CN111986737A - Durable concrete mixing proportion optimization method based on RF-NSGA-II - Google Patents

Durable concrete mixing proportion optimization method based on RF-NSGA-II Download PDF

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CN111986737A
CN111986737A CN202010787298.0A CN202010787298A CN111986737A CN 111986737 A CN111986737 A CN 111986737A CN 202010787298 A CN202010787298 A CN 202010787298A CN 111986737 A CN111986737 A CN 111986737A
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吴贤国
陈虹宇
陈彬
李铁军
胡毅
王帆
杨赛
刘茜
刘琼
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Huazhong University of Science and Technology
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Abstract

The invention belongs to the technical field of concrete mix proportion optimization design, and particularly discloses a durability concrete mix proportion optimization method based on RF-NSGA-II. The method comprises the following steps: constructing a concrete durability index system, collecting sample data of each variable in the concrete durability index system, and establishing an original sample set according to the sample data; training a random forest regression calculation model by adopting an original sample set, evaluating the trained random forest regression calculation model to respectively generate random forest prediction models of relative dynamic elastic modulus and chloride ion permeability coefficient of concrete, taking the random forest prediction models as target functions, taking the value range of concrete materials and the mix proportion relation among the materials as constraint conditions, and carrying out multi-target global optimization on the durable concrete mix proportion by adopting an NSGA-II model. The method has the advantages of high prediction precision, strong generalization capability and anti-noise capability, high optimization precision, strong robustness and capability of quickly obtaining the global optimal solution.

Description

Durable concrete mixing proportion optimization method based on RF-NSGA-II
Technical Field
The invention belongs to the technical field of concrete mix proportion optimization design, and particularly relates to a durability concrete mix proportion optimization method based on RF-NSGA-II.
Background
With the application of concrete structures in various engineering practices becoming more and more extensive, the problem of concrete durability under the severe cold corrosive environment becomes more and more prominent, and the influence of single or coupled environmental effects such as freeze thawing, salt invasion and the like on the concrete durability is larger and larger, so that the phenomena of concrete structure deterioration and damage caused by the single or coupled environmental effects are not negligible. The frost resistance and the impermeability of the concrete are used as two important indexes for evaluating the durability of the concrete and predicting the service life, and are related to raw materials and mixing ratio factors, so that the research on the mixing ratio optimization of the concrete based on the frost resistance and the impermeability has important engineering application value.
At present, the research method for optimizing the durability and the mix proportion of the concrete mainly focuses on the traditional orthogonal design test method, the method has more limit conditions, the experimental search range is limited, the research is long in time consumption and high in cost, and an ideal and close to actual mix proportion optimization result cannot be obtained. With the rise of artificial intelligence technology and machine learning algorithm, some researchers use artificial neural networks, BP neural networks and other methods to combine particle swarm optimization for mix proportion optimization, but because the neural networks have the problems that network structure parameters are not easy to determine, the learning speed is slow, and the prediction precision is low, and the particle swarm optimization cannot accurately obtain the global optimal solution when searching the optimal solution, the existing methods all have certain defects, and the existing research objects do not relate to the durability of concrete, and the application of mix proportion intelligent optimization for multiple targets is less. The RF algorithm is a statistical integration algorithm, the prediction results of the model are obtained by averaging the prediction results of the established decision sub-tree predictors, the model has the advantages of high training speed, high prediction precision, capability of effectively relieving overfitting, high generalization capability and anti-noise capability and the like, and the NSGA-II algorithm has the advantages of high optimization precision, high robustness and capability of quickly obtaining a global optimal solution.
Therefore, there is a need in the art to provide a method for performing a durable concrete mix optimization study using a model combining RF and NSGA-II.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a durability concrete mix proportion optimization method based on RF-NSGA-II, which comprises the steps of firstly establishing a high-precision concrete frost resistance and impermeability random forest prediction model, mapping the nonlinear regression function relationship between each raw material variable and durability performance indexes based on sample data, then taking the random forest prediction regression functions of two durability indexes as the objective function of an NSGA-II algorithm, constructing a concrete mix proportion multi-objective optimization model, and obtaining a Pareto front solution set through genetic algorithm optimization to determine a concrete mix proportion parameter combination which simultaneously meets the requirements of the concrete frost resistance and impermeability. The method has the advantages of high prediction precision, capability of effectively relieving overfitting, strong generalization capability and anti-noise capability, high optimization precision, strong robustness and capability of quickly obtaining the global optimal solution.
