Intelligent optimization design method for high-strength and corrosion-resistant epoxy resin concrete reinforced column

Abstract

This invention discloses an intelligent optimization design method for high-strength, corrosion-resistant epoxy resin concrete reinforced columns, belonging to the field of civil engineering structural reinforcement. The method first establishes a database of epoxy resin concrete material properties and a database of epoxy resin concrete reinforced column component properties; then, it trains a two-level neural network surrogate model to achieve rapid prediction from material mix proportions to component response; based on the NSGA-III algorithm, it performs multi-objective scheme optimization with ultimate bearing capacity, displacement ductility ratio, chloride ion diffusion coefficient, and cladding thickness as optimization objectives; it introduces an active learning mechanism to conduct experimental verification and iterative model updates for high-uncertainty design points until the prediction accuracy meets a preset threshold; finally, it outputs the experimentally verified optimized mix proportions and cladding thickness schemes, and clarifies the construction process and acceptance standards. This invention achieves multi-objective collaborative optimization of bearing capacity, ductility, durability, and economy, and features data-driven, self-learning, high efficiency, and reliability.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering structural reinforcement and durability improvement technology, and relates to an intelligent optimization design method for high-strength and corrosion-resistant epoxy resin concrete reinforced columns. Background Technology

[0002] Reinforced concrete columns, as critical load-bearing components, face severe durability degradation in coastal areas and environments exposed to chloride erosion such as de-icing salt. Their seismic performance is also a major concern. Traditional reinforcement methods, such as increasing cross-section or cladding with steel, often offer limited improvement in durability while increasing load-bearing capacity, and also suffer from drawbacks such as complex construction and increased self-weight. Epoxy resin concrete, as a high-performance composite material, combines high strength, high adhesion, and excellent impermeability and corrosion resistance, making it an ideal reinforcement material. However, its performance is significantly affected by the mix proportions, and the reinforcement effect and cladding thickness must comprehensively consider both load-bearing capacity improvement and corrosion protection. Traditional trial-and-error methods or empirical design struggle to achieve multi-objective synergistic optimization, leading to underutilization of material properties or conservative design.

[0003] Existing patents and analyses primarily focus on the material formulation or construction process of epoxy resin concrete. While existing patents disclose the mix proportions of epoxy resin concrete, they do not link them to the overall performance design of structural components. In academic research, although machine learning has been proven to be useful for predicting concrete performance, a complete closed-loop method integrating material formulation optimization with intelligent design of component disaster resistance and durability has not yet been established. Therefore, a data-driven, precise, and efficient design method is urgently needed. This invention can be applied to the reinforcement and renovation of existing reinforced concrete columns, as well as to the optimized design of reinforced columns in new structures, to achieve a dual optimization of structural safety and durability. Summary of the Invention

[0004] To address the problems existing in the prior art, this invention provides an intelligent optimization design method for high-strength and corrosion-resistant epoxy resin concrete reinforced columns. The aim is to construct a two-level database of materials and components, train a high-precision surrogate model, and integrate multi-objective optimization algorithms with active learning verification. Ultimately, it outputs a reinforcement scheme that simultaneously maximizes load-bearing capacity and ductility while minimizing chloride ion intrusion and economic costs. This achieves multi-objective synergistic optimization of load-bearing capacity, ductility, durability, and economy, and features data-driven, self-learning, high efficiency, and reliability.

[0005] To achieve the above objectives, the specific solution of the present invention is as follows:

[0006] A smart optimization design method for high-strength, corrosion-resistant epoxy resin concrete reinforced columns includes the following steps:

[0007] S1. Establish a database of epoxy resin concrete material properties and obtain multiple sets of epoxy resin concrete mix proportion data. The input variables for each set of data include the percentage of epoxy resin content in the total mass of cementitious materials, the type of curing agent, the percentage of curing agent content in the mass of epoxy resin, the percentage of reactive diluent content in the mass of epoxy resin, the water-cement ratio, the aggregate gradation, and the aggregate-cement ratio. The output variables include compressive strength, flexural strength, chloride ion diffusion coefficient, carbonation depth coefficient, and bond strength.

[0008] S2, establish a component performance database for epoxy resin reinforced columns. The component performance database is constructed based on the epoxy resin concrete material performance database in step S1. Component performance data for multiple reinforced columns are obtained through a combination of physical experimental calibration and numerical simulation. Input parameters include at least the core concrete strength, original column reinforcement ratio, epoxy resin coating thickness, epoxy resin concrete material performance indicators recorded in step S1, applied axial compression ratio, and load conditions, including axial compression, eccentric compression, and cyclic horizontal load. Output performance includes at least the failure mode, yield load, ultimate bearing capacity, displacement ductility ratio, and steel corrosion current density.

[0009] S3, train a two-level neural network proxy model, which includes a first-level model and a second-level model; the first-level model is a material performance prediction model, the input features include the mix proportion of epoxy resin concrete, and the output includes mechanical performance indicators and durability indicators; the second-level model is a component performance prediction model, the input features include the material performance indicators and geometric and load parameters output by the first-level model, and the output includes the overall performance indicators of the reinforced column.

