Bridge prestressed reinforcement post-tensioning method tensioning sequence prediction method based on machine learning

Abstract

The invention discloses a bridge prestressed reinforcement post-tensioning method tensioning sequence prediction method based on machine learning, and belongs to the field of machine learning, and the method comprises the steps: collecting basic information of a bridge structure, and generating effective prestress data under different tensioning sequences through finite element simulation based on the basic information; determining an optimal tensioning sequence according to the effective prestress data and constructing an original data set; the original data set is preprocessed and then input into a machine learning model for training, and a prediction model used for predicting the optimal tensioning sequence is obtained; and inputting the basic information of the bridge to be predicted into the prediction model, and outputting a corresponding optimal tensioning sequence. According to the method, the optimal tensioning sequence of the prestressed reinforcement can be accurately predicted, so that the prestress loss in the process of tensioning the prestressed reinforcement is reduced, the bearing capacity of a bridge is improved, the working efficiency is improved, and the working cost is reduced.

Description

Technical Field

[0001] The present invention belongs to the technical field of machine learning, and in particular relates to a method for predicting the tensioning sequence of post-tensioning prestressed steel bars in bridges based on machine learning. Background Art

[0002] Prestressed concrete beams contain multiple bundles of prestressed tendons. The structural system formed by the tendons and the beam body is similar to a multiply indeterminate structural system. Because concrete undergoes elastic compression when under pressure, the effective length of the prestressed tendons is shortened. Post-tensioning the prestressed steel bars will inevitably cause stress loss in the prestressed prestressed steel bars, which will cause internal forces and deformations in the bridge after completion, reducing the crack resistance of the bridge components. Different tensioning sequences result in different prestress losses. To solve this problem, it is necessary to explore an optimal prestressing sequence to reduce the loss of prestress caused by elastic compression.

[0003] For example, the paper "Optimization of the Tensioning Sequence of Post-Tensioned Box Girders Considering the Loss of the First Batch of Prestress" published in the Journal of Beijing University of Technology simulated the prestressing process of prestressed steel bars based on the principle of minimizing the loss of the first batch of prestressed steel bars, and compared the effects of different tensioning schemes on the mechanical properties of bridges. The results show that for box girders with different construction processes, the optimal tensioning sequence is different, and the tensioning sequence cannot be determined solely by construction experience. For complex prestressed structures of bridges, the optimal tensioning sequence should be obtained through finite element simulation.

[0004] However, there are certain limitations to only considering the optimal tensioning sequence of the first batch of prestress loss, and further research is still needed on the optimal tensioning sequence. For example, the "Finite Element Analysis of Post-Tensioned Prestressed Concrete Hollow Slab Beam Tensioning" was published in the Journal of Chongqing Jianzhu University. A tensioning test of post-tensioned prestressed concrete hollow slab was carried out, and the finite element analysis was performed to explore the changing laws of stress and deformation of hollow slab beams under various tensioning sequences. The results show that the tensioning sequence of prestressed tendons has a great influence on the prestress loss and stress of the slab beam. The bottom-up-then-top, left-right symmetrical construction sequence currently used in the project is more reasonable than the clockwise tensioning sequence, and the prestress loss caused during tensioning is minimized.

[0005] For example, the journal "China Civil Engineering Journal" published a paper titled "Research on the Tensioning Sequence of Prestressed Steel Tensioners on the Cross-Section of Curved Box Girder Bridges". By using finite element method to simulate the tensioning of prestressed tendons on the D ramp bridge of the Runyang Yangtze River Highway Bridge interchange, the paper proposed a symmetrical and balanced tensioning sequence principle for the construction of prestressed curved box girders, which should be outside first and inside later.

[0006] For example, the Chinese patent with publication number CN114790694A, entitled "Long-span Simply Supported T-Beam Tensioning Method and Tensioning Sequence," proposes arranging prestressed tendons in the middle beam of the T-beam, some of which have horizontal lateral bending, formulating multiple tensioning schemes, performing simulation calculations in a tensioning simulation model, and determining the optimal tensioning sequence.

[0007] All of the above methods can determine the optimal tensioning sequence of a beam, but they require complex simulation and data analysis, and are inefficient, not conducive to batch determination of tensioning sequences, and have great limitations.

