Method for predicting shear capacity of concrete beam with FRP bars based on RNN-MCFT

Abstract

The application discloses a kind of FRP tendon concrete beam shear capacity prediction method based on RNN-MCFT, including obtaining the experimental sample data of FRP tendon concrete beam shear capacity;Experimental data includes characteristic variable and corresponding target variable;Characteristic variable at least includes the beam section width of FRP tendon concrete beam, beam section effective height, shear span ratio, concrete compressive strength, maximum coarse aggregate particle size, longitudinal reinforcement ratio, longitudinal reinforcement fracture strength, longitudinal reinforcement elastic modulus and stirrup reinforcement ratio, stirrup fracture strength and stirrup elastic modulus;Target variable is shear capacity;Based on double-layer recurrent neural network RNN combined with correction pressure field theory MCFT, the optimal FRP tendon concrete beam shear capacity prediction model is constructed;According to the optimal FRP tendon concrete beam shear capacity prediction model, realize the FRP tendon concrete beam shear capacity prediction based on RNN-MCFT.The application solves the problem that existing method cannot effectively realize the FRP tendon concrete beam shear capacity prediction.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural technology, and in particular to a method for predicting the shear bearing capacity of FRP reinforced concrete beams based on RNN-MCFT. Background Technology

[0002] Fiber-reinforced polymer (FRP) bars are widely used in coastal infrastructure projects and those requiring signal transmission due to their lightweight, high strength, excellent corrosion resistance, and electromagnetic transparency. However, the elastic modulus of FRP bars is lower than that of ordinary steel bars, leading to a deterioration in the axial stiffness of members with the same reinforcement ratio. This results in deeper and wider cracks in the member cross-section, ultimately affecting the load-bearing capacity of the member. Currently, my country's standard GB 50608-2020, "Technical Standard for Engineering Application of Fiber Reinforced Composite Materials," allows the use of over-reinforced beams with FRP bars to prevent premature large deformations or wide cracks in the beams. However, the excessively high fracture strength of FRP bars is mismatched with the relatively low compressive strength of ordinary concrete, causing the beams to be more prone to shear failure and flexural-compression failure upon failure, especially when using over-reinforced beams.

[0003] The shear resistance mechanism of beams is complex, influenced by numerous factors, some of which interact with each other. Compared to normal section failure, oblique section failure is more brittle, and structural members must meet the design principle of "strong shear, weak bending." The failure mode of deeply bending members such as pile caps, cap beams, and shear walls is primarily shear failure. In engineering practice, the load-bearing capacity design of such deeply bending members is based on shear failure, and the contribution mechanisms of the various components of the beam to the shear resistance are complex.

[0004] Existing theoretical models are primarily derived through theoretical-empirical analysis, mathematical statistics, and data-driven approaches. However, the heterogeneity of concrete's mechanical properties and the uncertainties introduced by reinforcement techniques prevent the direct application of traditional mechanics of materials theories. This leads to theoretical analysis models relying on certain fundamental assumptions during operation. For example, the University of Toronto... Collins' Modified Pressure Field Theory (MCFT) assumes a complete bond between the longitudinal reinforcement and the concrete in its calculations, which does not reflect the actual working state of FRP reinforcement in cement-based materials. Although MCFT considers the softening of concrete under tensile-compressive stress in the shear-compression zone, the model does not provide a detailed explanation of the failure conditions in the shear-compression zone. The proposed two-parameter dynamic theory (2PKT) simplifies the MCFT and supplements the contribution of the MCFT to the compression zone, and considers the arching effect in deep beams. However, the quantitative analysis of the truss action is still limited by the assumption of complete bond between the longitudinal reinforcement and the concrete.

[0005] The shear capacity calculation models recommended by Canadian Standard CSA S806, Japanese Standard JSCE 97, and American Standard ACI CODE 441-2022 provide the following calculations for the shear capacity of the concrete component: The term is multiplied by one or a set of empirical coefficients obtained through regression of the experimental data. Wherein, f t , b and h These are the concrete tensile strength, beam cross-section width, and beam height, respectively. The code-recommended explicit expression-based semi-empirical, semi-theoretical model provides designers with a one-step method for assessing shear capacity. However, it also has the problem of underestimating the actual bearing capacity, leading to underutilization of material properties.

