PBL shear connector multi-objective optimization design method and system based on machine learning

Abstract

The invention discloses a multi-objective optimization design method for a PBL shear connector based on machine learning, and the method is characterized in that the method comprises the following steps: collecting the shear bearing capacity of a plurality of PBL shear connectors containing input parameters and output parameters, and deducing test data; firstly, a Catboost machine learning model is trained by utilizing the deduced test data, then the trained Catboost machine learning model is adopted to predict the shear bearing capacity of the PBL shear connector, the sensitivity of input parameters is analyzed in combination with an SHAP method, and finally, a multi-target genetic algorithm is introduced into the verified Catboost machine learning model, so that the shear bearing capacity of the PBL shear connector is predicted. And a multi-objective optimization model with the minimum hole opening number and the minimum steel quality as objective functions is established, and PBL shear connector optimization design is conducted through the multi-objective optimization model. The lightweight and efficient construction of the PBL shear connector can be realized on the premise of meeting the shear bearing capacity.

Description

Technical Field

[0001] This invention belongs to the field of PBL shear connector optimization design technology, specifically involving a multi-objective optimization design method and system for PBL shear connectors based on machine learning. Background Technology

[0002] PBL shear connectors, as key connection components in steel-concrete composite structures, are widely used in engineering practice due to their excellent mechanical properties. Compared with other shear connectors (such as studs and angle steel shear connectors), PBL shear connectors not only have better shear resistance but also exhibit excellent fatigue resistance under cyclic loading, thereby improving the long-term reliability and safety of steel-concrete composite structures.

[0003] However, predicting the shear capacity of PBL shear keys remains challenging. Although existing literature provides various formulas for predicting shear performance, most of them are obtained through regression analysis of small-scale experiments. Because PBL shear key tests exist in various forms, different tests exhibit significant differences in specimen size, steel plate embedment depth, concrete block size, reinforcement arrangement, loading methods, and boundary constraint conditions, leading to variations in their shear capacity results.

[0004] Based on the different test methods, PBL (Position-Bound Brace) specimens can be divided into standard ejection specimens and embedded ejection specimens. In the standard ejection test, the steel plate is only partially embedded in the concrete, the specimen size is relatively small, and the arrangement of the reinforcing bars in the hole is relatively simplified. It is mainly used to quickly evaluate the basic shear resistance of PBL connectors. In the embedded ejection test, the steel plate is usually completely or deeply embedded in the concrete slab, the specimen size is larger, and the steel plate hole is usually equipped with reinforcing bars to better simulate the stress state of the actual composite beam. These differences result in significant differences in the load-slip relationship, ultimate bearing capacity, and failure mode under different test methods.

[0005] Several shear capacity calculation formulas were evaluated, and regression evaluation indices were used to analyze the predictive performance. The results show that the coefficient of determination R of these formulas is... 2 The lowest value is 0.62, while the mean absolute percentage error can reach 42.2%, indicating that the prediction accuracy of existing formulas fluctuates significantly on some samples. This uncertainty means that designers still need to verify the load-bearing capacity through additional tests after using empirical formulas, leading to longer design cycles, increased design costs, and risks to structural safety.

[0006] In summary, the lack of a unified and reliable design standard for the shear bearing capacity of PBL shear connectors is a significant factor limiting their further and efficient application. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the prior art and provide a multi-objective optimization design method and system for PBL shear connectors based on machine learning, which realizes the optimized design of PBL connectors with the goal of lightweight and efficient construction.

[0008] To achieve the above objectives, the present invention is implemented using the following technical solution: On the one hand, this invention provides a multi-objective optimization design method for PBL shear connectors based on machine learning, including the following steps: Test data on the shear bearing capacity of 211 sets of PBL connectors, including input and output parameters, were collected to derive experimental data. The Catboost machine learning model was trained using the experimental data, and the trained Catboost machine learning model was used to predict the shear capacity of the PBL shear connector. The sensitivity of the input parameters was analyzed using the SHAP method, and the predicted shear capacity was compared and verified with empirical formulas. A multi-objective genetic algorithm was introduced into the validated Catboost machine learning model to construct a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions. The multi-objective optimization model was then used to optimize the design of PBL connectors.

