Multi-source solid waste cementitious material composition design method based on multi-objective collaborative optimization

Abstract

The application discloses a multi-source solid waste cementing material composition design method based on multi-target collaborative optimization, and belongs to the technical field of solid waste resource utilization and green building material. The method takes granulated blast furnace slag, fly ash, carbide slag and desulfurization gypsum as raw materials, firstly carries out a response surface test considering reliability, and adopts a neural network to construct a strength interval prediction multilayer perception machine model; simultaneously, an economic cost and carbon emission accounting model is established; subsequently, taking strength maximization, cost and carbon emission minimization as targets, an improved NSGA-III algorithm is used for multi-target global optimization to obtain a Pareto optimal solution set; finally, the CRITIC method is combined with the TOPSIS method to objectively decide and screen an optimal mixing ratio from the solution set. The application realizes collaborative optimization design of multi-source solid waste cementing material with high performance, low cost and low carbon emission.

Description

Technical Field

[0001] This invention belongs to the field of solid technology, and in particular relates to a method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization. Background Technology

[0002] With the continuous advancement of industrialization and urbanization in my country, the annual output of bulk industrial solid wastes such as granulated blast furnace slag, fly ash, carbide slag, and desulfurization gypsum remains high. If such solid wastes are stored haphazardly for a long time, they will not only occupy a large amount of land resources, but also easily cause a series of environmental problems such as soil pollution, water pollution, and dust pollution, while also causing a great waste of mineral resources. However, the targeted conversion of the above-mentioned multi-source industrial solid wastes into hydraulic cementitious materials to replace part or even all of the traditional silicate cement can significantly reduce the consumption of fossil energy and carbon dioxide emissions in the cement production process, help the building materials industry to achieve low-carbon transformation, and realize the large-scale, high-value-added resource utilization of industrial solid waste. It has environmental, economic, and social benefits and has become the core research direction in the field of comprehensive utilization of solid waste and green building materials.

[0003] Multi-source solid waste cementitious material systems are composed of various inert and potentially active solid waste components. Their hydration hardening mechanism, mechanical properties, and durability are highly dependent on the synergistic coupling effect between the components. Mix design is the core link that determines the comprehensive performance and application feasibility of the material. There are two major technical challenges in optimizing the mix design of this type of material: First, there are strong nonlinear interactions and hydration coupling effects among the multi-component raw materials. Traditional methods such as single-factor variable experiments and orthogonal experiments can only achieve local parameter optimization and cannot fully reveal the synergistic excitation and interaction inhibition mechanisms among the multi-components, making it difficult to cover the optimal range of the entire mix design space. Second, material optimization needs to simultaneously consider three core objectives: mechanical properties (compressive strength, setting time, etc.), economic cost, and environmental carbon emissions. Moreover, these three objectives have natural mutual constraints and conflicts, which is a typical high-dimensional multi-objective optimization problem. Single-dimensional optimization cannot meet the comprehensive application needs of practical engineering.

[0004] Currently, the mix design of existing solid waste-based cementitious materials mainly falls into two conventional technical paths: The first is the trial mixing method based on engineering experience and empirical formulas. This method relies on the industry experience of R&D personnel, requires a large number of repetitive indoor tests, has a long test cycle, high human and material costs, and is easily trapped in local optima due to random factors such as the operation of test personnel and the test environment, making it impossible to achieve global mix optimization; The second is the single-objective optimization method. Existing research mostly takes maximizing mechanical strength as the only optimization objective, ignoring the rigid constraints of economic cost and carbon emissions. The resulting mix design often has high raw material costs and insufficient carbon emission reduction effect, making it difficult to adapt to the economic and low-carbon requirements of large-scale engineering applications.

[0005] In recent years, some scholars have attempted to introduce multi-objective optimization algorithms to study the proportioning of solid waste cementitious materials. However, existing technologies still have many insurmountable defects, failing to meet the requirements for accurate, efficient, and reliable optimization: First, the experimental design process does not fully consider random errors and data dispersion in material preparation and performance testing, and does not incorporate reliability analysis and error correction mechanisms, resulting in insufficient accuracy and weak generalization ability of the constructed performance regression model, leading to low reliability of the optimization results; Second, the decision-making process for the Pareto optimal solution set obtained by multi-objective optimization lacks objective quantitative basis, often employing subjective weighting methods and experience-based judgment methods for scheme selection, resulting in highly subjective decision-making results with significant differences among different personnel, making it impossible to obtain standardized and universally applicable optimal proportions; Third, the environmental footprint accounting and economic cost calculation for the entire life cycle of materials are not systematic and comprehensive enough, and a unified optimization model with multi-objective collaborative constraints has not been established, resulting in a disconnect between optimization objectives and actual engineering needs, making it difficult to simultaneously address the three core demands of performance, cost, and low carbon emissions. Summary of the Invention

[0006] The purpose of this invention is to provide a design method for the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization, so as to solve the technical problems of poor reliability, single optimization objective, subjective decision-making, and difficulty in adapting to comprehensive engineering needs in the existing technology.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is a method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization, comprising the following steps:

[0008] S1: Taking multi-source solid waste components as the object, conduct a response surface experimental design considering reliability, prepare parallel specimens and obtain strength response data of different parallel specimens under each experimental ratio;

[0009] S2: Based on the intensity response data, an intensity interval prediction multilayer perceptron model is used with the intensity response data of different parallel specimens at each test point as the training target to learn the relationship between the input components and the intensity distribution, and output the mean and standard deviation of the intensity prediction.

[0010] S3: Establish an economic cost accounting model and a carbon emission accounting model for multi-source solid waste-based cementitious materials;

[0011] S4: Taking the maximization of the intensity of the multilayer perceptron model predicting the intensity range and the minimization of the cost and carbon emissions calculated by the economic cost accounting model and the carbon emission accounting model as the optimization objectives, a multi-objective evolutionary algorithm is used for global optimization to obtain the Pareto optimal solution set.

[0012] S5: Using the CRITIC method combined with the TOPSIS method, the optimal mix proportion of multi-source solid waste cementitious materials is objectively selected from the Pareto optimal solution set and determined as the final mix proportion after experimental verification.

[0013] Furthermore, the intensity interval prediction multilayer perceptron model described in step S2 is a feedforward neural network, and its structure and training process are as follows:

[0014] The input layer contains 4 nodes, corresponding to slag. fly ash calcium carbide slag Desulfurized gypsum Dosage;

[0015] The hidden layer is a single fully connected layer containing 32 neurons, and the activation function is a modified linear unit;

[0016] The output layer contains two nodes, which output the mean of the intensity prediction. and standard deviation Both the mean node and the standard deviation node use the modified linear unit activation function;

[0017] The model uses the Xavier initialization method to initialize the weights, and the biases are initialized to 0.

[0018] The data from each group of combinations obtained from the response surface methodology were randomly divided into training and validation sets at a ratio of 80% and 20%, respectively, and the input features were standardized.

[0019] During training, the optimizer used was Adam, with an initial learning rate of 0.001, a regularization coefficient of 0.0001, a batch size of 32, and a maximum number of training epochs of 1000.

[0020] After the model is trained, the mean of the output intensity prediction for a new input component dosage is... and standard deviation and take This serves as the 95% confidence interval for intensity prediction.

[0021] Furthermore, the economic cost accounting model described in step S3 is a unit quality economic cost calculation model:

[0022]

[0023] in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. f1 represents the unit cost coefficient for slag, fly ash, carbide slag, and desulfurized gypsum, and f2 represents the economic cost per unit mass.

