RC beam shock resistance analysis method based on enhanced automatic machine learning

Abstract

The invention relates to the technical field of RC beam impact resistance, and particularly discloses an RC beam impact resistance analysis method based on enhanced automatic machine learning, which is used for accurately predicting the mid-span deflection of an RC simply supported beam under the action of an impact load. The method aims to reduce a large amount of time and technical requirements required by traditional machine learning (ML) model development. Parameters and evaluation indexes are finely adjusted by using a tree-based pipeline optimization tool (TPOT), and a plurality of TPOT instances are operated at the same time, so that the model execution efficiency is remarkably improved; the method focuses on optimization of the TPOT algorithm to improve the efficiency and accuracy of the TPOT algorithm under specific experimental conditions, the optimization process comprises adjustment of parameters, evaluation indexes and operation modes to adapt to experimental settings, and the effectiveness of the improvements is verified through analysis of a comprehensive data set and comparative evaluation with other machine learning models. Research results confirm that the EI-AutoML method is feasible and effective, and the potential practicability of the EI-AutoML method in scientific application is shown.

Description

Technical Field

[0001] The present invention belongs to the technical field of RC beam anti-impact performance, and in particular relates to a method for analyzing the anti-impact performance of RC beams based on enhanced automatic machine learning. Background Art

[0002] Reinforced concrete (RC) beams are common components in engineering structures. During their service life, they may be subjected to strong dynamic loads such as earthquakes, explosions, and impacts, resulting in structural damage. The dynamic response of RC beams under local impact loads has significant strain rate effects and nonlinear structural dynamic characteristics, which has always been one of the focuses and challenges of extreme load resistance research in the field of structural engineering. Researchers usually use experimental, numerical simulation, and theoretical analysis methods to conduct related research. In order to evaluate the impact resistance of RC beams, researchers have carried out a large number of experimental studies. For example, Kishi et al. took 27 rectangular RC simply supported beams without shear reinforcement as the research object, used a 300 kg steel ball as an impact hammer, applied impact loads to the mid-span of the RC beams, and collected the impact force, reaction force, and mid-span deflection data caused by the impact hammer. In addition, in order to further obtain the impact test data of shear failure RC beams, Bhatti et al. conducted a drop hammer impact test on 12 rectangular RC simply supported beams with different shear reinforcement ratios and impact velocities, and applied impact loads to the mid-span of the RC beams. Tachibana et al. conducted a series of impact tests on RC beams with different spans, cross-sections, and main reinforcement configurations, and studied key parameters such as impact energy, impact duration, beam absorbed energy, and beam response values ​​and their interrelationships. These experiments provided valuable data support for subsequent numerical simulations and other research methods.

[0003] However, analyzing and improving the maximum displacement of reinforced concrete (RC) beams under impact loads is crucial to improving their impact resistance. In the prior art, an enhanced interpretable automated machine learning (EI-AutoML) method is proposed to accurately predict the mid-span deflection of RC simply supported beams subjected to impact loads. This method aims to reduce the large amount of time and technical requirements required for the development of traditional machine learning (ML) models. By fine-tuning the parameters and evaluation indicators using the tree-based pipeline optimization tool (TPOT) and running multiple TPOT instances simultaneously, the model execution efficiency was significantly improved. In the experimental group, the enhanced TPOT algorithm generated the optimal stacking model, while the control group used several commonly used traditional machine learning models. The results show that the stacking model of the enhanced TPOT exhibits excellent robustness and generalization ability, and its evaluation indicators are significantly better than those of traditional machine learning models. The coefficient of determination (R 2) reached 0.975, and the root mean square error (RMSE) was only 3.688 mm. In addition, three explanatory analysis methods including SHapley Additive exPlanation (SHAP) were used, and feature importance and parameter analysis were performed in combination with five-fold cross validation. The study also explored the interactive effects of different features on deflection, providing a theoretical basis for optimization in engineering practice. In order to apply it to actual engineering scenarios, symbolic regression analysis was performed based on the model to derive empirical formulas. In addition, a graphical user interface (GUI) was developed to improve its usability in engineering applications.

