A method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on the combination of cumulative heat release curve and CART-BA integrated model

Abstract

The present application relates to a kind of methods for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on the integration of cumulative heat release curve and CART-BA model, belonging to the technical field of civil engineering materials.The method comprises the following steps: S1, collect cumulative heat release curve data and mix proportion parameters, curing temperature;S2, the maximum heat release is obtained by three-parameter exponential equation regression, and then the reaction degree is calculated and corrected;S3, establish the age-reaction degree relationship data set of alkali-activated solid waste materials;S4, construct the age-reaction degree relationship prediction model of alkali-activated solid waste materials based on CART-BA;S5, based on the established prediction model, the age-reaction degree relationship prediction of alkali-activated solid waste materials with different mix proportions is realized.The present application fills the blank of the combination of cumulative heat release and machine learning for the prediction of reaction degree of alkali-activated solid waste materials, and can realize the prediction of reaction degree of alkali-activated solid waste materials with known mix proportion at any age, significantly improving the prediction efficiency and generalization ability.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering materials technology, specifically relating to a method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model. Background Technology

[0002] Alkali-activated solid waste materials exhibit excellent mechanical properties and low carbon emissions, making them highly promising cement substitutes. The macroscopic properties of these materials essentially depend on the hydration reaction process, which is influenced by a combination of factors, including precursor composition, activator parameters, and curing conditions, making the degree of reaction difficult to predict precisely. Accurate prediction of the reaction degree has significant theoretical and practical value for material design, performance control, and engineering applications.

[0003] Existing methods for calculating the degree of reaction mainly include image analysis and acid dissolution methods. Image analysis selects microscopic regions that are random and localized, lacking representativeness; acid dissolution methods suffer from incomplete dissolution and filtration residues, easily introducing significant errors. The cumulative heat release, as a thermal signal of the hydration reaction, has a physical correspondence with the degree of reaction; both increase monotonically with the reaction progress, and the reaction tends to terminate when the cumulative heat release reaches its maximum value. Therefore, calculating the degree of reaction using cumulative heat release has a clear physical basis and can effectively avoid the inherent defects of image analysis and acid dissolution methods.

[0004] In recent years, although some studies have attempted to introduce machine learning methods for predicting the performance of alkali-activated materials, several key shortcomings remain. Regarding prediction targets, existing methods mostly focus on carbonization depth (Chinese Patent CN 118551298A), compressive strength (Materials, 2024, 17, 5086), or residual strength after high temperature (Scientific Reports, 2026, 16:14475), etc., none of which address the degree of reaction in alkali-activated solid waste materials. The prediction targets are fundamentally different from the core object of this invention. Regarding input features, the method in Chinese Patent CN 118551298A has 12 input variables, and the study by Fang et al. (Materials, 2024, 17, 5086) has 25 input parameters, including a large number of redundant parameters. Excessive input dimensionality easily introduces noise interference, affecting the model's generalization performance, and too many parameters make acquisition inconvenient. Regarding algorithm applicability, the aforementioned studies generally adopted the XGBoost algorithm. However, XGBoost is quite sensitive to hyperparameters, and the model performance is highly dependent on hyperparameter tuning strategies such as grid search or Bayesian optimization, lacking robustness on different datasets. In terms of predictive ability, although Chinese patent CN 114577566A is based on the test of the setting and hardening degree of concrete by exothermic testing, it cannot achieve continuous prediction of the degree of reaction at any age; the method based on reaction kinetic model to characterize the degree of reaction has model parameters that change with the mix proportion (Journal of Composite Materials, 2026, 43(1): 359-371), and each time a new mix proportion is introduced, isothermal calorimetry experiments and parameter calibration need to be carried out again, and the model has poor universality; although Zuo (Experimental Study and Numerical Simulation of the Reaction Process and Microstructure Formation of Alkali-Activated Materials) calculates the degree of reaction of alkali-activated materials based on SEM image method, this method is only for single mix proportion samples. Once the mix proportion is changed, SEM image acquisition and other experimental tests and quantitative analysis need to be carried out again, which is time-consuming, labor-intensive and costly. Furthermore, the cumulative exothermic curve experimental results of different samples published in existing studies contain reaction process data under different mixing ratios and curing conditions. Due to the large amount of data and its significant differences, there is no method to reuse the above-mentioned multiple types of data to serve the prediction of the reaction degree of multiple samples, which to some extent leads to a waste of data resources.In summary, existing machine learning methods have not yet proposed a prediction scheme for the age-reaction degree relationship based on the cumulative exothermic curve for alkali-activated solid waste materials. Furthermore, they suffer from shortcomings in terms of target matching, input parameter simplification, algorithm robustness, and prediction result continuity, and fail to fully utilize and further mine the important parameter of reported cumulative exothermic heat. For model construction, a single algorithm struggles to balance accuracy and stability. While the CART algorithm has an intuitive structure, it is prone to overfitting, sensitive to data fluctuations, and its prediction output is the mean of samples covered by leaf nodes, making it difficult to smoothly fit the nonlinear relationship coupled with multiple factors. Although the BA algorithm can reduce variance through model averaging, it has limited improvement on the inherent bias of sub-learners. Other algorithms, such as Support Vector Machines and AdaBoost Regressors, may have low prediction accuracy when used alone to build models. Moreover, there are no publicly reported technical solutions combining cumulative exothermic heat with machine learning models to construct a high-precision prediction model for the age-reaction degree of alkali-activated solid waste materials. Therefore, there is an urgent need for a prediction method that integrates the structural transparency of CART and the stability of BA, and incorporates cumulative exothermic heat into the modeling. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention provides a method for predicting the age-reaction degree relationship of alkali-activated solid waste materials by combining the cumulative exothermic curve with the CART-BA integrated model. This method can accurately predict the reaction degree of alkali-activated solid waste materials of known proportions at any age.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, comprising the following steps:

