestressed steel bars and the pipe; This indicates losses caused by anchor deformation, rebar retraction, and joint compression.

[0104] Calculate the loss in each unit caused by friction between the prestressed steel bars and the duct. Losses caused by anchor deformation, rebar retraction, and joint compression. The anchor tension control stress minus and The effective prestress obtained is applied to each unit of the prestressed steel by the equivalent temperature change method, accurately simulating the prestress loss caused by pipe friction and anchor deformation, steel retraction and joint compression, and avoiding the influence of and on the experimental results.

[0105] The calculation formula of the loss caused by the elastic compression of concrete during the tensioning of the post-tensioning member is as follows:

[0106] ;

[0107] Among them, represents the normal stress of concrete caused by the post-tensioning prestressed steel at the center of gravity of the prestress when the calculation section is completed tensioning; represents the ratio of the elastic modulus of the prestressed steel to the elastic modulus of the concrete.

[0108] Under the condition that the elastic modulus of concrete and prestressed steel and the anchor control stress are fixed, the tensioning sequence plays a major role in the prestress loss caused by the elastic compression of concrete, and in the finite element simulation simulation used, the influence of the elastic compression loss of concrete can be automatically calculated.

[0109] In this embodiment, by finite element simulation, the solid bar method is used, the concrete uses the SOLID65 unit, the prestressed steel uses the LINK180 unit, the concrete unit and the prestressed steel unit are connected through coupling, the method of life and death unit is used to control the tensioning sequence, that is, when the first steel bar is tensioned, only the unit of the first steel bar is activated, and the units of other steel bars are killed, when the second steel bar is tensioned, the unit of the second steel bar is activated again, and so on until the tensioning is completed. The influence of the post-tensioning steel on the pre-tensioning steel is simulated, the necessary characteristic data of the optimal tensioning sequence prediction of the post-tensioning steel are extracted, and the effective tensioning stress of the steel bar is extracted. According to the principle of maximum effective tensioning prestress, the weighted average stress of the prestressed steel is calculated, the weighted average stress of the prestressed steel obtained under different tensioning sequences of the same structure bridge is compared, the optimal tensioning sequence is obtained, and the detailed finite element simulation collects the original data flow as Figure 2 shown.

[0110] Step S103: Preprocessing the original data collected in step S102, the preprocessing process includes: calculating derived features, dividing training set and test set, dimension unification, and encoding class labels.

[0111] ​Calculation of derived features: the interaction of the model is local, which may ignore global high-order features and cannot fully exert the performance of the model. According to the characteristics of the original data and the professional knowledge, new features are manually derived, and through the double-layer feature derivation of manual derivation and XGBoost model automatic feature interaction, the complex data relationship can be efficiently captured. The manually derived features are as follows:

[0112] The area ratio of the derived feature is calculated as follows:

[0113] ;

[0114] Among them, The ratio of the area of the steel bar to the area of the concrete is represented by a; The area of the i-th prestressed steel bar is represented by ai; The area of the concrete cross section is represented by Ac.

[0115] The stiffness ratio of the derived feature prestressed steel bar to the concrete cross section is calculated as follows:

[0116] ;

[0117] Among them, The stiffness ratio of the prestressed steel bar to the concrete cross section is represented by a; The eccentricity of the i-th prestressed steel bar is represented by ei; The elastic modulus of the prestressed steel bar is represented by Eps; The elastic modulus of the concrete is represented by Ec; The area of the i-th prestressed steel bar is represented by ai; The area of the concrete cross section is represented by Ac.

[0118] The total area of the derived feature steel bar is calculated as follows:

[0119] ;

[0120] Among them, The sum of the areas of the prestressed steel bars is represented by a; The total number of prestressed steel bars is represented by N.

[0121] Data set division: the optimal tensioning sequence data set collected in step S102 is divided. Due to the unbalanced class distribution of the original data, stratified sampling method is adopted to keep the class distribution in the training set and the test set consistent with the class distribution of the original data, avoiding the problem of missing of minority classes in the test set. Random seed is used to ensure the consistency of the division result of each run and the repeatability.

[0122] The test set sampling ratio of this embodiment is 0.3, that is, the training set data sample accounts for 70% of the original data, and the test set sample accounts for 30% of the original data. While ensuring sufficient training data, sufficient data is also reserved for model evaluation. The hyperparameter tuning of the XGBoost ensemble learning model is determined according to 5-fold cross-validation.

