A multi-objective optimization method for recycled aggregate concrete mix ratio

Abstract

The present invention discloses a multi-objective optimization method for recycled aggregate concrete mix ratio, comprising the following steps: establishing a prediction model for the performance of recycled aggregate concrete, using Gaussian process regression of Bayesian optimization to establish a prediction model for the performance of recycled aggregate concrete, and training the prediction model with a large amount of data; establishing an objective function for mix ratio optimization; iteratively searching for a mix ratio that meets the objective, using a multi-objective gray wolf optimization algorithm to search for the objective function value for each individual in the population and compare, updating the wolf group position to find the optimal value, and the optimal value corresponds to the target mix ratio. The present invention can learn according to raw materials in different regions, can design mix ratios for different raw material prices in various regions, and the present invention can be applied to different types of recycled aggregate concrete, and can design the required recycled aggregate concrete mix ratio according to different objective functions.

Description

Technical Field

[0001] The invention belongs to the technical field of recycled aggregate concrete mix ratio design in civil engineering, and specifically relates to a recycled aggregate concrete mix ratio multi-objective optimization method. Background Art

[0002] The traditional recycled aggregate concrete mix design experiment has a long cycle, is time-consuming and labor-intensive, and the mechanical properties of recycled aggregate concrete are different from those of traditional concrete. Machine learning methods provide convenience for establishing a mechanical property prediction model for recycled aggregate concrete and for mix optimization design based on the prediction model.

[0003] However, traditional mix design only considers the goal of meeting performance requirements, and does not take into account price and carbon dioxide emissions. This means that although the recycled aggregate concrete produced by the designed mix meets the performance requirements, the price and carbon dioxide emissions are relatively high. Therefore, it is important to find a mix design method that considers multiple objectives. Summary of the invention

[0004] The main purpose of the present invention is to propose a multi-objective mix optimization method for recycled aggregate concrete, obtain a performance prediction model for recycled aggregate concrete using a machine learning method, and on this basis use an intelligent algorithm to optimize the mix ratio of recycled aggregate concrete with performance, cost, and carbon dioxide emissions as the goals.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A multi-objective optimization method for recycled aggregate concrete mix ratio comprises the following steps:

[0007] Step 1: Establish a performance prediction model for recycled aggregate concrete. Use Bayesian optimized Gaussian process regression to establish a performance prediction model for recycled aggregate concrete. Establish a data set sample to train the prediction model.

[0008] The input parameters are set as the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete. The corresponding output parameters are the performance of recycled aggregate concrete.

[0009] Establish a Bayesian optimized Gaussian process regression model, training output y and test output f * The joint distribution of is: Where the superscript T represents the transpose of the matrix, N(·) represents the Gaussian distribution of the vector, and K represents the covariance function matrix of n×n, i.e. K(x i ,x j ), where i and j range from 1 to n, and n is the total number of training data used; Output probability y* The form is expressed as: * |y~N(K * K -1 y,K ** K -1 K * T ), the best predicted value is y * The mean value of mean(y * ), its expression is: mean(y * )=K * K -1 y;

[0010] Bayesian optimization is used to optimize the hyperparameters in Gaussian process regression. The main formula is: * =argminf(a), a∈A, where A represents the search space of a, a is a hyperparameter, f(x) is the absolute value of the difference between the predicted value and the actual value, and a i is the i-th hyperparameter set, f(a i ) is the value of the point;

[0011] Step 2: Establish the objective function for mix ratio optimization

[0012] (1) Performance function: f model (x) is the prediction model established in step 1; the independent variable x is the factor that affects the performance of recycled aggregate concrete, including the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete; (2) cost function: Where x i 、p i They are the amounts and unit prices of various raw materials used in producing recycled aggregate concrete. The prices of materials are selected based on actual conditions.

[0013] (3) Carbon dioxide emission function: E = 0.9*x 水泥 Carbon dioxide emissions are 0.9 times the amount of cement used;

[0014] For the recycled aggregate concrete mix design problem, constraints are set on the amount of each component according to the design regulations, including the range of the amount, the ratio of each amount, and the volume.