[0004] In the study of using numerical simulation methods to predict the impact response of shear failure RC beams, Kishi et al. conducted simulations to evaluate the impact resistance of these beams and compared their results with actual experimental conditions. This method verifies the effectiveness of the numerical simulation analysis method. In addition, in order to study the shear failure mode of RC beams under impact loads, Zhao et al. performed nonlinear finite element analysis using the LS-DYNA simulation program. They simulated the impact response of simply supported RC beams and verified the numerical simulation model through experimental results, summarizing different failure modes. Adhikary et al. conducted parametric impact analysis based on the experimentally verified numerical simulation model, revealing the significant effects of impact velocity, shear span ratio, and longitudinal and transverse reinforcement ratio on mid-span deflection. Bhatti et al. also used numerical simulation methods to evaluate the accuracy of the model in predicting impact force, reaction force, mid-span displacement, and lateral crack pattern. In addition, Adhikary et al., based on the work of Rabczuk et al., used fluid-particle coupling simulation technology to accurately simulate the cracking and fragmentation behavior of reinforced concrete (RC) beams under impact loads.

[0005] In theoretical studies, Adhikary et al. proposed a simplified single degree of freedom (SDOF) analysis model based on energy balance, assuming the load-deflection curve reference to accurately predict the maximum mid-span deflection of the beam. This method helps in the preliminary analysis and evaluation of RC beams under low-velocity impact conditions. Fujikake et al. focused on the effects of drop height and the number of longitudinal reinforcements and subsequently established a two-degree-of-freedom (TDOF) model. Their results showed that the bending failure response of the structure can be accurately predicted when the local response at the impact point is assumed to be highly damped. In addition, Yi et al. proposed a dual-mass model to simulate the local and global responses and achieved reasonable accuracy in evaluating the shear effect. In a recent study, Zhao et al. developed a three-degree-of-freedom analysis model combined with finite element analysis method to distinguish the maximum displacement response of shear failure and bending failure. They concluded that the empirical formula proposed by Fujikake et al. is specific to bending failure and introduced a shear failure evaluation method based on the mv diagram.

[0006] However, traditional research methods also face many challenges. Experimental research is usually costly, time-consuming and has poor repeatability, which complicates the implementation of multi-parameter impact analysis and the mitigation of size scaling effects. Numerical simulation methods face problems such as high model complexity, large computing resource requirements, and the accuracy of the results is highly dependent on the accuracy of material parameters and boundary conditions. These challenges are particularly prominent in material modeling and multi-scale analysis. Theoretical research relies on simplified assumptions, which limits its applicability and has difficulties in analyzing complex physical processes, dealing with nonlinear behaviors and multi-field coupling. In addition, the reliability of experimental verification is also affected by the inherent discreteness and uncertainty of experimental data. For this reason, an analysis method for the impact resistance of RC beams based on enhanced automatic machine learning is proposed. Summary of the invention

[0007] The object of the present invention is to provide a method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning to solve the problems raised in the above background technology.

[0008] To achieve the above object, the present invention provides the following technical solutions:

[0009] The impact resistance analysis method of RC beams based on enhanced automatic machine learning includes:

[0010] Implement optimization and improvement of the impact resistance of RC beams in the TPOT algorithm, optimize the parameters of the impact resistance of RC beams, multiple objectives, and parallel TPOT pipelines;

[0011] The automatic machine learning RC beam impact resistance analysis method also includes a drop hammer impact test device for testing the impact resistance of the RC beam.

[0012] Develop predictive analysis models using EI-AutoML and apply engineering practices based on this approach;

[0013] Preferably, the database format formula for the drop weight impact test is:

[0014] Δ={x i ,y i}where i=1,...,378,

[0015] x i ={H i ,B i ,L i ,M i ,V i ,Pl i ,Pt i ,Fc i ,Fs i ,Fst i ,N i}

[0016] y i =D i

[0017] The input variables of the drop hammer impact test sample are beam height (H), beam width (B), clear span (L), drop hammer mass (M), impact velocity (V), longitudinal reinforcement ratio (Pl), transverse reinforcement ratio (Pt), concrete compressive strength (Fc), longitudinal reinforcement yield strength (Fs), transverse reinforcement yield strength (Fst) and the number of impacts on the same target (N).

[0018] An automated machine learning module to simplify the process of modeling the impact performance of RC beams.

[0019] Preferably, the specific tasks of the automatic machine learning module include data preprocessing, feature engineering, model selection, hyperparameter tuning and model evaluation. By optimizing each module in the end-to-end pipeline, the best model can be automatically built during the search process. The tool of the automatic machine learning module is the TPOT pipeline, which is used to optimize the machine learning pipeline for the genetic algorithm to select the best performing model and tune the hyperparameters.