[0024] The carbon emission accounting model is a carbon emission calculation model per unit mass:

[0025]

[0026] in f3 represents the carbon emission factor corresponding to slag, fly ash, carbide slag, and desulfurization gypsum, and f3 represents the carbon emission per unit mass.

[0027] Furthermore, the specific process of step S4 includes:

[0028] S401. The optimization objectives are to maximize the intensity prediction range output by the intensity range prediction multilayer perceptron model, minimize the unit mass cost output by the economic cost accounting model, and minimize the unit mass carbon emission output by the carbon emission accounting model, with the design range of each component as the constraint condition; real number encoding is used, and each individual is represented as a four-dimensional vector. ,in For slag usage, This refers to the amount of fly ash used. For the amount of calcium carbide slag used, The amount of desulfurized gypsum used; initial population Depend on It consists of individual components, each generated within its corresponding design interval:

[0029]

[0030] For the first The first individual Each decision variable component; For the first The lower bound of the values ​​of each decision variable; For the first The upper limit of the values ​​that a decision variable can take;

[0031] S402, For each individual Calculate the values ​​of the three objective functions:

[0032] Intensity range: Call the intensity range prediction multilayer perceptron model trained in step S2 and output the mean. and standard deviation Take the interval ;

[0033] Unit cost:

[0034] Carbon emissions per unit:

[0035] in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. For slag, fly ash, carbide slag, and desulfurization gypsum, the unit cost coefficients are: The carbon emission factors corresponding to slag, fly ash, carbide slag, and desulfurization gypsum;

[0036] S403. Perform interval non-dominated sorting and define interval possibility. :

[0037]

[0038] in They are intervals The lower limit and the upper limit They are intervals The lower limit and the upper limit;

[0039] individual Dominant Individual The conditions are: or or And it is strictly true for at least one objective; among which and Each represents an individual and individuals The intensity range, f2 is the economic cost per unit mass, and f3 is the carbon emission per unit mass; based on the above dominance relationship, the population... Perform a fast nondominated sort to obtain multiple nondominated levels. And assign rank to each individual ;

[0040] S404. Perform reference point correlation and use the mean of intensity predictions. As a representative value of intensity, and , Construct a three-dimensional target vector The Das-Dennis method is used to generate reference points on the three-dimensional unit hyperplane: For One target, each coordinate axis is divided Number of reference points , Symbols representing combinations;

[0041] S405. Perform adaptive normalization on the target value. ,in For the first The scaling factor of an objective during the normalization process. For the normalized first One target value; For the first One target value; The first ideal point Each component.

[0042] Furthermore, it also includes:

[0043] S406. Use tournament selection, prioritizing individuals with smaller non-dominant ranking ranks. If the ranks are the same, select individuals with smaller habitat counts at associated reference points.

[0044] Simulated binary crossover is used to generate offspring individuals. , :

[0045]

[0046] in It is generated by the following formula:

[0047]

[0048] In crossover or mutation operations, for the first Random numbers generated independently for each decision variable; , For the two parent individuals participating in the crossover, in the first... The values ​​that can be taken on each decision variable; To simulate the expansion factor used to control the similarity between offspring and parents in binary crossover, by and cross-distribution index Calculated; This indicates that in crossover or mutation operations, the first... Random numbers generated independently for each decision variable; The cross-distribution index;

[0049] Variation of individuals using polynomial variation:

[0050]

[0051] This represents the value of the j-th decision variable in the offspring individual after the mutation operation;

[0052] in

[0053]

[0054] It is the distribution index of variation; This is a perturbation factor used to control the amplitude of the polynomial variation. For the first The lower bound of the values ​​that a decision variable can take. For the first The upper limit of the values ​​that a decision variable can take; In the mutation operation, the first generation of the parent individual to be mutated is... Values ​​of decision variables;

[0055] S407, Population Merging and Next Generation Selection

[0056] parental population and offspring population merged into ,right Perform a non-dominated sort and populate the next generation of the population according to the following rules. :

[0057] Add to the non-dominated layer in sequence until a certain layer The addition of [something] will cause the population to exceed [something]. ;

[0058] for Individuals within the layer: Based on the niche count of the reference point, individuals that are associated with the reference point and have a small niche count are selected first to maintain population diversity;

[0059] S408, Termination

[0060] Reaching the maximum number of generations Alternatively, the process can stop when the population converges, and output the non-dominated solutions in the final population as the Pareto optimal solution set.

[0061] Furthermore, the multi-objective evolutionary algorithm described in step S4 adaptively adjusts the reference point every 50 generations based on the current Pareto front boundary. The adjustment method involves determining the current minimum value of each objective function based on the current non-dominated solution set during the evolution process. and the current maximum value Then, on the scaled hyperplane, the reference point is regenerated using the following formula. :

[0062]

[0063] in, The number of objective functions. The first in the current Pareto frontier The minimum value of an objective function. The first in the current Pareto frontier The maximum value of each objective function. Let the direction vector uniformly distributed on the unit hyperplane be the first... One portion, The first direction vector One component;

[0064] When performing global optimization, an adaptive crossover and mutation probability strategy is adopted.

[0065] Furthermore, the CRITIC method combined with the TOPSIS method described in step S5 for objective decision screening specifically includes: constructing a Pareto solution set as alternative solutions; using intensity, cost, and carbon emissions as evaluation indicators in a multi-attribute decision matrix; using the CRITIC method to determine the objective weights of each evaluation indicator; using the TOPSIS method to calculate the closeness between each alternative solution and the ideal solution, and selecting the solution with the highest closeness as the optimal combination ratio.

[0066] Furthermore, the CRITIC method for determining objective weights includes: performing homogenization and range normalization on the decision matrix; calculating the variability and conflict of each indicator, where variability is measured by standard deviation and conflict is measured by the correlation coefficient between indicators; and determining the weights based on the information content of each indicator. Calculate the weights, where For the first The standard deviation of each indicator For the first The first indicator and the first The correlation coefficients of the indicators.

[0067] Furthermore, the response surface methodology considering reliability described in step S1 is as follows: the experimental scheme is constructed using the Box-Behnken design method, with slag, fly ash, carbide slag, and desulfurized gypsum as raw materials. The design ranges for each component are 210-270g for slag, 30-90g for fly ash, 15-45g for carbide slag, and 15-45g for desulfurized gypsum. Three parallel specimens are prepared for each experimental mix.

[0068] Furthermore, the raw materials for the multi-source solid waste-based cementitious material include granulated blast furnace slag, fly ash, carbide slag, and desulfurized gypsum; the economic cost accounting model and carbon emission accounting model are unit mass cost model and unit mass carbon emission model.

[0069] Compared with existing technologies, the beneficial effects of this invention include: By implementing response surface modeling that considers reliability, this invention effectively solves the problems of insufficient consideration of experimental errors and inadequate model reliability in traditional methods. Specifically, in the experimental design stage, three parallel specimens were prepared for each mix design, thereby obtaining the mean and standard deviation information of the intensity response for each design. During modeling, a multi-task learning framework surrogate model was used to construct the intensity prediction model. This method enables the final response surface model to not only reflect the average law of intensity variation with composition but also to characterize the prediction fluctuations caused by uncertainties in material preparation and testing processes, providing a more solid and complete data foundation for subsequent optimization and decision-making.