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

[0009] For example, the Chinese patent publication number CN119964334A, entitled Bridge Early Warning Method and System Based on Physical Information Neural Network and Machine Vision, proposes an early warning method based on physical information neural network and machine vision. The real-time dynamic response data is input into a trained physical information neural network model to evaluate the operating status of the bridge and check for abnormal information to generate early warning signals.

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

[0011] For example, the Chinese patent publication number CN119067967A, titled "An intelligent and precise measurement method for bridge deflection based on artificial intelligence," proposes using background modeling and a mixed Gaussian model MOG2 to separate bridge deflection features, extracting deflection features based on a foreground segmentation network U-Net, and enhancing the ability to capture bridge dynamic behavior through ST-GCN combined with LSTM spatiotemporal modeling.

[0012] For example, the Chinese patent with publication number CN114036258A, titled "A method for rapid identification of bridge technical condition grades based on natural language processing," proposes taking basic bridge information organized into text descriptions as input and the bridge technical condition grade as output, selecting the optimal model from four machine learning algorithms, namely DT, SVM, RF, and XGB, inputting a description of bridge defects, and obtaining the bridge technical condition grade.

[0013] For example, the paper "Technical Condition Assessment of Small and Medium-Span Bridges Based on Machine Learning" published in the Journal of Chang'an University proposed an intelligent assessment method for the technical condition of bridges based on machine learning. At the same time, it compared the evaluation performance of five machine learning algorithms: decision tree (CART), support vector machine (SVM), random forest (RF), improved gradient boosting tree (XGBoost), and adaptive boosting (AdaBoost). The results showed that the integrated algorithm is better than a single algorithm.

[0014] At present, studies have demonstrated the excellent evaluation performance of machine learning algorithms, but there are relatively few predictions on the tensioning sequence of bridges, and the level of tensioning sequence prediction needs to be further improved. Summary of the Invention

[0015] To address the problem of different prestress losses under different tensioning sequences due to elastic compression of concrete, the present invention provides a method for predicting the tensioning sequence of prestressed steel bars in bridges based on machine learning. By analyzing the basic information of the bridge structure and utilizing the Extreme Gradient Boosting (XGBoost) machine learning algorithm, the tensioning sequence of the prestressed steel bars in the bridge can be accurately predicted, thereby reducing prestress losses, improving the mechanical properties of the bridge, and ensuring safe operation during bridge construction.

[0016] To achieve the above objectives, the present invention provides a method for predicting the tensioning sequence of prestressed steel bars in bridges based on machine learning, comprising:

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

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

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

[0020] The basic information of the bridge to be predicted is input into the prediction model, and the corresponding optimal tensioning sequence is output.

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

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

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

[0024] Build a finite element model of the bridge and define the material properties of prestressed steel and concrete;

[0025] The activation-killing element technique is used to simulate the construction process of different tensioning sequences;

[0026] Calculate the weighted average effective tensioning stress of the prestressed steel bars under each tensioning sequence.

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

[0028] Compare the weighted average effective tension stress under different tensioning sequences;

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

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

[0031] Calculating derived features based on the original features, the derived features including the ratio of the steel bar area to the concrete area, the stiffness ratio of the prestressed steel bar to the concrete section, and the total steel bar area;

[0032] The dataset is standardized and divided into training and test sets using stratified sampling.

[0033] Preferably, the process of normalizing the data set includes:

[0034] 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.

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

[0036] A hybrid sampling strategy combining ADASYN and Tomek Links was used to balance the categories of the training set.

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

[0038] Preferably, the hybrid sampling strategy includes:

[0039] Adaptively generate minority class synthetic samples through ADASYN;

[0040] The Tomek Links algorithm is used to remove overlapping samples at the boundary between the majority class and the minority class.

[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 complexity of the model.

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

[0043] The numerical labels output by the prediction model are converted into the original tensioning order categories through reverse mapping.

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

[0045] (1) Improving the accuracy and stability of tensioning sequence prediction: Traditional methods for determining the tensioning sequence require simulation or simplified calculations. However, simulation modeling is complex and computationally expensive. The setting of some parameters requires reliance on experience, making it impossible to calculate the tensioning sequence of bridges in batches. Simplified calculations often result in insufficient accuracy and limited applicability. The machine learning-based prestressed tendon tensioning sequence prediction method adopted by the present invention can accurately predict the optimal tensioning sequence for bridges.