[0009] Furthermore, the experimental data includes 80% training data and 20% test data; The input parameters include the thickness of the perforated steel plate, the width of the perforated steel plate, the bearing area of ​​the perforated plate, the diameter of the perforation, the number of perforations, the spacing between perforations, the concrete strength, the number of perforated reinforcing bars, and the diameter of the reinforcing bars; the output parameter is the shear bearing capacity of the PBL connector.

[0010] Furthermore, the ejection test data includes non-pressure-bearing sample data and pressure-bearing sample data of the PBL connector end.

[0011] Furthermore, in the methods for determining the compressive strength of concrete from different sources, to eliminate the influence of size effects and ensure the consistency and reliability of the data, all compressive strength data were converted to standard cube dimensions of 150 mm × 150 mm × 150 mm. The strength conversion formula is expressed as follows: ; in, f c For the strength of concrete cubes, f c,other The compressive strength of a prism or cylinder. k This is the strength conversion factor. k The values ​​are 1.25 and 1.15 respectively.

[0012] Furthermore, in the model performance evaluation, the predicted shear capacity of the PBL connector was compared and verified with empirical formulas, using four indicators: coefficient of determination R², mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE). ; ; ; ; Where n is the number of database samples, The true value is the average of the true values. , which is the predicted value.

[0013] Furthermore, the multi-objective optimization model formula is expressed as: ; ; ; in, V req The predicted shear strength value is calculated by the Catboost regression model based on the design variables. L The length of the shear key. W The mass of the steel is calculated from the volume of the shear key and the density of the steel.

[0014] On the other hand, the present invention provides a multi-objective optimization design system for PBL shear connectors based on machine learning, comprising the following modules: The data collection module is used to collect test data on the shear bearing capacity of PBL connectors, including input and output parameters. The model training module is used to train the Catboost machine learning model using the experimental data, and to predict the shear bearing capacity of the PBL connector using the trained Catboost machine learning model. The training and validation module is used to analyze the sensitivity of input parameters using the SHAP method and to compare and validate the predicted shear capacity with empirical formulas. The optimization design module is used to introduce a multi-objective genetic algorithm into the validated Catboost machine learning model, construct a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions, and use the multi-objective optimization model to optimize the design of PBL connectors.

[0015] Compared with the prior art, the beneficial effects achieved by the present invention are as follows: The multi-objective optimization design method and system for PBL shear connectors based on machine learning provided by the present invention selects multiple key factors as input parameters and shear strength as output parameters. It combines a multi-objective genetic algorithm with the Catboost model to achieve the optimized design of lightweight and efficient construction of PBL shear keys with the goal of minimizing the number of openings and minimizing the steel mass. Attached Figure Description

[0016] Figure 1 A flowchart illustrating a machine learning-based multi-objective optimization design method for PBL shear connectors provided in an embodiment of the present invention.

[0017] Figures 2-11 This is a distribution diagram of the input and output parameters for the shear resistance of the dataset.

[0018] Figure 12 A heatmap of the Pearson correlation coefficient between input and output parameters.

[0019] Figures 13-17 This is a distribution diagram of shear capacity data in the training and test sets.

[0020] Figure 18 This is a distribution chart of the SHAP values ​​for each input parameter variable.

[0021] Figure 19 This is a distribution diagram of the stochastic feasible solution and the Pareto front solution in the three-dimensional space of "shear bearing capacity, number of openings, and steel quality".

[0022] Figure 20 This is a performance comparison chart of five machine learning models.

[0023] Figures 21-25 A scatter plot showing the overall agreement between the predicted and experimental results. Detailed Implementation

[0024] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0025] like Figure 1 As shown in the figure, this embodiment of the invention provides a multi-objective optimization design method for PBL shear connectors based on machine learning, including the following steps: Test data on the shear bearing capacity of PBL shear connectors, including input and output parameters, were collected from 211 sets of data. The Catboost machine learning model was trained using the experimental data, and the trained Catboost machine learning model was used to predict the shear capacity of the PBL shear connector. The sensitivity of input parameters was analyzed using the SHAP method, and the predicted shear capacity was compared and verified with empirical formulas. A multi-objective genetic algorithm was introduced into the verified Catboost machine learning model to construct a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions. The multi-objective optimization model was then used to optimize the design of PBL shear connectors.

[0026] Taking a steel box girder of a railway bridge across the Yellow River as an example, the original design had a steel plate thickness of 28 mm and a plate width of 400 mm. Eight holes with a diameter of 40 mm were installed, and 28 mm diameter perforated steel bars were used. The yield strength of the steel bars was 400 MPa, the yield strength of the steel plate was 500 MPa, and the concrete strength grade was C130.