[0070] This invention systematically solves the problems of previous methods' difficulty in balancing multiple conflicting objectives and decision-making reliance on subjective experience by integrating multi-objective global optimization and objective decision-making mechanisms. In the optimization phase, the method simultaneously aims to maximize intensity, minimize cost, and minimize carbon emissions, using a multi-objective evolutionary algorithm for global optimization. This yields a series of Pareto solutions that achieve optimal trade-offs across all three objectives, overcoming the limitations of single-intensity objective optimization. In the decision-making phase, an objective weighting method is used to determine the weights for intensity, cost, and carbon emissions. The calculations are based entirely on the dispersion and conflict of the data itself, eliminating the arbitrariness of subjective weighting. Subsequently, combined with multi-attribute decision-making methods such as TOPSIS, the optimal mix design is objectively selected from the Pareto solution set, providing a clear mathematical basis for the final decision.

[0071] The proposed method framework demonstrates excellent scalability and advanced integration advantages. It has been successfully applied not only to a quaternary solid waste system using slag, fly ash, carbide slag, and desulfurization gypsum as examples, but its core processes (reliability-considered experimental design, multi-objective modeling optimization, and objective decision-making) can be flexibly adapted to other multi-source solid waste systems and the combined optimization needs of different performance indicators. Furthermore, by introducing more advanced technical modules (such as the multi-task learning proxy model used in Example 2, the improved NSGA-III high-dimensional optimization algorithm, and the CRITIC-TOPSIS decision method), further improvements can be achieved in modeling accuracy, optimization capabilities in high-dimensional objective spaces, and decision rationality. This provides a superior and more forward-looking intelligent technical solution for the high-value utilization of industrial solid waste and the low-carbonization of the building materials industry. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a schematic diagram of the overall process of the method of the present invention;

[0074] Figure 2 This is a structural diagram of the MLP method of the present invention;

[0075] Figure 3 These are scatter plots of the machine learning intensity average prediction method of the present invention; wherein, (a) is the XGBoost intensity average prediction scatter plot, (b) is the MLP intensity average prediction scatter plot, (c) is the RF intensity average prediction scatter plot, and (d) is the SVR intensity average prediction scatter plot.

[0076] Figure 4 The above are scatter plots of standard deviation predictions for machine learning using the method of this invention; where (a) is a scatter plot of standard deviation predictions for XGBoost intensity, (b) is a scatter plot of standard deviation predictions for MLP intensity, (c) is a scatter plot of standard deviation predictions for RF intensity, and (d) is a scatter plot of standard deviation predictions for SVR intensity.

[0077] Figure 5 The following are Box-Behnken design proportions: (a) is the design proportion when the amount of desulfurized gypsum is 15g, (b) is the design proportion when the amount of desulfurized gypsum is 30g, and (c) is the design proportion when the amount of desulfurized gypsum is 45g.

[0078] Figure 6(a) is the response surface result of the effect of slag and fly ash dosage on the strength of cementitious materials; Figure 6(b) shows the response surface results of the effect of slag and carbide slag dosage on the strength of cementitious materials; Figure 6(c) is the response surface result of the effect of slag and desulfurized gypsum dosage on the strength of cementitious materials; Figure 6(d) shows the response surface results of the effect of fly ash and carbide slag dosage on the strength of cementitious materials. Figure 6(e) is the response surface result of the effect of fly ash and desulfurized gypsum dosage on the strength of cementitious materials; Figure 6(f) is the response surface result of the effect of the dosage of carbide slag and desulfurized gypsum on the strength of cementitious materials;

[0079] Figure 7 This is a schematic diagram of the Box-Behnken design proportions;

[0080] Figure 8 This is a comparison chart of the Pareto fronts obtained by the NSGA-II and improved NSGA-III algorithms; Detailed Implementation

[0081] 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 embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0082] This embodiment addresses the shortcomings of existing multi-source solid waste cementitious material mix design methods, such as insufficient reliability of experimental modeling, single optimization objective, strong subjectivity in scheme decision-making, and inability to consider the comprehensive engineering requirements of mechanical properties, economic costs, and environmental benefits. It provides a multi-objective collaborative optimization-based multi-source solid waste cementitious material composition design method, specifically a mix design method based on response surface methodology and intelligent optimization, to achieve multi-objective collaborative optimization and objective scientific decision-making.

[0083] In some specific implementation methods, such as Figure 1 The specific process of the multi-source solid waste cementitious material mix proportion optimization method is as follows:

[0084] S1. Response surface methodology considering reliability

[0085] Using four industrial solid wastes—granite slag (GGBS), fly ash (FA), calcium carbide slag (CS), and desulfurized gypsum (DG)—as raw materials, the design ranges for each component were determined: 210-270 g for slag, 30-90 g for fly ash, 15-45 g for calcium carbide slag, and 15-45 g for desulfurized gypsum. The center point ratio was 240 g for slag, 60 g for fly ash, 30 g for calcium carbide slag, and 30 g for desulfurized gypsum. The Box-Behnken design method was selected using Design-Expert software to construct the experimental scheme, resulting in 29 sets of experiments, including 16 factorial points, 8 pivot points, and 5 center points. Three parallel specimens were prepared for each experimental mix, with specimen dimensions of 40 mm × 40 mm × 40 mm. The specimen preparation was randomized to eliminate systematic errors. This implementation method repeatedly prepares parallel specimens, and the test response results contain errors. These data are used to build a prediction model, thus taking reliability into account. This is different from the traditional response surface methodology, where each ratio has only one response and no error.

[0086] S2. Intensity Response Surface Modeling and Reliability Analysis

[0087] Mechanical properties were tested on the specimens prepared by S1 to obtain the corresponding strength data under each mix proportion.

[0088] Optionally, a strength regression model for quaternary solid waste cementitious materials can be constructed based on a response surface methodology that considers reliability. Specifically, this involves: calculating the mean and standard deviation of the response values ​​at each test point using the test results of three parallel specimens; estimating the model parameters using weighted regression or generalized least squares, and fitting the model with the reciprocal of the standard deviation of each test point as the weight. This modeling method enables the regression model to not only fit the variation of the mean strength but also reflect the influence of experimental errors, ultimately yielding a response surface function of strength with respect to the four components, i.e., the strength regression model.

[0089] In response surface methodology (RSM) experiments, experimental errors at different test points often differ, exhibiting heteroscedasticity. Using ordinary least squares (OLS), which ignores heteroscedasticity, would assign equal weights to all test points. This implementation, however, by assigning different weights to different test points, more accurately reflects the reliability of the data, resulting in parameter estimates with smaller variances and improved model prediction accuracy. This implementation, by preparing three parallel specimens during the experimental design phase, allows for direct estimation of the error variance at each test point. Incorporating this variance information as weights into the model estimation effectively quantifies the reliability of the experiment and uses it to guide modeling, thereby making the resulting regression model more robust.

[0090] In some optional implementations, the weighted regression / generalized least squares process specifically includes:

[0091] 1. Model Setting

[0092] Assume there is a total Each test site The dosage of the four components is The corresponding intensity observation value is (Usually, the average of three parallel specimens is taken). This embodiment represents the relationship between strength and composition using a second-order response surface model:

[0093]

[0094] in, This is the constant term (intercept) of the regression model; For the first The linear regression coefficient of a component represents the linear effect of that component on the intensity alone; For the first Components and the first The interaction term of the components represents the nonlinear effect of the combined effect of the two factors or the square term; For the first The random error term for each test point; , For each test point The Components and the first Dosage of each component.

[0095] Write the model in matrix form:

[0096]

[0097] in for Response vector, for Design a matrix (containing constant terms, linear terms, interaction terms, and square terms). for Regression coefficient vector for Error vector.

