Ultra-high performance concrete strength prediction method considering particle close packing effect

Abstract

The invention relates to the technical field of ultra-high performance concrete, in particular to an ultra-high performance concrete strength prediction method considering a particle close packing effect, comprising the following steps: S1, acquiring a data set to be measured, the data set comprising a macroscopic proportioning material and a material particle gradation; s2, according to the particle size distribution of the solid particle material in the data set, calculating the volume percentage of which the cumulative volume is smaller than a preset particle size through a corrected Andersen-Andersen model; s3, calculating the stacking compactness according to the volume percentage with the accumulated volume smaller than the preset particle size; and S4, inputting the stacking compactness and the to-be-measured data set into a prediction model to obtain a predicted value of the compressive strength of the ultra-high performance concrete. And by introducing microstructure quantitative indexes such as grain composition and stacking compaction parameters as model input, the prediction precision and reliability are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of ultra-high performance concrete technology, and more specifically to a method for predicting the strength of ultra-high performance concrete that takes into account the effect of dense particle packing. Background Technology

[0002] Ultra-high performance concrete (UHPC) is widely used in major engineering structures due to its numerous advantages, including ultra-high strength, high toughness, high durability, and light weight. Accurately predicting the strength development law of UHPC is of great significance for optimizing mix design, ensuring construction quality, and assessing structural safety. However, with the increasing complexity of UHPC component design and the development of microstructure characterization techniques, traditional strength prediction methods face new challenges.

[0003] Current main methods for predicting the strength of ultra-high performance concrete include traditional empirical formulas, numerical simulations, and machine learning-based intelligent algorithms. Traditional empirical formulas, based on large amounts of experimental data, establish functional relationships between concrete strength and influencing factors through linear regression, nonlinear regression, and semi-empirical formulas. While computationally simple, their applicability is limited. Numerical simulations, by establishing numerical models at different scales and combining them with finite element analysis, reveal the relationship between the material's internal structure and properties. These methods provide reliable predictions but are computationally complex and difficult to determine parameters. Machine learning-based methods utilize algorithms such as neural networks and support vector machines to learn the complex nonlinear relationships between input parameters and strength from large amounts of data, constructing predictive models and improving prediction accuracy under complex conditions.

[0004] However, existing methods have obvious shortcomings. Whether it is empirical formulas or machine learning models, most of them use macroscopic component parameters as input variables and ignore the important influence of microscopic structural factors such as the particle packing state inside the concrete on the strength. This results in insufficient accuracy and reliability of existing prediction methods under complex conditions, making it difficult to meet the needs of engineering practice.

[0005] The following are publicly disclosed related patents in the prior art: Patent 1: A method for predicting the residual compressive strength of ultra-high performance concrete (UHPC) after high temperature based on machine learning, application number: CN202411068398.2. The input parameters of this method mainly focus on the macroscopic proportions of the materials and experimental conditions, failing to consider the quantitative characteristics of the UHPC microstructure, such as particle size distribution and packing density parameters. The performance of UHPC is highly dependent on the dense packing effect of cementitious particles and aggregates; ignoring this key factor will limit the model's prediction accuracy and generalization ability.

[0006] Patent 2: A method for predicting the compressive strength of ultra-high performance concrete based on the Grey Wolf Optimization Algorithm, Application No.: CN202411803119.2. This scheme improves the convergence speed and accuracy of the model through intelligent optimization algorithms, but its input parameters are still limited to the traditional material composition ratios and do not involve the physical characterization of the internal structure of the material.

