Sulfate-resistant concrete mix proportion design method based on interpretable machine learning

Abstract

The invention discloses a sulfate-resistant concrete mix proportion design method based on interpretable machine learning, which comprises the following steps: acquiring related data of sulfate-eroded concrete, and constructing a database; determining a prediction model of the expansion value generated by the sulfate erosion of the concrete; performing partial dependency graph and Shapley addition interpretation analysis on the expansion value prediction model; and establishing a multi-objective optimization model of the sulfate concrete, setting constraint conditions, and determining an optimal solution of the multi-objective optimization model by using an approximate ideal solution sorting method. According to the method, the machine learning model is used for performing mix proportion design, so that the time is remarkably saved, the material and test cost is reduced, the multi-objective optimization of the sulfate resistance, the environmental influence and the full life cycle cost is realized, and the design efficiency and precision are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of concrete mix design, and in particular to a sulfate-resistant concrete mix design method based on interpretable machine learning. Background Art

[0002] Concrete is one of the most widely used building materials in the world due to its wide availability of raw materials, excellent mechanical properties and outstanding durability. However, when exposed to aggressive environments containing sulfate ions, the service life of concrete will be significantly shortened. Therefore, understanding and predicting the expansion behavior of concrete under sulfate attack is crucial for the design and maintenance of durable concrete structures.

[0003] Since the sulfate attack on concrete involves complex physical and chemical changes, many factors such as cement type, water-cement ratio, temperature, pH value and amount of auxiliary cementitious materials will affect the process. Traditional sulfate resistance assessment methods usually rely on long-term exposure tests and empirical models. These methods based on control variables are not only time-consuming, but also difficult to accurately capture the relationship between complex factors, and may also have a negative impact on the environment. Summary of the invention

[0004] Purpose of the invention: In view of the above problems, the purpose of the present invention is to provide a sulfate-resistant concrete mix design method based on interpretable machine learning, taking into account the environmental impact of concrete structures and the full life cycle cost, and designing concrete with high sulfate resistance, low environmental impact and low full life cycle cost.

[0005] Technical solution: A sulfate-resistant concrete mix design method based on interpretable machine learning of the present invention comprises the following steps:

[0006] Step 1, obtaining relevant data of sulfate-attacked concrete and constructing a database; preprocessing the data in the database and dividing it into a training set and a test set in proportion;

[0007] Step 2, determining a prediction model for the expansion value of concrete caused by sulfate attack, wherein the input items of the expansion prediction model are concrete mix ratio and environmental variables, and the output item is the expansion value of concrete caused by sulfate attack;

[0008] Step 3, perform partial dependence diagram and Shapley addition interpretation analysis on the inflation value prediction model;

[0009] Step 4: Establish a multi-objective optimization model for sulfate concrete, set constraints, and use the approximate ideal solution sorting method to determine the optimal solution of the multi-objective optimization model.

[0010] Furthermore, preprocessing the data in the database includes:

[0011] Clean and standardize the database data.

[0012] Furthermore, the prediction model for determining the expansion value of concrete caused by sulfate attack includes:

[0013] A variety of machine learning algorithms are used to construct a machine learning model for the expansion value of concrete caused by sulfate attack. The training set data is used to train each machine learning model, and the machine learning model with the best performance is selected as the expansion value prediction model.

[0014] Furthermore, the machine learning model with the best performance is selected as the inflation value prediction model including:

[0015] The performance indicators used for comparison include the coefficient of determination R 2 , root mean square error RMSE, mean absolute error MAE, root mean square logarithmic error RMSLE and objective function OBJ. By analyzing each machine learning model in multiple performance indicators, the model with multiple performance indicators that are better than other machine learning models is selected as the inflation value prediction model.

[0016] Furthermore, the objective function of the multi-objective optimization model in step 4 is:

[0017]

[0018] EI=f(GWP)+f(ODP)+f(AP)+f(EP)+f(POCP)+f(ADP)

[0019] LCC=f(Direct costs)+f(Environmental costs)

[0020] Wherein, Expansion represents the expansion value, which is obtained through the expansion value prediction model; EI represents environmental impact factors, f(GWP), f(ODP), f(AP), f(EP), f(POCP), and f(ADP) represent global warming potential, ozone depletion potential, acidification potential, eutrophication potential, photochemical ozone generation potential, and abiotic resource consumption potential, respectively; LCC represents the life cycle cost, including direct costs f(Direct costs) and indirect costs f(Environmental costs);

[0021] The set constraints include volume constraints, mix ratio constraints and usage range constraints. The search space of all mix ratio schemes is obtained through the constraints; the volume constraint is:

