Data-driven prediction and design method for explosive damage of stirrup-reinforced concrete columns

Abstract

This invention relates to the field of explosion damage assessment and intelligent design of reinforced concrete, and is a data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups. The invention first determines the design parameters to be optimized, forming the optimization object, and sets the optimization objectives as minimizing the total cost and minimizing the damage index. Then, a non-dominated sorting genetic algorithm is used to iterate the optimization object until the population converges, outputting a non-dominated solution set. Finally, the entropy-weighted TOPSIS method is used to select the optimal individual from the non-dominated solution set as the final design scheme. This invention overcomes the current problem of lacking intelligent explosion-resistant design for reinforced concrete columns, which relies solely on manual methods. This invention combines high accuracy and high computational efficiency, and can intelligently design the optimal solution that balances safety and economy.

Description

Technical Field

[0001] This invention relates to the field of explosion damage assessment and intelligent design of reinforced concrete, and is a data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups. Background Technology

[0002] Reinforced concrete (RC) columns are core load-bearing components in engineering structures. They are susceptible to damage under explosive loads, potentially leading to structural collapse. Rapidly and reliably quantifying the damage level of RC columns is not only crucial for supporting post-disaster emergency rescue and repair decisions but also a prerequisite for achieving blast-resistant reverse design of structures. Current blast-resistant design of RC columns primarily relies on manual trial-and-error methods. This approach is not only time-consuming and labor-intensive but also limited by the designer's experience, making it difficult to find the optimal solution that balances safety and economy within a complex parameter space. Therefore, developing a real-time predictive model for RC column damage under explosive loads and constructing an intelligent reverse design system are of great significance for achieving rapid post-disaster assessment and guiding the optimization of blast-resistant structural design. Summary of the Invention

[0003] To overcome the problem that the existing technology lacks intelligent design for blast-resistant reinforced concrete columns and relies solely on manual methods, this invention proposes a data-driven method for predicting and designing blast damage to reinforced concrete columns with dense stirrups. This method combines high precision and high computational efficiency, and can intelligently design the optimal solution that balances safety and economy.

[0004] This invention proposes a data-driven method for predicting and designing explosion damage in reinforced concrete columns with high stirrup density. First, the design parameters to be optimized are determined to form the optimization object, and the optimization objectives are determined to minimize the total cost and minimize the damage index. Then, a non-dominated sorting genetic algorithm is used to iterate the optimization object until the population converges and the non-dominated solution set is output. Then, the entropy-weighted TOPSIS method is used to select the optimal individual from the non-dominated solution set as the final design scheme; The damage index of the design scheme is calculated as follows: First, a damage prediction model based on the TabPFN model is constructed and trained to calculate the damage index; then, the optimization object of the design scheme in each iteration is mapped to the input features of the damage prediction model and input into the damage prediction model to obtain the damage index.

[0005] Preferably, the optimization targets include: column width. w Column depth h Longitudinal reinforcement diameter D l , diameter of stirrups d t Number of longitudinal reinforcement barsn 1. Number of stirrup legs in column cross-section n 2. Spacing of stirrups in the reinforced zone s 1. Spacing of stirrups in non-confined areas s 2. Bottom encryption area height h 1. Height of the top encrypted area h 2. Length of the unencrypted central area h 3. Compressive strength of concrete cubes f cu longitudinal reinforcement yield strength f y and stirrup yield strength f s ; The input features of the damage prediction model include: column height H Column width w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r Explosive quality W and blast distance R Explosive quality W and blast distance R Used to determine the explosion plan.

[0006] Preferred:

[0007] in, n 2 represents the number of stirrup legs in the column section. A sv It is the area of ​​a single stirrup. a s It is the shortest distance from the outer edge of the concrete to the center of the longitudinal reinforcement. D l The diameter of the longitudinal reinforcement is... d t The diameter is the stirrup diameter.

[0008] Preferably, during the optimization process, constraints are set: 1) The stirrup spacing meets the following requirements: ; 2) The longitudinal reinforcement ratio meets the following requirements: ; 3) The volumetric stirrup ratio meets the requirements. ,in, This is the minimum characteristic value of the stirrups. This is the design value of the axial compressive strength of concrete. This is the design value for the tensile strength of the stirrups; 4) Axial compression ratio N r satisfy: .