[0027] Using the established CatBoost prediction model, the predicted shear capacity of the PBL shear connector is 973 kN / m. Subsequently, with the design shear capacity (i.e., the CatBoost predicted value) as the constraint, and the number of holes, steel plate thickness, reinforcement strength, and concrete strength as design variables, and with the optimization objectives of "minimum number of holes" and "minimum steel consumption," a multi-objective optimization analysis was conducted. The NSGA-II algorithm was used during the optimization process, resulting in a series of optimized schemes. The original design schemes and optimization results are summarized in Table 1.

[0028] Table 1 Frontier Solution plan <![CDATA[ t s (mm)]]> <![CDATA[ b s (mm)]]> <![CDATA[ n h (pieces / m) <![CDATA[ n r (pieces / m) <![CDATA[ d r (mm)]]> <![CDATA[ f c (MPa)]]> <![CDATA[ f y (MPa)]]> (kg / m) (kN / m) S1 16 400 6 6 28 55 335 43.3 1290 S2 18 400 5 5 28 60 400 55.6 1164 S3 20 400 4 4 28 80 400 62.0 1118 S4 22 400 3 3 28 100 400 71.5 1187 S5 24 400 6 6 28 55 400 77.02 1220 Compared to the original design, the proposed optimized schemes achieve overall weight reduction and hole count control while meeting shear capacity requirements. The steel plate thickness is reduced from 28 mm to approximately 16–24 mm, resulting in an overall reduction of steel consumption of approximately 10%–50%, and the hole count is adjusted from 8 holes / m to a more reasonable 3–6 holes / m. The shear capacity of all schemes is slightly higher than the original design. Overall, scheme S1 focuses more on ultimate weight reduction, scheme S4 ​​has a greater advantage in reducing the number of holes, while the other schemes offer a more balanced compromise between plate thickness, hole count, and material strength.

[0029] In some embodiments, the launch test data includes 80% training data and 20% test data; The input parameters include the thickness of the perforated steel plate, the width of the perforated steel plate, the bearing area of ​​the perforated plate, the diameter of the perforation, the number of perforations, the spacing between perforations, the concrete strength, the number of perforated reinforcing bars, and the diameter of the reinforcing bars; the output parameter is the shear bearing capacity of the PBL shear connector.

[0030] Experimental data from 211 sets of PBL connectors were collected to study the shear capacity performance of non-bearing PBL connectors. It should be noted that due to the limited number of non-bearing samples, end-bearing samples were introduced as a supplement to enhance the completeness of the database and the stability of the training model. Although the local stress state of end-bearing connectors under end compression conditions differs from that of non-bearing connectors, their key characteristic parameters (such as the diameter of the steel plate opening, the diameter of the perforated rebar, and the concrete strength) contribute to the shear capacity in a basically consistent manner. Therefore, introducing end-bearing samples will not significantly affect the prediction of the shear capacity of non-bearing connectors. In this way, the database provides a more reliable data foundation for modeling and optimizing the shear performance of non-bearing PBL connectors while ensuring a sufficient sample size.

[0031] The specimen input parameters include: the thickness of the perforated steel plate ( t s ), Width of perforated steel plate ( b s ), the bearing area of ​​the perforated steel plate ( A c ), opening diameter ( d h ), Number of openings ( n h ), hole spacing ( S h ), concrete strength ( f c ), number of perforated steel bars ( n r ), diameter of reinforcing bar ( d r The output parameter is the shear bearing capacity of the PBL connector.

[0032] All specimens exhibited similar failure models: concrete tenon crushing, bending deformation of perforated reinforcing bars, and extrusion deformation of the perforated steel plate hole walls. In the methods for determining the compressive strength of concrete from different sources, to eliminate the influence of size effects and ensure data consistency and reliability, all compressive strength data were converted to standard cube dimensions of 150 mm × 150 mm × 150 mm. The strength conversion formula is expressed as: ; in, f c For the strength of concrete cubes, f c,other The compressive strength of a prism or cylinder. k This is the strength conversion factor. k The values ​​are 1.25 and 1.15 respectively.