[0022]

[0023] The mix ratio constraints are:

[0024]

[0025]

[0026] The usage range constraints are:

[0027] Q i,min ≤Q i ≤Q i,max

[0028] Among them, V min is the lower limit of volume, V max is the upper limit of volume, Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag Respectively represent the amount of water, cement, coarse aggregate, sand, fly ash, silica fume and slag, U W , U Ce , U CA , U S , U FA , U SF and U Slag are the unit volume masses of water, cement, coarse aggregate, sand, fly ash, silica fume and slag respectively; Q1 is the lower limit of the water-binder ratio, Q2 is the upper limit of the water-binder ratio, Q3 is the lower limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q4 is the upper limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q5 is the lower limit of the amount of coarse aggregate in the total amount of concrete materials, and Q6 is the upper limit of the amount of coarse aggregate in the total amount of concrete materials; Q i Represents Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag , Q i,min Represents the minimum amount, Q i,max Represents the maximum amount.

[0029] Furthermore, the optimal solution of the multi-objective optimization model is determined by using the approximate ideal solution ranking method, including:

[0030] Determine the ideal solution and the negative ideal solution, calculate the distance between each mix ratio scheme and the ideal solution and the negative ideal solution in the search space, calculate the relative proximity of each scheme based on the distance, sort the relative proximity from large to small, and take the top one as the optimal solution of the multi-objective optimization model; the calculation formulas for the distance between each mix ratio scheme and the ideal solution and the negative ideal solution are:

[0031]

[0032] The calculation formula for relative proximity is:

[0033]

[0034] Where D i+ and D i- Respectively represent the distance from mix ratio scheme i to the ideal scheme and the negative ideal scheme, F i represents the target value of mix ratio scheme i, n represents the total amount of mix ratio scheme, F ideal represents the value of the ideal solution, F non-ideal Represents the value of the negative ideal solution.

[0035] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0036] 1. The method provided by the present invention can overcome the problems of time-consuming and poor effect of traditional experimental schemes, improve the design efficiency of sulfate-resistant concrete mix ratio, and reduce costs;

[0037] 2. The expansion value prediction model in the present invention is selected by comparing multiple evaluation indicators of various machine learning models, which ensures that the model has the best performance and high prediction accuracy, and provides accurate and reliable result support for PDP and SHAP analysis and mix design;

[0038] 3. The present invention uses a machine learning method with standardized input data to perform PDP and SHAP analysis, which improves the interpretability of the machine learning model, enables a better understanding of the model's behavior, and reduces the uncertainty caused by the "black box" model;

[0039] 4. The present invention adopts multi-objective optimization design to ensure the sulfate resistance of concrete while taking into account the environmental impact and life cycle cost of concrete, making up for the deficiency of traditional concrete mix design that only focuses on the single goal of sulfate resistance and improving the accuracy of prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The flowchart of the sulfate-resistant concrete mix design method based on interpretable machine learning is shown;

[0041] Figure 2 It is the cumulative distribution diagram of each parameter in the database;

[0042] Figure 3 A radar chart of evaluation indicators for machine learning models;

[0043] Figure 4 PDP analysis results for mix characteristics;

[0044] Figure 5 SHAP analysis results of mix characteristics;

[0045] Figure 6 Optimization target result graph. DETAILED DESCRIPTION

[0046] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0047] The sulfate-resistant concrete mix design method based on interpretable machine learning described in this embodiment includes at least the following steps 1 to 4, and the flow chart is as follows: Figure 1 shown.

[0048] Step 1: Obtain relevant data on sulfate-attacked concrete and build a database; preprocess the data in the database and divide it into a training set and a test set in proportion.

[0049] The relevant data of sulfate-attacked concrete include concrete mix ratio and related environmental variables, as well as the expansion value of concrete caused by sulfate attack. Among them, concrete mix ratio includes water-cement ratio x1, coarse aggregate cementitious material ratio x2, cement proportion x3, fly ash proportion x4, silica fume proportion x5, slag proportion x6, tricalcium silicate (C3A) proportion in cement x7, and related environmental variables include sulfate concentration in the attack solution x8, attack temperature x9, attack type x10 and exposure time x11. Figure 2 The cumulative distribution of concrete mix proportions and related environmental variables in the database is shown, where (a) is the water-cement ratio distribution map, (b) is the ratio distribution map of coarse aggregate to cementitious material in concrete, (c) is the cement proportion distribution map, (d) is the C3A content distribution map in cement, (e) is the pH distribution map of the erosion solution, (f) is the fly ash proportion distribution map, (g) is the slag proportion distribution map, (h) is the silica fume proportion distribution map, (i) is the erosion temperature distribution map, (j) is the erosion type distribution map, (k) is the sulfate concentration distribution map in the erosion solution, and (l) is the exposure time distribution map. Except for the temperature in (i) which is mainly distributed around 20-23°C, the distributions of other features are relatively uniform.