[0006] Data-driven models use experimental datasets to drive the training process of machine learning or deep learning models, resulting in a predictive model of shear capacity applicable to the research object. Data-driven models have good computational accuracy and stability, and do not require any basic assumptions. The predictive model can be obtained by performing a limited number of adaptive iterative corrections on the model itself using the residuals between the predicted and experimental values. Although data-driven models have good computational accuracy, they also have problems with interpretability and the fact that the importance of some influencing factors contradicts theoretical analysis. Summary of the Invention

[0007] This invention provides a method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT, in order to overcome the above-mentioned technical problems.

[0008] To achieve the above objectives, the technical solution of the present invention is as follows:

[0009] A method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT includes:

[0010] S1: Obtain experimental sample data on the shear bearing capacity of FRP-reinforced concrete beams;

[0011] The experimental sample data includes feature variables and corresponding target variables;

[0012] The characteristic variables include at least the beam section width, effective beam section height, shear span ratio, concrete compressive strength, maximum coarse aggregate particle size, longitudinal reinforcement ratio, longitudinal reinforcement fracture strength, longitudinal reinforcement elastic modulus, as well as stirrup reinforcement ratio, stirrup fracture strength, and stirrup elastic modulus; the target variable is the shear bearing capacity.

[0013] S2: Based on a two-layer recurrent neural network (RNN) combined with modified pressure field theory (MCFT), an optimal prediction model for the shear capacity of FRP-reinforced concrete beams is constructed according to experimental sample data; based on the optimal prediction model for the shear capacity of FRP-reinforced concrete beams, the prediction of the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT is realized.

[0014] Furthermore, the method for constructing the optimal FRP-reinforced concrete beam shear capacity prediction model described in S2 specifically includes the following steps:

[0015] S21: Randomly divide the experimental sample data into training and test sets according to a preset ratio;

[0016] S22: Using the feature variables as feature data and the target variable as feature label, train the pre-set two-layer recurrent neural network (RNN) model based on the training set to obtain the trained two-layer recurrent neural network (RNN).

[0017] S23: Based on the constructed composite loss function; and the composite loss function includes the numerical loss during the training process of the two-layer recurrent neural network RNN ​​and the physical information loss obtained by MCFT based on the feature variables;

[0018] The trained two-layer recurrent neural network (RNN) is validated using a validation set: that is, the output of the trained two-layer recurrent neural network (RNN) is determined to converge.

[0019] If the output of the trained double-layer recurrent neural network (RNN) converges, then the trained double-layer recurrent neural network (RNN) model is confirmed to be the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams.

[0020] Otherwise, based on the gradient descent method, the weight parameters of the trained double-layer recurrent neural network (RNN) are adaptively adjusted, and step S22 is repeated until the weight parameters of the trained double-layer recurrent neural network (RNN) with converged output are confirmed to be the optimal weight parameters, and the double-layer recurrent neural network (RNN) is reconstructed to obtain the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams.

[0021] Furthermore, the method for reducing physical information loss based on modified pressure field theory MCFT in S23 specifically includes the following steps:

[0022] S231: Based on the Modified Pressure Field Theory (MCFT), the predicted value of the shear bearing capacity of FRP-reinforced concrete beams is obtained according to the characteristic variables in the test set.

[0023] S232: Obtain the residual between the predicted value and the target variable in the test set, and define the residual as the physical information loss.

[0024] Furthermore, the method for obtaining the predicted value of the shear bearing capacity of the FRP-reinforced concrete beam in S231 is as follows:

[0025] S2311: Average principal tensile strain based on a given shear span region e 1 and the initial diagonal crack inclination angle i The contribution value of the interlocking effect between diagonal cracks to the shear bearing capacity is obtained based on the characteristic variables.

[0026] Furthermore, the formula for calculating the contribution of the interlocking effect between diagonal cracks to the shear bearing capacity is as follows:

[0027] ,

[0028] ,

[0029] ,

[0030] ,

[0031] In the formula: w Indicates the width of the diagonal crack; Indicates the initial diagonal crack dip angle i The average spacing of the diagonal cracks below; This represents the shear stress caused by the interlocking of aggregates between diagonal cracks. Indicates the compressive strength of concrete; Indicates the maximum coarse aggregate particle size; This indicates the spacing between the top and bottom chords of an FRP reinforced concrete beam. Indicates the width of the beam section; This represents the contribution of the interlocking action between diagonal cracks to the shear bearing capacity; d Indicates the effective height of the cross-section of the FRP-reinforced concrete beam;

[0032] S2312: The contribution of the residual strength of the concrete between the diagonal cracks to the shear capacity is calculated as follows:

[0033] ,

[0034] ,

[0035] In the formula: Indicates intermediate variables; This indicates the elastic modulus of concrete. This represents the contribution of the residual strength of the concrete between the diagonal cracks to the shear bearing capacity.