[0033] Table 2 describes the input and output data for shear strength. Input parameters unit Minimum value lower quartiles median Upper quartiles Maximum value average value Standard deviation <![CDATA[ t s ]]> (mm) 6.0 13.0 15.0 20.0 35.0 17.5 6.5 <![CDATA[ b s ]]> (mm) 65.0 100.0 127.0 150.0 400.0 148.7 67.2 <![CDATA[ d h ]]> (mm) 0.0 50.0 50.0 60.0 100.0 55.2 18.3 <![CDATA[ n h ]]> (unit) 0.0 1.0 2.0 3.0 4.0 2.0 1.0 <![CDATA[ s h ]]> (mm) 0.0 0.0 100.0 125.1 250.0 77.5 69.2 <![CDATA[ f c ]]> (MPa) 26.1 39.3 50.0 55.2 86.0 48.6 11.05 <![CDATA[ f y ]]> (MPa) 300.0 359.5 408.0 346.0 500.0 404.7 46.6 <![CDATA[ n r ]]> (unit) 0.0 1.0 2.0 3.0 4.0 1.75 1.09 <![CDATA[ d r ]]> (mm) 0.0 14 20.0 25.0 32.3 18.4 9.7 <![CDATA[ p u ]]> (kN) 113.9 346.5 543.2 1176.3 4134.0 952.4 967.6 Figures 2-11 The graph shows the distribution of input and output parameters for the shear resistance of the dataset, with the vertical axis representing the frequency of different categories. The shear key in the perforated steel plate has a wide range of values: steel plate thickness... t s Steel plate width between 6-35mm b s The span ranges from tens to hundreds of millimeters; the aperture diameter and number of apertures also show significant dispersion, with both unapertured samples and arrangements with multiple apertures and large spacing. Regarding material properties, the concrete strength... f c and steel strength f y It covers the strength grades of materials commonly used in engineering.

[0034] To analyze the complex relationship between input and output parameters, the Pearson correlation coefficient was calculated. Figure 12 A heatmap showing the Pearson correlation coefficients between all parameters is displayed, revealing that the steel plate thickness... t s and board width b s There is a strong positive correlation (0.78) and a significant positive correlation (0.69) with the aperture dh. This indicates that in practical design, the steel plate thickness, width, and aperture often increase simultaneously. Furthermore, the number of holes... n h Spacing between holes s h There was a moderate positive correlation (0.54), while the number of steel bars... nr With the diameter of the reinforcing bar dr It also shows a positive correlation (0.46), indicating that certain geometric parameters are interrelated in structural design. Steel plate thickness t s Number of holes n h A moderate negative correlation (-0.36) exists, indicating that thicker steel plates tend to have fewer holes. On the other hand, concrete strength... f cThe correlation coefficient with most geometric parameters is close to zero, indicating that it is largely independent of the dimensional features of the connector. CatBoost (Categorical Boosting) is an ensemble learning algorithm based on gradient boosting, which excels at handling categorical features. Its core advantage lies in its built-in categorical encoding methods (order boosting and target statistics), avoiding the curse of dimensionality problem caused by common one-hot encoding, while reducing the risk of overfitting. CatBoost exhibits high stability and generalization ability when handling small samples and high-dimensional sparse data. In addition, the algorithm supports the construction of symmetric tree structures, making the training and prediction process more efficient, and supports GPU acceleration. In complex nonlinear relationship modeling problems such as structural engineering and materials mechanics, CatBoost can balance prediction accuracy and computational efficiency, and is therefore widely used. In model performance evaluation, this invention uses four commonly used statistical indicators. The coefficient of determination (R²) is used to measure the degree of fit between the model's prediction results and the true values. Its value ranges between 0 and 1; the closer the value is to 1, the higher the prediction accuracy of the model. In addition, root mean square error (RMSE), mean absolute error (MAE), and mean square error (MSE) are introduced to characterize the magnitude of prediction error. These error metrics are all optimized for smaller values. RMSE and MSE are more sensitive to larger deviations, while MAE better reflects the overall prediction error level. By comparing the use of these metrics, the prediction performance of different machine learning algorithms can be comprehensively evaluated. In the model performance evaluation, the predicted shear capacity of the PBL connector is compared and verified with empirical formulas, using four metrics: coefficient of determination R², mean square error (MSE), root mean square error (RMSE), and mean absolute error (MAE). ; ; ; ; Where n is the number of database samples, The true value is the average of the true values. , These are predicted values.

