A method for predicting impact factor of a bridge structure under aircraft load

Abstract

This invention discloses a method for predicting the impact coefficient of bridge structures under aircraft loads, belonging to the field of engineering structural analysis technology. The method includes: constructing an impact coefficient sample library based on the dynamic response data of bridges under aircraft loads; constructing a gradient boosting regression model based on the impact coefficient sample library, with input parameters as input features and the impact coefficient as the target output; adaptively searching the hyperparameters of the gradient boosting regression model using a heuristic optimization algorithm to obtain multiple model optimization results; selecting the optimal gradient boosting regression model from the multiple model optimization results with the goal of minimizing the validation set error or achieving the optimal comprehensive evaluation index; and inputting the input parameters to be measured into the optimal gradient boosting regression model to obtain the predicted impact coefficient value. This invention comprehensively explores the hyperparameter space from different perspectives, significantly increasing the probability of finding the global optimal solution and providing a reliable guarantee for the accurate prediction of the impact coefficient of bridges under aircraft loads.

Description

Technical Field

[0001] This invention relates to the field of engineering structural analysis technology, and in particular to a method for predicting the impact coefficient of a bridge structure under aircraft load. Background Technology

[0002] In the design and evaluation of aircraft-loaded bridge structures such as airport runway bridges and taxiway bridges, the impact coefficient is an important indicator characterizing the amplification effect of aircraft dynamic loads on the bridge structure response. In current engineering practice, the determination of the impact coefficient usually relies on empirical values, simplified formulas, or numerical simulation results, which are insufficient to fully reflect the complex nonlinear dynamic characteristics under the combined action of multiple parameters such as aircraft landing conditions and bridge structural characteristics.

[0003] With the diversification of aircraft models and airport bridge structures, the impact coefficient exhibits nonlinear characteristics under different working conditions. Data-driven methods are gradually being introduced into the field of engineering structural analysis. By constructing a mapping relationship between input parameters and target responses, rapid prediction of complex dynamic problems can be achieved. The process of data-driven methods in the dynamic analysis of engineering structures includes: implementing machine-bridge coupled simulation based on finite element method and multibody dynamics to obtain structural dynamic response data under different working conditions and simultaneously calculating the corresponding impact coefficients; sorting and constructing input feature vectors (which may include load condition parameters and structural characteristic parameters, etc.), performing dimensionless / normalization, outlier processing, and necessary feature combinations on the samples to form a standardized training dataset; dividing the sample set into training / validation / test sets (or using cross-validation), selecting a regression-type machine learning model to learn the nonlinear mapping relationship between "input parameters and target responses," and training and generalizing the model through error indices; and solidifying the trained model into an engineering-callable predictor that can quickly output the target response given a new combination of parameters, thereby replacing a large number of repetitive and costly dynamic simulations and achieving rapid evaluation and scheme comparison for complex dynamic problems.

[0004] However, existing data-driven methods often employ a single optimization strategy or a fixed modeling process, with model parameter selection relying on human experience, making them prone to getting trapped in local optima and limiting the model's generalization ability. Summary of the Invention

[0005] Therefore, it is necessary to provide a method for predicting the impact coefficient of bridge structures under aircraft loads to address the aforementioned technical problems.

[0006] This invention provides a method for predicting the impact coefficient of an aircraft-loaded bridge structure, comprising: An impact coefficient sample library is constructed based on the dynamic response data of bridges under aircraft load. The impact coefficient sample library includes multiple sample combinations. Each sample combination consists of a set of input parameters and corresponding impact coefficient output values. The input parameters include aircraft landing state parameters and bridge structural characteristic parameters. Based on the impact coefficient sample library, a gradient boosting regression model is constructed with input parameters as input features and impact coefficient output value as the target output, and the hyperparameters of the gradient boosting regression model are preset. Bayesian optimization, genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and simulated annealing / random search and local search hybrid algorithm are used as heuristic optimization algorithms to adaptively search the hyperparameters of the gradient boosting regression model, and obtain multiple model optimization results. With the goal of minimizing the validation set error or the optimal comprehensive evaluation index, the optimal gradient boosting regression model is selected from the multiple model optimization results. The input parameters to be tested are input into the optimal gradient boosting regression model to obtain the corresponding predicted values ​​of the impact coefficient.

[0007] Alternatively, the impact coefficient output value can be determined based on the following formula: ; in, I c This is the output value of the impact coefficient. Y d,max The maximum vertical dynamic displacement response of the bridge structure caused by aircraft load. Y j,max The maximum static vertical displacement response of the bridge structure caused by aircraft load.

[0008] Optionally, the aircraft landing status parameters include: landing mass, touchdown speed, descent speed, pitch angle, and roll angle; Bridge structural characteristic parameters include: span, pier height, structural damping ratio, and three-dimensional unevenness of the bridge deck.

[0009] Optionally, an impact coefficient sample library is constructed based on the dynamic response data of bridges under aircraft loads, specifically including: Dynamic response data are obtained from one or more of the following: numerical simulation results, existing engineering analysis results, or experimental test results. Random average sample combinations are generated within the range of values ​​of dynamic response data using parameter space design methods, which include one or more of orthogonal experimental design, Latin hypercube sampling, uniform design, or Monte Carlo sampling.

[0010] Optionally, based on the impact coefficient sample library, a gradient boosting regression model is constructed, using the input parameters as input features and the impact coefficient as the target output, specifically including: The input parameters are preprocessed by dimensionless transformation, normalization, and outlier identification to obtain an initial feature set; A feature selection method based on mutual information or correlation coefficient is adopted to determine the correlation between each feature in the initial feature set and the output value of the impact coefficient, and to select features whose correlation meets the preset conditions to obtain the optimized initial feature set. Based on the optimized initial feature set and the output value of the impact coefficient, a gradient boosting decision tree framework is used to construct the base learner; The optimized initial feature set is used as the model input, and the impact coefficient output value is used as the model output. The base learner is trained through multiple rounds of iteration. The number of model iterations is determined by K-fold cross-validation and early stopping method to gradually approximate the nonlinear mapping relationship between the input parameters and the impact coefficient output value, thus obtaining the gradient boosting regression model. Specifically, for each iteration of the training process, the negative gradient between the predicted value of the base learner in the previous iteration and the output value of the impulse coefficient is used as the residual approximation value. The residual approximation value is then used as the target output of the base learner in the current iteration to obtain the base learner for the current iteration. The base learner in the current iteration is then fused with the base learner in the previous iteration to update the gradient boosting regression model.