[0036] S2313: Based on contribution value With contribution value Obtain the average principal tensile strain in a given shear span region. e1. The first shear capacity provided by concrete for:

[0037] = max{ , },

[0038] S2314: Calculate and obtain the second shear capacity provided by the truss action of FRP stirrups in FRP-reinforced concrete beams. for:

[0039] ,

[0040] ,

[0041] ,

[0042] In the formula: Indicates the strain of the stirrups; This represents the average longitudinal strain of the beam cross section; These represent the elastic modulus and breaking strength of the FRP stirrup, respectively. This indicates the stress in the FRP stirrups; This represents the given initial longitudinal reinforcement strain; Indicates the area of ​​the stirrup reinforcement; Indicates the spacing between stirrups;

[0043] S2315: Based on the first shear bearing capacity With the second shear bearing capacity Obtain the average principal tensile strain of an FRP-reinforced concrete beam in a given shear span region. e The third shear bearing capacity under 1 V for:

[0044] V = + ,

[0045] S2316: Based on the third shear bearing capacity V Obtain the updated longitudinal average strain of the cross section And based on the updated longitudinal average strain of the cross section Get the updated value of the initial diagonal crack dip angle i 1 is:

[0046] ,

[0047] ,

[0048] In the formula: Indicates the area of ​​longitudinal reinforcement; Indicates the elastic modulus of the longitudinal reinforcement; Indicates the shear span length of the FRP-reinforced concrete beam;

[0049] S2317: Based on the updated value i 1. Optimized value of longitudinal average strain of cross section e x and e x = 0.5( + Repeatedly execute S2311 to S2316, and when the parameters in each iteration satisfy any one of the constraints, record the corresponding third shear capacity. V This value is used as the shear bearing capacity under the average principal tensile strain of the corresponding shear span region;

[0050] The constraints include:

[0051] Constraint 1: ;

[0052] Constraint 2: ≥ / ;

[0053] Constraint 3:2 e x ≥ / ;

[0054] in, These represent the elastic modulus and breaking strength of the longitudinal reinforcement, respectively.

[0055] S2318: Until the preset maximum number of iterations is reached, compare and obtain all third shear capacity. V The maximum value in the range is used as the final calculation result of the shear bearing capacity of the FRP reinforced concrete beam, i.e., the predicted value of the shear bearing capacity of the FRP reinforced concrete beam.

[0056] Furthermore, the composite loss function constructed in S23 is:

[0057] ,

[0058] ,

[0059] ,

[0060] In the formula: NThis represents the total number of FRP-reinforced concrete beam specimens in the dataset; Indicates the first k The mean absolute error of the shear bearing capacity predicted by the two-layer recurrent neural network (RNN) after several iterations of training; Indicates the first k After several iterations of training, the mean absolute error of the shear bearing capacity of FRP-reinforced concrete beams predicted based on the Modified Pressure Field Theory (MCFT) is as follows: They represent the first k The mean absolute error after the second iteration of training and The corresponding weights; This represents the first value calculated based on the modified pressure field theory MCFT. i Predicted shear capacity of the root beam; , y (k) i They represent the first i The experimental value of the shear bearing capacity of the root beam and the predicted value of the shear bearing capacity obtained by the double-layer recurrent neural network (RNN); This represents the composite loss function.

[0061] Beneficial Effects: This invention provides a method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT. It utilizes a two-layer recurrent neural network (RNN) combined with modified pressure field theory (MCFT). Based on experimental sample data, an optimal prediction model for the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT is constructed. By using modified pressure field theory as a physical constraint and combining it with a two-layer recurrent neural network (RNN), this invention can obtain the optimal prediction model for the shear capacity of FRP-reinforced concrete beams by considering the contribution importance of factors influencing shear capacity and the alignment of their action directions with theoretical analysis results. This model improves prediction accuracy and exhibits a lower overfitting tendency, while also accelerating the iterative convergence speed during model training, effectively improving the prediction accuracy and efficiency of the shear capacity of FRP-reinforced concrete beams. Attached Figure Description

[0062] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0063] Figure 1 This is a flowchart of the method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT according to the present invention;

[0064] Figure 2 This is a schematic diagram of the optimal FRP-reinforced concrete beam shear capacity prediction model based on RNN-MCFT constructed in this embodiment.

