A multi-objective design method and system for concrete mix proportion outliers

Abstract

The present application relates to a kind of concrete outlying mix design method and system of multiple target, it is related to concrete intelligent design and material optimization technical field, including the acquisition of same region multiple groups of conventional and outlying concrete mix data, establish Gaussian process regression model;Select the hyperparameter combination of maximum logML to complete model training;Test set data is input into the model of training completion, and evaluation result is obtained;Build target function including multiple target performance;Batch bayesian optimization strategy is used, with expected improvement value as acquisition function to obtain the EI value of each candidate point, select m optimal mix ratio in combination with distance penalty mechanism;Experimental data and the prediction result of previous model are compared, and the model after updating is used in the next round batch bayesian optimization point optimization process.The beneficial effects of the present application are to overcome the low search efficiency of single-point optimization method, and the limitation of easy to fall into local optimum, significantly improve the convergence speed of design process.

Description

Technical Field

[0001] This invention relates to the field of intelligent concrete design and material optimization technology, and more specifically, to a multi-objective design method and system for outlier concrete mix proportions. Background Technology

[0002] The performance of concrete materials is influenced by the coupled effects of multiple components, including cementitious materials, fine aggregates, coarse aggregates, water, and admixtures. For a long time, mix design has relied primarily on empirical formulas and repeated trial mixing experiments. While this method remains feasible for ordinary concrete, the emergence of high-performance systems such as ultra-high performance concrete (UHPC) and engineering cement-based composites (ECC) has led to material compositions characterized by high admixture content, multi-scale processes, and strong coupling. Traditional, experience-based mix design methods are ill-suited to the complex formulation space, limiting both design efficiency and accuracy.

[0003] In recent years, using data-driven models to predict concrete performance and assist in mix design optimization has gradually become a research hotspot. However, high-performance concrete is often limited by factors such as high experimental costs and long preparation and testing cycles, resulting in a significant shortage of available data. With small sample sizes, common machine learning prediction models are prone to overfitting; that is, the model performs well on training data but shows significant errors on unseen mix design combinations. This unstable predictive ability directly affects the reverse design process, making it difficult to guarantee the reliability of model-recommended mix designs, thus increasing the risk of engineering applications. Furthermore, existing methods generally treat different concrete systems as independent learning objects, using only a small amount of data within a single system for modeling, failing to fully explore the potential commonalities between conventional and high-performance concrete, making it difficult for the model to gain sufficient material sensitivity knowledge in small sample scenarios. At the same time, mainstream single-point optimization strategies often determine the next experimental point only based on the current prediction results, failing to effectively utilize the model's uncertainty information, resulting in limited search efficiency and slow optimization processes in high-dimensional parameter spaces.

[0004] In summary, existing high-performance concrete mix design methods have the following shortcomings: First, traditional empirical methods are difficult to handle complex material systems; second, data-driven models are prone to overfitting under small sample conditions, resulting in insufficient prediction accuracy; third, the lack of cross-system knowledge transfer mechanisms leads to weak adaptability of the models in high-performance concrete systems; and fourth, existing optimization strategies do not make sufficient use of uncertainties, resulting in low design efficiency. Summary of the Invention

[0005] The purpose of this invention is to provide a multi-objective design method and system for outlier concrete mix proportions to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows: Firstly, this application provides a multi-objective design method for outlier concrete mix proportions, including: Collect multiple sets of conventional and outlier concrete mix proportion data from the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters; normalize the raw data, and divide the processed data into training set and test set according to a ratio of 80%-20%; Using the mix ratio parameter as the input vector and the corresponding compressive strength, workability and cost as the output targets, a Gaussian process regression model is established; a combination of four types of kernel functions is used for modeling and WhiteKernel is superimposed to represent observation noise; hyperparameters are learned by maximizing the log marginal likelihood, and the combination of hyperparameters with the largest logML is selected to complete the model training; The test set data is input into the trained model to obtain the predicted performance index values, which are then compared with the actual test data. The coefficient of determination R is calculated. 2 The mean squared error and mean absolute error are used as evaluation indicators to assess the model’s generalization ability and prediction accuracy, and the evaluation results are obtained. Based on the evaluation results and specific design requirements, an objective function containing multiple performance objectives is constructed, and corresponding constraints are set according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators. A batch Bayesian optimization strategy is adopted. Candidate mixing ratios are generated by Latin hypercube sampling. The Gaussian process regression model is used to calculate the predicted mean and uncertainty of candidate points. The expected improvement value is used as the acquisition function to obtain the EI value of each candidate point. The m optimal mixing ratios are selected by combining the distance penalty mechanism. The selected candidate mix proportions were actually prepared and their performance was tested to obtain experimental data on compressive strength, workability and material cost. The experimental data were compared with the prediction results of the previous model and added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model was used for the next round of batch Bayesian optimization point selection optimization process.

[0006] Preferably, the mix proportion data includes cement, mineral powder, fly ash, silica fume, water, water-reducing agent, fine aggregate, coarse aggregate, and steel fiber.

[0007] Preferably, the normalization process adopts the following calculation model: the normalized variable value is equal to the original variable value minus the minimum value of the variable, and then divided by the difference between the maximum and minimum values ​​of the variable.

[0008] Preferably, the specific process for establishing and optimizing the Gaussian process regression model is as follows: The refined concrete mix proportion parameters are used as input feature vectors, which include the composition ratios of cementitious materials, water, sand, stone, mineral admixtures and additives. The corresponding compressive strength, workability and material cost are provided as output variables to the GPR model. Four kernel function combinations were used for modeling: Matérn 5 / 2 kernel, Matérn 5 / 2 kernel with autocorrelation dimension mechanism, radial basis function kernel, and RBF kernel with autocorrelation dimension. WhiteKernel was superimposed on each kernel function. The optimization objective is to maximize the log-marginal likelihood, and the search range for hyperparameters is set. Twenty sets of hyperparameters are randomly initialized as the starting point for optimization. The gradient-based L-BFGS algorithm is used to iteratively solve the log-marginal likelihood. The optimized set of hyperparameters and their corresponding log-marginal likelihood values ​​are recorded. The set of hyperparameters with the highest log-marginal likelihood values ​​is selected as the optimal kernel function parameters, and the final Gaussian process regression model is trained accordingly.

