A deep learning approach for predicting tensile mechanical properties of high-toughness concrete

Abstract

The present invention discloses a deep learning method for predicting the tensile mechanical properties of high-toughness concrete, which belongs to the technical field of concrete tensile mechanical properties prediction, including: first, using a CNN deep learning model instead of traditional machine learning to improve the network's feature mining and prediction capabilities. Secondly, using Bayesian technology to achieve fully automatic optimization of multiple hyperparameters, that is, reducing time consumption and further improving prediction accuracy. The present invention uses 154 experimental samples collected from the literature to prove that the proposed BO-CNN method has good prediction capabilities in predicting ECC tensile strength and ultimate tensile strain.

Description

Technical Field

[0001] The present invention belongs to the technical field of concrete tensile mechanical properties prediction, and in particular relates to a deep learning method for predicting the tensile mechanical properties of high-toughness concrete. Background Art

[0002] Engineered Cementitious Composite (ECC) is a high-performance fiber-reinforced cementitious composite that has attracted much attention due to its unique pseudo-strain hardening behavior and excellent multiple cracking tensile properties. The composition of ECC mainly includes cementitious materials, fly ash, silica fume, fine silica sand, water, chemical additives and randomly distributed fibers. The latest research shows that the tensile properties of ECC not only depend on the fiber dosage, but also on the following factors: fiber properties (fiber mechanical properties, aspect ratio and volume fraction), matrix mechanical properties (related to its mix ratio), and fiber-matrix interface properties (chemical and friction bonding). However, at present, in order to fully understand the tensile properties of ECC under the influence of multiple factors (fiber, matrix, etc.), it is necessary to rely on a large number of experiments, which is very uneconomical and time-consuming. Therefore, based on the existing experimental data, we urgently need to establish a method that can quickly, efficiently and accurately predict the mechanical properties of ECC.

[0003] Machine Learning (ML) can establish a good mapping relationship between input parameters and prediction targets, so it is widely used in many prediction problems in civil engineering, such as structural damage detection. In recent years, some research teams have also tried to apply it to the prediction of concrete mechanical properties. At present, the commonly used machine learning in the field of predicting concrete mechanical properties can be divided into four categories: empirical risk minimization (for example: artificial neural network, ANN), structural risk minimization (for example, support vector machine, SVM), integrated algorithms (for example, decision trees and random forests) and evolutionary algorithms. The existing technology records the use of SVM to predict the compressive strength of concrete based on the research of concrete components. The use of DT algorithm to predict the compressive strength of concrete containing waste foundry sand. The use of integrated algorithms such as DT and XGBoost to predict the tensile stress and energy absorption capacity of ultra-high performance fiber concrete (UHPFRC) at the peak strain. The compressive strength of 3D printed fiber reinforced concrete (3DP-FRC) is predicted using 7 ML algorithms including SVR, DT, and RF. In addition to the above machine learning algorithms, neural networks are also a major type of machine learning algorithm, and have also begun to be applied to concrete performance prediction. For example, the artificial neural network (ANN) method was used to predict the compressive and tensile strength of PVA-ECC. Based on the ANN model, the full tensile stress-strain curve of ECC was predicted with 10 parameters (including the properties of all components and fibers in the mix design) as input. Furthermore, some scholars have begun to compare the prediction ability of ANN with other machine learning models in the mechanical properties of concrete. For example, BPNN and other three machine learning models (RF, LR, MLR) were used to predict the uniaxial compressive strength (UCS) and corresponding peak strain of rubber-modified recycled aggregate concrete (RRAC). Based on the validation of a data set containing 120 groups, BPNN has the best prediction performance compared with other ML algorithms. Six ML methods including SVM, RF, XGBoost and ANN were used to predict the compressive and tensile strength of concrete. The study found that ANN and XGBoost showed excellent prediction efficiency when facing a higher degree of missing data. From this point of view, ML performs well in predicting the mechanical properties of ECC and other concrete, and has certain potential in practical applications.

[0004] Convolutional neural networks (CNNs) are a new type of deep neural network that is different from traditional machine learning algorithms (such as ANN, SVM, and DT). CNN networks can mine and utilize deeper features from samples through built-in multi-layer hidden layers, thereby improving the network's representation and prediction capabilities in complex nonlinear problems. At present, CNN has been applied to many types of complex nonlinear problems and has begun to be used in the field of civil engineering. Among them, concrete surface crack detection based on CNNs has been widely used in practical engineering. For example, CNN was optimized by hybrid sea lion and dragonfly algorithms to predict the slump value of concrete, and good prediction results were achieved. A CNN model for predicting the compressive strength of recycled aggregate concrete was developed. Compared with the traditional ANN model, the model has stronger adaptive ability and can learn the deep features of the input variables. The CNN model was used to establish a compressive strength prediction model considering the influence of coarse aggregate type and gradation. The results show that the prediction performance of the CNN compressive strength model considering aggregate type and gradation is better than that of the ANN model. Therefore, CNN, as a representative deep learning algorithm, can better mine deep features related to concrete mechanical properties from input variables than ANN and other ML algorithms, and has better prediction accuracy. However, the prediction ability of CNN algorithm in ECC mechanical properties still needs to be further explored.