[0065] Figure 3 The values ​​are the test values ​​of shear bearing capacity in this embodiment. A schematic diagram of the parameter distribution;

[0066] Figure 4 This is a graph showing the training and prediction results generated by the model in this embodiment;

[0067] Figure 5 This diagram illustrates the interpretability analysis results, which are consistent with reality, based on the importance of factors influencing shear bearing capacity in this embodiment.

[0068] Figure 6 This is a comparison chart of the number of training rounds required for the model to converge and the loss value in this embodiment. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0070] This embodiment provides a method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT. The invention establishes a two-layer recurrent neural network (RNN) regression model using Modified Pressure Field Theory (MCFT) as constraints. This model consists of four parts:

[0071] A. Input layer: by D The input layer consists of several initial network nodes. D Indicates the number of features;

[0072] B. Hidden layer: The first hidden layer and the second hidden layer are connected in sequence, and the first hidden layer and the second hidden layer are composed of 64 and 32 recurrent neural network node units, respectively. No neurons are disabled during training.

[0073] C. Physical Constraint Layer: Based on the numerical residuals of the two-layer recurrent neural network (RNN) model itself, the residuals between the modified pressure field theory (MCFT) and the predicted values ​​are superimposed as a composite loss function, thereby introducing the physical constraints provided by MCFT into the two-layer recurrent neural network (RNN) model.

[0074] D. Output layer: Consists of a single network node. During training, it outputs the numerical values ​​generated during training and feeds back the residual gradient between the output layer and the experimental values ​​to the hidden layer to correct the weights of each neuron. After training is complete, it outputs the final predicted shear capacity.

[0075] The method described in this embodiment, such as Figure 1 to Figure 2 As shown, the specific steps include:

[0076] S1: Obtain experimental sample data on the shear bearing capacity of FRP-reinforced concrete beams;

[0077] The experimental sample data includes feature variables and corresponding target variables;

[0078] The characteristic variables include at least the beam section width, effective beam section height, shear span ratio, concrete compressive strength, maximum coarse aggregate particle size, longitudinal reinforcement ratio, longitudinal reinforcement fracture strength, longitudinal reinforcement elastic modulus, as well as stirrup reinforcement ratio, stirrup fracture strength, and stirrup elastic modulus; the target variable is the shear bearing capacity.

[0079] S2: Based on a two-layer recurrent neural network (RNN) combined with modified pressure field theory (MCFT), an optimal prediction model for the shear capacity of FRP-reinforced concrete beams is constructed according to experimental sample data; based on the optimal prediction model for the shear capacity of FRP-reinforced concrete beams, the prediction of the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT is realized.

[0080] Specifically, the method for constructing the optimal FRP-reinforced concrete beam shear capacity prediction model is as follows:

[0081] S21: Randomly divide the experimental sample data into training and test sets according to a preset ratio;

[0082] S22: Using the feature variables as feature data and the target variable as feature label, train the pre-set two-layer recurrent neural network (RNN) model based on the training set to obtain the trained two-layer recurrent neural network (RNN).

[0083] S23: Based on the constructed composite loss function; and the composite loss function includes the numerical loss during the training process of the two-layer recurrent neural network RNN ​​and the physical information loss obtained by MCFT based on the feature variables;

[0084] The trained two-layer recurrent neural network (RNN) is validated using a validation set: that is, the output of the trained two-layer recurrent neural network (RNN) is determined to converge.

[0085] If the output of the trained double-layer recurrent neural network (RNN) converges, then the trained double-layer recurrent neural network (RNN) model is confirmed to be the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams.

[0086] Otherwise, based on the gradient descent method, the weight parameters of the trained double-layer recurrent neural network (RNN) are adaptively adjusted, and step S22 is repeated until the weight parameters of the trained double-layer recurrent neural network (RNN) with converged output are confirmed to be the optimal weight parameters, and the double-layer recurrent neural network (RNN) is reconstructed to obtain the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams.