[0007] Patent 3: A method for predicting the tensile and flexural strength of ultra-high performance concrete, application number: CN202211275950.6. This method uses machine learning methods such as neural networks or support vector machines, taking material proportions, fiber types and dosages as input features to establish a strength prediction model. Its shortcomings are also reflected in the neglect of the influence of microstructure. Summary of the Invention

[0008] The purpose of this invention is to address the problem that existing prediction methods fail to fully consider the microstructural characteristics of UHPC, particularly the key intrinsic physical factors of particle size distribution and packing density. This invention proposes a method for predicting the strength of ultra-high performance concrete that considers the effect of close packing. Before using a machine learning model for prediction, the residual index between the theoretical and actual close packing curves is calculated. RSS This significantly improves the accuracy, reliability, and generalization ability of intensity prediction.

[0009] To achieve the above-mentioned objectives, the present invention provides the following technical solution: A method for predicting the strength of ultra-high performance concrete considering the effect of close particle packing includes the following steps: S1, Obtain the dataset to be tested, which includes macroscopic proportioned materials and material particle size distribution; S2, Based on the particle size distribution of solid particulate materials in the dataset, calculate the cumulative volume percentage of particles smaller than the preset particle size using the modified Andreasen-Andersen model; S3, calculate the packing density based on the cumulative volume percentage of particles smaller than the preset particle size; S4. Input the packing density and the dataset to be tested into the prediction model to obtain the predicted value of the compressive strength of ultra-high performance concrete.

[0010] Preferably, S2 includes the following steps: S21, Determine the particle size distribution index in the dataset based on the performance requirements of concrete; S22, determine the minimum particle size and the maximum particle size from the existing particles; S23, obtain the particle size distribution of the solid particulate material, and determine the corresponding cumulative volume percentage of particles smaller than the preset particle size based on the modified Andreasen-Andersen model.

[0011] Preferably, in step S21, the concrete properties are classified into self-compacting concrete, conventional pumped and vibratory compacted concrete, and dry-hard concrete, with corresponding particle size distribution indices of 0.21~0.29, 0.3~0.34, and 0.35~0.4, respectively.

[0012] Preferably, in step S23, the modified Andreasen-Andersen model is: ; in, Maximum particle size; Minimum particle size; The particle size is denoted as q; CPFT is the cumulative percentage of particles smaller than the preset particle size, and the superscript q indicates the particle size distribution index.

[0013] Preferably, step S3 includes the following steps: S31, the cumulative volume percentage of particles smaller than the preset particle size in each particle size range is taken as the theoretical passing percentage of that range, and the particle size range is divided. S32, based on the theoretical percentage and the actual percentage of particle size passing through, calculate the packing density for each particle size range, and sum the packing density of each particle size range to obtain the residual index. RSS The residual index RSS This refers to the packing density across the entire particle size range.

[0014] Preferably, in step S32, the formula for calculating the packing density is: ; Among them, F 实际 (Di) is the actual percentage of particles passing through with diameter Di; F 理论 (Di) is the theoretical pass rate; m is the number of particle size intervals, and i is the number of the particle size intervals.

[0015] Preferably, the prediction model employs a hybrid machine learning prediction model, comprising a base learner layer and a meta-learner layer; The base learner layer is used to input the packing density and the dataset to be tested, and outputs the first layer prediction result to the meta learner layer. The meta learner layer outputs the predicted value of the compressive strength of ultra-high performance concrete.

[0016] Preferably, the Catboost model, XGBoost model, LightGBM model, random forest model, gradient boosting decision tree, or support vector machine are used; the meta-learner layer adopts a linear regression model or a ridge regression model.

[0017] Preferably, the steps further include: calculating the SHAP value of each input feature, using the SHAP value to perform interpretability analysis on the hybrid machine learning prediction model, and identifying the factors that contribute the most to the compressive strength of ultra-high performance concrete.

[0018] Preferably, the prediction model is constructed using the Catboost algorithm.