[0011] Optionally, hyperparameters include one or more of the following: learning rate, number of weak learners, tree depth, minimum number of samples per leaf node, feature sampling ratio, sample sampling ratio, and regularization parameter.

[0012] Optionally, Bayesian optimization, genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and simulated annealing / random search and local search hybrid algorithm are used as heuristic optimization algorithms to adaptively search for the hyperparameters of the gradient boosting regression model, resulting in multiple model optimization results, including: The Bayesian optimization algorithm includes: representing the mapping relationship between hyperparameters and model error through a surrogate model, and selecting the next set of candidate hyperparameters through a collection function; Genetic algorithms include: population evolution search of hyperparameters through selection, crossover, and mutation; Differential evolution algorithm, including: global optimization of continuous hyperparameters through differential mutation and selection mechanisms; Particle swarm optimization algorithms include: iteratively and collaboratively searching for hyperparameters through particle velocity and position; The simulated annealing / random search and local search hybrid algorithm includes: global search through random perturbation, and global optimization of hyperparameters by combining the probabilistic acceptance criteria of local search and simulated annealing.

[0013] Optionally, the comprehensive evaluation index includes one or more of the following: mean absolute error, root mean square error, goodness of fit, and engineering safety deviation index.

[0014] The method for predicting the impact coefficient of an aircraft-loaded bridge structure provided in this embodiment of the invention has the following advantages compared with the prior art: This invention adaptively searches for hyperparameters of a gradient boosting regression model by integrating multiple heuristic optimization algorithms. The parallel use of these algorithms fully leverages their respective advantages: Bayesian optimization effectively approximates the global optimum by utilizing historical information; genetic algorithms and differential evolution effectively avoid local convergence through population evolution and mutation operations; particle swarm optimization accelerates the search through a group cooperation mechanism; and a hybrid strategy of simulated annealing and local search balances global exploration and local fine-tuning.

[0015] This diverse search mechanism complements each other, comprehensively exploring the hyperparameter space from different perspectives, greatly increasing the probability of finding the global optimum. It overcomes the limitations of single optimization strategies or manual parameter tuning, which are prone to getting trapped in local optima. This ensures that the selected model has the strongest generalization ability and robustness, providing a reliable guarantee for the accurate prediction of the bridge impact coefficient under aircraft load. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a method for predicting the impact coefficient of an aircraft-loaded bridge structure, as provided in one embodiment. Figure 2 This is a schematic diagram of a machine-bridge coupling analysis model for a method of predicting the impact coefficient of an aircraft-loaded bridge structure provided in one embodiment. Figure 3 This is a database distribution map of a method for predicting the impact coefficient of an aircraft-loaded bridge structure provided in one embodiment. Figure 3 (a) in the diagram is a schematic diagram of the impact coefficient sample library. Figure 3 (b) in the figure is a distribution map of the training database. Figure 3 (c) in the diagram represents the distribution range of the test database; Figure 4 This is a radar chart showing the impact coefficient analysis results of an aircraft-loaded bridge structure impact coefficient prediction method provided in one embodiment. Figure 4 (a) in the image is a radar chart showing the results of the root mean square error analysis. Figure 4 (b) in the image is a radar chart showing the goodness-of-fit analysis results. Figure 4 (c) in the image is a radar chart showing the results of the mean absolute error analysis. Figure 5 A flowchart illustrating the model construction process for a method for predicting the impact coefficient of an aircraft-loaded bridge structure, as provided in one embodiment. Figure 6 This is a schematic diagram illustrating the performance verification of an impact coefficient prediction method for an aircraft-loaded bridge structure provided in one embodiment. Figure 6(a) in the diagram is a performance verification diagram of the gradient boosting tree regression algorithm. Figure 6 (b) in the diagram is a performance verification illustration of the extreme gradient boosting tree regression algorithm. Figure 6 (c) in the figure is a schematic diagram of the performance verification of the lightweight gradient boosting decision tree regression algorithm. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0018] In the design and evaluation of aircraft-loaded bridge structures such as airport runway bridges and taxiway bridges, the impact coefficient is an important indicator that characterizes the amplification effect of aircraft dynamic loads on the bridge structure response.

[0019] (1) Highway and railway bridges.

[0020] Research on the impact coefficient of highway and railway bridges is relatively mature. Scholars mostly study the values ​​and calculation methods of the impact coefficient of highway and railway bridges through field measurements, numerical simulations, and theoretical analysis. Moreover, relevant design specifications have given clear provisions on the values ​​of their impact coefficient / dynamic coefficient: JTG D60-2015 stipulates that the impact coefficient of highway bridges is a function of the bridge's fundamental frequency, and its range is between 0.05 and 0.45; TB 10002-2017 stipulates that the value of the dynamic coefficient of railway bridges is related to the bridge span.

[0021] (2) Skid bridge.

[0022] A. Existing engineering examples: Currently, MH / T5063-2023, based on the survey results of typical airport taxiway bridges at home and abroad, has made provisions for the value of the impact coefficient of taxiway bridges, and recommends that it be taken as 0.45.

[0023] B. On-site measurement: Using aircraft running on the taxiway as the loading tool, displacement gauges, strain gauges and other measuring equipment were installed at the bottom of the taxiway to conduct load tests on the airport taxiway. The dynamic response of the taxiway under aircraft loads, such as deflection, stress and strain, was measured, and the value, distribution range and calculation formula of the bridge impact coefficient under different aircraft taxiing conditions were determined.

