Optimization method of sludge non-fired brick based on machine learning and pareto analysis

Abstract

The application discloses a sludge non-burned brick optimization method based on machine learning and Pareto analysis, relates to the technical field of machine learning and multi-objective optimization, and is applied to waste resourceization and building material preparation. In view of the problems that the preparation process parameters of the water supply sludge non-burned brick are many, there are nonlinear relationships among the parameters, and the mechanical properties and economic costs are difficult to be cooperatively optimized, the optimization is realized through the following steps: collecting raw material ratio, curing conditions, compressive strength and cost data; data preprocessing; feature construction; establishing an XGBoost double-output prediction model; using the Optuna framework to perform hyperparameter optimization; using the NSGA-II algorithm to perform multi-objective search by fusing three layers of constraint conditions; obtaining a non-dominated solution set through Pareto frontier analysis; calculating a comprehensive evaluation index to select an optimal scheme; and obtaining complete process parameters by using the law of conservation of mass. The application shortens the test cycle and realizes the cooperative optimization of the compressive strength and the cost.

Description

Technical Field

[0001] This invention relates to the fields of solid waste resource utilization and building material preparation, and also to the fields of machine learning and multi-objective optimization technology, particularly to an optimization method for sludge-fired bricks based on machine learning and Pareto analysis. Background Technology

[0002] Water supply sludge originates from the coagulation, sedimentation, and backwashing processes of water treatment plants. Its main components are inorganic and organic impurities in the raw water, as well as coagulants added during the coagulation process. Water supply sludge has a high inorganic content and cannot sustainably burn; incineration to reduce its volume would require a significant additional energy consumption.

[0003] Analysis of the sources of sewage sludge shows that its inorganic components are mainly Si, Al, and Fe, making it suitable for use in building materials. Compared to sintered brick production, using sewage sludge to produce non-fired bricks has advantages such as low energy consumption, no pollutant gas emissions, and large disposal capacity. The production of non-fired bricks from sewage sludge typically involves mixing it with building material raw materials such as cement, lime, and fly ash, then pressing it into brick blanks, and curing them under certain conditions for a period of time to form high-strength non-fired bricks. Process parameters such as raw material ratios, curing methods, and curing time affect both the compressive strength and production cost of non-fired bricks. However, these parameters often exhibit non-linear relationships, and there may be conflicts between compressive strength and cost. Traditional experimental methods involve adjusting process parameter combinations one by one, which has drawbacks such as long experimental cycles, numerous parameter combinations, and difficulty in accurately finding the optimal solution, making it impossible to effectively control production costs while ensuring the compressive strength of non-fired bricks.

[0004] Therefore, a new technical solution is needed to achieve intelligent optimization of the preparation process of non-fired bricks made from sludge in water supply, to control production costs while ensuring compressive strength, to solve the problem of difficulty in synergistic optimization of mechanical properties and economic costs, and to shorten the test cycle and reduce the number of parameter combination tests. Summary of the Invention

[0005] The technical problem to be solved by this invention is that in the existing process for preparing non-fired bricks from sludge in water supply, there are complex nonlinear relationships among parameters such as raw material ratio, curing method and curing time, and there is a conflict between compressive strength and cost. Traditional experimental methods are difficult to effectively control production costs while ensuring compressive strength, and there are problems such as long test cycles, many parameter combinations, and difficulty in accurately finding the optimal solution.

[0006] Technical solution of the present invention: The optimization method for sludge-fired non-fired bricks based on machine learning and Pareto analysis includes the following steps: S1. Data Collection: Acquire data related to the preparation process and performance evaluation of non-fired bricks made from water supply sludge. This data includes at least raw material proportioning data, curing conditions, compressive strength, and cost. The raw material proportioning data is characterized using normalized weighting coefficients and includes the amount of water supply sludge added. 1. Cement admixture 2. Lime dosage 3. Fly ash content 4, 1+ 2+ 3+ 4=1; The maintenance conditions include maintenance methods. 5 and maintenance time 6; The maintenance method described 5∈{S,W,H1,H4}, where S, W, H1, and H4 correspond to standard curing, water immersion curing, pre-autoclaving curing, and post-autoclaving curing, respectively; curing time 6 or 7 days ≤ 6≤28 days; S2. Dataset Construction: Preprocess the collected data, including outlier removal, missing value handling, encoding and transformation of categorical features, and design the output targets as stress resistance and cost. S3. Feature Engineering: Construct features based on the initial input features, and add a new feature: water supply sludge time interaction term. 7. Cement Time Interaction Item 8. Simultaneously delete the characteristic fly ash content. 4. Determine the model input features and output features, wherein: the water supply sludge time interaction term 7 is used to characterize the coupling effect between the amount of sludge added for water supply resource utilization and the curing process. 7= 1× 6. The cement time interaction item 8 is used to characterize the coupling effect between the component that contributes the most to strength and the curing process. 8= 2× 6; Model input features include the amount of sludge added to the water supply. 1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. Water supply sludge time interaction item 7. Cement Time Interaction Item 8; Model output features include compressive strength and cost , The unit is MPa. The unit is yuan / ton; S4. Establish a prediction model: Use a machine learning model to establish the relationship between input features and output features. The machine learning model is a dual-output regression model. S5. Model Training and Optimization: Adaptive search of hyperparameters for the machine learning model is performed using a hyperparameter optimization framework, with the dual-output evaluation index under cross-validation conditions as the objective function, to obtain the hyperparameter-optimized prediction model. S6. Design Constraints and Multi-Objective Optimization Solution: A multi-objective evolutionary algorithm is used to iteratively search the input variable space, incorporating constraints into the search process. The input variable space includes the amount of sludge added to the water supply. 1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. Use the prediction model to predict the compressive strength and cost of the candidate solutions; S7. Pareto Front Analysis and Comprehensive Evaluation Index Calculation: Screen candidate solutions for Pareto nondominated solutions to obtain Pareto front solution set; calculate comprehensive evaluation index for Pareto front solution set according to decision preference, and select the solution with the highest comprehensive evaluation index as the final optimized solution. S8. Input Feature Back-calculation: Based on the feature values ​​of the final optimized scheme, the mass conservation relationship is utilized. 1+ 2+ 3+ 4=1 to calculate fly ash content 4. Obtain complete process parameters for the preparation of non-fired bricks.