[0019] Compared to existing technologies, the advantages of this invention are as follows: This invention proposes a method for predicting the strength of ultra-high performance concrete that combines the theory of dense packing with artificial intelligence algorithms. It overcomes the limitations of macroscopic parameters by introducing particle packing density parameters as a quantitative indicator of microstructure. Based on this, it integrates physical mechanisms and data-driven approaches, employing machine learning algorithms to improve the model's accuracy and generalization ability. By introducing microstructure quantitative indicators such as particle size distribution and packing density parameters as model inputs, the prediction accuracy and reliability are significantly improved. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the method for predicting the strength of ultra-high performance concrete that takes into account the particle packing effect of the present invention. Figure 2 To reflect the particle size in the method of this invention D i A graph showing the relationship between the actual pass rate and the theoretical pass rate; Figure 3 This is a schematic diagram of the 5x cross-validation process for a single primary learner in the method of this invention; Figure 4 This is a schematic diagram of the network structure of the hybrid machine learning prediction model based on the Stacking ensemble learning approach of the present invention. Figure 5 This is a schematic diagram of the dataset statistics table during the verification process of the method of the present invention; Figure 6 This is a histogram of the statistical distribution of the data corresponding to the dataset statistical table in the method of this invention; Figure 7 The input parameters contain residual indices during the verification process of this invention. RSS Catboost prediction results; Figure 8 The input parameters did not include a residual index during the verification process of this invention. RSS The Catboost prediction results. Detailed Implementation

[0021] The present invention will now be described in further detail with reference to specific embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0022] This invention provides a method for predicting the strength of ultra-high performance concrete (UHPC) that integrates close packing theory and artificial intelligence algorithms, taking into account the close packing effect of particles. Its core objective is to address the problem that existing prediction methods fail to fully consider the microstructural characteristics of UHPC, particularly the key intrinsic physical factors of particle gradation and packing density, thereby significantly improving the accuracy, reliability, and generalization ability of strength prediction. The objectives of this invention are elaborated below from different perspectives.

[0023] The primary objective is to overcome the limitations of traditional macroscopic parameters and innovatively integrate close-packing theory into the strength prediction framework. By fully considering the particle size distribution of raw materials (including cementitious materials and aggregates), and using the close-packing principle to calculate key microstructural parameters such as packing density parameters, these quantitative indicators are used as important input variables for the strength prediction model. The aim is to establish a quantitative correlation between microstructure and macroscopic performance from the source of materials design, making the prediction model more scientific and mechanistic.

[0024] Another important objective is to achieve a complementary and deep integration of the advantages of physical mechanisms and data-driven approaches. On the one hand, close-packing theory provides the physical basis for UHPC to achieve high strength. The model learning process is indirectly constrained by this physical principle, which helps its learning path to better conform to the laws of materials science and may reduce its dependence on massive amounts of data. On the other hand, by learning the complex mapping relationship between UHPC strength and mix proportion under given close-packing conditions through machine learning algorithms, this integration aims to simultaneously improve the model's prediction accuracy and generalization ability.

[0025] Example 1 A method for predicting the strength of ultra-high performance concrete considering the effect of close particle packing is shown in the flowchart below. Figure 1 As shown, it includes the following steps: S1, Obtain the dataset to be tested, which includes the macroscopic proportions and particle size distribution of materials; S2, Based on the particle size distribution of solid particulate materials in the dataset, calculate the cumulative volume percentage of particles smaller than the preset particle size using the modified Andreasen-Andersen model; S3, calculate the packing density based on the cumulative volume percentage of particles smaller than the preset particle size; S4. Input the packing density and the dataset to be tested into the prediction model to obtain the predicted value of the compressive strength of ultra-high performance concrete.

