Method and system for predicting optimal proportion of fiber-reinforced environment-friendly cement mortar based on machine learning

Abstract

The invention discloses a method and a system for predicting the optimal ratio of fiber-reinforced environment-friendly cement mortar based on machine learning. The method comprises the following steps: collecting experimental data, and carrying out data preprocessing; screening features of extremely strong correlation and strong correlation by using a Pearson correlation coefficient; constructing a bidirectional gating circulation unit network prediction model based on an attention mechanism, extracting features through a bidirectional GRU layer, and weighting key information through an attention layer; training the model by adopting an adaptive moment estimation optimization algorithm, and performing hyper-parameter tuning in combination with a Bayesian optimization algorithm; and after the target performance index is input, the model outputs an optimal ratio combination meeting the requirement. The system comprises a data acquisition and preprocessing module, a feature screening module, a model construction and training module, a hyper-parameter tuning module and an optimal ratio prediction module. According to the method, the attention mechanism and the bidirectional GRU are fused, so that the prediction precision is improved, and an efficient and reliable solution is provided for proportioning optimization of the environment-friendly cement mortar.

Description

Technical Field

[0001] This invention relates to the field of intelligent design technology for building materials, specifically to a machine learning-based method and system for predicting the optimal mix ratio of fiber-reinforced environmentally friendly cement mortar, used to predict the optimal material mix ratio of fiber-reinforced environmentally friendly cement mortar. Background Technology

[0002] Fiber-reinforced environmentally friendly cement mortar, as a new type of green building material, has broad application prospects in the field of construction engineering. By adding recycled sand and polypropylene fibers, it not only realizes the resource utilization of construction waste but also significantly improves the mechanical properties and durability of the material. However, the performance of this material is affected by a variety of complex factors, including the replacement rate of recycled sand, fiber content, and water-cement ratio. These parameters often have nonlinear coupling relationships, making the design of the optimal mix design a highly challenging task.

[0003] Currently, the mix design of fiber-reinforced cement mortar mainly relies on traditional experimental methods, namely, determining the optimal proportions of each component through numerous trial-and-error experiments. This method is not only time-consuming and costly, but also difficult to comprehensively examine the interactions between various factors due to limitations in experimental conditions. Although some studies have attempted to use statistical analysis methods (such as response surface methodology) to optimize the mix proportions, these methods have significant limitations when dealing with high-dimensional nonlinear data, and their prediction accuracy is insufficient to meet the needs of engineering practice.

[0004] In recent years, machine learning technology has demonstrated strong application potential in the field of materials science. Some scholars have begun to explore the application of algorithms such as neural networks and support vector machines in the prediction of the properties of cement-based materials. However, existing research still has the following shortcomings: First, traditional machine learning models are difficult to effectively capture the temporal dependencies between material composition and properties; second, the hyperparameter optimization during model training relies heavily on human experience and lacks systematicity; in addition, the existing methods do not have a perfect weight allocation mechanism for key influencing factors, resulting in insufficient model interpretability and predictive stability.

[0005] To address the aforementioned technical bottlenecks, there is an urgent need to develop a novel intelligent prediction method capable of efficiently processing the multidimensional characteristic data of fiber-reinforced environmentally friendly cement mortar, accurately capturing the complex relationships between various factors, and achieving high-precision prediction of optimal mix proportions. This would not only significantly reduce experimental costs and shorten the research and development cycle but also provide reliable technical support for the industrial application of green building materials. Summary of the Invention

[0006] This invention proposes a machine learning-based method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar. By combining an attention mechanism with a bidirectional gated recurrent unit (ABiGRU), and through feature correlation screening, adaptive training, and Bayesian optimization, the optimal mix proportion prediction for multi-objective performance is achieved, significantly improving the accuracy and generalization ability of the model.

[0007] In a first aspect, embodiments of this application provide a method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning, the method comprising:

[0008] S1. Collect experimental data on fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength and flexural strength, and preprocess the data.

[0009] S2. Use Pearson correlation coefficient to analyze the correlation between input and output variables, and select highly correlated and strongly correlated features as model inputs;

[0010] S3. Construct a prediction model of ABiGRU based on attention mechanism, the model including input layer, bidirectional GRU layer, attention layer, fully connected layer and output layer;

[0011] S4. Divide the dataset into training and test sets, and use the AdamW adaptive moment estimation optimization algorithm to train the model.

[0012] S5. Use Bayesian optimization algorithm to tune hyperparameters, construct objective function, and find the optimal hyperparameter combination through Gaussian process modeling.

[0013] S6. Input the target performance index, and use the trained ABiGRU model to predict the optimal combination that meets the requirements.

[0014] Optionally, in one implementation of the first aspect of the present invention, the data preprocessing in step S1 includes the following steps:

[0015] Data normalization: The Min-Max normalization method is used to linearly transform the data to the [0,1] interval. The calculation formula is as follows:

[0016]

[0017] Among them, X norm X represents the normalized data, and X represents the original input data. max X min These represent the maximum and minimum values ​​in the data, respectively.

[0018] Missing value handling: For missing values ​​in the experimental data, one of the following methods is used for imputation:

[0019] Numerical features are filled with the mean or median; categorical features are filled with the mode.

[0020] Processing discrete variables: Categorical variables are converted to numerical values ​​using One-Hot coding technology;

[0021] Data standardization: Continuous features are standardized using Z-score, calculated as follows:

[0022]

[0023] Among them, X std This represents the standardized data, where μ represents the mean of the feature and σ represents the standard deviation of the feature;

[0024] Data cleaning: Outliers are identified and processed using box plots, and observations that significantly deviate from the normal range are removed using the 3σ principle or IQR method.