[0009] Preferred total cost C t Cost of concrete portion of column C 1. Cost of longitudinal reinforcement C 2. Cost of stirrups C sum of 3;

[0010] in, m c This refers to the price per cubic meter of concrete. m j For the price of longitudinal reinforcement, m g For the price of stirrups, P For the density of the reinforcing steel, n 3 represents the number of stirrups on the column facade. H The net height of the column.

[0011] Preferably, the damage index D for:

[0012] In the formula, P r This represents the residual axial bearing capacity of the column after the explosion. P N This represents the ultimate axial bearing capacity of the undamaged column.

[0013] Preferably, the damage index is calculated as follows: The design and blasting schemes were determined, and a finite element model of the reinforced concrete column was constructed. An axial load was applied to the top surface of the column, along with its own gravity load. After static equilibrium was reached, an blasting load was applied. Displacement was applied to the upper part of the damaged reinforced concrete column to obtain its residual axial bearing capacity. Displacement was also applied to the upper part of the undamaged column to obtain its ultimate axial bearing capacity. Finally, the damage index was calculated by combining the residual axial bearing capacity and the ultimate axial bearing capacity. D .

[0014] Preferably, the method also includes using SHAP analysis to perform parameter analysis on the damage prediction model to obtain the correlation between different parameters in the design variables and the damage index; then, the design variables can be manually fine-tuned to optimize the final design scheme.

[0015] This invention proposes a system for predicting and designing explosion damage to reinforced concrete columns with denser stirrups, comprising: The damage prediction module stores a damage prediction model and predicts the damage index based on the input design scheme and explosion scheme. The intelligent design module is used for human-computer interaction to obtain specified parameters and for iterative optimization of objects to obtain non-dominated solution sets. The intelligent design module is used to display the Pareto front distribution and the optimal solution decision results, and to display a list of non-dominated solution sets. By clicking on a specific data row in the list of non-dominated solution sets, the system will pop up the corresponding reinforcement construction details.

[0016] The advantages of this invention are: A non-dominated sorting genetic algorithm is employed, with the optimization objectives of minimizing total cost and minimizing the damage index. This approach simultaneously considers the economic efficiency and blast resistance of the structure, avoiding performance imbalances caused by single-objective optimization. Through iterative evolution and population convergence mechanisms of the genetic algorithm, the non-dominated solution set can be efficiently searched in complex design spaces, obtaining the Pareto front and providing designers with multiple trade-off solutions. The entropy-weighted TOPSIS method is introduced to objectively assign weights and sort the non-dominated solution set, avoiding interference from subjective weights in the selection of design schemes and improving the scientific rigor and reliability of the final design. This data-driven method can continuously optimize prediction accuracy as the training dataset expands, and is applicable to the prediction and design of blast damage in reinforced concrete columns with stirrup density within different parameter ranges, demonstrating good generalization ability and engineering application value.

[0017] This invention utilizes a pre-built and trained damage prediction model to calculate the damage index, mapping design parameters to input features. This enables rapid and accurate evaluation of the blast resistance performance of different design schemes, significantly reducing reliance on physical experiments or high-fidelity numerical simulations and improving design efficiency. This invention selects the TabPFN model, which possesses excellent generalization ability and prediction accuracy.

[0018] The system enables interactive visualization and efficient decision-making in blast-resistant design. The developed intelligent damage prediction and design system enhances engineering practicality. This system can provide reference and guidance for optimizing structural blast-resistant design and rapid post-disaster assessment.

[0019] In summary, with the dual optimization objectives of minimizing the damage index and minimizing engineering costs, a reverse design framework integrating the TabPFN prediction model and the NSGA-II algorithm was constructed. By introducing the entropy-weighted TOPSIS method for objective decision-making, intelligent optimization of the blast-resistant design scheme for reinforced concrete columns and automated generation of reinforcement diagrams were achieved. Based on this, an intelligent damage assessment system and an intelligent design system were developed. The damage assessment system meets the need for rapid and accurate assessment in sudden explosion scenarios, while the intelligent design system, compared with the traditional manual trial-and-error design mode, can design the best design scheme that balances safety and economy with high precision and efficiency. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the method flow of the present invention; Figures 2(a), 2(b), 2(c), and 2(d) show the comparison between the predicted and actual values ​​of four algorithms: RF, XGBoost, MLP, and TabPFN. Figure 3 Map showing the distribution of the Pareto front; Figure 4 The optimal solution decision result diagram; Figure 5 This is a detailed diagram of the reinforcement details and design parameters for the optimal reinforced concrete column selected by TOPSIS. Figure 6 A graphical user interface diagram for damage prediction; Figure 7 Design a graphical user interface for intelligence. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0022] Reference Figure 1 This embodiment proposes a data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups, comprising the following steps: S1. Define the characteristic parameters and damage index of the design scheme, and construct the RC column explosion damage dataset (hereinafter referred to as the dataset) to statistically analyze the damage index under different combinations of design schemes and explosion schemes. The data samples are denoted as (design scheme, explosion scheme; damage index).