[0026] In step S1, particle size distribution, also known as particle size distribution, refers to the proportion of particles of different sizes in powdered or granular materials (such as sand, soil, crushed stone, cement, etc.). It refers to the particle size distribution of the entire particle group. Particle size distribution is a key factor determining the engineering properties of granular materials (such as strength, density, permeability, workability, etc.). A good gradation means that the material has superior performance. The macroscopic proportion of materials, usually referred to as "mix ratio" or "mixture design" in engineering, refers to the proportional relationship between various constituent materials (such as cementitious materials, water, aggregates, admixtures, etc.) in concrete, mortar, asphalt mixtures, refractory materials, etc., determined to achieve predetermined technical performance and economic indicators. This proportion is usually expressed in units of mass or volume, and is based on one of the materials (usually cementitious materials or aggregates), expressed as a series of ratios. If "particle size distribution" focuses on the distribution of particles of different sizes within the same material, then "macroscopic proportion of materials" focuses on the mixing ratio relationship between multiple different component materials.

[0027] The relationship between macroscopic mix proportions and particle size distribution is complementary and inseparable. 1) Particle size distribution is the foundation of macroscopic mix proportion design. When designing concrete mix proportions, the particle size distribution of the sand and gravel used must first be known. Well-graded aggregates have low porosity, requiring less cement paste to fill voids and coat particles, thus allowing for a more economical and higher-performance mix design. If the aggregate gradation is poor, even if the macroscopic cement, sand, and gravel ratio is correct, the high porosity and unreasonable specific surface area of ​​the aggregates may lead to poor concrete workability, low strength, or lack of compaction. 2) Macroscopic mix proportions are the way to realize the advantages of particle size distribution. Good aggregate gradation itself only provides the possibility of preparing high-quality concrete. However, by determining the correct cement dosage and water-cement ratio through macroscopic mix proportions, an appropriate amount of cement paste can be used to fully fill and lubricate these well-graded aggregates, transforming the potential of aggregate gradation into real high-performance concrete. Simply put, each raw material (especially aggregates) is first optimized through "particle size distribution," and then these optimized raw materials are mixed together in the best proportion through "macro proportioning" to obtain the final ideal engineering material.

[0028] Based on the above considerations, the macroscopic proportions and particle size distribution of materials are used as datasets for model training and testing in this invention.

[0029] Preferably, in this embodiment, packing density is also taken into consideration. The cumulative volume percentage (CPFT) of particles smaller than a preset particle size is obtained through step S2 for calculating packing density. Step S2 includes the following steps: S21, Determine the particle size distribution index in the dataset based on the performance requirements of concrete; S22, determine the minimum particle size and the maximum particle size from the existing particles; S23, obtain the particle size distribution of the solid particulate material, and determine the corresponding cumulative volume percentage of particles smaller than the preset particle size based on the modified Andreasen-Andersen model.

[0030] Preferably, in step S21, the concrete properties are classified into self-compacting concrete, conventional pumped and vibratory compacted concrete, and dry-hard concrete, with corresponding particle size distribution indices of 0.21~0.29, 0.3~0.34, and 0.35~0.4, respectively.

[0031] Preferably, in step S23, the modified Andreasen-Andersen model is: ; in, Maximum particle size; Minimum particle size; D represents the particle size; CPFT represents the cumulative percentage of particles smaller than the preset size (cumulative sieve residue), and the superscript q refers to different particle size distribution indices.

[0032] Preferably, the calculation of packing density is performed through step S3, which includes the following steps: S31, the cumulative volume percentage of particles smaller than the preset particle size in each particle size range is taken as the theoretical passing percentage of that range, and the particle size range is divided. S32, based on the theoretical percentage and the actual percentage of particle size passing through, calculate the packing density for each particle size range, and sum the packing density of each particle size range to obtain the residual index. RSS The residual index RSS This refers to the packing density across the entire particle size range.

[0033] Preferably, in step S32, the formula for calculating the packing density is: ; Among them, F 实际 (Di) is the actual percentage of particles passing through with diameter Di; F 理论 (Di) is the theoretical passing percentage; m is the number of particle size ranges, which are determined by testing based on the raw materials (sand, stone, powder, etc.) on site. It is a residual index representing the packing density (i.e., the difference between the theoretical and actual dense packing curves). RSS The curve is as follows: Figure 2 As shown in the figure, the solid line is F. 理论 (Di), The dotted line in the diagram is F. 实际 (Di), RSS It is F理论 With F 实际 The sum of the squares of the differences.