[0009] Preferably, based on the evaluation results and specific design requirements, an objective function containing multiple performance objectives is constructed, and corresponding constraints are set according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators, including: Based on the design requirements, the compressive strength, workability and material cost of concrete are used as optimization objectives. The concrete mix proportion parameter vector is set as the amount or proportion of each raw material. The performance prediction value of any mix proportion is obtained by using the trained Gaussian process regression model. A comprehensive objective function is constructed with a negative strength term, a cost term, and a workability penalty term. The workability penalty function applies a penalty when the performance index deviates from the allowable construction range. The constraints include total material constraints, upper and lower limits of each material usage, water-cement ratio constraints, lower limit of workability constraints, and cost constraints.

[0010] Preferably, the batch Bayesian optimization strategy includes: n uniformly distributed candidate mix proportion points are generated within the design space using Latin hypercube sampling; The Gaussian process regression model was used to calculate the predicted mean and variance for each candidate point. Using the desired improvement value as the acquisition function, the EI value is calculated for each candidate point, which is defined as the product of the improvement amount and the corresponding standard normal distribution function value plus the product of the noise term and the standard normal probability density function value; the point with the largest EI is selected from the candidate set as the first experimental point in the batch.

[0011] Preferably, the selection of m optimal matching ratios using the combined distance penalty mechanism includes: calculating the Euclidean distance between any remaining candidate point and the selected points; constructing a penalty term as the penalty intensity parameter multiplied by the negative square of the distance; defining the penalty-corrected EI as the original EI minus the penalty term; selecting the next point based on the penalty-corrected EI value; recalculating the distance penalty for the remaining points and updating the penalty-corrected EI for each new point selected; and continuing to select points until n points are obtained. .

[0012] Preferably, the updated model is used in the next round of batch Bayesian optimization point selection process, including: the updated model serves as the basis for the next round of Bayesian optimization and is used again for objective function calculation and candidate point selection, thereby forming a closed-loop active learning mechanism of point selection-experiment-feedback-re-optimization.

[0013] Secondly, this application also provides a multi-objective design system for outlier concrete mix proportions, comprising: Data Acquisition Module: Used to collect multiple sets of conventional and outlier concrete mix proportion data from the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters; normalize the raw data, and divide the processed data into training set and test set according to a ratio of 80%-20%; A training module is established: a Gaussian process regression model is built with the mix ratio parameter as the input vector and the corresponding compressive strength, workability and cost as the output targets; a combination of four types of kernel functions is used to model the model and a WhiteKernel is superimposed to represent observation noise; hyperparameters are learned by maximizing the log marginal likelihood and the hyperparameter combination with the largest logML is selected to complete the model training. Evaluation module: Used to input test set data into the trained model, obtain predicted performance metrics, compare them with actual test data, and calculate the coefficient of determination R. 2 The mean squared error and mean absolute error are used as evaluation indicators to assess the model’s generalization ability and prediction accuracy, and the evaluation results are obtained. The building module is used to construct an objective function containing multiple performance objectives based on the evaluation results and specific design requirements, and to set corresponding constraints according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators. The calculation module is used to generate candidate mixing ratios by adopting a batch Bayesian optimization strategy, generating them through Latin hypercube sampling, calculating the predicted mean and uncertainty of candidate points using a Gaussian process regression model, obtaining the EI value of each candidate point using the expected improvement value as the acquisition function, and selecting m optimal mixing ratios by combining a distance penalty mechanism. The comparison and update module is used to conduct actual preparation and performance testing of the selected candidate mix proportions to obtain experimental data on the corresponding compressive strength, workability and material cost. The experimental data is compared with the prediction results of the previous model and added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model is used for the next round of batch Bayesian optimization point selection optimization process.

[0014] The beneficial effects of this invention are as follows: This invention first trains a Gaussian process regression model using large-scale conventional concrete mix proportion-performance data. Then, it fine-tunes the model's parameters on a small number of target systems and data points to calibrate its performance sensitivity to specific material systems. Based on this, a performance objective function is constructed, and a Bayesian optimization acquisition function is introduced. A batch of potentially optimal mix proportions is adaptively selected for experimentation based on the current predicted mean and uncertainty. The experimental results are continuously fed back to update the model and iteratively provide the next batch of experimental points. This achieves efficient proactive learning and optimization design within a limited number of rounds, effectively overcoming the limitations of traditional methods and improving design efficiency, accuracy, and solution diversity.

[0015] This invention employs a batch Bayesian optimization strategy, enabling the simultaneous selection of multiple potentially superior formulations in each optimization round. Combined with model uncertainty and spatial diversity constraints, it achieves efficient exploration, overcoming the limitations of single-point optimization methods such as low search efficiency and susceptibility to local optima, significantly improving the convergence speed of the design process. This scheme allows the model to continuously calibrate its perception of the target system's performance sensitivity during iterative iterations, achieving a smooth migration from conventional concrete systems to high-performance systems such as UHPC, making the optimization results more aligned with actual engineering needs. This mechanism maximizes the absorption of experimental information in each round, thereby reducing the number of experiments, shortening the design cycle, and improving overall optimization efficiency. Furthermore, the objective function and constraint strategy of this invention can simultaneously consider multiple engineering indicators such as compressive strength, workability, and material cost, generating diverse optimal solutions while satisfying the requirements of reasonable mix proportions and construction feasibility, thus improving the generalization ability and adaptability of the design results. The resulting mix proportions not only meet the comprehensive optimization requirements of multiple performance objectives but also outperform traditional manual design methods in terms of overall performance, economy, and constructability.