[0098] 2. Heteroscedasticity of errors

[0099] Since three parallel specimens were prepared for each test point, the sample variance of the strength at that point can be calculated. It reflects the magnitude of the random error in the experiment at that point. Typically, the variances at different experimental points may be unequal, i.e., heteroscedasticity exists. This implementation assumes that the errors at each point are independent, therefore the error covariance matrix is ​​a diagonal matrix:

[0100]

[0101] in, For random error The variance, denoted here as ; Represent a The diagonal matrix whose first... The diagonal elements are All off-diagonal elements are 0. In linear algebra, diag means diagonal matrix and is a commonly used symbol in mathematics. Error vector The covariance matrix, Cov, is also a commonly used symbol in mathematics, representing covariance; For the first The variance of the error term at each test point is exist The specific value that time takes.

[0102] 3. Weighted Least Squares Estimation (WLS)

[0103] To handle heteroscedasticity, weighted least squares is used. The core idea is to assign smaller weights to points with larger variance and larger weights to points with smaller variance. Typically, the weights are chosen as follows: .because Unknown; this implementation uses sample variance. Estimate, i.e. .

[0104] The objective of weighted least squares estimation is to minimize the weighted sum of squared residuals:

[0105]

[0106] Written in matrix form:

[0107]

[0108] in This is a weighted diagonal matrix.

[0109] right Taking the derivative and setting it to zero, we obtain the closed-form solution of the weighted least squares estimate:

[0110]

[0111] T represents the transpose matrix.

[0112] 4. Generalized Least Squares Estimation (GLS)

[0113] Generalized least squares is a generalization of weighted least squares, which allows for the error covariance matrix to be... Let be any positive definite matrix (not limited to diagonal matrices). When Given that, the GLS estimate is:

[0114]

[0115] In this embodiment, since each test point is independent of the others, The matrix is ​​a diagonal matrix, in which case GLS is equivalent to WLS, and the weight matrix is... Therefore, the "generalized least squares method" mentioned in this embodiment specifically refers to weighted least squares in the case of diagonal covariance.

[0116] Establish an intensity regression model:

[0117] ;

[0118] in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. This corresponds to the strength coefficient; it characterizes different factors. The contribution of each strength coefficient to the strength of cementitious materials was determined through regression analysis of the experimental results.

[0119] Preferably, a machine learning model is used instead of a weighted regression or generalized least squares estimation model. To select the most suitable machine learning model for predicting the strength of multi-source solid waste cementitious materials in this embodiment, four models were constructed: Multilayer Perceptron (MLP), Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Regression (SVR). The same training and validation sets (29 sets of BBD experimental data, 23 training sets and 6 validation sets) were used. Prediction accuracy (root mean square error RMSE and coefficient of determination R²) was used as the evaluation index. After comprehensive comparison, the MLP model achieved the lowest RMSE and the highest R² on the validation set, and was therefore selected as the interval strength prediction model of this invention. The structure is shown in [see details]. Figure 2 The comparison results are shown in Table 1. Figure 3-4 As shown.

[0120] Table 1 Comparison of Machine Learning Model Parameters and Results

[0121]

[0122] In this embodiment, the intensity interval prediction multilayer perceptron (MLP) model directly uses the intensity values ​​of three parallel specimens at each test point (intensity response data determined by S1) as the training target to learn the relationship between the input components and the intensity distribution, and outputs the mean and standard deviation of the intensity prediction, thereby quantifying the prediction uncertainty.

[0123] In some preferred embodiments, the method for constructing the intensity interval prediction multilayer perceptron model is as follows:

[0124] 1. The model structure adopts a feedforward neural network, the structure of which is as follows (see Figure 2 ):

[0125] Input layer: Contains 4 nodes, corresponding to slag ( ), fly ash ( ), carbide slag ( ), desulfurized gypsum ( Dosage of ).

[0126] Hidden layer: A single fully connected layer containing 32 neurons, with ReLU activation function.

[0127] Output layer: Contains 2 nodes, each outputting the average intensity. ) and standard deviation ( The mean node uses the ReLU activation function, and the standard deviation node uses the ReLU activation function.

[0128] 2. Model parameter initialization uses the Xavier initialization method to initialize the weights of the fully connected layer, and the bias is initialized to 0.

[0129] 3. Training Data Preparation

[0130] The 29 sets of experimental data were randomly divided into a training set (23 sets, approximately 80%) and a validation set (6 sets, approximately 20%). Input features (the amounts of the four components) were standardized. The target value for each sample was the mean and standard deviation of the strength of three parallel specimens at that mix ratio (denoted as ). and Let the first... The original values ​​of each feature in all samples are: ( Then the standardized formula is:

[0131]

[0132] Standardized features As input to a neural network. : No. Sample standard deviation of each feature (unbiased estimate); : No. The arithmetic mean of the features across all 29 samples; : No. In the nth sample The standardized value of each feature

[0133] 4. Loss Function

[0134] The mean squared error (MSE) loss is used to calculate the errors in mean prediction and standard deviation prediction, respectively:

[0135]

[0136] in For batch size, and The mean and standard deviation of the model predictions. and These are the measured mean and standard deviation.

[0137] 5. Optimization Algorithm

[0138] See Table 1.

[0139] 6. Training Process

[0140] In each round of training, the training set data is input into the model in batches, and forward propagation is performed to obtain... and Then, the negative log-likelihood loss is calculated, and the network parameters are updated through backpropagation.

[0141] 7. Predictive Applications

[0142] For newly input component dosages, the model directly outputs the mean of the intensity predictions. and standard deviation .Pick As a point estimate of the intensity, take As an interval of uncertainty regarding the intensity (approximately 95% confidence interval).

[0143] S3, Economic Costs and Carbon Emission Modeling

[0144] Market research was conducted on four types of solid waste materials to obtain the procurement, transportation, and pretreatment costs per unit mass of materials, and a unit mass economic cost calculation model was established.

[0145]

[0146] in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. This represents the corresponding unit cost coefficient.

[0147] Simultaneously, based on the life cycle assessment method, the carbon emission factors of each solid waste material from generation to utilization are calculated, and a carbon emission calculation model per unit mass is established:

[0148]

[0149] in This represents the corresponding carbon emission factor.

[0150] S4. Multi-objective global optimization based on interval NSGA-III

[0151] Using the intensity interval prediction multilayer perceptron model obtained in step S2, the unit mass cost function and the unit mass carbon emission function obtained in step S3 as objective functions, a multi-objective optimization model is established:

[0152] strength The mean value is obtained from the intensity interval prediction multilayer perceptron model. and standard deviation Take the interval (Approximate 95% confidence interval)

[0153] Minimize cost Unit quality cost function

[0154] Minimize carbon emissions Carbon emission function per unit mass

[0155] The constraints are the design ranges for each component. An improved interval NSGA-III algorithm is used for global optimization. Based on the standard NSGA-III, this algorithm introduces interval dominance relations to handle intensity uncertainty and retains a reference point mechanism to maintain the population diversity of the high-dimensional target space, thereby obtaining a uniformly distributed Pareto optimal front solution set.

[0156] In some optional implementations, the multi-objective evolutionary algorithm specifically proceeds as follows:

[0157] 1. Encoding and Initialization

[0158] Using real-number encoding, each individual represents a mixing ratio scheme, i.e., a four-dimensional vector (i.e., the amount of each material used). ,in For slag usage, This refers to the amount of fly ash used. For the amount of calcium carbide slag used, This refers to the dosage of desulfurized gypsum. Initial population. Depend on It consists of individual components, each generated within its corresponding design interval:

[0159]

[0160] For the first The first individual Each decision variable component; This is an index symbol, representing the sequence number of an individual in the population. ( (for population size) The index symbol represents the dimension number of the decision variable (material composition). These correspond to slag, fly ash, carbide slag, and desulfurized gypsum, respectively. For the first The lower bound of the values ​​of each decision variable; For the first The upper limit of the values ​​of each decision variable; in this embodiment , . Representing an interval A continuous uniform distribution on the surface, the symbol "U" usually represents a uniform distribution.

