Expressway bridge support settlement prediction method based on random forest

Abstract

The invention provides an expressway bridge support settlement prediction method based on a random forest. The expressway bridge support settlement prediction method comprises the following steps of S1, acquiring relevant data of an expressway bridge support; s2, preprocessing an original data set; s3, constructing a fusion prediction model fusing the random forest, the simple pendulum wave algorithm and the adaptive inertia weight particle swarm optimization algorithm; s4, training and optimizing a fusion prediction model; s5, verifying the fusion prediction model; and S6, predicting settlement of the expressway bridge support. According to the method, the defect that a traditional prediction model is insufficient in adaptation to a complex service environment is overcome, through deep fusion of the random forest, the simple pendulum wave algorithm and the self-adaptive inertia weight particle swarm optimization, the fitting capacity of the model to multi-dimensional influence factors is improved, high-precision prediction of the settlement is achieved, and prediction errors are reduced.

Description

Technical Field

[0001] This invention relates to the field of highway bridge maintenance and intelligent prediction technology, and in particular to a method for predicting highway bridge bearing settlement based on random forest. Background Technology

[0002] As a core component connecting the superstructure and substructure of a highway bridge, the bearings play a crucial role in transferring loads and adapting to structural deformation. Their settlement directly affects the structural safety and traffic stability of the bridge. As the service life of a bridge increases, the bearings are prone to cumulative settlement under the combined effects of long-term loads, environmental erosion, and other factors. If the settlement exceeds the allowable range specified in the standards, it may lead to uneven stress distribution in the bridge structure, reduced bridge deck flatness, and even structural safety hazards.

[0003] Currently, bridge bearing settlement prediction mainly relies on traditional methods: First, numerical simulation methods based on structural mechanics, which require the establishment of complex mechanical models, have high requirements for parameter settings, and are difficult to fully consider the coupled effects of multiple factors, resulting in limited generalization ability; second, prediction methods based on empirical formulas, which rely on the professional experience of engineers, are highly subjective, and the prediction accuracy is limited by the degree of experience accumulation; and third, single machine learning methods, which, although capable of using data-driven methods to uncover settlement patterns, suffer from problems such as insufficient optimization of model parameters, easy overfitting or underfitting, and poor adaptability to complex working conditions.

[0004] Furthermore, existing fusion algorithms mostly employ a one-way adaptation model of optimization algorithm + prediction model. The optimization algorithm is only used to adjust some parameters of the prediction model, lacking dynamic interaction and collaborative optimization between algorithms. This results in the optimization effect not being fully translated into improved prediction performance, making it difficult to meet the high requirements for accuracy, reliability, and generalization ability in predicting highway bridge bearing settlement. Therefore, there is an urgent need for a prediction method that can achieve deep fusion of multiple algorithms and dynamic interactive optimization to overcome the limitations of traditional methods. Summary of the Invention

[0005] This invention provides a random forest-based method for predicting the settlement of highway bridge bearings. It overcomes the problems of high parameter dependence, poor adaptability to multi-factor coupling, and strong subjectivity and limited generalization ability of traditional structural mechanics numerical simulation methods, as well as the limitations of empirical formula prediction. This method improves the accuracy and reliability of bearing settlement prediction, adapting to the needs of mining bearing settlement patterns under different service years, environmental conditions, and load conditions. It accurately captures the settlement evolution patterns under the coupled effects of multiple factors such as bearing characteristics, environmental erosion, and long-term loads, providing highway bridge management departments with scientific and reliable settlement prediction results. This supports the early formulation and precise implementation of maintenance decisions, reduces bridge structural safety risks, and extends bridge service life.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: A method for predicting the settlement of highway bridge bearings based on random forests includes the following steps: S1: Collect the self-parameters, environmental impact parameters, load parameters, and actual settlement data of the highway bridge bearings to form the original dataset; S2: Preprocess the original dataset to obtain the training set and the test set; S3: Construct a fusion prediction model that integrates random forest, single pendulum wave algorithm and adaptive inertial weighted particle swarm optimization algorithm; S4: Input the training set into the fusion prediction model for model training and optimization. Complete the model optimization through error evaluation and parameter adjustment to obtain the optimized fusion prediction model. S5: Input the test set into the optimized fusion prediction model to verify it, ensuring that the model meets the preset performance standards, and obtain the final usable fusion prediction model; S6: Collect the support data to be predicted and preprocess it according to the method in S2. Input the preprocessed support data into the final usable fusion prediction model and output the support settlement prediction result.

[0007] In this specification, both the training and test sets contain feature vectors and corresponding true settlement values. The working process of the fusion prediction model is as follows: the Adaptive Inertial Weighted Particle Swarm Optimization (AIOPE) algorithm calculates particle fitness values ​​based on feature vectors and true settlement values ​​to obtain an average fitness value; the Pendulum Wave Algorithm receives the average fitness value and generates a dynamic displacement signal; the AIOPE adjusts the inertial weights based on this dynamic displacement signal and searches for the optimal structure parameters of the Random Forest; the Random Forest uses these optimal structure parameters to process the feature vectors and outputs predicted values, while simultaneously calculating the prediction error and the average node splitting threshold, which are fed back to the AIOPE and the Pendulum Wave Algorithm, respectively; the AIOPE adjusts the learning factor based on the prediction error, and the Pendulum Wave Algorithm adjusts the angular frequency based on the average node splitting threshold and outputs an amplitude signal; the Random Forest adjusts the decision tree weights based on this amplitude signal. Through the above closed-loop data flow, the three algorithms achieve bidirectional interaction and model parameter optimization.

[0008] In this manual, in S1, the bearing parameters themselves are derived from the bridge design drawings and the bearing manufacturer's technical specifications, the environmental impact parameters are derived from meteorological observation data and on-site environmental monitoring records, the load parameters are derived from the traffic flow monitoring system and the bridge structure stress calculation report, and the actual settlement data are obtained by monitoring and calculating through measuring equipment.

[0009] In this specification, the preprocessing of S2 is as follows: outliers are detected and replaced using the box plot method; missing values ​​are filled according to the mean of the same type of bearing data or the mean of the bearing data within the same bridge; numerical parameters are standardized; categorical parameters are one-hot encoded; and training and test sets are randomly divided proportionally.

[0010] In this specification, the model training optimization in S4 includes: evaluating the training error using root mean square error, mean absolute error, and coefficient of determination; if the coefficient of determination does not reach the preset threshold, adjusting the adjustment coefficient of the pendulum wave algorithm and the maximum number of iterations of the particle swarm optimization algorithm, and returning to S3 to perform closed-loop optimization again until the training performance requirements are met.

[0011] In this manual, the settlement prediction results for S6 include the annual settlement prediction value and the future cumulative settlement prediction value for a single support. The annual settlement prediction value is marked with the prediction error range, and the cumulative settlement prediction value is obtained by accumulating the prediction values ​​year by year. At the same time, the support settlement risk level and maintenance recommendations based on the prediction results are output.

[0012] In this specification, the particle fitness value is calculated based on the root mean square error of the random forest prediction. The smaller the error, the better the corresponding particle fitness value.