[0020] Preferably, the predefined indicators of the TPOT pipeline include accuracy, precision, mean square error and mean absolute error;

[0021] Preferably, the mathematical expressions of the mean square error, root mean square error, mean absolute error and determination coefficient evaluation index are:

[0022]

[0023] Among them, y e represents the actual measured displacement of the beam, y p Represents the predicted value of the model output, and n represents the total number of samples in the data set;

[0024] Through the setting of the above technical solution, it should be noted that: the mean square error (MSE) is used to measure the difference between the model prediction value and the actual value, indicating the standard deviation of the prediction error; the root mean square error (RMSE) is the square root of the MSE, providing a more intuitive reflection of the actual size of the prediction error; the mean absolute error (MAE) calculates the average absolute difference between the model prediction value and the actual value, reflecting the average deviation between them; the lower the values ​​of MSE, RMSE and MAE, the higher the prediction accuracy; the coefficient of determination (R 2 ) is an indicator for evaluating the model fit, which indicates the ratio of the model to explain the variance of the experimental data; R 2 The closer the value is to 1, the stronger the model fit is, showing the improved ability of the model in explaining the test data;

[0025] The aspects of improvement on the impact resistance of RC beams are as follows: parameter configuration, increase of evaluation indexes and enhancement of operation mechanism;

[0026] The optimization of the parameter settings is "Generations" = 75 and "Population_size" = 75. TPOT achieves excellent model performance within a reasonable time range and successfully balances search accuracy and time cost. The performance evaluation indicators in TPOT include MAE and determination coefficient (R 2 ), the parallel optimization of TPOT is achieved by running multiple TPOT instances simultaneously through multiple processes, and the memory space of the computer is used to optimize the model selection process;

[0027] Through the setting of the above technical solutions, this study demonstrated an efficient EI-AutoML method by taking TPOT as a case study. Figure 1 Various optimizations and improvements implemented in the TPOT algorithm are demonstrated, such as parameter optimization, multi-objective optimization, and parallel optimization of the TPOT pipeline. These improvements are implemented from three aspects: parameter configuration, increase in evaluation indicators, and enhancement of operation mechanisms. The goal is to improve the accuracy of the generated model, minimize the time cost, and improve the efficiency of the model.

[0028] In the parameter optimization part, this study mainly adjusted two key parameters: "Generations" (default value is 20) and "Population_size" (default value is 50), such as Figure 2As shown in the figure, this study conducted several control experiments by changing these two sets of parameters in TPOT, and ran simulations to observe the corresponding model accuracy and running time. When the parameter combination reached 75×75 or above, the rate of decrease of RMSE slowed down significantly, while the running time increased quadratically. Based on comprehensive considerations, this study optimized the parameter settings to "Generations" = 75 and "Population_size" = 75. Under this parameter, TPOT achieved excellent model performance within a reasonable time range, successfully balancing the search accuracy and time cost.

[0029] This study expands the performance evaluation indicators in TPOT and adds MAE and determination coefficient (R 2 ), it should be noted that TPOT usually uses a single evaluation indicator by default. In the context of single-objective optimization, TPOT mainly focuses on maximizing or minimizing a specific performance indicator. For classification tasks, TPOT optimizes accuracy by default; for regression tasks, RMSE is used by default to evaluate the performance of the regression model. In this experiment, two commonly used indicators (MAE and R 2 ) in order to more comprehensively evaluate the model performance. This extension enables TPOT to evaluate the performance of the model from multiple perspectives, thereby identifying models that are not only superior in performance but also more suitable for the specific needs of this study. Multi-indicator evaluation provides rich information support for making more informed decisions.

[0030] The parallel optimization of TPOT is achieved by running multiple TPOT instances simultaneously through multiple processes, and the computer's memory space is used to optimize the model selection process. The code below shows the overall method of running TPOT parallel optimization in pseudocode form. The first four lines of code are used to configure TPOT parameters and create instance objects, where the number of "config" corresponds to the number of TPOT instances running in parallel. Lines 5 to 8 create independent processes for each TPOT configuration to run in parallel and store the results in a dictionary. Lines 9 to 12 are responsible for starting and waiting for all parallel processes to complete. Line 13 is used to identify the model with the best performance. In theory, increasing the number of TPOT instances running in parallel can improve the efficiency of the entire TPOT process. However, running multiple TPOT instances in parallel will significantly consume computer resources and may cause system crashes or deadlocks when approaching the computer capacity limit. Therefore, it is necessary to adjust and determine the appropriate number of TPOT instances running in parallel through experiments.

