Ultra-high performance concrete proportion design method based on intelligent algorithm and function requirements

Abstract

The invention provides an ultra-high performance concrete proportion design method based on an intelligent algorithm and functional requirements. The method comprises the following steps: S1, constructing an ultra-high performance concrete performance prediction database; s2, automatically selecting key variables based on function requirements; s3, training and predicting a machine learning model based on function requirements; and S4, optimal design of the ratio of the ultra-high performance concrete. According to the unsupervised anomaly detection method based on the isolation forest, the database is preprocessed, and the ultra-high performance concrete proportion design key variables are selected through the automatic variable selection method, so that rapid mapping from the mixing amount of each component of the ultra-high performance concrete to each function demand index is realized; through the particle swarm optimization (PSO), the ultra-high performance concrete with specific function requirements is subjected to proportioning design, and finally the ultra-high performance concrete proportioning value closest to the function requirement index is obtained, so that the problems of time and labor consumption, low efficiency and resource waste are solved.

Description

Technical Field

[0001] The present invention provides an ultra-high performance concrete mix ratio design method based on an intelligent algorithm and functional requirements, and belongs to the technical field of cement preparation. Background Art

[0002] Ultra-high performance concrete (UHPC) is a revolutionary new cement-based composite material with exceptional mechanical and durability properties, possessing enormous potential and value in engineering construction. UHPC mix design is based on the theory of closest packing. This particle-based close packing model is based on the theoretical packing model of particles in a dry state. However, concrete particles pack in a wet state (with the addition of water and a water-reducing agent). This is accompanied by hydration, particle agglomeration, and water film wrapping, which negates the prerequisites for the closest packing of particles in a wet state. Furthermore, this model is only applicable to optimizing solid particle packing and fails to consider the disruption and damage to the packing system caused by the addition of fibers. Consequently, the particle packing theory lacks scientific guidance in UHPC mix design, resulting in a "usable" mix rather than an optimal one. In addition, ultra-high performance concrete configuration technology also involves the chemistry of cement and various mineral admixtures, the chemistry of water reducers and other admixtures, and their interactions and compatibility with concrete raw materials. Moreover, the types, chemical or mineral compositions of cement, mineral admixtures, admixtures, etc. are diverse. At present, it is impossible to quantify the development and process of the entire ultra-high performance concrete chemical system, and it still needs to be formulated based on experimental data. This kind of experimental work is large in workload and time-consuming, and can no longer fully meet its design, production and application requirements. Therefore, building a scientific and intelligent new technology system for ultra-high performance concrete configuration is both an urgent task and the only way for the innovation and development of concrete materials.

[0003] The material properties of ultra-high performance concrete are mainly manifested in ultra-high strength and excellent durability. Due to its excellent mechanical properties, it has shown great application potential in specific fields. In addition to the compressive strength requirements, corresponding special functional requirements, such as ultra-high flexural strength, ultra-high material fracture energy and other toughness functions, maintenance-free long-term durability, resistance to nuclear radiation, ultra-large fluidity, ultra-short or ultra-long initial setting time, minimum carbon emissions, optimal price, etc. Some of the listed functional requirements of ultra-high performance concrete have far exceeded the scope of application of traditional mix design methods. Relying on experiments to screen component materials and optimize mix proportions, the number of experiments required will increase exponentially with the increase in variables (combination of factors and levels). A large number of experiments means spending a lot of time and resources, including manpower and funds.

[0004] Announcement No. CN118506903A discloses a method for designing the mix ratio of concrete production. Based on empirical values and the mass method, the concrete mix ratio is calculated through six steps. This method is only an improvement on the traditional mix ratio design method and does not get rid of the multiple assumptions of the traditional mix ratio design method. In addition, its actual implementation is still very complicated.

[0005] Publication No. CN117577241A describes a machine learning-based method for predicting the compressive strength of magnesium phosphate cement-based composites. This method develops five machine learning models and accurately predicts the cubic compressive strength of magnesium phosphate cement-based materials using 18 input parameters, including component proportions, raw material type, and specimen size. While this method uses machine learning algorithms to determine the strength of materials at specific mix ratios, it cannot map specific properties to mix ratios, and cannot quickly determine the concrete mix ratio for a given functional requirement.

[0006] Announcement No. CN101609515A is an artificial intelligence-based concrete mix design method that uses artificial neural network methods and genetic algorithms to design and optimize concrete mix proportions. It only designs the mix proportions for ordinary concrete with fewer components and single functions.

[0007] Publication No. CN115964954A describes a method for optimizing the mix design of ultra-high performance concrete (UHPC). This method uses machine learning to predict the performance of multiple random mixes. It also establishes a comprehensive UHPC performance evaluation model using the Analytic Hierarchy Process (AHP). This method compares multiple random mixes and determines the optimal mix, taking into account metrics such as cost per unit volume and carbon emissions per unit volume. While this method can select a set of mixes with the highest AHP scores from 50,000 mix combinations, it cannot generate an optimal mix that meets user-specified functional requirements. Instead, it prioritizes the optimal mix based on cost and carbon emissions.

[0008] The above prior art has the following technical problems:

[0009] (1) The applicability of existing models is limited. Each model is applicable to a limited number of variables. For example, CN115964954A only uses silica fume, fly ash, mineral powder, fine bone content, coarse bone content, water-binder ratio, steel fiber content, and water-reducing agent content.