[0016] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the multi-objective design method for outlier concrete mix proportions described in this embodiment of the invention; Figure 2 This is a schematic diagram of the multi-objective design system for outlier concrete mix proportions described in this embodiment of the invention. Figure 3 This is a schematic diagram of the multi-objective design equipment for outlier concrete mix proportions described in this embodiment of the invention; Figure 4 This is an example of the optimized mix proportion of the multi-objective design method for outlier concrete mix proportions described in this embodiment of the invention.

[0019] In the diagram: 701, Acquisition Module; 702, Training Module; 703, Evaluation Module; 704, Construction Module; 705, Calculation Module; 706, Comparison and Update Module; 800, Multi-objective Design Equipment for Outlier Concrete Mix Proportions; 801, Processor; 802, Memory; 803, Multimedia Component; 804, I / O Interface; 805, Communication Component. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0021] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance. Example 1:

[0022] Traditional concrete mix design relies primarily on empirical formulas or local search algorithms, which suffer from high computational costs, poor optimization convergence, and unstable design results, making it difficult to meet the increasingly complex performance requirements of high-strength and high-durability concrete systems. While commonly used data-driven models can establish mapping relationships between material parameters and performance, they often face significant overfitting risks for high-performance concrete systems with limited sample sizes, leading to decreased prediction accuracy and even producing mix proportions that deviate from actual performance during reverse engineering, compromising engineering feasibility. Furthermore, existing methods typically ignore potential correlations between different concrete systems, preventing models from fully utilizing existing knowledge in small-sample scenarios and limiting design accuracy and generalization ability. Simultaneously, mainstream optimization strategies lack full utilization of model uncertainties, exhibiting limited search efficiency in high-dimensional formulation spaces and failing to provide reliable decision-making basis for experimental design.

[0023] To address the aforementioned shortcomings, this invention aims to propose a novel intelligent design method for outlier concrete mix proportions that integrates transfer learning and Bayesian optimization. By pre-training a Gaussian process model using large-scale conventional concrete data and fine-tuning its parameters with a small number of target system samples, the model can maintain stable performance sensitivity representation under small sample conditions. Based on this, a performance objective function is constructed, and combined with an uncertainty-based Bayesian data acquisition strategy, the most promising experimental points are adaptively selected and continuously updated, achieving efficient active learning and iterative optimization within a limited number of rounds. This invention aims to effectively solve the problem that existing methods struggle to balance prediction accuracy, optimization efficiency, and scheme reliability in small sample scenarios, providing a precise, robust, and scalable reverse design approach for high-performance concrete systems.

[0024] This embodiment provides a multi-objective design method for outlier concrete mix proportions.

[0025] See Figure 1 The figure shows that the method includes steps S100, S200, S300, S400 and S500.

[0026] S100. Collect multiple sets of conventional and outlier concrete mix proportion data from the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters; normalize the raw data, and divide the processed data into training set and test set according to a ratio of 80%-20%.

[0027] It is understood that the mix proportion data in this step includes cement, mineral powder, fly ash, silica fume, water, water-reducing agent, fine aggregate, coarse aggregate, and steel fiber. The normalization process uses the following calculation model: the normalized variable value equals the original variable value minus the minimum value of that variable, divided by the difference between the maximum and minimum values ​​of that variable.

[0028] In other words, in this embodiment, multiple sets of conventional concrete mix proportions and outlier concrete mix proportion data are collected from the same region, and the mechanical and workability indicators corresponding to each formula are collected simultaneously, including performance parameters such as compressive strength, slump or spread, and material cost. The original mix proportion data are normalized to eliminate the dimensional differences between different indicators and improve the stability and convergence of the model training process. The normalized data covers the input of cementitious materials, aggregates, and admixtures, as well as their corresponding strength, workability, and cost performance information. Subsequently, the processed dataset is divided into training and testing sets according to a ratio of 80%–20%. The training set is used for model learning, and the testing set is used for subsequent evaluation of the generalization performance of the Gaussian process regression model.

[0029] S200. Using the mix proportion parameters as the input vector and the corresponding compressive strength, workability, and cost as the output targets, a Gaussian process regression model is established. Four types of kernel functions are combined for modeling and WhiteKernel is superimposed to represent observation noise. Hyperparameters are learned by maximizing the log marginal likelihood, and the hyperparameter combination with the largest logML is selected to complete the model training.

[0030] Understandably, the specific process of establishing and optimizing the Gaussian process regression model in this step is as follows: The refined concrete mix proportion parameters are used as input feature vectors, which include the composition ratios of cementitious materials, water, sand, stone, mineral admixtures and additives. The corresponding compressive strength, workability and material cost are provided as output variables to the GPR model. Four kernel function combinations were used for modeling: Matérn 5 / 2 kernel, Matérn 5 / 2 kernel with autocorrelation dimension mechanism, radial basis function kernel, and RBF kernel with autocorrelation dimension. WhiteKernel was superimposed on each kernel function. With maximizing the log-marginal likelihood as the optimization objective, the search range for the hyperparameters is set, and the calculation formula is as follows: In the formula, X is the hyperparameter vector of the Gaussian process model, including the length scale of each kernel function, the signal variance, and the noise variance of the WhiteKernel; X is the input matrix (design matrix) of the training samples, with each row being the independent variable of a sample; y is the observation output (target value) vector corresponding to each sample in . * This represents the optimal hyperparameter vector obtained through optimization.