[0031] Pseudo code for parallel optimization in TPOT:

[0032] 1: tpot_configs=[config1,config2,config3,config4]

[0033] 2:manager=Manager()

[0034] 3:results=manager.dict()

[0035] 4:processes=[]

[0036] 5:Forconfigintpot_configsdo 6:

[0038] p=Process(target=run_tpot,args=(X_train,y_train,X_test,y_test,config,results))

[0039] 7:processes.append(p)

[0040] 8:Endfor

[0041] 9:Forprocessinprocessesdo

[0042] 10:process.start()

[0043] 11:process.join()

[0044] 12:Endfor

[0045] 13:best_model=max(results,key=lambdax:results[x]['score'])

[0046] Figure 3The experimental data is presented. After enabling parallel optimization, the average accuracy of the output model is significantly improved, and it shows an upward trend as the number of parallel instances increases. This shows the effectiveness of parallel optimization in improving model accuracy. Before reaching five parallel instances, parallel optimization has little effect on the average running time. However, when the number of parallel instances reaches five, the running time increases significantly. This may be due to the system approaching capacity limits, resulting in system delays, which seriously reduces the running efficiency of TPOT. During the experiment, the system deadlocked twice when there were four to five parallel instances, and when the number of parallel instances reached six or more, the system deadlock continued to occur, indicating that the current workstation configuration cannot support more than five TPOT instances running in parallel. In view of the system delays observed when using five parallel TPOT instances, this study finally selected four parallel instances as the optimal setting. In short, this experiment determined that under the current hardware configuration, the optimal number of TPOT parallel instances is four, which can not only improve model accuracy, but also avoid system overload, ensuring the efficient operation of TPOT.

[0047] This study generated and selected an optimal stacking model through the improved TPOT. Figure 4 The basic algorithm and operation logic of the model are shown. First, the model uses quadratic polynomial features, then stacks two gradient boosting regressors, each with a unique hyperparameter configuration. Then, the entire model uses RobustScaler for data scaling, and finally uses LassoLarsCV for linear regression. On the target dataset, the model performs well, achieving an R of 0.975 2 It is noteworthy that this performance significantly exceeds the R of the best stacked model generated by standard TPOT. 2 The value is (0.961), which strongly proves the effectiveness of the optimization of the TPOT model in this study. For the sake of distinction, the stacking model generated by the improved TPOT is recorded as TPOT-E, while the stacking model generated by the standard TPOT is recorded as TPOT-S. Figure 5 The fitting curve and error distribution of the TPOT-E model are shown. From the error distribution of the predicted deflection D, the larger errors are mainly concentrated in the case of larger deflection, with an error of about 10%. Overall, the model shows strong prediction performance and is suitable for prediction tasks, and the errors of most prediction targets are relatively small.

[0048] The present invention uses the TPOT-E stacking model integrated with OSGA for symbolic regression and successfully establishes an empirical formula for predicting the mid-span deflection of reinforced concrete beams subjected to impact loads. Evaluation and analysis confirm the validity of the formula. The deflection calculation formula of the drop weight impact test device is:

[0049] The meanings of the symbols in the deflection calculation formula of the drop hammer impact test device are as follows: D represents the mid-span deflection, MV 2 represents the kinetic energy of the drop hammer, Fc represents the compressive strength of concrete, PlFs represents the longitudinal steel ratio multiplied by the yield strength, PtFst represents the transverse steel ratio multiplied by the yield strength. The limitation range of the deflection calculation formula of the drop hammer impact test device is: the size of the concrete beam is 70 < B < 250 mm, 70 < H < 400 mm, 400 < L < 3200 mm, and the mass of the drop hammer is 0.005 < M < 2.5 tons;

[0050] By using the dataset of this study for cross-validation, the effectiveness and robustness of this empirical formula were verified, Figure 6 The scatter plot in shows the prediction distribution of the empirical formula on the test set and training set of this dataset. The R 2 value of this formula reached 0.8023, the mean absolute error (MAE) was 4.648, and the root mean square error (RMSE) was 7.536. The empirical formula showed high prediction accuracy;