[0007] S1. Collect the cumulative exothermic curve data of alkali-activated solid waste materials, i.e., t~Q, where t represents time in days and Q represents heat release in J / g; at the same time, collect the mixing ratio parameters and curing temperature corresponding to each curve.

[0008] S2. The cumulative heat release curves are fitted using a three-parameter exponential equation to calculate the maximum cumulative heat release Q corresponding to each curve. max The unit is J / g. Then, the degree of reaction of each group of samples under different curing ages is calculated to obtain the age-reaction degree data of each group of samples.

[0009] S3. Based on the mixing ratio parameters and curing temperature collected in S1 and the degree of reaction at different ages calculated in S2, establish a dataset of the age-reaction degree relationship of alkali-activated solid waste materials.

[0010] S4. Establish a prediction model for the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA integrated algorithm;

[0011] S5. Based on the prediction model established in S4, the age-reaction degree relationship of alkali-activated solid waste materials with different mixing ratios is predicted.

[0012] Preferably, in step S1, the proportioning parameters include precursor composition and content, alkali content, activator modulus, and water-binder ratio;

[0013] Wherein: the precursor type is one or more types of industrial solid waste materials, and the content of each type of precursor is the mass percentage of the precursor in the total precursor; the alkali doping amount is the mass percentage of sodium oxide in the activator to the total precursor, and the activator modulus is the molar ratio of silicon dioxide to sodium oxide in the activator; the water-cement ratio is the mass ratio of water to the total precursor; the activator uses sodium hydroxide and sodium silicate, and the sodium oxide in the activator is sodium oxide in sodium hydroxide and sodium oxide in sodium silicate; the silicon dioxide in the activator is silicon dioxide in sodium silicate.

[0014] Preferably, step S2 specifically includes the following:

[0015] S21. Using the three-parameter exponential equation of equation (1), regression fitting is performed on the cumulative heat release curve to obtain the corresponding maximum cumulative heat release. ;

[0016] S22, Q(t) obtained from the cumulative heat release curve data and S21 max The uncorrected degree of response α(t) at age t is calculated using equation (2). uncorrected ;

[0017] S23. Considering the presence of crystalline phases in different types of precursors, the α(t) calculated by equation (2) uncorrected Multiply by the mass fraction of amorphous phase in the total precursor to obtain the corrected degree of reaction. As shown in equation (3). The amorphous phase content in the total precursor is calculated using equation (4). For the reaction degree corresponding to the curing age exceeding the end time of the cumulative exothermic curve test, it is first extrapolated using equation (1). Then, the results are obtained by calculating from equation (2) to equation (4) in sequence;

[0018] (1)

[0019] (2)

[0020] (3)

[0021] (4)

[0022] In the formula: Q(t) is the cumulative heat release over a curing period of t, [J / g]; Q max The maximum cumulative heat release is given by [J / g]; τ and β are the reaction time and shape parameters, respectively; α(t) uncorrected The response level is the uncorrected maintenance age as t; f amorphous f is the mass fraction of the amorphous phase in the total precursor; p is the precursor type index, p=1, 2, …, n, f p,amorphous P represents the mass fraction of the amorphous phase in the p-th type of precursor; p α(t) is the ratio of the mass of the p-th type of precursor to the total precursor mass, where the total precursor mass is equal to the sum of the masses of all types of precursors; α(t) is the degree of reaction of the sample with a curing age of t.

[0023] Preferably, in step S3, the input parameters of the alkali-activated solid waste material age-reaction degree relationship dataset are: precursor content, alkali dosage, activator modulus, water-cement ratio, curing temperature, and curing age for each type; the output parameter is the reaction degree, and the reaction degree value range is [0,1].