[0010] S4 uses the second-level model of S3 as the performance evaluator and defines a multi-objective optimization problem: the optimization variables include the epoxy resin concrete mix proportion and the outer coating thickness, the optimization objectives include maximizing the ultimate bearing capacity, maximizing the displacement ductility ratio, minimizing the chloride ion diffusion coefficient, and minimizing the outer coating thickness, and the constraints include that the reinforcement ratio and axial compression ratio must be within the preset engineering range; the NSGA-III algorithm is used to solve the multi-objective optimization problem and outputs the Pareto optimal solution set;

[0011] S5, Introducing an active learning closed loop: In the Pareto front solution set obtained in S4, the uncertainty of the model prediction is quantified using an ensemble learning method to select the design point with the highest uncertainty for component testing. The new data obtained from the test is added to the epoxy resin concrete material performance database of step S1 and the component performance database of the epoxy resin reinforced column of step S2. The two-level neural network surrogate model of step S3 is retrained. S4 and S5 are iterated repeatedly until the prediction error of the two-level neural network surrogate model on the validation set meets the preset threshold. The preset threshold includes the ultimate load prediction error threshold, the displacement ductility ratio prediction error threshold, and the chloride ion diffusion coefficient prediction error threshold. The optimal solution verified by the experiment is output.

[0012] S6, Output the final design scheme: Select the scheme that meets the engineering constraints from the optimal scheme output in step S5 after experimental verification, and output the target mix proportion of epoxy resin concrete and the design thickness of the outer coating.

[0013] Furthermore, the epoxy resin concrete material performance database mentioned in step S1 is established through a combination of physical experiments and numerical expansion. The physical experiments employ orthogonal experimental design to test the effects of resin content, water-cement ratio, and bone-cement ratio. The numerical expansion uses Kriging interpolation to generate virtual data points in the variable space. The calculation formula for Kriging interpolation is as follows:

[0014] ,

[0015] In the formula, It's at the new point The predicted value at that location; These are new mix proportion parameters; The number of known experimental points; The weight coefficient for the i-th known point; The experimental value of the i-th known point; The input variable is the i-th known point; after calculation, high-confidence virtual data is obtained, and finally the amount of data that satisfies the model training is obtained, and the relationship between material ratio and performance is obtained.

[0016] Furthermore, the epoxy resin concrete mix proportion data mentioned in step S1 is obtained through physical experiments in no less than 70 sets. The chloride ion diffusion coefficient is tested by the RCM method, the bond strength is tested by the splitting tensile test, and the compressive strength and flexural strength are both test values ​​at 28 days.

[0017] Furthermore, in the finite element model used in the numerical simulation described in step S2: the core concrete adopts a plastic damage model, the epoxy resin concrete adopts an elastic-plastic model based on the material property data input in step S1, and the interface between the outer layer and the core concrete adopts a cohesive model. The bond-slip constitutive relation parameters of this cohesive model are determined by the bond strength and corresponding fracture energy measured in step S1. The finite element model is calibrated by physical experiments and used for parametric analysis. The input parameters for parametric analysis include the core concrete strength, epoxy resin outer layer thickness, original column reinforcement ratio, material property indicators in step S1, axial compression ratio, and load conditions.

[0018] Furthermore, in step S3, the first-level model adopts a fully connected feedforward neural network, whose loss function is the mean squared error loss function with an added L2 regularization term, and is trained using the Adam optimizer. The ratio of the training set to the validation set is 80%:20%; the formula of the loss function is as follows;

[0019] ,

[0020] In the formula, This is the total loss function; For the i-th true value, For the i-th predicted value, The regularization coefficient is . represents the network weights; N represents the number of samples, i.e., the total number of samples in the training set.

[0021] Furthermore, in step S3, the second-level model employs a fully connected network with an attention mechanism. The attention weights of the input features of the second-level model to the predicted target are calculated. The output of the second-level model is Z-score normalized and trained using mean squared error loss and the Adam optimizer. The formula for calculating the attention weights is as follows:

[0022] ,

[0023] In the formula, α i Attention weights; It is an exponential function; For the scoring attention function; h i q is the input feature vector, and q is the context query vector; This represents the total number of input features.

[0024] Furthermore, the preset engineering range mentioned in step S4 includes: an outer layer thickness of 20mm to 100mm and an adhesion strength of not less than 2.0MPa.

[0025] Furthermore, the NSGA-III algorithm described in step S4 includes the following steps:

[0026] S41, use the second-level model in step S3 to evaluate the objective function value and generate an initial population containing N individuals;

[0027] S42 divides the initial population into multiple non-dominated front layers, pre-sets a set of uniformly distributed reference points on the standardized target hyperplane, and associates each individual with its nearest reference point.

[0028] S43, select individuals with high frontier priority, and within the same frontier, prioritize individuals corresponding to reference points with fewer associated individuals to enter the next generation;

[0029] S44, crossover and mutation are performed on the selected individuals to generate offspring population;

[0030] S45, merge the parent and child generations, and repeat steps S42 to S44 until the preset number of iterations is reached, output the final non-dominated Pareto front solution set, and obtain the optimal balance design scheme.

[0031] Furthermore, in step S5, ensemble learning is used to quantify the uncertainty of the model predictions. Five second-level models with identical structures but different initializations are trained. For the design point on the Pareto front solution set, the standard deviation of the prediction results from multiple models is used as a measure of uncertainty. The formula for calculating the standard deviation is:

[0032] ,

[0033] In the formula, For the predicted standard deviation; The number of models is 5; For the first The predicted values ​​of each model, To predict the mean, component experiments were conducted at 3-8 design points with the highest uncertainty.