[0161] 2. Fitness Evaluation

[0162] For each individual Calculate the values ​​of the three objective functions:

[0163] Intensity range: Call the range prediction model trained in step S2 and output the mean. and standard deviation Take the interval ;

[0164] Unit cost

[0165] Unit carbon emissions

[0166] 3. Interval Non-Dominant Sort

[0167] Define the probability of an interval: for two intervals and ,calculate Greater than Possibility:

[0168]

[0169] in They are intervals The lower and upper limits, They are intervals The lower and upper limits.

[0170] when At that time, the interval is considered Superior The likelihood is greater.

[0171] Interval dominance relationship: Individual Dominant Individual (recorded as) If and only if:

[0172] For intensity targets: (Right now The strength is not less than The probability is no less than 50%);

[0173] and : Representing individuals and individuals The intensity range.

[0174] Regarding costs: ;

[0175] Regarding carbon emissions: ;

[0176] And it is strictly true for at least one objective: or or .

[0177] Based on the aforementioned dominance relationship, the population Perform a fast nondominated sort to obtain multiple nondominated levels. And assign rank to each individual ( Indicates the first frontier; the larger the value, the worse the performance.

[0178] 4. Reference point association (NSGA-III)

[0179] To associate an individual with a reference point, the midpoint of the intensity interval is used. (i.e., the mean) is used as a representative value of strength, in relation to cost. Carbon emissions Construct a three-dimensional target vector .

[0180] Reference point generation: Generated on the 3D unit hyperplane using the Das-Dennis method. A uniformly distributed reference point. For One target, each coordinate axis is divided Number of reference points This implementation method takes... ,but .

[0181] Adaptive normalization:

[0182] Calculate the ideal point of all individuals in the current population. ;

[0183] The midpoint of the strength of all individuals in the current population. The minimum value;

[0184] The minimum cost per unit mass of all individuals in the current population;

[0185] : The minimum carbon emissions per unit mass of all individuals in the current population.

[0186] The intercept is obtained by calculating the extreme points on each target axis using the ASF function. ;

[0187] Normalized target value: , .

[0188] Association operation: Calculate the Euclidean distance between the normalized midpoint vector of each individual and each reference point, associate it with the nearest reference point, and record the niche count of that reference point (i.e., the number of individuals associated with that reference point).

[0189] in ( ) is the first The scaling factor of an objective during the normalization process. For the normalized first One target value; For the first One target value; The first ideal point Each component

[0190] 6. Selection, crossover, and mutation

[0191] Selection: Tournament selection is used. For NSGA-III, individuals with lower ranks are preferred; if ranks are the same, individuals with lower associated reference point counts are selected.

[0192] Crossover: Simulated binary crossover (SBX) is used, and the offspring individuals are generated as follows:

[0193]

[0194] in It is generated by the following formula:

[0195]

[0196] In crossover or mutation operations, for the first Each decision variable generates an independently generated random number, which follows the... A uniform distribution on the surface is denoted as , For the two parent individuals participating in the crossover (denoted as...) and ) in the The values ​​that can be taken on each decision variable; To simulate the expansion factor used to control the similarity between offspring and parents in binary crossover, by and cross-distribution index Calculated; This indicates that in crossover or mutation operations, the first... Each decision variable generates an independently generated random number, which follows the... Uniform distribution on; The cross-distribution index is set to 20 in this implementation.

[0197] Mutation: Polynomial mutation is used, resulting in the following individual:

[0198]

[0199] in

[0200]

[0201] The variation distribution index (set to 20 in this implementation); This is the perturbation factor used to control the amplitude of the polynomial variation, derived from... and variation distribution index Calculated. For the first The lower bound of the values ​​of each decision variable; For the first The upper limit of the values ​​that a decision variable can take; In the mutation operation, the first generation of the parent individual to be mutated is... Values ​​of decision variables.

[0202] 7. Population Merging and Next Generation Selection

[0203] parental population and offspring population merged into (scale ),right Perform a non-dominated sort and populate the next generation of the population according to the following rules. :

[0204] Add to the non-dominated layer in sequence until a certain layer The addition of [something] will cause the population to exceed [something]. .

[0205] for Individuals within the layer: Based on the niche count of the reference point, individuals that are associated with the reference point and have a small niche count are selected first to maintain population diversity.

[0206] 8. Termination Conditions

[0207] Reaching the maximum number of generations (In this implementation, the number of generations is set to 400) or the process stops when the population converges (e.g., the change in the Pareto front is less than the threshold), and the non-dominated solutions in the final population are output as the Pareto optimal solution set.

[0208] Regarding adaptive crossover and mutation probabilities, the crossover probability in the standard algorithm... and mutation probability A fixed value cannot adapt to the needs of different evolutionary stages. This implementation method adopts an adaptive strategy, dynamically adjusting according to the population's evolutionary state:

[0209] Early evolution (first 100 generations): Use a higher crossover probability. and higher mutation probability This enhances global search capabilities and avoids getting trapped in local optima.

[0210] Mid-evolutionary stage (generations 100-250): Gradually reduce parameters. , Balance exploration and development.

[0211] Late evolution (after 250 generations): further reduced to , This accelerates convergence.

[0212] For adaptive generation of reference points in NSGA-III, the fixed distribution of reference points in standard NSGA-III may lack flexibility in regions where the target range varies drastically. This implementation introduces adaptive reference point adjustment: every 50 generations, the reference points are recalculated based on the current Pareto front boundary, matching the reference point distribution to the front shape and improving the uniformity of solution distribution. Specific method:

[0213] Calculate the minimum value of each objective in the current nondominated solution. and maximum value .

[0214] Regenerate the reference point on the scaled hyperplane. :

[0215]

[0216] in, This represents the number of objective functions. In this implementation... (Strength, Cost, GWP); The index of the objective function. Here, it serves as the summation index, which differs from the independent variable dimension index in the aforementioned response surface model (the latter ranges from 1 to 4). Indicates the number of calculations currently in progress. The target sequence number corresponding to each reference point component. The left side of the formula It is the first The coordinates of the reference point in each target direction; The first in the current Pareto frontier The minimum value of an objective function; The first in the current Pareto frontier The maximum value of each objective function; Let the direction vector uniformly distributed on the unit hyperplane be the first... One portion, Let the direction vector uniformly distributed on the unit hyperplane be the first... Each component.

[0217] S5. Objective decision-making based on CRITIC-TOPSIS

[0218] A multi-attribute decision matrix is ​​constructed, using the Pareto solution set obtained in step S4 as candidate solutions, with intensity, cost, and carbon emissions as evaluation indicators. An objective weighting method is used to determine the weights of each indicator. Subsequently, a multi-attribute decision method is used to calculate the closeness of each candidate solution to the ideal solution, sorting them by closeness and selecting the solution with the highest closeness as the optimal mix ratio. Preferably, the objective weighting method is the CRITIC method. In this embodiment, CRITIC combined with TOPSIS (multi-attribute decision method) considers both indicator variability and conflict, thus more comprehensively reflecting the importance of the indicators. It should be noted that the Pareto optimal frontier solution set mentioned in S4 is a set of non-dominant feasible solutions obtained through the NSGA-III algorithm, where each solution corresponds to a candidate mix ratio. The ideal solution, however, is a theoretical solution composed of the optimal values ​​of each evaluation indicator; it is not an actual existing mix ratio. The reference point is the maximum value of each column of indicators extracted from the current Pareto solution set.