[0023] The characteristic parameters of the design scheme include: column height. H Column width w Column depthh , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r .

[0024] The characteristic parameters of the explosion scheme include the mass of the explosive. W and blast distance R .

[0025] The formula for calculating the damage index D is:

[0026] In the formula, P r This represents the residual axial bearing capacity of the column after the explosion. P N The ultimate axial bearing capacity of the undamaged column can be obtained through finite element simulation.

[0027] In this embodiment, the correspondence between damage index and damage degree is defined, as shown in Table 1 below.

[0028] Table 1: Damage Assessment Criteria for Reinforced Concrete Columns

[0029] When constructing the dataset, first confirm the data samples (design scheme, explosion scheme), then obtain the residual axial bearing capacity and ultimate axial bearing capacity of each sample through finite element simulation; then calculate the damage index. D .

[0030] The finite element simulation method is as follows: construct a finite element model of a reinforced concrete column based on the column section constraint type; apply an axial load to the top surface of the column, and simultaneously apply the column's own gravity load; after it reaches static equilibrium, apply an explosive load; apply displacement to the upper part of the damaged reinforced concrete column to obtain the column's residual axial bearing capacity; apply displacement to the upper part of the undamaged column to obtain the column's ultimate axial bearing capacity. In the specific implementation process, in order to facilitate batch operations, existing keyword files are modified in batches using MATLAB programs to obtain batches of new keyword files. Finite element software then simulates each of the new keyword files in batches. MATLAB programs, along with LS-DYNA and LS-Prepost software, automatically calculate and extract data in batches to obtain the dataset {input features, damage index}.

[0031] In MATLAB programs, new keyword files can be automatically generated by modifying their parameters, thus quickly obtaining numerical simulation data samples. In this embodiment, the column height in the design scheme is set... H and axial force N 1 is a specified parameter. N r pass N 1. w and h Column width is calculated dynamically. w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v Design variables are denoted as design variables. X 1 = { w , h , ρ l , ρ v , f cu , f y , f s In MATLAB programs, design variables are used as modification parameters to modify keyword files.

[0032] In practice, data samples can be obtained by integrating file data samples and numerical simulations.

[0033] S2. Train a damage prediction model on the dataset. This model predicts the damage index based on the design and explosion schemes. The input features of the damage prediction model include: column height. H Column width w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strengthf y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r Explosive quality W Explosion distance R There are 11 input features, and the model output is the damage index. D .

[0034] S3, Design variables X 1. The mapping is a combination of parameters directly designed, denoted as the optimization object. X 3. The optimization objectives are defined as minimizing the total cost and minimizing the damage index; a non-dominated sorting genetic algorithm is used to optimize the object. X 3. Iterate until the population converges and then output the non-dominated solution set.

[0035] Specifically, column width w and column depth h For cross-sectional design parameters, the compressive strength of the concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s The column width is a material design parameter. w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Add directly to the optimization object X 3.

[0036] Longitudinal reinforcement ratio ρ l and volumetric stirrup ratio ρ v The following formula is used for calculation:

[0037] in, n 1 represents the number of longitudinal reinforcement bars. A s It is the area of ​​a single longitudinal reinforcement bar. w For column width, h For column depth;

[0038] in, n 2 represents the number of stirrup legs in the column section. A sv It is the area of ​​a single stirrup. a s It is the shortest distance from the outer edge of the concrete to the center of the longitudinal reinforcement. D l The diameter of the longitudinal reinforcement is... d t The diameter of the stirrup; s 1 represents the spacing of the stirrup-reinforced zone. A reinforced concrete column with stirrups includes both reinforced and unreinforced zones. The volumetric stirrup ratio of the unreinforced zone should not be less than 50% of that of the reinforced zone. Let the stirrup spacing in the reinforced zone be denoted as... s 1. The spacing of stirrups in the non-confined zone is denoted as... s 2.