[0005] In existing research, from the perspective of methods, the models currently used to predict the mechanical properties of ECC and other concrete materials still have the following shortcomings: (1) They are mainly based on traditional machine learning such as ANN and SVM. These models have limitations in deeply mining features and dealing with complex nonlinear problems, which affects the prediction accuracy of the model; (2) The various hyperparameters in the machine learning models currently used in this field are usually adjusted through manual intervention or exhaustive search, which limits the search space and model performance and consumes a lot of time, which is not conducive to the application of the model in actual engineering; from the perspective of research objects, there are not many studies on the use of ML to predict the mechanical properties of ECC materials. Existing studies often focus on the prediction of ECC compressive strength and tensile strength, and lack relevant research on ECC ultimate tensile strain. Especially for ECC ultimate tensile strain, the discreteness of the data is higher than that of tensile strength, which increases the difficulty of model prediction. Therefore, it is necessary to further explore it. Summary of the invention

[0006] In order to solve the above technical problems, the present invention proposes a deep learning method for predicting the tensile mechanical properties of high-toughness concrete to solve the problems existing in the above-mentioned prior art.

[0007] To achieve the above object, the present invention provides a deep learning method for predicting the tensile mechanical properties of high-toughness concrete, comprising:

[0008] Construct a feature dataset based on the characteristics of cement samples;

[0009] Preprocessing the feature data set to obtain a preprocessed data set;

[0010] Constructing a Bayesian optimization convolutional neural network based on a Bayesian optimization algorithm and a convolutional neural network, training the Bayesian optimization convolutional neural network through the preprocessed data set to obtain an ultimate tensile strength prediction model;

[0011] The tensile mechanical properties of high-toughness concrete are predicted based on the ultimate tensile strength prediction model.

[0012] Preferably, the cement sample comprises:

[0013] The characteristics of the cement samples include: ordinary Portland cement, fly ash, slag, lime powder, silica fume, sand, water and PE fiber;

[0014] The characteristics of the cement sample include input characteristics and output characteristics;

[0015] The input characteristics include: the mass ratio of cement to cementitious material, the mass ratio of fly ash to cementitious material, the mass ratio of slag to cementitious material, the mass ratio of lime powder to cementitious material, the mass ratio of silica fume to cementitious material, the mass ratio of sand to cementitious material, the mass ratio of water to cementitious material, fiber content, fiber length and fiber diameter;

[0016] The output characteristics include: tensile strength and ultimate tensile strain.

[0017] Preferably, the feature data set is preprocessed to obtain the preprocessed data set, comprising:

[0018] Performing maximum and minimum normalization processing on the feature data set to obtain a normalized data set;

[0019] The normalized data set is divided based on a cross-validation method to obtain the preprocessed data set.

[0020] Preferably, the process of constructing a Bayesian optimization convolutional neural network based on the Bayesian optimization algorithm and the convolutional neural network includes:

[0021] Construct a convolutional neural network model based on input layer, convolution layer, rectified linear unit, pooling layer and fully connected layer;

[0022] Calculating the hyperparameters of the convolutional neural network model based on a Bayesian optimization algorithm to obtain a global optimal solution;

[0023] The global optimal solution is fed back to the convolutional neural network model to generate a Bayesian optimized convolutional neural network.

[0024] Preferably, the expression of the convolutional layer operation is:

[0025] ;

[0026] in, For the The output feature value of the sample after the convolution operation in the current layer, For the The data sample is in The value of the feature, is the weight of the two-dimensional convolution kernel, and Respectively Samples and features, m and n are the dimensions of the convolution kernel.

[0027] Preferably, the corrected linear unit is a ReLU activation function;

[0028] The expression of the ReLU activation function is:

[0029] ;

[0030] in, is the output value, is the input value of the previous neural network layer.

[0031] Preferably, the expression of the Bayesian optimization algorithm is:

[0032] ;

[0033] in For the The feature vector of samples, X is the parameter set to be optimized, is the objective function, which means the model is The prediction performance or loss of samples, is the objective function The optimal solution on the domain X.

[0034] Preferably, the Bayesian optimization algorithm uses the UCB function as a sampling function, and the expression of the sampling function is:

[0035] ;

[0036] and are the first The predicted mean (expected value of regression prediction) of the samples and The uncertainty of the prediction results for each sample (the variance or standard deviation of the prediction), To balance the parameters of exploration and exploitation, For the The input variables for the sample.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] The present invention proposes a fully automatic ECC tensile mechanical properties prediction model based on deep learning and Bayesian optimization technology. First, the CNN deep learning model is used to replace the traditional machine learning to improve the network's feature mining and prediction capabilities. Secondly, Bayesian technology is used to achieve fully automatic optimization of multiple hyperparameters, which reduces time consumption and further improves prediction accuracy. The present invention uses 154 experimental samples collected from the literature to prove that the proposed BO-CNN method has good prediction ability in predicting ECC tensile strength and ultimate tensile strain, and the corresponding evaluation index R 2 are 0.911 and 0.701 respectively. This method is not only superior to neural networks such as CNN and ANN, but also superior to 9 machine learning methods including SVM. In addition, the present invention also explains the contribution of each input feature in the prediction of ECC tensile properties through Shapley. In summary, the BO-CNN method proposed in the present invention realizes fully automated modeling, improves modeling efficiency and prediction accuracy, and provides an efficient and reliable solution for the actual prediction of ECC tensile properties. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0040] Figure 1 A histogram of variables according to an embodiment of the present invention;