[0219] In some optional implementations, the specific process of determining the weights of each indicator using the improved objective weighting method (CRITIC-TOPSIS method) of this implementation is as follows: Assume there are a total of There are several alternative solutions (Pareto solutions). One evaluation index (in this implementation method) (Intensity, cost, carbon emissions). The original decision matrix is: ,in Indicates the first The first scheme Individual indicator values.

[0220] Step 1: Indicator alignment and normalization

[0221] For positive indicators (strength), range normalization is used:

[0222]

[0223] For negative indicators (cost, carbon emissions), reverse range normalization is used:

[0224]

[0225] After normalization And all of them are positive indicators (the higher the better); For the first The first scheme The values ​​of each indicator after range normalization are dimensionless and range from [value range]. For positive indicators ( ), The closer to 1, the higher the intensity; for negative indicators ( ), The closer to 1, the lower the cost or GWP.

[0226] Step 2: Calculate the standard deviation of the index

[0227]

[0228] in The larger the standard deviation, the greater the difference between the options within that indicator, and the richer the information.

[0229] Step 3: Calculate the correlation coefficient matrix between the indicators

[0230]

[0231] Correlation coefficient Reflects the indicators With indicators The degree of correlation (positive or negative).

[0232] Step 4: Calculate the information content of the indicators

[0233] No. The amount of information contained in each indicator Defined as:

[0234]

[0235] in Indicates the first The conflict (lack of correlation) between this indicator and other indicators. If this indicator is highly correlated with other indicators (…), then… If the value is close to 1, the conflict is small and the amount of information is reduced.

[0236] Step 5: Determine the weights

[0237]

[0238] Weight satisfy and .

[0239] In some optional implementations, the multi-attribute decision-making method calculates the closeness of each alternative to the ideal solution as follows:

[0240] Step 1: Construct the weighted normalized matrix

[0241] Normalized matrix With weight vector Multiplying them together yields the weighted normalized matrix. :

[0242]

[0243] For the first The weight of each indicator, v ij It contains the data in the weighted normalized matrix, which is the result matrix obtained by multiplying the normalized matrix by the weight vector. For the first The first scheme The values ​​of each index after range normalization are dimensionless.

[0244] Step 2: Determine the positive and negative ideal solutions

[0245] Positive Ideal Solution Composed of the maximum values ​​of each indicator:

[0246] Negative ideal solution It consists of the minimum values ​​of each indicator:

[0247] Step 3: Calculate the Euclidean distance between each solution and the positive and negative ideal solutions.

[0248] No. Distance between each solution and the ideal solution for:

[0249]

[0250] Distance from the negative ideal solution for:

[0251]

[0252] Step 4: Calculate the relative proximity

[0253] No. The relative similarity of the two schemes for:

[0254]

[0255] Obviously , The closer the value is to 1, the better the solution.

[0256] Step 5: Sorting the Schemes

[0257] according to Sort the solutions from largest to smallest and select... The largest possible combination is taken as the optimal mix ratio.

[0258] S6. Experimental verification of the optimal mix proportion

[0259] Specimens were prepared according to the optimal mix proportion selected in step S5, and strength tests were conducted. The measured values ​​were then compared with the predicted values ​​from the model in step S2 for verification. If the relative error was within an acceptable range, the mix proportion was confirmed as the final optimized result; if the error exceeded the range, experimental data were supplemented, the response surface model was updated, and optimization was performed again.

[0260] Comparative approach (basic scheme: weighted regression + NSGA-II + entropy-weighted TOPSIS):

[0261] 1. Response surface methodology considering reliability

[0262] Four types of industrial solid waste were selected as raw materials: blast furnace slag from a steel plant, fly ash from a coal-fired power plant, calcium carbide slag from a chemical plant, and desulfurization gypsum. The design ranges for each component were determined as follows: blast furnace slag 210-270g, fly ash 30-90g, calcium carbide slag 15-45g, and desulfurization gypsum 15-45g, with a center point ratio of 240g:60g:30g:30g. The experimental scheme was designed using Design-Expert software, and a total of 29 sets of experiments were conducted, including 16 factorial points, 8 axis points, and 5 center points. (See...) Figure 5 (a)~(c). Three specimens with dimensions of 40mm×40mm×40mm were prepared for each group of formulations, molded in random order, and tested for compressive strength after standard curing for 28 days.

[0263] Table 2. Response surface methodology and response test results

[0264]

[0265] 2. Intensity Response Surface Modeling and Reliability Analysis

[0266] Using the mean data in Table 2 and considering the standard deviation of each test point, a quadratic polynomial response surface model was fitted using the weighted least squares method (with weights taken as the reciprocals of the standard deviations). Figures 6(a) to 6(f) show the results of the response surface considering reliability, reflecting the changing patterns of the effects of slag, fly ash, carbide slag, and desulfurized gypsum dosage on the strength of the cementitious material. Regression analysis was performed using Design-Expert software to obtain the regression equations for the actual variables of strength regarding slag (x1), fly ash (x2), carbide slag (x3), and desulfurized gypsum (x4):

[0267] ;

[0268] Analysis of variance (ANOVA) showed that the model's coefficient of determination (R²) > 0.95, and the lack-of-fit term was not significant, indicating a good model fit. The ANOVA results are shown in Table 3. A comparison between the model's predicted values ​​and the measured values ​​is shown in [Table 3]. Figure 7 As shown.

[0269] Table 3. ANOVA analysis of the weighted response surface model

[0270]

[0271] 3. Economic Cost and Carbon Emission Analysis

[0272] Cost parameters for four solid waste materials were obtained through market research: slag 0.15 yuan / kg, fly ash 0.08 yuan / kg, calcium carbide slag 0.10 yuan / kg, and desulfurization gypsum 0.12 yuan / kg. Carbon emission factors were calculated based on life cycle assessment methods and database analysis: slag... fly ash calcium carbide slag Desulfurized gypsum The life cycle inventory is shown in Table 4, from which the unit mass cost function and carbon emission function are established.

[0273] Unit quality cost function:

[0274] Table 4 Lifecycle List

[0275]

[0276] Carbon emission function per unit mass:

[0277] in The unit is g.

[0278] 4. Multi-objective global optimization based on NSGA-II

[0279] Using the intensity response surface model from step 2 and the cost function and carbon emission function from step 3 as objectives, an NSGA-II algorithm program was written on the MATLAB platform. The population size was set to 200, crossover probability to 0.8, mutation probability to 0.1, and maximum number of generations to 400. Running the algorithm yielded a Pareto front consisting of 200 non-dominated solutions. Figure 8 ( Figure 8 This is a comparison chart of the Pareto fronts obtained by the NSGA-II / NSGA-III algorithms. The chart is a three-dimensional scatter plot, showing the Pareto front solution sets obtained by performing multi-objective optimization on the three objectives of intensity, cost, and carbon emissions using the NSGA-II and NSGA-III algorithms respectively. It covers the trade-off space of intensity 18-32 MPa, cost 0.125-0.140 yuan / kg, and carbon emissions 0.017-0.021 kgCO2-eq / kg.

[0280] 5. Objective decision-making based on entropy weight TOPSIS

[0281] A decision matrix was constructed for the 200 options in the Pareto solution set, and range normalization was used to process the index data. The entropy values ​​of each index were calculated: intensity entropy 0.83, cost entropy 0.91, and carbon emission entropy 0.89. Weights were calculated based on the entropy values, resulting in an intensity weight of 0.38, a cost weight of 0.29, and a carbon emission weight of 0.33. The TOPSIS method was used to calculate the proximity of each option, and the options were sorted from highest to lowest proximity. The option with the highest proximity was selected as the optimal mix design. The results are as follows: .