[0010] (2) The existing data on ultra-high performance concrete mix proportions are limited. Such a small data set has low generalization performance, resulting in overfitting and affecting prediction accuracy.

[0011] (3) The datasets used to train machine learning models have outliers, which reduces prediction accuracy, but it is unclear how to identify and remove outliers.

[0012] (4) Given the target concrete properties, it is unclear which mixture design variables should be selected as input variables. Including unnecessary variables will reduce the accuracy and efficiency of the prediction.

[0013] (5) How to effectively optimize the hyperparameters of machine learning models remains unclear.

[0014] The aforementioned challenges have significantly hindered the wider acceptance of data-driven approaches in the development and application of UHPC. Summary of the Invention

[0015] Ultra-high performance concrete Ultra-high performance concrete is a mixture of multiple components, resulting in a highly complex material with a large number of possible combinations, relative proportions and properties. The relationship between the functional properties of ultra-high performance concrete and its mixture components is highly nonlinear, especially after the addition of supplementary cementitious materials (materials required for special functions). The addition of supplementary cementitious materials has a greater impact on the evaluation of ultra-high performance concrete performance, which makes the behavior of ultra-high performance concrete more difficult to predict.

[0016] The present invention provides an ultra-high performance concrete (UHPC) mix design method based on intelligent algorithms and functional requirements. It proposes an unsupervised anomaly detection method based on isolation forests to preprocess the database, and an automatic variable selection method to select key variables for UHPC mix design. This effectively addresses the time-consuming, labor-intensive, inefficient, and resource-wasting problem of traditional testing methods for UHPC performance. By establishing a machine learning model with excellent predictive capabilities, it accurately predicts the functional indicators of UHPC. Using a particle swarm optimization (PSO) algorithm, it conducts a global search for UHPC mix combinations with specific functional requirements, ultimately obtaining a set of UHPC mixes that best match the given functional requirements.

[0017] This invention aims to address the challenges of extensive and time-consuming testing during the mix design process for ultra-high performance concrete (UHPCC), as well as the inability of traditional mix design methods to fully consider the impact of each of UHPCC's fundamental raw material parameters on specific functional requirements. Building on the fundamental strength of UHPCC, this invention addresses specific functional requirements such as radiation resistance, toughening, carbon emission reduction, reduced silica fume usage, early strength, slow setting, and radar wave resistance and stealth, by incorporating machine learning and intelligent optimization algorithms.

[0018] The present invention addresses the mix design problem of ultra-high performance concrete (UHPC) and provides an ultra-high performance concrete (UHPC) mix design method based on an intelligent algorithm and functional requirements. The method preprocesses a database based on an unsupervised anomaly detection method of an isolation forest and selects key variables for ultra-high performance concrete mix design using an automatic variable selection method, thereby achieving rapid mapping of the dosage of each component of ultra-high performance concrete to each functional requirement indicator. Based on a trained machine learning model, the particle swarm optimization (PSO) algorithm is used to design the mix of ultra-high performance concrete with specific functional requirements, ultimately obtaining the ultra-high performance concrete mix value that is closest to the functional requirement indicator. This method can effectively solve the problem of using traditional test methods to measure the performance of ultra-high performance concrete, which is time-consuming, labor-intensive, inefficient, and wastes resources.

[0019] The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements includes the following steps:

[0020] S1. Construction of ultra-high performance concrete performance prediction database;

[0021] By extracting structured and unstructured data, and using automatic anomaly detection methods to improve the dataset by eliminating or mitigating anomalies, a database of ultra-high performance concrete component materials X (basic raw materials and their specific functional materials) and the corresponding ultra-high performance concrete performance indicator data Y for each component material is constructed. The unsupervised isolation forest method is then used to improve the dataset to identify and remove anomalies.

[0022] S2, automatic selection of key variables based on functional requirements;

[0023] The univariate linear regression method and the automatic variable selection method of F statistics are used to identify key design variables (i.e., functional correlation component materials), so as to select key material variables Xi according to the functional requirements of ultra-high performance concrete to improve the prediction accuracy of the machine learning model.

[0024] S3, machine learning model training and prediction based on functional requirements;

[0025] Hyperparameter adjustment was performed using a selected machine learning method of grid search and cross-validation, and the resulting machine learning model was able to predict and output the corresponding ultra-high performance concrete performance indicators by inputting the relevant parameters of the ultra-high performance concrete component materials.

[0026] S4. Optimization design of ultra-high performance concrete mix ratio

[0027] Based on the trained machine learning model, an intelligent optimization algorithm is used to establish an ultra-high performance concrete mix ratio optimization model. According to the functional demand indicators specified by the user, the mix ratio that meets the requirements is output, and the output mix ratio is verified using experimental methods.