[0013] In this specification, when the single pendulum wave algorithm generates a dynamic displacement signal, it first adjusts its amplitude and period by means of the average fitness value, and then constructs a displacement function based on the adjusted amplitude, period and angular frequency to obtain the dynamic displacement signal.

[0014] In this specification, the optimal structural parameters of the random forest, including the number of decision trees, the maximum depth of the decision trees, and the minimum number of sample splits for each decision tree node, are all determined by the adaptive inertial weighted particle swarm optimization algorithm through group cooperative search.

[0015] In this specification, the closed-loop termination conditions for the three algorithms are: the number of iterations reaches the preset maximum number of iterations, or the global optimal fitness value of the adaptive inertial weighted particle swarm optimization algorithm is less than the preset error threshold.

[0016] In summary, the present invention has at least the following beneficial effects: 1. Improve the reliability and generalization ability of prediction: By integrating random forest, single pendulum wave algorithm and adaptive inertial weighted particle swarm optimization algorithm, the ensemble learning advantage of random forest is brought into play, and the intelligent optimization algorithm is used to dynamically adjust the model parameters and structure. This effectively avoids the overfitting and underfitting problems of single algorithms, enabling the model to adapt to the support settlement law under different service environments and load conditions, and improve the prediction stability under complex working conditions.

[0017] 2. Achieve adaptive and precise parameter optimization: Breaking through the limitations of traditional unidirectional optimization, a closed-loop feedback mechanism between algorithms is constructed. The dynamic adjustment characteristics of the single pendulum wave algorithm are combined with the global search capability of the adaptive inertial weighted particle swarm optimization algorithm to achieve adaptive optimization of random forest structure parameters and decision tree weights. This solves the subjectivity and limitations of manually setting parameters and improves the adaptability of model parameters.

[0018] 3. Enhance the model's adaptability to the coupled effects of multiple factors: By collecting multi-dimensional data on the support itself, the environment, and the load, and combining standardized preprocessing to eliminate data noise and dimensional differences, the model can fully learn the settlement law under the coupled effects of multiple factors and improve its ability to capture complex influencing factors.

[0019] 4. Provide scientific support for maintenance decisions: The prediction results can accurately reflect the settlement trend and risk level of the bearings, avoid the delay in maintenance decisions caused by the accumulation of errors in traditional prediction methods, help management departments to formulate targeted maintenance measures in advance, reduce the safety risks of bridge structures, and extend the service life of bridges. Attached Figure Description

[0020] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 This is a flowchart illustrating the random forest-based method for predicting the settlement of highway bridge bearings involved in this invention.

[0022] Figure 2 This is a schematic diagram of the data acquisition and preprocessing process involved in this invention.

[0023] Figure 3 This is a flowchart illustrating the bidirectional interaction of the three algorithm parameters involved in this invention.

[0024] Figure 4 This is a schematic diagram illustrating the training, optimization, and verification process of the fusion model involved in this invention. Detailed Implementation

[0025] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of the embodiments of the invention. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0026] The following disclosure provides many different implementations or examples for carrying out different structures of the embodiments of the present invention. To simplify the disclosure of the embodiments of the present invention, specific examples of components and arrangements are described below. Of course, these are merely examples and are not intended to limit the embodiments of the present invention. Furthermore, reference numerals and / or reference letters may be repeated in different examples of the embodiments of the present invention; such repetition is for simplification and clarity and does not in itself indicate a relationship between the various implementations and / or arrangements discussed.

[0027] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0028] like Figure 1 As shown, this embodiment provides a method for predicting the settlement of highway bridge bearings based on random forests, including: S1: Data Collection Related to Highway Bridge Bearings The data acquisition and preprocessing process for collecting multi-dimensional parameters and measured settlement data of highway bridge bearings is as follows: Figure 2 As shown. Specific implementation details are as follows: Define the scope and target of data collection: Select 30 highway bridges that have been in operation for more than 5 years within a certain city and cover different structural types. For each bridge, select 8 representative bearings according to the key stress areas of the bearings, including three types: fixed bearings, unidirectional movable bearings, and bidirectional movable bearings, to form a total of 240 bearing samples, covering different service environments, load conditions and bearing types, to ensure sample diversity.

[0029] Determine the data acquisition type and technology source: Bearing parameters: including bearing model, such as GPZ(Ⅱ)3.0GD, GPZ(Ⅱ)4.0DX, GPZ(Ⅱ)5.0SX, etc.; bearing material, such as rubber bearing, steel bearing, PTFE bearing; design bearing capacity; bearing height; all data are extracted from bridge design drawings, construction archives and technical specifications provided by bearing manufacturers. Environmental impact parameters: annual average temperature, annual average rainfall, annual average relative humidity, and number of freeze-thaw cycles. The meteorological data comes from the city's meteorological bureau's official observation database for the past 5 years, and the number of freeze-thaw cycles is calculated by combining the on-site environmental monitoring records of the bridge maintenance department with local climate characteristics. Load parameters: average daily traffic flow, average axle load of vehicles, cumulative number of heavy vehicles passing through the bridge, and long-term dead load borne by the supports. The data are from the traffic flow monitoring system of the highway management department and the stress calculation report of the bridge structure. Settlement measurement data: The initial installation height of the bearings was recorded using an electronic level during the bridge's completion and acceptance. Subsequent settlement monitoring was conducted annually in spring (March-April) and autumn (September-October), using both an electronic level and a total station for simultaneous measurements. The average of the two measurements was taken as the actual height for that year, and monitoring continued for five years. The settlement amount was calculated as the difference between the initial installation height and the actual height for that year.

[0030] Data Acquisition and Integration: A customized data acquisition terminal is used, integrating a sensor data receiving module to interface with traffic flow monitoring systems and environmental monitoring equipment. A manual input module is used to input design parameters and measured heights. All data is stored in a unified format. Each data record corresponds to a complete set of parameters for a single bearing and its corresponding annual settlement. The data record format is: [Bearing model, bearing material, design load capacity, bearing height, average annual temperature, average annual rainfall, average annual relative humidity, freeze-thaw cycles, average daily traffic flow, average axle load, cumulative number of heavy vehicles passing through, long-term dead load, settlement]. This ultimately forms 240 complete raw datasets. .

[0031] S2: Preprocessing of the original dataset To eliminate data noise, standardize data format, and ensure the effectiveness of model training, the original dataset undergoes multi-step preprocessing, as detailed below: Outlier Detection and Handling: For the Original Dataset Eleven numerical parameters, including design bearing capacity, bearing height, and average annual temperature, were analyzed, and outlier identification was performed using box plots. The first quartile (Q1), third quartile (Q3), and interquartile range (IQR) were calculated for each numerical indicator, where IQR = Q3 - Q1. Values ​​exceeding the range of Q1 - 1.5IQR to Q3 + 1.5IQR were identified as outliers. Instead of directly deleting detected outliers, their corresponding bearing groups were searched, and the median of the corresponding indicator in that group was used to replace them, thus avoiding data loss and resulting in a dataset free of outliers. .

[0032] Missing value imputation: imputing missing values ​​in the dataset A field-by-field missing value check is performed. If a data record has a missing field, it is first grouped according to the dataset of the same type of bearing with the same model and material. The mean of the corresponding missing field within the group is calculated, and the missing value is filled using this mean. If the sample size of the same type of bearing is insufficient (less than 10), the sample size is expanded to the mean of the corresponding field of all bearings within the same bridge to ensure that the filled data conforms to the actual attribute characteristics of the bearing, thus forming a dataset without missing values. .