[0041] Figure 2 Schematic diagram of density distribution of different material mass ratios according to an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of density distribution of volume fraction according to an embodiment of the present invention;

[0043] Figure 4 Schematic diagram of the density distribution of length according to an embodiment of the present invention;

[0044] Figure 5 Schematic diagram of the density distribution of diameters according to an embodiment of the present invention;

[0045] Figure 6 It is a feature correlation matrix heat map of an embodiment of the present invention;

[0046] Figure 7 This is a schematic diagram of 9-fold cross validation according to an embodiment of the present invention;

[0047] Figure 8 A flow chart of a deep learning method for predicting tensile mechanical properties of high-toughness concrete according to an embodiment of the present invention;

[0048] Fig. 9 Schematic diagram of the structure of a convolutional neural network according to an embodiment of the present invention;

[0049] Fig.10 It is a tensile strength loss function diagram of the BO-CNN model of an embodiment of the present invention;

[0050] Fig.11 It is a diagram of the ultimate tensile strain loss function of the BO-CNN model of an embodiment of the present invention;

[0051] Fig.12 This is a tensile strength performance diagram of the BO-CNN model for predicting ECC according to an embodiment of the present invention;

[0052] Fig.13 The ultimate tensile strain performance diagram of the BO-CNN model for predicting ECC according to an embodiment of the present invention;

[0053] Fig.14 It is a scatter plot of tensile strength prediction of BO-CNN tensile strength of the data set according to an embodiment of the present invention;

[0054] Fig.15 It is a scatter plot of the tensile strength BO-CNN ultimate tensile strain prediction of the data set of an embodiment of the present invention;

[0055] Fig.16 The tensile strength distribution and density map of the BO-CNN prediction error of the embodiment of the present invention;

[0056] Fig.17 The limit tensile strain distribution and density map of the BO-CNN prediction error of the embodiment of the present invention;

[0057] Fig.18 It is a line graph of the actual value of the test set of the embodiment of the present invention and the tensile strength prediction results of BO-CNN, GS-CNN and GS-ANN;

[0058] Fig.19 It is a line graph of the true value of the test set of the embodiment of the present invention and the prediction results of the ultimate tensile strain of BO-CNN, GS-CNN and GS-ANN;

[0059] Fig. 20 A comparison chart of tensile strength performance indicators in a test set of an embodiment of the present invention;

[0060] Fig.21 It is a comparison chart of the ultimate tensile strain performance indicators in the test set of the embodiment of the present invention. DETAILED DESCRIPTION

[0061] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0062] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0063] Embodiment 1

[0064] This embodiment provides a deep learning method for predicting the tensile mechanical properties of high-toughness concrete, including:

[0065] The first step in developing a prediction model is data collection, which is usually time-consuming because it is necessary to ensure the comprehensiveness of the data. The data set used in this example is compiled from published ECC material research literature. The data set includes 154 samples, and the raw materials of the samples include ordinary Portland cement 52.5R (C), fly ash (FA), slag (GGBS), lime powder (LP), silica fume (SF), sand (S), water (W) and PE fiber. The samples cover 12 features, of which there are 10 input features and 2 output targets. The input features include matrix composition and fiber performance indicators, specifically: the mass ratio of cement to cementitious material (C / B), the mass ratio of fly ash to cementitious material (FA / B), the mass ratio of slag to cementitious material (GGBS / B), the mass ratio of lime powder to cementitious material (LP / B), the mass ratio of silica fume to cementitious material (SF / B), the mass ratio of sand to cementitious material (S / B), the mass ratio of water to cementitious material (W / B), fiber content (Vf), fiber length (Lf) and fiber diameter (Df), etc. The mass of cementitious material (B) is the sum of the masses of C, FA, GGBS, LP and SF. The output targets are tensile strength (TS) and ultimate tensile strain (UTS). The statistical information of the above variables is detailed in Table 1. Figure 1 Histograms of the above variables are also shown.

[0066] Table 1

[0067]

[0068] Figure 2The density distribution of the ratio of the mass of each component material, sand and water in the cementitious material to the mass of the cementitious material is shown. As can be seen from the figure, the mass ratio of different components to the cementitious material is widely distributed in the sample and there is a significant peak, which shows the diversity and representativeness of the selected sample materials in composition. The diversity of the composition of the selected sample materials helps to improve the reliability and generalization ability of the prediction model to a certain extent, and its representativeness can more accurately reflect the common proportions in real projects.

[0069] Figure 3-5 Density distribution plot of fiber properties (volume fraction, length, and diameter). Figure 3 It shows that the fiber content is mainly 0.01 and 0.02 of the ECC volume, indicating that the fiber volume fraction is relatively uniform in most samples; Figure 4 The density distribution diagram of fiber length shows two peaks, one at 12 mm and the other at 18 mm, reflecting that the fiber length selection in the sample is relatively concentrated; Figure 5 The density distribution graph of fiber diameter shows a significant peak at 24μm and another peak at 18μm, indicating that the selection of fiber diameter in the sample is also highly uniform. These clear distribution patterns are beneficial for model building because they provide clear trends and predictable variable behaviors, which help the model learn and predict material properties more accurately. Uniform data distribution can reduce noise in model training, make the model easier to converge, and improve the reliability and accuracy of predictions. This information is very important for designing machine learning algorithms and conducting scientific research to ensure the quality of model input features and thus optimize model performance.