[0034] Preferably, the prediction model can be constructed using the Catboost algorithm to build the strength prediction model. CatBoost can be either a standalone model or a base learner in a hybrid machine learning prediction model, both of which can be used for predicting the compressive strength of ultra-high performance concrete.

[0035] Preferably, the prediction model can also employ a hybrid machine learning prediction model, including a base learner layer and a meta-learner layer; The base learner layer is used to input the packing density and the dataset to be tested, and outputs the first layer prediction result to the meta learner layer. The meta learner layer outputs the predicted value of the compressive strength of ultra-high performance concrete.

[0036] The base learner layer can be selected from Catboost, XGBoost, LightGBM, Random Forest, Gradient Boosting Decision Tree, and Support Vector Machine; the meta-learner layer uses linear regression and ridge regression models.

[0037] The 5x cross-validation method used in this embodiment is employed to train and evaluate each primary learner (or base learner in the base learner layer) that constitutes the hybrid machine learning prediction model. A schematic diagram of the 5x cross-validation process for a single primary learner is shown below. Figure 3 As shown, this method randomly but uniformly divides the original training dataset into five non-overlapping subsets. Then, five independent training and validation cycles are performed: in each cycle, four subsets are used sequentially as the training set to train the model, and the remaining subset is used as the validation set to evaluate the model's performance. Finally, by averaging these five validation results, a robust and unbiased evaluation of the performance of the primary learner is obtained.

[0038] Preferably, the hyperparameters in the hybrid machine learning prediction model are tuned using a Bayesian optimization algorithm. Key hyperparameters in the hybrid model (such as the learning rate of XGBoost, the maximum depth of the trees, etc.) are automatically tuned using a Bayesian optimization algorithm. During training, a relatively loose maximum number of iterations (e.g., 100-200 times) is set as a "safety valve." Within this range, once the model performance (e.g., R² on the validation set) is optimized, the model is ready to be tested. 2 An optimization method is considered to have successfully converged and terminated early if the performance (≥0.97, RMSE≤3, MAPE≤3) is better than a preset absolute threshold. This method prioritizes achieving the required absolute performance, avoiding unnecessary searches once the performance meets the application requirements, and directly improving optimization efficiency. This is more practically valuable in engineering than simply relying on the number of iterations.

[0039] The formula for calculating RMSE (Root Mean Square Error) is: ; in, It is the true value of the i-th data point. is the predicted value of the i-th data point, n is the total number of samples, i is the index of the sample, and represents the i-th data point.

[0040] The formula for calculating MAPE (Mean Absolute Percentage Error) is: ; in, It is the true value of the i-th data point. is the predicted value of the i-th data point, n is the total number of samples, i is the index of the sample, representing the i-th data point, | | is the absolute value symbol.

[0041] R 2 The formula for calculating the (determination coefficient) is: ; in, It is the true value of the i-th data point. is the predicted value of the i-th data point, n is the total number of samples, i is the index of the sample, and represents the i-th data point.

[0042] Preferably, the steps further include: calculating the SHAP value of each input feature, using the SHAP value to perform interpretability analysis on the hybrid machine learning prediction model, and identifying the factors that contribute the most to the compressive strength of ultra-high performance concrete.

[0043] Example 2 Example 2 is a specific theoretical implementation of the scheme in Example 1, and the training process and the actual measurement process are explained simultaneously. This example describes a method for predicting the strength of ultra-high performance concrete (UHPC) considering the effect of dense particle packing. By quantifying the microstructural characteristics of UHPC and combining it with a hybrid machine learning model, it achieves high-precision and interpretable prediction of the compressive strength of UHPC. The main steps include: (1) establishing a basic dataset and preprocessing; (2) calculating the packing density parameters using a modified Andreasen-Andersen model; (3) constructing a hybrid machine learning prediction model; and (4) hyperparameter tuning based on Bayesian optimization. The specific steps are as follows: (1) Establishing the basic dataset and preprocessing.