[0034] Further, in step S5, for the selected design point with the highest uncertainty, specimens are fabricated and tested to obtain performance data. The performance data obtained from the experiment is added to the component performance database of the epoxy resin reinforced column from step S2. An incremental learning strategy is adopted, using the old model weights as initialization, to retrain the second-level model. After each iteration, the prediction error of the model on the independent validation set is calculated. When the mean absolute error of the ultimate load is ≤4MPa, the mean absolute error of the displacement ductility ratio is ≤0.15, and the mean absolute error of the chloride ion diffusion coefficient is ≤50×10⁻⁶, the prediction error is considered satisfactory. -14 m 2 The iteration terminates at / s.

[0035] Advantages of the present invention

[0036] This invention proposes an intelligent optimization design method for high-strength, corrosion-resistant epoxy resin concrete reinforced columns. It establishes a two-level database of material properties and component properties, trains a neural network surrogate model to achieve rapid prediction from material mix proportions to component response. Based on the NSGA-III algorithm, it optimizes the scheme by considering ultimate bearing capacity, displacement ductility ratio, chloride ion diffusion coefficient, and outer casing thickness. An active learning mechanism is introduced to experimentally verify high-uncertainty design points and iteratively update the model until the prediction accuracy meets the target. Finally, it outputs the experimentally verified optimized mix proportions and outer casing thickness schemes, and clarifies the construction process and acceptance standards. Compared with existing technologies, this method has the following significant advantages:

[0037] (1) Achieving multi-objective collaborative optimization and breaking through the limitations of traditional design: This invention is the first to incorporate multiple optimization objectives, such as load-bearing capacity, ductility, durability and economy, which are often conflicting in actual engineering, into a unified intelligent optimization framework. By solving the Pareto optimal solution set through the NSGA-III algorithm, a globally optimal or suboptimal balanced design scheme can be obtained systematically, overcoming the limitations of single-objective optimization or performance trade-offs based on experience in traditional methods.

[0038] (2) Constructing a data-driven intelligent closed loop with self-evolution capability: This invention establishes a complete iterative process of "data acquisition - model training - intelligent optimization - experimental verification - data feedback". By introducing an active learning mechanism, experimental verification of high uncertainty design points is carried out and the model is iteratively updated, so that the design method has the ability to learn and evolve. As the number of iterations increases, the model prediction accuracy continues to improve and the design results are more scientific and reliable.

[0039] (3) Significantly improves design efficiency and material utilization: This invention uses a two-level neural network proxy model to replace complex physical experiments and numerical simulations, combined with an efficient multi-objective optimization algorithm, which can complete the full-domain search of tens of thousands of design schemes within hours and quickly lock in the high-performance design range. This design method fully utilizes the material potential of epoxy resin concrete and avoids material waste caused by insufficient design or excessive conservatism.

[0040] (4) Clear engineering implementation, which can guide production and construction: The final output of this invention is a specific target mix proportion of epoxy resin concrete and a design thickness of the outer coating, and strict performance verification standards are set based on active learning closed loop. The output scheme has been verified by experiments and the construction process and acceptance standards have been clarified. It can be directly used to guide engineering design and construction, realizing the connection from theoretical research to industrial application.

[0041] (5) Wide range of applications, compatible with reinforcement and new construction: The method described in this invention can be applied to the reinforcement and renovation of existing reinforced concrete columns, as well as to the optimization design of reinforced columns in new construction, and has good engineering adaptability and promotion value.

[0042] In summary, this invention features data-driven, self-learning, high efficiency and reliability, and achieves multi-objective synergistic optimization of load-bearing capacity, ductility, durability and economy. Attached Figure Description

[0043] Figure 1 This is a flowchart of the intelligent optimization design method for high-strength and corrosion-resistant epoxy resin concrete reinforced columns according to the present invention.

[0044] Figure 2 A flowchart for multi-objective optimization and active learning iteration. Detailed Implementation

[0045] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.

[0046] like Figure 1 As shown in the figure, this specific embodiment provides a smart optimization design method for high-strength and corrosion-resistant epoxy resin concrete reinforced columns, including the following steps:

[0047] S1. A database of epoxy resin concrete material properties was established through a combination of physical experiments and numerical expansion.

[0048] First, the data structure and acquisition standards must be determined. At least 70 sets of epoxy resin concrete mix proportion data should be obtained through physical experiments. The input variables for each set of data include the percentage of epoxy resin content in the total mass of the cementitious material, the type of curing agent, the percentage of curing agent content in the mass of epoxy resin, the percentage of reactive diluent content in the mass of epoxy resin, the water-cement ratio, aggregate gradation, and the aggregate-cement ratio. In this embodiment, the total mass of the cementitious material refers to the sum of the masses of epoxy resin, curing agent, and reactive diluent. Output variables include 28-day compressive strength (loading rate 0.5 MPa / s), 28-day flexural strength, chloride ion diffusion coefficient tested using the RCM method, and carbonation depth coefficient determined using the rapid carbonation test method specified in GB / T50082. The carbonation depth coefficient measured after 28 days of carbonation in this embodiment is calculated using the following formula:

[0049] ,

[0050] In the formula, K is the carbonization depth coefficient; Depth of carbonization; This refers to the carbonization time.

[0051] The bond strength of old concrete was tested using a splitting tensile test.

[0052] The aggregate gradation adopts continuous gradation and is characterized by the maximum particle size and fineness modulus. In this embodiment, the maximum particle size of the coarse aggregate is 10 mm and the fineness modulus is 2.6~2.9.