[0007] The beneficial effects of this invention are: (1) This invention establishes a nonlinear mapping relationship between process parameters and compressive strength and cost through a machine learning model, which can accurately predict the performance and cost of non-fired bricks under different combinations of process parameters. This avoids the problem that traditional experimental methods require testing a large number of parameter combinations one by one, significantly shortens the experimental cycle, and reduces the experimental cost. (2) This invention uses a multi-objective evolutionary algorithm combined with Pareto front analysis, which can simultaneously optimize two conflicting objectives, compressive strength and cost, and obtain a series of Pareto optimal solutions. This provides decision-makers with a variety of options to balance mechanical performance and economic cost, and solves the problem that traditional methods are difficult to optimize multiple objectives in a coordinated manner. (3) This invention constructs new variables through feature engineering and performs feature screening, extracting the feature combination that has the most significant impact on the performance of non-fired bricks, thereby improving the prediction accuracy and generalization ability of the model and making the optimization results more reliable; (4) The present invention sets up multi-layer constraints, including physical quantity legality constraints, minimum strength constraints and decision preference constraints, to ensure that the optimization scheme not only meets the physical constraints of actual production, but also meets the performance requirements and decision preferences of engineering applications, thereby improving the practicality of the optimization scheme; (5) The present invention uses a hyperparameter optimization framework to adaptively tune the machine learning model, and takes the dual-output evaluation index under cross-validation conditions as the objective function to ensure that the model has good predictive performance in both the compressive strength and cost output dimensions, thus avoiding the blindness and inefficiency of manual parameter tuning. (6) The present invention provides an input feature back-calculation step, which can convert the optimized feature values ​​into original process parameters that can be directly used in actual production, realizing a complete closed loop from theoretical optimization to practical application, which is convenient for engineering implementation. Attached Figure Description

[0008] Figure 1 This is a technical roadmap of the method of the present invention; Figure 2 This is a histogram ranking the importance of the input features of the XGBoost model in step S3 of Example 1; Figure 3 This is a scatter plot comparing the predicted and measured values ​​of the XGBoost model for compressive strength and cost in step S4 of Example 1. Figure 4 This is the convergence curve of the Optuna hyperparameter optimization process in step S5 of Example 1; Figure 5 This is a schematic diagram of the NSGA-II multi-objective optimization population evolution process in step S6 of Example 1; Figure 6 This is a schematic diagram of the Pareto front solution set and the comprehensive evaluation index I value of each scheme in step S7 of Example 1; Figure 7 These are scanning electron microscope (SEM) images of the unfired brick samples prepared using the selected and control schemes in Example 2. Detailed Implementation

[0009] The specific embodiments of the present invention will be combined with Figure 1A detailed explanation is provided below. For ease of description, the following concepts in this field will be introduced first. Water supply sludge refers to dried sludge that can be mixed with building material raw materials after drying, with a moisture content generally below 30%. Wet sludge refers to dewatered sludge produced by water supply plants, with a moisture content generally between 60% and 80%. After mixing water supply sludge with building material raw materials such as cement, lime, and fly ash, a certain amount of water is sprayed to moisten its surface. Then, it is placed in a brick-making mold and pressed under pressure to form brick blanks. The brick blanks are then immediately transferred to different curing conditions. Standard curing refers to curing the brick blanks at 95% humidity and 25℃. Water immersion curing refers to first immersing the brick blanks in water for 3 days, and then curing them under standard curing conditions. Pre-autoclaving curing refers to curing the brick blanks under a steam pressure of 200 kPa for 6 hours on the first day, and then curing them under standard curing conditions. Post-autoclaving refers to curing the brick blanks under standard curing conditions for 3 days, then curing them under 200 kPa steam pressure for 6 hours on the fourth day, and then continuing curing under standard curing conditions. Curing time refers to the total duration of curing from the start to the end of curing. The curing time for water immersion curing, pre-autoclaving curing, and post-autoclaving curing includes the time spent in water immersion or autoclaving.