[0025] Optionally, in one implementation of the first aspect of the present invention, the feature filtering in step S2 specifically includes the following steps:

[0026] Calculate the Pearson correlation coefficients between each input variable and the output variable, where the input variables include the recycled sand replacement rate and the polypropylene fiber content, and the output variables include compressive strength and flexural strength. The formula is as follows:

[0027]

[0028] Where r represents the Pearson correlation coefficient, n represents the sample size, X represents the input variable, and Y represents the output variable;

[0029] Features are categorized and filtered based on the absolute value of the Pearson correlation coefficient.

[0030] Select highly correlated and strongly correlated features as input features for the model;

[0031] For the selected features, a correlation coefficient matrix heatmap is generated for visual analysis to verify the correlation between features.

[0032] Optionally, in one implementation of the first aspect of the present invention, in step S3, the model includes:

[0033] Input layer: Receives preprocessed feature data;

[0034] Bidirectional GRU layer: Composed of forward GRU and backward GRU, it extracts time series features from the forward and backward directions respectively. Its calculation process is as follows:

[0035] zt =σ(W z ·[h t-1 ,x t ]+b z ),

[0036] r t =σ(W r ·[h t-1 ,x t ]+b r ),

[0037]

[0038] Among them, z t This indicates updating the output of the gate, r t This indicates that the output of the reset door is being reset. H represents the candidate state. t w represents the hidden state at the current time step. z w r Let b represent the weight matrix. z b r b indicates the bias term, x t σ represents the input at the current time;

[0039] The backward GRU uses the same structure to perform reverse computation;

[0040] Attention layer: Calculates the importance weights of features at each time step.

[0041]

[0042]

[0043] Among them, e t Indicates attention score, a t Let c represent the attention weights, and v represent the context vector. a w a b represents the attention weight parameter. a The term represents the bias of the attention mechanism, and T represents the total number of time steps;

[0044] Fully connected layer: maps attention-weighted features to the prediction space;

[0045] Output layer: Outputs the predicted compressive and flexural strength values.

[0046] Optionally, in one implementation of the first aspect of the present invention, step S4 involves training the model using an adaptive moment estimation optimization algorithm, with the parameter update formula being:

[0047] m t =β1m t-1+(1-β1)g t ,

[0048] v t =β2v t-1 +(1-β2)g t 2 ,

[0049]

[0050] Where, m t v t Indicates the estimation of first and second moments. This is the corresponding bias correction, where β1 and β2 represent the exponential decay rate, and g t This represents the gradient at the current time step, η is the learning rate, which determines the step size for parameter updates, and λ is the weight decay coefficient. It is a small constant to prevent the denominator from being zero, θ t Indicates model parameters.

[0051] Optionally, in one implementation of the first aspect of the present invention, step S5 involves using a Bayesian optimization algorithm for hyperparameter tuning. The execution steps of the Bayesian optimization algorithm are as follows:

[0052] Initialization phase: Latin hypercube sampling is used to generate an initial sample set in the hyperparameter space, and the objective function value is evaluated;

[0053] Gaussian process modeling: Based on the evaluated hyperparameter combinations and their objective function values, a Gaussian process surrogate model is constructed, where the kernel function adopts the radial basis function;

[0054] Acquisition function optimization: Select the next combination of hyperparameters to be evaluated by the expected improvement function, where the balancing parameter ξ is dynamically adjusted with the number of iterations;

[0055] Iterative update: Evaluate the objective function value of the new hyperparameter combination, update the Gaussian process model, and check for early stopping conditions;

[0056] Output: When the early stopping condition is met, the optimization is terminated and the historical best hyperparameter combination is output.

[0057] Optionally, in one implementation of the first aspect of the present invention, the objective function is defined as follows:

[0058]

[0059] Where f(θ) represents the objective function, represents the loss value of the model under the current parameters θ plus the regularization term, N represents the number of samples, and y i Let x represent the true label value of the i-th sample. iLet represent the input value of the i-th sample, γ represent the regularization coefficient, ||W||2 represent the L2 norm, represents the square root of the sum of squares of the weight vector W, and f represents the bias term;

[0060] Find the optimal combination of hyperparameters by modeling Gaussian processes.

[0061] Optionally, in one implementation of the first aspect of the present invention, step S6, inputting the target performance index and predicting the optimal combination of proportions that meets the requirements using a trained ABiGRU model, includes:

[0062] Input the target performance index and use it together with the preset process parameter range as model input;

[0063] Multi-objective prediction is performed using the trained ABiGRU model, and candidate combination ratios that meet performance requirements and their confidence scores are output.

[0064] Based on Pareto front analysis, the optimal ratio is selected from candidate combinations to ensure a balance among various performance indicators;

[0065] Output the optimal ratio combination and its predicted performance curve for user decision-making reference.

[0066] Secondly, embodiments of this application provide a machine learning-based optimal mix proportion prediction system for fiber-reinforced environmentally friendly cement mortar, applied to the machine learning-based optimal mix proportion prediction method for fiber-reinforced environmentally friendly cement mortar as described in the first aspect. The system includes:

[0067] The data acquisition and preprocessing module is used to collect experimental data of fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength and flexural strength, and to preprocess the data.

[0068] The feature selection module is used to analyze the correlation between input and output variables using the Pearson correlation coefficient, and to select highly correlated and strongly correlated features as model input.

[0069] The model building module is used to build a prediction model of ABiGRU based on the attention mechanism. The model includes an input layer, a bidirectional GRU layer, an attention layer, a fully connected layer, and an output layer.

[0070] The model training and validation module is used to divide the dataset into training and test sets, and to train the model using the AdamW adaptive moment estimation optimization algorithm.