[0051] Through the setting of the above technical solutions, to improve the deflection prediction ability in the drop hammer impact test and ensure the practicability of the model, the present invention developed a user-friendly graphical user interface (GUI) based on the Tkinter library in Python, Figure 7 which shows a screenshot of the prediction interface. Engineers can easily input parameter values to use the TPOT-E model in this study for mid-span deflection prediction. The GUI also shows the core structure of the TPOT-E model and a schematic diagram of the symbols representing physical characteristics to help users better understand the model;

[0052] It should be noted that these conclusions are based on the analysis of the dataset obtained by the present invention and are applicable to reinforced concrete beams with rectangular cross-sections, specific span-depth ratios, and compressive strengths within the range of this dataset. Differences in data distribution and scale may require further verification of these conclusions. In addition, the limitation of the sample size may affect the generalization ability of the model. Subsequent research should focus on expanding the sample size and diversity and exploring the damage characteristic differences between rectangular beams and other geometric shapes under impact loads to enhance the comprehensiveness of the research.

[0053] Compared with the prior art, the beneficial effects of the present invention are:

[0054] This paper introduces an EI-AutoML method for predicting the mid-span deflection of reinforced concrete beams subjected to impact loads. Based on existing literature, a comprehensive dataset of 378 data points was compiled. The data came from experiments on rectangular beams subjected to drop weight impact. The experimental group was established in a controlled experiment using AutoML and a high-performance control group model. This paper improved the AutoML tool TPOT pipeline and achieved good results.

[0055] This paper focuses on optimizing the TPOT algorithm to improve its efficiency and accuracy under specific experimental conditions (such as device memory limitations). The optimization process includes adjusting parameters, evaluation indicators and operating modes to adapt to the experimental settings. The effectiveness of these improvements is verified through analysis of comprehensive datasets and comparative evaluation with other machine learning models. The research results confirm that the EI-AutoML method is both feasible and effective, demonstrating its potential practicality in scientific applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 This is a flow chart of the TPOT improvement method of the present invention;

[0057] Figure 2 Contour plot of TPOT parameter design for model error and calculation time of the present invention;

[0058] Figure 3 Line and bar graphs of experimental data for parallel optimization of the present invention;

[0059] Figure 4 This is a brief introduction to the TPOT-E model stacking algorithm of the present invention;

[0060] Figure 5 is the fitting curve and error distribution histogram of the optimal stacking model of the present invention;

[0061] Figure 6 It is a scatter plot of the predicted value and the actual value of the empirical formula of the present invention;

[0062] Figure 7 It is a GUI diagram of the reinforced concrete beam deflection prediction system of the present invention;

[0063] Figure 8 It is a three-dimensional scatter plot of the evaluation indicators of each model of the present invention. DETAILED DESCRIPTION

[0064] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0065] like Figure 1-8 As shown, the impact resistance analysis method of RC beams based on enhanced automatic machine learning includes: developing a predictive analysis model using EI-AutoML, and engineering practice application based on this method;

[0066] The present invention further specifically details that the damage modes of RC beams under impact loads are classified into three types: bending failure, bending-shear failure, and shear failure;

[0067] The automatic machine learning RC beam impact resistance analysis method also includes a drop hammer impact test device, which is used to test the impact resistance of the RC beam.

[0068] The present invention further specifically describes that the database format formula for the drop weight impact test is:

[0069] Δ={x i ,y i}where i = 1, ..., 378,

[0070] x i ={H i ,B i ,L i ,M i ,V i ,Pl i ,Pt i ,Fc i ,Fs i ,Fst i ,N i}

[0071] y i =D i

[0072] The input variables of the drop weight impact test specimens are beam height (H), beam width (B), clear span (L), drop weight mass (M), impact velocity (V), longitudinal reinforcement ratio (Pl), transverse reinforcement ratio (Pt), concrete compressive strength (Fc), longitudinal reinforcement yield strength (Fs), transverse reinforcement yield strength (Fst), and the number of impacts on the same target (N);

[0073] This study generated and selected an optimal stacking model through the improved TPOT. Figure 4The basic algorithm and operation logic of the model are shown. First, the model uses quadratic polynomial features, and then stacks two gradient boosting regressors, each with a unique hyperparameter configuration. Then, the entire model uses RobustScaler for data scaling, and finally LassoLarsCV for linear regression. On the target dataset, the model performs well, achieving an R of 0.975. 2 It is worth noting that this performance significantly exceeds the R of the best stacked model generated by standard TPOT. 2 value (0.961). This result strongly proves the effectiveness of the optimization of the TPOT model in this study. For the sake of distinction, the stacking model generated by the improved TPOT is recorded as TPOT-E, while the stacking model generated by the standard TPOT is recorded as TPOT-S. Figure 5 The fitting curve and error distribution of the TPOT-E model are shown. From the error distribution of the predicted deflection D, the larger errors are mainly concentrated in the case of larger deflection, with an error of about 10%. Overall, the model shows strong prediction performance and is suitable for prediction tasks, and the errors of most prediction targets are relatively small.