[0039] The column is divided into three zones along its height: for the first-floor column, the bottom reinforced zone is [height missing]. h 1 ≥ H / 3, Height of the top encrypted area h 2 ≥ {w, h , H / 6,500} mm, length of the unencrypted central area h 3 = H – h 1– h 2; Combined with design variables X Based on formula 1 and above, the optimization target is determined as follows: X 3 = { w , h , D l , d t , n 1, n 2, s 1, s 2, h 1, h 2, h 3, f cu , f y , f s}

[0040] During the optimization of object iteration, the following constraints must be met: 1) The stirrup spacing meets the following requirements: ; 2) The longitudinal reinforcement ratio meets the following requirements: ; 3) The volumetric stirrup ratio meets the requirements. ,in, This is the minimum characteristic value of the stirrups. This is the design value of the axial compressive strength of concrete. This is the design value for the tensile strength of the stirrups; 4) Axial compression ratio N r satisfy: .

[0041] Each optimization object X 3. Parameters can be specified with RC columns. X 2 = { H , N l , W , R Combine the elements to determine the design and explosion schemes; among them, N 1 represents the axial load, used to calculate the axial compression ratio in the following formula. N r :

[0042] in, It refers to the axial compressive strength of concrete, which is determined according to relevant specifications.

[0043] This implementation constructs a bi-objective optimization problem, aiming to simultaneously minimize the structural damage index. D With total cost C t These are two competing goals. Among them, D The value is predicted by a pre-trained machine learning agent model, while C t Then calculate according to the formula.

[0044] Specifically: During population iteration, it is necessary to optimize the target population for each individual. X 3. Mapped to design variables X 1. Incorporate design variables X 1 and specified parameters X 2 = { H , N l , W , R} combination, will N l Mapped to axial compression ratio N r This allows us to obtain the design and explosion schemes corresponding to the optimized object, which are then input into the damage prediction model to obtain the damage index. D And calculate the total cost based on the design scheme. C t .

[0045] Cost of concrete column section C 1. Cost of longitudinal reinforcement C 2. Cost of stirrups C 3 and total cost C t for:

[0046] in, m c Price per cubic meter of concrete (yuan / m³) 3 ), m j Price of longitudinal reinforcement (RMB / t). m g Price of stirrups (RMB / t). P The density of the reinforcing steel is generally taken as 7.85 t / m. 3 , n 3 represents the number of stirrups on the column facade. H The unit of length in the above formulas is mm, where is the net height of the column.

[0047] The NSGA-II algorithm generates offspring through selection, crossover, and mutation operations. It continuously optimizes the solution space through exploration and development. After each generation, the algorithm employs an elitist strategy to merge parent and offspring, selecting the optimal individuals for the next generation based on non-dominated hierarchy and crowding distance. This process iterates until the termination condition is met. After optimization, NSGA-II yields a set of non-dominated solutions (Pareto front), which is the set of optimal solutions.

[0048] S4. The optimal individual is selected from the non-dominated solution set optimized by NSGA-II using the entropy weight method as the final design scheme.

[0049] This step introduces the TOPSIS method based on entropy weight to select the final design scheme from the solution set; the specific steps are as follows: First, calculate each indicator (damage index) D Construction cost C t The information entropy is used to determine the damage index. D objective weight w 1 and C t objective weight w 2. Eliminate the influence of subjective empowerment; Then, substitute the objective weights to calculate the positive and negative ideal solutions for each scheme; Then use the following formula to calculate the relative closeness. S i ;

[0050] in, and Representing the first i Euclidean distances from each solution to the positive and negative ideal solutions; S i Indicates the first i The relative similarity of the two solutions.

[0051] S i The closer the value is to 1, the better the design scheme is in balancing safety and economy; therefore, the final selection is... S i The best solution is the one that yields the best results in reverse engineering.

[0052] The following specific embodiments illustrate and verify the above-mentioned data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups.

[0053] Example 1: Screening damage prediction models.