[0015] Step 3: Use the multi-objective gray wolf optimization algorithm to find the target mix ratio

[0016] (1) Set the population size, the number of storage bins, and the maximum number of iterations, initialize the gray wolf population, randomly generate the positions of wolves and prey, represent their position vectors as matrices, and calculate the position fitness of each wolf according to the objective function;

[0017] (2) Based on the positions of wolf α, wolf β, and wolf δ, the position of the wolf is updated to the average function of the positions of all wolves, and the value of the next position of the wolf is determined;

[0018] (3) The size of the position vector matrix is ​​continuously reduced during the iteration process. During each iterative optimization, the wolf's position is updated to the optimal solution based on the wolf's dominant position, and the optimal solution is stored in a set.

[0019] Furthermore, in step 1, a Bayesian optimized Gaussian process regression model is established in the following manner:

[0020] The Gaussian process regression process y(x) is determined by the mean function μ(x) and the covariance function k(x,x'), and its expression is: y(x)~N(μ(x),k(x,x'))+ε, where ε is a normal distribution. Noise error, where x is the input parameter;

[0021] In step 3, the value of the wolf's next position is determined as follows:

[0022] D α =C 1 ·X α ,D β =C 2 ·X β ,D δ =C 3 ·X δ

[0023] X 1 =X α -A 1 ·D α ,X 2 =X β -A 2 ·D β ,X 3 =X δ -A 3 ·D δ

[0024]

[0025] Among them, t is the current iteration number, X α , X β , X δ are the positions of α, β, and δ wolves respectively, and D α , D β , D δ Respectively represent the distance between the wolf's position and the prey's position; X 1 , X 2 , X 3They represent the candidate position vectors of the next wolf respectively; A and C are coefficient vectors, and their expressions are: A = 2a·r 1 -a,C=2·r 2 , where “·” represents the Hadamard product, a is a value that decreases linearly from 2 to 0, and r 1 、r 2 is a random vector distributed in [0,1].

[0026] Compared with the prior art, the present invention has the following beneficial effects:

[0027] (1) The present invention can be used to study the raw materials in different regions and optimize the mix ratio according to the different material prices in different regions. The present invention can also be applied to other types of concrete and the mix ratio can be designed according to different needs.

[0028] (2) With the enrichment of the training database, the accuracy of the present invention will be greatly improved. During the optimization process, the convergence speed will be improved. On the basis of saving manpower and material resources, the performance of recycled aggregate concrete can meet the requirements while minimizing the cost and carbon dioxide emissions. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Flowchart for mix ratio optimization DETAILED DESCRIPTION

[0030] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described in combination with the embodiments below. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0031] The embodiment of the present invention discloses a multi-objective optimization method for recycled aggregate concrete mix ratio, comprising the following steps:

[0032] 1. Establish a performance prediction model for recycled aggregate concrete. Use Bayesian optimized Gaussian process regression to establish a performance prediction model for recycled aggregate concrete. Establish a data set sample to train the prediction model.

[0033] The input parameters are set as the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete. The corresponding output parameters are the performance of recycled aggregate concrete.

[0034] Build a Gaussian process regression model with Bayesian optimization:

[0035] The Gaussian process regression process y(x) is determined by the mean function μ(x) and the covariance function k(x,x'), and its expression is: y(x)~N(μ(x),k(x,x'))+ε, where ε is a normal distribution. Noise error, where x is the input parameter;

[0036] Training output y and test output f * The joint distribution of is: Where the superscript T represents the transpose of the matrix, N(·) represents the Gaussian distribution of the vector, and K represents the covariance function matrix of n×n, i.e. K(x i ,x j ), where i and j range from 1 to n, and n is the total number of training data used; Output probability y * The form is expressed as: The best predicted value is y * The mean value of mean(y * ), its expression is: mean(y * )=K * K -1 y;

[0037] Bayesian optimization is used to optimize the hyperparameters in Gaussian process regression. The main formula is: * =argminf(a), a∈A, where A represents the search space of a, a is a hyperparameter, f(x) is the absolute value of the difference between the predicted value and the actual value, and a i is the i-th hyperparameter set, f(a i ) is the value of the point;

[0038] 2. Establish the objective function of mix ratio optimization

[0039] (1) Performance function: f model (x) is the prediction model established in step 1; the independent variable x is a factor that affects the performance of recycled aggregate concrete, including the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete;

[0040] (2) Cost function: Where x i 、p i They are the amounts and unit prices of various raw materials used in producing recycled aggregate concrete. The prices of materials are selected based on actual conditions.