[0123] Dimension unification: Due to the large difference in the dimensions of different features in the original data set, such as beam length, beam height, bridge cross-sectional area, bridge cross-sectional moment of inertia, prestressed steel area, and prestressed steel weighted stress, the gradient boosting algorithm is used inside the XGBoost ensemble algorithm. During training, the large difference in the dimensions of different features will lead to unstable weight updates, causing the model to be biased towards features with large numerical values, thereby ignoring small numerical value features and misjudging the importance of the original features. Standardization can eliminate the influence of dimension difference on model performance and effectively improve the performance of the model. When standardizing, the mean and standard deviation of the training set are used to standardize the test set, otherwise data leakage may occur, causing the model evaluation to be biased and unable to accurately reflect the performance of the model.

[0124] This embodiment uses Z-score standardization to unify the dimensions of the original data features. The standardization formula is as follows:

[0125] ;

[0126] wherein, represents the standardized feature value; represents the feature in the original data; represents the mean of a certain feature in the original data; represents the standard deviation of a certain feature in the original data.

[0127] Category label encoding: mapping encoding using LabelEncoder to convert non-numeric category label variables into continuous numeric variables. Mapping encoding uses numbers as label encoding to ensure the independence of categories. For unordered encoding such as optimal tension order, numerical encoding will not introduce false numerical relationships. If there are categories, use values between 0 and to encode the target label. Each category name variable is mapped to a unique numerical code through mapping encoding.

[0128] For example, prestressed steel is numbered from the lower part of the bridge to the upper part as A, B, and C. The optimal tension order of the bridge is divided into ABC, ACB, BAC, BCA, CAB, and CBA. After mapping, each optimal tension order will be assigned a number between 0 and 5. ​

[0129] This embodiment selects only the top 20 features with importance ranking, and the data feature importance is shown as Figure 3 .

[0130] Step S104: data balancing processing. This embodiment uses a hybrid sampling strategy combining ADASYN and Tomek Links to balance the standardized training set, generate minority class samples, increase the number of minority class samples, and obtain a balanced data set. ADASYN balances by generating synthetic samples. The Tomek Links method is used to remove the overlapping area between the majority class and the minority class, reduce the influence of noise data, and solve the problem of data imbalance.

[0131] ADASYN is an adaptive oversampling technique that balances the data set by generating synthetic samples of the minority class. Its goal is to increase the learning ability of the classifier for minority class samples, thereby improving the overall performance of the model. This technique adaptively generates new minority class samples based on the distribution of the samples and the classification difficulty. ADASYN evaluates the classification difficulty of minority class samples by calculating their k-nearest neighbors, which represents the density of the minority class samples. A small density indicates a high classification difficulty. For samples with high classification difficulty, more synthetic samples are generated. These synthetic samples are generated by interpolation, that is, a point is randomly selected between the minority class sample and its nearest neighbor. The formula is as follows:

[0132] ;

[0133] wherein, represents the synthetic sample; represents the minority class sample; represents the neighbor of the minority class sample; represents a random number .

[0134] ADASYN technology can specifically enhance the boundary region of the minority class and effectively improve the model's recognition ability for boundary samples. Due to the adaptive generation strategy, SMOTE is less likely to introduce noise, and the effect is obvious for data sets with few and unevenly distributed minority class samples. The Tomek Links algorithm removes noise samples and overlapping samples near the boundary to optimize the classification boundary, making the boundary clear and improving the performance of the model. This algorithm only removes majority class samples, without removing majority classes, effectively protecting the minority class samples. The combined sampling scheme of ADASYN and Tomek Links combines the advantages of ADASYN oversampling technology and Tomek Links undersampling technology. By integrating the advantages of oversampling and undersampling techniques, it can effectively solve the imbalance problem and also solve the noise problem, reducing the risk of overfitting and improving the generalization ability of the model.

[0135] In the practical application of ADASYN and Tomek Links mixed sampling strategy, first, ADASYN oversampling is used to adaptively generate new samples, and the number of samples of each minority class is increased to the same as the number of majority class samples. Then, Tomek Links is used for undersampling to reduce the noise in the training set until the data set is balanced. This strategy balances the training set data through phased fine sampling, cleans the classification boundary, retains clean classification boundary, generates balanced data, improves the performance of the ensemble learning model, and enables the model to complete the task of multi-class imbalance classification.

[0136] It is worth mentioning that when dealing with the problem of original data class imbalance, only the training set after data division is balanced, and the test set still maintains the original class imbalance distribution, avoiding data leakage, improving the generalization ability of the model in actual application, and making the model more robust. If the test set is also balanced, it will cause the evaluation index to deviate and not consistent with the actual result.