[0044] Data Collection: An UHPC strength prediction dataset was established by collecting experimental data from publicly published literature both domestically and internationally. Input parameters should comprehensively cover the macroscopic proportions of materials (e.g., the amounts of cement, silica fume, fly ash, mineral powder, coarse aggregate, fine aggregate, steel fiber, synthetic fiber, water, water-reducing agent, etc., in kg / m³) and particle size distribution (e.g., cement, silica fume, fly ash, mineral powder, coarse aggregate, fine aggregate). Simultaneously, the particle size distribution was combined with the proportions using a modified Andreasen-Andersen model to calculate the particle packing density parameters (see step 2 for details).

[0045] Data preprocessing: The dataset is cleaned (outliers are removed) and normalized to eliminate the influence of unit dimensions. Then, the dataset is divided into training and testing sets.

[0046] (2) The packing density parameters were calculated using the modified Andreasen-Andersen model. First, determine the modified Andreasen-Andersen model parameters: (1) in, Maximum particle size; Minimum particle size; D represents the particle size; CPFT represents the cumulative volume percentage of particles smaller than the preset size; q is the particle size distribution index, which is typically between 0.2 and 0.4. A larger q value indicates a higher proportion of relatively coarse particles, resulting in lower workability of the mixture. The distribution coefficient q is usually an empirical coefficient. Based on previous research, it is recommended that q = 0.21–0.29 for self-compacting concrete; q = 0.3–0.34 for conventional pumped and vibratory compacted concrete; and q = 0.35–0.4 for dry-hard concrete.

[0047] Secondly, the packing density is calculated. For each UHPC mix proportion, based on the particle size of its raw materials, the residual index between the theoretical and actual close-packed curves is calculated using the modified Andreasen-Andersen model. RSS , namely packing density, is used as an input parameter for the intensity prediction model.

[0048]

[0049] F 实际 ( D i Particle size D i The actual pass rate; F 理论 (D i Theoretical pass rate: The theoretical pass rate is the cumulative volume percentage of particles smaller than the preset particle size. m Number of particle size ranges.

[0050] (3) Constructing a hybrid machine learning prediction model Model Selection: The Stacking ensemble learning framework was adopted, as its predictive performance outperforms that of a single model. A schematic diagram of the network structure of the hybrid machine learning prediction model based on Stacking ensemble learning is shown below. Figure 4 As shown, the framework consists of two layers: Base learner layer: Catboost model, XGBoost model, LightGBM model, random forest model, gradient boosting decision tree, and support vector machine are selected. Training method: k-fold cross-validation is used to train the base learner to reduce the risk of overfitting and make full use of the data. Meta learner layer: The prediction results of the base learner are used as new feature inputs. The linear regression (LR) model is usually used for secondary fusion as the second layer model. Ridge regression model can also be used. (4) Hyperparameter tuning based on Bayesian optimization Bayesian optimization algorithms are used to automatically tune key hyperparameters in the mixture model, such as the learning rate of XGBoost and the maximum depth of the tree. Bayesian optimization balances "exploration" and "development" through Gaussian process modeling and acquisition functions, improving efficiency compared to traditional methods such as grid search and finding better parameter combinations.

[0051] (5) Intensity prediction and model validation The macroscopic proportions, particle size distribution, and residual indices of the UHPC to be predicted will be used. RSS The predicted compressive strength can be obtained by inputting the data into the trained model. The model performance is evaluated on the test set using metrics such as root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²).