[0070] Figure 6The correlation coefficients between all features are shown to measure the degree of correlation between features. As can be seen from the figure, for tensile strength, the correlation coefficient of W / B is -0.73, indicating that the relationship between water-cement ratio and the tensile strength of ECC shows the most obvious correlation and is negatively correlated, which is also in line with the law obtained by most experiments-the larger the water-cement ratio, the lower the tensile strength of the tensile specimen. Secondly, the correlation coefficient between GGBS / B and tensile strength is 0.54, indicating that the increase of GGBS / B plays a positive role in tensile strength. For the ultimate tensile strain, the correlation coefficients between Vf and Lf and the ultimate tensile strain of ECC are 0.37 and 0.41, respectively, indicating that the increase of fiber volume fraction and the use of longer fiber length play a key role in improving the ultimate tensile strain of ECC; while the correlation coefficients between SF / B and Df and the ultimate tensile strain of ECC are -0.23 and -0.18, respectively, indicating that to a certain extent, the increase of SF content and fiber diameter will reduce the ultimate tensile strain of ECC. From the absolute value of the correlation coefficient with the ultimate tensile strain of ECC, it can be seen that the fiber properties in ECC play a more important role in affecting the tensile strain.

[0071] Before training the model, the input features are normalized to the minimum and maximum values. After normalization, all features are converted to the range of 0 to 1. This avoids the problem of uneven contribution to the model output due to different scales of feature parameters. Normalizing the data can also accelerate the convergence of the model training process and enhance the stability of the prediction model.

[0072] ;

[0073] In the formula, is the minimum value of an input feature, is the maximum value of an input feature.

[0074] First, the data set is randomly divided into a training set and a test set. Then, in order to reduce the overfitting problem that may be caused by a limited data set, this embodiment adopts a cross-validation method. Figure 7 As shown in the figure, specifically, the training set accounts for 90% of the dataset and is further divided into 9 folds. In each training, 8 folds are selected as training sets to train the model, and the remaining 1 fold is used as a validation set to adjust the model's hyperparameters. This process is repeated 9 times, and the average performance of the 9 validation sets is used as the performance evaluation result of the model in this training. The test set accounts for 10% of the dataset and is used to evaluate the final performance of the model. This division strategy not only ensures that the performance of the model on unseen data can be fairly evaluated, but also maintains good generalization ability.

[0075] During the training process, the model adopted an early stopping strategy, in which the maximum number of iterations of the model was set to 2000, the performance improvement threshold was set to 0.01, and the patience value was set to 20 iterations. That is, during the 2000 iterations of the model, if the MSE of the validation set did not decrease by 0.001 after 20 consecutive iterations, the model would stop iterating early and use the weight of the last training as the optimal weight of the model. This strategy not only allows the model to stop iterating early when there is little improvement during training, thereby saving computing resources, but also can avoid model overfitting to a large extent.

[0076] This embodiment proposes a CNN model for predicting ECC tensile properties based on Bayesian optimization technology. The model involves 10 input features and 2 output targets. The 10 input features include: matrix components (C, FA, LP, GGBS, S, SF, W,) and fiber properties (Vf, Lf, Df). The 2 output targets are: tensile strength (TS) and ultimate tensile strain (UTS). According to the statistical parameters (R 2 , MSE, RMSE, SD, MAE, MAPE, etc.) to evaluate the prediction performance of the model, and compare the proposed BO-CNN with CNN, ANN and other traditional machine learning (including RF, SVM, DT, etc.) using grid optimization. The flowchart is shown in Figure 8 shown.

[0077] like Fig. 9 As shown in Figure 1, CNN is a feedforward neural network that can extract features from data with a convolutional structure. Unlike traditional feature extraction methods, CNN does not require manual feature extraction. The success of CNN is mainly due to its local connectivity and weight sharing, which can reduce the number of weights, making the network easy to optimize, and reduce the risk of overfitting. The most commonly used layers in CNN include: (1) input layer; (2) convolution layer; (3) rectified linear units (ReLUs); (4) pooling layer and (5) fully connected layer. The input layer of the CNN model is a matrix with equal rows and columns, and features are extracted by sliding and convolving the matrix with filters. The core structure of CNN is the convolution layer characterized by local receptive field. When each neuron in the convolution layer is connected to the input domain only in a small area, a local receptive field is generated. This configuration enables CNN to understand the spatial correlation between image units well when image data (grid data) is available, thereby improving the accuracy of classification or regression. The expression of the convolution operation is:

[0078] ;

[0079] in, For the The output feature value of the sample after the convolution operation in the current layer, For the The data sample is in The value of the feature, is the weight of the two-dimensional convolution kernel, and Respectively Samples and features, m and n are the dimensions of the convolution kernel.

[0080] The activation function is intended to give the CNN model nonlinear fitting capabilities. In this embodiment, the ReLU activation function is used to improve the nonlinear fitting capabilities of the model, which can save computing resources and reduce gradient vanishing and overfitting due to its sparse characteristics. The formula is:

[0081] ;

[0082] in, is the output value, is the input value of the previous neural network layer.

[0083] Pooling layer, also called subsampling layer, usually follows convolutional layer. In pooling layer, there are no weights and activation functions in the unit. Its main function is to further reduce the number of learnable parameters using typical downsampling operation, which reduces the dimensionality of feature map plane. The most common application of pooling algorithm is max pooling, which extracts blocks from input feature map, returns the maximum value in each block, and discards other values.