[0041] (3) Carbon dioxide emission function: E = 0.9*x 水泥 Carbon dioxide emissions are 0.9 times the amount of cement used;

[0042] For the recycled aggregate concrete mix design problem, constraints are set on the amount of each component according to the design regulations, including the range of the amount, the ratio of each amount, and the volume.

[0043] 3. Use the multi-objective gray wolf optimization algorithm to find the target mix ratio

[0044] (1) Set the population size, the number of storage bins, and the maximum number of iterations, initialize the gray wolf population, randomly generate the positions of wolves and prey, represent their position vectors as matrices, and calculate the position fitness of each wolf according to the objective function;

[0045] (2) Based on the positions of wolf α, wolf β, and wolf δ, the position of the wolf is updated to the average function of the positions of all wolves, and the value of the next position of the wolf is determined:

[0046] D α =C 1 ·X α ,D β =C 2 ·X β ,D δ =C 3 ·X δ

[0047] X 1 =X α -A 1 ·D α ,X 2 =X β -A 2 ·D β ,X 3 =X δ -A 3 ·D δ

[0048]

[0049] Among them, t is the current iteration number, X α , X β , X δ are the positions of α, β, and δ wolves respectively, and D α , D β , D δ Respectively represent the distance between the wolf's position and the prey's position; X 1 , X 2 , X 3 They represent the candidate position vectors of the next wolf respectively; A and C are coefficient vectors, and their expressions are: A = 2a·r 1 -a,C=2·r 2 , where “·” represents the Hadamard product, a is a value that decreases linearly from 2 to 0, and r1 、r 2 is a random vector distributed in [0,1];

[0050] (3) The size of the position vector matrix is ​​continuously reduced during the iteration process. During each iterative optimization, the wolf's position is updated to the optimal solution based on the wolf's dominant position, and the optimal solution is stored in a set.

[0051] Example 1

[0052] A recycled aggregate concrete mix design, wherein the components of the recycled aggregate concrete are five raw materials, namely, recycled coarse aggregate, natural coarse aggregate, sand, water and cement.

[0053] Based on the above conditions, this embodiment provides a multi-objective optimization method for recycled aggregate concrete mix ratio, including the following steps:

[0054] 1. Establish a performance prediction model for recycled aggregate concrete. Use Bayesian optimized Gaussian process regression to establish a performance prediction model for recycled aggregate concrete, and train the prediction model with data set samples.

[0055] The input parameters used are the replacement rate of recycled coarse aggregate r, the water absorption rate of mixed coarse aggregate W a , water-cement ratio W / C, fine aggregate to total aggregate ratio FA / TA (i.e. sand ratio), coarse aggregate to cement ratio CA / C, saturated surface dry density SG of mixed coarse aggregate ssd The difference in water absorption and saturated surface dry density reflects the different coarse aggregates used, so the input parameters are the above 6. Among them, the replacement rate of recycled coarse aggregate r, the water absorption rate of mixed coarse aggregate W a , saturated surface dry density of mixed coarse aggregate SG ssd The formula is as follows:

[0056] r=(m Ra / SG Ra ) / (m Ra / SG Ra +m Na / SG Na )

[0057] W a =W aRa ×r+W aNa ×(1-r)

[0058] SG ssd =SG Ra ×r+SG Na ×(1-r)

[0059] Where r is the volume fraction of recycled coarse aggregate, m Ra is the recycled coarse aggregate content, mNa is the natural coarse aggregate content; SG ssd is the saturated surface dry density of mixed coarse aggregate, SG Ra is the saturated surface dry density of recycled coarse aggregate, SG Na W is the saturated surface dry density of natural coarse aggregate; a is the water absorption rate of mixed coarse aggregate, W aRa Water absorption of recycled coarse aggregate, W aNa Water absorption of natural coarse aggregate.

[0060] The output parameter is the 28-day cube compressive strength of recycled aggregate concrete.

[0061] The principle of establishing a Bayesian optimized Gaussian process regression model is as follows

[0062] Determine the mean function μ(x) and covariance function k(x,x'). A Gaussian process regression is determined by the mean function and covariance function, that is, y(x)~N(μ(x),k(x,x'))+ε, where ε is the noise error and it follows a normal distribution. Here x is the input parameter.