[0137] In this embodiment, due to the uneven distribution of class samples, the number of ACB tensioning sequences is much lower than that of other tensioning sequence categories. In order to avoid the influence of minority class samples on data, ADASYN and Tomek Links mixed sampling strategy is used, in which ADASYN oversampling is set to automatically balance all minority classes to the majority class level, the number of nearest neighbors is 5, and the threshold value in TomekLinks is the default setting. Such settings can maintain data balance and effectively eliminate noise influence, improve model performance, and make prediction results more accurate and more robust. The balanced training set class distribution is shown in Table 1.

[0138] Table 1

[0139] Optimal tensioning order Original training set data Balanced training set data ABC 287 567 ACB 27 572 BAC 349 602 BCA 270 525 CAB 573 573 CBA 346 599

[0140] Step 105: Constructing an ensemble learning model. In this step, an XGBoost ensemble learning model is constructed to predict the optimal tensioning sequence of post-tensioned prestressed reinforcement.

[0141] In this embodiment, first, the XGBoost ensemble learning model is hyperparameter optimized through grid search. The balanced training set is divided into 5 subsets maintaining the class distribution using 5-fold cross-validation method. Each hyperparameter combination is used to train four subsets and validate the remaining one subset to evaluate the model performance, i.e., balanced accuracy. The process is repeated five times, each time using a different subset as the validation subset. Finally, the average value of the five validations is calculated, and the parameter combination with the highest average value is selected as the best hyperparameter combination.

[0142] Secondly, the model is trained according to the balanced training set data obtained in step S104, and the objective function is optimized to obtain the best objective function. The objective function of the ensemble learning model in this embodiment adopts a multi-classification logarithmic loss function, and the formula is as follows:

[0143] ;

[0144] wherein represents the objective function of multi-classification, represents a loss function, which measures the difference between the predicted value of the model and the true value; represents a regularization term, which controls the complexity of the model and prevents overfitting; represents the total number of samples; represents the true value of the i-th sample, represents the predicted value of the i-th sample; represents the total number of trees; represents the regularization term of the j-th tree;

[0145] For a multi-classification problem, the loss function adopts a multi-classification logarithmic loss function, also known as classification cross-entropy, and the formula is as follows:

[0146] ;

[0147] wherein represents the total number of samples; represents the total number of categories; represents the true classification, if the i-th sample belongs to the j-th category, then =1, otherwise =0; represents the probability that the model predicts that the i-th sample belongs to the j-th category;

[0148] The regularization term formula is as follows:

[0149] ;

[0150] wherein T represents the number of leaf nodes of the current tree; represents a penalty coefficient of the number of leaf nodes of the current tree, which controls the number of leaf nodes and the depth of the tree; represents an L1 regularization term parameter; represents an L2 regularization term parameter; represents the value of the j-th leaf node. In this embodiment, the penalty coefficient of the number of leaf nodes is set to ; the parameter of the L2 regularization term is ; and the parameter of the L1 regularization term is .

[0151] ​Finally, through the gradient boosting method, the decision tree is iteratively added to reduce the residual error, and the final model is obtained. The final XGBoost ensemble learning model can accurately predict the optimal tensioning order of the post-tensioning method of prestressed steel bars, thereby effectively improving the efficiency of determining the optimal tensioning order in actual engineering and improving the mechanical properties of the bridge in work.

[0152] Further, after step S105, the following steps are further included:

[0153] Step S106: evaluate and verify the ensemble learning model using evaluation indexes, and evaluate the model on the test set, wherein the evaluation indexes include accuracy, precision, recall and F1 score, and the evaluation index calculation formula is as follows:

[0154] Accuracy:

[0155] ;

[0156] Wherein Accuracy represents the proportion of correctly predicted samples to the total samples, which measures the accuracy of the model; TP represents the number of samples that are actually positive and predicted to be positive, i.e. the number of correctly predicted samples; FN represents the number of samples that are actually negative and predicted to be negative, i.e. the number of correctly predicted samples; FP represents the number of samples that are actually negative and predicted to be positive, i.e. the number of incorrectly predicted samples; FN represents the number of samples that are actually positive and predicted to be negative, i.e. the number of incorrectly predicted samples.

[0157] Precision:

[0158] ;

[0159] Wherein, n represents the proportion of actually positive samples to predicted positive samples, which measures the accuracy of the model in predicting positive samples; , As above.