[0028] Specific S1 includes:

[0029] S1.1. Data collection

[0030] Collect structured (e.g., tabular data) and unstructured (e.g., graphical) data on ultra-high performance concrete basic raw materials, specific functional materials, and related performance indicators from authoritative literature, authoritative testing institutions and laboratories, and the Internet (testing is required after verification). The data includes:

[0031] (1) Material types include: a) basic raw materials: cement, quartz sand, quartz powder, silica fume, fly ash, water, water reducer; b) mineral admixtures (ground slag powder, metakaolin, steel slag powder, industrial waste slag powder, tailings powder, boron carbide, rubber, ceramics, barite, graphite, zeolite powder, perlite, etc.); c) chemical admixtures (various chemical admixtures corresponding to retarding setting, accelerating setting, early strength, air entraining, defoaming, expansion, water reduction, antifreeze, etc.); d) various fibers (steel fiber, basalt fiber, glass fiber, polyacrylonitrile fiber, etc. various synthetic fibers).

[0032] (2) Material parameters include: mechanical properties / performance indicators / grade, density, surface characteristics (including equivalent particle size), price, etc.

[0033] The above data form a database as shown in Table 1, which contains K L pieces of data, k i Indicates a piece of collected ratio data. k i Each material in X i Use 4 columns of parameters to mark, such as cement is marked with X1, and its mechanical properties / performance indicators / grade, density, apparent characteristics (including equivalent particle size), price and other 4 parameters are marked with X i1 、X i2 、X i3 and X i4 Mark, a total of X n Materials; Y1-Y m It is the performance index of ultra-high performance concrete, including compressive strength, flexural strength, tensile strength, radiation performance, initial setting time, and impermeability grade.

[0034] Table 1 Database of ultra-high performance concrete materials and performance parameters

[0035] <![CDATA[X 11 ]]> <![CDATA[X 12 ]]> <![CDATA[X 13 ]]> <![CDATA[X 14 ]]> … <![CDATA[X i1 ]]> <![CDATA[X i2 ]]> <![CDATA[X i3 ]]> <![CDATA[X i4 ]]> … <![CDATA[X n1 ]]> <![CDATA[X n2 ]]> <![CDATA[X n3 ]]> <![CDATA[X n4 ]]> <![CDATA[Y1]]> … <![CDATA[Y j ]]> … <![CDATA[Y m ]]> <![CDATA[K1]]> <![CDATA[K2]]> … <![CDATA[K t ]]> … <![CDATA[K L ]]>

[0036] S1.2. Data Preprocessing

[0037] The collected data has abnormal data due to different reasons, such as data entry errors, instrument errors, and data processing errors. These abnormal data will reduce the prediction accuracy of the machine learning model. For this reason, the unsupervised method of isolation forest is used to improve the dataset to identify and remove abnormal data:

[0038] (1) Construct a decision tree based on the database, namely the isolation tree.

[0039] (2) Each data is evaluated according to the isolation tree and an anomaly score is assigned to describe the degree of abnormality of the data.

[0040] If the anomaly score of a data instance is greater than a certain value, the data instance is considered an anomaly. The percentage of anomaly data in the database is defined as the contamination rate of the dataset.

[0041] S2. The specific method of automatic variable selection is:

[0042] Since ultra-high performance concrete has many requirements, each function involves the variable X i The number of parameters is large, so it is crucial to select variables appropriately according to functional requirements for training the prediction model. By excluding unnecessary variables, the model complexity and training time can be reduced, which helps to avoid overfitting and improve prediction accuracy. The univariate linear regression method is used to evaluate the variable X. i and ultra-high performance concrete properties Y i The correlation between:

[0043]

[0044] In formula (1): C(X i , Y i ) represents the correlation coefficient, and Represents X i A certain performance index value and Y j The average value of a characteristic value, std(X i ) and std(Y i ) represent X i A parameter value and Y j The standard deviation of .

[0045] Based on the correlation coefficient, F statistics is used to test the degree of association between multiple variables, namely:

[0046]

[0047] In formula (2): F(X i , Y i ) represents X i and Yi The larger the F statistic, the higher the value. i and Y i The high correlation between them, n represents the number of statistics.

[0048] By calculating the F statistic for each material variable, the key material variable X is selected. i To improve the prediction accuracy of machine learning models.

[0049] S3 model training and prediction specifically include:

[0050] S3.1. Hyperparameter Tuning and Evaluating Predictive Models

[0051] The goal of hyperparameter tuning is to improve model performance, avoid overfitting, and enhance the model's generalization capabilities. Because ultra-high performance concrete (UHPC) has numerous functions and involves numerous materials and parameters, hyperparameter tuning employs grid search and cross-validation (to accurately assess the effectiveness of hyperparameter configurations) to improve the model's generalization capabilities. The goal is to find the optimal hyperparameter combination that yields the strongest predictive capability for the random forest model trained using this set of hyperparameters.

[0052] (1) Grid search is to traverse all possible combinations of the specified parameter range to find the optimal hyperparameters, such as the number of decision trees, the maximum depth of the decision tree, the number of leaf nodes, and other hyperparameters;

[0053] (2) After generating multiple hyperparameter combinations using the grid search method, the optimal set of parameters is selected using the cross-validation method. That is, the dataset is divided into K subsets (or "folds"), and one of the subsets is selected as the test set each time, while the remaining subsets are used as the training set. This process is repeated K times, with a different subset selected as the test set each time, ensuring that each subset is used as the test set once. Finally, the performance index of the results of the K tests is averaged as the performance index value of this set of hyperparameters. Each set of hyperparameters undergoes the above cross-validation process to obtain a performance index value.