[0024] C. Numerical Simulation: A numerical analysis model of the bridge was established using finite element software such as ANSYS and ABAQUS. The aircraft load was applied to the bridge structure as a moving load. The relationship between the impact coefficient of the taxiway bridge and the influencing parameters such as bridge surface smoothness, aircraft taxiing speed, and bridge cross-sectional shape was analyzed. Based on this, the distribution range, influencing parameters, and calculation formula of the impact coefficient of the taxiway bridge were studied.

[0025] (3) Runway bridge.

[0026] Different scholars have different considerations regarding the values ​​of the impact coefficient / dynamic coefficient of runway bridges. Some scholars, through analysis of existing runway bridges, have pointed out that the impact force on runway bridges is significant, potentially exceeding 100% of the aircraft's weight. However, considering the vibration reduction of the cushioning system and fuel consumption, they suggest a runway bridge impact coefficient of 0.6. Other scholars have noted that the runway bridge dynamic coefficient can reach 1.8 during Boeing 747-400 landings, and even as high as 4.0 when pilot mishandling causes abnormal impact. To address the ambiguity in the runway bridge impact coefficient value, some scholars have statistically analyzed the impact coefficient characteristics based on numerical results and established an impact coefficient regression model using stepwise linear regression.

[0027] As can be seen from the above description of existing technologies, in current engineering practice, the determination of the impact coefficient usually relies on empirical values, simplified formulas, or numerical simulation results, which are insufficient to fully reflect the complex nonlinear dynamic characteristics under the combined action of multiple parameters such as aircraft landing conditions and bridge structural characteristics. With the diversification of aircraft types and airport bridge structural forms, the impact coefficient exhibits nonlinear characteristics under different operating conditions. Simply relying on empirical formulas or linear regression models makes it difficult to balance prediction accuracy and applicability. Furthermore, although refined numerical simulations can obtain highly accurate dynamic response results, their high computational cost and complex parameter combinations make them difficult to directly serve the need for rapid assessment of impact coefficients under multiple operating conditions in the engineering design phase.

[0028] This invention provides a method for predicting the impact coefficient of bridge structures under aircraft loads, addressing the nonlinear characteristics of the bridge impact coefficient under aircraft loads due to multi-parameter coupling. By constructing a sample dataset of impact coefficients including input variables such as aircraft landing state parameters and bridge structural characteristic parameters, a nonlinear mapping relationship is established between the impact coefficient and multi-dimensional influencing parameters, thereby achieving rapid prediction and reliable assessment of the impact coefficient under different working conditions.

[0029] Meanwhile, this invention introduces a unified heuristic optimization framework to adaptively search and optimize the key hyperparameters of the gradient boosting regression model, reducing the uncertainty caused by manual parameter selection and improving the model's accuracy, stability, and generalization ability. Through these technical means, this invention significantly reduces the computation and trial calculation costs in engineering applications while ensuring prediction accuracy, providing effective support for the rapid determination of impact coefficients, scheme comparison, and risk assessment in the airport bridge design phase.

[0030] Specifically, such as Figure 1 As shown. The present invention includes:

[0031] An impact coefficient sample library is constructed based on the dynamic response data of bridges under aircraft loads. The impact coefficient sample library includes multiple sample combinations. Each sample combination consists of a set of input parameters and corresponding impact coefficient output values. The input parameters include aircraft landing state parameters and bridge structural characteristic parameters.

[0032] Based on an impact coefficient sample library, a gradient boosting regression model is constructed, which uses input parameters as input features and impact coefficients as the target output. Hyperparameters of the gradient boosting regression model are preset, including one or more of the following: learning rate, number of weak learners, tree depth, minimum number of samples per leaf node, feature sampling ratio, sample sampling ratio, and regularization parameters.

[0033] Bayesian optimization, genetic algorithm, differential evolution algorithm, particle swarm optimization, and a hybrid algorithm combining simulated annealing / random search and local search are used as heuristic optimization algorithms to adaptively search for the hyperparameters of the gradient boosting regression model, resulting in multiple model optimization results. The optimal gradient boosting regression model is selected from these results with the goal of minimizing the validation set error or achieving the best overall evaluation index.

[0034] The input parameters to be tested are input into the optimal gradient boosting regression model to obtain the corresponding predicted values ​​of the impact coefficient.

[0035] As a preferred implementation, a gradient boosting regression model is constructed based on an impact coefficient sample library, using input parameters as input features and impact coefficient output as the target output. Specifically, this includes: The input parameters are preprocessed by dimensionless transformation, normalization, and outlier identification to obtain an initial feature set.

[0036] A feature selection method based on mutual information or correlation coefficient is adopted to determine the correlation between each feature in the initial feature set and the output value of the impact coefficient, and to select features whose correlation meets the preset conditions, thus obtaining the optimized initial feature set.

[0037] Based on the optimized initial feature set and the impact coefficient output value, a gradient boosting decision tree framework is used to construct the base learner.

[0038] The optimized initial feature set is used as the model input, and the impact coefficient output value is used as the model output. The base learner is trained through multiple rounds of iteration. The number of model iterations is determined by K-fold cross-validation and early stopping to gradually approximate the nonlinear mapping relationship between the input parameters and the impact coefficient output value, thus obtaining the gradient boosting regression model.

[0039] In each iteration of the training process, the negative gradient between the predicted value of the base learner in the previous iteration and the output value of the impulse coefficient is used as the residual approximation. This residual approximation is then fitted as the target output of the base learner in the current iteration to obtain the base learner for that iteration. The base learner for the current iteration is then fused with the base learner from the previous iteration to update the gradient boosting regression model.