[0071] The model tuning module is used to perform hyperparameter tuning using the Bayesian optimization algorithm, construct the objective function, and find the optimal hyperparameter combination through Gaussian process modeling.

[0072] The optimal ratio prediction module is used to input target performance indicators and predict the optimal ratio combination that meets the requirements through a trained ABiGRU model.

[0073] Thirdly, embodiments of this application provide an electronic device, including:

[0074] processor;

[0075] Memory used to store processor-executable instructions;

[0076] The processor is configured to implement the machine learning-based optimal mix proportion prediction method for fiber-reinforced environmentally friendly cement mortar as described in the first aspect when executing the instructions.

[0077] Fourthly, embodiments of this application provide a computer-readable storage medium storing a program that instructs a device to execute the machine learning-based optimal mix proportion prediction method for fiber-reinforced environmentally friendly cement mortar as described in the first aspect.

[0078] This invention discloses a machine learning-based method and system for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar. The method includes the following steps: collecting experimental data and performing data preprocessing; using Pearson correlation coefficients to screen highly correlated and strongly correlated features; constructing a bidirectional gated recurrent unit network prediction model based on an attention mechanism, extracting features through a bidirectional GRU layer, and weighting key information in the attention layer; training the model using an adaptive moment estimation optimization algorithm, and combining it with a Bayesian optimization algorithm for hyperparameter tuning; after inputting the target performance index, the model outputs the optimal mix proportion combination that meets the requirements. The system includes modules for data acquisition and preprocessing, feature selection, model construction and training, hyperparameter tuning, and optimal mix proportion prediction. This invention improves prediction accuracy by integrating an attention mechanism and a bidirectional GRU, providing an efficient and reliable solution for optimizing the mix proportion of environmentally friendly cement mortar.

[0079] Beneficial effects:

[0080] 1. By integrating bidirectional GRU and attention mechanism, the model can effectively capture the complex nonlinear relationship between material composition and performance. The visual weight allocation of the attention mechanism (such as the contribution of recycled sand replacement rate to compressive strength) enhances the interpretability of the model, helps researchers quickly locate key influencing factors, and significantly improves prediction accuracy.

[0081] 2. Breakthrough in Multi-Objective Optimization Efficiency. Combining Pareto front analysis, conflicting indices such as compressive strength and flexural strength can be optimized simultaneously, outputting no fewer than five sets of non-dominated solutions, significantly improving decision-making efficiency. The Bayesian optimizer uses the Matérn 5 / 2 kernel function, improving hyperparameter search efficiency compared to grid search, and converges to the optimal solution in just 50 iterations. Attached Figure Description

[0082] Figure 1 This is a schematic diagram of a machine learning-based method for predicting the optimal mix ratio of fiber-reinforced environmentally friendly cement mortar, provided in an embodiment of this application.

[0083] Figure 2 This application provides a collaborative technical solution for the ABiGRU model architecture and Bayesian optimization in one embodiment.

[0084] Figure 3 A diagram of the ABiGRU model architecture provided in an embodiment of this application.

[0085] Figure 4 (a)-(d) are experimental data graphs of apparent density, compressive strength and flexural strength provided in an embodiment of this application.

[0086] Figure 5 A diagram illustrating the architecture of a machine learning-based optimal mix proportion prediction system for fiber-reinforced environmentally friendly cement mortar, provided in one embodiment of this application.

[0087] Figure 6 A schematic diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0088] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0089] It should be noted that, in the embodiments of this application, "at least one" refers to one or more, and "more than one" refers to two or more. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the specification of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application.

[0090] It should be noted that in the embodiments of this application, the terms "first," "second," etc., are used only for descriptive purposes and should not be construed as indicating or implying relative importance, nor as indicating or implying order. Features specified as "first" or "second" may explicitly or implicitly include one or more of the stated features. In the description of the embodiments of this application, words such as "exemplary" or "for example" are used to indicate examples, illustrations, or explanations. Any embodiment or design scheme described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design schemes. Specifically, the use of words such as "exemplary" or "for example" is intended to present the relevant concepts in a concrete manner.

[0091] Based on the embodiments described in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0092] Example 1

[0093] Figure 1 This is a schematic diagram of a machine learning-based method for predicting the optimal mix ratio of fiber-reinforced environmentally friendly cement mortar, provided in an embodiment of this application.

[0094] like Figure 1 As shown, a machine learning-based method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar includes:

[0095] S1. Collect experimental data on fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength, and flexural strength, and preprocess the data. First, it is necessary to collect experimental data on fiber-reinforced environmentally friendly cement mortar, including variables such as recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength, and flexural strength. This data needs to be preprocessed to ensure it is suitable for subsequent modeling and analysis.

[0096] Specifically, in this embodiment, the data preprocessing in step S1 includes the following steps:

[0097] To scale data of different units to the same interval and avoid the impact of unit differences on model training, data normalization is necessary. This includes using the Min-Max normalization method to linearly transform the data to the [0,1] interval. The calculation formula is as follows:

[0098]

[0099] Among them, X norm X represents the normalized data, and X represents the original input data. max X min These represent the maximum and minimum values ​​in the data, respectively.

[0100] Furthermore, to fill in missing values ​​in the experimental data and ensure data integrity, it is necessary to perform missing value processing. This includes using one of the following methods to fill in missing values ​​in the experimental data.

[0101] Numerical features are filled with the mean or median; categorical features are filled with the mode.

[0102] Processing discrete variables: Categorical variables are converted into numerical values ​​using One-Hot encoding technology.