[0054] Taking 5-fold cross validation as an example, one of the subsets is selected as the test set each time, and the remaining 4 subsets are used as training sets. The model is trained and evaluated, and the model performance index is R 2 This process is repeated 5 times, and the average R of the 5 tests is taken. 2 The R value is used as the performance evaluation of the model. 2 value, select R 2 The highest set of hyperparameters (i.e., the optimal set of hyperparameters) is used for subsequent model training.

[0055]

[0056] Yj is the true value of the functional indicator in the database, is the functional index value predicted by the machine learning model, is the mean of the predicted values and N is the number of data.

[0057] S3.2. Random Forest Model Training

[0058] The primary purpose of model training is to enable the algorithm to learn data patterns, improve prediction accuracy, and adapt to new situations. Given the diverse functions of ultra-high performance concrete (UHPC), the wide variety of materials and their properties involved, and the nonlinear relationship between materials and functions, a random forest model is used to train and predict samples. This establishes a mapping between UHPC's basic raw material parameters (X) and UHPC's performance indicators (Y). A random forest is an ensemble learning model based on a bagging strategy that effectively handles nonlinear problems and excels at processing large numbers of samples and features. The training process is as follows:

[0059] (1) Initialize the model. The database shown in Table 1 is divided into a training set and a test set in a ratio of 7:3. The main function of the training set is to allow the machine learning model to learn the characteristics and patterns of the data, so that the model can continuously adjust its internal parameters to better fit the data. The function of the test set is to evaluate the performance of the model on unseen data, thereby simulating the performance of the model in actual applications.

[0060] (2) Training. Use the optimal set of hyperparameters obtained in “Hyperparameter Tuning and Prediction Model Evaluation” to set the structure of the random forest model (i.e., set the number of decision trees, the number of leaf nodes, and other parameters in the random forest model to build the random forest model framework). Input the training set into the model for training. After multiple iterations, the UHPCC performance index prediction model is finally obtained. This establishes the mapping relationship between the UHPCC basic raw material parameter X and the UHPCC performance index y.

[0061] (3) Testing. Input the feature matrix X of the test set into the trained UHPCC performance index prediction model, and obtain the corresponding UHPCC performance index prediction value through model calculation. (The predicted performance index of ultra-high performance concrete is a column vector, that is, compressive strength = xxx, flexural strength = xxx, ..., wave absorption capacity = xxx), the true value of the ultra-high performance concrete performance index of the test set Y j and the predicted values of the machine learning model Bring in R 2 Calculate in the formula to get the R predicted by the model on the test set 2 Value. 2The value range is between 0 and 1. The closer the value is to 1, the better the prediction performance of the model. 2 Close to 0, it means that the model has almost no ability to predict actual data; if R 2 A negative number indicates that the model's prediction performance is worse than the simple average. If the model's prediction performance is poor, you need to retrain the model and test it again until the model has stronger prediction ability.

[0062] S4. Ultra-high performance concrete mix design

[0063] Based on the prediction of ultra-high performance concrete performance (the ultra-high performance concrete performance prediction model has been obtained, that is, the mapping relationship between the basic raw material parameters X of ultra-high performance concrete and the performance index Y of ultra-high performance concrete has been established), the parameters of the raw materials in the ultra-high performance concrete mix are optimized and adjusted through the intelligent optimization algorithm to provide an optimal mix ratio that can meet the target performance requirements. The ultra-high performance concrete mix ratio optimization model needs to set the objective function, constraints and optimization algorithm parameters according to the actual situation of the optimization task, namely:

[0064] (1) Objective function. The purpose of the present invention for the design of the ultra-high performance concrete mix ratio is to meet the functional requirements while expecting the optimal cost. Therefore, the objective function consists of two parts: the performance index of the ultra-high performance concrete and the price. The objective function is specifically expressed as follows:

[0065]

[0066] The first part of the formula is the performance index of ultra-high performance concrete, Y tar It is the target value of the performance index corresponding to the functional requirements of ultra-high performance concrete. is the predicted value of the UHPCC performance index, which is obtained by inputting a set of material parameters X of the UHPCC matrix into the machine learning model. i The predicted price is P, which is the price of ultra-high performance concrete. It can be calculated based on the unit price of the base material and X. i Therefore, the objective function is actually the material parameter X of the ultra-high performance concrete matrix. i Related functions, then the optimization task becomes to find a set of material parameters X of the ultra-high performance concrete matrix i , so that the Y value is minimized.

[0067] (2) Constraints. Before solving the optimization problem, it is necessary to specify the value range of the material parameters of the ultra-high performance concrete substrate, that is, to specify the upper and lower limits of each parameter, so that the material parameters X of the ultra-high performance concrete substrate can be i The search will only be performed within the scope specified above.

[0068] (3) Intelligent optimization parameter setting. When optimizing the mix ratio of ultra-high performance concrete, the particle swarm optimization algorithm (PSO) is selected. By setting parameters such as the number of particles (i.e., the number of candidate solutions to be searched), the number of iterations (the total number of iterations the algorithm will perform), the speed (the speed at which particles move in the solution space), the inertia weight (the weight of the particles adjusting their positions based on their own experience and the experience of the group), the individual learning factor (the size of the particle's tendency to move toward its personal historical best position), and the group learning factor (the size of the particle's tendency to move toward the global best position in the entire group), the particle swarm has the advantages of strong optimization ability and fast convergence speed.