In order to achieve the aim, the invention provides a durable concrete mixing proportion optimization method based on RF-NSGA-II, which comprises the following steps:
s1, constructing a concrete durability index system according to the material and the mixing proportion factors which influence the frost resistance and the impermeability of the concrete, collecting sample data of each variable in the concrete durability index system, and establishing an original sample set according to the sample data;
s2, training the random forest regression calculation model by adopting the original sample set, and evaluating the trained random forest regression calculation model to respectively generate random forest prediction models of the relative dynamic elastic modulus and the chloride ion permeability coefficient of concrete;
s3, the two random forest prediction models are used as an objective function for optimizing the mix proportion of concrete, the value range of concrete materials and the mix proportion relation among the materials are used as constraint conditions, an NSGA-II model is constructed, and multi-objective global optimization of the mix proportion of the durable concrete is carried out according to set iteration termination conditions, so that a Pareto optimal solution of the objective function is generated.
Preferably, the concrete durability index system comprises influencing factors and durability evaluation indexes, wherein the influencing factors comprise water-cement ratio, cement strength, cement using amount, fly ash, fine aggregate, coarse aggregate and a water reducing agent, and the influencing factors are input variables in the training process of the random forest regression calculation model;
the durability evaluation index comprises a concrete relative dynamic elastic modulus and a concrete chloride ion permeability coefficient, and the concrete relative dynamic elastic modulus and the concrete chloride ion permeability coefficient are output variables in the training process of the random forest regression calculation model respectively.
Further preferably, step S1 further includes the steps of: after the original sample set is established, normalization processing is carried out on data in the original sample set, so that the dimensions of the data in the original sample set are uniform.
More preferably, step S2 specifically includes the following steps:
dividing an original sample set into K sub-sample sets by adopting a K-fold cross verification method, randomly taking a K-1 sub-sample set as a training subset, taking the rest sub-sample set as a verification subset, training a new decision tree of a random forest regression calculation model by adopting the K sub-sample sets, verifying the prediction precision of the new decision tree by adopting the verification subset, and selecting the new decision tree with the highest prediction precision as an optimal branch;
and taking the optimal branch as the input of the random forest regression calculation model, dividing the node into two branches according to the characteristics in the corresponding decision tree, then searching the characteristics with the classification effect meeting the requirement from the rest characteristics, and recursively constructing the branches of the decision tree so as to ensure that the decision tree fully grows without any cutting until the random forest regression calculation model can accurately classify and train subsets to complete the training of the random forest regression calculation model, thus respectively generating the random forest prediction models of the concrete relative dynamic elastic modulus and the chloride ion permeability coefficient.
More preferably, in step S2, the root mean square error RMSE and the goodness of fit R are used2Evaluating a trained random forest regression calculation model, wherein the calculation model of the root mean square error RMSE is as follows:
Figure BDA0002622474030000031
the goodness of fit R2The calculation model of (a) is:
Figure BDA0002622474030000041
wherein, yobsSample data observations, y, in the original sample setpredIs the predicted value of the random forest prediction model,
Figure BDA0002622474030000042
the average value of all sample data observed values in the original sample set is obtained, and n is the number of samples.
More preferably, step S3 specifically includes the following steps:
s31, constructing an objective function for optimizing the concrete mixing ratio based on two random forest prediction models:
Figure BDA0002622474030000043
wherein x is1Is the ratio of water to glue, x2Is the cement strength, x3Is the amount of cement, x4Is fly ash, x5Is a fine aggregate, x6As coarse aggregate, x7Is a water reducing agent;
s32, constructing constraint conditions based on the value range of the concrete material and the mixing proportion relation among the materials;
s33, constructing an NSGA-II model according to the objective function of the optimized concrete mixing ratio and the constraint conditions, and performing multi-objective optimization on the concrete mixing ratio according to the set iteration termination conditions to generate a Pareto optimal solution of the concrete durability objective function.