[0084] The output of the last convolutional or pooling layer is converted into a one-dimensional vector, and the vector is connected to a fully connected layer with learnable weights between the input and output vectors. The feature vector generated by the convolutional or pooling layer is mapped to the final output of the model through a subset of fully connected layers, which outputs classification probabilities or regression values ​​for different learning tasks. For regression tasks, the output node count of the last fully connected layer is 1. Similarly, a ReLU activation function is embedded after each fully connected layer to enhance the nonlinear fitting ability of the model.

[0085] When applying CNN or ANN for regression tasks, the number of hidden layers, number of neurons and learning rate are hyperparameters that need to be determined before training the model. Generally, researchers set hyperparameters based on experience, which can save training costs, but often leads to poor model prediction performance. Bayesian optimization (BO) is a very effective global optimization algorithm whose goal is to find the global optimal solution in the parameter space. In mathematics, the problem can be uniformly described as finding the global optimal solution to the unknown objective function:

[0086] ;

[0087] in For the The feature vector of samples, X is the parameter set to be optimized, is the objective function, which means the model is The prediction performance or loss of samples, is the objective function The optimal solution on the domain X.

[0088] There are generally two basic requirements for Bayesian optimization algorithms. First, determine the form of the prior function based on the distribution assumption of the optimization function. For this purpose, Gaussian processes are chosen due to their flexibility and manageability. Second, construct an acquisition function that determines the next point in parameter space to evaluate using the updated posterior distribution.

[0089] Generally speaking, the selection of the next sampling point is considered from two aspects: utilization and exploration. The former is to explore around the mainstream optimal solution to find the global optimal solution. The latter is a method that attempts to search for sample points that are not estimated to avoid falling into the local optimal solution. Commonly used capture functions include expected improvement function, confidence upper limit function and probability improvement function. This embodiment uses the UCB function as the sampling function, and its mathematical expression is

[0090] ;

[0091] and are the first The predicted mean (expected value of regression prediction) of the samples and The uncertainty of the prediction results for each sample (the variance or standard deviation of the prediction), To balance the parameters of exploration and exploitation, For the The input variables for the sample.

[0092] It can be seen from the formula that by adjusting the size of the parameter 𝜀, the selection of sampling points is balanced.

[0093] Grid search (GS) is a widely used global optimization technique for searching for optimal solutions in the hyperparameter space. In mathematical terms, grid search requires researchers to predefine a list of values ​​for all hyperparameters of interest and evaluate each possible combination through model training and validation. This process involves a lot of computation as it requires exploring all possible combinations to determine the best settings.

[0094] A key advantage of grid search is that it is simple and intuitive, making it straightforward to implement. It ensures that each parameter combination is evaluated fairly, thereby ensuring the identification of the best solution. However, this means that grid search can be particularly time-consuming when the hyperparameter space is large or the cost of training each model is high.

[0095] Therefore, although grid search is inefficient in dealing with high-dimensional hyperparameter spaces, it is still a popular parameter optimization technique in the field of machine learning, especially when the number of hyperparameters is relatively small.

[0096] This embodiment uses 11 machine learning methods to compare with the Bayesian optimized convolutional neural network (BO-CNN), including grid search optimized convolutional neural network (GS-CNN), grid search optimized artificial neural network (GS-ANN), decision tree (DT), random forest (RF), XGBoost (XGB), and other classic machine learning models.

[0097] To evaluate the performance accuracy of the model, four basic error metrics from basic statistics were used. These metrics are used to predict ( ) and actual ( ) results. Pearson correlation coefficient (R), determination coefficient ( ), mean square error (MSE), root mean square error (RMSE), standard deviation (SD), mean absolute error (MAE), and mean absolute percentage error (MAPE).

[0098]

[0099]

[0100]

[0101]

[0102]

[0103]

[0104]

[0105] in Indicates the number of samples. The value measures the proportion of the variance in the output explained by the regression model. The smaller the MSE, RMSE, MAE, and MAPE, the closer they are to 0. The closer the value is to 1, the higher the prediction accuracy.

[0106] In order to give full play to the advantages of Bayesian optimization technology in automatic search of hyperparameters, this embodiment defines the search space of the model as comprehensively as possible, so that each hyperparameter and model can reach the optimal solution, thereby improving the prediction performance of BO-CNN. Specifically, Bayesian technology adjusts hyperparameters such as the number of convolutional layers, the number of convolutional kernels in each convolutional layer, and the size of the convolutional kernels in each convolutional layer to facilitate the model to extract features more effectively. At the same time, by adjusting hyperparameters such as the dropout rate, the purpose of preventing the model from overfitting and enhancing the generalization ability of the model is achieved. The hyperparameters optimized by this model are detailed in Table 2;

[0107] Table 2

[0108]

[0109] Furthermore, this example uses the BO-CNN model for predicting tensile strength as an example to demonstrate the Bayesian optimization process. Unlike the exhaustive search of grid optimization, the hyperparameters in the Bayesian optimization process are determined by the Tree-structuredParzenEstimator (TPE), and the value that maximizes the expected improvement is selected. As the number of Bayesian optimizations increases, the trend of selecting two convolutional layers becomes more and more obvious, and the corresponding R 2 The average value gradually increases and then stabilizes, indicating that as the number of Bayesian optimization increases, the model's hyperparameter selection gradually stabilizes, and the model's prediction performance also improves and stabilizes. For the conversion layer type, the model finally chooses the flattening layer because the flattening layer has stable performance in the CNN model and can more completely retain the data features after the convolution layer than the global pooling layer. For the optimizer, the model finally chooses RMSProp because it can maintain excellent and stable model performance and reduce computing resources in most cases. In the initial stage of Bayesian optimization, the values ​​or types of the hyperparameters of the BO-CNN model are relatively scattered. As the number of Bayesian optimization increases, each hyperparameter gradually focuses on the value or type that can bring the greatest expected improvement.