[0087] This embodiment also includes the basic assumptions proposed based on the Modified Pressure Field Theory (MCFT): (1) During loading, the longitudinal reinforcement and stirrups of the FRP-reinforced concrete beam are fully bonded to the concrete; (2) The stress and strain of the longitudinal reinforcement are equal throughout the entire length; (3) The longitudinal reinforcement and stirrups of the FRP-reinforced concrete beam are arranged at equal intervals along the transverse and longitudinal directions, respectively, and the reinforcement area is uniformly distributed; (4) The diagonal crack inclination angle of the FRP-reinforced concrete beam is consistent with the principal compressive stress, or the azimuth angle of the diagonal compression bar; The method for obtaining physical information loss based on the Modified Pressure Field Theory (MCFT) in this embodiment specifically includes the following steps:

[0088] The method for losing physical information based on modified pressure field theory MCFT in S23 specifically includes the following steps:

[0089] S231: Based on the Modified Pressure Field Theory (MCFT), predict the shear capacity of FRP-reinforced concrete beams by analyzing characteristic variables in the test set; specifically, the steps include:

[0090] S2311: Average principal tensile strain based on a given shear span region e 1 and the initial diagonal crack inclination angle i The contribution value of the interlocking effect between diagonal cracks to the shear bearing capacity is obtained based on the characteristic variables.

[0091] Furthermore, the formula for calculating the contribution of the interlocking effect between diagonal cracks to the shear bearing capacity is as follows:

[0092] (1)

[0093] (2)

[0094] (3)

[0095] (4)

[0096] In the formula: w Indicates the width of the diagonal crack; Indicates the initial diagonal crack dip angle iThe average spacing of the diagonal cracks below; This represents the shear stress caused by the interlocking of aggregates between diagonal cracks. Indicates the compressive strength of concrete; Indicates the maximum coarse aggregate particle size; This represents the spacing between the top and bottom chords of an FRP-reinforced concrete beam, assumed to be 0.9. d ; Indicates the width of the beam section; This represents the contribution of the interlocking action between diagonal cracks to the shear bearing capacity; in this embodiment, the initial strain value of the longitudinal reinforcement is 10. -6 The dip angle of the diagonal crack is expressed as ( a / d );in, ( ) is used to find the arctangent value; a / d Indicates the shear span ratio of the beam; a , d These represent the shear span length and effective section height of the FRP-reinforced concrete beam, respectively.

[0097] S2312: The contribution of the residual strength of the concrete between the diagonal cracks to the shear capacity is calculated as follows:

[0098] (5)

[0099] (6)

[0100] In the formula: Indicates intermediate variables; This indicates the elastic modulus of concrete. This represents the contribution of the residual strength of the concrete between the diagonal cracks to the shear bearing capacity.

[0101] S2313: Based on contribution value With contribution value Obtain the average principal tensile strain in a given shear span region. e 1. The first shear capacity provided by concrete for:

[0102] = max{ , }(7)

[0103] S2314: Calculate and obtain the second shear capacity provided by the truss action of FRP stirrups in FRP-reinforced concrete beams. for:

[0104] (8)

[0105] (9)

[0106] (10)

[0107] In the formula: Indicates the strain of the stirrups; This represents the average longitudinal strain of the beam cross section; These represent the elastic modulus and breaking strength of the FRP stirrup, respectively. This indicates the stress in the FRP stirrups; This represents the given initial longitudinal reinforcement strain; Indicates the area of ​​the stirrup reinforcement; Indicates the spacing between stirrups;

[0108] S2315: Based on the first shear bearing capacity With the second shear bearing capacity Obtain the average principal tensile strain of an FRP-reinforced concrete beam in a given shear span region. e The third shear bearing capacity under 1 V for:

[0109] V = + (11)

[0110] S2316: Based on the third shear bearing capacity V Obtain the updated longitudinal average strain of the cross section And based on the updated longitudinal average strain of the cross section Get the updated value of the initial diagonal crack dip angle i 1 is:

[0111] (12)

[0112] (13)

[0113] In the formula: Indicates the area of ​​longitudinal reinforcement; Indicates the elastic modulus of the longitudinal reinforcement; Indicates the shear span length of the FRP-reinforced concrete beam;

[0114] S2317: Based on the updated value i 1. Optimized value of longitudinal average strain of cross section e x and e x = 0.5( + Repeatedly execute S2311 to S2316, and when the parameters in each iteration satisfy any one of the constraints, record the corresponding third shear capacity. V This value is used as the shear bearing capacity under the average principal tensile strain of the corresponding shear span region;

[0115] The constraints include:

[0116] Constraint 1: ;

[0117] Constraint 2: ≥ / ;

[0118] Constraint 3:2 e x ≥ / ;

[0119] in, These represent the elastic modulus and breaking strength of the longitudinal reinforcement, respectively.