[0033] Data standardization: processing the dataset All numerical parameters are standardized, mapping the data to the [0,1] interval to eliminate the impact of differences in units and numerical ranges between different indicators on model training. During processing, the maximum and minimum values ​​of each numerical indicator are first calculated, and then each original value is converted into a standardized value within the corresponding interval through a linear transformation, ensuring that all numerical features are of the same order of magnitude and improving model convergence speed.

[0034] Categorical data encoding: for datasets The classification parameters, such as support model and support material, are numerically converted using one-hot encoding. There are 6 types of support models, which are encoded into 6 binary features, with a feature of 1 corresponding to a certain model and 0 for the rest. There are 3 types of support materials, which are encoded into 3 binary features. This method converts non-numerical features into numerical features that the model can recognize, while avoiding ordinal bias in classification features.

[0035] Dataset partitioning: The standardized and encoded complete dataset was randomly divided into a training set and a training set using a 7:3 ratio. and test set During the sampling process, a random seed of 42 was set to ensure the repeatability of the partitioning results. The final training set contains 168 data records for model training and parameter optimization; the test set contains 72 data records for model performance validation. Each data record after partitioning is represented by a feature vector. and the corresponding actual value of settlement Composition, in the format [X,y]; feature vector It includes 6 bearing model coding features, 3 bearing material coding features, and 10 standardized numerical features, for a total of 19 feature dimensions.

[0036] S3: Construction of a prediction model integrating random forest, pendulum wave algorithm, and adaptive inertia weighted particle swarm optimization algorithm. 3.1 Construction of the basic model of random forest As an ensemble learning algorithm, random forest's core advantage lies in reducing the risk of overfitting and improving prediction stability through collaborative decision-making among multiple decision trees.

[0037] First, determine the core structural parameters of the random forest: the parameters that need to be optimized include the number of decision trees. Maximum depth of a single decision tree Minimum number of sample splits for a decision tree node During the initial iteration, temporarily set , , At the same time, initial weights are assigned to each decision tree. , For decision tree indexing, To ensure a balanced contribution of the initial decision tree, we set... This ensures that the sum of the initial weights of all decision trees satisfies .

[0038] Next, we construct the decision tree model: We use the CART (Classification and Regression Tree) regression decision tree as the base model because CART trees are computationally efficient and highly interpretable in continuous value prediction problems, making them suitable for the continuous value prediction of support settlement. For the training set... eigenvectors in To determine the optimal splitting feature, feature importance assessment is required. Here, the Gini coefficient is chosen as the feature splitting criterion. The Gini coefficient reflects the purity of the sample set; a smaller coefficient indicates a more concentrated sample category after feature splitting, resulting in higher prediction accuracy. The formula for calculating the Gini coefficient is: ; In the formula, Representing the eigenvector The first in One characteristic, , This refers to the number of value categories for this feature, such as the support material feature. ; For the first The feature is taken as the first The proportion of samples from each category in the total training set. After calculating the Gini coefficient for each of the 19 features, the feature with the smallest coefficient is selected as the splitting feature for the current decision tree node, and the splitting threshold is... The median of this feature in the training set is used to recursively split the decision tree nodes until the preset maximum depth is reached. Or the number of node samples is less than the minimum number of splits. .

[0039] Finally, the basic random forest model was assembled: bootstrap sampling was used to extract data from the training set. Randomly selected from There are 1 sample subsets, and the number of samples in each subset is equal to the number of samples in the subset. Consistency is ensured by allowing repeated sample extraction to guarantee the diversity of training data for each decision tree and avoid model homogenization. Each sample subset is input into a separate CART decision tree for training, resulting in... These are the trained decision trees, and all of them together form the base model of the random forest. The model's prediction output is a weighted sum of the predictions from each decision tree, i.e.: ; In the formula, This represents the final predicted value of the random forest base model; For the first The weights of the decision trees are initially set to... The results will be dynamically adjusted through algorithmic integration in the future. For the first The prediction value of a single sample by a decision tree.

[0040] 3.2 Construction of Single Pendulum Wave Algorithm Model The pendulum wave algorithm simulates the periodic vibration characteristics of a simple pendulum in physics. Its displacement changes have dynamic adjustment capabilities and can be used for adaptive parameter adjustment in the optimization process.

[0041] First, define the core physical parameters of the pendulum wave algorithm: the initial amplitude of the pendulum. Amplitude reflects the maximum range of displacement change; initial period The period unit is consistent with the number of optimization iterations, reflecting the time interval of the vibration; initial angular frequency. Angular frequency is inversely proportional to the period and describes the speed of vibration; initial phase The phase reflects the initial position of the vibration; to achieve dynamic adjustment of the parameters, an amplitude adjustment coefficient is introduced. Periodic adjustment coefficient Angular frequency adjustment coefficient This is used to adjust the pendulum wave parameters based on feedback from other algorithms.

[0042] Based on the above parameters, a pendulum wave displacement function is constructed. The output of this function will serve as a dynamic adjustment signal to optimize the inertia weights of the particle swarm optimization algorithm and the decision tree weights of the random forest. The formula for calculating the pendulum wave displacement function is: ; In the formula, For the first The displacement value of the pendulum wave in the next iteration For the number of iterations, , The maximum number of iterations is preset. For the first Real-time amplitude at the next iteration For the first Real-time angular frequency at the next iteration For the first The real-time phase during the next iteration; the phase update rule is: ( The core characteristic of this displacement function is that it dynamically changes the amplitude and angular frequency, thus... During the iteration process, it exhibits a trend of large-scale exploration followed by small-scale convergence, adapting to the needs of different stages of parameter optimization.

[0043] 3.3 Construction of Adaptive Inertia Weighted Particle Swarm Optimization Algorithm Model Particle Swarm Optimization (PSO) simulates the collaborative behavior of flocks of birds foraging and has the advantages of strong global search capabilities and fast convergence speed. However, the fixed inertial weights of traditional PSO can easily lead to premature convergence or insufficient convergence accuracy.

[0044] First, define the core parameter of the model: particle swarm size. That is, the number of parameter combinations searched simultaneously; particle dimension. The three parameters to be optimized in the random forest are... , , The position vector of each particle is denoted as... , For particle index, where , , The first During the nth iteration The number of decision trees corresponding to each particle, the maximum depth of the decision tree, and the minimum number of sample splits; the velocity vector of the particle is denoted as... This describes the update rate of particle positions; to avoid parameter values ​​exceeding a reasonable range, particle position boundaries are defined: , , Particle velocity boundary , This prevents particles from jumping out of the optimal solution region due to excessively rapid position updates.

[0045] In addition, the learning parameters for the particle swarm optimization are defined as: initial inertia weights. The degree to which particles inherit their history speed; minimum inertial weight. Maximum inertia weight Initial learning factor Individual cognitive factors reflect the degree of trust a particle has in its optimal position; The social cooperation factor reflects the degree of trust a particle has in the group's optimal position; the individual particle's optimal position... , No. During the nth iteration The optimal parameter combination found by each particle; the global optimal position of the particle swarm. , No. The optimal combination of parameters found by all particles in the next iteration.