[0040] like Figure 2 As shown, a dynamic model of the interaction between an aircraft and a bridge structure during landing is presented, including an aircraft model (including landing gear and fuselage), a bridge structure model (such as beams, piers, and supports), and the contact and coupling relationship between the two. This provides an intuitive understanding of how aircraft loads are transferred to the bridge, and the deformation and response characteristics of the bridge under the dynamic action of the aircraft, offering a basic framework for simulation analysis in the construction of an impact coefficient sample library.

[0041] A specific embodiment of the present invention is provided: An impact coefficient sample library was constructed based on bridge dynamic response data under aircraft loads. Building upon this, the system systematically analyzed influencing parameters such as aircraft landing state parameters and bridge structural characteristic parameters, and conducted parameter sensitivity analysis and impact coefficient statistical analysis to clarify the distribution characteristics of the impact coefficient. Furthermore, a gradient boosting regression prediction model was constructed, and a heuristic optimization algorithm was introduced to adaptively search and optimize the model's hyperparameters, ultimately forming an impact coefficient prediction model and value selection method that can be used for rapid engineering assessment.

[0042] The dynamic response data sources for the impact coefficient sample library include one or more of the following: numerical simulation results, existing engineering analysis results, or experimental test results. The data sources are only used as a method of sample acquisition; this invention does not limit the specific software used to construct the dynamic analysis model, the modeling process, or the coupling implementation method.

[0043] The impact coefficient of a continuous beam bridge during aircraft landing is defined as the ratio of the increment of the bridge's vertical displacement caused by the aircraft load to the static displacement. The impact coefficient output value can be expressed as: ; In the formula, I c This is the output value of the impact coefficient. Y d,max The maximum vertical dynamic displacement response of the bridge structure caused by aircraft load. Y j,max The maximum static vertical displacement response of the bridge structure caused by aircraft load.

[0044] The influencing parameters include both aircraft landing status parameters and bridge structural characteristic parameters.

[0045] (1) The landing parameters of an aircraft include landing mass, touchdown speed, descent speed, pitch angle, and roll angle.

[0046] (2) Bridge structural characteristic parameters include span, pier height, structural damping ratio, and three-dimensional unevenness of the bridge deck.

[0047] The sample construction employs a parameter space design method to generate random average sample combinations within a given value range. The parameter space design method includes one or more of orthogonal experimental design, Latin hypercube sampling, uniform design, or Monte Carlo sampling. The samples are then dedimensionalized / normalized and outlier-handled to form a standardized training dataset.

[0048] like Figure 3 The diagram shown is a distribution map of the database, used to illustrate the distribution of the impact coefficient sample library and its divided training and test sets in the feature space.

[0049] Figure 3 (a) is a schematic diagram of the impact coefficient sample library: it shows the distribution of all samples in the multidimensional space composed of input parameters (such as aircraft landing state parameters and bridge structural characteristic parameters), reflecting the coverage and density of the samples.

[0050] Figure 3 (b) in the figure is a distribution range diagram of the training database: it shows the distribution of a portion of the samples used for model training in the feature space, and should generally maintain a distribution characteristic similar to that of the overall samples.

[0051] Figure 3 (c) in the diagram shows the distribution of the test database: it illustrates the distribution of samples used for model testing, verifying whether it can represent new working conditions not involved in training, thereby evaluating the model's generalization ability. The impact coefficient distribution characteristics were determined through statistical analysis, including: statistically analyzing the main distribution range and variation patterns of the impact coefficient under different aircraft types, bridge types, or landing conditions. Statistical analysis included, but was not limited to, one or more of the following: frequency / histogram statistics, mean and standard deviation, quantile intervals, confidence intervals, and outlier identification, and outputting corresponding statistical summary results and suggested value ranges.

[0052] The gradient boosting regression prediction model is an ensemble regression model based on regression trees. Its training process iteratively fits the residuals and integrates the output. Its key hyperparameters include one or more of the following: learning rate, number of weak learners, tree depth, minimum number of samples per leaf node, feature sampling ratio, sample sampling ratio, and regularization parameter.

[0053] Among them, heuristic optimization algorithms are used for adaptive search and update of hyperparameters in gradient boosting regression models. Heuristic optimization algorithms include, but are not limited to: (a) Bayesian optimization algorithm: The mapping relationship between hyperparameters and model error is represented by a surrogate model, and the next set of candidate hyperparameters is selected by the acquisition function.

[0054] First, each hyperparameter is assigned a corresponding value range or candidate set according to its type (continuous or discrete), which together constitute the search space of the hyperparameter.

[0055] Secondly, the mapping relationship between hyperparameter combinations and model performance is regarded as an unknown black box function, and a Gaussian process is used as a surrogate model to model this black box function. The Gaussian process describes the probability distribution of the model performance corresponding to any hyperparameter combination through the mean function and covariance function, and can quantify the uncertainty of prediction.

[0056] Then, an iterative optimization process is performed, with each iteration including the following steps: (1) Based on the current agent model, construct the acquisition function; the acquisition function is used to make a trade-off between exploration and exploitation, that is, to select the next set of candidate hyperparameters to be evaluated between the hyperparameter region that has not been fully explored (exploration) and the hyperparameter region with better known performance (exploitation); commonly used acquisition functions include one of expectation boosting, probability boosting or confidence upper limit; (2) Optimize the acquisition function and select the set of hyperparameters that maximize the acquisition function value from the hyperparameter search space as the candidate hyperparameter combination to be evaluated in this round; (3) Substitute the candidate hyperparameter combination into the gradient boosting regression model, train it on the training set, and evaluate the model performance on the validation set to obtain the validation set error or comprehensive evaluation index value corresponding to the hyperparameter combination. (4) Add the newly evaluated “hyperparameter combination-performance index” data pairs to the historical observation dataset, and retrain the Gaussian process surrogate model using the updated dataset to more accurately approximate the true mapping relationship between hyperparameters and model performance.

[0057] Repeat the above iterative process until the preset maximum number of iterations is reached or the performance index shows no significant improvement for several consecutive rounds.