[0069] The process of the PSO algorithm first randomly generates multiple sets of material parameters X of the ultra-high performance concrete substrate. i , X i Bring it into the objective function to calculate multiple Y values; then update each group of X in the direction of decreasing Y value i Calculate the value of Y again, and repeat the above steps several times to find the groups of X with the smallest Y value. i The value is taken as the optimal mix ratio of ultra-high performance concrete.

[0070] To verify the feasibility and applicability of the UHPC mix optimization model, several optimal UHPC mixes derived from the model were trial-mixed. After curing, their specific performance indicators were tested and compared with the set target values. If the performance indicators differed significantly from the target values, the mix optimization process was repeated until the trial-mixed UHPC performance indicators met the target values.

[0071] The beneficial effects of the present invention are mainly reflected in the following aspects:

[0072] (1) Improve design efficiency: By introducing machine learning algorithms and intelligent optimization algorithms, rapid mapping and global search from ratios to functional requirement indicators are achieved, greatly improving design efficiency.

[0073] (2) Comprehensive consideration of functional requirements: It can comprehensively consider the comprehensive impact of the dosage of each component of ultra-high performance concrete on specific functional requirements and meet the functional requirements in different application scenarios.

[0074] (3) Propose an unsupervised anomaly detection method to improve the dataset with the ability to eliminate or mitigate abnormal data;

[0075] (4) Develop an automatic variable selection method to select the key design variables required for ultra-high performance concrete mix proportions

[0076] (5) Reduce experimental costs: It reduces the large amount of experimental work required by traditional experimental methods, and reduces experimental costs and time costs.

[0077] In terms of machine learning model construction, other machine learning algorithms can be used as substitutes (but these algorithms have lower efficiency and prediction accuracy) to adapt to different data sets and prediction requirements. In terms of particle swarm optimization, other optimization algorithms (such as genetic algorithms and simulated annealing algorithms) can be used as substitutes to further improve search efficiency and accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a general implementation flow chart of the present invention;

[0079] Figure 2 This is a flow chart of the ratio design method of the present invention;

[0080] Figure 3 Schematic diagram of 5-fold cross validation of the present invention;

[0081] Figure 4 This is the random forest model stress resistance training and testing diagram in Example 1;

[0082] Figure 5 This is the training and testing diagram of the flexural strength of the random forest model in Example 2

[0083] Figure 6 Schematic diagram of the PSO algorithm process of the present invention;

[0084] Figure 7 The objective function value of 500 iterations of Example 1 is shown in the figure;

[0085] Figure 8 This is the random forest model stress resistance training and testing diagram in Example 1;

[0086] Figure 9 This is the training and testing diagram of the flexural strength of the random forest model in Example 2

[0087] Figure 10 The objective function value of 500 iterations of Example 2 is shown in the figure. DETAILED DESCRIPTION

[0088] The process of the present invention is as follows Figure 1 and Figure 2 As shown, the following is a detailed description of the specific implementation of the technical solution of the present invention:

[0089] 1. Data collection and preprocessing

[0090] To build the machine learning model, we first collected a large amount of UHPCC raw materials and their corresponding performance data from various sources, including China National Knowledge Infrastructure (CNKI), China Science Documentation Service (CSCD), Google Scholar (https: / / scholar.google.com / ), Web of Science (www.isiknowledge.com), Elsevier / SD (www.sciencedirect.com), the State Intellectual Property Office / China Patent Publication Bulletin (http: / / epub.cnipa.gov.cn / ), and the Enterprise Yellow Pages (www.ypshop.net).

[0091] (1) Basic raw materials: 537 mix ratio designs including cement, quartz sand, quartz powder, silica fume, fly ash, etc.;

[0092] (2) Mineral admixtures: 219 sets of data including ground slag powder, metakaolin, steel slag powder, various industrial waste slag powders, tailings powder, boron carbide powder, rubber powder, ceramic powder, barite powder, graphite powder, zeolite powder, and perlite powder;

[0093] (3) Chemical admixtures: 187 sets of data on various chemical admixtures including retarding, accelerating, early-strengthening, air-entraining, defoaming, expansion, water-reducing, and antifreeze agents;

[0094] (4) Fiber: 27 groups including steel fiber, basalt fiber, glass fiber, polyacrylonitrile fiber, etc.;

[0095] A total of 486 raw materials were collected, and each raw material included four parameters: origin, main mechanical properties / performance indicators / grade, density, apparent characteristics (including equivalent particle size), and price. The relationship between the dosage, mechanical properties / performance indicators / grade, apparent characteristics (including equivalent particle size) and performance indicators of ultra-high performance concrete of each raw material was also collected, totaling 1,370 mix designs.

[0096] The unsupervised isolation forest method was used to preprocess 970 data sets, and 887 valid data were obtained.

[0097] Example 1

[0098] The mix design process is given with a compressive strength of 150MPa and a tensile strength of 10MPa as functional requirements:

[0099] 1. Automatic variable selection

[0100] In order to select the key variables that have the greatest impact on compressive strength and tensile strength, F statistics are used for variable selection. The specific steps are as follows:

[0101] (1) Calculate the correlation coefficient: Use formula (1) to calculate the correlation coefficient between each variable (such as cement content, quartz sand content, etc.) and compressive strength and tensile strength;

[0102] (2) F statistic test: Based on the correlation coefficient, the F statistic of each variable is calculated using formula (2) to evaluate the degree of association between the variable and the performance indicator;

[0103] (3) Select key variables: According to the size of the F statistic, select the variables that have the greatest impact on compressive strength and tensile strength as key variables.