[0046] To measure the quality of a particle's position, a fitness function is defined: based on the random forest base model on the training set... The root mean square error (RMSE) of predictions is used as the fitness value. A smaller fitness value indicates better performance of the random forest parameter combination corresponding to the particle. The fitness function is calculated as follows: ; In the formula, For the first During the nth iteration The fitness value of each particle. For training set The number of samples, For the first The true value of settlement for each sample. For the first The feature vector of each sample To adopt the first The parameters corresponding to each particle The constructed random forest model for the first The predicted value for each sample.

[0047] 3.4 Deep Integration and Interaction of the Three Algorithms The core of the integration of the three algorithms lies in bidirectional interaction and dynamic feedback: the single-pendulum wave algorithm provides dynamic adjustment signals for parameter optimization, the adaptive inertial weighted particle swarm optimization algorithm is responsible for searching the optimal structure parameters of the random forest, and the prediction performance of the random forest is fed back to the first two algorithms to adjust their operating parameters, forming a closed-loop optimization system. The process of bidirectional interaction of the three algorithm parameters is as follows: Figure 3 As shown, the specific content is as follows: 3.4.1 Bidirectional Interaction between Single Pendulum Wave Algorithm and Adaptive Inertia Weighted Particle Swarm Optimization Algorithm 1. Parameter adjustment of particle swarm optimization using the single pendulum wave algorithm Inertial weights of particle swarm The inertia weight directly affects the algorithm's search capability: a larger inertia weight is needed in the early stages of iteration to enhance global search capability and avoid getting trapped in local optima; a smaller inertia weight is needed in the later stages of iteration to improve local convergence accuracy. Displacement value of a single pendulum wave. It exhibits periodic dynamic change characteristics, and the inertia weight can be adaptively adjusted through its absolute value. The adjustment formula is as follows: ; In the formula, For the first Inertia weights in the next iteration This represents the absolute value of the pendulum wave displacement. In the initial stages of iteration, the pendulum wave amplitude is relatively large. Approaching 1, near This enhances the global search; as iterations proceed, the amplitude gradually decreases. reduce, Towards This mechanism improves local convergence accuracy by leveraging the dynamic characteristics of a single pendulum wave to ensure that changes in inertia weights align with the stage requirements of parameter optimization, thus overcoming the shortcomings of fixed inertia weights in traditional PSO (Precision Optimization Sort).

[0048] 2. Parameter feedback of the particle swarm optimization algorithm for a single pendulum wave Amplitude of a simple pendulum wave and cycle The adjustment effect of the displacement signal directly affects the search state of the particle swarm, i.e., the magnitude of the model error. When the average fitness value of the particle swarm is large, i.e., the model error is large, the amplitude and period need to be increased to expand the displacement change range and help the particle swarm escape the local optimum. When the average fitness value is small, i.e., the model error is small, the amplitude and period need to be decreased to make the displacement change more refined and help with accurate convergence.

[0049] First calculate the... The average fitness value of the particle swarm at the next iteration: ; In the formula, The average fitness value of the particle swarm. For particle swarm scale, For the first The fitness value of each particle.

[0050] The amplitude and period of the pendulum wave are adjusted based on feedback from the average fitness value: ; ; In the formula, , Given the initial amplitude and period, , This is the adjustment coefficient. Meanwhile, the real-time angular frequency of the pendulum wave is derived from its period: ; This feedback mechanism enables the vibration characteristics of the pendulum wave to be matched with the search state of the particle swarm in real time, forming a positive cycle of particle swarm search state → pendulum wave parameter adjustment → particle swarm performance improvement.

[0051] 3.4.2 Bidirectional Interaction between Adaptive Inertia Weighted Particle Swarm Optimization Algorithm and Random Forest 1. Parameter optimization of random forest by particle swarm optimization The structural parameters of random forest ( , , The particle swarm directly determines model performance; it searches for the optimal parameter combination through collective cooperation. The global optimal position of the particle swarm in the next iteration. The optimal parameter combination found in the current search is directly updated to the real-time parameters of the random forest. The update formula is as follows: ; ; In the formula, , , For the first The number of decision trees, maximum depth, and minimum number of sample splits in the random forest during each iteration. Through this update mechanism, the structural parameters of the random forest are continuously optimized with the iterative search of the particle swarm, avoiding the subjectivity and limitations of manually setting parameters.

[0052] 2. Random Forest's Adjustment of Particle Swarm Optimization Learning Factor Particle swarm optimization learning factor (Individual cognitive factors) and (Social cooperation factor) determines the particle search strategy: The larger the particle is, the more it tends to follow its own historical best position, and the stronger its exploration ability. The larger the learning factor, the more likely particles are to follow the optimal position of the group, resulting in stronger convergence. The learning factor needs to be dynamically adjusted based on the prediction error of the random forest to achieve a balance between exploration and convergence.

[0053] First calculate the... The mean absolute error (MAE) of the random forest at the nth iteration: ; In the formula, The mean absolute error of the random forest is... The number of samples in the training set. For the first The actual settlement of each sample For the first In the nth iteration, the random forest... The predicted value for each sample, For the initial iteration ( The average absolute error at that time is used as the error benchmark value.

[0054] Adjust the learning factor based on the prediction error: ; ; In the formula, , This is the initial learning factor. When... When the error is large, i.e., the model error is large, Enlarge Decreasing the particle's individual exploration ability helps in searching for a better parameter region; when Smaller, meaning the model error is small. Reduce This increases the swarm optimization capability, enhancing the collective cooperation of particles and accelerating convergence to the optimal parameters. This feedback mechanism allows the particle swarm search strategy to adapt to the performance state of the random forest in real time, improving parameter optimization efficiency.

[0055] 3.4.3 Two-way interaction between the single-pendulum wave algorithm and random forest 1. Angular frequency adjustment of the single pendulum wave algorithm using random forest. The splitting threshold of decision tree nodes in a random forest reflects the fineness of feature splitting. A higher average splitting threshold indicates coarser feature splitting, potentially leading to underfitting in the model; conversely, a lower threshold indicates finer splitting, potentially leading to overfitting. This average threshold is fed back into the pendulum wave algorithm to adjust the angular frequency. This enables precise control over the pace of parameter optimization.

[0056] First calculate the... The average node splitting threshold of all decision trees in the random forest at the next iteration: ; In the formula, The average node splitting threshold. For the first The total number of nodes in all decision trees of the random forest at the time of the next iteration. For the first During the nth iteration The splitting threshold of each node is determined by the Gini coefficient minimization criterion of the CART tree.

[0057] Adjusting the angular frequency of a pendulum wave based on the average splitting threshold: ; In the formula, The initial angular frequency, This is the angular frequency adjustment coefficient. When... When the value is large, indicating model underfitting, As the frequency of the pendulum wave displacement increases, it accelerates the particle swarm's parameter adjustments, optimizing the model structure. When the risk of model overfitting is relatively small, The reduction in displacement of the pendulum wave makes the changes more stable, which helps the particle swarm to accurately fine-tune the parameters and balance the model's complexity and generalization ability.