[0160] Recall:

[0161] ;

[0162] Wherein, n represents the proportion of correctly predicted positive samples to actually positive samples, which measures the ability of the model to find all positive samples; , As above.

[0163] F1 Score:

[0164] ;

[0165] wherein, The harmonic mean of precision and recall is an index for comprehensively measuring precision and recall.

[0166] The index of evaluating the model in the embodiment is: the accuracy is 0.88, the precision is 0.881, the recall is 0.88, and the F1 score is 0.88, in addition, the confusion matrix of the prediction result and the ROC curve are respectively as shown in Figure 4 、 Figure 5 .

[0167] To sum up, the application provides a bridge prestressed steel post-tensioning method tensioning sequence prediction method based on machine learning, through bridge basic information collection, finite element simulation, data preprocessing, data set category balance, integrated learning and other steps, a reliable bridge prestressed steel post-tensioning method tensioning sequence prediction model is constructed, which provides decision-making technology for the establishment of post-tensioning method prestressed steel tensioning sequence. The application adopts integrated learning and finite element simulation and other technologies in machine learning, combines various data preprocessing methods and model integration methods, can accurately predict the tensioning sequence of prestressed steel, so that the model will be more accurate, provides an important scientific basis for bridge tensioning prestressed steel. Compared with the traditional method, the application has high work efficiency and accurate prediction performance, has wide application development space and superior economic benefits.

[0168] The above is only a preferred specific embodiment of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of changes or replacements within the technical range disclosed by the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A machine learning-based method for predicting the tensioning sequence of post-tensioned prestressed steel bars in bridges, characterized in that, include: Collect basic information about the bridge structure, and generate effective prestress data for different tensioning sequences through finite element simulation based on the basic information. The optimal tensioning sequence is determined based on the effective prestress data, and the original dataset is constructed. The original dataset is preprocessed and then input into a machine learning model for training to obtain a prediction model for predicting the optimal tensioning sequence. Input the basic information of the bridge to be predicted into the prediction model, and output the corresponding optimal tensioning sequence. The process of generating effective prestress data for different tensioning sequences using finite element simulation based on the aforementioned basic information includes: Establish a finite element model of the bridge and define the material properties of prestressed steel bars and concrete; The activation and deactivation of cells is used to simulate the construction process with different tensioning sequences; Calculate the weighted average effective tensile stress of prestressed steel bars for each tensioning sequence.

2. The method according to claim 1, characterized in that, The process of collecting basic information about a bridge structure includes: Obtain the bridge's beam length, beam height, reinforcement area, bend angle, cross-sectional area, cross-sectional moment of inertia, and reinforcement eccentricity parameters.

3. The method according to claim 1, characterized in that, The process of determining the optimal tensioning sequence based on the effective prestress data includes: Compare the weighted average effective tensile stress under different tensioning sequences; The tensioning sequence with the highest weighted average effective tensile stress is marked as the optimal tensioning sequence.

4. The method according to claim 1, characterized in that, The preprocessing process for the original dataset includes: Derived features are calculated based on the original features. The derived features include the ratio of steel reinforcement area to concrete area, the stiffness ratio of prestressed steel reinforcement to concrete section, and the total steel reinforcement area. The dataset is standardized and stratified sampling is used to divide it into training and test sets.

5. The method according to claim 1, characterized in that, The process of standardizing a dataset includes: The Z-score standardization formula is used to unify the dimensions of continuous features, where the standardized feature values ​​of the test set are calculated based on the mean and standard deviation of the training set.

6. The method according to claim 1, characterized in that, The process of training a machine learning model includes: A hybrid sampling strategy combining ADASYN and Tomek Links is used to perform class balancing on the training set; The balanced training set was trained using the XGBoost ensemble learning algorithm, and the hyperparameters were optimized using grid search and cross-validation.

7. The method according to claim 6, characterized in that, The hybrid sampling strategy includes: Adaptive generation of minority class synthetic samples using ADASYN; The Tomek Links algorithm is used to remove overlapping samples at the boundaries between the majority and minority classes.

8. The method according to claim 1, characterized in that, The objective function of the machine learning model is a multi-class log loss function, and the regularization term includes L1 and L2 regularization parameters, which are used to control the model complexity.

9. The method according to claim 1, characterized in that, The corresponding optimal tensioning order includes: The numerical labels output by the prediction model are converted into the original tensioning order category through reverse mapping.

Images