[0054] In this embodiment, four machine learning (ML) models were evaluated based on four performance evaluation metrics, including those using Random Forest (RF), Extreme Gradient Boosting (XGBoost), Deep Perceptron (MLP), and TabPFN (Table Prior Data Fitting Network). Each model includes column height. H Column width w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r Explosive quality W Explosion distance R There are a total of 11 input features and 1 damage index. D Output features; In this embodiment, 3133 sets of data samples were constructed through data integration and data simulation, denoted as {( w , h , ρl , ρ v , f cu , f y , f s , H , N r , W , R );D} Among them, column height H Column width w Column depth h , compressive strength of concrete cube f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r Composition of design scheme; quality of explosives W and blast distance R This constitutes an explosion plan.

[0055] In this embodiment, the data samples are divided into a training set and a test set. Then, each model is trained on the training set, and the trained model is tested on the test set.

[0056] RF, XGBoost, and MLP use the Optuna framework for model hyperparameter optimization, while TabPFN uses default parameters; the coefficient of determination (R²) is selected. 2 The four standard indicators—mean absolute error (MAE), root mean square error (RMSE), and median absolute error (MedAE)—are used for quantitative evaluation. The definitions and calculation formulas for each indicator are as follows:

[0057] in, , , These represent the actual value, the predicted value, and the average of the actual values, respectively. n This represents the total number of samples in the dataset.

[0058] Figures 2(a), 2(b), 2(c), and 2(d) show a comparison of the predicted and true values ​​for the training and test sets, with most data points located in... y = x Near the line, it indicates that the predicted value matches the true value well. Furthermore, Table 2 comprehensively summarizes the performance metrics used to evaluate machine learning models, comparing R... 2 The four performance evaluation metrics are MAE, RMSE, MedAE, and MedAE. A high R... 2 Low MAE, RMSE, and MedAE scores indicate good model performance. Table 2 shows that the performance evaluated on the training set is definitely higher than that on the test set, and it can be seen that the lowest R... 2 The value of 0.958 for the MLP model indicates that these machine learning models can accurately predict the damage index of RC columns under explosive loading. Among the four machine learning models, two models stand out, with R based on the XGBoost training set being the most effective. 2 =0.999, MAE=0.006, RMSE=0.008, MedAE=0.004 and R on the test set 2 =0.986, MAE=0.024, RMSE=0.034, MedAE=0.018; R based on TabPFN training set 2 =0.997, MAE=0.008, RMSE=0.015, MedAE=0.005 and R on the test set 2 =0.989, MAE=0.018, RMSE=0.030, MedAE=0.011. To evaluate the actual performance of the model, the accuracy of the test set is more important. Among the four evaluated models, the model based on the TabPFN algorithm showed the best performance on the test set.

[0059] Table 2: Performance metrics for each machine learning model

[0060] Therefore, subsequent embodiments selected reverse design optimization based on the TabPFN model and the NSGA-II algorithm.

[0061] Example 2: Selection of optimization parameters.

[0062] In this embodiment, SHAP analysis is used to reveal the evolution of damage by characteristic parameters for the TabPFN model, thereby selecting the parameters that have the greatest impact on the damage index for subsequent experiments.

[0063] Example 3: Verification of the overall solution.

[0064] Considering the high risk of the bottom columns of RC frame structures, a typical bottom RC column of a building was selected as the research object to carry out reverse design optimization of blast resistance performance and economic cost.

[0065] The specified parameter is designed as: column height. H = 5000 mm, axial load N 1 = 3,000,000 N, mass of explosive W = 35kg, blast distance R = 1 m.

[0066] In actual engineering projects, frame columns typically use a square cross-section. Considering the actual construction conditions, the column width ( w ) and column depth ( h It adopts a 50 mm module, and the cross-sectional dimensions range from 300 × 300 mm to 700 × 700 mm; regarding the cross-sectional dimensions ( w × h ), longitudinal reinforcement diameter ( D l ), stirrup diameter ( d t ), the number of longitudinal ribs ( n 1) Number of stirrup legs ( n 2) Specific value ranges are set for key parameters such as stirrup spacing, which can be found in Table 3; the stirrup spacing in the reinforced zone is [value missing]. s 1 = {50, 100} mm, with a value of in the unencrypted area. s 2 = {50, 100, 150, 200 mm}; Compressive strength of concrete cube f cu The values ​​are 30, 35, 40, 45, 50, 55, and 60 MPa, representing the yield strength of the longitudinal reinforcement. f y The values ​​are 335, 400, and 500 MPa, representing the stirrup yield strength. f s The values ​​are 335 and 400 MPa.