[0031] Twenty sets of hyperparameters were randomly initialized as the starting point for optimization. The gradient-based L-BFGS algorithm was used to iteratively solve the log marginal likelihood. The optimized set of hyperparameters and their corresponding log marginal likelihood values ​​were recorded. The set of hyperparameters with the highest log marginal likelihood values ​​was selected as the optimal kernel function parameters, and the final Gaussian process regression model was trained accordingly.

[0032] This step involves constructing a nonlinear mapping model from material parameters to performance indices. Using concrete mix proportions as the input vector and the corresponding compressive strength, workability, and cost as the output targets, a Gaussian process regression (GPR) model is established. To enhance the model's ability to characterize complex nonlinear relationships, this invention selects four types of kernel function combinations for modeling: the Matérn 5 / 2 kernel, the Matérn 5 / 2 kernel with autocorrelation dimension (ARD), the RBF kernel, and the RBF kernel with ARD. A WhiteKernel is uniformly superimposed to represent observation noise, and hyperparameters are learned by maximizing the log-marginal likelihood. Finally, the hyperparameter combination with the largest logML is selected as the optimal model parameters, and the GPR model is trained accordingly.

[0033] Specifically, ① the concrete mix proportion parameters refined in step S1 are used as the input feature vector 𝑋, which includes the proportions of cementitious materials, water, sand, aggregate, mineral admixtures, and additives; the corresponding compressive strength, workability, and material cost are provided as output variables 𝑦 to the GPR model. This model assumes that the output variables follow a multivariate Gaussian distribution and uses a kernel function to characterize the correlation between samples in the input space.

[0034] ② To enhance the model's ability to express complex nonlinear relationships in high-performance concrete systems, this invention employs four kernel function combinations for modeling, including: (1) Matérn 5 / 2 kernel; (2) Matérn 5 / 2 kernel with Automatic Related Dimension (ARD) mechanism; (3) Radial Basis Function (RBF) kernel; (4) RBF kernel with ARD; and a WhiteKernel is superimposed on each kernel function to handle measurement noise that may exist in the data. The ARD mechanism introduces independent length scales for different input features, enabling the model to automatically learn the strength of the influence of each concrete component on performance, thereby improving the model's adaptability in complex systems. To obtain the optimal kernel function hyperparameters, this invention uses maximizing the log-marginal likelihood (logML) as the optimization objective, which takes the form: Here, 𝜃 includes hyperparameters such as length scale, signal variance, and noise variance. To improve optimization stability and avoid local optima, this invention sets reasonable search ranges for the hyperparameters: log-length scale range [log(0.05), log(10)], log-signal variance range [log(0.1), log(10)], and log-noise variance range [log(0.1), log(10)]. [log(10−4),log(1)].

[0035] ③ Within the aforementioned range, 20 sets of hyperparameters were randomly initialized as the starting point for optimization. The gradient-based L-BFGS algorithm was used to iteratively solve for logML, and the optimized hyperparameter set 𝜃′ and its corresponding logML value were recorded after each optimization. After completing all randomly initialized optimization processes, the set of hyperparameters with the highest logML value was selected as the optimal kernel function parameters, and the final Gaussian process regression model was trained accordingly. This model can achieve high-precision fitting of the concrete mix proportion-performance mapping relationship based on multi-kernel function and multi-dimensional automatic adjustment, providing a reliable predictive basis for subsequent model validation and Bayesian optimization steps.

[0036] The predicted value for each sample in the test set is denoted as 𝑦^𝑖=𝜇(𝑥𝑖), and compared with its true value 𝑦𝑖 to quantitatively evaluate the model's prediction accuracy and generalization ability. This invention preferably uses indicators such as the coefficient of determination (𝑅2), root mean square error (RMSE), and mean absolute error (MAE) for comprehensive evaluation, and their calculation formulas are as follows: in, The mean of the true performance metrics in the test set is denoted by , and ttest represents the number of test samples. A higher t2 value and lower RMSE and MAE values ​​indicate that the model maintains good predictive accuracy on data not used for training.

[0037] S300. Input the test set data into the trained model to obtain the predicted performance index values ​​and compare them with the measured data. Calculate the coefficient of determination R. 2 The mean squared error and mean absolute error are used as evaluation indicators to assess the model's generalization ability and prediction accuracy, and the evaluation results are obtained.

[0038] Understandably, in this step, the test set data is input into the trained Gaussian process regression model to obtain predicted values ​​for performance indicators such as compressive strength, workability, and cost, which are then compared and analyzed with the measured data. The model's generalization ability and prediction accuracy are evaluated by calculating evaluation metrics such as the coefficient of determination (r²), mean squared error (MSE), and mean absolute error (MAE).

[0039] S400. Based on the evaluation results and specific design requirements, construct an objective function that includes multiple performance objectives, and set corresponding constraints according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators.

[0040] Understandably, in this step, based on specific design requirements, an objective function is constructed that includes multiple performance objectives (such as maximizing compressive strength, meeting specified workability ranges, and controlling material costs). Corresponding constraints are then set according to engineering requirements, such as limiting the amount of cementitious materials, admixture dosage, and the range of key performance indicators. The objective function and constraints guide the Bayesian optimization process, ensuring that the generated mix design meets requirements in terms of performance, workability, and economy.

[0041] Specifically, based on the design requirements and engineering performance requirements of high-performance concrete, an objective function for the Bayesian optimization process is constructed, and constraints satisfying material workability, safety, and economy are set as search criteria for subsequent batch Bayesian optimization point selection. The process includes the following steps: ① Based on the specific requirements of the design task, this invention uses key performance indicators of concrete, such as compressive strength, workability (e.g., slump, spread), and material cost, as optimization objectives. Let the concrete mix proportion parameter vector be... Each element represents the amount or proportion of different raw materials (such as cementitious materials, powder materials, sand, stone, water, and admixtures). Using the Gaussian process regression model trained in step S2, the performance prediction value φ^φ(φ) (e.g., performance items such as strength, workability, and cost) of any mix proportion φ can be obtained.