[0053] In this embodiment, the input variable for the mix proportion of epoxy resin concrete takes the following values:

[0054] Epoxy resin content: 12%~21% (percentage of total mass of cementitious materials);

[0055] Curing agent dosage: 20%~25% (percentage of epoxy resin mass);

[0056] Reactive diluent dosage: 5%~12% (percentage of epoxy resin mass);

[0057] Water-to-binder ratio: 0.22~0.31;

[0058] Bone glue ratio: 3.0~4.5;

[0059] The above range of values ​​is an optimization interval determined based on orthogonal experimental design. Within this range, the material properties change significantly and continuously. Outside this range, the bond strength is lower than 2.0 MPa or the chloride ion diffusion coefficient increases significantly.

[0060] Within the above-mentioned range of values, multiple mix proportions were designed using orthogonal experimental design. The data covered different performance-emphasis ratios from high strength to high toughness. Experimental data for some of the preferred schemes are shown in Table 1.

[0061] Table 1: Mix proportions and performance data of epoxy resin concrete (partial preferred schemes)

[0062]

[0063] The physical experiment employed orthogonal experimental design to test the effects of resin content, water-to-glue ratio, and bone-to-glue ratio. To expand the completed experimental data, Kriging interpolation was used to generate virtual data points in the variable space. The calculation formula for Kriging interpolation is as follows:

[0064] ,

[0065] In the formula, It's at the new point The predicted value at that location; These are new mix proportion parameters; The number of known experimental points; The weight coefficient for the i-th known point; The experimental value of the i-th known point; Let i be the input variable for the i-th known point;

[0066] This embodiment is based on 16 sets of measured data (each set of data fully records the dosage of curing agent and reactive diluent), and uses the Kriging interpolation method to generate high-confidence virtual data, expanding the effective training samples to 70 sets. The expanded dataset fully covers the entire mix proportion space, can accurately reveal the relationship between material proportion and performance, and provide sufficient training samples for the neural network model.

[0067] S2, Establish a component performance database for epoxy resin reinforced concrete columns.

[0068] The component performance database is constructed based on the epoxy resin concrete material performance database in step S1; the component performance data of 40 reinforced columns are obtained by combining physical experimental calibration with system parameterized numerical simulation.

[0069] Physical experiment calibration:

[0070] Eight sets of calibration specimens were prepared: the core concrete was C30, with dimensions of 150mm×150mm×300mm; epoxy resin concrete with different mix proportions from the S1 database and outer thicknesses of 20mm, 40mm, and 60mm were used; the loading regimes were axial compression ratios of 0.3 and 0.5, and eccentricities of 0 and 0.15. Destructive tests were conducted on an axial compression-eccentric compression composite loading device or a quasi-static testing machine, with the linear polarized resistance method (LPR) used to monitor the steel reinforcement potential and corrosion current simultaneously. Tests included load-displacement curves, steel reinforcement potential monitoring, steel reinforcement corrosion current density, and crack development. The steel reinforcement corrosion current density was measured using the linear polarized resistance method (LPR) under the following conditions: a scan range of ±10mV relative open circuit potential, a scan rate of 0.1mV / s, and a three-electrode system with the steel reinforcement as the working electrode, a stainless steel plate as the counter electrode, and a saturated calomel electrode (SCE) as the reference electrode. Measurements were taken periodically during accelerated corrosion under energized conditions.

[0071] Numerical simulation and parametric analysis:

[0072] A refined finite element model was established using ABAQUS. The core concrete adopted the plastic damage CDP model, while the epoxy resin concrete adopted the elastic-plastic model input from step S1. The interface between the outer layer and the core concrete was simulated using the cohesive force (CZM) model. The bond-slip constitutive parameters of the cohesive force model were determined by the bond strength and corresponding fracture energy measured in step S1. The finite element model was calibrated by physical experiments and used to accurately simulate axial compression ratio, eccentricity, and reciprocating displacement loading data.

[0073] The finite element model was further used for parametric analysis. The input parameters for parametric analysis included: core concrete strength, epoxy resin cladding thickness, original column reinforcement ratio, material performance indicators from step S1, axial compression ratio, and load conditions. By running simulations in batches, data such as yield load, peak point, and ultimate displacement were obtained to economically and efficiently expand the data sample and cover the multidimensional variable space.

[0074] Database build results:

[0075] The final established performance database of epoxy resin reinforced concrete column components includes at least the following component variables: core concrete strength, original column reinforcement ratio (including volumetric reinforcement ratio and longitudinal reinforcement ratio), epoxy resin coating thickness, epoxy resin concrete material performance indicators recorded in step S1, applied axial compression ratio, and load conditions, including axial compression, eccentric compression, and reciprocating horizontal load.

[0076] The output performance includes at least the failure mode, yield load, ultimate bearing capacity, displacement ductility ratio, and the corrosion current density of steel bars monitored by the linear polarization resistance method in the accelerated corrosion test.

[0077] The above method yields the mapping relationship between material properties and design parameters on the overall performance of the component. A partial example of the component database is shown in Table 2.