[0103] To ensure that the mean of different features is 0 and the standard deviation is 1, thereby enhancing the stability of model training, data standardization is necessary. This includes Z-score standardization for continuous features, calculated using the following formula:

[0104]

[0105] Among them, X std This represents the standardized data, where μ represents the mean of the feature and σ represents the standard deviation of the feature.

[0106] Furthermore, in order to identify and handle outliers and improve data quality, data cleaning is required: outliers are identified and handled using box plots, and observations that significantly deviate from the normal range are removed using the 3σ principle or IQR method.

[0107] The above preprocessing steps ensure that the data input into the model has good numerical characteristics, thereby improving the model's training efficiency and prediction accuracy.

[0108] Specifically, in this embodiment,

[0109] S2. Use Pearson correlation coefficient analysis to analyze the correlation between input and output variables, and select highly correlated and strongly correlated features as model inputs. This step helps reduce model complexity and improve prediction accuracy.

[0110] Specifically, in this embodiment, the feature selection in step S2 includes the following steps:

[0111] For each input variable (e.g., recycled sand replacement rate, polypropylene fiber content) and output variable (e.g., compressive strength, flexural strength), calculate the Pearson correlation coefficient between them. The formula for calculating the Pearson correlation coefficient is:

[0112]

[0113] Where r represents the Pearson correlation coefficient, n represents the sample size, X represents the input variable, and Y represents the output variable.

[0114] Features are categorized and filtered based on the absolute value of the Pearson correlation coefficient. Specifically, features are divided into different levels according to the absolute value of the Pearson correlation coefficient. Typically, the correlation coefficient ranges from -1 to 1; the larger the absolute value, the stronger the correlation between the variables. For example, 0.8–1.0 indicates a very strong correlation, 0.6–0.8 indicates a strong correlation, 0.4–0.6 indicates a moderate correlation, 0.2–0.4 indicates a weak correlation, and 0–0.2 indicates a very weak or no correlation.

[0115] Features with extremely strong correlation and strong correlation are selected as input features for the model. Specifically, features with extremely strong correlation (|r|≥0.8) and strong correlation (0.6≤|r|<0.8) with the output variable are chosen as input features. These features have a significant impact on the output variable, provide more information, and help improve the model's predictive performance.

[0116] For the selected features, a correlation coefficient matrix heatmap is generated for visual analysis to verify the correlation between features. The heatmap allows for the rapid identification of highly correlated features, thus further optimizing the feature selection process. For example, if the correlation coefficient between two features is close to 1 or -1, it indicates that they may provide similar information, and one of the features can be removed to reduce model complexity. Through these steps, features with strong correlation to the output variable can be effectively selected, providing high-quality input data for subsequent model construction.

[0117] Calculation Example (Taking recycled sand replacement rate vs. compressive strength as an example)

[0118] Assume the experimental data are as shown in the table below:

[0119]

[0120] Substitute into the formula to calculate:

[0121]

[0122] The Pearson correlation coefficient between the recycled sand replacement rate and compressive strength is -0.54, which is a moderately negative correlation (|r|=0.54∈[0.4,0.6)). The negative sign indicates that the compressive strength decreases as the recycled sand replacement rate increases.

[0123] S3. Construct an ABiGRU prediction model based on an attention mechanism, comprising an input layer, a bidirectional GRU layer, an attention layer, a fully connected layer, and an output layer. This structure allows the model to better capture long-term dependencies in time-series data and focus on key features during prediction.

[0124] Figure 2 This application provides a collaborative technical solution for the ABiGRU model architecture and Bayesian optimization in one embodiment. Figure 3 This is a diagram of the ABiGRU model architecture provided in one embodiment of this application. Specifically, as shown... Figure 2 , 3 As shown, in this embodiment, in step S3, the model includes:

[0125] Input Layer: Receives preprocessed feature data, including features such as recycled sand replacement rate and polypropylene fiber content. After normalization, standardization, and missing value processing, this data is used as the model input. Specifically, the preprocessed 6-dimensional feature vector X = [x1, x2, ..., x6] ∈ R... n×T×6 n: Batch size, T: Time step (e.g., experimental batch sequence), features include: recycled sand replacement rate, polypropylene fiber content, flowability, density, compressive strength, and flexural strength.

[0126] Bidirectional GRU layer: Composed of a forward GRU and a backward GRU, extracting time series features from the forward and backward directions respectively. Its calculation process is as follows:

[0127] z t =σ(W z ·[h t-1 ,x t ]+b z ),

[0128] r t =σ(W r ·[h t-1 ,x t ]+b r ),

[0129]

[0130] Among them, z t This indicates updating the output of the gate, r t This indicates that the output of the reset door is being reset. H represents the candidate state. t w represents the hidden state at the current time step. z w r Let b represent the weight matrix. z b r b indicates the bias term, x t σ represents the input at the current time, and σ represents the activation function; the backward GRU uses the same structure for reverse computation.

[0131] Attention layer: Calculates the importance weights of features at each time step.

[0132]

[0133] Among them, e t Indicates attention score, a t Let c represent the attention weights, and v represent the context vector. a w a b represents the attention weight parameter. a This represents the bias term of the attention mechanism, and T represents the total number of time steps.

[0134] Fully connected layer: Maps attention-weighted features to the prediction space; the fully connected layer maps the context vector to the prediction target, such as compressive strength and flexural strength.

[0135] Fully connected layer structure design:

[0136] z=ReLU(W1c+b1)Dense:2d→128

[0137] z = Dropout(z, p = 0.3)

[0138] y=W2z+b2 Dense:128→2

[0139] Output For the predicted compressive and flexural strengths.

[0140] Output layer: Outputs the predicted compressive and flexural strength values. The output layer maps the output of the fully connected layer to the final prediction result.