[0120] This embodiment also includes the average principal tensile strain in the original given shear span region. e Based on 1, add a step size of 10. -5 The backward push yields a new average principal tensile strain. e '1 and e '1= e 1+ 10 -5 When satisfied After confirming the mean principal tensile strain of two adjacent pairs V Is the absolute value of the difference less than 10? -3 Right now If yes, stop the iterative calculation; otherwise, continue executing S2311 to S2316.

[0121] S2318: Until the preset maximum number of iterations is reached, compare and obtain all third shear capacity. V The maximum value in the range is used as the final calculation result of the shear bearing capacity of the FRP reinforced concrete beam, i.e., the predicted value of the shear bearing capacity of the FRP reinforced concrete beam.

[0122] S232: Obtain the residual between the predicted value and the target variable in the test set, and define the residual as the physical information loss.

[0123] In this embodiment, shear bearing capacity is used as the target variable in the collected experimental dataset, and the feature variables are introduced into a two-layer recurrent neural network for model training. The model employs an adaptive momentum (Adam) optimizer, which minimizes the loss function obtained from the training set during iterative training. This is done to accelerate the convergence speed of the training process, improve the model's prediction accuracy, reduce the risk of overfitting, and ensure that the model's calculation results are consistent with physical information. The numerical loss function of the two-layer recurrent neural network (RNN) is... Based on this, a physical information loss function is proposed. For the value of a certain physical quantity ( y The composite loss function used in model training L (k) for:

[0124] (14)

[0125] (15)

[0126] (16)

[0127] In the formula: N This represents the total number of FRP-reinforced concrete beam specimens in the dataset; Indicates the first k The mean absolute error of the shear bearing capacity predicted by the two-layer recurrent neural network (RNN) after several iterations of training; Indicates the first k After several iterations of training, the mean absolute error of the shear bearing capacity of FRP-reinforced concrete beams predicted based on the Modified Pressure Field Theory (MCFT) is as follows: They represent the first k The mean absolute error after the second iteration of training and The corresponding weights; This represents the first value calculated based on the modified pressure field theory MCFT. i Predicted shear capacity of the root beam; , y (k) i They represent the first i The experimental value of the shear bearing capacity of the root beam and the predicted value of the shear bearing capacity obtained by the double-layer recurrent neural network (RNN).

[0128] For a given feature, the prediction based on the modified pressure field theory MCFT is... V It is a constant value, while the two-layer recurrent neural network (RNN) predicts... V It depends not only on the features, but also on the weights between RNN nodes, in the th... kAfter the nth iteration of training, if the composite loss function has The numerical percentage is higher than L (k) From 90%, it begins to gradually decrease. and increase ;at the same time It is always equal to 1- This aims to further optimize the optimal FRP-reinforced concrete beam shear capacity prediction model based on RNN-MCFT while adhering to physical constraints. This embodiment employs... R 2 With root mean square error ( RMSE To evaluate the training and prediction performance of the model: During the training process, record the average values ​​of the training and test sets. R 2 Using these as model evaluation metrics, and iteratively adjusting the learning rate and loss weights based on their changing trends (overfitting / underfitting signals). BL 1 / L Parameters such as the ratio (1), input batch size, and number of training epochs are used to continuously optimize the model's recognition performance and generalization ability. Two evaluation metrics are:

[0129] (17)

[0130] (18)

[0131] In the formula: They represent the first i Predicted and experimental values ​​of shear capacity of root beam; i , N These represent the serial number and total number of FRP-reinforced concrete beams, respectively; mean() indicates taking the average value. This embodiment also includes the storage of output physical quantities: during the training process, the loss value of each iteration is recorded, and after training is completed, the training time and loss value sequence are saved as follows. Text document, and the model itself as Save the files to the results folder, then export the model training results, test results, and the corresponding dataset's SHAP values, feature values, and annotations. Save the table file and the results folder together.