[0110] This example discusses the prediction results of BO-CNN on the training set and test set in detail to verify the accuracy and versatility of the proposed BO-CNN model. First, Figure 10-11The loss curves of the training set and the validation set are shown respectively when the BO-CNN model predicts the tensile strength (TS) and the ultimate tensile strain (UTS) under the network with the optimal hyperparameters. As can be seen from the figure, the loss function gradually converges to close to 0 with the increase of the number of iterations, indicating that the model does not have underfitting problems during the training process. The difference between the loss curves of the training set and the validation set is small, which further proves that the model does not have overfitting, thus showing that the model has good accuracy, stability and generalization ability. In addition, it can be observed that the two models successfully stopped training when the model performance no longer increased significantly through the early stopping method (EarlyStopping) within a maximum of 2000 iterations, thereby effectively avoiding the risk of overfitting and the waste of computing resources. This strategy ensures a balance between training efficiency and model quality. Table 3 shows the R obtained by the trained BO-CNN model predicting the test set. 2 With MAPE.

[0111] Table 3

[0112]

[0113] Figure 12-13 The predicted and actual values ​​of tensile strength and ultimate tensile strain by the BO-CNN model on the training set, validation set, and test set are intuitively displayed. Figure 14-15 The scatter plot of the predicted values ​​and actual values ​​of tensile strength (TS) and ultimate tensile strain (UTS) by the BO-CNN model is shown. The diagonal line is the best predicted value, i.e. (in represents the predicted value of the model, represents the true value). As can be seen from the figure, most of the data points are concentrated in Nearby, a few data points are located on the blue dashed line and green dashed line The error between the predicted values ​​of BO-CNN model and the actual values ​​on tensile strength (TS) and ultimate tensile strain (UTS) is mostly within 20%. As can be seen from the figure, the accuracy of the model in predicting the tensile strength of ECC is above 90% ( , the prediction effect is good. In addition, it is worth noting that the accuracy of the model in predicting the ultimate tensile strain is lower than that in predicting the tensile strength ( This is because the strain capacity of ECC generally has a greater dispersion than the tensile strength due to its sensitivity to the casting and loading processes and is therefore difficult to estimate. 2 The value is 61%. Therefore, the effect of BO-CNN model in predicting the ultimate tensile strain is better than that of existing studies.

[0114] In order to further verify the performance of the BO-CNN model, Figure 16-17 The error distribution and density curve of the model in predicting tensile strength (TS) and ultimate tensile strain (UTS) are plotted in Figure 2. Figure 16-17 It can be seen that the vast majority of errors in tensile strength are concentrated between -1.5MPa and 1.5MPa, and the vast majority of errors in ultimate tensile strain are mainly concentrated between -1.5% and 1.5%. The statistical peak values ​​of the errors are close to 0, and the overall standard deviations of the data sets are 0.737 and 0.753, respectively, indicating that the predicted values ​​of the BO-CNN model are consistent with the actual values. In addition, it can be seen from the figure that the error distributions between the training set, validation set, and test set for predicting tensile strength and ultimate tensile strain are also consistent, indicating that the model is fully trained during the training process, avoiding the undesirable results of overfitting and underfitting, and has good generalization ability.

[0115] This embodiment aims to deeply explore the effectiveness of convolutional neural networks and Bayesian optimization techniques in BO-CNN. In addition to convolutional neural networks and Bayesian optimization techniques, GS is a representative hyperparameter optimization technology that is currently widely used, and ANN is a classic neural network that is currently widely used in the field of concrete performance prediction. Therefore, this embodiment uses GS-CNN and GS-ANN as comparison models to explore the prediction accuracy of three models including BO-CNN in tensile strength and ultimate tensile strain. GS-CNN in this embodiment refers to the convolutional neural network optimized by GS. GS-ANN refers to the traditional neural network optimized by GS.

[0116] Figure 18-19 The prediction results of the three models on the test set are given. Overall, the prediction curve of BO-CNN is closer to the true value, indicating that the prediction performance of the BO-CNN model is the best. Figure 20-21 The three evaluation indicators of the three models in predicting tensile strength and ultimate compressive strength are quantitatively shown ( ). For tensile strength, Fig. 20 As shown in Figure 2, the BO-CNN, GS-CNN, and GS-ANN models They are 0.91, 0.86, and 0.81, respectively, which shows that BO-CNN has the highest prediction accuracy, followed by GS-CNN, and GS-ANN is the worst. The values ​​are 0.71, 0.95 and 1.08 respectively. The values ​​are 0.59, 0.69 and 0.86 respectively, which shows that BO-CNN has the smallest prediction deviation and prediction error, followed by GS-CNN, and GS-ANN is the worst. From the above results, it can be seen that compared with the traditional ANN network, the convolutional neural network, as a classic deep neural network, can more effectively perform feature mining on the data and obtain features that are more sensitive to the prediction target. At the same time, the above results show that Bayesian optimization technology is superior to the traditional GS grid search method. Especially for neural network models, hyperparameters have a greater impact on their performance. Exhaustive search in a limited hyperparameter search space cannot fully tap the potential of the model. The use of Bayesian technology can obtain the best hyperparameters in an infinite hyperparameter search space to ensure that the model achieves the best performance. It is worth noting that for predicting the ultimate tensile strength, the data is more discrete, and the advantages of the BO-CNN model proposed in this embodiment are more obvious. For , the accuracy of BO-CNN model is improved by 12.28% and 17.82% compared with GS-CNN and GS-ANN models. and ,Compared to the GS-CNN and GS-ANN models, the BO-CNN model reduced the performance by 31.58%,34.71% and 37.42%,40.85%, respectively.