[0046] (2) Solve the difficulties in collecting raw data: Collecting parameters such as the effective prestress of bridge prestressed steel bars, bridge deflection, and concrete stress during the tensioning process through on-site post-tensioning tests is costly, complex, and inefficient. However, the present invention extracts the bridge beam length, beam height, steel bar area, bending angle, and effective prestress through a large number of finite element analyses, thereby improving the efficiency of data collection, increasing the number of raw data samples, and enhancing the accuracy of the machine learning model.

[0047] (3) Improving the generalization ability of the model: The present invention adopts the ensemble learning XGBoost method, which has a faster training speed when processing large-scale data sets, effectively prevents model overfitting through regularization parameters, performs well when processing various types of data sets, and has good generalization ability. The ensemble learning provides a rich set of hyperparameter settings: such as tree depth, learning rate, regularization penalty coefficient, sampling ratio, etc., which can improve the recognition ability of minority class samples and improve the accuracy of the model for the optimal tensioning order of prestressed steel bars.

[0048] (4) Overcoming the problem of imbalanced original data categories: The present invention introduces a method combining ADASYN and Tomek Links to balance the data. By generating samples and removing the overlapping areas between the majority class and the minority class, the influence of noise data is reduced, and the influence of the imbalanced original data category on the model's ability to identify minority class samples is overcome, thereby improving the accuracy of the prediction of the optimal tensioning sequence of prestressed steel bars.

[0049] (5) Simplified data preprocessing: This invention designs data preprocessing, calculates derived features, unifies dimensions, and divides training and test sets. The calculation of derived features generates new features through professional knowledge, which can improve the model's ability to capture interactions between features, enhance interpretability, and improve model performance.

[0050] (6) Universal applicability and accuracy in engineering: The data of the present invention includes mainstream bridge types such as T-beams and box girders. Data collection uses parameters common to different types of bridges, such as section inertia moment, cross-sectional area, and steel bar bending angle. The model can adapt to the prediction of the optimal tensioning sequence for different types of bridges. Finite element simulation only needs to be run once during the data collection phase, without repeated runs, to collect a large amount of data. In actual engineering applications, it can quickly and accurately provide decision support and design guidance for construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The accompanying drawings, which constitute part of this application, are intended to provide a further understanding of this application. The exemplary embodiments and descriptions of this application are intended to explain this application and do not constitute an improper limitation on this application. In the accompanying drawings:

[0052] Figure 1 Flowchart of a method for predicting the tensioning sequence of prestressed steel bars in post-tensioning method according to an embodiment of the present invention;

[0053] Figure 2 This is a flow chart of obtaining original data using finite element simulation technology according to an embodiment of the present invention;

[0054] Figure 3 This is a schematic diagram of the feature importance ranking results of an embodiment of the present invention;

[0055] Figure 4 Schematic diagram of a confusion matrix according to an embodiment of the present invention;

[0056] Figure 5 Schematic diagram of the ROC curve of an embodiment of the present invention. DETAILED DESCRIPTION

[0057] It should be noted that, in the absence of conflict, the embodiments and features of the embodiments in this application can be combined with each other. 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 flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0059] Machine learning technology is applicable to data sets of different sizes and can continuously optimize the model as new data is input. The model trained on the training set can be generalized to the test set. It has strong generalization ability and can accurately predict the optimal tensioning sequence of prestressed steel bars in bridges. Finite element simulation technology can accurately and efficiently analyze the effective tensioning stress of prestressed steel bars, effectively reducing the cost of optimal tensioning sequence analysis. In addition, the relevance and importance of each feature are taken into account. By balancing the unbalanced categories, the derived feature calculation enhances the generalization ability of the model.

[0060] like Figure 1 As shown, this embodiment provides a method for predicting the tensioning sequence of prestressed steel bars in a bridge based on machine learning, including:

[0061] Collect basic information about the bridge structure and generate effective prestress data under different tensioning sequences through finite element simulation based on this basic information;

[0062] Determine the optimal tensioning sequence based on the effective prestress data and construct the original data set;

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

[0064] The basic information of the bridge to be predicted is input into the prediction model, and the corresponding optimal tensioning sequence is output.