[0058] Finally, from all evaluated hyperparameter combinations, the set of hyperparameters that minimizes the validation set error or optimizes the overall evaluation index is selected as the optimal hyperparameter combination obtained by the Bayesian optimization algorithm, and the optimal gradient boosting regression model is constructed based on this combination.

[0059] (b) Genetic algorithm: The hyperparameters are searched for through population evolution by selection, crossover and mutation.

[0060] First, the hyperparameters to be optimized are encoded to form chromosomes in the genetic algorithm: for continuous hyperparameters (such as the learning rate), real-number encoding or binary encoding is used; for discrete hyperparameters (such as the number of weak learners or tree depth), integer encoding or binary encoding can be used directly. Each chromosome represents a set of candidate hyperparameter combinations.

[0061] Secondly, within the hyperparameter search space, N chromosomes are randomly generated as the initial population, with the population size N set according to the problem complexity (usually between 20 and 100). Each chromosome corresponds to a set of hyperparameter values.

[0062] Then, each chromosome in the population is decoded into specific hyperparameter values, which are substituted into the gradient boosting regression model. The model is trained on the training set and its performance is evaluated on the validation set. The fitness value is the reciprocal of the validation set error (such as root mean square error) or a comprehensive evaluation index (such as mean absolute error, goodness of fit, etc.). That is, the better the model performance, the higher the fitness value.

[0063] Next, the iterative evolution process of the genetic algorithm begins, with the following operations performed in each generation: (1) Selection operation: Select superior individuals from the current population based on their fitness values ​​to serve as parents for the next generation. Commonly used selection methods include roulette wheel selection, tournament selection, or sorting selection. Individuals with higher fitness have a greater probability of being selected.

[0064] (2) Crossover operation: Selected parent chromosomes are crossed with a certain crossover probability (usually 0.6~0.9) to generate offspring individuals. For real-number encoding, simulated binary crossover or arithmetic crossover can be used; for binary encoding, single-point crossover, multi-point crossover, or uniform crossover can be used. The crossover operation aims to combine the superior genes of parent individuals and explore new hyperparameter combinations.

[0065] (3) Mutation operation: The gene positions of offspring individuals are perturbed with a certain mutation probability (usually 0.01~0.1) to maintain population diversity and prevent premature convergence. For real number encoding, polynomial mutation or Gaussian mutation can be used; for binary encoding, bit-flip mutation can be used. Mutation operation helps the algorithm escape local optima and expand the search range.

[0066] (4) Elite preservation strategy: The most fit individuals (elites) in the current population are directly copied to the next generation to protect the optimal solution from being lost.

[0067] After completing the above operations, a new generation of population is generated, and the fitness of all individuals is reassessed.

[0068] Repeat the above iterative process until the preset maximum number of generations is reached, or until the optimal fitness of the population does not improve significantly over multiple generations.

[0069] Finally, from all individuals that have appeared in all evolutionary generations, the chromosome with the highest fitness (i.e., the smallest validation set error or the best comprehensive evaluation index) is selected, decoded to obtain the optimal hyperparameter combination, and then used to construct the optimal gradient boosting regression model.

[0070] (c) Differential evolution algorithm: global optimization of continuous hyperparameters through differential mutation and selection mechanism.

[0071] First, determine the hyperparameters to be optimized and their search space: for continuous hyperparameters (such as learning rate and regularization parameter), set their value range; for discrete hyperparameters (such as the number of weak learners and tree depth), integer encoding can be used directly and rounded down after mutation and crossover operations.

[0072] Secondly, within the hyperparameter search space, NP D-dimensional real vectors (individuals) are randomly generated. Each individual represents a set of candidate hyperparameter combinations, where D is the number of hyperparameters to be optimized and NP is the population size (usually 5D~10D). Each dimension of each individual is randomly initialized within the value range of the corresponding hyperparameter.

[0073] Then, each individual in the population is decoded into specific hyperparameter values ​​(discrete hyperparameters need to be rounded down), substituted into the gradient boosting regression model, trained on the training set, and the model performance is evaluated on the validation set. The validation set error (such as root mean square error) or a comprehensive evaluation index (such as mean absolute error, goodness of fit, etc.) is used as the fitness value, and the objective is usually to minimize the validation set error.

[0074] Next, the iterative evolutionary process of differential evolution begins, where each generation performs the following operations on each target individual in the current population: (1) Mutation operation: For each target individual in the current population x i Three distinct individuals are randomly selected from the current population. x r1 , x r2 , x r3 Generate mutation vectors according to the differential mutation strategy. v i Common mutation strategies include:

[0075] v i = x r1 + F ·( xr2 - x r3 ); in, F is a scaling factor, usually a constant between [0.4, 1], used to control the scaling factor of the difference vector.

[0076] (2) Cross operation: target individual x i With the mutation vector v i Perform binomial crossover (or exponential crossover) to generate test vectors. u i For each dimension component j It shall be determined according to the following rules:

[0077] ; in, CR The crossover probability is usually a constant between [0, 1], used to control the proportion of components inherited from the mutation vector; rang j A uniformly random number between [0, 1]; j rand The index is randomly selected to ensure that at least one dimension of the experimental vector comes from the mutated vector, avoiding being exactly the same as the target vector.

[0078] (3) Boundary constraint handling: If the experimental vector u i If a certain component of a hyperparameter exceeds the range of its corresponding hyperparameter, it is corrected to the feasible region by means of boundary absorption or random re-initialization.

[0079] (4) Selection operation: A greedy selection strategy is adopted to select the test vector. u i Decode the hyperparameters into a combination and evaluate their fitness (validation set error). If the fitness of the experimental vector is better than that of the target individual... x i If the fitness of the experimental vector is high enough, the experimental vector replaces the target individual in the next generation; otherwise, the target individual is retained.

[0080] After performing the above operations on all target individuals in sequence, a new generation of population is generated.

[0081] Repeat the above iterative process until the preset maximum number of generations is reached, or until the optimal fitness of the population does not improve significantly over multiple generations.