[0024] Preferably, step S4 specifically includes the following:

[0025] S41. Divide the dataset established in step S3 into a training set and a test set;

[0026] S42. Perform min-max standardization on the feature parameter data in the training set, linearly mapping them to the [0,1] interval. The standardization formula is as follows:

[0027] (5)

[0028] In the formula: v j v is the value of the j-th input feature parameter; j,min and v j,max These are the minimum and maximum values ​​corresponding to the j-th input feature parameter in the dataset, respectively.

[0029] S43. Construct a prediction model based on the CART-BA ensemble algorithm. Adopt a two-layer stacked ensemble strategy, using Classification and regression tree (CART) and Bootstrap aggregating regression (BA) algorithms as the first-layer base learners, and using linear regression algorithm as the meta-learner in the second layer.

[0030] S431, The CART algorithm described above divides the feature space into... A number of non-overlapping leaf node regions And assign a constant predicted value to each region. For the input sample Its prediction expression is:

[0031] (6)

[0032] In the formula: This is an indicator function; it takes the value 1 when the condition is met and 0 otherwise. During training, the optimal splitting feature and split point are determined by minimizing the squared error of each node until the preset stopping condition is met.

[0033] The BA algorithm described above generates data through sampling with replacement. training subset Train a CART sub-model independently on each subset. The final prediction is the arithmetic mean of the outputs of all sub-models:

[0034] (7)

[0035] In the formula: B is the number of sub-models;

[0036] S432, base learner hyperparameter optimization uses grid search and 5-fold cross-validation; among them, CART hyperparameters include maximum depth, minimum number of samples required for splitting, and minimum number of samples in leaf nodes; BA hyperparameters include number of sub-models, sampling ratio, and feature sampling ratio; the 5-fold cross-validation in this step is used for hyperparameter selection, and is a separate operation from the 5-fold cross-validation used to generate meta-features in S433, belonging to different stages;

[0037] S433. To prevent data leakage, the training data for the meta-learner is generated through 5-fold cross-validation; let the training set be... ,in For the first The original feature vector of each sample, This corresponds to the actual level of reaction. This represents the total number of training samples. The training set is then evenly divided into 5 subsets. For each fold ( ), to exclude the first The CART and BA models were trained using the 4-fold data outside the fold, and then the data from the fold were used to train the CART and BA models. Each sample of the compromise Prediction is performed to obtain two-dimensional feature vectors. ,in and They respectively represent based on the first The CART and BA models trained on the training subset are folded; after traversing all folds, the two-dimensional meta-features of all samples are reconstructed into a meta-feature matrix in their original order:

[0038] (8)

[0039] S434, the meta-feature matrix As input, the initial degree of reaction As output, train the linear regression meta-learner:

[0040] (9)

[0041] In the formula: , The first The predicted values ​​of CART and BA in the meta-feature matrix corresponding to each sample; , , The regression coefficients are obtained using the least squares method. ,Right now:

[0042] (10)

[0043] S44. Evaluate the performance of the trained CART-BA ensemble model using the test set. The evaluation metrics include the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The formulas for each metric are as follows:

[0044] (11)

[0045] (12)

[0046] (13)

[0047] In the formula: y i The degree of response of the i-th sample; This is the predicted response level for the i-th sample. N represents the average response level across all samples in the test set, where N is the number of samples.

[0048] S45. Model saving: Save the trained prediction model of the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA ensemble algorithm as a file using the joblib library.

[0049] Preferably, in step S5, the mixing ratio parameters, curing temperature, and curing age of the alkali-activated solid waste material to be predicted are input into the prediction model established in step S4. The model directly predicts and outputs the corresponding degree of reaction, thereby obtaining the age-degree of reaction relationship corresponding to the mixing ratio and curing temperature.

[0050] The beneficial effects of this invention are:

[0051] 1) This invention characterizes the degree of reaction based on the cumulative heat release. The cumulative heat release, as the accumulation of the heat signal of the hydration reaction in the time dimension, has a clear physical correspondence with the degree of reaction. Calculating the degree of reaction based on the cumulative heat release can effectively avoid the inherent defects of traditional image methods such as insufficient representativeness and large operational errors of acid dissolution methods, and provides reliable physical prior support for data-driven prediction.

[0052] 2) This invention uses CART and BA as base learners in a stacked ensemble model. By performing weighted regression on the prediction results of the two through a meta-learner, the strong fitting ability of CART and the stability advantage of BA are combined, effectively suppressing the risk of overfitting and achieving a synergistic improvement in prediction accuracy and generalization ability, thus realizing high-precision prediction of the reaction degree.

[0053] 3) This invention combines cumulative heat release curve regression with the CART-BA integrated algorithm, filling the gap in using cumulative heat release and machine learning to predict the reaction degree of alkali-activated solid waste materials. In the reaction degree calculation stage before dataset establishment, this invention further introduces a correction process based on the amorphous phase content, utilizing the physical information of cumulative heat release and the data-driven nonlinear mapping advantage of the CART-BA integrated algorithm to ultimately achieve high-precision prediction of the age-reaction degree relationship of alkali-activated solid waste materials.