[0078] Table 2:

[0079]

[0080] S3, Training a two-level neural network proxy model

[0081] The two-level neural network proxy model includes a first-level model and a second-level model. First, the first-level model is trained. This first-level model is a material performance prediction model. Input features include the mix proportion of epoxy resin concrete, with the mix proportion parameters including at least the dosage of each component. Outputs include mechanical performance indicators and durability indicators. The mechanical performance indicators include at least compressive strength and flexural strength; the durability indicators include at least the chloride ion diffusion coefficient. The curing agent type in the mix proportion parameters is a categorical variable, processed using one-hot encoding in this embodiment: T31 type encoding is [1,0,0], 593 type encoding is [0,1,0], and 651 type encoding is [0,0,1]. If more types are involved, the dimensions can be expanded accordingly. A regression neural network is then trained. The first-level model replaces complex physicochemical calculations by establishing a fast nonlinear mapping relationship between "material mix proportion" and "material performance."

[0082] The first-level model uses a 4-layer fully connected feedforward neural network with an input layer, 2 hidden layers, and an output layer to establish the network structure. Its loss function is the mean squared error loss function with an L2 regularization term added. The formula of the loss function is as follows:

[0083] ,

[0084] In the formula, This is the total loss function; For the i-th true value, For the i-th predicted value, The regularization coefficient is . represents the network weights; N represents the number of samples, i.e., the total number of samples in the training set.

[0085] Next, the Adam optimizer was used for training on 80% of the data and validation on 20%.

[0086] Furthermore, a second-level model is trained. This second-level model is a component performance prediction model, employing a fully connected network with an attention mechanism. Its input features include 4-5 material performance indicators output from the first-level model, as well as geometric and load parameters. The geometric and load parameters include at least the outer casing thickness, reinforcement ratio, and axial compression ratio. Then, the attention weights of the second-level model's input features to the prediction target are calculated to enhance the model's interpretability. These attention weights... The calculation formula is as follows:

[0087] ,

[0088] In the formula, α i Attention weights; It is an exponential function; For the scoring attention function; h i q is the input feature vector; q is the context query vector; This represents the total number of input features.

[0089] The output features are the overall performance indicators of the reinforced column, which include at least the ultimate load, displacement-to-ductility ratio, and corrosion current density. This second-level model is trained using a regression neural network. This second-level model replaces time-consuming nonlinear finite element analysis by establishing a rapid predictive relationship between "material properties and design parameters" and "component response."

[0090] Next, the three outputs of the second-level model with different dimensions are Z-score normalized, and then trained using mean squared error (MSE) loss and Adam optimizer to obtain a neural network model that can make predictions quickly.

[0091] The final training results are as follows:

[0092] (1. Ultimate load prediction MAE: 3.2MPa;)

[0093] (2. Displacement ductility ratio prediction MAE: 0.12;)

[0094] (3. Corrosion current density prediction MAE: 8.5 nA / cm².)

[0095] S4. Multi-objective optimization design based on NSGA-III (third-generation non-dominated sorting genetic algorithm).

[0096] Using the second-level model from step S3 as the performance evaluator, a multi-objective optimization problem is defined: optimization variables include the epoxy resin concrete mix proportion and outer cladding thickness, which indirectly determine material properties; optimization objectives include maximizing the ultimate bearing capacity, maximizing the displacement ductility ratio, minimizing the chloride ion diffusion coefficient, and minimizing the outer cladding thickness; constraints include that the reinforcement ratio and axial compression ratio must be within a preset engineering range; the NSGA-III algorithm is used to solve the multi-objective optimization problem, effectively searching in the high-dimensional objective space, and finally outputting a Pareto optimal solution set; each solution in this Pareto optimal solution set represents a feasible design scheme that achieves different balances between bearing capacity, ductility, corrosion resistance, and economy, selected according to engineering priority. The preset engineering range includes: an outer cladding thickness of 20mm to 100mm and a bond strength of not less than 2.0MPa. Specifically:

[0097] Multi-objective optimization based on the NSGA-III algorithm first requires defining the optimization problem mathematically, transforming the design problem into a standard multi-objective optimization problem to obtain the decision variable vector. ,in, These are the mix proportion parameters for epoxy resin concrete. The thickness of the outer cladding layer;

[0098] The objective function vector is:

[0099] ,

[0100] In the formula, Ultimate bearing capacity (MPa), take the maximum value; Displacement ductility ratio Take the maximum value; Chloride ion diffusion coefficient (×10) -12 m 2 Take the minimum value for / s; Outer layer thickness (mm) Take the minimum value to meet the economic requirements.

[0101] Meeting the constraints of construction feasibility and economy ≤ 20mm ≤100mm; Interface failure constraint The bond strength is ≥2.0 MPa; All mix proportion variables must be within the empirical range defined in the S1 database.

[0102] Furthermore, a reference point mechanism is used to maintain population diversity in the high-dimensional target space, followed by the NSGA-III algorithm process, including the following steps:

[0103] S41, use the second-level model in step S3 to evaluate the objective function value and generate an initial population containing N individuals;

[0104] S42 divides the initial population into multiple non-dominated front layers, pre-sets a set of uniformly distributed reference points on the standardized target hyperplane, and associates each individual with its nearest reference point.

[0105] S43, select individuals with high frontier priority, and within the same frontier, prioritize individuals corresponding to reference points with fewer associated individuals to enter the next generation;

[0106] S44, crossover and mutation are performed on the selected individuals to generate offspring population;

[0107] S45, merge the parent and child generations, and repeat steps S42 to S44 until the preset number of iterations is reached. After the algorithm converges, output the final non-dominated Pareto front solution set to obtain the optimal balance design scheme among the four objectives.