[0010] The technical solution of this invention will be further described below. For example... Figure 1 As shown, the optimization method for sludge-fired non-fired bricks based on machine learning and Pareto analysis includes the following steps: S1. Data collection: Acquire data related to the preparation process and performance evaluation of water supply sludge non-fired bricks. The data shall include at least: (1) Raw material ratio data, characterized by normalized weighting coefficients, including the amount of water supply sludge added. 1. Cement admixture 2. Lime dosage 3. Fly ash content 4. Mass fraction of other building materials; (2) Curing conditions, including curing methods 5 and maintenance time 6. The curing methods are standard curing, water immersion curing, pre-autoclaving curing or post-autoclaving curing, corresponding to S, W, H1 and H4 respectively; (3) The compressive strength and production cost of the prepared non-fired bricks, wherein the compressive strength is obtained by testing the prepared non-fired bricks with a universal testing machine, and the production cost C is calculated according to the following formula: Where C represents the production cost (in yuan / ton). , , and These are the masses (in tons) of dried sludge, fly ash, cement, and lime required to produce 1 ton of non-fired bricks. Price per ton of dried sewage sludge (in yuan). , and The prices per ton of fly ash, cement, and lime are respectively. and These are the steam and electricity costs (in yuan) required to produce 1 ton of unfired bricks, assuming the curing method does not require steam. R represents the land required for curing 1 ton of non-fired bricks (in yuan / day), and Q represents the curing time for non-fired bricks (in days); price of dried sewage sludge. Calculate using the following formula: in, The mass of wet sludge at the time of leaving the water treatment plant (in tons). The cost paid by the water plant for the treatment of wet sludge (in yuan / ton of wet sludge; for the brick factory, this is revenue, so it is recorded as a negative value when calculating costs). Expenses for transporting wet sludge to the brick factory (unit: yuan / ton of wet sludge). The cost of drying wet sludge into dried water supply sludge for brick factories (unit: yuan / ton of wet sludge). The moisture content of wet sludge. This represents the moisture content of the dried sludge.

[0011] S2. Dataset Construction: Initial input features include the amount of sludge added to the water supply system. 1. Cement admixture 2. Lime dosage 3. Fly ash content 4. Maintenance methods 5 and maintenance time 6, denoted as ,in 1+ 2+ 3+ 4=1; Preprocess the collected data, including outlier removal, missing value handling, and categorical features. 5. Perform encoding conversion, such as using one-hot encoding to convert it into input variables that can be recognized by machine learning models; design the output target as compressive strength. The unit is MPa. The unit is yuan / ton.

[0012] S3. Feature Engineering: Construct features based on the initial input features, adding two new input features: a time interaction term for water supply sludge. 7. Cement Time Interaction Item 8. Simultaneously, the fly ash content was removed. 4 ( 4 and 1. 2. 3. Collinearity exists, that is... 1+ 2+ 3+ 4=1), thus determining the model input features as follows: Feature engineering helps improve prediction accuracy and enhances the engineering interpretability and practicality of the final formulation optimization results.

[0013] S4. Establish a prediction model: A machine learning model is used to establish the relationship between input and output features. This machine learning model is a dual-output regression model, preferably an XGBoost dual-output regression model. A gradient boosting strategy is used to fit the prediction errors on both output dimensions round by round and accumulate the tree model output, thereby achieving joint prediction of stress intensity and cost. The prediction formula is as follows: ,in Let T be the prediction function for a single regression tree in the XGBoost model, where T is the total number of trees and t is the tree index, and the summation is the accumulation of all T trees.

[0014] S5. Model Training and Optimization: Define the hyperparameter combination of the XGBoost model as the vector to be optimized. , This indicates the last hyperparameter. Representing natural numbers, this is an example and not a limitation. There are a total of 9 in this invention, among which... The number of trees is n_estimators. The maximum depth of the tree is max_depth. learning rate, For sample sampling rate, subsample For the feature sampling rate colsample_bytree, The minimum child node weight is min_child_weight. The minimum splitting loss threshold gamma, The L1 regularization coefficient is reg_alpha. Let reg_lambda be the L2 regularization coefficient; and let the dual-output evaluation index Score under cross-validation conditions be the objective function. The dual-output evaluation index Score is defined as: in Let be the coefficient of determination of the compressive strength of the i-th fold. Let be the cost determination coefficient of the i-th fold, and K be the number of cross-validation folds. The Optuna framework is used to adaptively search the hyperparameter space. Optuna constructs a distribution of superior and inferior parameters based on historical experimental results, and prioritizes sampling in the region of high-potential parameters, thereby improving the efficiency of hyperparameter search and obtaining better model performance, and finally obtaining the prediction model after hyperparameter optimization.

[0015] S6. Design Constraints and Multi-Objective Optimization Solution: A multi-objective evolutionary algorithm is used to iteratively search the input variable space, incorporating constraints into the search process. The input variable space includes the amount of sludge added to the water supply. 1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. Use the prediction model to predict the compressive strength and cost of the candidate solutions; In S6, the multi-objective evolutionary algorithm is the NSGA-II algorithm, which directly integrates the physical quantities and engineering constraints between variables into the NSGA-II search process. The input variable space includes the amount of sludge added to the water supply. 1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. During the iterative search process, according to 7= 1× 6. 8= 2× 6. Calculate the newly added features.

[0016] Specifically, the constraints include three layers: The first layer of constraints consists of physical quantity legality and engineering condition constraints, including the water supply sludge content of 0.2 ≤ ≤0.8, cement admixture 0≤ 2≤0.3, Maintenance method 5∈{S,W,H1,H4}, curing time 7 days ≤ 6≤28 days 1+ 2+ 3≤1, where 1+ 2+ 3≤1 is the physical quantity legality constraint, meaning the sum of the amounts of sludge, cement, and lime added to the water supply must not exceed 1; the second layer of constraint is the minimum strength constraint, and a constraint violation function is defined. ,in Minimum allowable compressive strength, Let g(i) be the predicted compressive strength of the i-th candidate scheme. In the comparison between candidate schemes a and b: if g(i) is the predicted compressive strength of scheme a, then g(i) is the predicted compressive strength of the i-th candidate scheme. ) = 0 and the g( of scheme b) If g() > 0, then option a is better than option b; if g() > 0, then option a is better than option b. If all ) are greater than 0, then g( The smaller value is preferred; in the constraint violation degree function middle, The minimum allowable compressive strength, and The first layer represents the vector of decision variables in the optimization problem, i.e., the input variables; the third layer of constraints is the decision preference constraint, which guides the search direction through the comprehensive evaluation index in S7.