[0035] To ensure a fair and objective evaluation of the predictive performance of the machine learning model, this invention employs a K-fold cross-validation method. In this method, the original dataset is divided into K equal-sized subsets, where each subset serves as the validation set during the validation process, and the remaining K-1 subsets serve as the training set, thus guaranteeing that each sample can be used once during both training and validation. In this study, K is set to 5, meaning the dataset is divided into 5 equal subsets for cross-validation and hyperparameter tuning. Furthermore, to further examine the model's generalization performance, this study uses random sampling to divide the dataset into training and test sets. 80% of the data is used for model training and hyperparameter optimization, while the remaining 20% ​​serves as an independent test set for final performance evaluation.

[0036] Figures 13-17 The distribution of shear capacity data across the training and test sets is presented. As can be seen from the figure, the overall data distribution remains consistent across both datasets, avoiding evaluation bias caused by imbalanced data partitioning.

[0037] Grid search is a commonly used method for hyperparameter tuning in machine learning algorithms. By pre-setting the possible combinations of hyperparameter values ​​and calculating the model's performance metrics for each combination, the optimal hyperparameter combination can be determined, allowing the model to achieve its best performance.

[0038] Table 3 Hyperparameter Table Machine learning models depth Number of iterations Learning rate Minimum number of leaves Minimum number of split samples Maximum number of features Subsample number Column sampling number Catboost 4 500 0.1 - - - - - GB 11 300 0.05 2 2 3 1 - RF None 500 - 1 2 3 - - XGBoost 2 1000 0.03 - - - 0.8 1 EX None 300 - 1 5 None - - The SHAP method is widely used in interpretive research of machine learning models. Originating from the concept of Shapley values ​​in game theory, its core idea is to measure the importance of each input feature in the prediction result by assigning a "contribution value." Specifically, SHAP treats a complex machine learning model as an interpretable linear combinatorial model, where the predicted value can be decomposed into the sum of the contributions of each input feature. Thus, the SHAP value of each feature reflects the marginal impact of that feature on the prediction result.

[0039] The advantage of SHAP analysis lies in its ability to quantify the importance of individual variables and demonstrate the positive and negative effects of features on predictions at different sample levels, thus enabling both global and local interpretations of "black box" models. Its basic mathematical form can be expressed as: ; in, f(x) This represents the interpretation results of the model. , k For the number of features, It is a constant. φ j For the firstj The SHAP value of each feature.

[0040] SHAP (SHapley Additive exPlanations) analysis is a method for quantifying the contribution of each input feature to the predictions of a machine learning model. This method assesses the importance of each feature by calculating its marginal contribution to the model's output under different feature combinations. Compared to traditional feature importance metrics, SHAP provides consistent and interpretable values, ensuring that the sum of feature contributions equals the model's predicted output. This allows SHAP to reveal not only the impact of individual features but also the interactions between features, providing strong support for the interpretability of black-box models. In applications such as structural engineering or materials performance prediction, SHAP analysis can be used to identify key parameters.

[0041] Figure 18 The distribution of SHAP values ​​for each input variable is shown in the figure. As can be seen from the figure, the SHAP value range for the number of openings is the widest, with the largest span between positive and negative contributions, and the high values ​​(red) are mainly concentrated in the positive contribution region. This indicates that increasing the number of openings not only significantly improves the bearing capacity, but its improvement effect also has good stability and reliability. The SHAP distribution for rebar strength also shows a clear positive correlation trend, but its upper and lower limits of contribution are slightly smaller than those for the number of openings. The SHAP value ranges for opening diameter and rebar number also show a clear positive extension. (Opening spacing...) S h The SHAP values ​​are mostly distributed in the positive direction, indicating that increasing the spacing between openings helps improve shear capacity, but the improvement is relatively small. This is because when the spacing is too small, a "group effect" occurs, weakening the local bearing capacity; while appropriately increasing the spacing can reduce this reduction effect.

[0042] Genetic algorithm (GA) is an optimization method that simulates the biological evolution process in nature. Its core idea is to gradually approach the global optimum by selecting, crossing over and mutating candidate solutions in each generation through iterative evolution of the population. Compared with traditional gradient optimization methods, GA does not depend on the differentiability of the objective function and has obvious advantages in dealing with high-dimensional, nonlinear, multi-peak or complex constraint problems. This study proposes a multi-objective optimization method based on the aforementioned Catboost machine learning model and combined with genetic algorithm to meet the design requirements of PBL shear connectors. The aim is to achieve a balance between shear strength, material utilization and opening arrangement. Specifically, it includes the following two optimization objectives: (1) minimizing steel consumption; (2) maximizing the opening spacing.