[0108] After 200 generations of evolution, the Pareto front solution set was obtained, containing 35 non-dominated solutions. The front distribution is shown as follows:

[0109] (1. The trade-off between load-bearing capacity and thickness is obvious;)

[0110] (2. There is a certain positive correlation between ductility and corrosion resistance;)

[0111] (3. The optimal solution is concentrated in the region with a resin content of 18-21% and a thickness of 40-50mm.)

[0112] The Pareto optimal solution set obtained from the S4 multi-objective optimization will enter the S5 active learning closed loop, through uncertainty quantification, component testing verification, and model iterative updates, until the prediction accuracy meets the preset threshold. This complete iterative process is as follows: Figure 2 As shown.

[0113] S5: Active Learning and Iterative Model Updates. To overcome the initial prediction uncertainty of the surrogate model, an active learning closed loop is introduced.

[0114] 1. Quantification of uncertainty

[0115] Ensemble learning is used to quantify the uncertainty of model predictions. Five second-level models with identical structures but different initializations are trained. The uncertainty of the predicted value for any design point X on the Pareto front solution set is calculated. The standard deviation of the predictions from multiple models is used as a measure of uncertainty. The formula for calculating the standard deviation is:

[0116] ,

[0117] In the formula, For the predicted standard deviation; The number of models (the number of models is 5). For the first The predicted values ​​of each model, To predict the mean; then calculate ( To account for the uncertainty of the design, 3-8 design points with the highest uncertainty are selected for component testing.

[0118] Other ways to quantify uncertainty include using the variance of the output of a Bayesian neural network, or the dispersion of predictions from multiple neural network models.

[0119] Specifically, five integrated models were used to calculate the prediction variance, with the highest uncertainty design point being 19.5% resin content, 45mm outer thickness, and ultimate load ±4.8MPa.

[0120] 2. Experimental verification

[0121] From the Pareto front solution set obtained in S4, the 3-8 design schemes with the highest prediction uncertainty were selected for mix proportions and thicknesses. Experimental verification was then conducted. For the selected high-risk design points, specimens were fabricated and tested strictly according to the S2 standard to obtain actual ultimate load, displacement ductility ratio, and chloride ion diffusion coefficient data.

[0122] Three specimens were prepared for quasi-static tests, and the measured results were as follows: ultimate load was 1520±25KN, displacement ductility ratio was 4.2±0.1, and corrosion current density was 78±5nA / cm².

[0123] 3. Data feedback and model update

[0124] The new data obtained from the experiment were added to the epoxy resin concrete material performance database of step S1 and the component performance database of the epoxy resin reinforced column of step S2. An incremental learning strategy was adopted, using the weights of the old model as initialization, to retrain the second-level model (i.e., retrain the two-level neural network surrogate model of step S3, especially the second-level model), which accelerated the convergence under the new data distribution. Through incremental learning, the validation set error was reduced by 15%.

[0125] 4. Iteration Termination Condition

[0126] After each iteration, the prediction error of the model on the independent validation set is calculated. S4 and S5 are repeated until the prediction error of the two-level neural network surrogate model on the validation set for newly added experimental data meets a preset threshold. This preset threshold includes a threshold for the ultimate load prediction error, a threshold for the displacement ductility ratio prediction error, and a threshold for the chloride ion diffusion coefficient prediction error. Specifically, under the ultimate load... Mean absolute error ≤ 4MPa, displacement ductility ratio Mean absolute error ≤ 0.15, chloride ion diffusion coefficient Mean absolute error ≤ 50 × 10 -14 m 2 The iteration terminates after the condition is met, and finally, a highly reliable optimal solution and a more powerful prediction model are obtained after experimental verification.

[0127] After three rounds of active learning iterations (with a total of 15 supplementary specimens), the model accuracy reached: a MAE of 3.1 MPa for the ultimate load prediction (<4 MPa threshold), a MAE of 0.11 for the displacement ductility ratio prediction (<0.15 threshold), and a MAE of 42 × 10⁻¹ for the chloride ion diffusion coefficient prediction. 4 m² / s (<50×10⁻¹) 4 (m² / s threshold).

[0128] 5. Final Output

[0129] Ultimately, we obtained a highly reliable optimal solution and a more powerful prediction model that were verified through experiments.

[0130] S6 outputs the final reinforcement design scheme and guides construction.

[0131] 1. Scheme Selection and Output

[0132] From the optimal solution output in step S5 that has been experimentally verified, select the solution that meets the engineering constraints and output the target mix proportion of epoxy resin concrete and the design thickness of the outer coating.

[0133] Specifically, from the final Pareto optimal solution set verified by experiments and iteratively updated by the model, the optimal solution that meets all engineering constraints is selected, and the final target mix proportion of epoxy resin concrete and the design thickness of the outer cladding layer are output. The selected optimal solutions are shown in Table 3:

[0134] Table 3:

[0135]

[0136] The scheme must meet the following performance verification standards: under the 30-year chloride ion erosion environment prediction based on the Frick second law time-varying model, the steel corrosion current density is ≤100nA / cm²; under rare earthquake action, the structural displacement ductility ratio is ≥4.0.

[0137] 2. Performance Prediction

[0138] Furthermore, performance predictions were made, with the ultimate bearing capacity being 1580kN (an increase of 36%), the displacement ductility ratio being 4.3, the 28-day chloride ion diffusion coefficient being 1.8×10⁻¹²m² / s, the 30-year corrosion current density being predicted to be 82nA / cm², and the bond strength being 3.1MPa.