[0017] S7. Pareto Front Analysis and Comprehensive Evaluation Index Calculation: Screen candidate solutions for Pareto nondominated solutions to obtain Pareto front solution set; calculate comprehensive evaluation index for Pareto front solution set according to decision preference, and select the solution with the highest comprehensive evaluation index as the final optimized solution. In S7, the Pareto nondominated solution screening includes: for any two solutions satisfying g( Given candidate solutions a and b with ) = 0, if solution b satisfies and Or solution b satisfies and Then, it is determined that scheme b dominates scheme a, where, and These are the predicted compressive strength values ​​for schemes a and b. and The cost prediction values ​​for schemes a and b are given; both the compressive strength prediction value and the cost prediction value are retained to two decimal places before participating in the dominance relationship determination, so as to reduce the interference of small numerical fluctuations on the scheme comparison results; all non-dominated solutions together form the Pareto front solution set.

[0018] In S7, the comprehensive evaluation index for calculating the Pareto front solution set is calculated using the following formula: in, The overall score for scheme j is... Let j be the predicted compressive strength value. Let j be the predicted cost of option j. and The Pareto front solution yields the highest and lowest values ​​of the concentrated compressive strength. and The highest and lowest values ​​of the concentrated cost of the Pareto front solution are given. The minimum allowable compressive strength is given by α, the weighting coefficient of compressive strength is given by β, the weighting coefficient of cost is given by α+β=1, and λ is the penalty coefficient. The scheme with the highest comprehensive evaluation index is selected as the final optimized scheme.

[0019] S8. Input Feature Back-calculation: Based on the feature values ​​of the final optimized scheme, the mass conservation relationship is utilized. 1+ 2+ 3+ 4=11 to calculate fly ash content 4. Obtain complete process parameters for the preparation of non-fired bricks.

[0020] Based on the above specific implementation method: taking economically developed provinces and cities in the east as an example, the water supply plant pays the brick factory approximately 300 yuan per ton of wet sludge for treatment, i.e. =300 yuan / ton of wet sludge. The brick factory's cost for transporting wet sludge to the factory is approximately 50 yuan / ton of wet sludge, i.e. =50 yuan / ton of wet sludge. The brick factory's cost for drying wet sludge into dried sludge is approximately 157 yuan / ton of wet sludge, i.e. =157 yuan / ton of wet sludge. The moisture content of wet sludge before drying is generally 70%, and the moisture content after drying is generally 30%, that is... =0.7, =0.3. For a unit mass of wet sludge... When the weight is 1 ton, substituting into the above formula, the price of dried water supply sludge is: Yuan / ton That is, since the brick factory receives more revenue from the upstream water supply plant than it spends on producing dried sludge, the price of dried sludge is negative.

[0021] When calculating the production cost of non-fired bricks, the price of fly ash is considered. =60 yuan / ton, cement price Lime price: 400 yuan / ton =350 yuan / ton, price of dried water supply sludge = -217 yuan / ton, the electricity cost required to produce 1 ton of non-fired bricks =12 yuan / ton, the land cost for maintaining 1 ton of non-fired bricks is R = 2 yuan / day. For example, when producing 1 ton of non-fired bricks, the mass of dried water supply sludge used... =0.6 tons, fly ash mass =0.2 tons, cement mass =0.1 tons, lime mass =0.1 tons, using standard curing (no steam expenditure, only electricity expenditure), curing time Q=7 days, substituting into the formula, we can get Yuan / ton.

[0022] As shown in the specific implementation method, when the amount of sludge added to the water supply in the non-fired brick sample is high, the production cost of the non-fired brick will be negative. After machine learning and Pareto analysis, candidate solutions with negative costs will also appear in the Pareto front solution set. This means that the treatment fees obtained by the brick factory through waste treatment can cover the production cost of non-fired bricks or even generate a surplus. The lower the negative value, the greater the surplus and the better the economic efficiency.

[0023] The technical solution of the present invention will be further described below through three embodiments and corresponding drawings; wherein: Figure 2 This is a bar chart showing the importance ranking of the input features of the XGBoost model in step S3 of Example 1, illustrating the time interaction terms of the sludge in the water supply system. 7. Cement time interaction item The importance contribution of each input feature to the model prediction; Figure 3 This is a scatter plot comparing the predicted and measured values ​​of compressive strength and cost of the XGBoost model in step S4 of Example 1. The left figure (a) shows the comparison between the predicted and measured values ​​of compressive strength (R²=0.8318), and the right figure (b) shows the comparison between the predicted and measured values ​​of cost (R²=0.9669). Figure 4 This is a convergence curve of the Optuna hyperparameter optimization process in step S5 of Example 1, showing the optimization process from 0.8993 to 0.9068, where the Score value for each experiment and the current best Score converge. Figure 5 This is a schematic diagram of the NSGA-II multi-objective optimization population evolution process in step S6 of Example 1, showing the distribution changes of the 1st, 50th, 100th and final generation populations in the compressive strength-cost objective space and the evolution trend of the Pareto front. Figure 6 This is a schematic diagram of the Pareto front solution set and the comprehensive evaluation index I value of each scheme in step S7 of Example 1; Figure 7 These are scanning electron microscope images of the non-fired brick samples prepared by the selected scheme and the control scheme in Example 2, where (a) is the selected scheme and (b) is the control scheme.