[0054] 4) After model training, isothermal calorimetry or microscopic imaging tests are not required for the predicted samples. Only the mix proportion and curing regime parameters need to be input to predict the degree of reaction under known mix proportions, arbitrary ages, or continuous ages, obtaining the age-reaction relationship between the mix proportion and the curing conditions, significantly improving prediction efficiency. Compared with kinetic models that rely on a single mix proportion and require recalibration of parameters every time a new mix proportion is introduced, the model established in this invention has stronger generalization ability and a wider range of applicability. Attached Figure Description

[0055] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0056] Figure 1This is a flowchart of the method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on the combination of cumulative exothermic curves and CART-BA integrated algorithm according to the present invention.

[0057] Figure 2 This is a schematic diagram of the cumulative heat release curve in an embodiment of the present invention;

[0058] Figure 3 This is a schematic diagram of regression fitting of the cumulative heat release curve using a three-parameter exponential equation in an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram of the age-reaction degree relationship dataset of alkali-activated solid waste materials established in the embodiments of the present invention;

[0060] Figure 5 This is a flowchart illustrating the construction of a prediction model for the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA integrated algorithm in this embodiment of the invention.

[0061] Figure 6 This is a comparison between the predicted values ​​of the age-response relationship prediction model based on the CART-BA ensemble algorithm and the response degree calculated based on the regression of the cumulative exothermic curve in this embodiment of the invention.

[0062] Figure 7 This invention presents a comparison of the predicted age-reaction degree relationship of alkali-activated slag slurry under the same mix ratio and curing conditions, the reaction degree of alkali-activated slag slurry based on SEM images reported in the literature, and the uncorrected reaction degree calculated by existing methods.

[0063] Figure 8 This invention presents a comparison of the predicted age-reaction degree relationship of alkali-activated fly ash slurry under the same mix ratio and curing conditions, the reaction degree of alkali-activated fly ash slurry based on SEM images reported in the literature, and the uncorrected reaction degree calculated by existing methods.

[0064] Figure 9 This invention presents the predicted results of the age-reaction degree relationship of alkali-activated slag-fly ash slurry under the same mix ratio and curing conditions in this embodiment. It compares the results of the reaction degree of alkali-activated slag-fly ash slurry based on SEM images reported in the literature with the uncorrected reaction degree calculated by existing technical methods. Detailed Implementation

[0065] The technical solution of the present invention will now be described in conjunction with the accompanying drawings and embodiments. The described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of the present invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] See Figure 1 A method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model includes the following steps:

[0067] S1. Collect the cumulative exothermic curve data of alkali-activated solid waste materials, i.e., t~Q, the schematic diagram of which is shown in [reference needed]. Figure 2 Where t represents the curing period in days; Q represents the cumulative heat release in J / g; and the mixing ratio parameters and curing temperature corresponding to each curve are collected simultaneously; in this embodiment, the alkali-activated solid waste material includes three types: alkali-activated slag slurry, alkali-activated fly ash slurry, and alkali-activated slag-fly ash slurry;

[0068] Furthermore, the mixing parameters include precursor composition and content, alkali content, activator modulus, and water-cement ratio;

[0069] The precursors are slag and fly ash, which are industrial solid waste materials. The slag content is the mass percentage of slag in the total precursors, and the fly ash content is the mass percentage of fly ash in the total precursors. The alkali content is the mass percentage of sodium oxide in the activator to the total precursors, and the activator modulus is the molar ratio of silicon dioxide to sodium oxide in the activator. The water-cement ratio is the mass ratio of water to the total precursors. The total precursor mass is the sum of the masses of slag and fly ash. The activator uses sodium hydroxide and sodium silicate. The sodium oxide in the activator is the sodium oxide in sodium hydroxide and the sodium oxide in sodium silicate. The silicon dioxide in the activator is the silicon dioxide in sodium silicate.

[0070] S2. Based on the cumulative heat release curve data, a three-parameter exponential equation regression fitting is used to obtain the maximum cumulative heat release Q corresponding to each curve. max Then, the degree of reaction of each group of samples under different curing ages was calculated to obtain the age-reaction degree data of each group of samples.