[0067] Table 3: Value range of key parameters for RC columns

[0068] When calculating costs, the reference price is 70 yuan / m³ for concrete grades C30, C35, C40, C45, C50, C55, and C60. 3 385 yuan / m 3 400 yuan / m 3 475 yuan / m 3 490 yuan / m 3 505 yuan / m 3and 520 yuan / m 3 The prices for HRB335, HRB400, and HRB500 steel bars are 4200 yuan / t, 4050 yuan / t, and 4300 yuan / t, respectively.

[0069] The NSGA-II algorithm uses an initial population size of 100 and a maximum number of generations of iterations of 50. Selection is performed using a tournament selection strategy based on crowding distance. Crossover is performed using mixed crossover with a crossover probability of 0.9. Mutation is performed using Gaussian mutation with a mutation probability of 0.1.

[0070] Figure 3 The graph illustrates the distribution of the solution set during the optimization process. The blue dots represent the dominant solutions generated during the evolution, while the red dots form the final Pareto front. From... Figure 3 As can be seen from this, if the damage index is to be controlled at an extremely low level ( D If the cost is below 0.3, the construction cost will increase. Conversely, low-cost solutions often come with greater costs. D value.

[0071] like Figure 4 As shown, the Pareto front and the entropy-weighted TOPSIS method decision-making results are presented. The objective weights of each objective are calculated using the entropy-weighted method, and the weight of the damage index is... w 1 = 0.6076, the weight of cost is w 2 = 0.3924. This indicates that within this optimization space, the dispersion of the damage index data has a slightly greater impact on the decision than on the cost. The highest TOPSIS score (yellow dot) calculated based on this weight is the final optimal solution. This solution is located near the knee of the Pareto front, effectively controlling the cost (approximately 1759.23 RMB) while maintaining the damage index at a low level. D =0.3652), avoiding paying excessive costs for pursuing minor performance improvements.

[0072] The detailed design parameters and reinforcement details of the optimal RC column selected by TOPSIS are as follows: Figure 5 As shown, figures a and b represent the side view and cross-sectional view, respectively. The design parameter vector corresponding to this optimal solution is: X 3 = {550 mm, 550 mm, 20 mm, 10mm, 12, 8, 100 mm, 200 mm, 1700 mm, 900 mm, 2400 mm, 60 MPa, 400 MPa, 400 MPa}.

[0073] like Figure 5As shown in the side view (a), the optimization results automatically generated a non-uniform stirrup arrangement scheme. Stirrup reinforcement zones with heights of 900 mm and 1700 mm were set at the top and bottom of the column, respectively, with stirrup spacing... s 1 = 100 mm. Within a 2400 mm radius of the middle of the column, the spacing of the stirrups is widened to... s 2 = 200 mm, effectively reducing steel consumption while ensuring structural requirements are met. Under this design scheme, the damage index predicted by the model is... D = 0.3652. According to the damage assessment criteria, the column suffered moderate damage under the set explosion conditions. The main structure remained intact and only simple repairs were needed for continued use, achieving the dual goals of safety and economy.

[0074] like Figure 6 As shown, the damage prediction model can quickly output the damage index and level based on the input structural and explosion parameters, thus realizing the rapid evaluation of the structure's blast resistance performance.

[0075] like Figure 7 As shown, the intelligent design module allows users to start a multi-objective optimization process simply by entering specified parameters. Clicking "View Optimization Process Graph" provides a visual representation of the Pareto front distribution (see reference). Figure 3 ) and the optimal solution decision results (reference) Figure 4 In addition, the bottom of the interface displays a list of non-dominated solution sets sorted by the entropy-weighted TOPSIS method. Users can click on specific data rows in the table to bring up the corresponding reinforcement details (see reference). Figure 5 This enables interactive visualization and efficient decision-making in explosion-proof design.

[0076] Of course, those skilled in the art will recognize that the present invention is not limited to the details of the exemplary embodiments described above, but also includes the same or similar structures that can be implemented in other specific forms without departing from the spirit or essential characteristics of the invention. Therefore, the embodiments should be considered illustrative and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of equivalents of the claims are intended to be included within the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

[0077] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

[0078] The technologies, shapes, and structures not described in detail in this invention are all known technologies.