[0043] The optimization process is implemented based on the DEAP framework, and the Pareto optimal solution set is solved using NSGA-II. The fitness function considers two optimization objectives simultaneously, with weights set to -1 and -1, corresponding to minimizing steel mass and minimizing the number of openings, respectively. The main parameters of the optimization design process are: population size 200, number of generations 200, crossover probability 0.7, and mutation probability 0.2. Two-point crossover and random mutation operators are used during the evolutionary process to maintain the diversity of solutions.

[0044] The multi-objective optimization model is expressed as follows: ; ; ; in, V req The predicted shear strength value is calculated by the Catboost regression model based on the design variables. L The length of the shear key. W The mass of the steel is calculated from the volume of the shear key and the density of the steel.

[0045] Figure 19 The figure shows the distribution of stochastic feasible solutions and Pareto front solutions in the three-dimensional space of "shear bearing capacity, number of openings, and opening spacing". The black dots represent feasible samples, i.e., random samples that meet the constraints, and the red dots represent Pareto optimal solutions.

[0046] Figure 13 The distribution of randomly generated feasible solutions and Pareto optimal solutions in a three-dimensional space composed of "number of holes, steel consumption and shear bearing capacity" is shown. Among them, blue points represent feasible solutions that satisfy all constraints, and red points represent Pareto optimal solutions. Overall, the random samples are relatively dispersed in the solution space and cover a large area. However, these points are mostly not ideal in terms of weight, bearing capacity and performance balance, often showing that: either the self-weight is too large and the bearing capacity is insufficient, or although there is sufficient bearing capacity, there is obvious material redundancy. In contrast, the Pareto optimal points are concentrated near the boundary of the solution space, forming a set of non-dominated solutions, representing the optimal compromise between multiple objectives. Further observation of each projection plane reveals the following pattern: (1) In WP On the plane, the Pareto front is mainly concentrated in the regions of 20-60 kg / m and 500-2500 kN / m; (2) in Wn h On the plane, the Pareto front mainly lies in the range of 2–10 pcs / m and 20–40 kg / m; (3) in n h -POn the plane, the Pareto front is mainly concentrated in the ranges of 2–10 count / m and 500–2500 kN / m. The distribution of Pareto optimal points indicates that the optimization results generally exhibit a trend of "fewer holes, lower steel consumption, and higher shear capacity." The multi-objective optimization algorithm NSGA-II can effectively find a balanced solution that achieves a reasonable trade-off between the number of holes, steel consumption, and shear capacity.

[0047] Figure 20 This presentation compares the performance of five machine learning models—CatBoost, GB, RF, XGBoost, and EX—on the training and test sets, with R² as the evaluation metric. 2 Table X presents the error values ​​of the machine learning models on the training and test sets. By finding the optimal hyperparameters for each machine learning model and calculating the error using four standard methods, the predictive performance of the five machine learning models is evaluated as follows: CatBoost achieved the highest coefficient of determination (R²) on both the training and test sets, at 0.987 and 0.956 respectively, indicating its best prediction accuracy. GB and RF followed, while EX and XGBoost had slightly lower R² values. Regarding error metrics, CatBoost consistently showed the lowest error on the test data, with MAE, MAPE, and RMSE of 134.906, 218.353, and 17.029% respectively, validating its strong generalization ability. In contrast, EX achieved the lowest error on the training set, indicating excellent fitting ability but some overfitting. GB and RF maintained moderate error levels on both datasets, while XGBoost showed significant differences in performance between the training and test sets.

[0048] When performing machine learning prediction on the shear performance of PBL shear connectors, the training data was also divided into training and validation sets, while independent test data was retained. First, learning was performed on the training set, and then performance evaluation was conducted on the validation set. This process was repeated multiple times to ensure the stability of the model training and the reliability of the results. Table 7 shows the R² error values ​​for the training data. The results show that the CatBoost algorithm has the best performance with an average R² of 0.987 on the training data for the shear bearing capacity of PBL connectors.