[0050] Furthermore, preprocessing the data in the database includes:

[0051] First, the data in the database is cleaned to remove abnormal data, and then the database is standardized to eliminate the dimensional influence between the data. After preprocessing, the data in the database can be divided into a training set and a test set according to a ratio (such as 6:4).

[0052] The standardization operation can be used for Z-score standardization, that is, converting the data into a standard normal distribution with a mean of 0 and a standard deviation of 1. After standardization, the feature data can be compared on the same scale, reducing the deviation caused by different feature magnitudes. The standardized features can be analyzed using Shapley's addition method (SHAP) to more directly reflect the relative contribution of these features without being affected by the feature magnitude, thereby making the interpretability analysis of the subsequent inflation index prediction model more accurate.

[0053] Step 2, determining a prediction model for the expansion value of concrete caused by sulfate attack, wherein the input items of the expansion prediction model are concrete mix ratio and environmental variables, and the output item is the expansion value of concrete caused by sulfate attack.

[0054] Specifically, the prediction model for determining the expansion value of concrete caused by sulfate attack includes:

[0055] A variety of machine learning algorithms are used to construct a machine learning model for the expansion value of concrete caused by sulfate attack. The training set data is used to train each machine learning model, and the machine learning model with the best performance is selected as the expansion value prediction model.

[0056] Furthermore, the machine learning model with the best performance is selected as the inflation value prediction model including:

[0057] The performance indicators used for comparison include R 2 , RMSE, MAE, RMSLE and OBJ. By analyzing each machine learning model in multiple performance indicators, the model with multiple performance indicators that are better than other machine learning models is selected as the inflation value prediction model.

[0058] In one example, four algorithms, namely kernel ridge regression (KRR), random forest (RF), extreme gradient boosting (XGBoost) and multi-layer perceptron (MLP), were used to build models respectively, and then the four models were trained using the training set data. The input variables of each model were concrete mix ratio and environmental variables, and the output variable was the expansion value of concrete caused by sulfate erosion. The training was stopped when each model reached the training performance. The performance of the four models was then compared, using the performance indicators: R 2 , RMSE, MAE, RMSLE and OBJ, where R 2 The closer the result of the indicator is to 1, the better the performance is. The smaller the results of other performance indicators are, the better. Through a comprehensive analysis of the performance of each model on multiple indicators, the model that is better than other models in multiple indicators (the area of ​​the connecting line of the radar chart is the largest) is selected as the best model, and the best model is used as the inflation value prediction model. Figure 3The following are radar charts of the evaluation indicators of the four models. Figure (a) is a comparison chart of the model evaluation indicators when using the training set, and Figure (b) is a comparison chart of the model evaluation indicators when using the test set. The R 2 , RMSE, RMSLE and OBJ performance are better than other models, and its R 2 The highest value is 0.945, and the lowest value of RMSE is 0.032, indicating that the MLP model prediction has high accuracy. Its connecting line area in the radar chart is the largest, so the MLP model is selected for the next explanatory analysis. The PDP and SHAP methods are used to analyze the different characteristics of the MLP model and the impact of different samples on the output to improve the interpretability of the model. Figure 4 In order to use the PDP method to obtain the influence of different mix characteristics such as the water-binder ratio in Figure (a), the cement proportion in Figure (b), the ratio of coarse aggregate to cementitious material in concrete in Figure (c), the fly ash proportion in Figure (d), the slag proportion in Figure (e) and the silica fume proportion in Figure (f) on the output variables of the MLP model, it can be seen that the influence of different mix characteristics on the output variables at different values. Figure 5 In order to use the SHAP method to obtain the impact of different input features and samples on the output variables of the MLP model, the impact of different features on the output variables is arranged from top to bottom in the figure, and the impact of samples with different values ​​on the model output variables is obtained.

[0059] Step 3, perform partial dependence diagram and additive interpretation analysis on the inflation value prediction model.

[0060] Partial dependence plots (PDP) and SHAP analysis were used to analyze the different characteristics of the inflation value prediction model and the impact of different samples on the output to improve the interpretability of the model.