[0042] ② To achieve the design objective of "maximizing strength + minimizing cost + meeting workability requirements", this invention constructs the following comprehensive objective function: in: The predicted compressive strength; Forecast material costs; The penalty function is used to describe the deviation of the workability from the target range; 𝑤1, 𝑤2, 𝑤3 are empirically set weight coefficients; the intensity is used as the maximization objective, so it is negative in front, which transforms the optimization process into a "minimization" problem.

[0043] ③ To ensure that the workability meets the construction requirements, this invention adopts an interval-type penalty function, such as: Where 𝑎 and 𝑏 represent the allowable construction range, such as an expansion of 250–300 mm; 𝜆 is the penalty factor, which automatically suppresses points that deviate from the range during the optimization process.

[0044] ④ While constructing the objective function, to ensure that the mix proportions meet the physical rationality in engineering applications, the present invention also sets the following constraints: (1) Total material constraints: Where 𝑀total is the target total mass of concrete per unit volume.

[0045] (2) Upper and lower limits of material usage: (3) Water-to-binder ratio constraint: (4) Lower limit constraint on workability: (5) Cost constraints: S500 employs a batch Bayesian optimization strategy, generates candidate mixing ratios through Latin hypercube sampling, calculates the predicted mean and uncertainty of candidate points using a Gaussian process regression model, obtains the EI value of each candidate point using the expected improvement value as the acquisition function, and selects m optimal mixing ratios by combining a distance penalty mechanism.

[0046] Understandably, in this step, a batch Bayesian optimization strategy is employed to actively select multiple representative experimental points in the high-dimensional concrete mix design space. First, Latin hypercube sampling (LHS) is used to generate *k* candidate mix proportions in the design space, and a pre-trained Gaussian process regression model is used to calculate the predicted mean *k*(*k*) and uncertainty *k*(*k*) for each candidate point. Then, using the expected improvement value (EI) as the acquisition function, the EI value for each candidate point is obtained, and the point with the largest EI is selected as the first experimental point. To avoid excessive concentration of selected points within a batch, a penalty term is applied to the remaining candidate points based on their distance from the first selected point, thereby suppressing the EI values ​​of spatially adjacent points. The penalized EI distribution is then used for optimal point selection again to determine the second experimental point, and the "distance penalty—point selection" step is repeated until *k* optimal mix proportions constituting a batch are obtained. The obtained batch of candidate points can be used simultaneously in actual experiments to improve optimization efficiency and promote rapid convergence of the model during iterative updates. The n candidate mix proportions obtained from batch Bayesian optimization were actually prepared and tested according to requirements to obtain experimental data such as compressive strength, workability, and material cost. These newly acquired actual performance results were compared with the prediction results of the previous model, and then added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. Through incremental training of the model, the parameters were continuously corrected based on feedback from new data, reducing prediction uncertainty and improving the performance sensitivity characterization ability of the target system, thereby achieving round-by-round adaptive optimization of the model. The updated model will be used in the next round of batch Bayesian optimization point selection process, effectively improving the model's convergence speed and design efficiency.

[0047] Specifically, a batch Bayesian optimization strategy is used to select a group of the most promising experimental points from the high-dimensional concrete mix design space for the next round of actual preparation and performance testing. This includes the following steps: ① Initial candidate point generation in the design space: First, n uniformly distributed candidate mix ratio points are generated within the design space n using Latin hypercube sampling (LHS): The role of LHS is to achieve uniform coverage in high-dimensional space and improve the diversity of candidate points.

[0048] ② GPR Model Prediction: Using the Gaussian process regression model obtained in step S2, calculate the predicted mean and variance for each candidate point 𝑥𝑖: The predicted mean reflects the potential performance at that point, while the predicted variance reflects the uncertainty of the model, and are important sources of information for Bayesian optimization.

[0049] ③ Calculate the expected improvement value EI: EI is the main data acquisition function for point selection in this invention, and its definition is: in, Φ(⋅) is the standard normal distribution function, φ(⋅) is the standard normal probability density function, φbest is the currently known best objective function value, and φ is the exploration parameter (usually taken as 0–0.01). For each candidate point, calculate EI: ④ Select the first optimal point in the batch: Select the point with the largest EI from the candidate set as the first experimental point in the batch: ⑤ Distance Penalty Mechanism: To avoid the concentration of selected points in the same area, this invention introduces a distance penalty function to adjust the EI value of the remaining candidate points. The Euclidean distance between any remaining candidate point 𝑥𝑗 and the selected point 𝑥(1) is calculated: Construct penalty terms: Where 𝛼>0 controls the penalty intensity. The penalized EI is defined as: The closer the distance, the greater the penalty, making the points within the batch more dispersed.

[0050] ⑥ Iteratively select points 2 to m: Select the next point based on the penalized EI value: For each new point selected, the distance penalty is recalculated for the remaining points, the EI is updated after the penalty, and the selection of points continues until k points are obtained: .

[0051] S600. The selected candidate mix proportions are actually prepared and their performance is tested to obtain the corresponding experimental data on compressive strength, workability and material cost. The experimental data are compared with the prediction results of the previous model and added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model is used for the next round of batch Bayesian optimization point selection optimization process.