[0058] 2. Single Pendulum Wave Algorithm for Decision Tree Weight Adjustment in Random Forest In random forests, the prediction accuracy of each decision tree varies. Therefore, the weights of the decision trees need to be dynamically adjusted to give higher-accuracy decision trees a greater weight in the final prediction, thereby improving the overall model performance. (The amplitude of a pendulum wave...) The amplitude reflects the confidence level of the current parameter optimization: the larger the amplitude, the higher the uncertainty of the optimization process, and the more necessary it is to balance the weights of each decision tree; the smaller the amplitude, the closer the optimization is to the optimal solution, and the more the contribution of the high-quality decision tree can be highlighted.

[0059] Adjusting decision tree weights based on pendulum wave amplitude: ; In the formula, For the first During the nth iteration The weights of each decision tree For real-time amplitude, The initial amplitude, These are the initial weights. To ensure that the sum of all decision tree weights is 1, the adjusted weights are normalized: ; This adjustment mechanism enables the decision tree weights to dynamically change with the oscillation state of the pendulum wave, achieving adaptive weighting of high-quality decision trees to emphasize their contributions and low-quality decision trees to weaken their influence, thereby improving the prediction accuracy of random forests.

[0060] 3.4.4 Iterative Optimization Process of the Fusion Model The iterative optimization process of the fusion model is the core of the interaction and collaboration among the three algorithms. Through iterative iteration, continuous parameter optimization and model performance improvement are achieved. The specific steps are as follows: 1. Initialization phase ( ): Set the maximum number of iterations Preset error threshold (Iteration stops if the fitness value is less than this threshold); the initial positions of the particle swarm are randomly generated. and initial velocity Ensure that the position and velocity meet the preset boundary constraints; initialize the pendulum wave parameters. , , , Initialize random forest parameters , , Initial weights of the decision tree .

[0061] 2. Fitness calculation: based on the current particle position. The corresponding random forest parameters are used to construct a temporary random forest model, which is then input into the training set. Calculate the fitness value for each particle. Compare the fitness value of each particle with its own historical best value, and update the optimal position of each particle. Among the individual optimal positions of all particles, the position with the smallest fitness value is selected as the global optimal position of the particle swarm. .

[0062] 3. Algorithm Interaction and Parameter Update: Based on the bidirectional interaction formulas in 3.4.1-3.4.3, a full parameter update is completed: The average fitness value of the particle swarm Update the amplitude of the pendulum wave ,cycle and angular frequency ; Displacement value of a single pendulum wave Update the inertia weights of the particle swarm ; Random forest prediction error Update the learning factor of particle swarm optimization , ; Average splitting threshold of random forest Secondary fine-tuning of the pendulum wave angular frequency ; The amplitude of a single pendulum wave Update the decision tree weights of the random forest ; The global optimal position of the particle swarm Update the structure parameters of the random forest , , .

[0063] 4. Particle position and velocity update: based on the updated particle swarm parameters , , The particle's velocity and position are updated according to the following formula: ; ; In the formula, and To increase the randomness of the search, the search is performed by generating independent random numbers within the interval [0,1]. and The first During the nth iteration The velocity and position of each particle; if Exceeding If the velocity boundary is reached, then the value is truncated to the corresponding boundary value, such as... Time to take ;like If the position exceeds the boundary, it will be truncated to a reasonable range for the corresponding parameter, such as... At that time, take .

[0064] 5. Iteration Termination Judgment: Set the iteration count... Updated to Repeat steps 2-4 until any of the following conditions are met: Number of iterations ; Global optimal fitness value of particle swarm .

[0065] 6. Fusion Model Determination: After stopping iteration, output the final globally optimal parameters. Optimized pendulum wave parameters , , and the optimized decision tree weights ;use Construct the core structure of a random forest, combined with A weighted prediction is achieved, forming a final prediction model that integrates the three algorithms. Its prediction output formula is: ; In the formula, This represents the final predicted value of the fusion model. For the optimized first Weights of each decision tree For the optimized first The predicted values ​​of each decision tree.

[0066] This fusion model achieves a closed-loop mechanism of parameter optimization, performance feedback, and dynamic adjustment through the bidirectional interaction of three algorithms. It leverages the ensemble prediction advantages of random forests while addressing the issues of strong subjectivity and insufficient generalization ability in traditional random forest parameter settings through the dynamic adjustment of the single pendulum wave algorithm and the global search capability of particle swarm optimization.

[0067] S4: Training and Optimization of Fusion Predictive Model The preprocessed training set is input into the fusion prediction model constructed by S3. Through systematic training and iterative optimization, the prediction accuracy and generalization ability of the model are improved. The training, optimization, and validation of the fusion model are as follows: Figure 4 As shown. Specific implementation details are as follows: Model training implementation: The training set The 168 data records were input one by one into the fusion prediction model. The model then used its internally optimized random forest structure (including the optimal number of decision trees) to perform the prediction. Maximum depth Minimum number of sample splits ) and decision tree weights For the feature vector of each sample ( Perform the calculation and output the corresponding predicted settlement value. During training, the prediction results of each decision tree and the overall output of the model are recorded in real time, providing data support for subsequent error analysis and parameter adjustment.

[0068] Training error evaluation: Three core metrics are used to quantitatively evaluate the model's performance on the training set, namely root mean square error. Mean absolute error and coefficient of determination The root mean square error (RMSE) reflects the overall deviation between the predicted and actual values; the mean absolute error (MAE) directly reflects the average error of a single prediction; and the coefficient of determination measures the model's fit to the data's changing patterns, with a value ranging from [0,1]. A value closer to 1 indicates a better model fit. The formulas for calculating these three indicators are as follows: ; ; ; in, The number of samples in the training set. For the first The true value of settlement for each sample. This is the model's predicted value for this sample. This represents the mean sedimentation value of all samples in the training set.

[0069] Model iterative optimization: Set the training set performance threshold as follows If the model is trained If the threshold is not reached, it indicates that the model fit is insufficient and parameter adjustments are needed. The adjustment strategy is to adjust the amplitude coefficient of the single pendulum wave algorithm. Adjusted to 0.15, periodic adjustment coefficient Adjusted to 0.08, angular frequency adjustment coefficient Adjusted to 0.05, and the maximum number of iterations for particle swarm optimization was also reduced. Increase the value to 150 to extend the parameter search time. After adjustment, return to the iterative optimization process of S3, and re-perform the global search and fusion optimization of model parameters until the training set... The trained fusion prediction model is obtained. .

[0070] S5: Validation of the fusion prediction model To verify the generalization ability and prediction reliability of the trained model, a systematic validation was performed using an independent test set, as follows: Validate the data input: Use the test set The 72 data records were processed for consistency according to the preprocessing standards of the training set, and then input one by one into the trained fusion prediction model. The model outputs a predicted settlement value for each test sample through its internally optimized algorithm. , .

[0071] Verification error calculation: The same three core metrics as the training set are used. , , The validation performance of the model is evaluated using the same calculation logic as the training set error metric, except that the number of samples is replaced with 72 samples in the test set, ensuring the uniformity of the evaluation criteria and the comparability of the results.