[0061] Step 4: Establish a multi-objective optimization model for sulfate concrete, set constraints, and use the approximate ideal solution sorting method to determine the optimal solution of the multi-objective optimization model.

[0062] Specifically, the objective function of the multi-objective optimization model in step 4 is:

[0063]

[0064] EI=f(GWP)+f(ODP)+f(AP)+f(EP)+f(POCP)+f(ADP)

[0065] LCC=f(Direct costs)+f(Environmental costs)

[0066] The goal of the objective function is to minimize the expansion value, environmental impact and life cycle cost. In the formula, Expansion represents the expansion value, which is obtained by the expansion value prediction model; EI represents the environmental impact factor, f(GWP), f(ODP), f(AP), f(EP), f(POCP), and f(ADP) represent the global warming potential, ozone depletion potential, acidification potential, eutrophication potential, photochemical ozone generation potential, and abiotic resource consumption potential, respectively; LCC represents the life cycle cost, including direct costs f(Direct costs) and indirect costs f(Environmental costs), f(Direct costs) is the sum of the products of the mass of each component of concrete and its unit mass price, and f(Environmental costs) is the sum of the products of the mass of each component of concrete and its unit mass environmental cost.

[0067] The set constraints include volume constraints, mix ratio constraints and usage range constraints. The search sample space of all mix ratio schemes is obtained through the constraints; the volume constraint is:

[0068]

[0069] The mix ratio constraints are:

[0070]

[0071] The usage range constraints are:

[0072] Q i,min ≤Q i ≤Q i,max

[0073] Among them, V min is the lower limit of volume, V max is the upper limit of volume, Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag Respectively represent the amount of water, cement, coarse aggregate, sand, fly ash, silica fume and slag, U W , U Ce , U CA , U S , U FA , U SF and U Slagare the unit volume masses of water, cement, coarse aggregate, sand, fly ash, silica fume and slag respectively; Q1 is the lower limit of the water-binder ratio, Q2 is the upper limit of the water-binder ratio, Q3 is the lower limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q4 is the upper limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q5 is the lower limit of the amount of coarse aggregate in the total amount of concrete materials, and Q6 is the upper limit of the amount of coarse aggregate in the total amount of concrete materials; Q i Represents Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag , Q i,min Represents the minimum amount, Q i,max Represents the maximum amount.

[0074] In one example, V in the above volume constraint can be min Take the value 0.9, V max The value is 1.1. In the mix ratio constraint, Q1 is 0.3, Q2 is 1.5, Q3 is 1.5, Q4 is 4.5, Q5 is 0.35, and Q6 is 0.5. Through the above constraints, a search space containing all mix ratio schemes can be obtained.

[0075] Furthermore, the optimal solution of the multi-objective optimization model is determined by using the top-ranking method of near-ideal solutions (TOPSIS) method, including:

[0076] Determine the ideal solution and the negative ideal solution. The ideal solution is the optimal value combination of each indicator, which represents the most ideal situation in theory, that is, the combination of the minimum expansion value, the minimum environmental impact and the minimum life cycle cost in the sample space; the negative ideal solution is the worst value combination of each indicator, which represents the most undesirable situation in theory, that is, the combination of the maximum expansion value, the maximum environmental impact and the maximum life cycle cost in the sample space. Calculate the distance between each mix ratio scheme in the search space and the ideal solution and the negative ideal solution, calculate the relative proximity of each scheme based on the distance, sort the relative proximity from large to small, and arrange the first one as the optimal solution of the multi-objective optimization model; the calculation formulas for the distance between each mix ratio scheme and the ideal solution and the negative ideal solution are:

[0077]

[0078] The calculation formula for relative proximity is:

[0079]

[0080] Where D i+ and D i-Respectively represent the distance from mix ratio scheme i to the ideal scheme and the negative ideal scheme, F i represents the target value of mix ratio scheme i, n represents the total amount of mix ratio scheme, F ideal represents the value of the ideal solution, F non-ideal Represents the value of the negative ideal solution.

[0081] Figure 6 The performance comparison results of the target mix ratio obtained by TOPSIS method are shown, where Figure (a) is the optimization target result of the whole life cycle cost, and Figure (b) is the optimization target result of the environmental impact. The experimental data in the figure are real experimental data, and the best data are the results obtained by the expansion index prediction model. Figure 6 The best data obtained in the experiment can have low life cycle cost and low environmental impact while maintaining low expansion value, which verifies the feasibility and superiority of the mix design method in the present invention.