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

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

[0067] The activation-killing element technique is used to simulate the construction process of different tensioning sequences;

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

[0069] Furthermore, the process of determining the optimal tensioning sequence based on the effective prestressing data includes:

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

[0071] The tensioning sequence with the largest weighted average effective tensioning stress is marked as the optimal tensioning sequence.

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

[0073] Based on the basic information of the bridge, finite element simulation was carried out to establish a simulation model of the prestress loss of the bridge under different tensioning sequences. The effective tensioning stress data of the prestressed steel bars of different bridges were obtained. The data was processed to obtain the optimal tensioning sequence of the prestressed steel bars of different bridge structures.

[0074] Furthermore, the process of preprocessing the original data set includes:

[0075] Calculate derived features based on the original features. The derived features include the ratio of steel area to concrete area, the stiffness ratio of prestressed steel to concrete section, and the total steel area.

[0076] The dataset is standardized and divided into training and test sets using stratified sampling.

[0077] Furthermore, the process of standardizing the dataset includes:

[0078] 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.

[0079] Furthermore, the process of inputting the machine learning model for training includes:

[0080] A hybrid sampling strategy combining ADASYN and Tomek Links was used to balance the categories of the training set.

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

[0082] Furthermore, the hybrid sampling strategy includes:

[0083] Adaptively generate minority class synthetic samples through ADASYN;

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

[0085] Furthermore, we use a sampling method that combines ADASYN and Tomek Links to sample the training set, generate new samples based on the classification difficulty, remove noise at the classification boundaries, and balance the number of samples in each category.

[0086] Based on the balanced training set, the performance of different hyperparameter combinations was evaluated through grid search and 5-fold cross-validation. The optimal hyperparameters were used to stack multiple decision trees on the entire training set using a gradient boosting method to obtain the final ensemble learning model. This ensemble learning model was used to predict the post-tensioning sequence of bridges.

[0087] Furthermore, 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 to control the complexity of the model.

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

[0089] The numerical labels output by the prediction model are converted into the original tensioning order categories through reverse mapping.

[0090] The method of this embodiment effectively solves the problem of difficulty in determining the tensioning order due to the loss of prestress caused by concrete compression in prestressing steel bar tensioning projects. The method provides a solution that combines finite element simulation technology with machine learning algorithms. The original data set is generated by finite element simulation, the original data is preprocessed, and the training set is sampled using a mixed sampling strategy of ADASYN and Tomek Links to increase the number of minority class samples and eliminate boundary noise; the optimal hyperparameter combination is selected through grid search combined with a 5-fold cross-validation method, and the model is trained using the balanced training set to optimize the objective function to obtain the final integrated learning model. The present invention can accurately predict the optimal tensioning order of prestressed steel bars, thereby reducing the prestress loss in tensioning prestressed steel bars, improving the bearing capacity of the bridge, improving work efficiency, and reducing work costs. Specifically, the method includes the following steps S101 to S105.

[0091] Step S101: Data collection. According to the standard bridge construction drawings, basic information of various T-beams and box girders is collected, such as beam length, beam height, steel bar area, bending angle, cross-sectional area, cross-sectional moment of inertia, steel bar eccentricity, and other basic bridge information.

[0092] The data in this example was collected from standard bridge construction drawings and supplemented with the original data from the bridge construction drawings to extract the necessary bridge structural parameters required for finite element analysis. This example collected data for two mainstream bridge types: T-beams and box girders.

[0093] Step S102: Finite element simulation to obtain the optimal tensioning sequence. Based on the basic information of the bridge, a finite element simulation is performed. Through the finite element simulation, different bridge structures are established. For each bridge structure, numerical calculations are performed for different tensioning sequences. The effective tensioning stress of the prestressed steel bars under different tensioning sequences are calculated. Based on the principle of maximizing the effective tensioning stress, the optimal post-tensioning sequence of the prestressed steel bars for different bridge structures is determined.