[0104] After the above automatic variable selection process, the key variables and their F statistics are shown in Table 2:

[0105] Table 2 Automatically selected key variables and F statistics

[0106] variable F statistic Cement content (X1) 123.45 Quartz sand content (X2) 89.76 Quartz powder dosage (X3) 45.67 Silica fume content (X4) 78.90 Fly ash content (X5) 23.45 Steel fiber content (X6) 156.78 Water reducing agent dosage (X7) 67.89 Water (X8) 75.32

[0107] 2. Hyperparameter tuning and evaluating the prediction model

[0108] The random forest model hyperparameters were tuned using grid search and 5-fold cross validation. The selected hyperparameters, search intervals, and the optimal hyperparameter combination are shown in Table 3:

[0109] Table 3 Optimal hyperparameters

[0110]

[0111] Where (a, b, c) represents the search interval and interval, a represents the lower bound of the search interval, b represents the upper bound of the search interval, and c represents the search interval. The optimal score is the average R obtained from 5 cross-validations using formula (3) 2 Values, such as Figure 3 shown.

[0112] 3. Random Forest Model Training

[0113] The 887 data points were randomly divided into training and test sets in a ratio of 7:3. X1 to X8 were used as the input of the machine learning model, and the compressive strength and tensile strength were used as the output of the machine learning model. The random forest model was constructed using the optimal hyperparameter combination selected in 2. Hyperparameter Tuning (n_estimators = 200, max_depth = 15, min_samples_leaf = 1, min_samples_split = 2). The training and test results are shown in Figure 2. Figure 4 .

[0114] Compressive strength: test set R 2 =0.983, training set R2 =0.961

[0115] Flexural strength: test set R 2 =0.976, training set R 2 =0.955

[0116] The above results show that the prediction model has excellent prediction ability and can be used to predict the compressive strength and flexural strength of UHPC.

[0117] 4. Ultra-high performance concrete mix design

[0118] According to formula (4), an objective function that comprehensively considers the compressive strength, flexural strength and price of UHPC is constructed, where the target values of compressive strength and flexural strength are 150 MPa and 10 MPa, respectively.

[0119] The ratio constraints of the optimization model are shown in Table 4:

[0120] Table 4 Constraints of proportion components and materials

[0121] variable Lower limit Upper limit of value Cement content (X1) 600 700 Quartz sand content (X2) 850 1020 Quartz powder dosage (X3) 125 205 Silica fume content (X4) 180 250 Fly ash content (X5) 50 100 Steel fiber content (X6) 120 180 Water reducing agent dosage (X7) 20 35 Water (X8) 145 160 UHPC bulk density 2380 2530

[0122] like Figure 6 The particle swarm optimization algorithm shown in Table 5 has parameter settings as shown in Table 5:

[0123] Table 5 Parameter values of particle swarm algorithm

[0124]

[0125] The objective function value of 500 iterations is as follows Figure 7 As shown in the figure, after multiple iterative calculations, three groups of optimal ratios are finally obtained.

[0126] The following three groups of optimal mixes were tested and the measured compressive and flexural strengths and unit prices are shown in Table 6. After comprehensive comparison, Group X was finally selected as the optimal mix, which has the lowest price while meeting the requirements of compressive strength greater than 150 MPa and tensile strength greater than 10 MPa.

[0127] Table 6 Optimal ratio

[0128]

[0129]

[0130] 5. Experimental verification

[0131] Based on the three groups of ratio design results, test verification was carried out, and the performance test indicators are shown in the following table, all of which meet the expected functional requirements.

[0132] Table 7 Test verification results

[0133] Group 1 Group 2 Group 3 Compressive strength (MPa) 166 170 167.5 Tensile strength (MPa) 11.4 11.7 11.5

[0134] Example 2

[0135] The ratio design process is given with the functional requirements of anti-γ-ray radiation and compressive strength of 120MPa:

[0136] 1. Automatic variable selection

[0137] After the above automatic variable selection process, the key variables and their F statistics are shown in Table 8:

[0138] Table 8 Automatically selected key variables and F statistics

[0139]

[0140] 2. Hyperparameter tuning and evaluating the prediction model

[0141] The random forest model hyperparameters were tuned using grid search and 5-fold cross validation. The selected hyperparameters, search intervals, and the optimal hyperparameter combination are shown in Table 9:

[0142] Table 9 Optimal hyperparameters

[0143]

[0144] Where (a, b, c) represents the search interval and interval, a represents the lower bound of the search interval, b represents the upper bound of the search interval, and c represents the search interval. The optimal score is the average R obtained from 5 cross-validations using formula (3) 2 value.

[0145] 3. Random Forest Model Training

[0146] The 537 data points were randomly divided into training and test sets in a ratio of 7:3. X1 to X10 were used as the input of the machine learning model, and the compressive strength and radiation resistance indicators were used as the output of the machine learning model. The optimal hyperparameter combination selected in 2. Hyperparameter Tuning (n_estimators = 300, max_depth = 13, min_samples_leaf = 3, min_samples_split = 6) was used to construct a random forest model. The training and test results are shown in the figure below. Figure 8 and Figure 9 shown.