[0074] To verify the excellent prediction performance of TPOT-E in drop hammer impact test, this study compared it with ten widely used machine learning methods for regression tasks, including: (1) adaptive boosting (AdaBoost), (2) category boosting (CatBoost), (3) extreme gradient boosting (XGBoost), (4) K-nearest neighbor (KNN), (5) random forest (RF), (6) support vector regression (SVR), (7) decision tree (DT), (8) logistic regression (LR), (9) ridge regression (RR), and (10) TensorFlow (TF). All these machine learning models, including the best model TPOT-E generated by EI-AutoML, were trained on the same dataset and computing environment. Figure 8 The performance of these models is presented in the form of a 3D scatter plot. Obviously, some models based on simple machine learning algorithms, such as logistic regression (LR) and support vector regression (SVR), performed mediocrely. In contrast, machine learning algorithms based on ensemble learning, such as random forest (RF) and K-nearest neighbor (KNN), performed well. In particular, ensemble learning algorithms based on gradient boosted trees, such as XGBoost and CatBoost, performed particularly well, second only to the stacked model generated by optimized TPOT. The model generated by optimized TPOT, TPOT-E, performed best on the test set, achieving an R of 0.975. 2values, while RMSE and MAE are significantly lower than those of other models. These results highlight the success of TPOT optimization in this study and emphasize the effectiveness of the EI-AutoML approach in solving these problems.

[0075] like Figure 1-8 As shown, the aspects of improvement on the impact resistance of RC beams are as follows: parameter configuration, increase in evaluation indicators, and enhancement of the operating mechanism;

[0076] The present invention further specifically describes that the optimization of the parameter settings is "Generations" = 75 and "Population_size" = 75. TPOT achieves excellent model performance within a reasonable time range and successfully balances search accuracy and time cost. The performance evaluation indicators in TPOT include MAE and determination coefficient (R 2 ), the parallel optimization of TPOT is achieved by running multiple TPOT instances simultaneously through multiple processes, and using the computer's memory space to optimize the model selection process;

[0077] From the above, we can see that this study demonstrates an efficient EI-AutoML method by taking TPOT as an example. Figure 1 Various optimizations and improvements implemented in the TPOT algorithm are demonstrated, such as parameter optimization, multi-objective optimization, and parallel optimization of the TPOT pipeline. These improvements are implemented from three aspects: parameter configuration, increase in evaluation indicators, and enhancement of operation mechanisms. The goal is to improve the accuracy of the generated model, minimize the time cost, and improve the efficiency of the model.

[0078] In the parameter optimization part, this study mainly adjusted two key parameters: "Generations" (default value is 20) and "Population_size" (default value is 50), such as Figure 2 As shown in the figure, this study conducted several control experiments by changing these two sets of parameters in TPOT, and ran simulations to observe the corresponding model accuracy and running time. When the parameter combination reached 75×75 or above, the rate of decrease of RMSE slowed down significantly, while the running time increased quadratically. Based on comprehensive considerations, this study optimized the parameter settings to "Generations" = 75 and "Population_size" = 75. Under this parameter, TPOT achieved excellent model performance within a reasonable time range, successfully balancing the search accuracy and time cost.

[0079] This study expands the performance evaluation indicators in TPOT and adds MAE and determination coefficient (R 2), it should be noted that TPOT usually uses a single evaluation indicator by default. In the context of single-objective optimization, TPOT mainly focuses on maximizing or minimizing a specific performance indicator. For classification tasks, TPOT optimizes accuracy by default; for regression tasks, RMSE is used by default to evaluate the performance of the regression model. In this experiment, two commonly used indicators (MAE and R 2 ) in order to more comprehensively evaluate the model performance. This extension enables TPOT to evaluate the performance of the model from multiple perspectives, thereby identifying models that are not only superior in performance but also more suitable for the specific needs of this study. Multi-indicator evaluation provides rich information support for making more informed decisions.