[0094] Prestress loss in post-tensioning: loss caused by friction between the prestressing steel bars and the pipes , losses caused by anchor deformation, steel bar shrinkage and joint compression , loss caused by elastic compression of concrete Under the action of the tensioning sequence, the prestress loss caused by different concrete compression in the bridge is analyzed.

[0095] When post-tensioning components are tensioned, the loss caused by friction between the prestressed steel bars and the pipes The calculation formula is as follows:

[0096] ;

[0097] in, Indicates the tension control stress under the prestressed steel anchor; Indicates the friction coefficient between the prestressed steel bar and the pipe; It represents the sum of the angles between the tensioning end and the tangent line of the pipe part of the calculated section curve; Indicates the influence coefficient of local deviation of each meter of pipeline on friction coefficient; Indicates the pipe length from the tensioning end to the calculation section.

[0098] When post-tensioned members are tensioned, the losses caused by anchor deformation, steel bar shrinkage and joint compression are The calculation formula is as follows:

[0099] ;

[0100] in Values ​​representing deformation of the tensioning end anchorage, steel bar shrinkage, and joint compression; Indicates the distance between the tensioning end and the anchorage section; It represents the elastic modulus of prestressed steel bars.

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

[0102] ;

[0103] Where T represents the temperature applied to the unit; Indicates the linear expansion coefficient of steel bars; represents the elastic modulus of the prestressed steel bar; Indicates the tension control stress under the prestressed steel anchor; Indicates the loss caused by friction between prestressed steel bars and pipes; Represents losses caused by anchor deformation, reinforcement shrinkage and joint compression.

[0104] Calculate the loss of each unit due to friction between the prestressed steel bars and the pipe and losses caused by anchor deformation, steel bar shrinkage and joint compression , tension the anchor to control stress minus and The effective prestress obtained is applied to each unit of the prestressed steel bar through the equivalent temperature change method, accurately simulating the prestress loss caused by pipeline friction and anchor deformation, steel bar shrinkage, and joint compression, avoiding and The impact on the experimental results.

[0105] Losses caused by elastic compression of concrete during tensioning of post-tensioned members The calculation formula is as follows:

[0106] ;

[0107] in, It represents the normal stress of concrete generated by the subsequent batch of prestressed steel bars at the center of gravity of the prestressed steel bar when the prestressing is completed in the calculated section; It represents the ratio of the elastic modulus of prestressed steel bars to the elastic modulus of concrete.

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

[0109] This embodiment uses finite element simulation, solid reinforcement method, SOLID65 units for concrete, LINK180 units for prestressed steel bars, concrete units and prestressed steel bar units are connected by coupling, and the tensioning order is controlled by the method of life and death units, that is, when tensioning the first steel bar, only the unit of the first steel bar is activated, and the units of other steel bars are killed. When tensioning the second steel bar, the unit of the second steel bar is activated, and so on until the tensioning is completed. The influence of the post-tensioned steel bars on the pre-tensioned steel bars is simulated, and the necessary characteristic data for predicting the optimal tensioning order of the prestressed steel bars by the post-tensioning method is extracted, and the effective tensioning stress of the steel bars is extracted. Based on the principle of maximizing the effective prestressing, the weighted average stress of the prestressed steel bars is calculated, and the weighted average stress of the prestressed steel bars obtained under different tensioning orders for bridges of the same structure is compared to obtain the optimal tensioning order. The detailed finite element simulation process of collecting raw data is as follows. Figure 2 shown.

[0110] Step S103: pre-processing the raw data collected in step S102. The pre-processing process includes: calculating derived features, dividing the training set and the test set, unifying the dimensions, and encoding the category labels.

[0111] Calculating derived features: Model interactions are local and may ignore global high-order features, failing to fully utilize model performance. New features are manually derived based on raw data features combined with professional knowledge. This dual-layer feature derivation, through manual derivation and automatic feature interaction with the XGBoost model, can efficiently capture complex data relationships. Manually derived features are as follows:

[0112] Calculate the derived characteristic area ratio using the following formula:

[0113] ;

[0114] in, It represents the ratio of the steel bar area to the concrete area; represents the area of ​​the i-th prestressed steel bar; Represents the cross-sectional area of ​​concrete.