[0117] This example aims to study the advantages of CNN model over other machine learning models. Table 4 shows the prediction effect of each model in predicting tensile strength in the test set. The prediction effect is mainly evaluated by three evaluation indicators ( ). As can be seen from Table 4, for all machine learning algorithms, BO-CNN has the highest accuracy, corresponding to The value is 0.911. At the same time, the BO-CNN model and The values ​​are also the lowest, which are 0.701 and 0.066 respectively, indicating that the prediction results of this model have the smallest deviation and error. In general, there is a complex nonlinear relationship between multiple input features of ECC and tensile strength. As a classic deep learning algorithm, convolutional neural network can better handle such nonlinear problems. At the same time, Bayesian technology automatically retrieves and obtains the optimal values ​​of each hyperparameter of the CNN model, maximizing the network potential of CNN, so that the BO-CNN network has the best prediction performance. Other machine learning models, such as GS-CNN and RF integrated algorithms, also show good prediction accuracy. The value is greater than 0.8. In contrast, The prediction effects of algorithms such as NN, SVR and LinearRegression are not good. The values ​​are all lower than 0.7. NN is based on The algorithm principle is not suitable for solving this problem. The default kernel function in the SVR algorithm is not suitable for capturing complex nonlinear relationships, and SVR training is time-consuming. LinearRegression assumes that there is a linear relationship between data, and has limited modeling capabilities for nonlinear problems.

[0118] Table 5 shows the prediction effect of each model on the ultimate tensile strength in the test set. As can be seen from Table 5, the prediction effect of each model for the ultimate tensile strain is not as good as that for the tensile strength. This is because the sensitivity of the preparation and test process of ECC concrete specimens leads to a higher discreteness of the ultimate tensile strain data itself, which increases the difficulty of model prediction. It can also be seen from Table 5 that for analyzing more discrete data and more complex nonlinear problems, the BO-CNN model still has the highest prediction accuracy compared with other machine learning models ( ) and the lowest prediction error ( =1.174 and ). It can be seen that the BO-CNN model can more effectively identify and utilize complex relationships in the data when predicting tensile strength and ultimate tensile strain. Among them, for tensile strength, the BO-CNN model has the greatest performance improvement compared to the KNeighbors model, R 2 The performance of the machine learning model was improved by 336.15%, and the RMSE and MAPE were reduced by 66.68% and 70.40%, respectively. This shows that there is a weak correlation between the tensile strength, a mechanical property indicator, and the 10 input features used, which makes it difficult for the distance-based KNeighbors model to accurately predict the tensile strength. For the ultimate tensile strain, the performance improvement of the BO-CNN model is much greater than that of the neural network model compared with other traditional machine learning models, which shows that for the complex mechanical property of the ultimate tensile strain, the neural network model can better explore the input features and its data features, but the BO-CNN model is more accurate in predicting the ultimate tensile strain. In addition, the prediction model of the ECC ultimate tensile strain designed in the existing research is It is 0.610, so the model proposed in this embodiment is reliable and superior to existing research.

[0119] Table 4

[0120]

[0121] Table 5

[0122]

[0123] For the BO-CNN model predicting tensile strength, W / B is at the top, indicating that it is the most important and has the greatest impact on the predicted value. As W / B increases, the predicted value of ECC tensile strength decreases. At low W / B, the tensile strength is higher. This shows that the value of W / B is negatively correlated with the predicted value of tensile strength as a whole, which is consistent with the experimental results. In the experimental study of ECC concrete, the water-binder ratio often has the greatest impact on tensile strength. The tensile strength of ECC concrete with a small water-binder ratio is usually higher, and increasing the water-binder ratio tends to reduce its tensile strength. This shows that the BO-CNN model captures the important characteristic of water-binder ratio when predicting tensile strength through these 10 features, and the prediction law of the model is consistent with the experimental results. Through the same analysis, for the BO-CNN model predicting the ultimate tensile strain, the fiber properties Vf and Lf are the two most important features affecting the predicted value, and the relationship between them and the ultimate tensile strain is positively correlated. With the increase of fiber length and fiber volume fraction, the predicted value of ECC ultimate tensile strain also increases, and this prediction result is consistent with the existing research results. This is why many scholars are now paying attention to the effect of fiber on the tensile properties of FRP concrete. In general, for different outputs, although the input features are exactly the same, the BO-CNN model can still successfully capture the key information of each input feature for different output targets, and can predict the size of the output target value in the same trend as the research results obtained through experiments. This shows that the BO-CNN model can deeply explore the complex relationship between input features and output targets through its multi-level, highly complex and effective nonlinear network architecture, thereby obtaining accurate prediction results. In addition, the model maintains stable prediction performance for different output targets, further verifying its applicability and reliability.