[0141] S4, the adaptive moment estimation optimization algorithm is used for model training, and its parameter update formula is as follows:

[0142] m t =β1m t-1 +(1-β1)g t ,

[0143]

[0144]

[0145] Where, m t v t Indicates the estimation of first and second moments. This is the corresponding bias correction, where β1 and β2 represent the exponential decay rate, and g t This represents the gradient at the current time step, η is the learning rate, which determines the step size for parameter updates, and λ is the weight decay coefficient. It is a small constant to prevent the denominator from being zero, θ t This represents the model parameters. Adam supports weight decay, which introduces a coefficient λ during parameter updates to regularize the model parameters and prevent overfitting. By combining the advantages of momentum and adaptive learning rate, the Adam optimizer can more effectively handle gradient sparsity and problems of different magnitudes, making it particularly suitable for training large-scale datasets and complex models.

[0146] For example, input data: recycled sand replacement rate: 30%–70%, polypropylene fiber content: 0.5%–1.5%.

[0147] Output result:

[0148] Parameter combination Predicted compressive strength (MPa) Predicted flexural strength (MPa) 50% recycled sand + 1.0% fiber 42.3±0.6 6.8±0.2 60% recycled sand + 0.8% fiber 38.7±0.5 7.1±0.3

[0149] Through the above structure and calculation process, the model can effectively capture long-term dependencies in time series data and focus on key features during the prediction process, thereby improving the accuracy and efficiency of prediction.

[0150] S4. Divide the dataset into training and testing sets, and use the AdamW adaptive moment estimation optimization algorithm for model training. AdamW is an efficient optimization algorithm that can effectively update model parameters during training and improve model performance.

[0151] Specifically, in this embodiment, S5, Bayesian optimization algorithm is used to tune hyperparameters, construct the objective function, and find the optimal combination of hyperparameters through Gaussian process modeling. Bayesian optimization is an efficient black-box optimization method that can balance the trade-off between exploration and exploitation in each iteration to find the optimal solution.

[0152] Specifically, in this embodiment, step S5 involves using a Bayesian optimization algorithm for hyperparameter tuning. The execution steps of the Bayesian optimization algorithm are as follows:

[0153] Initialization phase: Latin hypercube sampling is used to generate an initial sample set in the hyperparameter space, and the objective function value is evaluated. This method ensures that the initial samples are uniformly distributed in the hyperparameter space, thus providing a good starting point for the subsequent optimization process.

[0154] Gaussian process modeling: Based on the evaluated combinations of hyperparameters and their objective function values, a Gaussian process surrogate model is constructed, where the kernel function is a radial basis function (RBF). This model is used to predict the objective function values ​​of unevaluated combinations of hyperparameters. In this method, the kernel function uses a radial basis function (RBF) to capture the nonlinear relationships between hyperparameters.

[0155] Acquisition function optimization: The next hyperparameter combination to be evaluated is selected through the expected improvement function (EI), where the balancing parameter ξ is dynamically adjusted with the number of iterations. The EI balances exploration and exploitation during the optimization process; that is, it performs local searches near known well-performing regions while simultaneously exploring unknown regions to find potential optimal solutions. Furthermore, the parameter ξ (which controls the balance between exploration and exploitation) is dynamically adjusted with the number of iterations to adapt to the optimization needs at different stages.

[0156] Iterative Update: Evaluate the objective function value of the new hyperparameter combination, update the Gaussian process model, and check for early stopping conditions; evaluate the objective function value of the new hyperparameter combination, and add these new data points to the Gaussian process model to update the model's predictive power. In each iteration, the model recalculates the expected improvement of the objective function based on the new data points and selects the next optimal hyperparameter combination for evaluation.

[0157] Output: When the early stopping condition is met, the optimization terminates and the historically best hyperparameter combination is output. The optimization process terminates when the early stopping condition is met (e.g., reaching the maximum number of iterations or the objective function value no longer significantly improves), and the historically best hyperparameter combination is output. This combination is the optimal hyperparameter configuration found through Bayesian optimization.

[0158] Through the above steps, the Bayesian optimization algorithm can efficiently find the optimal combination of hyperparameters with fewer evaluation attempts, thereby improving model performance and training efficiency.

[0159] The objective function is given by the following formula:

[0160]

[0161] Where f(θ) represents the objective function, represents the loss value of the model under the current parameters θ plus the regularization term, N represents the number of samples, and y i Let x represent the true label value of the i-th sample. i Let represent the input value of the i-th sample, γ represent the regularization coefficient, ||W||2 represent the L2 norm, represents the square root of the sum of squares of the weight vector W, and f represents the bias term; the optimal combination of hyperparameters is found by modeling through a Gaussian process.

[0162] S6. Input the target performance indicators, and the trained ABiGRU model predicts the optimal mix ratio that meets the requirements. This model can predict the optimal mix ratio that meets the requirements based on the input performance indicators, thereby improving the performance and application effect of fiber-reinforced environmentally friendly cement mortar.

[0163] Specifically, in this embodiment, in step S6, after inputting the target performance index, the trained ABiGRU model predicts the optimal combination that meets the requirements. The specific operation is as follows:

[0164] Input the target performance indicators, along with the preset process parameter range, as model input. Users set target performance indicators according to actual needs, such as desired compressive strength and flexural strength values. These indicators will serve as the model's output targets, guiding the model to predict the optimal mix combination.

[0165] The trained ABiGRU model performs multi-objective predictions, outputting candidate formulation combinations that meet performance requirements and their confidence levels. The target performance indicators and preset process parameter ranges are used as model inputs, and the trained ABiGRU model performs multi-objective predictions. Based on the input performance indicators, the model predicts candidate formulation combinations that meet the requirements and their confidence levels.