Preferably, in step S32, the value ranges of the concrete materials and the mix ratio of the concrete materials are limited according to the actual engineering situation and the relevant specification requirements, so as to construct the constraint conditions of the NSGA-II model, where the calculation model of the constraint conditions is:
Figure BDA0002622474030000051
wherein x is1Is the ratio of water to glue, x2Is the cement strength, x3Is the amount of cement, x4Is fly ash, x5Is a fine aggregate, x6As coarse aggregate, x7Is a water reducing agent, fcu,kThe standard value of the cubic compressive strength of the concrete.
More preferably, step S33 specifically includes the following steps:
s331, constructing an NSGA-II model according to an objective function for optimizing the mixing proportion of the concrete and constraint conditions, and then performing parameter definition and initialization on the mixed NSGA-II model according to each variable forming a concrete durability index system;
s332, defining Y concrete durability index systems as an initial population Y with a population scale of Y, enabling each concrete durability index system to form an individual of the initial population Y, enabling influencing factors and durability evaluation indexes to form chromosomes of the individual, enabling variables in the influencing factors and the durability evaluation indexes to form genes of the chromosomes, and initializing the individual;
s333, calculating the fitness value of each individual in the initial population y, acquiring the non-dominated sorting level of each individual in the initial population y according to the fitness value, and selecting mating individuals according to the non-dominated sorting level and the crowding degree of each individual to form a mating pool;
s334, crossing and mutating genes of chromosomes of individuals in a mating pool according to the crossing probability and the mutation probability defined in the NSGA-II model to form new individuals;
s335, outputting a genetic algorithm according to an iteration termination condition set in the NSGA-II model to iteratively generate a Pareto optimal solution of the objective function for optimizing the concrete mixing ratio.
Preferably, in step S333, screening each individual in the initial population y by using a binary tournament, wherein for different fitness values, the individual with the larger fitness value is selected and added to the mating pool; and comparing the crowdedness of the individuals with the same fitness value, selecting the individual with the high crowdedness to add into the mating pool, and otherwise, randomly selecting one individual to add into the mating pool until the capacity of the mating pool is reached.
More preferably, the crossing of genes of chromosomes of individuals in the mating pool in step S334 specifically includes the following steps: randomly selecting one or more genes at the same position of a certain same chromosome which forms two individuals for interchange to obtain two new individuals;
the mutation of the genes of the chromosomes of the individuals in the mating pool specifically comprises the following steps: other parameters are randomly selected to replace one or more gene segments of a chromosome that constitutes an individual, thereby resulting in a new individual.
Generally, compared with the prior art, the above technical solution conceived by the present invention mainly has the following technical advantages:
1. the method comprises the steps of firstly establishing a high-precision random forest prediction model of the frost resistance and the impermeability of the concrete, mapping a nonlinear regression function relation between each raw material variable and a durability index based on sample data, then taking the random forest prediction regression functions of the two durability indexes as an objective function of an NSGA-II algorithm, constructing a multi-objective optimization model of the mix proportion of the concrete, and obtaining a Pareto front solution set through optimization of a genetic algorithm to determine a concrete mix proportion parameter combination which simultaneously meets the requirements of the concrete on the optimum frost resistance and the impermeability. The method has the advantages of high prediction precision, capability of effectively relieving overfitting, strong generalization capability and anti-noise capability, high optimization precision, strong robustness and capability of quickly obtaining the global optimal solution.
2. The method carries out parameter optimization on the random forest regression algorithm model, establishes the high-precision prediction model of the relative dynamic elastic modulus and the chloride ion permeability coefficient of the concrete, and ensures that the prediction result of the relative dynamic elastic modulus and the chloride ion permeability coefficient of the concrete is more accurate and reliable.