[0124] The main conclusions of this example are as follows:

[0125] The proposed BO-CNN model outperforms the nine basic ML models in terms of prediction accuracy, with the highest prediction accuracy and the lowest prediction error. 2 , RMSE and MAPE are 0.911, 0.701 and 0.066 respectively; in predicting the ultimate tensile strain, its R 2 , RMSE and MAPE are 0.775, 1.174 and 0.238 respectively. It is worth noting that for the prediction problem of ultimate tensile strain with stronger data discreteness, the BO-CNN model proposed in this embodiment has more obvious advantages than other ML models.

[0126] The proposed BO-CNN model is superior to the traditional GS optimized neural network model in terms of prediction accuracy. In predicting tensile strength, the prediction accuracy of the BO-CNN model is 12.28% and 17.82% higher than that of the GS-CNN and GS-ANN models. In predicting ultimate tensile strain, the prediction accuracy of the BO-CNN model is 8.32% and 10.99% higher than that of the GS-CNN and GS-ANN models. Because for neural network models, hyperparameters have a great influence on their performance, exhaustive search in a limited hyperparameter search space cannot fully tap the model's potential. The use of Bayesian technology can obtain the best hyperparameters in an infinite hyperparameter search space to ensure that the model achieves the best performance.

[0127] Through the SHAP value analysis of the BO-CNN model, the contribution of each input feature to the output target prediction result in the BO-CNN model was obtained, and how the output target value changes with each feature was revealed. The study found that W / B, Vf and Lf are the key influencing factors of the tensile properties of ECC concrete, which is consistent with the existing experimental results.

[0128] In summary, the BO-CNN model can use Bayesian optimization technology to obtain the best model from an infinite hyperparameter search space through a finite number of iterations, and can use deep learning algorithms to establish a nonlinear mapping relationship between input features and output targets, effectively predicting output target values ​​(tensile strength and ultimate tensile strain), and has good prediction accuracy and generalization performance.

[0129] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A deep learning method for predicting the tensile mechanical properties of high-toughness concrete, characterized in that: The following steps are involved: Construct a feature dataset based on the characteristics of cement samples; Preprocessing the feature data set to obtain a preprocessed data set; Constructing a Bayesian optimization convolutional neural network based on a Bayesian optimization algorithm and a convolutional neural network, training the Bayesian optimization convolutional neural network through the preprocessed data set to obtain an ultimate tensile strength prediction model; Predicting the tensile mechanical properties of high-toughness concrete based on the ultimate tensile strength prediction model; The process of constructing a Bayesian optimization convolutional neural network based on the Bayesian optimization algorithm and the convolutional neural network includes: Construct a convolutional neural network model based on input layer, convolution layer, rectified linear unit, pooling layer and fully connected layer; Calculating the hyperparameters of the convolutional neural network model based on a Bayesian optimization algorithm to obtain a global optimal solution; Feeding back the global optimal solution to the convolutional neural network model to generate a Bayesian optimized convolutional neural network; The expression of the operation of the convolutional layer is: ； in, Indicates The output feature value of the sample after the convolution operation in the current layer, Indicates The data sample is in The value of the feature, represents the weight of the two-dimensional convolution kernel, and Respectively represent Samples and features, m and n represent the dimensions of the convolution kernel; The corrected linear unit is a ReLU activation function; The expression of the ReLU activation function is: ； in, is the output value, is the input value of the previous neural network layer.

2. The deep learning method for predicting tensile mechanical properties of high-toughness concrete according to claim 1, characterized in that: The cement samples include: The characteristics of the cement samples include: ordinary Portland cement, fly ash, slag, lime powder, silica fume, sand, water and PE fiber; The characteristics of the cement sample include input characteristics and output characteristics; The input characteristics include: the mass ratio of cement to cementitious material, the mass ratio of fly ash to cementitious material, the mass ratio of slag to cementitious material, the mass ratio of lime powder to cementitious material, the mass ratio of silica fume to cementitious material, the mass ratio of sand to cementitious material, the mass ratio of water to cementitious material, fiber content, fiber length and fiber diameter; The output characteristics include: tensile strength and ultimate tensile strain.

3. The deep learning method for predicting tensile mechanical properties of high-toughness concrete according to claim 1, characterized in that: The process of preprocessing the feature data set to obtain the preprocessed data set includes: Performing maximum and minimum normalization processing on the feature data set to obtain a normalized data set; The normalized data set is divided based on a cross-validation method to obtain the preprocessed data set.

4. The deep learning method for predicting tensile mechanical properties of high-toughness concrete according to claim 1, characterized in that: The expression of the Bayesian optimization algorithm is: ； in, For the The feature vector of samples, X is the parameter set to be optimized, f ( ) is the objective function, which indicates that the model The prediction performance or loss of samples, is the objective function f ( ) is the optimal solution on the domain X.

5. The deep learning method for predicting tensile mechanical properties of high-toughness concrete according to claim 1, characterized in that: The Bayesian optimization algorithm uses the UCB function as the sampling function, and the expression of the sampling function is: ； in, and are the first The predicted mean of the samples and the The uncertainty of the prediction results of each sample, To balance the parameters of exploration and exploitation, For the The input variables for the sample.

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