[0052] Understandably, in this step, the batch of candidate mix proportions selected in the previous steps are actually mixed and tested according to the formulation requirements to obtain experimental data such as their actual compressive strength, workability, and material cost. Subsequently, these newly obtained experimental results, along with the corresponding mix proportion parameters, are added to the existing training dataset. The expanded data is then used to update the Gaussian process regression model, allowing the model to continuously correct its predicted distribution, reduce uncertainty, and enhance its sensitivity to the performance of the target high-performance concrete system in each round of experimental feedback. The updated model will serve as the basis for the next round of Bayesian optimization, again used for objective function calculation and candidate point selection, thus forming a closed-loop active learning mechanism of "point selection—experiment—feedback—re-optimization." This enables the model's performance to continuously migrate and adapt from conventional concrete systems to the target high-performance concrete system, ultimately improving the efficiency and reliability of the overall optimization design.

[0053] In this embodiment, it should be noted that the Bayesian optimization method based on transfer learning used in this invention for concrete outlier mix design specifically includes the following steps: Step 1: First, collect 1000 sets of conventional concrete mix proportions and their corresponding compressive strength, scalar spread, and material cost data for the region, and collect 18 sets of UHPC test data for fine-tuning the Gaussian process model. All input raw material indicators (including cement, silica fume, quartz sand, fiber, water, water-reducing agent, etc.) are normalized using Min–Max, and performance output indicators (strength, scalar spread, cost) are standardized. The UHPC data are divided into training and test sets at 80% / 20% for performance evaluation of the transferred model. Step 2: Using conventional concrete data as the source domain samples, a Gaussian process regression model was established using a combination of kernel functions such as Matérn 5 / 2, RBF (including ARD), and WhiteNoise. Hyperparameters were optimized by maximizing the log-marginal likelihood. Subsequently, the trained model was loaded as a transfer model and fine-tuned using UHPC training data to ensure stable predictive performance even with small sample sizes. The model achieved strength prediction R²=0.93, scalability prediction R²=0.90, and cost prediction R²=0.95 on the UHPC test set, indicating that the transferred model possesses good generalization ability. Step 3: This embodiment aims to "improve strength, meet flowability requirements, and control material costs." The objective function consists of three parts: maximizing 28-day compressive strength; ensuring the spread meets the construction requirement of 250–300 mm; and ensuring material costs do not exceed 1250 yuan / m². 3At the same time, engineering constraints such as the total amount of cementitious materials, the upper limit of fiber content, and the water-cement ratio range are set to ensure the workability and material rationality of the candidate mix proportions.

[0054] Step 4: 400 candidate mixing schemes are generated using Latin hypercube sampling within the normalized design space. The predicted mean and variance of each candidate point are calculated using the GPR model after transfer learning. The expected improvement value (EI) is used as the acquisition function, and a distance penalty strategy is combined to select the 5 optimal candidate points in each batch. After two rounds of batch selection, a total of 10 high-potential UHPC mixing schemes are generated, covering high-intensity and medium-expansion areas, and ensuring sufficient diversity among the points. Step 5: Each batch of candidate mix proportions is mixed and tested according to standard laboratory methods to obtain its actual compressive strength, scalability, and material cost. The new data is then added to the training set to further optimize the GPR model. After model updates, Bayesian optimization is re-executed, ultimately completing three rounds of active learning iterations. Step 6: After three rounds of batch Bayesian optimization, this embodiment finally obtained a UHPC mix proportion that meets engineering requirements and has excellent performance. Its 28-day compressive strength reaches 158 MPa, its spread is 270 mm, and the cost is controlled at 1235 yuan / m². 3 Furthermore, this mix design was not initially included in the original UHPC dataset, representing a typical "outlier" search result, demonstrating the high-efficiency optimization capability of the method in high-dimensional, small-sample concrete systems. Compared to traditional UHPC mix design methods that rely on numerous experiments, this embodiment achieves performance improvement and feasibility screening through only three rounds and 15 sets of experimental points, reducing the number of experiments by over 70% and significantly improving design efficiency. Figure 4 As shown. Example 2:

[0055] like Figure 2 As shown, this embodiment provides a multi-objective design system for outlier concrete mix proportions. See [link to documentation]. Figure 2 The system includes: Data Acquisition Module 701: Used to collect multiple sets of conventional and outlier concrete mix proportion data from the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters; normalize the raw data, and divide the processed data into training set and test set according to a ratio of 80% to 20%; Training module 702 is established to build a Gaussian process regression model with the mix ratio parameter as the input vector and the corresponding compressive strength, workability and cost as the output targets. Four types of kernel functions are combined to model the model and WhiteKernel is superimposed to represent observation noise. Hyperparameters are learned by maximizing the log marginal likelihood and the hyperparameter combination with the largest logML is selected to complete the model training. Evaluation module 703: Used to input test set data into the trained model, obtain predicted performance metrics, compare them with actual test data, and calculate the coefficient of determination R. 2 The mean squared error and mean absolute error are used as evaluation indicators to assess the model’s generalization ability and prediction accuracy, and the evaluation results are obtained. Module 704: Used to construct an objective function containing multi-objective performance based on the evaluation results and specific design requirements, and to set corresponding constraints according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators; Calculation module 705: Used to adopt a batch Bayesian optimization strategy, generate candidate mixing ratios through Latin hypercube sampling, calculate the predicted mean and uncertainty of candidate points using a Gaussian process regression model, obtain the EI value of each candidate point using the expected improvement value as the acquisition function, and select m optimal mixing ratios by combining the distance penalty mechanism; The comparison and update module 706 is used to conduct actual preparation and performance testing of the selected candidate mix proportions, obtain experimental data on the corresponding compressive strength, workability and material cost, compare the experimental data with the prediction results of the previous model, and add them back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model is used for the next round of batch Bayesian optimization point selection optimization process.