[0052] (6) SHAP-based interpretability analysis The Shapley Additive Explanations (SHAP) values ​​were used to analyze the interpretability of the model. By calculating the SHAP value of each input feature, the importance of the feature can be quantified: it can be clarified which factors (such as steel fiber content, age, particle packing density parameters, etc.) contribute the most to the strength prediction. At the same time, it can reveal the direction of influence: determine whether the relationship between the feature and the strength is positive or negative, and make the model decision-making process transparent.

[0053] (7) Iterative optimization and application of the model Judgment and Iteration: If the model's accuracy on the test set (e.g., R) is...2 If the value does not reach the preset threshold, return to steps 1 to 4 and perform iterative optimization by expanding data sources, optimizing feature engineering, or optimizing hyperparameters.

[0054] Final Application: Once the model's accuracy meets the requirements, it can be used for actual UHPC mix design and strength prediction. By inputting the designed material mix proportions into the model, predicted strength values ​​can be obtained quickly, thereby reducing experimental trial-and-error costs and accelerating the materials research and development process.

[0055] A method for predicting the strength of ultra-high performance concrete that integrates the theory of dense packing and artificial intelligence algorithms is proposed. The main features are reflected in steps 1 to 6. By breaking through the limitations of macroscopic parameters, the particle packing density parameter is introduced as a quantitative index of microstructure. On this basis, physical mechanisms and data-driven approaches are integrated, and machine learning algorithms are used to improve the accuracy and generalization ability of the model.

[0056] Example 3 This embodiment uses specific data to verify the methods of Embodiments 1 and 2. This includes the construction of the dataset, comparison and analysis of model training results, and the specific steps are as follows: (1) Dataset Using ultra-high performance concrete data, the dataset comprises 46×16 sets of data. The first 15 columns represent the following per cubic meter of concrete: cement (Cement), silica fume (SF), blast furnace slag powder (BFS), stone powder (LP), quartz powder (QP), microbeads, expansion agent, steel fiber, water, fine aggregate (sand), coarse aggregate (stone), superplasticizer, water-cement ratio (W / B), and residual indices. RSS (The bulk density parameters were calculated using a modified Andreasen-Andersen model) and the mortar ratio B / S. Column 16 represents the concrete compressive strength. Information such as the name, total, maximum, minimum, mean, and standard deviation of each data set is provided. Figure 5 The dataset statistics table is shown in the image. To gain a more comprehensive understanding of the data distribution, a histogram of the statistical distribution of each group of data was drawn, as shown below. Figure 6 As shown.

[0057] (2) Model training results After data preprocessing, model training, and hyperparameter optimization, the following parameters were selected: cement (Cement), silica fume (SF), blast furnace slag powder (BFS), stone powder (LP), quartz powder (QP), microbeads, expansion agent, steel fiber, water, fine aggregate (sand), coarse aggregate (stone), superplasticizer, water-cement ratio (W / B), and residual indices. RSS Using the binder-sand ratio (B / S) as the input parameter for model training, and dividing the training and test sets into 90% and 10% respectively, an intensity prediction model based on the Catboost algorithm was established. The input parameters included residual indices. RSS The Catboost prediction results are as follows Figure 7 As shown, there is no residual index in the input parameters. RSS The Catboost prediction results are as follows Figure 8 As shown.

[0058] In summary, residual index RSS As an input variable, it can effectively improve the fitting accuracy and generalization ability of the CatBoost model and reduce the risk of overfitting, playing a key role in the performance optimization of concrete strength prediction models.

[0059] This invention provides a method for predicting the strength of ultra-high performance concrete that integrates close-packing theory and artificial intelligence algorithms. It effectively overcomes the limitations of traditional methods that rely solely on macroscopic mix proportions, enabling the model to more accurately capture the intrinsic physical laws governing the relationship between the material's internal structure and strength. By introducing microscopic structural quantification indicators such as particle size distribution and packing density parameters as model inputs, the prediction accuracy and reliability are significantly improved. The introduction of close-packing theory provides physical constraints for the AI ​​model, reducing its over-reliance on data volume when facing fluctuations in raw materials or new admixtures. Instead, it makes inferences based on the fundamental principles of particle packing. The core algorithm architecture utilizes a Stacking ensemble learning model, combined with Bayesian optimization and other techniques to optimize hyperparameters, thereby significantly improving the model's generalization ability. Simultaneously, interpretable techniques such as SHAP can clearly quantify the contribution of each input variable (including close-packing parameters) to the prediction results. This transforms the model's decision-making process from a "black box" to "transparent," providing clear scientific guidance for concrete mix design.