[0080] The parallel optimization of TPOT is achieved by running multiple TPOT instances simultaneously through multiple processes, and the computer's memory space is used to optimize the model selection process. The code below shows the overall method of running TPOT parallel optimization in pseudocode form. The first four lines of code are used to configure TPOT parameters and create instance objects, where the number of "config" corresponds to the number of TPOT instances running in parallel. Lines 5 to 8 create independent processes for each TPOT configuration to run in parallel and store the results in a dictionary. Lines 9 to 12 are responsible for starting and waiting for all parallel processes to complete. Line 13 is used to identify the model with the best performance. In theory, increasing the number of TPOT instances running in parallel can improve the efficiency of the entire TPOT process. However, running multiple TPOT instances in parallel will significantly consume computer resources and may cause system crashes or deadlocks when approaching the computer capacity limit. Therefore, it is necessary to adjust and determine the appropriate number of TPOT instances running in parallel through experiments.

[0081] Pseudo code for parallel optimization in TPOT:

[0082] 1: tpot_configs=[config1,config2,config3,config4]

[0083] 2: manager = Manager()

[0084] 3: results = manager.dict()

[0085] 4: processes = []

[0086] 5:Forconfigintpot_configsdo 6:

[0088] p=Process(target=run_tpot,args=(X_train,y_train,X_test,y_test,config,results))

[0089] 7: processes.append(p)

[0090] 8: Endfor

[0091] 9: Forprocessinprocessesdo

[0092] 10: process.start()

[0093] 11: process.join()

[0094] 12: Endfor

[0095] 13: best_model=max(results,key=lambdax:results[x]['score']) Figure 3 The experimental data is presented. After enabling parallel optimization, the average accuracy of the output model is significantly improved, and it shows an upward trend as the number of parallel instances increases. This shows the effectiveness of parallel optimization in improving model accuracy. Before reaching five parallel instances, parallel optimization has little effect on the average running time. However, when the number of parallel instances reaches five, the running time increases significantly. This may be due to the system approaching capacity limits, resulting in system delays, which seriously reduces the running efficiency of TPOT. During the experiment, the system deadlocked twice when there were four to five parallel instances, and when the number of parallel instances reached six or more, the system deadlock continued to occur, indicating that the current workstation configuration cannot support more than five TPOT instances running in parallel. In view of the system delays observed when using five parallel TPOT instances, this study finally selected four parallel instances as the optimal setting. In short, this experiment determined that under the current hardware configuration, the optimal number of TPOT parallel instances is four, which can not only improve model accuracy, but also avoid system overload, ensuring the efficient operation of TPOT.

[0096] The present invention further specifically describes that, by using the TPOT-E stacking model integrated with OSGA for symbolic regression, an empirical formula for predicting the mid-span deflection of reinforced concrete beams subjected to impact loads was successfully established, and the evaluation and analysis confirmed the validity of the formula. The deflection calculation formula of the drop weight impact test device is:

[0097] The symbols in the deflection calculation formula of the drop weight impact test device represent the following meanings: D represents the mid-span deflection, MV2 It represents the drop hammer kinetic energy, Fc represents the compressive strength of concrete, PlFs represents the longitudinal steel ratio multiplied by the yield strength, and PtFst represents the transverse steel ratio multiplied by the yield strength. The limitation range of the deflection calculation formula of the drop hammer impact test device is as follows: for the concrete beam, the size is 70 < B < 250 mm, 70 < H < 400 mm, 400 < L < 3200 mm, and the mass of the drop hammer is 0.005 < M < 2.5 tons;

[0098] By using the dataset of this study for cross-validation, the effectiveness and robustness of this empirical formula were verified. Figure 6 The scatter plot in [reference] shows the prediction distribution of the empirical formula on the test set and training set of this dataset. The R 2 value reached 0.8023, the mean absolute error (MAE) was 4.648, and the root mean square error (RMSE) was 7.536. The empirical formula showed high prediction accuracy.

[0099] Through the setting of the above technical solutions, to improve the deflection prediction ability in the drop hammer impact test and ensure the practicability of the model, the present invention developed a user-friendly graphical user interface (GUI) based on the Tkinter library in Python. Figure 7 The screenshot of the prediction interface is shown. Engineers can easily input parameter values to use the TPOT-E model in this study for mid-span deflection prediction. The GUI also shows the core structure of the TPOT-E model and the schematic diagram of symbols representing physical characteristics, helping users better understand the model.