[0139] 3. Durability verification

[0140] The durability was verified using a time-varying model based on Fick's second law, with the following formula:

[0141]

[0142] in, for Time depth Chloride ion concentration at the location; The concentration of chloride ions on the surface. The apparent diffusion coefficient is... For the time period (30 years). The error function is given. Calculations show that after 30 years, the chloride ion concentration on the steel reinforcement surface is 0.25%, which is below the corrosion threshold of 0.40%.

[0143] 4. Construction guidance

[0144] Construction will be guided based on the final selected plan:

[0145] For reinforcement scenarios: During construction, the surface of the original column needs to be roughened, cleaned, and coated with epoxy resin interface agent. Then, formwork is erected and epoxy resin concrete is poured in one go to ensure that the new and old materials work together. For new construction scenarios, it can be poured directly according to the design ratio.

[0146] Furthermore, guidance will be provided for construction, and the requirements for construction techniques are as follows:

[0147] (1. Surface treatment (for reinforcement scenarios): roughen to a depth of 3-5mm to expose coarse aggregate; sandblast to achieve a cleanliness level of Sa2.5; apply epoxy resin interface agent (dosage 0.4kg / m²).

[0148] (2. Steel formwork is used for formwork support, and its rigidity meets the 48mm pouring requirement; the installation spacing is controlled at ±2mm;

[0149] (3. Epoxy resin concrete is poured in one go to avoid construction joints; vibration time is 30-40 seconds / point; curing conditions are 20±5℃, humidity>90%, 7 days.)

[0150] (4. Quality control indicators: the bonding strength in the field pull-out test is ≥2.5MPa; the allowable thickness deviation is ±3mm; the appearance quality is free of honeycomb and pitting.)

[0151] For newly constructed scenes, the casting is directly poured according to the design specifications.

[0152] 5. Experimental verification results

[0153] Experimental verification was conducted, and the laboratory verification results are as follows:

[0154] (1) Mechanical properties: The actual ultimate load is 1565kN (0.95% error compared to the prediction); the failure mode is bending failure, and there is no peeling of the outer cladding; the hysteresis curve is full, and the energy dissipation capacity is good.

[0155] (2) Durability: The chloride ion diffusion coefficient is 1.7×10⁻¹²m² / s after 90 days; the bond strength retention rate is 92% after 300 dry and wet cycles; the corrosion potential is >-250mV in the accelerated corrosion test.

[0156] Ultimately, the beneficial effects of this method are: 22% reduction in material costs compared to the traditional method of increasing the cross-section; 35% reduction in construction period (no need for curing or wet work); and 40% reduction in space compared to the traditional method of increasing the cross-section.

Claims

1. A method for intelligent optimization design of high-strength, corrosion-resistant epoxy resin concrete reinforced columns, characterized in that, Includes the following steps: S1. Establish a database of epoxy resin concrete material properties and obtain multiple sets of epoxy resin concrete mix proportion data. The input variables for each set of data include the percentage of epoxy resin content in the total mass of cementitious materials, the type of curing agent, the percentage of curing agent content in the mass of epoxy resin, the percentage of reactive diluent content in the mass of epoxy resin, the water-cement ratio, the aggregate gradation, and the aggregate-cement ratio. The output variables include compressive strength, flexural strength, chloride ion diffusion coefficient, carbonation depth coefficient, and bond strength. S2, establish a component performance database for epoxy resin reinforced columns. The component performance database is constructed based on the epoxy resin concrete material performance database in step S1. Component performance data for multiple reinforced columns are obtained through a combination of physical experimental calibration and numerical simulation. Input parameters include at least the core concrete strength, original column reinforcement ratio, epoxy resin coating thickness, epoxy resin concrete material performance indicators recorded in step S1, applied axial compression ratio, and load conditions, including axial compression, eccentric compression, and cyclic horizontal load. Output performance includes at least the failure mode, yield load, ultimate bearing capacity, displacement ductility ratio, and steel corrosion current density. S3, train a two-level neural network proxy model, which includes a first-level model and a second-level model; the first-level model is a material performance prediction model, the input features include the mix proportion of epoxy resin concrete, and the output includes mechanical performance indicators and durability indicators; the second-level model is a component performance prediction model, the input features include the material performance indicators and geometric and load parameters output by the first-level model, and the output includes the overall performance indicators of the reinforced column. S4 uses the second-level model of S3 as the performance evaluator and defines a multi-objective optimization problem: the optimization variables include the epoxy resin concrete mix proportion and the outer coating thickness, the optimization objectives include maximizing the ultimate bearing capacity, maximizing the displacement ductility ratio, minimizing the chloride ion diffusion coefficient, and minimizing the outer coating thickness, and the constraints include that the original column reinforcement ratio and axial compression ratio must be within the preset engineering range; the NSGA-III algorithm is used to solve the multi-objective optimization problem and outputs the Pareto optimal solution set; S5, Introducing an active learning closed loop: In the Pareto optimal solution set obtained in S4, the uncertainty of the model prediction is quantified using an ensemble learning method to select the design point with the highest uncertainty for component testing. The new data obtained from the component testing is added to the epoxy resin concrete material performance database of step S1 and the component performance database of the epoxy resin reinforced column of step S2. The two-level neural network surrogate model of step S3 is retrained. S4 and S5 are repeated iteratively until the prediction error of the two-level neural network surrogate model on the validation set meets the preset threshold. The preset threshold includes the ultimate load prediction error threshold, the displacement ductility ratio prediction error threshold, and the chloride ion diffusion coefficient prediction error threshold. The optimal solution verified by experiments is output. S6, Output the final design scheme: Select the scheme that meets the engineering constraints from the optimal scheme output in step S5 after experimental verification, and output the target mix proportion of epoxy resin concrete and the design thickness of the outer coating.