[0060] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements 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 strength of ultra-high performance concrete considering the effect of dense particle packing, characterized in that, Includes the following steps: S1, Obtain the dataset to be tested, which includes macroscopic proportioned materials and material particle size distribution; S2, Based on the particle size distribution of solid particulate materials in the dataset, calculate the cumulative volume percentage of particles smaller than the preset particle size using the modified Andreasen-Andersen model; S3, calculate the packing density based on the cumulative volume percentage of particles smaller than the preset particle size; S4. Input the packing density and the dataset to be tested into the prediction model to obtain the predicted value of the compressive strength of ultra-high performance concrete.

2. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 1, characterized in that, S2 includes the following steps: S21, Determine the particle size distribution index in the dataset based on the performance requirements of concrete; S22, determine the minimum particle size and the maximum particle size from the existing particles; S23, obtain the particle size distribution of the solid particulate material, and determine the corresponding cumulative volume percentage of particles smaller than the preset particle size based on the modified Andreasen-Andersen model.

3. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 2, characterized in that, In step S21, the properties of concrete are divided into self-compacting concrete, conventional pumped and vibratory compacted concrete, and dry-hard concrete, with corresponding particle size distribution indices of 0.21~0.29, 0.3~0.34, and 0.35~0.4, respectively.

4. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 2, characterized in that, In step S23, the modified Andreasen-Andersen model is as follows: ； in, Maximum particle size; Minimum particle size; The particle size is denoted as q; CPFT is the cumulative percentage of particles smaller than the preset particle size, and the superscript q indicates the particle size distribution index.

5. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 2, characterized in that, Step S3 includes the following steps: S31, the cumulative volume percentage of particles smaller than the preset particle size in each particle size range is taken as the theoretical passing percentage of that range, and the particle size range is divided. S32, based on the theoretical percentage and the actual percentage of particle size passing through, calculate the packing density for each particle size range, and sum the packing density of each particle size range to obtain the residual index. RSS The residual index RSS This refers to the packing density across the entire particle size range.

6. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 5, characterized in that, In step S32, the formula for calculating the packing density is: ； Among them, F 实际 (Di) is the actual percentage of particles passing through with diameter Di; F 理论 (Di) is the theoretical pass rate; m is the number of particle size intervals, and i is the number of the particle size intervals.

7. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in any one of claims 1-6, characterized in that, The prediction model employs a hybrid machine learning prediction model, including a base learner layer and a meta-learner layer; The base learner layer is used to input the packing density and the dataset to be tested, and outputs the first layer prediction result to the meta learner layer. The meta learner layer outputs the predicted value of the compressive strength of ultra-high performance concrete.

8. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 7, characterized in that, The base learner layer can be selected from Catboost, XGBoost, LightGBM, Random Forest, Gradient Boosting Decision Tree, and Support Vector Machine; the meta-learner layer uses linear regression and ridge regression models.

9. The method for predicting the strength of ultra-high performance concrete considering the close packing effect of particles as described in claim 8, characterized in that, The steps also include: calculating the SHAP value of each input feature, using the SHAP value to perform interpretability analysis on the prediction model, and identifying the factors that contribute the most to the compressive strength of ultra-high performance concrete.

10. The method for predicting the strength of ultra-high performance concrete considering the particle compaction effect as described in any one of claims 1-6, characterized in that, The prediction model is constructed using the Catboost algorithm.

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