[0082] Finally, from all individuals that have appeared in all evolutionary generations, the individual with the best fitness (i.e., the smallest validation set error or the best comprehensive evaluation index) is selected, decoded to obtain the optimal hyperparameter combination, and then used to construct the optimal gradient boosting regression model.

[0083] (d) Particle swarm optimization algorithm: Hyperparameters are searched through iterative and collaborative searching of particle velocity and position.

[0084] First, for each hyperparameter, a corresponding value range (for continuous hyperparameters) or a discrete candidate set (for discrete hyperparameters) is set according to its type, which together constitute the search space of the hyperparameter.

[0085] Secondly, initialize the particle swarm and set its size to [value missing]. N (Typically 20-50), each particle represents a set of candidate hyperparameter combinations. The position vector of each particle is randomly initialized within the search space. X i =[ x i1 , x i2 , ..., x iD] , D This represents the number of hyperparameters to be optimized. Simultaneously, the velocity vector for each particle is randomly initialized. V i = [ v i1 , v i2 , ..., v iD The initial values ​​of each dimension of velocity are usually limited to a certain percentage (e.g., 20%) of the corresponding search space width. For discrete hyperparameters, they can be rounded after initialization or a special encoding method can be used.

[0086] Then, the position vector of each particle is decoded into specific hyperparameter values ​​(discrete hyperparameters need to be rounded down), substituted into the gradient boosting regression model, trained on the training set, and the model performance evaluated on the validation set. The fitness value is used as the validation set error (e.g., root mean square error) or a comprehensive evaluation metric (e.g., mean absolute error, goodness of fit, etc.), typically aiming to minimize the validation set error. The current optimal position of each particle is recorded. pbest i (i.e., the position corresponding to the particle's historical best fitness), and the global best position of the entire particle swarm. gbest (i.e., the optimal position among all the best fitnesss in the history of all particles).

[0087] Next, we proceed with the iterative update process of particle swarm optimization, performing the following operations on each particle in each generation: (1) Velocity update: Based on the current velocity, the individual optimal position, and the global optimal position, the particle velocity is updated according to the following formula: in, This is the inertial weight, used to balance global and local search capabilities (usually taken as 0.4~0.9, which can decrease linearly with iteration). and These are learning factors, representing the degree to which a particle learns towards its individual optimum and global optimum, respectively. and The values ​​are uniformly random numbers within the interval [0,1], used to increase the randomness of the search. The updated velocity dimensions must be limited to a preset maximum velocity range to prevent particles from flying out of the search space.

[0088] (2) Position update: Update the particle's position based on the updated velocity: After the update, it is necessary to check whether each dimension of the particle exceeds the value range of the corresponding hyperparameter. If it does, its boundary value should be set and the corresponding velocity can be set to zero or reversed.

[0089] (3) Fitness evaluation and optimal update: The updated particle position is decoded into a hyperparameter combination, the gradient boosting regression model is retrained, and the validation set error is calculated. If the current fitness is better than the historical optimal value of the particle... pbest i Then update pbest i If it is better than the current global optimum gbest Then update gbest .

[0090] Repeat the above iterative process until the preset maximum number of iterations is reached, or until the global optimal fitness does not improve significantly for multiple consecutive rounds.

[0091] Ultimately, the globally optimal position will be determined. gbest Decode the optimal combination of hyperparameters and use it to construct the optimal gradient boosting regression model.

[0092] (e) Hybrid algorithm of simulated annealing / random search and local search: global exploration is carried out in the search space through random perturbation, and local search is combined to perform neighborhood fine optimization of the current solution. The probability acceptance criterion of simulated annealing is introduced to balance exploration and exploitation, thereby improving search efficiency and reducing the probability of getting trapped in local optima, and global optimization hyperparameters.

[0093] First, determine the search space: for continuous hyperparameters, set the range of values; for discrete hyperparameters, set a candidate set or use continuous encoding followed by rounding.

[0094] Next, algorithm initialization is performed. An initial solution is randomly generated within the hyperparameter search space. x 0 represents a set of initial hyperparameter combinations. The initial temperature is set. T start and termination temperature T end (or maximum number of iterations), and the Markov chain length at each temperature. L (i.e., the number of internal circulation cycles). Set the temperature decay coefficient. It is usually taken as 0.8~0.99 to control the cooling rate.

[0095] Then, the fitness of the initial solution is evaluated. The initial solution... x 0 is decoded into specific hyperparameter values, which are then substituted into the gradient boosting regression model. The model is trained on the training set, and its performance is evaluated on the validation set to obtain the validation set error (such as root mean square error) or a comprehensive evaluation index value. E ( x 0), the objective is usually to minimize this error. The current solution x curr Set as x 0, the current optimal solution x best Set as x 0, current temperature T = T start .

[0096] Next, we enter the main loop of simulated annealing, at the temperature... T Next L In each iteration of the inner loop, the following operations are performed: (1) Random perturbation (global search): in the current solution x curr Based on this, a new solution is generated through a random perturbation mechanism. x new The perturbation method can involve random sampling within the search space, or applying a random offset to each dimension of the current solution with a certain probability (the offset decreases as temperature decreases). For continuous hyperparameters, Gaussian noise can be added; for discrete hyperparameters, random mutation can be used. (Generated...) x new It is necessary to ensure that each component is within the range of the corresponding hyperparameter; if it exceeds the range, boundary processing should be performed.

[0097] (2) Local search (neighborhood optimization): x new Starting from a given point, a local neighborhood search is performed to find a better solution within that neighborhood. Local searches can employ pattern search, coordinate rotation methods, or simple neighborhood sampling (such as in...). xnew Multiple candidate points are randomly generated within a small vicinity, and the optimal one is selected. The optimal solution obtained from the local search is denoted as... x local And assess its fitness. E ( x local If a better solution is not found through local search, then x local = x new .

[0098] (3) Fitness assessment: x local Decode, train the gradient boosting regression model and calculate the validation set error. E ( x local ).