[0115] Calculate the derived characteristic prestressed steel bar to concrete section stiffness ratio using the following formula:

[0116] ;

[0117] in, It represents the stiffness ratio of the prestressed steel bar to the concrete section; represents the eccentricity of the i-th prestressed steel bar; represents the elastic modulus of the prestressed steel bar; represents the elastic modulus of concrete; represents the area of ​​the i-th prestressed steel bar; Represents the cross-sectional area of ​​concrete.

[0118] Calculate the total area of ​​the derived feature reinforcement using the following formula:

[0119] ;

[0120] in, represents the sum of the areas of prestressed steel bars; Indicates the total number of prestressed steel bars.

[0121] Dataset partitioning: The optimal tensioning order dataset collected in step S102 is partitioned. Due to the imbalanced category distribution of the original data, a stratified sampling method is used to keep the category distribution in the training set and test set consistent with the category distribution of the original data, avoiding the problem of a few categories being missing in the test set. A random seed is used to ensure that the results of each partition run are consistent and repeatable.

[0122] The test set sampling ratio set in this embodiment is 0.3, that is, the training set data samples account 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 retained for model evaluation. The hyperparameter tuning of the XGBoost ensemble learning model is determined based on 5-fold cross-validation.

[0123] Dimensional unification: Due to the large dimensional differences between 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 XGBoost integrated algorithm uses a gradient boosting algorithm. During training, the large dimensional differences between different features will lead to unstable weight updates, causing the model to favor features with larger values, thereby ignoring features with small values, and then misjudging the importance of the original features. Standardization can effectively improve the performance of the model by eliminating the impact of dimensional differences on model performance. When standardizing, the test set is standardized using the mean and standard deviation of the training set. Otherwise, data leakage may occur, leading to deviations in model evaluation and an inability to accurately reflect the performance of the model.

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

[0125] ;

[0126] in, represents the standardized eigenvalue; Represents features in the original data; Represents the mean of a feature of the original data; Represents the standard deviation of a feature in the original data.

[0127] Category label encoding: Use LabelEncoder's mapping encoding 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 disordered encoding such as optimal tension order, digital encoding will not introduce false numerical relationships. If there are categories, using 0 to The target label is encoded by the value between , and each category name variable is mapped to a unique numerical code through mapping encoding.

[0128] For example, the prestressed steel bars are numbered A, B, and C from the bottom to the top of the bridge. The optimal tensioning sequence of the bridge is divided into six tensioning sequences: ABC, ACB, BAC, BCA, CAB, and CBA. After mapping, each optimal tensioning sequence will be assigned a A number between .

[0129] This example selects only the top 20 features in terms of importance. The importance of data features is as follows: Figure 3 shown.

[0130] Step S104: Data Balancing. This embodiment utilizes a hybrid sampling strategy combining ADASYN and Tomek Links to balance the data of the standardized training set, generating minority class samples and increasing the number of minority class samples to obtain a balanced dataset. ADASYN performs balancing by generating synthetic samples. Tomek Links is then used to remove overlap between the majority and minority classes, reducing the impact of noise data and addressing data imbalance.

[0131] As an adaptive oversampling technique, ADASYN balances the dataset by generating synthetic samples of the minority class. Its goal is to increase the classifier's ability to learn minority class samples, thereby improving the overall performance of the model. The technique adaptively generates new minority class samples based on the sample distribution and classification difficulty. ADASYN evaluates the classification difficulty of minority class samples by calculating the k-nearest neighbors of the minority class samples, that is, the density of minority class samples. A low 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 calculation formula is as follows:

[0132] ;

[0133] in, represents the synthesized sample; Represents minority class samples; Represents the neighbors of the minority class samples; Indicates yes A random number.

[0134] ADASYN technology can be used to specifically enhance minority class boundary areas, effectively improving the model's ability to identify boundary samples. Because the adaptive generation strategy is less likely to introduce noise than SMOTE, it is effective for datasets with very few minority class samples and uneven distribution. The Tomek Links algorithm optimizes the classification boundaries by removing noise samples and overlapping samples near the boundaries, making the boundaries clear and improving model performance. This algorithm only removes majority class samples, not the majority class, effectively protecting minority class samples. The common sampling scheme of ADASYN and Tomek Links combines ADASYN oversampling technology and Tomek Links undersampling technology. By integrating the advantages of oversampling and undersampling technologies, it can effectively solve the imbalance problem while also solving the noise problem, reducing the risk of overfitting and improving the generalization ability of the model.