[0024] Details are as follows: Example 1: According to the method of the present invention ( Figure 1 Taking the optimization of the preparation process of non-fired bricks made from water supply sludge as an example, and combining experimental data, steps S1 to S8 were executed completely.

[0025] Step S1 (Data Collection): Test the non-fired bricks made from water supply sludge obtained by different preparation methods, and collect data including the amount of water supply sludge added. 1. Cement admixture 2. Lime dosage 3. Fly ash content 4. Maintenance methods 5. Maintenance time 6. Compressive strength and cost, among which 1+ 2+ 3+ 4 = 1.

[0026] The raw data of the collected water supply sludge non-fired brick samples are shown in Table 1: Table 1. Original data of samples of non-fired bricks made from water supply sludge A total of 61 original sample data were collected, covering four curing methods: standard curing (S), water immersion curing (W), pre-autoclaving curing (H1), and post-autoclaving curing (H4). Curing times were 7 or 28 days. The amounts of sludge added to the water supply varied from 0 to 1, cement from 0 to 0.2, lime from 0 to 0.1, and fly ash from 0 to 1. Compressive strength varied from 0 to 18.15 MPa, and cost varied from -148.28 yuan to 196.00 yuan. The cost calculation comprehensively considered the impact of building material raw material costs, energy costs during production, disposal fees from upstream water plants, sludge drying and processing costs, and the curing time of the non-fired bricks.

[0027] Step S2 (Dataset Construction): Preprocess the 61 data entries from Step S1, including outlier removal and missing value handling; maintenance method. Categorical features are converted into input variables that can be recognized by machine learning models using one-hot encoding; the output target is designed as compressive strength. (Unit: MPa) and cost (Unit: Yuan / ton).

[0028] Step S3 (Feature Engineering): Based on the initial input features ( Constructing a new feature: Water supply sludge time interaction term , = × Characterizing the coupled effect of the target waste resource utilization dosage and curing process; cement time interaction term , = × This characterizes the coupling effect between the component that contributes the most to strength and the curing process. Simultaneously, the fly ash content was removed. .

[0029] Table 2 shows the comparison results of the impact of feature engineering design on the prediction accuracy of the XGBoost dual-output model. It also compares the 5-fold cross-validation results of constructing the XGBoost dual-output model using three different feature combinations: initial features ( The overall evaluation score is 0.8748; (retain) 4 and add 7. The score for 8 is 0.8934; delete. 4 and add 7. 8 means ( The highest score was 0.8993, with compressive strength R² at 0.8318 and cost R² at 0.9669. The comprehensive evaluation index is calculated using the formula... Calculation shows K=5. Therefore, the model input features are determined as follows: The importance ranking of each input feature for XGBoost model prediction is as follows: Figure 2 As shown, the time interaction term for water supply sludge 7. Cement time interaction item The feature 8 is significantly more important than other features, which verifies the rationality of the feature engineering design of the present invention.

[0030] Table 2. Impact of Feature Engineering on Model Prediction Accuracy Step S4 (Building a Predictive Model): Based on the determined input features ( Based on this, the 61 sample data points from step S4 were divided into a training set (49 data points) and a test set (12 data points) at a ratio of 80% and 20%, respectively. XGBoost dual-output regression models and Random Forest (RF) dual-output regression models were then established and compared. The XGBoost dual-output regression model uses a gradient boosting strategy to fit the prediction errors on both output dimensions round by round and accumulates the tree model output to achieve joint prediction of stress intensity and cost. The comparison results of the dual-output prediction accuracy of the XGBoost model and the Random Forest model show that the predicted values ​​of stress intensity and cost by the XGBoost model are compared with the measured values. Figure 3 As shown, the scatter points are distributed near the ideal prediction diagonal, verifying the model's prediction accuracy.

[0031] Table 3. Dual-output prediction accuracy of XGBoost and RF models The XGBoost model has a robustness R² of 0.8318, a cost R² of 0.9669, and a score of 0.8993; the RF model has a robustness R² of 0.7258, a cost R² of 0.9598, and a score of 0.8428. The XGBoost model demonstrates higher prediction accuracy in both output dimensions than the RF model; therefore, this invention selects the XGBoost dual-output regression model as the prediction model.

[0032] Step S5 (Model Training and Optimization): The Optuna framework was used to adaptively optimize the hyperparameters of the XGBoost model. Nine hyperparameters were defined as the optimization vector: number of trees (n_estimators), maximum tree depth (max_depth), learning rate (learning_rate), sample sampling rate (subsample), feature sampling rate (colsample_bytree), minimum child weight (min_child_weight), minimum split loss threshold (gamma), L1 regularization coefficient (reg_alpha), and L2 regularization coefficient (reg_lambda). The objective function was the dual-output evaluation metric (Score) under 5-fold cross-validation. Optuna constructed a distribution of superior and inferior parameters based on historical experimental results, prioritizing sampling in regions with high-potential parameters. Before optimization, the Score was 0.8993; after optimization, the Score reached 0.9068, an improvement of 0.0075, indicating that Optuna hyperparameter optimization has a significant effect. The optimized hyperparameter combination is: n_estimators=750, max_depth=4, learning_rate=0.0994, subsample=0.5158, colsample_bytree=0.9758, min_child_weight=1, gamma=1.5554, reg_alpha=0.4838, reg_lambda=2.8436, as shown in Table 4. Table 4. XGBoost Hyperparameter Optimization Results The convergence curve of the Optuna hyperparameter optimization process is as follows: Figure 4 As shown, with the increase of the number of trials, the score gradually converged from 0.8993 to 0.9068, indicating that the Optuna framework can effectively guide the hyperparameter search to converge to the high-potential region.