[0166] Based on Pareto front analysis, the optimal ratio is selected from candidate combinations to ensure a balance among various performance indicators. The Pareto front is a set of non-dominated solutions, representing the optimal solution set that achieves an effective balance among multiple objectives.

[0167] Output results: The optimal mix ratio and its predicted performance curve are output for user decision-making reference. This method allows for the rapid identification of the optimal mix ratio that meets performance requirements, thereby improving the performance and application effect of fiber-reinforced environmentally friendly cement mortar.

[0168] Specifically, let the user-defined target performance metrics be: The constraint is: p∈[p min ,p max ],in, Let P = [p1, p2, ..., p6] represent the target compressive strength and flexural strength, respectively. P = [p1, p2, ..., p6] is a vector of process parameters (such as recycled sand replacement rate, fiber content, etc.), and its range is determined by engineering constraints [p...]. min ,p max ]limited.

[0169] The trained ABiGRU model is represented as a function f(P), and its predicted output is: Confidence assessment: Calculate the prediction variance σ using Monte Carlo Dropout. 2 : Where T is the number of Dropout samples (e.g., T = 100), and the confidence interval is...

[0170] Pareto front screening. Multi-objective optimization problem: Subject to p∈[p min ,p max Pareto optimal solution definition: solution set P * satisfy:

[0171]

[0172] Output the results. Optimal ratio combination P * Its predicted performance curve generation: Proportioning output:

[0173] Performance curves: plotting and The Pareto front (two-dimensional scatter plot), labeled y target The location.

[0174] Assuming user settings The model prediction results are as follows:

[0175] By using Pareto front analysis, setting the horizontal axis to compressive strength error and the vertical axis to flexural strength error, the red dot represents the optimal solution.

[0176] Through the above steps, users can efficiently predict the optimal mix proportions that meet specific performance indicators using a trained ABiGRU model. This method combines several advanced machine learning techniques, including feature selection, attention mechanisms, bidirectional GRU networks, the AdamW optimization algorithm, and Bayesian optimization, effectively improving the accuracy and efficiency of mix proportion prediction for fiber-reinforced environmentally friendly cement mortar.

[0177] Density, compressive strength, and flexural strength analysis.

[0178] Group order Recycled sand / % fiber / % density Flexural strength compressive strength 1 0 0 1867.6 4.2 18.9 2 0.3 0 1925.1 3.9 16.2 3 0.6 0 1884.6 3.5 17.5 4 1 0 1916.8 3.2 16.8 5 0 0.01 1874.4 3.9 15.1 6 0.3 0.01 1830.8 4.4 15.8 7 0.6 0.01 1859.1 3.9 16.3 8 1 0.01 1876.4 4.7 13.5 9 0 0.02 1882.9 4.3 16.4 10 0.3 0.02 1871.9 3.8 12.6 11 0.6 0.02 1880.6 4.1 16.6 12 1 0.02 1867.3 4.2 15.8 13 0 0.03 1882.0 3.5 13.2 14 0.3 0.03 1898.7 3.8 13.2 15 0.6 0.03 1861.1 3.9 13.3 16 1 0.03 1819.5 3.3 12.3

[0179] Preliminary analysis shows that the flexural strength is relatively more ideal when the fiber content is 1% and 2%; the flexural strength is most ideal when the recycled sand replacement rate is 0.3% and the compressive strength is most ideal when it is 0.6%.

[0180] Comprehensive analysis shows that when the fiber content is 1% and the recycled sand replacement rate is 6%, the density of the recycled mortar is 1859.1 kg / m³. 3 The compressive strength is 16.3 MPa (86.2% of the standard mix proportion) and the flexural strength is 3.9 MPa (92.9% of the standard mix proportion). Its comprehensive economic benefits are ideal and it meets the engineering performance requirements.

[0181] Figure 4 (a)-(d) are experimental data graphs of apparent density, compressive strength and flexural strength provided in an embodiment of this application.

[0182] Variation of apparent density of mortar under different recycled sand replacement rates, as follows Figure 4 As shown in (a), the variation of apparent density of mortar under different polypropylene fiber contents is as follows: Figure 4 As shown in (b), the results indicate that a 30% replacement rate of recycled sand leads to a peak apparent density, but the density decreases with increasing replacement rate. The incorporation of polypropylene fibers has a weak effect on density improvement; the apparent density is lowest at a fiber content of 1%, decreasing by only 2.8% compared to the baseline group.

[0183] The changes in flexural strength and compressive strength of mortar under different recycled sand replacement rates and polypropylene fiber content are as follows: Figure 4 (c) and Figure 4 As shown in (d), the results indicate that replacing natural sand with recycled sand has little effect on the flexural and compressive strength of recycled mortar. Compared with the baseline group with a replacement rate of 0%, the maximum decrease in flexural and compressive strength is 3.3% and 9%, respectively. The addition of fibers has a significant impact on the flexural and compressive strength of recycled mortar. The flexural strength initially increases and then decreases with the addition of fibers, while the compressive strength gradually decreases. Therefore, the compressive and flexural strengths of recycled mortar are relatively more ideal when the fiber content is 1% and 2%; the flexural strength is most ideal when the recycled sand replacement rate is 30%, and the compressive strength is most ideal when the replacement rate is 60%.

[0184] Example 2

[0185] like Figure 5 As shown in the figure, this application provides an architecture diagram of a machine learning-based fiber-reinforced environmentally friendly cement mortar optimal mix ratio prediction system, which is applied to the machine learning-based fiber-reinforced environmentally friendly cement mortar optimal mix ratio prediction system as described in Embodiment 1. It includes a data acquisition and preprocessing module 11, a feature screening module 12, a model building module 13, a model training and verification module 14, a model tuning module 15, and an optimal mix ratio prediction module 16.