[0099] (4) Metropolis acceptance criterion: Calculate the increment Δ of the objective function. E = E ( x local )− E ( x curr If Δ E If the value is less than 0 (meaning the new solution is better), then accept. x local As the new current solution x curr = x local And update the current optimal solution. x best (like E ( x local )< E ( x best If Δ E If ≥0, then by probability exp (−Δ E / T If a solution is deemed inferior, it is accepted, meaning that a certain probability is allowed to escape the local optimum; otherwise, the solution is rejected, and the current solution remains unchanged.

[0100] After completing one inner loop, if the number of inner loop iterations is reached... L Then lower the temperature T = αT It then resets the inner circulation count and enters the outer circulation of the next temperature layer.

[0101] Repeat the external circulation process as described above until the temperature drops to [temperature value missing]. T endThe process continues until the optimal solution shows no significant improvement across multiple consecutive temperature levels, or until the preset maximum number of external cycles is reached.

[0102] Finally, the globally optimal solution recorded during the search process will be... x best Decode the optimal combination of hyperparameters and use it to construct the optimal gradient boosting regression model.

[0103] The final model is selected from the results of the above heuristic optimization algorithm based on the criterion of minimizing the validation set error or achieving the best overall evaluation metric. The overall evaluation metrics include: Mean Absolute Error (MAE), Root Mean Square Error (RMSE), and Goodness of Fit (R²). 2 The model's generalization performance is verified through cross-validation or training / validation / test set splitting, and one or more of the following indicators: (i) engineering safety bias indicators.

[0104] like Figure 4 The image shows a radar chart of the impact coefficient analysis results, used to compare multiple indicators of the impact coefficient prediction performance under different models or hyperparameter combinations.

[0105] Figure 4 (a) in the diagram is a radar chart of the root mean square error analysis results: each axis represents the root mean square error value of different models or parameter combinations. The smaller the value, the closer it is to the center, which intuitively shows the relative size of the prediction error.

[0106] Figure 4 (b) in the diagram is a radar chart showing the goodness-of-fit analysis results: displaying the coefficient of determination R. 2 In comparison, the closer the value is to 1, the better, reflecting the model's ability to explain data variation.

[0107] Figure 4 (c) is a radar chart of the mean absolute error analysis results: it shows the comparison of mean absolute errors, and the smaller the error, the higher the model prediction accuracy.

[0108] The output includes not only the predicted value of the impact coefficient, but also the suggested range of impact coefficient values ​​obtained based on distribution analysis or error statistics, which can be used for rapid comparison and risk assessment in the engineering design stage.

[0109] like Figure 5 As shown, another specific embodiment of the present invention is provided, which illustrates in detail the complete modeling process from sample preprocessing, feature selection, model training to hyperparameter optimization.

[0110] Step 1: Constructing the impact coefficient sample library.

[0111] The range of values ​​for aircraft landing state parameters and bridge structural characteristic parameters is defined, and random average sample combinations are generated based on parametric space design methods. These methods include one or more of orthogonal experimental design, Latin hypercube sampling, uniform design, or Monte Carlo sampling. For each sample group, the bridge's dynamic response data under aircraft load is obtained, and the corresponding static response is calculated. The impact coefficient is defined as the ratio of the bridge's vertical displacement increment caused by aircraft load to its static displacement, forming an "input parameter - impact coefficient" sample library.

[0112] Step 2: Analysis of influencing parameters and sample preprocessing.

[0113] The system sorts out the influencing parameters and constructs feature vectors, including: (1) aircraft landing state parameters including landing mass, touchdown velocity, sinking velocity, pitch angle, and roll angle; (2) bridge structural characteristic parameters including span, pier height, structural damping ratio, and three-dimensional unevenness of the bridge deck. The sample data is dimensionless / normalized, outlier is identified, and necessary feature combination processing is performed to form a standardized training dataset.

[0114] Step 3: Sensitivity analysis and key parameter screening.

[0115] Based on the sample database, parameter sensitivity analysis is conducted to identify key parameters that significantly affect the impact coefficient, and feature selection or feature set optimization is performed accordingly to reduce the impact of redundant variables on model training and generalization performance.

[0116] Step 4: Statistical analysis and distribution pattern extraction of impact coefficient.

[0117] Under different aircraft types, bridge types, or landing conditions, statistical analysis is performed on the impact coefficient to determine its main distribution range and variation patterns. Statistical analysis includes, but is not limited to, one or more of the following: frequency / histogram statistics, mean and standard deviation, quantile intervals, confidence intervals, and outlier identification. The corresponding statistical summary results and suggested value ranges are then output.

[0118] Step 5: Constructing a gradient boosting regression prediction model.

[0119] A gradient boosting ensemble regression model based on regression trees is constructed. The residuals are iteratively fitted and integrated to establish a nonlinear mapping relationship between input parameters and impact coefficients. Key hyperparameters include one or more of the following: learning rate, number of weak learners, tree depth, minimum number of samples per leaf node, feature sampling ratio, sample sampling ratio, and regularization parameter.

[0120] Step 6: Heuristic optimization-driven hyperparameter adaptive search and optimization.

[0121] A heuristic optimization framework is constructed, using validation set error or a comprehensive evaluation index as the objective function, to adaptively search and update the key hyperparameters of the gradient boosting regression model, thereby obtaining the optimal gradient boosting regression model. Heuristic optimization algorithms include, but are not limited to: Bayesian optimization, genetic algorithms, differential evolution, particle swarm optimization, and hybrid algorithms combining simulated annealing / random search and local search. The final model is selected from the results of various optimization algorithms based on the criterion of "minimum validation set error or optimal comprehensive evaluation index."

[0122] Step 7: Model training, performance evaluation, and engineering output.