[0033] Step S6 (Design Constraints and Multi-Objective Optimization Solution): Using the XGBoost prediction model after hyperparameter optimization obtained in Step S5 as a surrogate evaluator, the NSGA-II algorithm is used to evaluate the input variable space. Perform an iterative search. During the NSGA-II iterative search process, according to... 7= 1× 6. 8= 2× 6. Real-time calculation of new features, Input XGBoost model to predict compressive strength and cost Set the first level of constraints (physical quantity validity constraints): 0.2≤ 1≤0.8, 0≤ 2≤0.3, 5∈{S,W,H1,H4}, 7 days ≤ 6≤28 days 1+ 2+ 3≤1; Second layer constraint (minimum strength constraint): minimum allowable compressive strength =10MPa, constraint violation function For the i-th candidate scheme, in the NSGA-II iteration process, any two candidate schemes a and b are compared pairwise: if the g( ) = 0 and the g( of scheme b) If g( )>0, then solution a is better than solution b; if g( )>0, then solution a is better than solution b; )>0 while the g( of scheme b) If g( ) = 0, then solution b is better than solution a; if g( ) = 0, then solution b is better than solution a. If all ) are greater than 0, then g( The smaller one is better; if both g( If all values ​​are 0, then proceed to the S7 Pareto dominance determination. Non-dominated solutions are selected with the goal of maximizing stress resistance and minimizing cost. Both stress resistance and cost predictions are rounded to two decimal places before participating in the dominance determination. The third layer of constraints (decision preference constraints) has the following weighting coefficients: stress resistance α = 0.5, cost β = 0.5, and penalty coefficient λ = 3. The evolutionary process of the NSGA-II population in different iterations is as follows: Figure 5 As shown, as the iteration proceeds, infeasible solutions (g( As the population gradually decreases (>0), it gradually converges towards the feasible region and the Pareto front.

[0034] Step S7 (Pareto Front Analysis and Comprehensive Evaluation Index Calculation): The Pareto front solution set is obtained through iterative search in Step S6, such as... Figure 6 As shown. For any two solutions a and b in the Pareto front solution set, if solution b satisfies and Or solution b satisfies and Then, it is determined that scheme b dominates scheme a, where, and These are the predicted compressive strength values ​​for schemes a and b. and The predicted costs for schemes a and b are given. Both the predicted compressive strength and cost are rounded to two decimal places before being used in the dominance determination to reduce the interference of minor numerical fluctuations on the scheme comparison results, making the comparison between candidate schemes more stable and the resulting Pareto front solution set more practical for engineering applications. All non-dominated solutions together constitute the Pareto front solution set. After obtaining the Pareto front solution set, a comprehensive evaluation index is calculated based on decision preferences. The calculation formula is as follows: in, The overall score for scheme j is... Let j be the predicted compressive strength value. Let j be the predicted cost of option j. and The Pareto front solution yields the highest and lowest values ​​of the concentrated compressive strength. and The highest and lowest values ​​of the concentrated cost of the Pareto front solution are given. The minimum allowable compressive strength is given by α, where α is the weighting factor for compressive strength and β is the weighting factor for cost. λ is the penalty coefficient, and the scheme with the highest comprehensive evaluation index is selected as the final optimized scheme.

[0035] The specific preparation parameters and comprehensive evaluation index I value of representative Pareto front solution schemes are detailed in Table 5 below: Table 5. Specific preparation parameters and comprehensive evaluation indicators of representative Pareto front solution schemes. The above lists representative schemes from the Pareto front solution set. The scheme with the highest comprehensive evaluation index is the selected scheme: water supply sludge admixture. 1=0.7572, cement admixture 2=0.1691, Lime dosage 3=0.0229, maintenance time 6 = 27.83 days, maintenance method 5 = W (water immersion curing), corresponding to a predicted compressive strength of 15.54 MPa, a predicted cost of -9.05 yuan / ton, and a comprehensive evaluation index of 0.6840.

[0036] Step S8 (Input Feature Back-Calculation): Based on the final optimization scheme selected in Step S7, the mass conservation relationship is utilized. 1+ 2+ 3+ 4=1 to calculate fly ash content 4 = 1 - 0.7572 - 0.1691 - 0.0229 = 0.0508, thus obtaining the complete process parameters for the preparation of non-fired bricks: water supply sludge content 0.7572, cement content 0.1691, lime content 0.0229, fly ash content 0.0508, curing method water immersion curing, curing time 27.83 days.

[0037] The second scheme has the following composition: sludge mass fraction of water supply is 0.6366062, cement mass fraction is 0.2182331, lime mass fraction is 0.1426797, fly ash mass fraction is 0.0024811, curing time is 27.8309392 days, curing condition is W, compressive strength is 15.69 MPa, cost is -5.08 yuan, and I value is 0.65445637.

[0038] The third scheme has the following composition: sludge mass fraction of water supply is 0.6465982, cement mass fraction is 0.2471785, lime mass fraction is 0.0606840, fly ash mass fraction is 0.0455393, curing time is 27.2989918 days, curing condition is W, compressive strength is 15.76 MPa, cost is 2.13 yuan, and I value is 0.55984548.

[0039] The fourth scheme has the following composition: water supply sludge mass fraction of 0.7675243, cement mass fraction of 0.0664657, lime mass fraction of 0.0293879, fly ash mass fraction of 0.1366221, curing time of 27.7192511 days, curing condition of W, compressive strength of 14.24 MPa, cost of -18.22 yuan, and I value of 0.55918396.