[0063] Training output y and test output f * The joint distribution of

[0064]

[0065] The superscript T represents the transpose of the matrix, N represents the Gaussian distribution, and K represents the n×n covariance function matrix, that is, K(x i ,x j ), where the values ​​of i and j range from 1 to n, and n is the total number of training data used; To obtain the posterior distribution of the function, the joint prior distribution is restricted to contain only functions consistent with the observed data points. The prediction is expressed as follows, where y * Output probability, expressed as a Gaussian distribution

[0066]

[0067] The best predicted value is the mean of the above formula, mean(y * ) is expressed as:

[0068] mean(y * )=K * K -1 y

[0069] The main formula for optimizing hyperparameters in Gaussian process regression using Bayesian optimization is:

[0070] a *=argminf(a),a∈A

[0071] Where A represents the search space of a, where a is a hyperparameter, and f(a) is the absolute value of the difference between the predicted value and the actual value. Let a i is the i-th hyperparameter set, f(a i ) is the value of this point.

[0072] 2. Establish the objective function of mix ratio optimization

[0073] (1) Performance function: f model (x) is the prediction model established in step 1. The independent variables in the performance function are the amount of raw materials of recycled aggregate concrete and the ratio of various amounts.

[0074] (2) Cost function: Where x i ,p i They are the amount and unit price of recycled coarse aggregate, natural coarse aggregate, water, cement and sand respectively. In this example, their unit prices are 0.12, 0.06, 0.0041, 0.53 and 0.15 respectively.

[0075] (3) Carbon dioxide emission function: E = 0.9*x 水泥 The carbon dioxide emissions are 0.9 times the amount of cement used.

[0076] For the recycled aggregate concrete mix design problem, constraints are set on the dosage of each component according to the design regulations, including dosage range constraints, ratio constraints between various dosages, and volume constraints.

[0077] 3. Use the multi-objective grey wolf optimization algorithm to find the optimal solution. The optimal solution corresponds to the target mix ratio being found.

[0078] The specific steps are:

[0079] (1) Set the population size, the number of repositories, and the maximum number of iterations, initialize the gray wolf population, randomly generate solutions for wolves and prey, represent their position vectors as matrices, and calculate the position fitness of each wolf according to the objective function.

[0080] (2) Based on the positions of α, β, and δ, the wolf's position is updated to the average function of all wolves, thereby determining the value of the wolf's next position. The specific formula is as follows:

[0081] D α =C 1 ·X α ,D β =C 2 ·X β ,D δ =C 3 ·Xδ

[0082] X 1 =X α -A 1 ·D α ,X 2 =X β -A 2 ·D β ,X 3 =X δ -A 3 ·D δ

[0083]

[0084] In the above formula, t is the current iteration, D α , D β , D δ Respectively represent the distance between the wolf's position and the prey's position; X α , X β , X δ are the positions of α, β, and δ wolves; A, C are the coefficient vectors A = 2a·r 1 -a,C=2·r 2 , where “·” represents the Hadamard product, a decreases linearly from 2 to 0, r 1 、r 2 is a random vector in [0,1].

[0085] (3) The size of the position vector matrix is ​​continuously reduced during the iteration process. During each iterative optimization, the wolf's position is updated to the optimal solution through the wolf's dominant position. The multi-objective optimization gray wolf algorithm can store the Pareto optimal solution in a set.

[0086] In this example, the matching results are as follows

[0087]

[0088] Example 2

[0089] The invention discloses an optimized mix design of recycled aggregate concrete with fly ash added, wherein the components are recycled coarse aggregate, natural coarse aggregate, sand, water, cement and fly ash, which are totally 6 raw materials.

[0090] 1. Establish a 28-day recycled aggregate concrete cube compressive strength prediction model and train the prediction model with a large number of data samples. The input is the amount of 6 raw materials and the output is the 28-day cube compressive strength.

[0091] 2. Establish the objective function. The objective function used in this example is:

[0092] (1) Performance function f established in step 1 model (x) is the prediction model.

[0093] (2) Cost function Where x i ,p i They are the dosage and unit price of recycled coarse aggregate, natural coarse aggregate, water, cement, fly ash and sand respectively, and the prices are selected based on actual conditions.

[0094] (3) Carbon dioxide function E = 0.9*x 水泥 The carbon dioxide emissions are 0.9 times the amount of cement used.

[0095] For the recycled aggregate concrete mix design problem, constraints are set on the dosage of each component according to the design regulations, including dosage range constraints, ratio constraints between various dosages, and volume constraints.