[0071] S21. Using the three-parameter exponential equation of equation (1), the cumulative heat release curve is fitted by regression, as follows: Figure 3 As shown, the corresponding maximum cumulative heat release is obtained. ;

[0072] S22, Q(t) obtained from the cumulative heat release curve data and S21 max The uncorrected degree of response α(t) at age t is calculated using equation (2).uncorrected ;

[0073] S23. Considering the presence of crystalline phases in different types of precursors, the α(t) calculated by equation (2) uncorrected Multiply by the mass fraction of amorphous phase in the total precursor to obtain the corrected degree of reaction. As shown in equation (3). The amorphous phase content in the total precursor is calculated using equation (4). For the reaction degree corresponding to the curing age exceeding the end time of the cumulative exothermic curve test, it is first extrapolated using equation (1). ,like Figure 3 As shown, the results are then obtained sequentially from equation (2) to equation (4);

[0074] (1)

[0075] (2)

[0076] (3)

[0077] (4)

[0078] In the formula: Q(t) is the cumulative heat release over a curing period of t, [J / g]; Q max The maximum exothermic reaction is given by [J / g]; τ and β are the reaction time and shape parameters, respectively; α(t) uncorrected The response level is the uncorrected maintenance age as t; f amorphous f is the mass fraction of the amorphous phase in the total precursor; p is the precursor type index, p=1, 2, …, n, f p,amorphous Let P be the mass fraction of the amorphous phase in the p-th type of precursor, where the amorphous phase mass fraction is 93% for slag and 73% for fly ash; p α(t) is the ratio of the mass of the Pth type of precursor to the total precursor mass, where the total precursor mass is equal to the sum of the masses of all types of precursors; α(t) is the degree of reaction of the sample with a curing age of t.

[0079] S3. Based on the mixing ratio parameters and curing temperature collected in S1 and the degree of reaction at different ages calculated in S2, establish a dataset of the age-reaction degree relationship of alkali-activated solid waste materials.

[0080] Furthermore, the dataset established in this embodiment contains 7 input parameters and 1 output parameter. The input parameters and their value ranges are: slag content 0-1, fly ash content 0-1, alkali content 0.76%-15.02%, activator modulus 0-2.7, water-cement ratio 0.2-0.785, curing temperature 10-85℃, and curing time 0-1080 days. The output parameter is the degree of reaction, with a value range of 0-1. Figure 4 This is a schematic diagram of the dataset in this embodiment.

[0081] S4. Establish a prediction model for the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA integrated algorithm. The flowchart is shown below. Figure 5 ;

[0082] S41. The dataset established in step S3 is randomly divided into a training set and a test set according to a ratio of 80% to 20%; to ensure the randomness and repeatability of the division, the random seed is set to 42.

[0083] S42. Perform min-max standardization on the feature parameter data in the training set, linearly mapping them to the [0,1] interval. The standardization formula is as follows:

[0084] (5)

[0085] In the formula: v j v is the value of the j-th input feature parameter; j,min and v j,max These are the minimum and maximum values ​​corresponding to the j-th input feature parameter in the dataset, respectively;

[0086] S43. Construct a prediction model based on the CART-BA ensemble algorithm. Adopt a two-layer stacked ensemble strategy, using Classification and regression tree (CART) and Bootstrap aggregating regression (BA) algorithms as the first-layer base learners, and using linear regression algorithm as the meta-learner in the second layer.

[0087] S431, The CART algorithm described above divides the feature space into... A number of non-overlapping leaf node regions And assign a constant predicted value to each region. For the input sample Its prediction expression is:

[0088] (6)

[0089] In the formula: This is an indicator function; it takes the value 1 when the condition is met and 0 otherwise. During training, the optimal splitting feature and split point are determined by minimizing the squared error of each node until the preset stopping condition is met.

[0090] The BA algorithm described above generates data through sampling with replacement. training subset Train a CART sub-model independently on each subset. The final prediction is the arithmetic mean of the outputs of all sub-models:

[0091] (7)

[0092] In the formula: B is the number of sub-models;

[0093] S432. Base learner hyperparameter optimization employs a grid search method and 5-fold cross-validation. The grid search method iterates through preset hyperparameter combinations and selects the optimal combination based on the cross-validation results. CART hyperparameters include maximum depth, minimum number of samples required for splitting, and minimum number of samples per leaf node. BA hyperparameters include the number of sub-models, sampling ratio, and feature sampling ratio. The base learner algorithm hyperparameter settings and optimal hyperparameter values ​​are shown in Tables 1 and 2. The 5-fold cross-validation in this step is used for hyperparameter selection and is a separate operation from the 5-fold cross-validation used to generate meta-features in S433, belonging to different stages.

[0094] Table 1. Hyperparameter settings and optimization values ​​for the base learner CART

[0095]

[0096] Table 2. Hyperparameter settings and optimization values ​​for the base learner (BA)

[0097]

[0098] S433. To prevent data leakage, the training data for the meta-learner is generated through 5-fold cross-validation; let the training set be... ,in For the first The original feature vector of each sample, This corresponds to the actual level of reaction. This represents the total number of training samples. The training set is then evenly divided into 5 subsets. For each fold ( ), to exclude the first The CART and BA models were trained using the 4-fold data outside the fold, and then the data from the fold were used to train the CART and BA models. Each sample of the compromise Prediction is performed to obtain two-dimensional feature vectors. ,in and They respectively represent based on the first The CART and BA models trained on the training subset are folded; after traversing all folds, the two-dimensional meta-features of all samples are reconstructed into a meta-feature matrix in their original order:

[0099] (8)

[0100] S434, the meta-feature matrix As input, the initial degree of reaction As output, train the linear regression meta-learner:

[0101] (9)

[0102] In the formula: , The first The predicted values ​​of CART and BA in the meta-feature matrix corresponding to each sample; , , The regression coefficients are obtained using the least squares method. ,Right now:

[0103] (10)

[0104] S44. Evaluate the performance of the trained CART-BA ensemble model using the test set. The evaluation metrics include the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The formulas for each metric are as follows:

[0105] (11)

[0106] (12)

[0107] (13)

[0108] In the formula: y i The degree of response of the i-th sample; This is the predicted response level for the i-th sample. N represents the average response level across all samples in the test set, where N is the sample size.

[0109] For the alkali-activated slag-fly ash system in this embodiment, the evaluation parameters of the age-reaction degree relationship prediction model based on the CART-BA ensemble algorithm on the test set are R... 2 =0.9958, RMSE=0.016, MAE=0.007. In this embodiment, the predicted values ​​of the age-response relationship prediction model based on the CART-BA ensemble algorithm are compared with the response degree calculated based on the cumulative exothermic curve regression. See [link to relevant documentation]. Figure 6 ;

[0110] The performance evaluation parameters of the age-response relationship prediction model based on the CART-BA ensemble algorithm established in this invention were compared with those of prediction models established by other machine learning algorithms (CART, BA, Linear Regression, Support Vector Regression, Multi-layer Perceptron Regressor, AdaBoost Regressor, Gradient Boosting Regressor) to illustrate the feasibility and accuracy of the proposed CART-BA ensemble model. Table 3 lists the hyperparameter settings and values ​​for prediction models established by each algorithm individually, and Table 4 compares the model performance evaluation parameter results. Compared with prediction models established by other machine learning algorithms individually, the age-response relationship prediction model based on the CART-BA ensemble algorithm established in this invention exhibits the best performance evaluation parameters.

[0111] Table 3. Hyperparameter settings and values ​​for prediction models built separately for CART, BA, and other algorithms.

[0112]

[0113] Table 4. Comparison of the evaluation parameters of the age-response relationship prediction model of the CART-BA ensemble algorithm of this invention with the evaluation parameters of the prediction models established by CART, BA and other algorithms individually.

[0114]

[0115] S45. Model saving: Save the trained prediction model of the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA ensemble algorithm as a file using the joblib library.

[0116] S5. Based on the prediction model established in S4, the relationship between the age and the degree of reaction of alkali-activated solid waste materials with different mixing ratios is predicted.

[0117] Furthermore, the mixing ratio parameters (slag content, fly ash content, alkali dosage, activator modulus, water-cement ratio), curing temperature, and curing age of the alkali-activated solid waste material to be predicted are input into the prediction model established in step S4. The model directly predicts and outputs the corresponding degree of reaction, thereby obtaining the age-degree of reaction relationship corresponding to the mixing ratio and curing temperature.

[0118] This invention characterizes the degree of reaction based on the cumulative heat release. The cumulative heat release, as the accumulation of the heat signal of the hydration reaction over time, has a clear physical correspondence with the degree of reaction. Calculating the degree of reaction based on the cumulative heat release can effectively avoid the inherent defects of traditional image methods, such as insufficient representativeness and large operational errors in acid dissolution methods, and provides reliable physical prior support for data-driven prediction.

[0119] This invention uses CART and BA as base learners in a stacked ensemble model. By performing weighted regression on the prediction results of the two through a meta-learner, the strong fitting ability of CART and the stability advantage of BA are combined, effectively suppressing the risk of overfitting and achieving a synergistic improvement in prediction accuracy and generalization ability, thus realizing high-precision prediction of reaction degree.

[0120] This invention combines cumulative heat release curve regression with the CART-BA ensemble algorithm, filling the gap in using cumulative heat release and machine learning to predict the reaction degree of alkali-activated solid waste materials. In the reaction degree calculation stage before dataset establishment, this invention further introduces a correction process based on the amorphous phase content, utilizing the physical information of cumulative heat release and the data-driven nonlinear mapping advantage of the CART-BA ensemble algorithm to ultimately achieve high-precision prediction of the age-reaction degree relationship of alkali-activated solid waste materials.

[0121] After model training, isothermal calorimetry experiments or microscopic imaging tests are no longer required for predicting samples. Only the mix proportion and curing regime parameters need to be input to predict the degree of reaction under known mix proportions, arbitrary ages, or continuous ages. This yields the age-reaction relationship between the mix proportion and the curing conditions, significantly improving prediction efficiency. Compared to kinetic models that rely on a single mix proportion and require parameter recalibration for each new mix proportion, the model established in this invention has stronger generalization ability and a wider range of applicability.