[0282] Under this scheme, the dosage of each component is substituted into the actual strength regression equation:

[0283] .

[0284] Unit cost calculation:

[0285] ;

[0286] Carbon emissions per unit:

[0287] ;

[0288] 6. Experimental verification of the optimal mix ratio

[0289] Three parallel specimens were prepared again according to the above optimal mix ratio. The measured 28-day compressive strengths were 30.8 MPa, 31.5 MPa and 31.2 MPa, respectively, with an average of 31.2 MPa. The relative error between the measured value and the model prediction of 31.3 MPa was 0.32%, which verified the reliability of the optimization results.

[0290] Example (Preferred solution: Multi-task learning agent model + NSGA-III + CRITIC-TOPSIS):

[0291] 1. Response surface methodology considering reliability: Similar to the comparative example, the data in Table 2 are used.

[0292] 2. Intensity Response Surface Modeling and Reliability Analysis: The most suitable machine learning model for predicting the intensity of multi-source solid waste cementitious materials was selected. Four models were constructed: Multilayer Perceptron (MLP), Extreme Gradient Boosting (XGBoost), Random Forest (RF), and Support Vector Regression (SVR). The same training and validation sets (29 sets of BBD experimental data, 23 training sets and 6 validation sets) were used. Prediction accuracy (Root Mean Square Error (RMSE) and Coefficient of Determination (R²)) were used as evaluation metrics. After comprehensive comparison, the MLP model achieved the lowest RMSE and the highest R² on the validation set. Therefore, the MLP model was selected for interval intensity prediction. The structure is shown below. Figure 2 The comparison results are shown in Table 1. Figure 3 (a)-(d) and Figure 4 As shown in (a) and (d).

[0293] A multilayer perceptron (MLP) model for intensity interval prediction was adopted to replace traditional response surface methodology. A single-hidden-layer (32 neurons, ReLU activation function) feedforward neural network was constructed. The input layer consisted of four component parameters, and the output layer had two nodes, outputting the mean μ and standard deviation σ (ReLU activation) of the intensity prediction, respectively. The measured mean and standard deviation of three parallel specimens at each test point were used as training objectives. The mean squared error (MSE) loss function was used, and the Adam optimizer (learning rate 0.001) was employed for 1000 training epochs. Input features were standardized. The final model can output a 95% confidence interval for intensity prediction (…). ), quantifying the uncertainty of prediction.

[0294] 3. Economic Costs and Carbon Emissions Analysis: Same as the comparison.

[0295] 4. Multi-objective global optimization based on NSGA-III: An improved interval-based NSGA-III algorithm is used to optimize three objectives: intensity (interval), cost, and carbon emissions. The intensity objective for each individual is defined as an interval... (95% confidence interval) indicates that cost and carbon emissions are deterministic single values. Non-dominated ordination is dominated by interval probability (comparison probability P>0.5 for intensity intervals determines superiority). Reference point association uses the midpoint of the intensity interval (i.e., the mean μ) for normalization and association. Other mechanisms (reference point generation, niche preservation, adaptive crossover mutation, and adaptive adjustment of reference points) are consistent with the standard NSGA-III. The population size is set to 200, reference points are generated using the Das-Dennis method, and the maximum number of generations is 400. The Pareto front is obtained; see [link to Pareto front]. Figure 8 Compared with the comparative NSGA-II results, the Pareto front obtained by NSGA-III is more uniform in distribution and has a wider coverage (intensity 17-33 MPa, cost 0.124-0.142 yuan / kg, carbon emissions...). This demonstrates its advantages in high-dimensional multi-objective optimization problems.

[0296] 5. Objective Decision Making Based on CRITIC-TOPSIS: After constructing the decision matrix, the CRITIC method is used to determine the weights of the indicators. The CRITIC method considers not only the variability (standard deviation) of the indicators but also the conflict between them (correlation coefficient). The calculated weights are: intensity 0.40, cost 0.32, and carbon emission 0.28 (compared to the entropy weight method of the comparative method, the CRITIC method, considering the stronger conflict between cost and carbon emissions, results in a more reasonable weight allocation). Subsequently, the TOPSIS method is used to calculate the closeness of each option, ranking and selecting the optimal option. The results are as follows: .

[0297] Under this scheme, the intensity prediction value f1 (output of the multi-task learning model) is 31.2 MPa.

[0298] Unit cost calculation:

[0299] f2 = (0.15×240 + 0.08×60 + 0.10×30 + 0.12×30) / 360 = (36.0 + 4.8 + 3.0 + 3.6) / 360 = 47.4 / 360 = 0.1317 yuan / kg

[0300] Carbon emissions per unit:

[0301]

[0302] 6. Experimental verification of the optimal mix ratio: Three parallel specimens were prepared according to the optimal mix ratio. The measured 28-day compressive strengths were 31.4 MPa, 31.0 MPa and 31.8 MPa, respectively, with an average of 31.4 MPa. The relative error between the average and the predicted value of 31.2 MPa by the multi-task learning model was 0.64%, indicating that the model is reliable.

[0303] Figure 8 The optimal solution in the comparative model is marked with a green pentagram (strength 31.3 MPa, cost 0.1322 yuan / kg, carbon emissions). The optimal solution of the embodiment (strength 31.2 MPa, cost 0.1317 yuan / kg, carbon emissions) is marked with an orange pentagram. Both optimal solutions are located in the knee region of the Pareto front, achieving a good balance among the three objectives. To quantitatively evaluate the beneficial effects of different embodiments of this implementation, a comprehensive comparison of the comparative scheme (basic solution) and the implementation scheme (improved solution) is conducted, and the results are shown in Table 5.

[0304] Table 5. Comparison of optimal mix proportions and performance obtained by different methods.

[0305]

[0306] Note: The overall closeness score is calculated using the TOPSIS method based on three indicators: intensity, cost, and carbon emissions. A higher value indicates better overall performance. The prediction RMSE is the root mean square error of the model's predictions on the validation set.

[0307] As can be seen from Table 5:

[0308] 1. The comparative study achieved a good balance between the three objectives of intensity, cost, and carbon emissions, with an overall closeness of 0.87.

[0309] 2. The embodiment further improves model accuracy (RMSE reduced by 31%), optimizes a lower cost and lower carbon emission solution, and achieves an overall similarity of 0.94, which is 8% higher than the comparison ratio, fully demonstrating the superiority of this embodiment.

[0310] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, the system embodiments are basically similar to the method embodiments, so the description is relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0311] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization, characterized in that, Includes the following steps: S1: Taking multi-source solid waste components as the object, conduct a response surface experimental design considering reliability, prepare parallel specimens and obtain strength response data of different parallel specimens under each experimental ratio; S2: Based on the intensity response data, an intensity interval prediction multilayer perceptron model is used with the intensity response data of different parallel specimens at each test point as the training target to learn the relationship between the input components and the intensity distribution, and output the mean and standard deviation of the intensity prediction. S3: Establish an economic cost accounting model and a carbon emission accounting model for multi-source solid waste-based cementitious materials; S4: Taking the maximization of the intensity of the multilayer perceptron model predicted by the intensity interval, and the minimization of the cost and carbon emissions calculated by the economic cost accounting model and the carbon emission accounting model as the optimization objectives, a multi-objective evolutionary algorithm is used for global optimization to obtain the Pareto optimal solution set. S5: Using the CRITIC method combined with the TOPSIS method, the optimal mix proportion of multi-source solid waste cementitious materials is objectively selected from the Pareto optimal solution set and determined as the final mix proportion after experimental verification.

2. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The intensity interval prediction multilayer perceptron model mentioned in step S2 is a feedforward neural network, and its structure and training process are as follows: The input layer contains 4 nodes, corresponding to slag. fly ash calcium carbide slag Desulfurized gypsum Dosage; The hidden layer is a single fully connected layer containing 32 neurons, and the activation function is a modified linear unit; The output layer contains two nodes, which output the mean of the intensity prediction. and standard deviation Both the mean node and the standard deviation node use the modified linear unit activation function; The model uses the Xavier initialization method to initialize the weights, and the biases are initialized to 0. The data from each group of combinations obtained from the response surface methodology were randomly divided into training and validation sets at a ratio of 80% and 20%, respectively, and the input features were standardized. During training, the optimizer used was Adam, with an initial learning rate of 0.001, a regularization coefficient of 0.0001, a batch size of 32, and a maximum number of training epochs of 1000. After the model is trained, the mean of the output intensity prediction for a new input component dosage is... and standard deviation and take This serves as the 95% confidence interval for intensity prediction.

3. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The economic cost accounting model mentioned in step S3 is a unit quality economic cost calculation model: ； in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. f1 represents the unit cost coefficient for slag, fly ash, carbide slag, and desulfurized gypsum, and f2 represents the economic cost per unit mass. The carbon emission accounting model is a carbon emission calculation model per unit mass: ； in f3 represents the carbon emission factor corresponding to slag, fly ash, carbide slag, and desulfurization gypsum, and f3 represents the carbon emission per unit mass.

4. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The specific process of step S4 includes: S401. The optimization objectives are to maximize the intensity prediction range output by the intensity range prediction multilayer perceptron model, minimize the unit mass cost output by the economic cost accounting model, and minimize the unit mass carbon emission output by the carbon emission accounting model, with the design range of each component as the constraint condition; real number encoding is used, and each individual is represented as a four-dimensional vector. ,in For slag usage, This refers to the amount of fly ash used. For the amount of calcium carbide slag used, The amount of desulfurized gypsum used; initial population Depend on It consists of individual components, each generated within its corresponding design interval: ； For the first The first individual Each decision variable component; For the first The lower bound of the values ​​of each decision variable; For the first The upper limit of the values ​​that a decision variable can take; S402, For each individual Calculate the values ​​of the three objective functions: Intensity range: Call the intensity range prediction multilayer perceptron model trained in step S2 and output the mean. and standard deviation Take the interval [ −2σ,μ+2σ]; Unit cost: ; Carbon emissions per unit: ; in The dosages are slag, fly ash, carbide slag, and desulfurization gypsum, respectively. For slag, fly ash, carbide slag, and desulfurization gypsum, the unit cost coefficients are: The carbon emission factors corresponding to slag, fly ash, carbide slag, and desulfurization gypsum; S403. Perform interval non-dominated sorting and define interval possibility. : ； in They are intervals The lower limit and the upper limit They are intervals The lower limit and the upper limit; individual Dominant Individual The conditions are: or or And it is strictly true for at least one objective; among which and Each represents an individual and individuals The intensity range, f2 is the economic cost per unit mass, and f3 is the carbon emission per unit mass; based on the above dominance relationship, the population... Perform a fast nondominated sort to obtain multiple nondominated levels. And assign rank to each individual ; S404. Perform reference point correlation and use the mean of intensity predictions. As a representative value of intensity, and , Construct a three-dimensional target vector The Das-Dennis method is used to generate reference points on the three-dimensional unit hyperplane: For One target, each coordinate axis is divided Number of reference points , Symbols representing combinations; S405. Perform adaptive normalization on the target value. ,in For the first The scaling factor of an objective during the normalization process. For the normalized first One target value; For the first One target value; The first ideal point Each component.

5. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 4, characterized in that, Also includes: S406. Use tournament selection, prioritizing individuals with smaller non-dominant ranking ranks. If the ranks are the same, select individuals with smaller habitat counts at associated reference points. Simulated binary crossover is used to generate offspring individuals. , : ； in It is generated by the following formula: ； In crossover or mutation operations, for the first Random numbers generated independently for each decision variable; , For the two parent individuals participating in the crossover, in the first... The values ​​that can be taken on each decision variable; To simulate the expansion factor used to control the similarity between offspring and parents in binary crossover, by and cross-distribution index Calculated; This indicates that in crossover or mutation operations, the first... Random numbers generated independently for each decision variable; The cross-distribution index; Variation of individuals using polynomial variation: ； This represents the value of the j-th decision variable in the offspring individual after the mutation operation; in ； It is the distribution index of variation; This is a perturbation factor used to control the amplitude of the polynomial variation. For the first The lower bound of the values ​​that a decision variable can take. For the first The upper limit of the values ​​that a decision variable can take; In the mutation operation, the first generation of the parent individual to be mutated is... Values ​​of decision variables; S407, Population Merging and Next Generation Selection parental population and offspring population merged into ,right Perform a non-dominated sort and populate the next generation of the population according to the following rules. : Add to the non-dominated layer in sequence until a certain layer The addition of [something] will cause the population to exceed [something]. ; for Individuals within the layer: Based on the niche count of the reference point, individuals that are associated with the reference point and have a small niche count are selected first to maintain population diversity; S408, Termination Reaching the maximum number of generations Alternatively, the process can stop when the population converges, and output the non-dominated solutions in the final population as the Pareto optimal solution set.

6. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The multi-objective evolutionary algorithm described in step S4 adaptively adjusts the reference point every 50 generations based on the boundary of the current Pareto front. The adjustment method is to determine the current minimum value of each objective function based on the current non-dominated solution set during the evolution process. and the current maximum value Then, on the scaled hyperplane, the reference point is regenerated using the following formula. : ； in, The number of objective functions. The first in the current Pareto frontier The minimum value of an objective function. The first in the current Pareto frontier The maximum value of each objective function. Let the direction vector uniformly distributed on the unit hyperplane be the first... One portion, The first direction vector One component; When performing global optimization, an adaptive crossover and mutation probability strategy is adopted.

7. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The objective decision-making screening using the CRITIC method combined with the TOPSIS method described in step S5 specifically includes: constructing a Pareto solution set as alternative solutions; using intensity, cost, and carbon emissions as evaluation indicators in a multi-attribute decision matrix; using the CRITIC method to determine the objective weights of each evaluation indicator; using the TOPSIS method to calculate the closeness between each alternative solution and the ideal solution, and selecting the solution with the highest closeness as the optimal combination ratio.

8. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 7, characterized in that, The CRITIC method for determining objective weights includes: performing direction-orientation and range normalization on the decision matrix; calculating the variability and conflict of each indicator, where variability is measured by standard deviation and conflict is measured by the correlation coefficient between indicators; and determining the weights based on the information content of each indicator. Calculate the weights, where For the first The standard deviation of each indicator For the first The first indicator and the first The correlation coefficients of the indicators.

9. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The reliability-considered response surface methodology described in step S1 is as follows: The experimental scheme is constructed using the Box-Behnken design method, with slag, fly ash, carbide slag, and desulfurized gypsum as raw materials. The design ranges for each component are 210-270g for slag, 30-90g for fly ash, 15-45g for carbide slag, and 15-45g for desulfurized gypsum. Three parallel specimens are prepared for each experimental mix.

10. The method for designing the composition of multi-source solid waste cementitious materials based on multi-objective collaborative optimization according to claim 1, characterized in that, The raw materials for the multi-source solid waste-based cementitious material include granulated blast furnace slag, fly ash, carbide slag, and desulfurized gypsum; the economic cost accounting model and carbon emission accounting model are unit mass cost model and unit mass carbon emission model.

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