3. According to the method, the RF regression prediction function replaces the traditional mathematical function to serve as the fitness function of the genetic algorithm to be used in multi-objective optimization, the complex nonlinear relation between the anti-freezing and anti-permeability performance of the concrete and the raw material mixing ratio factors is accurately mapped, and more accurate optimization is realized.
4. The invention adopts NSGA-II to establish a multi-objective optimization model, compared with the traditional genetic algorithm, the NSGAII algorithm has an elite strategy, ensures the superiority of individuals and the diversity of population, and has high optimization precision and high convergence speed.
5. The effectiveness and the correctness of the random forest regression algorithm model on the prediction effect of the relative dynamic elastic modulus and the chloride ion permeability coefficient of the concrete are verified through the goodness of fit and root mean square error analysis.
6. According to the invention, the intelligent model is used for optimizing the mix proportion by taking the frost resistance and the impermeability of the concrete as targets, so that the workload of the mix proportion optimization design test can be obviously reduced, the precision and the efficiency are improved, and the cost is reduced.
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FIG. 1 is a flow chart of a method for optimizing the mix proportion of durable concrete based on RF-NSGA-II according to an embodiment of the present invention;
fig. 2 is a parameter selection diagram for adjusting n _ estimators in a prediction model generated by a random forest regression calculation model according to an embodiment of the present invention, where (a) in fig. 2 is a parameter selection diagram for adjusting n _ estimators in a concrete relative dynamic elastic modulus prediction model, and (b) in fig. 2 is a parameter selection diagram for adjusting n _ estimators in a concrete chloride ion permeability coefficient prediction model;
fig. 3 is a schematic diagram of a prediction result of the prediction model for the relative dynamic elastic modulus of concrete provided in the embodiment of the present invention, where (a) in fig. 3 is a schematic diagram of a prediction result of the prediction model for the relative dynamic elastic modulus of concrete in the training subset, and (b) in fig. 3 is a schematic diagram of a prediction result of the prediction model for the relative dynamic elastic modulus of concrete in the verification subset;
fig. 4 is a schematic diagram of a prediction result of the prediction model for the permeability coefficient of the concrete chloride ion provided by the embodiment of the present invention, where (a) in fig. 4 is a schematic diagram of a prediction result of the prediction model for the permeability coefficient of the concrete chloride ion in the training subset, and (b) in fig. 4 is a schematic diagram of a prediction result of the prediction model for the permeability coefficient of the concrete chloride ion in the verification subset;
fig. 5 is a Pareto frontier graph obtained based on NSGA-II optimization provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, an RF-NSGA-II (random forest and genetic algorithm) -based durable concrete mix proportion optimization method provided by an embodiment of the present invention includes the following steps:
step one, constructing a concrete durability index system according to the material and mixing proportion factors influencing the frost resistance and impermeability of the concrete, collecting sample data of all variables in the concrete durability index system, and establishing an original sample set according to the sample data. The concrete durability index system comprises influencing factors and durability evaluation indexes, wherein the influencing factors comprise a water-cement ratio, cement strength, cement using amount, fly ash, fine aggregate, coarse aggregate and a water reducing agent, and the influencing factors are input variables in the training process of the random forest regression calculation model; the durability evaluation index comprises a concrete relative dynamic elastic modulus and a concrete chloride ion permeability coefficient, and the concrete relative dynamic elastic modulus and the concrete chloride ion permeability coefficient are output variables in the training process of the random forest regression calculation model respectively. After the original sample set is established, normalization processing is carried out on data in the original sample set, so that the dimensions of the data in the original sample set are uniform. Because the selected input variable dimensions are different, in order to avoid that the prediction precision and convergence performance of the model are influenced by overlarge or undersize data in the sample, normalization preprocessing is carried out on the data, so that the unification of data dimensions is realized, and the collected original data sample is normalized to the range of [ -1,1 ].
And step two, training the random forest regression calculation model by adopting the original sample set, evaluating the trained random forest regression calculation model to respectively generate random forest prediction models of the concrete relative dynamic elastic modulus and the chloride ion permeability coefficient, namely respectively establishing the concrete relative dynamic elastic modulus and the chloride ion permeability coefficient prediction models by utilizing a random forest regression algorithm (RF), and evaluating the model performance to obtain two trained random forest prediction functions.