[0056] In summary, the Bayesian optimization method based on transfer learning proposed in this invention can effectively overcome the problems of difficult mix design, overfitting of prediction models, and low optimization efficiency in high-performance concrete under small sample conditions. By introducing large-scale conventional concrete data as source knowledge and using a small amount of target system data for transfer fine-tuning of the model, this scheme significantly improves the prediction accuracy and stability of the Gaussian process regression model in the target material system, effectively reducing performance fluctuations and design uncertainties caused by data scarcity, and making the optimization process more reliable. Compared with traditional mix design methods that rely on empirical formulas or a large number of trial mixing experiments, this invention can fully utilize existing data to complete the intelligent search of high-dimensional material parameter space without increasing experimental costs. By employing a batch Bayesian optimization strategy, multiple potentially superior formulations can be selected simultaneously in each optimization round. Combined with model uncertainty and spatial diversity constraints, efficient exploration is achieved, overcoming the limitations of single-point optimization methods, such as low search efficiency and susceptibility to local optima. This significantly improves the convergence speed of the design process and enables the model to continuously calibrate its perception of the target system's performance sensitivity during iterations. This allows for a smooth migration from conventional concrete systems to high-performance systems such as UHPC, making the optimization results more in line with actual engineering needs.

[0057] It should be noted that the specific methods by which each module performs operations in the system described in the above embodiments have been described in detail in the embodiments related to the method, and will not be elaborated here. Example 3:

[0058] Corresponding to the above method embodiments, this embodiment also provides a multi-objective design device for outlier concrete mix proportions. The multi-objective design device for outlier concrete mix proportions described below and the multi-objective design method for outlier concrete mix proportions described above can be referred to in correspondence.

[0059] Figure 3 This is a block diagram illustrating a multi-objective design device 800 for outlier concrete mix proportions according to an exemplary embodiment. (e.g.) Figure 3 As shown, the multi-objective design device 800 for outlier concrete mix proportions includes a processor 801 and a memory 802. The multi-objective design device 800 for outlier concrete mix proportions also includes one or more of a multimedia component 803, an I / O interface 804, and a communication component 805.

[0060] The processor 801 controls the overall operation of the multi-objective design device 800 for outlier concrete mix proportions to complete all or part of the steps in the aforementioned multi-objective design method for outlier concrete mix proportions. The memory 802 stores various types of data to support the operation of the multi-objective design device 800 for outlier concrete mix proportions. This data may include, for example, instructions for any application or method operating on the multi-objective design device 800 for outlier concrete mix proportions, as well as application-related data such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as a keyboard, mouse, or buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the multi-objective design device 800 for outlier concrete mix proportions and other devices. Wireless communication includes, for example, Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, or an NFC module.

[0061] In an exemplary embodiment, the multi-objective design device 800 for outlier concrete mix proportions may be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the aforementioned multi-objective design method for outlier concrete mix proportions.

[0062] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided, which, when executed by a processor, implement the steps of the multi-objective design method for outlier concrete mix proportions described above. For example, the computer-readable storage medium may be the memory 802 including the program instructions described above, which may be executed by the processor 801 of the multi-objective design device 800 for outlier concrete mix proportions to complete the multi-objective design method for outlier concrete mix proportions described above. Example 4:

[0063] Corresponding to the above method embodiments, this embodiment also provides a readable storage medium. The readable storage medium described below and the multi-objective design method for outlier concrete mix proportions described above can be referred to in correspondence.

[0064] A computer program is stored on a readable storage medium, and when executed by a processor, the computer program implements the steps of the multi-objective design method for outlier concrete mix proportions in the above-described method embodiments.

[0065] Specifically, the readable storage medium can be a USB flash drive, a portable hard drive, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk, or any other readable storage medium capable of storing program code.

[0066] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A multi-objective design method for outlier concrete mix proportions, characterized in that, include: Collect multiple sets of conventional and outlier concrete mix proportion data from the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters. The original data is normalized, and the processed data is divided into training set and test set according to the ratio of 80%-20%. Using the mix ratio parameter as the input vector and the corresponding compressive strength, workability and cost as the output targets, a Gaussian process regression model is established; a combination of four types of kernel functions is used for modeling and WhiteKernel is superimposed to represent observation noise; hyperparameters are learned by maximizing the log marginal likelihood, and the combination of hyperparameters with the largest logML is selected to complete the model training; The test set data is input into the trained model to obtain a performance index prediction value and compare the performance index prediction value with the measured data 2 , and evaluation indexes such as a determination coefficient R, a mean square error and a mean absolute error are calculated to evaluate the generalization ability and the prediction accuracy of the model, and an evaluation result is obtained. Based on the evaluation results and specific design requirements, an objective function containing multiple performance objectives is constructed, and corresponding constraints are set according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators. A batch Bayesian optimization strategy is adopted. Candidate mixing ratios are generated by Latin hypercube sampling. The Gaussian process regression model is used to calculate the predicted mean and uncertainty of candidate points. The expected improvement value is used as the acquisition function to obtain the EI value of each candidate point. The m optimal mixing ratios are selected by combining the distance penalty mechanism. The selected candidate mix proportions were actually prepared and their performance was tested to obtain experimental data on compressive strength, workability and material cost. The experimental data were compared with the prediction results of the previous model and added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model was used for the next round of batch Bayesian optimization point selection optimization process.

2. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The mix proportion data includes cement, mineral powder, fly ash, silica fume, water, water-reducing agent, fine aggregate, coarse aggregate, and steel fiber.

3. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The normalization process uses the following calculation model: the normalized variable value is equal to the original variable value minus the minimum value of the variable, and then divided by the difference between the maximum and minimum values ​​of the variable.

4. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The specific process of establishing and optimizing the Gaussian process regression model is as follows: The refined concrete mix proportion parameters are used as input feature vectors, which include the composition ratios of cementitious materials, water, sand, stone, mineral admixtures and additives. The corresponding compressive strength, workability and material cost are provided as output variables to the GPR model. Four kernel function combinations were used for modeling: Matérn 5 / 2 kernel, Matérn 5 / 2 kernel with autocorrelation dimension mechanism, radial basis function kernel, and RBF kernel with autocorrelation dimension, and WhiteKernel was superimposed on each kernel function; With maximizing the log-marginal likelihood as the optimization objective, the search range for the hyperparameters is set, and the calculation formula is as follows: In the formula, Let X be the hyperparameter vector of the Gaussian process model, including the length scale of each kernel function, signal variance, and noise variance of the WhiteKernel. Let X be the input matrix of the training samples, with each row representing the independent variable of a sample. Let y be the observation output vector corresponding to each sample in X. * The optimal hyperparameter vector obtained through optimization; Twenty sets of hyperparameters were randomly initialized as the starting point for optimization. The gradient-based L-BFGS algorithm was used to iteratively solve the log marginal likelihood. The optimized set of hyperparameters and their corresponding log marginal likelihood values ​​were recorded. The set of hyperparameters with the highest log marginal likelihood values ​​was selected as the optimal kernel function parameters, and the final Gaussian process regression model was trained accordingly.

5. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The determination coefficient R is calculated. 2 The mean squared error and mean absolute error are used as evaluation metrics to assess the model's generalization ability and prediction accuracy. The calculation formulas are as follows: In the formula, where y i To determine the true value of the i-th sample in the test set; Let be the corresponding predicted value; Ntest ​​represents the mean of the actual performance metrics in the test set, and Ntest ​​represents the number of test samples.

6. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, Based on the evaluation results and specific design requirements, an objective function encompassing multiple performance objectives is constructed, and corresponding constraints are set according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators, including: Based on the design requirements, the compressive strength, workability and material cost of concrete are used as optimization objectives. The concrete mix proportion parameter vector is set as the amount or proportion of each raw material. The performance prediction value of any mix proportion is obtained by using the trained Gaussian process regression model. A comprehensive objective function is constructed with a negative strength term, a cost term, and a workability penalty term. The workability penalty function applies a penalty when the performance index deviates from the allowable construction range. The constraints include total material constraints, upper and lower limits of each material usage, water-cement ratio constraints, lower limit of workability constraints, and cost constraints.

7. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The batch Bayesian optimization strategy includes: n uniformly distributed candidate mix proportion points are generated within the design space using Latin hypercube sampling; The Gaussian process regression model was used to calculate the predicted mean and variance for each candidate point. Using the desired improvement value as the acquisition function, the EI value is calculated for each candidate point. It is defined as the product of the improvement amount and the corresponding standard normal distribution function value, plus the product of the noise term and the standard normal probability density function value. The calculation formula is as follows: In the formula, X is the candidate point, μ(x) is the predicted mean of the Gaussian process at x; 𝜎(x) is the predicted standard deviation of the Gaussian process at x, 𝜙(·) is the standard normal probability density function, fbest is the currently known best objective function value, 𝜉 is the exploration parameter, and Z is the standardized improvement amount; The point with the highest EI in the candidate set is selected as the first experimental point in the batch.

8. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The combined distance penalty mechanism selects m optimal matching ratios, including: calculating the Euclidean distance between any remaining candidate point and the selected points; constructing a penalty term as the penalty intensity parameter multiplied by the negative square of the distance; defining the penalty-corrected EI as the original EI minus the penalty term; selecting the next point based on the penalty-corrected EI value; recalculating the distance penalty for the remaining points and updating the penalty-corrected EI for each new point selected; and continuing to select points until m points are obtained. .

9. The multi-objective design method for outlier concrete mix proportions according to claim 1, characterized in that, The updated model is used in the next round of batch Bayesian optimization point selection process, which includes: the updated model serves as the basis for the next round of Bayesian optimization and is used again for objective function calculation and candidate point selection, thus forming a closed-loop active learning mechanism of point selection-experiment-feedback-re-optimization.

10. A multi-objective design system for outlier concrete mix proportions, based on the multi-objective design method for outlier concrete mix proportions as described in claim 1, characterized in that, include: Data acquisition module: used to collect multiple sets of conventional and outlier concrete mix proportion data in the same region, and simultaneously collect corresponding compressive strength, slump or spread, and material cost performance parameters; The original data is normalized, and the processed data is divided into training set and test set according to the ratio of 80%-20%. A training module is established: a Gaussian process regression model is built with the mix ratio parameter as the input vector and the corresponding compressive strength, workability and cost as the output targets; a combination of four types of kernel functions is used to model the model and a WhiteKernel is superimposed to represent observation noise; hyperparameters are learned by maximizing the log marginal likelihood and the hyperparameter combination with the largest logML is selected to complete the model training. Evaluation module: Used to input test set data into the trained model, obtain predicted performance metrics, compare them with actual test data, and calculate the coefficient of determination R. 2 The mean squared error and mean absolute error are used as evaluation indicators to assess the model’s generalization ability and prediction accuracy, and the evaluation results are obtained. The building module is used to construct an objective function containing multiple performance objectives based on the evaluation results and specific design requirements, and to set corresponding constraints according to engineering requirements, including limiting the amount of cementitious materials, the amount of admixtures, and the range of values ​​for key performance indicators. The calculation module is used to generate candidate mixing ratios by adopting a batch Bayesian optimization strategy, generating them through Latin hypercube sampling, calculating the predicted mean and uncertainty of candidate points using a Gaussian process regression model, obtaining the EI value of each candidate point using the expected improvement value as the acquisition function, and selecting m optimal mixing ratios by combining a distance penalty mechanism. The comparison and update module is used to conduct actual preparation and performance testing of the selected candidate mix proportions to obtain experimental data on the corresponding compressive strength, workability and material cost. The experimental data is compared with the prediction results of the previous model and added back to the training dataset as new samples to update the posterior distribution of the Gaussian process regression model. The updated model is used for the next round of batch Bayesian optimization point selection optimization process.

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