[0147] Compressive strength: test set R 2 =0.973, training set R 2 =0.967

[0148] Gamma ray shielding: test set R 2=0.988, training set R 2 =0.976

[0149] The above results show that the prediction model has excellent prediction ability and can be used to predict the compressive strength and radiation resistance of UHPC.

[0150] 4. Ultra-high performance concrete mix design

[0151] According to formula (4), an objective function that comprehensively considers the compressive strength, radiation resistance index and price of UHPC is constructed, where the target values of compressive strength and radiation resistance index are 120 MPa and the anti-γ-ray protection ratio is not less than 40%, respectively.

[0152] The ratio constraints of the optimization model are shown in Table 10:

[0153] Table 10 Constraints on the proportion of components and materials

[0154]

[0155]

[0156] The parameter values of the particle swarm optimization algorithm are set as shown in Table 11:

[0157] Table 11 Parameter values of particle swarm algorithm

[0158]

[0159] The objective function value of 500 iterations is as follows Figure 10 As shown in the figure, after multiple iterative calculations, three groups of optimal ratios are finally obtained.

[0160] The three groups of optimal mixes in Table 12 below were tested and the measured compressive strength, radiation resistance index and unit price are as follows. After comprehensive comparison, Group X was finally selected as the optimal mix. It has the lowest price while meeting the requirements of compressive strength greater than 120 MPa and anti-γ-ray protection ratio of not less than 40%.

[0161] Table 12 Optimal ratio

[0162]

[0163] 5. Experimental verification

[0164] Table 13 Test verification results

[0165]

[0166]

[0167] Based on the design results of the three groups of ratios, test verification was carried out, and the performance test indicators are shown in Table 13, all of which meet the expected functional requirements.

Claims

1. Ultra-high performance concrete mix design method based on intelligent algorithm and functional requirements, characterized by: The following steps are involved: S1. Construction of ultra-high performance concrete performance prediction database; By extracting structured and unstructured data, an automatic anomaly detection method is used to improve the dataset by eliminating or mitigating abnormal data. A database of ultra-high performance concrete component materials X and the corresponding ultra-high performance concrete performance index data Y for each component material is constructed. The unsupervised method of isolation forest is used to improve the dataset to identify and remove abnormal data. S2, automatic selection of key variables based on functional requirements; The univariate linear regression method and the automatic variable selection method of F statistics are used to identify key design variables. In this way, the key material variables Xi are selected according to the functional requirements of ultra-high performance concrete to improve the prediction accuracy of the machine learning model. S3, machine learning model training and prediction based on functional requirements; Hyperparameter adjustment was performed using a selected machine learning method using grid search and cross-validation. The resulting machine learning model was able to predict the corresponding UHPC performance indicators based on the relevant parameters of the UHPC components. S4. Optimal design of ultra-high performance concrete mix ratio; Based on the trained machine learning model, an intelligent optimization algorithm is used to establish an ultra-high performance concrete mix ratio optimization model. According to the functional demand indicators specified by the user, the mix ratio that meets the requirements is output, and the output mix ratio is verified using experimental methods.

2. The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements according to claim 1 is characterized in that: S1 includes: S1.

1. Data collection; Collect structured and unstructured data on ultra-high performance concrete basic raw materials, their specific functional materials and related performance indicators; The data includes: (1) Material types include: a) basic raw materials: cement, quartz sand, quartz powder, silica fume, fly ash, water, water reducer; b) mineral admixtures; c) chemical admixtures; d) various fibers; (2) Material parameters include: mechanical properties / performance indicators / grade, density, surface characteristics, and price; The above data form a database, which contains K L pieces of data, k i Indicates a piece of collected ratio data; k i Each material in X i Use 4 columns of parameters to mark, namely mechanical properties / performance index / grade, density, surface characteristics, and price. i1 、X i2 、X i3 and X i4 Mark, a total of X n Materials; Y1-Y m It is the performance index of ultra-high performance concrete, including compressive strength, flexural strength, tensile strength, radiation performance, initial setting time, and impermeability grade; S1.

2. Data preprocessing; The collected data has abnormal data due to different reasons. The unsupervised method of isolation forest is used to improve the dataset to identify and remove abnormal data: (1) Construct a decision tree based on the database, namely the isolation tree; (2) Evaluate each data point according to the isolation tree and assign an anomaly score to describe the degree of abnormality of the data point; If the anomaly score of a data instance is greater than a certain value, the data instance is considered anomaly; the percentage of anomaly data in the database is defined as the contamination rate of the dataset.

3. The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements according to claim 1 is characterized in that: The specific method of automatic variable selection in S2 is: The univariate linear regression method is used to evaluate the variable X i and ultra-high performance concrete properties Y i The correlation between: In formula (1): C(X i , Y i ) represents the correlation coefficient, and Represents X i A certain performance index value and Y j The average value of a characteristic value, std(X i ) and std(Y i ) represent X i A parameter value and Y j The standard deviation of Based on the correlation coefficient, F statistics is used to test the degree of association between multiple variables, namely: In formula (2): F(X i , Y i ) represents X i and Y i The larger the F statistic, the higher the value. i and Y i The high correlation between them, n represents the number of statistical data; By calculating the F statistic for each material variable, the key material variable X is selected. i To improve the prediction accuracy of machine learning models.