Claims

1. A sulfate-resistant concrete mix design method based on interpretable machine learning, characterized in that: The steps include: Step 1, obtaining relevant data of sulfate-attacked concrete and constructing a database; preprocessing the data in the database and dividing it into a training set and a test set in proportion; Step 2, determining a prediction model for the expansion value of concrete caused by sulfate attack, wherein the input items of the expansion prediction model are concrete mix ratio and environmental variables, and the output item is the expansion value of concrete caused by sulfate attack; Step 3, perform partial dependence diagram and Shapley addition interpretation analysis on the expansion value prediction model; Step 4: Establish a multi-objective optimization model for sulfate concrete, set constraints, and use the approximate ideal solution sorting method to determine the optimal solution of the multi-objective optimization model.

2. The method for designing sulfate-resistant concrete mix proportion based on interpretable machine learning according to claim 1, characterized in that: Preprocessing of database data includes: Clean and standardize the database data.

3. The sulfate-resistant concrete mix design method based on explainable machine learning according to claim 1, characterized in that: The predictive model for determining the expansion value of concrete due to sulfate attack includes: A variety of machine learning algorithms are used to construct a machine learning model for the expansion value of concrete caused by sulfate attack. The training set data is used to train each machine learning model, and the machine learning model with the best performance is selected as the expansion value prediction model.

4. The method for designing sulfate-resistant concrete mix proportion based on explainable machine learning according to claim 3, characterized in that: The best performing machine learning models selected as inflation value prediction models include: The performance indicators used for comparison include the coefficient of determination R 2 , root mean square error RMSE, mean absolute error MAE, root mean square logarithmic error RMSLE and objective function OBJ. By analyzing each machine learning model in multiple performance indicators, the model with multiple performance indicators that are better than other machine learning models is selected as the inflation value prediction model.

5. The method for designing sulfate-resistant concrete mix proportion based on explainable machine learning according to claim 1, characterized in that: The objective function of the multi-objective optimization model in step 4 is: EI=f(GWP)+f(ODP)+f(AP)+f(EP)+f(POCP)+f(ADP) LCC=f(Direct costs)+f(Environmental costs) Where, Expansion represents the expansion value, which is obtained through the expansion value prediction model; EI represents environmental impact factors, f(GWP), f(ODP), f(AP), f(EP), f(POCP), and f(ADP) represent global warming potential, ozone depletion potential, acidification potential, eutrophication potential, photochemical ozone generation potential, and abiotic resource consumption potential, respectively; LCC represents the life cycle cost, including direct costs f(Direct costs) and indirect costs f(Environmental costs); The set constraints include volume constraints, mix ratio constraints and usage range constraints. The search space of all mix ratio schemes is obtained through the constraints; the volume constraint is: The mix ratio constraints are: The usage range constraints are: Q i,min ≤Q i ≤Q i,max Among them, V min is the lower limit of volume, V max is the upper limit of volume, Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag Respectively represent the amount of water, cement, coarse aggregate, sand, fly ash, silica fume and slag, U W , U Ce , U CA , U S , U FA , U SF and U Slag are the unit volume masses of water, cement, coarse aggregate, sand, fly ash, silica fume and slag respectively; Q1 is the lower limit of the water-binder ratio, Q2 is the upper limit of the water-binder ratio, Q3 is the lower limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q4 is the upper limit of the ratio of the amount of coarse aggregate to the amount of cementitious materials, Q5 is the lower limit of the amount of coarse aggregate in the total amount of concrete materials, and Q6 is the upper limit of the amount of coarse aggregate in the total amount of concrete materials; Q i Represents Q W , Q Ce , Q CA , Q S , Q FA , Q SF and Q Slag , Q i,min Represents the minimum amount, Q i,max Represents the maximum amount.

6. The method for designing sulfate-resistant concrete mix proportions based on explainable machine learning according to claim 5, characterized in that: The optimal solution of the multi-objective optimization model is determined by the method of approximating the ideal solution ranking method, including: Determine the ideal solution and the negative ideal solution, calculate the distance between each mix ratio scheme and the ideal solution and the negative ideal solution in the search space, calculate the relative proximity of each scheme based on the distance, sort the relative proximity from large to small, and take the top one as the optimal solution of the multi-objective optimization model; the calculation formulas for the distance between each mix ratio scheme and the ideal solution and the negative ideal solution are: The calculation formula for relative proximity is: Where D i+ and D i- Respectively represent the distance from mix ratio scheme i to the ideal scheme and the negative ideal scheme, F i represents the target value of mix ratio scheme i, n represents the total amount of mix ratio scheme, F ideal represents the value of the ideal solution, F non-ideal Represents the value of the negative ideal solution.

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