[0072] Verification Result Judgment: The criteria for passing model verification are set as follows: , and If the model meets this criterion, it indicates good generalization ability and can be used for actual support settlement prediction; if it does not meet the criterion, adjustments need to be made by tracing back the previous steps: first, return to S2 to check the data preprocessing process, and replace the outlier handling method with the Z-score method (identifying outliers through the mean and standard deviation), or adjust the missing value imputation grouping strategy; if there are no obvious problems with the data preprocessing, return to S3 to adjust the initial parameters of the algorithm, such as increasing the particle swarm size. Increase the number of parameters to 40, expand the parameter search range, and rebuild and train the model again until the model meets the validation criteria, finally obtaining a usable fusion prediction model. .

[0073] S6: Prediction of Settlement of Highway Bridge Bearings The final validated fusion prediction model was applied to predict the settlement of actual highway bridge bearings, providing data support for bridge maintenance decisions. The specific implementation process is as follows: Data Collection for Prediction: For highway bridge bearings requiring settlement prediction, complete parameter data of the bearings are collected according to the data source standard and collection method of S1, including bearing parameters, environmental impact parameters, and load parameters, forming the dataset for prediction. Each data record to be predicted contains only a feature vector. Without the actual settlement value, the data type and accuracy of the collected data are kept consistent with the training set to avoid increased prediction error due to data differences.

[0074] Preprocessing of data to be predicted: The preprocessing workflow of S2 was followed, including standardization, categorized data encoding, and missing value imputation. The standardization parameters and encoding rules of the training set were strictly adhered to during the process to ensure the accuracy of the preprocessed dataset for prediction. The feature format and numerical range are completely consistent with the training set, eliminating the impact of data preprocessing differences on the prediction results.

[0075] Settlement prediction calculation: The pre-treated... Input the final usable fusion prediction model The model, through the synergistic effect of an internally optimized random forest, pendulum wave algorithm, and adaptive inertia weighted particle swarm optimization algorithm, calculates the feature vector of each support to be predicted and outputs the corresponding predicted annual settlement value. .

[0076] Prediction Results Output and Application: The output prediction results consist of two parts: first, the predicted annual settlement value for a single bearing, accurate to 0.001 mm, with the prediction error range indicated; second, the predicted cumulative settlement value for the next 5 years, calculated by summing the predicted settlement values ​​for each year. The prediction results are compiled into a report, clearly indicating the settlement risk level of the bearings, providing targeted maintenance recommendations to highway management departments. For example, bearings with large settlement may require shorter monitoring cycles or reinforcement treatment, achieving precise alignment between prediction results and maintenance decisions.

[0077] In some embodiments, a gated recurrent unit (GRU) algorithm is introduced to mine the temporal evolution patterns of sedimentation data. The gated recurrent unit has the core advantage of capturing the dependencies of temporal data, which complements the shortcomings of the random forest model in temporal feature modeling and provides temporal dimension prediction support for the fusion model.

[0078] Gated Recurrent Unit (GRU) Algorithm Model Construction 1. Definition of core parameters and time-series processing of GRU model First, the input data is reconstructed temporally: the training set... The five-year monitoring data for each support were organized into a time-series sample sequence according to the time order from year 1 to year 5, and each time-series sample was denoted as . ,in For training set sample index, This refers to the number of time series steps, corresponding to a 5-year monitoring cycle. For the first The first support The feature vector for the year; the corresponding time-series label sequence is , For the first The first support The actual value of annual settlement.

[0079] Define the core parameters of the GRU model: the dimension of the GRU hidden layer is... Parameters to be optimized, initial values Input dimensions Corresponding to the feature vector dimension, output dimension The corresponding single-step settlement prediction value; the GRU reset gate weight matrix is Update the gate weight matrix as follows The candidate hidden state weight matrix is ; Reset the gate bias vector to Update the gate bias vector as The candidate hidden state bias vector is The GRU output layer weight matrix is: The output layer bias vector is The GRU learning rate is initial value The number of training iterations is initial value .

[0080] 2. Gating Mechanism and Output Calculation of GRU Model GRU dynamically adjusts the retention and forgetting of time-series information through reset and update gates to adapt to the characteristics of slow accumulation and time-series correlation of settlement. The specific gating mechanism and output calculation process are as follows: Reset Gate Calculation: The reset gate determines the degree to which historical hidden states are forgotten. The closer the output value is to 0, the more historical information is forgotten; the closer it is to 1, the more historical information is retained. The calculation formula is: ; In the formula, For the first Step-time reset gate output, dimension , It is a sigmoid activation function with a value range of [0,1]. For the first The GRU hidden state of the step, with dimension . Initial hidden state , zero vector; This represents concatenating the historical hidden state with the current step feature vector, with a dimension of [missing information]. .

[0081] Update gate calculation: The update gate determines the fusion ratio of historical information and current information in the current hidden state. The closer the output value is to 1, the more historical information is retained; the closer it is to 0, the more emphasis is placed on current information. The calculation formula is: ; In the formula, For the first The update gate output of the step sequence, with dimension . .

[0082] Candidate hidden state calculation: After adjusting the historical hidden states based on the reset gate output, candidate hidden states are generated by combining them with the feature vector of the current step, capturing new information in the current time series. The calculation formula is as follows: ; In the formula, For the first Candidate hidden states of each step (dimension) ), is the hyperbolic tangent activation function, with a value range of [-1, 1]. This is element-wise multiplication, multiplying element by element to achieve proportional forgetting of historical hidden states.

[0083] Final hidden state calculation: By fusing the historical hidden states and candidate hidden states through the update gate output, the final hidden state of the current step is obtained. This state contains the temporal feature information up to the current step. The calculation formula is: ; In the formula, For the first The final hidden state of the step, with dimension . ; Indicates the weight of the new information. This indicates the weight of historical information.

[0084] GRU single-step output calculation: The final hidden state is mapped to the single-step settlement prediction value through the output layer. The calculation formula is as follows: ; In the formula, For the GRU model, the first The first support Predicted annual subsidence, dimension 1.

[0085] 2. GRU Model Training Process The training objective of the GRU model is to minimize the temporal loss between the single-step predicted value and the true value. The mean squared error (MSE) is used as the loss function, calculated as follows: ; In the formula, This represents the temporal loss value of the GRU model. The number of samples in the training set. For the number of timing steps, For the first The first support The actual value of annual settlement.

[0086] The GRU's weight matrices and bias vectors are updated using a stochastic gradient descent (SGD) optimizer. The parameter update formula is: ; In the formula, Represents any parameter of the GRU that needs to be updated. This is the partial derivative (gradient) of the loss function with respect to that parameter. This is the learning rate.

[0087] During training, each iteration Calculate the training set temporal loss once, if continuous The decrease in loss value in the next iteration is less than If the training stops, the initial training of the GRU model is obtained. .

[0088] 3. Bidirectional interaction and integration of GRU with three existing algorithms GRU interacts bidirectionally with Random Forest (RF), Single Pendulum Wave (SS), and Adaptive Inertial Weighted Particle Swarm Optimization (PSO) in pairs. Through parameter transfer and feedback adjustment, it achieves deep synergy between temporal feature modeling and traditional ensemble learning and optimization algorithms. The specific interaction mechanism is as follows: (1) Bidirectional interaction between GRU and Random Forest (RF) GRU enhances the features of random forests. GRU's final hidden state The temporal evolution characteristics of support settlement are included and concatenated as additional temporal features into the input feature vector of the random forest, enhancing the random forest's ability to capture temporal dependencies. The feature concatenation formula is as follows: ; In the formula, Input feature vectors (dimensions) to the enhanced random forest ), For the first The first support The original feature vector of the year, 19 dimensions; For GRU The final hidden state of the step. dimension.