[0135] In practical applications of the hybrid sampling strategy of ADASYN and Tomek Links, ADASYN oversampling is first used to adaptively generate new samples, increasing the number of samples in each minority class to the same number as the majority class. Tomek Links is then used to undersample the training set to reduce noise until the dataset is balanced. This strategy balances the training set data through phased, refined sampling, and then cleans up the classification boundaries, preserving clean boundaries and generating balanced data. This improves the performance of the ensemble learning model and enables the model to handle multi-class imbalanced classification tasks.

[0136] It's worth noting that when addressing the imbalance in the original data categories, only the training set is balanced after the data is partitioned, while the test set retains the original imbalanced distribution. This prevents data leakage, improves the model's generalization ability in practical applications, and makes the model more robust. Balancing the test set as well can lead to deviations in the evaluation metrics, making them inconsistent with the actual results.

[0137] In this example, due to the uneven distribution of class samples (for example, the number of ACB tensioning orders is far lower than that of other tensioning order categories), a hybrid sampling strategy of ADASYN and Tomek Links was adopted to avoid the influence of minority class samples on the data. ADASYN oversampling was set to automatically balance all minority classes to the majority class level, the number of nearest neighbors was set to 5, and the threshold in Tomek Links was set to the default setting. This setting maintains data balance and effectively eliminates the influence of noise, improving model performance and making prediction results more accurate and robust. The balanced class distribution of the training set is shown in Table 1.

[0138] Table 1

[0139] Optimal tensioning sequence 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: Construct an ensemble learning model. In this step, a prediction model for the optimal tensioning sequence of prestressed steel bar post-tensioning is constructed through XGBoost ensemble learning.

[0141] This example first performs hyperparameter tuning on the XGBoost ensemble learning model through grid search, and adopts the 5-fold cross-validation method to divide the balanced training set into 5 subsets that maintain the category distribution. Four of the subsets are trained using each hyperparameter combination, and the remaining subset is validated to evaluate the performance of the model, i.e., the balanced accuracy. This is repeated five times, each time using a different subset as the validation subset. Finally, the average of the five validations is calculated, and the parameter combination with the highest validation average is selected as the optimal hyperparameter combination.

[0142] Next, the model is trained based on the balanced training set data obtained in step S104, and the objective function is optimized to obtain the optimal 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] in represents the objective function of multi-classification, represents the loss function, which measures the difference between the model's predicted value and the true value; Represents the 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; Indicates the total number of trees; Indicates the Regularization term of the tree;

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

[0146] ;

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

[0148] The regularization formula is as follows:

[0149] ;

[0150] Where T represents the number of leaf nodes in the current tree; Indicates the penalty coefficient for the number of leaf nodes in the current tree, which controls the number of leaf nodes and the depth of the tree; represents the L1 regularization parameter; represents the L2 regularization parameter; Indicates the value of the jth leaf node. This embodiment sets the penalty coefficient of the number of leaf nodes ; Parameters of the L2 regularization term ; Parameters of the L1 regularization term .

[0151] Finally, through gradient boosting, the decision trees were iteratively added to reduce the residual error, resulting in the final model. The final XGBoost ensemble learning model can accurately predict the optimal tensioning sequence for post-tensioning prestressed steel bars, effectively improving the efficiency of determining the optimal tensioning sequence in actual projects and enhancing the mechanical performance of bridges during operation.

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

[0153] Step S106: Evaluate and verify the ensemble learning model using evaluation indicators. The model is evaluated on the test set. The evaluation indicators include accuracy, precision, recall, and F1 score. The evaluation indicator calculation formula is as follows:

[0154] Accuracy:

[0155] ;

[0156] in It represents the proportion of correctly predicted samples to the total samples, which measures the accuracy of the model; Indicates the number of samples that are actually positive and predicted to be positive, that is, the number of samples predicted correctly; Indicates the number of samples that are actually negative and predicted to be negative, that is, the number of samples predicted correctly; Indicates the number of samples that are actually negative but predicted to be positive, that is, the number of samples with incorrect predictions; It indicates the number of samples that are actually positive but predicted to be negative, that is, the number of samples with incorrect predictions.