Claims

1. A data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups, characterized in that: First, the design parameters to be optimized are determined to form the optimization object, and the optimization objectives are determined to minimize the total cost and minimize the damage index. Then, a non-dominated sorting genetic algorithm is used to iterate the optimization object until the population converges and the non-dominated solution set is output. Then, the entropy-weighted TOPSIS method is used to select the optimal individual from the non-dominated solution set as the final design scheme; The damage index of the design scheme is calculated as follows: First, a damage prediction model based on the TabPFN model is constructed and trained to calculate the damage index; then, the optimization object of the design scheme in each iteration is mapped to the input features of the damage prediction model and input into the damage prediction model to obtain the damage index.

2. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 1, characterized in that, The optimization targets include: column width w Column depth h Longitudinal reinforcement diameter D l , diameter of stirrups d t Number of longitudinal reinforcement bars n 1. Number of stirrup legs in column cross-section n 2. Spacing of stirrups in the reinforced zone s 1. Spacing of stirrups in non-confined areas s 2. Bottom encryption area height h 1. Height of the top encrypted area h 2. Length of the unencrypted central area h 3. Compressive strength of concrete cubes f cu longitudinal reinforcement yield strength f y and stirrup yield strength f s ; The input features of the damage prediction model include: column height H Column width w Column depth h , concrete cube compressive strength f cu longitudinal reinforcement yield strength f y Yield strength of stirrups f s Longitudinal reinforcement ratio ρ l Volumetric stirrup ratio ρ v axial compression ratio N r Explosive quality W and blast distance R Explosive quality W and blast distance R Used to determine the explosion plan.

3. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 2, characterized in that: in, n 2 represents the number of stirrup legs in the column section. A sv It is the area of ​​a single stirrup. a s It is the shortest distance from the outer edge of the concrete to the center of the longitudinal reinforcement. D l The diameter of the longitudinal reinforcement is... d t The diameter is the stirrup diameter.

4. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 2, characterized in that, During the optimization of object iteration, set constraints: 1) The stirrup spacing meets the following requirements: ; 2) The longitudinal reinforcement ratio meets the following requirements: ; 3) The volumetric stirrup ratio meets the requirements. ,in, This is the minimum characteristic value of the stirrups. This is the design value of the axial compressive strength of concrete. This is the design value for the tensile strength of the stirrups; 4) Axial compression ratio N r satisfy: .

5. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 2, characterized in that, Total cost C t Cost of concrete portion of column C 1. Cost of longitudinal reinforcement C 2. Cost of stirrups C sum of 3; in, m c This refers to the price per cubic meter of concrete. m j For the price of longitudinal reinforcement, m g For the price of stirrups, P For the density of the reinforcing steel, n 3 represents the number of stirrups on the column facade. H The net height of the column.

6. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 1, characterized in that, Damage Index D for: In the formula, P r This represents the residual axial bearing capacity of the column after the explosion. P N This represents the ultimate axial bearing capacity of the undamaged column.

7. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 6, characterized in that, The damage index is calculated as follows: Determine the design scheme and blasting scheme, and construct the finite element model of the reinforced concrete column; apply axial load to the top surface of the column, and simultaneously apply the column's own gravity load. After it reaches static equilibrium, apply the blasting load. Displacement was applied to the upper part of the damaged reinforced concrete column to obtain the residual axial bearing capacity; displacement was applied to the upper part of the undamaged column to obtain the ultimate axial bearing capacity; then, the damage index was calculated by combining the residual axial bearing capacity and the ultimate axial bearing capacity. D .

8. The data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in claim 1, characterized in that, It also includes using the SHAP analysis method to perform parameter analysis on the damage prediction model, to obtain the degree of correlation between different parameters in the design variables and the damage index; then, the design variables can be manually fine-tuned to optimize the final design scheme.

9. A system for implementing the data-driven method for predicting and designing explosion damage in reinforced concrete columns with dense stirrups as described in any one of claims 1-9, characterized in that, include: The damage prediction module stores a damage prediction model and predicts the damage index based on the input design scheme and explosion scheme. The intelligent design module is used for human-computer interaction to obtain specified parameters and for iterative optimization of objects to obtain non-dominated solution sets. The intelligent design module is used to display the Pareto front distribution and the optimal solution decision results, and to display a list of non-dominated solution sets. By clicking on a specific data row in the list of non-dominated solution sets, the system will pop up the corresponding reinforcement construction details.

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