[0122] To verify the reliability of the method disclosed in the above embodiments for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on the cumulative exothermic curve and the CART-BA integrated model, the reaction degree of alkali-activated slag slurry, alkali-activated fly ash slurry, and alkali-activated slag-fly ash slurry with known mix proportions was predicted using the age-reaction degree relationship prediction model of alkali-activated solid waste materials established in this embodiment. The reaction degree was compared with that of samples with the same mix proportion and curing conditions reported in the literature based on SEM images. At the same time, to illustrate the importance and necessity of the reaction degree correction proposed in this invention using formulas (3) and (4), the reaction degree calculated using existing technical methods (i.e., formulas (1) and (2)), i.e. the uncorrected reaction degree obtained by formulas (1) and (2) in this invention, was compared with the reaction degree based on SEM images reported in the literature and the reaction degree predicted by the age-reaction degree relationship prediction model of this invention.

[0123] (1)

[0124] (2)

[0125] Table 5 shows the mix proportions and curing temperature parameters used to predict the age-reaction degree relationship of the alkali-activated slag-fly ash solid waste material system.

[0126] Table 5. Mix proportions and curing temperature parameters for alkali-activated slag-fly ash solid waste material systems used for predicting the age-reaction degree relationship.

[0127]

[0128] For the three types of alkali-activated solid waste materials in Table 5, the prediction results based on the CART-BA integrated algorithm model established in this invention, the reaction degree reported in the literature based on SEM images, and the uncorrected reaction degree calculated using existing formulas (1) and (2) are compared as follows: Figures 7-9 The SEM image-based reaction results of alkali-activated slag slurry, alkali-activated fly ash slurry, and alkali-activated slag-fly ash slurry in Table 5 reported in the literature are from reference [1].

[0129] [1] Zuo Y. Experimental Study and Numerical Simulation of theReaction Process and Microstructure Formation of Alkali-Activated Materials[D]. Delft: Delft University of Technology. 2019.

[0130] from Figures 7-9 As can be seen from the above, the method provided in this embodiment for predicting the age-reaction degree relationship of alkali-activated solid waste materials by combining the cumulative exothermic curve with the CART-BA integrated model is close to the reaction degree results based on SEM images reported in the literature, which shows the reliability of the method proposed in this invention.

[0131] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, characterized in that, Includes the following steps: S1. Collect the cumulative exothermic curve data of alkali-activated solid waste materials, i.e., t~Q, where t represents the curing age in days and Q represents the cumulative heat release in J / g; at the same time, collect the sample mix ratio parameters and curing temperature corresponding to each curve. S2. The cumulative heat release curves are fitted using a three-parameter exponential equation to obtain the maximum cumulative heat release Q corresponding to each curve. max The unit is J / g. Then, the degree of reaction of each group of samples under different curing ages is calculated to obtain the age-reaction degree data of each group of samples. S3. Based on the mixing ratio parameters and curing temperature collected in S1 and the degree of reaction at different ages calculated in S2, establish a dataset of the age-reaction degree relationship of alkali-activated solid waste materials. S4. Establish a prediction model for the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA integrated algorithm; S5. Based on the prediction model established in S4, the age-reaction degree relationship of alkali-activated solid waste materials with different mixing ratios is predicted.

2. The method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, as described in claim 1, is characterized in that... In step S1, the proportioning parameters include precursor composition and content, alkali dosage, activator modulus, and water-cement ratio; The precursor type is one or more types of industrial solid waste materials, and the content of each type of precursor is the mass percentage of that precursor in the total precursor; the alkali content is the mass percentage of sodium oxide in the activator to the total precursor, the activator modulus is the molar ratio of silicon dioxide to sodium oxide in the activator; the water-cement ratio is the mass ratio of water to the total precursor; the activator uses sodium hydroxide and sodium silicate, and the sodium oxide in the activator is sodium oxide in sodium hydroxide and sodium oxide in sodium silicate; the silicon dioxide in the activator is silicon dioxide in sodium silicate.

3. The method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, as described in claim 1, is characterized in that... Step S2 specifically includes the following: S21. Using the three-parameter exponential equation of equation (1), regression fitting is performed on the cumulative heat release curve to obtain the corresponding maximum cumulative heat release. ; S22, Q(t) obtained from the cumulative heat release curve data and S21 max The uncorrected degree of response α(t) at age t is calculated using equation (2). uncorrected ; S23. Considering the presence of crystalline phases in different types of precursors, the α(t) calculated by equation (2) uncorrected Multiply by the mass fraction of amorphous phase in the total precursor to obtain the corrected degree of reaction. As shown in equation (3); the amorphous phase content in the total precursor is calculated using equation (4); for the reaction degree corresponding to the curing age exceeding the end time point of the cumulative exothermic curve test, it is first extrapolated using equation (1). Then, the results are obtained by calculating from equation (2) to equation (4) in sequence; （1） （2） （3） （4） In the formula: Q(t) is the cumulative heat release over a curing period of t, [J / g]; Q max The maximum cumulative heat release is given by [J / g]; τ and β are the reaction time and shape parameters, respectively; α(t) uncorrected The response level is the uncorrected maintenance age as t; f amorphous The mass fraction of amorphous phase in the total precursor; p is the precursor type index, p = 1, 2, …, n, f p,amorphous denoted as the mass fraction of the amorphous phase in the p-th type of precursor; P p α(t) is the ratio of the mass of the p-th type of precursor to the total precursor mass, where the total precursor mass is equal to the sum of the masses of all types of precursors; α(t) is the degree of reaction of the sample with a curing age of t.