[0132] This embodiment also includes the following application examples:

[0133] We collected a dataset of bending-shear tests on 672 rectangular beams subjected to three- or four-point loading, reported in 61 papers. The parameters required for training the model and making predictions included at least the beam cross-section width. b Effective height of beam section d , shear span ratio a / d Concrete compressive strength Maximum coarse aggregate particle size Longitudinal reinforcement ratio Fracture strength of longitudinal reinforcement Elastic modulus of longitudinal reinforcement Longitudinal reinforcement ratio The breaking strength of stirrups and the elastic modulus of the stirrups The target variable to be predicted is the shear capacity of the beam. V .like Figure 3 The figure shows the above parameters as a function of shear bearing capacity test values. The distribution of data was analyzed. During the training of the two-layer recurrent neural network model, the data from 672 collected beams were subjected to Latin hypercube sampling, and divided into training and test sets at a 4:1 ratio before being imported into the model. The global random seed was set to 42 for subsequent replication. The maximum number of training epochs in this case was set to 2000. The loss value and training time for each epoch were recorded and exported as a text document. After training, the SHAP value of the model training set, as well as the training and prediction results, were exported as... The document states that the model benefits from training with a composite loss function, resulting in high accuracy in both training and prediction. Figure 4 As shown, the importance of factors affecting shear bearing capacity was analyzed, and an interpretable analysis result consistent with reality was generated. Figure 5 As shown, the introduction of MCFT physical constraints reduces the number of training iterations required for model convergence, and also lowers the loss value during training. Figure 6 As shown. Compared with the prior art, the beneficial effects of the method described in this embodiment are as follows: Based on a two-layer recurrent neural network (RNN) combined with modified pressure field theory (MCFT), an optimal prediction model for the shear capacity of FRP-reinforced concrete beams is constructed based on experimental sample data. In this embodiment, by using modified pressure field theory as a physical constraint and combining it with a two-layer recurrent neural network (RNN), the optimal prediction model for the shear capacity of FRP-reinforced concrete beams can be obtained by considering the contribution importance of factors affecting shear capacity and the analysis results that the direction of action conforms to the theory. The model improves the prediction accuracy and has a low overfitting tendency, while accelerating the iterative convergence speed during model training, effectively improving the prediction accuracy and efficiency of the shear capacity of FRP-reinforced concrete beams.

[0134] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT, characterized in that, The specific steps include: S1: Obtain experimental sample data on the shear bearing capacity of FRP-reinforced concrete beams; The experimental sample data includes feature variables and corresponding target variables; The characteristic variables include at least the beam section width, effective beam section height, shear span ratio, concrete compressive strength, maximum coarse aggregate particle size, longitudinal reinforcement ratio, longitudinal reinforcement fracture strength, longitudinal reinforcement elastic modulus, as well as stirrup reinforcement ratio, stirrup fracture strength, and stirrup elastic modulus; the target variable is the shear bearing capacity. S2: Based on a two-layer recurrent neural network (RNN) combined with modified pressure field theory (MCFT), an optimal prediction model for the shear capacity of FRP-reinforced concrete beams is constructed according to experimental sample data; based on the optimal prediction model for the shear capacity of FRP-reinforced concrete beams, the prediction of the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT is realized. The method for constructing the optimal FRP-reinforced concrete beam shear capacity prediction model specifically includes the following steps: S21: Randomly divide the experimental sample data into training and test sets according to a preset ratio; S22: Using the feature variables as feature data and the target variable as feature label, train the pre-set two-layer recurrent neural network (RNN) model based on the training set to obtain the trained two-layer recurrent neural network (RNN). S23: Based on the constructed composite loss function; and the composite loss function includes the numerical loss during the training process of the two-layer recurrent neural network RNN ​​and the physical information loss obtained by MCFT based on the feature variables; The method for reducing the loss of physical information obtained by modified pressure field theory MCFT specifically includes the following steps: S231: Based on the Modified Pressure Field Theory (MCFT), the predicted value of the shear bearing capacity of FRP-reinforced concrete beams is obtained according to the characteristic variables in the test set. S232: Obtain the residual between the predicted value and the target variable in the test set, and define the residual as the physical information loss; The trained two-layer recurrent neural network (RNN) is validated using a validation set: that is, the output of the trained two-layer recurrent neural network (RNN) is determined to converge. If the output of the trained double-layer recurrent neural network (RNN) converges, then the trained double-layer recurrent neural network (RNN) model is confirmed to be the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams. Otherwise, based on the gradient descent method, the weight parameters of the trained double-layer recurrent neural network (RNN) are adaptively adjusted, and step S22 is repeated until the weight parameters of the trained double-layer recurrent neural network (RNN) with converged output are confirmed to be the optimal weight parameters, and the double-layer recurrent neural network (RNN) is reconstructed to obtain the optimal prediction model for the shear bearing capacity of FRP-reinforced concrete beams.