[0049] Compare the Catboost prediction results with empirical formulas, from... Figures 21-25From the scatter plot distribution, CatBoost's prediction results are more concentrated, with most data points falling within the ±20% error band, and showing a good linear correlation with experimental values. This indicates that the model has strong stability and adaptability at different shear capacity levels. The prediction results of various empirical formulas are generally more dispersed, with some formulas exhibiting significant underestimation or overestimation in the high-capacity range. For example, the formula proposed by Yang Y et al. deviates significantly from experimental values, with many data points falling outside the ±20% error band; the formula by Oguejiofor et al. also has similar issues.

[0050] On the other hand, the present invention provides a multi-objective optimization design system for PBL shear connectors based on machine learning, comprising the following modules: The data collection module is used to collect 211 sets of test data on the shear bearing capacity of PBL connectors, including input and output parameters; The model training module is used to train the Catboost machine learning model using the experimental data, and to predict the shear bearing capacity of the PBL connector using the trained Catboost machine learning model. The training and validation module uses the SHAP method to analyze the sensitivity of input parameters and compares the predicted shear capacity with empirical formulas for validation. The optimization design module introduces a multi-objective genetic algorithm into the validated Catboost machine learning model to construct a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions, and uses the multi-objective optimization model to optimize the design of PBL shear connectors.

[0051] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for multi-objective optimization design of PBL shear connectors based on machine learning, characterized in that, The method comprises the following steps: Collecting a plurality of push-out test data of PBL connectors containing input parameters and output parameters; Training a Catboost machine learning model using the push-out test data, and predicting the shear capacity of the PBL shear connector using the trained Catboost machine learning model; Analyzing the sensitivity of the input parameters using the SHAP method, and comparing and verifying the predicted shear capacity with an empirical formula; Introducing a multi-objective genetic algorithm into the verified Catboost machine learning model, constructing a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions, and using the multi-objective optimization model to optimize the design of the PBL shear connector.

2. The machine learning based PBL shear connector multi-objective optimization design method according to claim 1, characterized in that, The push-out test data includes 80% training data and 20% test data; The input parameters include the thickness of the opening steel plate, the width of the opening steel plate, the bearing area of the opening plate, the diameter of the opening, the number of openings, the spacing between openings, the concrete strength, the number of perforated steel bars, and the diameter of the steel bars; and the output parameter is the shear capacity of the PBL shear connector. 3.The method of claim 1, wherein, The push-out test data includes non-bearing sample data and PBL shear connector end bearing sample data.

4. The machine learning based PBL shear connector multi-objective optimization design method of claim 1, wherein, In the determination method of the compressive strength of concrete in different source tests, in order to eliminate the size effect and ensure the consistency and reliability of the data, all the compressive strength data are converted to the standard cubic size of 150 mm × 150 mm × 150 mm, and the strength conversion formula is expressed as: ； wherein, f c is the concrete cube strength, f c,other is the prismatic or cylindrical compressive strength, k is the strength conversion factor, k and take the values 1.25, 1.15, respectively.

5. The machine learning based PBL shear connector multi-objective optimization design method of claim 1, wherein, In the model performance evaluation, the predicted results of the shear capacity of the PBL connector are compared and verified with the empirical formula, and four indexes of determination coefficient R², mean square error MSE, root mean square error RMSE, and mean absolute error MAE are used: ； ； ； ； wherein n is the database sample, is the true value, and the average of the true values is , is the predicted value.

6. The machine learning based PBL shear connector multi-objective optimization design method of claim 1, wherein, The multi-objective optimization model formula is expressed as: ； ； ； wherein, V req is the shear strength prediction value calculated by the Catboost regression model according to the design variables, L is the length of the shear key, W represents the mass of steel, calculated from the volume of the shear key and the density of steel.

7. A machine learning based multi-objective optimization design system for PBL shear connectors, characterized in that, The method comprises the following modules: A data collection module for collecting a plurality of push-out test data of PBL connectors containing input parameters and output parameters; A model training module for training a Catboost machine learning model using the push-out test data, and predicting the shear capacity of the PBL connector using the trained Catboost machine learning model; A training and verification module for quantitatively correlating the input parameters and the predicted results of the shear capacity of the PBL connector using the SHAP method, and comparing and verifying the predicted results of the shear capacity of the PBL connector with an empirical formula; An optimization design module for introducing a multi-objective genetic algorithm into the verified Catboost machine learning model, constructing a multi-objective optimization model with the minimum number of openings and the minimum steel mass as objective functions, and using the multi-objective optimization model to optimize the design of the PBL shear connector.

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