[0096] 3. Use the multi-objective grey wolf optimization algorithm to find the optimal solution. The optimal solution corresponds to the target mix ratio being found.

[0097] By optimizing and solving the objective function using the multi-objective Grey Wolf optimization algorithm, the required target mix ratio can be obtained.

[0098] Finally, it should be noted that this article uses examples to illustrate the principles and implementation methods of the present invention, so that professionals in the field can implement or use the present invention. Without departing from the principles of the present invention, the present invention may also be improved and modified, and these improvements and modifications are within the technical scope of the present invention.

Claims

1. A multi-objective optimization method for recycled aggregate concrete mix ratio, It is characterized in that The following steps are involved: Step 1: Establish a performance prediction model for recycled aggregate concrete. Use Bayesian optimized Gaussian process regression to establish a performance prediction model for recycled aggregate concrete. Establish a data set sample to train the prediction model. The input parameters are set as the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete. The corresponding output parameters are the performance of recycled aggregate concrete. Establish a Bayesian optimized Gaussian process regression model, training output y and test output f * The joint distribution of is: Where the superscript T represents the transpose of the matrix, N(·) represents the Gaussian distribution of the vector, and K represents the covariance function matrix of n×n, i.e. K(x i ,x j ), where i and j range from 1 to n, and n is the total number of training data used; Output probability y * The form is expressed as: The best predicted value is y * The mean value of mean(y * ), its expression is: mean(y * )=K * K -1 y; Bayesian optimization is used to optimize the hyperparameters in Gaussian process regression. The main formula is: * =arg min f(a), a∈A, where A represents the search space of a, a is a hyperparameter, f(x) is the absolute value of the difference between the predicted value and the actual value, let a i is the i-th hyperparameter set, f(a i ) is the value of the point; Step 2: Establish the objective function for mix ratio optimization (1) Performance function: f model (x) is the prediction model established in step 1; the independent variable x is a factor that affects the performance of recycled aggregate concrete, including the amount of various raw materials of recycled aggregate concrete or the ratio of various amounts that affect the performance of recycled aggregate concrete; (2) Cost function: Where x i 、p i They are the amounts and unit prices of various raw materials used in producing recycled aggregate concrete. The prices of materials are selected based on actual conditions. (3) Carbon dioxide emission function: E = 0.9*x 水泥 Carbon dioxide emissions are 0.9 times the amount of cement used; For the recycled aggregate concrete mix design problem, constraints are set on the amount of each component according to the design regulations, including the range of the amount, the ratio of each amount, and the volume. Step 3: Use the multi-objective gray wolf optimization algorithm to find the target mix ratio (1) Set the population size, the number of storage bins, and the maximum number of iterations, initialize the gray wolf population, randomly generate the positions of wolves and prey, represent their position vectors as matrices, and calculate the position fitness of each wolf according to the objective function; (2) Based on the positions of wolf α, wolf β, and wolf δ, the position of the wolf is updated to the average function of the positions of all wolves, and the value of the next position of the wolf is determined; (3) The size of the position vector matrix is ​​continuously reduced during the iteration process. During each iterative optimization, the wolf's position is updated to the optimal solution based on the wolf's dominant position, and the optimal solution is stored in a set.

2. A multi-objective optimization method for recycled aggregate concrete mix ratio according to claim 1, It is characterized in that In step 1, a Bayesian optimized Gaussian process regression model is established in the following manner: The Gaussian process regression process y(x) is determined by the mean function μ(x) and the covariance function k(x,x'), and its expression is: y(x)~N(μ(x),k(x,x'))+ε, where ε is a normal distribution. Noise error, where x is the input parameter; In step 3, the value of the wolf's next position is determined in the following manner: D α =C 1 ·X α ,D β =C 2 ·X β ,D δ =C 3 ·X δ X 1 =X α -A 1 ·D α ,X 2 =X β -A 2 ·D β ,X 3 =X δ -A 3 ·D δ Among them, t is the current iteration number, X α , X β , X δ are the positions of α, β, and δ wolves respectively, and D α , D β , D δ Respectively represent the distance between the wolf's position and the prey's position; X 1 , X 2 , X 3 They represent the candidate position vectors of the next wolf respectively; A and C are coefficient vectors, and their expressions are: A = 2a·r 1 -a,C=2·r 2 , where "·" represents the Hadamard product, a is a value that decreases linearly from 2 to 0, and r 1 、r 2 is a random vector distributed in [0,1].

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