2. The method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT according to claim 1, characterized in that, The method for obtaining the predicted value of the shear bearing capacity of the FRP-reinforced concrete beam described in S231 is as follows: S2311: Average principal tensile strain based on a given shear span region ε 1 and the initial diagonal crack inclination angle θ The contribution value of the interlocking effect between diagonal cracks to the shear bearing capacity is obtained based on the characteristic variables. Furthermore, the formula for calculating the contribution of the interlocking effect between diagonal cracks to the shear bearing capacity is as follows: In the formula: w Indicates the width of the diagonal crack; Indicates the initial diagonal crack dip angle θ The average spacing of the diagonal cracks below; This represents the shear stress caused by the interlocking of aggregates between diagonal cracks. Indicates the compressive strength of concrete; Indicates the maximum coarse aggregate particle size; This indicates the spacing between the top and bottom chords of an FRP reinforced concrete beam. Indicates the width of the beam section; This represents the contribution of the interlocking action between diagonal cracks to the shear bearing capacity; d Indicates the effective height of the cross-section of the FRP-reinforced concrete beam; S2312: The contribution of the residual strength of the concrete between the diagonal cracks to the shear capacity is calculated as follows: In the formula: Indicates intermediate variables; This indicates the elastic modulus of concrete. This represents the contribution of the residual strength of the concrete between the diagonal cracks to the shear bearing capacity. S2313: Based on contribution value With contribution value Obtain the average principal tensile strain in a given shear span region. ε 1. The first shear capacity provided by concrete for: = max{ , } S2314: Calculate and obtain the second shear capacity provided by the truss action of FRP stirrups in FRP-reinforced concrete beams. for: In the formula: Indicates the strain of the stirrups; This represents the average longitudinal strain of the beam cross section; These represent the elastic modulus and breaking strength of the FRP stirrup, respectively. This indicates the stress in the FRP stirrups; This represents the given initial longitudinal reinforcement strain; Indicates the area of ​​the stirrup reinforcement; Indicates the spacing between stirrups; S2315: Based on the first shear bearing capacity With the second shear bearing capacity Obtain the average principal tensile strain of an FRP-reinforced concrete beam in a given shear span region. ε The third shear bearing capacity under 1 V for: V = + S2316: Based on the third shear bearing capacity V Obtain the updated longitudinal average strain of the cross section And based on the updated longitudinal average strain of the cross section Get the updated value of the initial diagonal crack dip angle θ 1 is: In the formula: Indicates the area of ​​longitudinal reinforcement; Indicates the elastic modulus of the longitudinal reinforcement; Indicates the shear span length of the FRP-reinforced concrete beam; S2317: Based on the updated value θ 1. Optimized value of longitudinal average strain of cross section ε * x and ε * x = 0.5( + Repeatedly execute S2311 to S2316, and when the parameters in each iteration satisfy any one of the constraints, record the corresponding third shear capacity. V This value is used as the shear bearing capacity under the average principal tensile strain of the corresponding shear span region; The constraints include: Constraint 1: ; Constraint 2: ≥ / ; Constraint 3:2 ε * x ≥ / ; in, These represent the elastic modulus and breaking strength of the longitudinal reinforcement, respectively. S2318: Until the preset maximum number of iterations is reached, compare and obtain all third shear capacity. V The maximum value in the range is used as the final calculation result of the shear bearing capacity of the FRP reinforced concrete beam, i.e., the predicted value of the shear bearing capacity of the FRP reinforced concrete beam.

3. The method for predicting the shear capacity of FRP-reinforced concrete beams based on RNN-MCFT according to claim 2, characterized in that, The composite loss function constructed in S23 is: In the formula: N This represents the total number of FRP-reinforced concrete beam specimens in the dataset; Indicates the first k The mean absolute error of the shear bearing capacity predicted by the two-layer recurrent neural network (RNN) after several iterations of training; Indicates the first k After several iterations of training, the mean absolute error of the shear bearing capacity of FRP-reinforced concrete beams predicted based on the Modified Pressure Field Theory (MCFT) is as follows: They represent the first k The mean absolute error after the second iteration of training and The corresponding weights; This represents the first value calculated based on the modified pressure field theory MCFT. i Predicted shear capacity of the root beam; , y (k) i They represent the first i The experimental value of the shear bearing capacity of the root beam and the predicted value of the shear bearing capacity obtained by the double-layer recurrent neural network (RNN); This represents the composite loss function.

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