[0123] The selected model is trained and its generalization performance is verified using a training / validation / test set partitioning or cross-validation mechanism. Model performance evaluation metrics include: MAE, RMSE, and R². 2 In addition, it includes one or more of the engineering safety deviation indicators. The final output is the predicted value of the impact coefficient, and combined with distribution analysis or error statistics, it outputs a suggested range of impact coefficient values ​​for rapid comparison and risk assessment during the engineering design phase.

[0124] like Figure 6 The diagram shown illustrates the performance verification, comparing the performance of different gradient boosting regression algorithms on the impact coefficient prediction task.

[0125] Figure 6 (a) in the diagram is a performance verification diagram of the gradient boosting tree regression algorithm: it shows the scatter distribution between the predicted value and the true value of the algorithm, or the trend of error change with the sample, which is used to evaluate its prediction accuracy.

[0126] Figure 6 (b) in the diagram is a performance verification diagram of the extreme gradient boosting tree regression algorithm: similarly, the prediction performance of the XGBoost algorithm is shown, which may include error metrics or fitting effect diagrams.

[0127] Figure 6 (c) in the figure is a performance verification diagram of the Lightweight Gradient Boosting Decision Tree Regression algorithm: it shows the prediction results of the LightGBM algorithm and highlights the advantages and disadvantages of different algorithms on the same dataset by comparing them with the aforementioned algorithms.

[0128] The embodiments described above are merely examples of several implementations of the present invention, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for predicting the impact coefficient of a bridge structure under aircraft load, characterized in that, include: An impact coefficient sample library is constructed based on the dynamic response data of bridges under aircraft load. The impact coefficient sample library includes multiple sample combinations. Each sample combination consists of a set of input parameters and corresponding impact coefficient output values. The input parameters include aircraft landing state parameters and bridge structural characteristic parameters. Based on the impact coefficient sample library, a gradient boosting regression model is constructed with input parameters as input features and impact coefficient output value as the target output, and the hyperparameters of the gradient boosting regression model are preset. Bayesian optimization, genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and simulated annealing / random search and local search hybrid algorithm are used as heuristic optimization algorithms to adaptively search the hyperparameters of the gradient boosting regression model, and obtain multiple model optimization results. With the goal of minimizing the validation set error or the optimal comprehensive evaluation index, the optimal gradient boosting regression model is selected from the multiple model optimization results. The input parameters to be tested are input into the optimal gradient boosting regression model to obtain the corresponding predicted values ​​of the impact coefficient.

2. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The impact coefficient output value is determined based on the following formula: ； in, I c This is the output value of the impact coefficient. Y d,max The maximum vertical dynamic displacement response of the bridge structure caused by aircraft load. Y j,max The maximum static vertical displacement response of the bridge structure caused by aircraft load.

3. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The aircraft landing parameters include: landing mass, touchdown speed, descent speed, pitch angle, and roll angle; The bridge structural characteristic parameters include: span, pier height, structural damping ratio, and three-dimensional unevenness of the bridge deck.

4. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The impact coefficient sample library constructed based on the dynamic response data of bridges under aircraft loads specifically includes: Dynamic response data are obtained from one or more of the following: numerical simulation results, existing engineering analysis results, or experimental test results. Random average sample combinations are generated within the range of values ​​of the dynamic response data using a parameter space design method, which includes one or more of orthogonal experimental design, Latin hypercube sampling, uniform design, or Monte Carlo sampling.

5. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The step of constructing a gradient boosting regression model based on an impact coefficient sample library, with input parameters as input features and impact coefficient output as the target output, specifically includes: The input parameters are preprocessed by dimensionless transformation, normalization, and outlier identification to obtain an initial feature set; A feature selection method based on mutual information or correlation coefficient is used to determine the correlation between each feature in the initial feature set and the output value of the impact coefficient, and features whose correlation meets the preset conditions are selected to obtain the optimized initial feature set. Based on the optimized initial feature set and the impact coefficient output value, a base learner is constructed using a gradient boosting decision tree framework. The optimized initial feature set is used as the model input, and the impact coefficient output value is used as the model output. The base learner is trained through multiple rounds of iteration. The number of model iterations is determined by K-fold cross-validation and early stopping method to gradually approximate the nonlinear mapping relationship between the input parameters and the impact coefficient output value, thus obtaining the gradient boosting regression model. Specifically, for each iteration of the training process, the negative gradient between the predicted value of the base learner in the previous iteration and the output value of the impulse coefficient is used as the residual approximation value. The residual approximation value is then used as the target output of the base learner in the current iteration to obtain the base learner for the current iteration. The base learner in the current iteration is then fused with the base learner in the previous iteration to update the gradient boosting regression model.

6. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The hyperparameters include one or more of the following: learning rate, number of weak learners, tree depth, minimum number of samples per leaf node, feature sampling ratio, sample sampling ratio, and regularization parameter.

7. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The method employs Bayesian optimization, genetic algorithm, differential evolution algorithm, particle swarm optimization algorithm, and a hybrid algorithm combining simulated annealing / random search and local search as heuristic optimization algorithms to adaptively search for the hyperparameters of the gradient boosting regression model, obtaining multiple model optimization results, specifically including: The Bayesian optimization algorithm includes: representing the mapping relationship between hyperparameters and model error through a surrogate model, and selecting the next set of candidate hyperparameters through a collection function; The genetic algorithm includes: performing a population evolution search for hyperparameters through selection, crossover, and mutation; The differential evolution algorithm includes: globally optimizing continuous hyperparameters through differential mutation and selection mechanisms; The particle swarm optimization algorithm includes: iteratively and collaboratively searching for hyperparameters through particle velocity and position; The simulated annealing / random search and local search hybrid algorithm includes: performing a global search through random perturbation, and combining the probabilistic acceptance criteria of local search and simulated annealing to globally optimize hyperparameters.

8. The method for predicting the impact coefficient of an aircraft-loaded bridge structure as described in claim 1, characterized in that, The comprehensive evaluation index includes one or more of the following: mean absolute error, root mean square error, goodness of fit, and engineering safety deviation index.

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