4. The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements according to claim 1 is characterized in that: S3 specifically includes: S3.

1. Hyperparameter Tuning and Evaluating Predictive Models Grid search and cross-validation are used to tune hyperparameters to find the optimal hyperparameter combination. The random forest model trained with this set of hyperparameters has the strongest predictive ability. (1) Grid search is to traverse all possible combinations of the specified parameter range to find the best hyperparameters; (2) After generating multiple hyperparameter combinations through the grid search method, the cross-validation method is used to select the optimal set of parameters, that is, the data set is divided into K subsets or "folds", and one of the subsets is selected as the test set each time, and the remaining subsets are used as the training set; this process is repeated K times, and a different subset is selected as the test set each time to ensure that each subset is used as the test set once; finally, the performance index of the results of the K tests is averaged as the performance index value of this set of hyperparameters. Each set of hyperparameters is subjected to the above cross-validation process to obtain a performance index value; Each time, one of the subsets is selected as the test set, and the remaining subsets are used as the training set. The model is trained and evaluated, and the model performance index is R 2 ; This process is repeated many times, and the average R of multiple tests is finally taken 2 The R value is used as the performance evaluation of the model; the R value of the model with different hyperparameters is compared. 2 value, select R 2 The highest set of hyperparameters is used for subsequent model training; Y j is the true value of the functional indicator in the database, is the functional index value predicted by the machine learning model, is the average value of the predicted value, N is the number of data; S3.

2. Random Forest Model Training The random forest model is used to train and predict samples, and a mapping relationship between the basic raw material parameters X of ultra-high performance concrete and the performance index Y of ultra-high performance concrete is established. The training process is as follows: (1) Initialize the model. Divide the database into a training set and a test set in a ratio of 7:

3. The purpose of the training set is to allow the machine learning model to learn the characteristics and patterns of the data, so that the model can continuously adjust its internal parameters and fit the data. The purpose of the test set is to evaluate the performance of the model on unseen data, thereby simulating the performance of the model in actual applications. (2) Training: Using a set of optimal hyperparameters obtained from hyperparameter tuning and evaluation of the prediction model, the structure of the random forest model is set, and the training set is input into the model for training. After multiple iterations, a prediction model for the performance index of ultra-high performance concrete is finally obtained, thereby establishing a mapping relationship between the basic raw material parameters X of ultra-high performance concrete and the performance index y of ultra-high performance concrete; (3) Testing: Input the feature matrix X of the test set into the trained UHPCC performance index prediction model, and obtain the corresponding UHPCC performance index prediction value through model calculation. The true value Y of the ultra-high performance concrete performance index of the test set j and the predicted values of the machine learning model Bring in R 2 Calculate in the formula to get the R predicted by the model on the test set 2 value.

5. The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements according to claim 1 is characterized in that: The specific method of S4 is: On the basis of realizing the performance prediction of ultra-high performance concrete, the parameters of the raw materials in the ultra-high performance concrete mix ratio are optimized and adjusted through the intelligent optimization algorithm to provide an optimal mix ratio that can meet the target performance requirements; the ultra-high performance concrete mix ratio optimization model needs to set the objective function, constraints and optimization algorithm parameters according to the actual situation of the optimization task, namely: (1) Objective function: The objective function consists of two parts: the performance index and price of ultra-high performance concrete. The objective function Y is specifically expressed as follows: The first part of the formula is the performance index of ultra-high performance concrete, Y tar It is the target value of the performance index corresponding to the functional requirements of ultra-high performance concrete. is the predicted value of the UHPCC performance index, which is obtained by inputting a set of material parameters X of the UHPCC matrix into the machine learning model. i The predicted value is P, which is the price of ultra-high performance concrete. i Multiply the mass of the substrate in to get; The objective function is related to the material parameters X of the ultra-high performance concrete matrix i The optimization task becomes to find a set of material parameters X of the ultra-high performance concrete matrix i , so that the Y value is minimized; (2) Constraints: Before solving the optimization problem, it is necessary to specify the value range of the material parameters of the ultra-high performance concrete substrate, that is, to specify the upper and lower limits of each parameter, and the material parameters X of the ultra-high performance concrete substrate. i The search will only be performed within the specified range; (3) Intelligent optimization parameter setting: When optimizing the mix ratio of ultra-high performance concrete, the selected intelligent optimization algorithm is the particle swarm algorithm (PSO), which is achieved by setting the number of particles, number of iterations, speed, inertia weight, individual learning factor and group learning factor parameters. The particle swarm has the advantages of strong optimization ability and fast convergence speed.

6. The ultra-high performance concrete mix design method based on intelligent algorithms and functional requirements according to claim 5 is characterized in that: The process of the PSO algorithm is to first randomly generate multiple sets of material parameters X of the ultra-high performance concrete substrate. i , X i Bring it into the objective function to calculate multiple Y values; then update each group of X in the direction of decreasing Y value i Calculate the value again to get multiple Y values, repeat several times, and finally find the groups of X with the smallest Y value. i The value is taken as the optimal mix ratio of ultra-high performance concrete.

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