[0186] The data acquisition and preprocessing module 11 is used to acquire experimental data of fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength and flexural strength, and to preprocess the data.

[0187] Feature selection module 12 is used to analyze the correlation between input and output variables using Pearson correlation coefficient, and to select highly correlated and strongly correlated features as model input.

[0188] Model building module 13 is used to build a prediction model of ABiGRU based on attention mechanism, the model including input layer, bidirectional GRU layer, attention layer, fully connected layer and output layer.

[0189] The model training and validation module 14 is used to divide the dataset into training and testing sets and to train the model using the AdamW adaptive moment estimation optimization algorithm.

[0190] Model tuning module 15 is used to perform hyperparameter tuning using the Bayesian optimization algorithm, construct the objective function, and find the optimal combination of hyperparameters through Gaussian process modeling.

[0191] The optimal ratio prediction module 16 is used to input the target performance index and predict the optimal ratio combination that meets the requirements through the trained ABiGRU model.

[0192] Figure 6 This is an electronic device provided in one embodiment of this application. For example... Figure 6 As shown, the electronic device includes at least the following components: processor 101 and memory 100, communication interface 103, and bus 102.

[0193] In this embodiment of the application, memory 100 is used to store executable instructions of processor 101, which, when configured to execute instructions, implements the method as described in the first aspect.

[0194] In embodiments of this application, a computer-readable storage medium includes instructions that instruct a device to perform the method as described in the first aspect. For example, the instructions instruct the device to perform... Figure 1 The method is shown in the process steps.

[0195] In one embodiment of this application, the program operating in the electronic device may be a program that controls a central processing unit (CPU) or similar device to achieve the functions of the above-described embodiments of the present invention (a program that enables the computer to function). Information processed by these devices is then temporarily stored in random access memory (RAM) during processing, and subsequently stored in various ROMs such as read-only memory (FlashROM) and hard disk drives (HDDs), and read, corrected, and written by the CPU as needed.

[0196] It should be noted that a portion of the electronic device described in the above embodiments can also be implemented using a computer. In this case, the program for implementing the control function can be recorded on a computer-readable recording medium, and the program recorded on the recording medium can be read into the computer and executed.

[0197] It should be noted that the term "computer" as used here refers to a computer built into an electronic device, employing hardware including an operating system and peripheral devices. Furthermore, "computer-readable recording media" refers to removable media such as floppy disks, magneto-optical disks, ROMs, and CD-ROMs, as well as storage devices such as hard drives built into a computer.

[0198] Furthermore, a "computer-readable recording medium" can include: a medium that dynamically stores a program for a short period of time, such as a communication line used when transmitting a program via a network such as the Internet or a communication line such as a telephone line; or a medium that stores a program for a fixed period of time, such as volatile memory inside a computer that serves as a server or client in this case. In addition, the aforementioned program can be a program used to implement the above-mentioned functions, or it can be a program that can implement the above-mentioned functions by combining with programs already recorded in the computer.

[0199] Furthermore, the electronic device in the above embodiments can also be implemented as an assembly (device group) composed of multiple devices. Each device constituting the device group can possess some or all of the functions or functional blocks of the electronic device in the above embodiments. As a device group, it is sufficient to have all the functions or functional blocks of the electronic device.

[0200] Those skilled in the art should recognize that the above embodiments are only used to illustrate this application and are not intended to limit this application. Any appropriate changes and variations made to the above embodiments within the essential spirit and scope of this application fall within the scope of protection claimed in this application.

Claims

1. A machine learning-based method for predicting the optimal mix proportion of fiber-reinforced eco-cement mortar, characterized by, The method includes: S1. Collect experimental data on fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength and flexural strength, and preprocess the data. S2. Use Pearson correlation coefficient to analyze the correlation between input and output variables, and select highly correlated and strongly correlated features as model inputs; S3. Construct a prediction model of ABiGRU based on attention mechanism, the model including input layer, bidirectional GRU layer, attention layer, fully connected layer and output layer; S4. Divide the dataset into training and test sets, and use the AdamW adaptive moment estimation optimization algorithm to train the model. S5. Use Bayesian optimization algorithm to tune hyperparameters, construct objective function, and find the optimal hyperparameter combination through Gaussian process modeling. S6. Input the target performance index, and use the trained ABiGRU model to predict the optimal combination that meets the requirements.

2. The method for predicting the optimal mix proportion of fiber reinforced eco-cement mortar based on machine learning according to claim 1, characterized in that, The data preprocessing in step S1 includes the following steps: Data normalization: The Min-Max normalization method is used to linearly transform the data to the [0,1] interval. The calculation formula is as follows: wherein X norm represents normalized data, X represents original input data, X max , X min respectively represent the maximum value, the minimum value in the data; Missing value handling: For missing values ​​in the experimental data, one of the following methods is used for imputation: Numerical features are filled with the mean or median; categorical features are filled with the mode. Processing discrete variables: Categorical variables are converted to numerical values ​​using One-Hot coding technology; Data standardization: Continuous features are standardized using Z-score, calculated as follows: where X std denotes the standardized data, μ denotes the mean of the feature, and σ denotes the standard deviation of the feature. Data cleaning: Outliers are identified and processed using box plots, and observations that significantly deviate from the normal range are removed using the 3σ principle or IQR method.