[0089] Random forests use enhanced feature vectors After training and predicting the decision tree, the prediction output formula of the random forest is updated as follows: ; In the formula, To enhance features, random forests are applied to the first... Predicted annual subsidence For the first The decision tree is based on the enhanced features of the first Step-by-step predicted value , The number and weights of the optimized decision trees.

[0090] Random Forest's Loss Feedback Adjustment for GRU The prediction error of the random forest is fed back to the GRU, and the learning rate of the GRU is dynamically adjusted. This improves the training accuracy of GRU. First, the training accuracy of the random forest is calculated. Step prediction error : ; In the formula, For the random forest The absolute error of the step.

[0091] The learning rate of the GRU is adjusted based on this error, using the following formula: ; In the formula, For the first The dynamic learning rate of the GRU in step-time sequence, The initial learning rate, This is the learning rate adjustment coefficient for the GRU. When the random forest error is large, the learning rate is increased to speed up the GRU parameter updates; when the error is small, the learning rate is decreased to finely adjust the parameters.

[0092] (2) Bidirectional interaction between GRU and single pendulum wave algorithm (SS) Gating threshold adjustment of GRU using a single pendulum wave algorithm Displacement value of a simple pendulum wave This reflects the dynamic state of parameter optimization and is used to adjust the effective threshold of the GRU update gate, balancing the preservation of temporal information with the update rhythm. The dynamic threshold of the GRU update gate is defined. : ; In the formula, For the first The dynamic threshold of the update gate is set in step [0.2, 0.8]). For the first The displacement value of the pendulum wave in the next iteration.

[0093] When updating the gate output When it is determined to be a strong temporal memory mode, more historical hidden state information is retained; when When this is determined to be a strong current update mode, it focuses on learning the feature information of the current step, and the adjustment formula is: ; In the formula, The adjusted update gate output is used to match the GRU's temporal memory rhythm with the dynamic optimization state of the pendulum wave, improving the targeting of temporal feature capture. The adjusted GRU hidden state update formula is synchronously corrected as follows: ; GRU Amplitude Feedback Adjustment for Single Pendulum Wave Algorithm GRU's reset gate output Reflects the degree of forgetting historical information. A smaller value indicates more forgotten historical information (new temporal patterns need to be explored), which is then fed back into the pendulum wave algorithm to dynamically adjust the amplitude. This enhances the dynamic adjustment adaptability of the pendulum wave. The amplitude adjustment formula is: ; In the formula, For the first The mean of the reset gate output for all training samples. This is the amplitude adjustment coefficient for a single pendulum wave. For the first in S3412 The amplitude of the pendulum wave in the next iteration. When the time is relatively short (a large amount of historical time sequence information is forgotten). Increasing the range of displacement variation of the pendulum wave helps the particle swarm explore better parameters; when When it is large, Stable, with finely adjustable parameters.

[0094] (3) Bidirectional interaction between GRU and adaptive inertial weighted particle swarm optimization (PSO) Particle swarm optimization for GRU parameter optimization Hiding the core parameters to be optimized in GRU: Dimension Initial learning rate Output layer weights The key elements are incorporated into the optimization dimension of the particle swarm optimization, expanding the particle position vector and improving the parameter rationality of the GRU model. The expanded particle position vector is: ; In the formula, For the first The dimension of the GRU hidden layer corresponding to each particle, and the boundary. ; For the first The initial learning rate of the GRU for each particle, and the boundary value. ; For the first The GRU output layer weights corresponding to each particle, and the boundary .

[0095] Accordingly, the particle fitness function is updated to a weighted sum of the random forest prediction error and the GRU time-series loss, and the performance of the fusion model is comprehensively evaluated: ; In the formula, These are weighting coefficients used to balance the errors of the two models; For the first The GRU time-series loss value corresponding to each particle. Through this fitness function, the particle swarm optimization simultaneously optimizes the core parameters of the random forest and GRU, achieving collaborative adaptation between the two.

[0096] GRU inertial weight feedback adjustment of particle swarm GRU time series prediction loss The accuracy of the temporal modeling is reflected and fed back to the particle swarm optimization algorithm to dynamically adjust the inertia weights. This improves the parameter search efficiency of the particle swarm optimization. First, the normalized value of the GRU temporal loss is calculated: ; In the formula, For the first The normalized value range of the GRU loss in the next iteration is [0,1]. This represents the minimum GRU loss during the iteration process. This represents the maximum value of the GRU loss during the iteration process.

[0097] The particle swarm inertia weight is adjusted based on the normalized loss, and the adjustment formula is as follows: ; In the formula, For the first The particle swarm inertia weight of the next iteration, This is the particle swarm inertia weight adjustment coefficient. When the GRU timing loss is large, Approaching 1, Reduce the loss to enhance the local search capability of the particle swarm optimization and quickly optimize the relevant parameters of GRU; when the loss is small, Stability is maintained by balancing global search with local convergence.

[0098] (4) Supplementary iterative optimization of the four-algorithm fusion model containing GRU Based on the iterative optimization process, additional parameter initialization and update steps related to GRU are added to form a complete iterative process integrating four algorithms: 1. Initialization phase, : Initialize the new GRU parameters. , Weight matrix Random initialization, following a uniform distribution in the range [-0.1, 0.1]; bias vector Initialize to a zero vector; expand the particle position vector and fitness function, and synchronously initialize the expanded particle positions. .

[0099] 2. Fitness Calculation Stage: A new GRU temporal loss calculation is added, based on the GRU parameters corresponding to the current particle position during training. ,calculate Substitute the updated fitness function to calculate .

[0100] 3. Algorithm Interaction and Parameter Update Stage: A new bidirectional interaction step is added to complete the parameter inter-tuning between GRU and RF, SS, and PSO, such as GRU feature enhancement, learning rate adjustment, single pendulum wave amplitude adjustment, and particle swarm inertia weight adjustment.

[0101] 4. Model determination after iteration termination: After stopping iteration, output the optimized GRU parameters. Construct the optimized GRU model The final output of the fusion model is a weighted fusion of the random forest predictions and the GRU predictions, with the weights determined through iterative optimization. , The formula is: ; In the formula, This represents the final predicted settlement value from the four-algorithm fusion model. To optimize the predictions of the random forest, To optimize the predictions of GRU, To integrate weights, satisfy .

[0102] The four-algorithm fusion model supplements the temporal modeling capability with GRU, and at the same time realizes the collaborative mining of temporal and non-temporal features and dynamic optimization of parameters through two-way bidirectional interaction, which significantly improves the prediction accuracy and generalization ability of bridge bearing settlement.