2. The method according to claim 1, characterized in that, The epoxy resin concrete material performance database mentioned in step S1 was established through a combination of physical experiments and numerical expansion. The physical experiments employed orthogonal experimental design to test the effects of resin content, water-cement ratio, and bone-cement ratio. The numerical expansion used Kriging interpolation to generate virtual data points in the variable space. The calculation formula for Kriging interpolation is as follows: ， In the formula, It's at the new point The predicted value at that location; These are new mix proportion parameters; The number of known experimental points; The weight coefficient for the i-th known point; The experimental value of the i-th known point; The input variable is the i-th known point; after calculation, high-confidence virtual data is obtained, and finally the amount of data that satisfies the model training is obtained, and the relationship between material ratio and performance is obtained.

3. The method according to claim 1, characterized in that, The epoxy resin concrete mix proportion data mentioned in step S1 was obtained through physical experiments, with no fewer than 70 sets of data. The chloride ion diffusion coefficient was tested using the RCM method, the bond strength was tested using the splitting tensile test, and the compressive strength and flexural strength were both measured values ​​at 28 days of age.

4. The method according to claim 1, characterized in that, In the finite element model used for numerical simulation in step S2: the core concrete adopts a plastic damage model, the epoxy resin concrete adopts an elastic-plastic model based on the material property data input in step S1, and the interface between the outer layer and the core concrete adopts a cohesive model. The bond-slip constitutive relation parameters of the cohesive model are determined by the bond strength and corresponding fracture energy measured in step S1. The finite element model is calibrated by physical experiments and used for parametric analysis. The input parameters for parametric analysis include the core concrete strength, epoxy resin outer layer thickness, original column reinforcement ratio, material property indicators in step S1, axial compression ratio, and load conditions.

5. The method according to claim 1, characterized in that, In step S3, the first-level model uses a fully connected feedforward neural network with a loss function of mean squared error plus an L2 regularization term. It is trained using the Adam optimizer, and the ratio of the training set to the validation set is 80%:20%. The formula for the loss function is as follows. ， In the formula, This is the total loss function; This is the i-th true value; This is the i-th predicted value; The regularization coefficient is used. is the network weight; N is the number of samples, i.e., the total number of samples in the training set.

6. The method according to claim 1, characterized in that, In step S3, the second-level model employs a fully connected network with an attention mechanism. The attention weights of the input features of the second-level model to the predicted target are calculated. The output of the second-level model is Z-score normalized and trained using mean squared error loss and the Adam optimizer. The formula for calculating the attention weights is as follows: ， In the formula, α i Attention weights; It is an exponential function; For the scoring attention function; h i q is the input feature vector, and q is the context query vector; This represents the total number of input features.

7. The method according to claim 1, characterized in that, The preset engineering range mentioned in step S4 includes: an outer layer thickness of 20mm to 100mm and an adhesion strength of not less than 2.0MPa.

8. The method according to claim 1, characterized in that, The NSGA-III algorithm described in step S4 includes the following steps: S41, use the second-level model in step S3 to evaluate the objective function value and generate an initial population containing N individuals; S42 divides the initial population into multiple non-dominated front layers, pre-sets a set of uniformly distributed reference points on the standardized target hyperplane, and associates each individual with its nearest reference point. S43, select individuals with high frontier priority, and within the same frontier, prioritize individuals corresponding to reference points with fewer associated individuals to enter the next generation; S44, crossover and mutation are performed on the selected individuals to generate offspring population; S45, merge the parent and child generations, and repeat steps S42 to S44 until the preset number of iterations is reached, output the final non-dominated Pareto front solution set, and obtain the optimal balance design scheme.

9. The method according to claim 1, characterized in that, In step S5, ensemble learning is used to quantify the uncertainty of model predictions. Five second-level models with identical structures but different initializations are trained. For the design point on the Pareto front solution set, the standard deviation of the prediction results from multiple models is used as a measure of uncertainty. The formula for calculating the standard deviation is as follows: ， In the formula, For the predicted standard deviation; The number of models is 5; For the first The predicted values ​​of each model, To predict the mean, component experiments were conducted at 3-8 design points with the highest uncertainty.

10. The method according to claim 1, characterized in that, In step S5, for the selected design point with the highest uncertainty, specimens are fabricated and tested to obtain performance data. The performance data obtained from the experiment is added to the component performance database of the epoxy resin reinforced column from step S2. An incremental learning strategy is adopted, using the old model weights as initialization, to retrain the second-level model. After each iteration, the prediction error of the model on the independent validation set is calculated. When the mean absolute error of the ultimate load is ≤4MPa, the mean absolute error of the displacement ductility ratio is ≤0.15, and the mean absolute error of the chloride ion diffusion coefficient is ≤50×10⁻⁶, the prediction error is considered satisfactory. -14 m 2 The iteration terminates at / s.

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