[0100] It should be noted that these conclusions are based on the analysis of the dataset obtained by the present invention and are applicable to reinforced concrete beams with rectangular cross-sections, specific span-depth ratios, and compressive strengths within the range of this dataset. Differences in data distribution and scale may require further verification of these conclusions. In addition, the limitation of the sample size may affect the generalization ability of the model. Subsequent research should focus on expanding the sample size and diversity and exploring the damage characteristic differences between rectangular beams and other geometric shapes under impact loads to enhance the comprehensiveness of the research.

[0101] In summary, by comparing the AutoML experimental group with the high-performance control group, it was found that the stacked model generated by the TPOT pipeline of the AutoML tool was significantly superior to other models in the control group in terms of prediction accuracy and error. This model showed excellent prediction accuracy and minimal error, highlighting its great potential in mid-span deflection prediction and other prediction fields. The research results show that adopting AutoML technology instead of traditional machine learning technology proves its superiority in terms of effect and efficiency.

[0102] This paper focuses on optimizing the TPOT algorithm to improve its efficiency and accuracy under specific experimental conditions (such as device memory limitations). The optimization process includes adjusting parameters, evaluation indicators and operating modes to adapt to the experimental settings. The effectiveness of these improvements is verified through analysis of comprehensive datasets and comparative evaluation with other machine learning models. The research results confirm that the EI-AutoML method is both feasible and effective, demonstrating its potential practicality in scientific applications.

[0103] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning, characterized in that: include: Implement optimization and improvement of the impact resistance of RC beams in the TPOT algorithm, optimize the parameters of the impact resistance of RC beams, multi-objectives, and parallelization of the TPOT pipeline; The aspects of improvement on the impact resistance of RC beams are as follows: parameter configuration, increase of evaluation indicators and enhancement of operating mechanism.

2. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 1, characterized in that: The optimization of the parameter settings is "Generations"=75 and "Population_size"=75.

3. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 1, characterized in that: The performance evaluation indicators in the TPOT include MAE and determination coefficient (R 2 ).

4. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 1, characterized in that: The parallel optimization of TPOT is achieved by running multiple TPOT instances simultaneously through multiple processes, and the computer's memory space is used to optimize the model selection process. The automatic machine learning RC beam impact resistance performance analysis method also includes a drop hammer impact test device for testing the impact resistance of the RC beam.

5. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 4 is characterized in that: The database format formula for the drop weight impact test is: Δ={x i ,y i }where i=1,...,378, x i ={H i ,B i ,L i ,M i ,V i ,Pl i ,Pt i ,Fc i ,Fs i ,Fst i ,N i } y i =D i The input variables of the drop hammer impact test sample are beam height (H), beam width (B), clear span (L), drop hammer mass (M), impact velocity (V), longitudinal reinforcement ratio (Pl), transverse reinforcement ratio (Pt), concrete compressive strength (Fc), longitudinal reinforcement yield strength (Fs), transverse reinforcement yield strength (Fst) and the number of impacts on the same target (N).

6. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 1, characterized in that: The specific tasks of the automatic machine learning module include data preprocessing, feature engineering, model selection, hyperparameter tuning and model evaluation.

7. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 1, characterized in that: The tool of the automatic machine learning module is the TPOT pipeline, which is used to optimize the machine learning pipeline for the genetic algorithm to select the best performing model and tune the hyperparameters.

8. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 7 is characterized in that: The predefined indicators of the TPOT pipeline include accuracy, precision, mean square error, and mean absolute error.

9. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 8, characterized in that: The mathematical expressions of the mean square error, root mean square error, mean absolute error and determination coefficient evaluation index are: Among them, y e represents the actual measured displacement of the beam, y p Represents the predicted value of the model output, and n represents the total number of samples in the data set.

10. The method for analyzing the impact resistance of RC beams based on enhanced automatic machine learning according to claim 5, characterized in that: The deflection calculation formula of the drop weight impact test device is: The meanings represented by the symbols in the deflection calculation formula of the drop hammer impact test device are as follows: D represents the mid-span deflection, MV 2 represents the kinetic energy of the drop hammer, Fc represents the compressive strength of concrete, PlFs represents the longitudinal steel ratio multiplied by the yield strength, PtFst represents the transverse steel ratio multiplied by the yield strength. The limitation range of the deflection calculation formula of the drop hammer impact test device is: the size of the concrete beam is 70 < B < 250 mm, 70 < H < 400 mm, 400 < L < 3200 mm, and the mass of the drop hammer is 0.005 < M < 2.5 tons.

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