[0157] Precision:

[0158] ;

[0159] in, n represents the ratio of actual positive samples to predicted positive samples, which measures the accuracy of the model in predicting the positive class; 、 Same as above.

[0160] Recall:

[0161] ;

[0162] in, It represents the ratio of samples that are correctly predicted to be positive to samples that are actually positive, and measures the ability of the model to find all positive samples; 、 Same as above.

[0163] F1 Score:

[0164] ;

[0165] in, It represents the harmonic mean of precision and recall, and is an indicator that comprehensively measures precision and recall.

[0166] The indicators of the evaluation model in this embodiment are: accuracy rate is 0.88, precision rate is 0.881, recall rate is 0.88, F1 score is 0.88, and the confusion matrix and ROC curve of the prediction results are as follows: Figure 4 、 Figure 5 shown.

[0167] In summary, the present invention provides a method for predicting the post-tensioning order of prestressed steel bars in bridges based on machine learning. Through the steps of collecting basic information of the bridge, finite element simulation, data preprocessing, data set category balancing, integrated learning, etc., a reliable model for predicting the post-tensioning order of prestressed steel bars in bridges is constructed, providing a decision-making technology for establishing the tensioning order of post-tensioned prestressed steel bars. The present invention adopts technologies such as integrated learning and finite element simulation in machine learning, and combines a variety of data preprocessing methods and model integration methods. It can accurately predict the tensioning order of prestressed steel bars, making the model more accurate, and providing an important scientific basis for tensioning prestressed steel bars in bridges. Compared with traditional methods, the present invention has high work efficiency and accurate prediction performance, and has a broad application development space and superior economic benefits.

[0168] The above are merely preferred embodiments of the present application, but the scope of protection of the present application is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A method for predicting the tensioning sequence of post-tensioning prestressed steel bars in bridges based on machine learning, characterized in that: include: Collecting basic information of the bridge structure, and generating effective prestress data under different tensioning sequences through finite element simulation based on the basic information; Determine the optimal tensioning sequence according to the effective prestress data and construct an original data set; After preprocessing the original data set, the data set is input into a machine learning model for training to obtain a prediction model for predicting the optimal tensioning sequence; The basic information of the bridge to be predicted is input into the prediction model, and the corresponding optimal tensioning sequence is output.

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

3. The method according to claim 1, characterized in that The process of generating effective prestress data under different tensioning sequences through finite element simulation based on the basic information includes: Build a finite element model of the bridge and define the material properties of prestressed steel and concrete; The activation-killing element technique is used to simulate the construction process of different tensioning sequences; Calculate the weighted average effective tensioning stress of the prestressed steel bars under each tensioning sequence.

4. The method according to claim 1, wherein The process of determining the optimal tensioning sequence according to the effective prestressing data includes: Compare the weighted average effective tension stress under different tensioning sequences; The tensioning sequence with the largest weighted average effective tensioning stress is marked as the optimal tensioning sequence.

5. The method according to claim 1, wherein The process of preprocessing the original data set includes: Calculating derived features based on the original features, the derived features including the ratio of the steel bar area to the concrete area, the stiffness ratio of the prestressed steel bar to the concrete section, and the total steel bar area; The dataset is standardized and divided into training and test sets using stratified sampling.

6. The method according to claim 1, characterized in that The process of normalizing 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.

7. The method according to claim 1, characterized in that The process of inputting into a machine learning model for training includes: A hybrid sampling strategy combining ADASYN and Tomek Links was used to balance the categories of the training set. The XGBoost ensemble learning algorithm is used to train the balanced training set, and the hyperparameters are optimized through grid search and cross-validation.

8. The method according to claim 7, characterized in that The hybrid sampling strategy includes: Adaptively generate minority class synthetic samples through ADASYN; The Tomek Links algorithm is used to remove overlapping samples at the boundary between the majority class and the minority class.

9. The method according to claim 1, characterized in that 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, which are used to control the complexity of the model.

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

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