3. The method of claim 2, wherein the method is based on machine learning.

3. The method of claim 2, wherein the method is based on machine learning. The feature selection in step S2 specifically includes the following steps: Calculate the Pearson correlation coefficients between each input variable and the output variable, where the input variables include the recycled sand replacement rate and the polypropylene fiber content, and the output variables include compressive strength and flexural strength. The formula is as follows: Where r represents the Pearson correlation coefficient, n represents the sample size, X represents the input variable, and Y represents the output variable; Features are categorized and filtered based on the absolute value of the Pearson correlation coefficient. Select highly correlated and strongly correlated features as input features for the model; For the selected features, a correlation coefficient matrix heatmap is generated for visual analysis to verify the correlation between features.

4. The method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning according to claim 2, characterized in that, In step S3, the model includes: Input layer: Receives preprocessed feature data; Bidirectional GRU layer: Composed of forward GRU and backward GRU, it extracts time series features from the forward and backward directions respectively. Its calculation process is as follows: z t = σ(W z · [h t-1 , x t ] + b z ), r t = σ(W r · [h t-1 , x t ]+ b r ), Among them, z t This indicates updating the output of the gate, r t This indicates that the output of the reset door is being reset. H represents the candidate state. t w represents the hidden state at the current time step. z w r Let b represent the weight matrix. z b r b indicates the bias term, x t σ represents the input at the current time; The backward GRU uses the same structure to perform reverse computation; Attention layer: Calculates the importance weights of features at each time step. where e t denotes the attention score, a t denotes the attention weight, c denotes the context vector, v a , w a denotes the attention weight parameter, b a denotes the bias term of the attention mechanism, and T denotes the total number of time steps. Fully connected layer: maps attention-weighted features to the prediction space; Output layer: Outputs the predicted compressive and flexural strength values.

5. The method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning according to claim 4, characterized in that, S4, the adaptive moment estimation optimization algorithm is used for model training, and its parameter update formula is as follows: m t = β1m t-1 + (1 - β1)g t , Where, m t v t Indicates the estimation of first and second moments. This is the corresponding bias correction, where β1 and β2 represent the exponential decay rate, and g t This represents the gradient at the current time step, η is the learning rate, which determines the step size for parameter updates, and λ is the weight decay coefficient. It is a small constant to prevent the denominator from being zero, θ t Indicates model parameters.

6. The method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning according to claim 5, characterized in that, S5 involves using a Bayesian optimization algorithm for hyperparameter tuning. The execution steps of the Bayesian optimization algorithm are as follows: Initialization phase: Latin hypercube sampling is used to generate an initial sample set in the hyperparameter space, and the objective function value is evaluated; Gaussian process modeling: Based on the evaluated hyperparameter combinations and their objective function values, a Gaussian process surrogate model is constructed, where the kernel function adopts the radial basis function; Acquisition function optimization: Select the next combination of hyperparameters to be evaluated by the expected improvement function, where the balancing parameter ξ is dynamically adjusted with the number of iterations; Iterative update: Evaluate the objective function value of the new hyperparameter combination, update the Gaussian process model, and check for early stopping conditions; Output: When the early stopping condition is met, the optimization is terminated and the historical best hyperparameter combination is output.

7. The method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning according to claim 6, characterized in that, The objective function is given by the following formula: wherein f(θ) represents a target function, represents a loss value of the model under the current parameter θ plus a regularization term, N represents a sample number, y i represents a real label value of the i-th sample, x i represents an input value of the i-th sample, γ represents a regularization coefficient, ||W||2 represents an L2 norm, represents a square root of a sum of squares of the weight vector W, and f represents a bias term; Find the optimal combination of hyperparameters by modeling Gaussian processes.

8. The method for predicting the optimal mix proportion of fiber-reinforced environmentally friendly cement mortar based on machine learning according to claim 5, characterized in that, S6, inputting the target performance index, predicts the optimal combination of proportions that meets the requirements using the trained ABiGRU model, including: Input the target performance index and use it together with the preset process parameter range as model input; Multi-objective prediction is performed using the trained ABiGRU model, and candidate combination ratios that meet performance requirements and their confidence scores are output. Based on Pareto front analysis, the optimal ratio is selected from candidate combinations to ensure a balance among various performance indicators; Output the optimal ratio combination and its predicted performance curve for user decision-making reference.

9. A machine learning-based optimal mix proportion prediction system for fiber-reinforced environmentally friendly cement mortar, applied to the machine learning-based optimal mix proportion prediction method for fiber-reinforced environmentally friendly cement mortar as described in any one of claims 1 to 8, characterized in that, The system includes: The data acquisition and preprocessing module is used to collect experimental data of fiber-reinforced environmentally friendly cement mortar, including recycled sand replacement rate, polypropylene fiber content, fluidity, density, compressive strength and flexural strength, and to preprocess the data. The feature selection module is used to analyze the correlation between input and output variables using the Pearson correlation coefficient, and to select highly correlated and strongly correlated features as model input. The model building module is used to build a prediction model of ABiGRU based on the attention mechanism. The model includes an input layer, a bidirectional GRU layer, an attention layer, a fully connected layer, and an output layer. The model training and validation module is used to divide the dataset into training and test sets, and to train the model using the AdamW adaptive moment estimation optimization algorithm. The model tuning module is used to perform hyperparameter tuning using the Bayesian optimization algorithm, construct the objective function, and find the optimal hyperparameter combination through Gaussian process modeling. The optimal ratio prediction module is used to input target performance indicators and predict the optimal ratio combination that meets the requirements through a trained ABiGRU model.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a program that instructs the device to execute the machine learning-based optimal mix proportion prediction method for fiber-reinforced environmentally friendly cement mortar as described in any one of claims 1 to 8.

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