[0040] The fifth scheme has the following mass fractions: 0.7715339 for water supply sludge, 0.0624662 for cement, 0.0564197 for lime, 0.1095801 for fly ash, a curing time of 26.0905870 days, curing conditions W, a compressive strength of 14.30 MPa, a cost of -15.56 yuan, and an I value of 0.53119693.

[0041] The sixth scheme has the following composition: water supply sludge mass fraction of 0.6731066, cement mass fraction of 0.1698969, lime mass fraction of 0.0135224, fly ash mass fraction of 0.1434741, curing time of 27.7945103 days, curing condition W, compressive strength of 15.92 MPa, cost of 6.29 yuan, and I value of 0.52947012.

[0042] The seventh scheme has the following mass fractions: 0.7894904 for sludge, 0.0307143 for cement, 0.0585117 for lime, 0.1212836 for fly ash, 27.9768185 days for curing, W for curing conditions, 13.92 MPa for compressive strength, -20.52 yuan for cost, and I value of 0.52910789.

[0043] The eighth scheme has the following composition: water supply sludge mass fraction of 0.6603379, cement mass fraction of 0.2230702, lime mass fraction of 0.1070398, fly ash mass fraction of 0.0095522, curing time of 27.2312952 days, curing condition of W, compressive strength of 16.08 MPa, cost of 10.39 yuan, and I value of 0.50249800.

[0044] The ninth scheme has the following composition: water supply sludge mass fraction of 0.7850784, cement mass fraction of 0.0332273, lime mass fraction of 0.0144457, fly ash mass fraction of 0.1672487, curing time of 27.6512050 days, curing condition of W, compressive strength of 13.61 MPa, cost of -22.75 yuan, and I value of 0.50183130.

[0045] The tenth scheme has the following mass fractions: 0.7493732 for water supply sludge, 0.0687702 for cement, 0.0241532 for lime, 0.1577034 for fly ash, 25.5015473 days for curing, W for curing conditions, 14.31 MPa for compressive strength, -11.06 yuan for cost, and I value of 0.46532744.

[0046] Example 2: Based on the selected scheme with the highest comprehensive evaluation index in Example 1, a sample of water supply sludge-fired bricks was prepared, denoted as the "selected scheme". Simultaneously, a control scheme sample was prepared under standard curing conditions with a water supply sludge content of 0.4%, cement content of 0.1%, lime content of 0.1%, fly ash content of 0.4%, and a curing time of 7 days, denoted as the "control scheme". Test results showed that the measured compressive strength of the selected scheme sample was 15.01 MPa, meeting the requirement of the Shanghai Municipal Standard "Technical Specification for Sludge Treatment and Disposal of Urban Water Supply Plants" (DB31 / T 1432-2023) that the compressive strength of water supply sludge-fired bricks should not be lower than 10 MPa; the measured compressive strength of the control scheme sample was 6.23 MPa, not meeting the above standard requirement. The measured compressive strength of the selected scheme (15.01 MPa) is close to the predicted compressive strength (15.54 MPa), verifying the accuracy of the XGBoost prediction model in Example 1. Figure 7 As shown, the microstructure of the unfired bricks prepared by the two schemes was further observed using scanning electron microscopy: (a) The unfired bricks prepared by the selected scheme generated a large number of needle-like and network-like hydration products inside, with small gaps between particles and a dense microstructure. The cement and lime fully reacted with the active components in the sewage sludge to form a high-strength cementitious structure, thus resulting in high compressive strength; (b) The unfired bricks prepared by the control scheme had larger internal gaps, very few hydration products, and the activity of the raw materials was not effectively activated, resulting in loose particle packing and thus lower compressive strength. Example 2 experimentally verified that the method of the present invention can effectively guide the optimization of the preparation of unfired bricks made from sewage sludge. By combining machine learning prediction models with multi-objective optimization algorithms, the optimal preparation process parameters that balance high compressive strength and low cost can be found without a large number of experiments.

Claims

1. An optimization method for sludge-fired non-fired bricks based on machine learning and Pareto analysis, characterized in that, Includes the following steps: S1. Data Collection: Acquire data related to the preparation process and performance evaluation of non-fired bricks made from water supply sludge. This data includes at least raw material proportioning data, curing conditions, compressive strength, and cost. The raw material proportioning data is characterized using normalized weighting coefficients and includes the amount of water supply sludge added.

1. Cement admixture 2. Lime dosage 3. Fly ash content 4, 1+ 2+ 3+ 4=1; The maintenance conditions include maintenance methods. 5 and maintenance time 6; The maintenance method described 5∈{S,W,H1,H4}, where S, W, H1, and H4 correspond to standard curing, water immersion curing, pre-autoclaving curing, and post-autoclaving curing, respectively; curing time 6 or 7 days ≤ 6≤28 days; S2. Dataset Construction: Preprocess the collected data, including outlier removal, missing value handling, encoding and transformation of categorical features, and design the output targets as stress resistance and cost. S3. Feature Engineering: Construct features based on the initial input features, and add a new feature: water supply sludge time interaction term.

7. Cement Time Interaction Item 8. Simultaneously delete the characteristic fly ash content.

4. Determine the model input features and output features, wherein: the water supply sludge time interaction term 7 is used to characterize the coupling effect between the amount of sludge added for water supply resource utilization and the curing process. 7= 1× 6. The cement time interaction item 8 is used to characterize the coupling effect between the component that contributes the most to strength and the curing process. 8= 2× 6; Model input features include the amount of sludge added to the water supply.