[0103] Based on the newly added GRU-related content, the training, validation, and prediction content adapted to GRU in S4-S6 is supplemented as follows: S4: Model Training The training phase adds core GRU-related steps to the original process: In the initialization phase, new GRU structural parameters such as hidden layer dimensions and initial learning rate are added, along with the initialization of gating / output layer weight biases. The particle swarm position vector is also expanded to incorporate GRU core parameters into the optimization dimension, and the interaction coefficients and fusion weights between GRU and other algorithms are initialized. During iterative training, GRU temporal prediction is completed first, and temporal loss is calculated. Then, bidirectional interaction between GRU and RF, SS, and PSO is implemented sequentially. GRU outputs hidden states to enhance RF input features, and RF prediction errors inversely adjust the GRU learning rate. GRU resets the gate mean to adjust SS amplitude, and SS displacement dynamically adjusts the GRU gate threshold. GRU normalizes the loss to optimize PSO inertial weights, and PSO synchronously optimizes GRU core parameters through an expanded fitness function. Finally, the fusion loss is calculated, and the iteration termination condition is determined. After training, in addition to solidifying the original algorithm parameters, the GRU gating, output layer, structural parameters, and the final determined fusion weights are also solidified.

[0104] S5: Model Validation During the validation phase, the validation set data is first reconstructed temporally according to the training set format; in terms of evaluation dimensions, T-MAE, T-RMSE, and T-RMSE are added. Time-series metrics were used to specifically evaluate the time-series prediction performance of GRU. A comparative experiment with and without interaction was designed to verify the effectiveness of bidirectional interaction between GRU and random forest, single-pendulum wave, and particle swarm optimization in reducing model loss and improving convergence speed. Finally, the MAE, RMSE, and other metrics of the fusion model were integrated. Calculate the comprehensive evaluation score and compare it with the original three algorithm models to verify the overall performance improvement effect after introducing GRU.

[0105] S6: Model Application In the application phase, the monitoring data of the supports to be predicted are first preprocessed into time series, and missing year data are filled in by linear interpolation. Then, time series prediction is completed based on the fixed GRU parameters, including stepwise calculation of gating states and predicted values, and prediction of settlement in future years based on the trend extension of hidden states. At the same time, the interaction parameters such as GRU gating parameters, PSO inertial weights, and the number of RF decision trees are adjusted in real time according to the missing rate and noise level of the data to be predicted. Finally, the prediction results of GRU and RF are merged and output, and the actual monitoring error is fed back to the training stage. When the error exceeds the engineering threshold, data is added and the model is retrained. The global error is summarized periodically and the fusion weights are iteratively optimized.

Claims

1. A highway bridge support settlement prediction method based on random forest, characterized in that, Includes the following steps: S1: Collect the self-parameters, environmental impact parameters, load parameters, and actual settlement data of the highway bridge bearings to form the original dataset; S2: Preprocess the original dataset to obtain the training set and the test set; S3: Construct a fusion prediction model that integrates random forest, single pendulum wave algorithm and adaptive inertial weighted particle swarm optimization algorithm; S4: Input the training set into the fusion prediction model for model training and optimization. Complete the model optimization through error evaluation and parameter adjustment to obtain the optimized fusion prediction model. S5: Input the test set into the optimized fusion prediction model to verify it, ensuring that the model meets the preset performance standards, and obtain the final fusion prediction model; S6: Collect the support data to be predicted and preprocess it according to the method in S2. Input the preprocessed support data into the final usable fusion prediction model and output the support settlement prediction result.

2. The random forest-based highway bridge support settlement prediction method of claim 1, wherein, Both the training and test sets contain feature vectors and corresponding true settlement values. The fusion prediction model works as follows: the Adaptive Inertial Weighted Particle Swarm Optimization (AIOPE) algorithm calculates particle fitness values ​​based on the feature vectors and true settlement values ​​to obtain the average fitness value; the Pendulum Wave Algorithm receives the average fitness value and generates a dynamic displacement signal; the AIOPE adjusts the inertial weights based on this dynamic displacement signal and searches for the optimal structure parameters of the Random Forest; the Random Forest uses these optimal structure parameters to process the feature vectors and outputs predicted values, while simultaneously calculating the prediction error and the average node splitting threshold, which are fed back to the AIOPE and the Pendulum Wave Algorithm, respectively; the AIOPE adjusts the learning factor based on the prediction error, and the Pendulum Wave Algorithm adjusts the angular frequency based on the average node splitting threshold and outputs an amplitude signal; the Random Forest adjusts the decision tree weights based on this amplitude signal. Through this closed-loop data flow, the three algorithms achieve bidirectional interaction and model parameter optimization. 3.The random forest-based highway bridge support settlement prediction method of claim 1, wherein, In S1, the bearing parameters themselves are derived from the bridge design drawings and the bearing manufacturer's technical specifications, the environmental impact parameters are derived from meteorological observation data and on-site environmental monitoring records, the load parameters are derived from the traffic flow monitoring system and the bridge structure stress calculation report, and the settlement measurement data are obtained by monitoring and calculating through measuring equipment. 4.The random forest-based highway bridge support settlement prediction method of claim 1, wherein, The preprocessing of S2 is as follows: outliers are detected and replaced using box plot method; missing values ​​are filled according to the mean of the same type of bearing data or the mean of the bearing data within the same bridge; numerical parameters are standardized; categorical parameters are one-hot encoded; and training and test sets are randomly divided proportionally. 5.The random forest-based highway bridge support settlement prediction method of claim 1, wherein, The model training optimization in S4 includes: evaluating the training error using root mean square error, mean absolute error, and coefficient of determination; if the coefficient of determination does not reach the preset threshold, adjusting the adjustment coefficient of the pendulum wave algorithm and the maximum number of iterations of the particle swarm optimization algorithm, and returning to S3 to perform closed-loop optimization again until the training performance requirements are met. 6.The random forest-based highway bridge support settlement prediction method of claim 1, wherein, The settlement prediction results of S6 include the annual settlement prediction value and the future cumulative settlement prediction value of a single support. The annual settlement prediction value is marked with the prediction error range, and the cumulative settlement prediction value is obtained by accumulating the prediction values ​​year by year. At the same time, the settlement risk level of the support and maintenance recommendations based on the prediction results are output. 7.The random forest-based highway bridge support settlement prediction method of claim 2, wherein, The particle fitness value is calculated based on the root mean square error of the random forest prediction; the smaller the error, the better the corresponding particle fitness value. 8.The random forest-based highway bridge support settlement prediction method of claim 2, wherein, When generating dynamic displacement signals using the single pendulum wave algorithm, the amplitude and period of the wave are first adjusted by the average fitness value, and then the displacement function is constructed based on the adjusted amplitude, period and angular frequency to obtain the dynamic displacement signal. 9.The random forest-based highway bridge support settlement prediction method of claim 2, wherein, The optimal structural parameters of random forests include the number of decision trees, the maximum depth of decision trees, and the minimum number of sample splits for each decision tree node. These parameters are determined by the adaptive inertial weighted particle swarm optimization algorithm through a collaborative search. 10.The random forest-based highway bridge support settlement prediction method of claim 2, wherein, The closed-loop termination conditions for the three algorithms are: the number of iterations reaches the preset maximum number of iterations, or the global optimal fitness value of the adaptive inertial weighted particle swarm optimization algorithm is less than the preset error threshold.

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