4. The method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, as described in claim 3, is characterized in that... In step S3, the input parameters of the alkali-activated solid waste material age-reaction degree relationship dataset are: precursor content, alkali dosage, activator modulus, water-cement ratio, curing temperature, and curing age for each type; the output parameter is the reaction degree, and the reaction degree value ranges from [0,1].

5. The method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, as described in claim 1, is characterized in that... Step S4 specifically includes the following: S41. Divide the dataset established in step S3 into a training set and a test set; S42. Perform min-max standardization on the feature parameter data in the training set, linearly mapping them to the [0,1] interval. The standardization formula is as follows: （5） In the formula: v j v is the value of the j-th input feature parameter; j,min and v j,max These are the minimum and maximum values ​​corresponding to the j-th input feature parameter in the dataset, respectively; S43. Construct a prediction model based on the CART-BA ensemble algorithm. Adopt a two-layer stacked ensemble strategy, using Classification and regression tree (CART) and Bootstrap aggregating regression (BA) algorithms as the first-layer base learners, and using linear regression algorithm as the meta-learner in the second layer. S431, The CART algorithm described above divides the feature space into... A number of non-overlapping leaf node regions And assign a constant prediction value to each region. For input samples Its prediction expression is: （6） In the formula: This is an indicator function; it takes the value 1 when the condition is met and 0 otherwise. During training, the optimal splitting feature and split point are determined by minimizing the squared error of each node until the preset stopping condition is met. The BA algorithm described above generates data through sampling with replacement. training subset Train a CART sub-model independently on each subset. The final prediction is the arithmetic mean of the outputs of all sub-models: （7） In the formula: B is the number of sub-models; S432, base learner hyperparameter optimization uses grid search and 5-fold cross-validation; among them, CART hyperparameters include maximum depth, minimum number of samples required for splitting, and minimum number of samples in leaf nodes; BA hyperparameters include number of sub-models, sampling ratio, and feature sampling ratio; the 5-fold cross-validation in this step is used for hyperparameter selection, and is a separate operation from the 5-fold cross-validation used to generate meta-features in S433, belonging to different stages; S433. To prevent data leakage, the training data for the meta-learner is generated through 5-fold cross-validation; let the training set be... ,in For the first The original feature vector of each sample, This corresponds to the actual level of reaction. The total number of training samples; the training set is evenly divided into 5 subsets. For each fold ( ), to exclude the first The CART and BA models were trained using the 4-fold data outside the fold, and then the data from the fold were used to train the CART and BA models. Each sample of the compromise Prediction is performed to obtain two-dimensional feature vectors. ,in and They respectively represent based on the first The CART and BA models trained on the training subset are folded; after traversing all folds, the two-dimensional meta-features of all samples are reconstructed into a meta-feature matrix in their original order: （8） S434, the meta-feature matrix As input, the initial degree of reaction As output, train the linear regression meta-learner: （9） In the formula: , The first The predicted values ​​of CART and BA in the meta-feature matrix corresponding to each sample; , , The regression coefficients are obtained using the least squares method. ,Right now: （10） S44. Evaluate the performance of the trained CART-BA ensemble model using the test set. The evaluation metrics include the coefficient of determination (R²), root mean square error (RMSE), and mean absolute error (MAE). The formulas for each metric are as follows: （11） （12） （13） In the formula: y i The degree of response of the i-th sample; This is the predicted response level for the i-th sample. N represents the average response level across all samples in the test set, where N is the sample size. S45. Model saving: Save the trained prediction model of the age-reaction degree relationship of alkali-activated solid waste materials based on the CART-BA ensemble algorithm as a file using the joblib library.

6. The method for predicting the age-reaction degree relationship of alkali-activated solid waste materials based on a combination of cumulative exothermic curves and a CART-BA integrated model, as described in claim 5, is characterized in that... In step S5, the mixing ratio parameters, curing temperature, and curing age of the alkali-activated solid waste material to be predicted are input into the prediction model established in step S4. The model directly predicts and outputs the corresponding degree of reaction, thereby obtaining the age-degree of reaction relationship corresponding to the mixing ratio and curing temperature.

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