1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. Water supply sludge time interaction item 7. Cement Time Interaction Item 8; Model output features include compressive strength and cost , The unit is MPa. The unit is yuan / ton; S4. Establish a prediction model: Use a machine learning model to establish the relationship between input features and output features. The machine learning model is a dual-output regression model. S5. Model Training and Optimization: Adaptive search of hyperparameters for the machine learning model is performed using a hyperparameter optimization framework, with the dual-output evaluation index under cross-validation conditions as the objective function, to obtain the hyperparameter-optimized prediction model. S6. Design Constraints and Multi-Objective Optimization Solution: A multi-objective evolutionary algorithm is used to iteratively search the input variable space, incorporating constraints into the search process. The input variable space includes the amount of sludge added to the water supply.

1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. Use the prediction model to predict the compressive strength and cost of the candidate solutions; S7. Pareto Front Analysis and Comprehensive Evaluation Index Calculation: Screen candidate solutions for Pareto nondominated solutions to obtain Pareto front solution set; calculate comprehensive evaluation index for Pareto front solution set according to decision preference, and select the solution with the highest comprehensive evaluation index as the final optimized solution. S8. Input Feature Back-calculation: Based on the feature values ​​of the final optimized scheme, the mass conservation relationship is utilized. 1+ 2+ 3+ 4=1 to calculate fly ash content 4. Obtain complete process parameters for the preparation of non-fired bricks.

2. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 1, characterized in that, In S4, the dual-output regression model is an XGBoost dual-output regression model. It uses a gradient boosting strategy to fit the prediction errors on both output dimensions round by round and accumulates the tree model output. The prediction formula is... ,in Let T be the prediction function for a single regression tree in the XGBoost model, where T is the total number of trees, t is the tree index, and the summation is the accumulation over all T trees. The model input features are... .

3. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 2, characterized in that, In S5, the hyperparameter optimization framework is the Optuna framework, which defines the hyperparameter combination of the XGBoost model as the vector to be optimized. , This indicates the last hyperparameter. Representing natural numbers, the hyperparameters include the number of trees (n_estimators), maximum tree depth (max_depth), learning rate (learning_rate), sample sampling rate (subsample), feature sampling rate (colsample_bytree), minimum child weight (min_child_weight), minimum split loss threshold (gamma), L1 regularization coefficient (reg_alpha), and L2 regularization coefficient (reg_lambda). The dual-output evaluation metric Score is calculated as follows: Score = ,in Let be the coefficient of determination of the compressive strength of the i-th fold. denoted as the cost determination coefficient of the i-th fold, and K as the cross-validation fold number. Optuna constructs a distribution of superior and inferior parameters based on historical experimental results, and prioritizes sampling in the region of high-potential parameters, thereby improving the efficiency of hyperparameter search and obtaining better model performance.

4. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 3, characterized in that, In S6, the multi-objective evolutionary algorithm is the NSGA-II algorithm, which directly integrates the physical quantities and engineering constraints between variables into the NSGA-II search process. The input variable space includes the amount of sludge added to the water supply.

1. Cement admixture 2. Lime dosage 3. Maintenance methods 5. Maintenance time 6. During the iterative search process, according to 7= 1× 6. 8= 2× 6. Calculate the newly added features.

5. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 4, characterized in that, In S6, the constraints include three layers: the first layer of constraints consists of physical quantity legality and engineering condition constraints, including the amount of sludge added to the water supply ≤ 0.

2. 1≤0.8, cement admixture 0≤ 2≤0.3, Maintenance method 5∈{S,W,H1,H4}, curing time 7 days ≤ 6≤28 days 1+ 2+ 3≤1, where 1+ 2+ 3≤1 is the physical quantity legality constraint, meaning the sum of the amounts of sludge, cement, and lime added to the water supply must not exceed 1; the second layer of constraint is the minimum strength constraint, and a constraint violation function is defined. ,in Minimum allowable compressive strength, Let g(i) be the predicted compressive strength of the i-th candidate scheme. In the comparison between candidate schemes a and b: if g(i) is the predicted compressive strength of scheme a, then g(i) is the predicted compressive strength of the i-th candidate scheme. ) = 0 and the g( of scheme b) If g() > 0, then option a is better than option b; if g() > 0, then option a is better than option b. If all ) are greater than 0, then g( The smaller value is preferred; the third layer of constraints is the decision preference constraint, which guides the search direction through the comprehensive evaluation index in S7.

6. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 5, characterized in that, In S7, the Pareto nondominated solution screening includes: for any two solutions satisfying g( Given candidate solutions a and b with ) = 0, if solution b satisfies and Or solution b satisfies and Then, it is determined that scheme b dominates scheme a, where, and These are the predicted compressive strength values ​​for schemes a and b. and The cost prediction values ​​for schemes a and b are given; both the compressive strength prediction value and the cost prediction value are retained to two decimal places before participating in the dominance relationship determination, so as to reduce the interference of small numerical fluctuations on the scheme comparison results; all non-dominated solutions together form the Pareto front solution set.

7. The sludge-based non-fired brick optimization method based on machine learning and Pareto analysis according to claim 6, characterized in that, In S7, the comprehensive evaluation index for calculating the Pareto front solution set is calculated using the following formula: in, The overall score for scheme j is... Let j be the predicted compressive strength value. Let j be the predicted cost of option j. and The Pareto front solution yields the highest and lowest values ​​of the concentrated compressive strength. and The highest and lowest values ​​of the concentrated cost of the Pareto front solution are given by: The minimum allowable compressive strength is given by α, the weighting coefficient of compressive strength is given by β, the weighting coefficient of cost is given by α+β=1, and λ is the penalty coefficient. The scheme with the highest comprehensive evaluation index is selected as the final optimized scheme.

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