More specifically, in the second step, establishing a random forest prediction model of the relative dynamic elastic modulus and the chloride ion permeability coefficient of the concrete by using the RF comprises the following steps:
(1) data pre-processing
Because the selected input variable dimensions are different, in order to avoid that the prediction precision and convergence performance of the model are influenced by overlarge or undersize data in the sample, normalization preprocessing is carried out on the data, so that the unification of data dimensions is realized, and the collected original data sample is normalized to the range of [ -1,1 ].
(2) Parameter optimization
Step 1: selecting the optimal branch by a K-fold cross verification method: and finally, taking the average value of the prediction precisions of the K models as a final estimation value of the model prediction precision, and selecting the splitting mode with the highest prediction precision as the optimal branch. Dividing an original sample set into K sub-sample sets by adopting a K-fold cross verification method, randomly taking a K-1 sub-sample set as a training subset, taking the rest sub-sample set as a verification subset, training a new decision tree of a random forest regression calculation model by adopting the K sub-sample sets, verifying the prediction precision of the new decision tree by adopting the verification subset, and selecting the new decision tree with the highest prediction precision as an optimal branch.
Step 2: the parameters are preferably as follows: in the process of generating the tree, M characteristics are randomly selected from all the characteristic sets for each node, and an optimal characteristic value mtry is selected from the M characteristics as a splitting variable value according to a criterion that the information gain ratio reaches the maximum. And establishing a random forest model, observing the trends of the ntree and the mean square error, and selecting the corresponding decision tree with the minimum root mean square error as the optimal ntree value, namely the regression tree number. In the growth process of the decision tree of the random forest regression algorithm, randomly selecting M variables from the training subset as characteristic variables, selecting an optimal characteristic value from the M characteristic variables as a splitting variable value of the random forest regression algorithm model according to a criterion that the information gain ratio reaches the maximum, and selecting the decision tree corresponding to the random forest regression algorithm with the minimum root mean square error as the optimal ntree value.
(3) Establishing a training model: and taking the optimal branch as random forest input, dividing the node into 2 branches according to the characteristics, and then searching the characteristics with the best effect from the rest characteristics, so as to recursively construct the branches of the classification tree, grow the regression tree to the maximum extent, do not cut any, and generate a decision tree. And repeating the process to establish a random forest prediction model. The optimal branch is used as the input of the random forest regression calculation model, the node is divided into two branches according to the characteristics in the corresponding decision tree, then the characteristics with good classification effect are searched from the rest characteristics, the branches of the decision tree are constructed in a recursion way, so that the decision tree grows fully without any cutting until the random forest regression calculation model can accurately classify and train subsets, the training of the random forest regression calculation model is completed, and in this way, the random forest prediction models of the concrete relative dynamic elasticity modulus and the chloride ion permeability coefficient are respectively generated.
More specifically, the implementation manner in step two is as follows:
the random forest regression calculation model is a classifier consisting of a plurality of decision trees, wherein each decision tree is mutually independent and is distributed with random vectors in the same distribution, under the condition that the number of the decision trees is certain, an independent variable, namely an influence factor, is given, and finally, all the decision trees are used for comprehensively voting to determine an output result;
in the training process of the random forest regression calculation model, a bootstrap resampling method is adopted to extract a specified number of samples from original samples to generate a training subset, each training subset corresponds to a decision tree,
utilizing each training subset to produce a single classification tree, namely a decision tree, randomly selecting M feature vectors from the M feature vectors at each node of the tree, and selecting one feature from the M feature vectors as a classification attribute of the node according to the principle of minimum node purity;
and dividing the nodes into 2 branches according to the characteristics, searching the characteristics with the best classification effect from the rest characteristics, and recursively constructing the branches of the decision tree so that the decision tree grows fully, the impurity degree of each node is minimum, and pruning is not performed until the tree can accurately perform a subset of the training disciplines, thereby completing the training of the random forest regression calculation model.
As a preferred embodiment of the present invention, in order to analyze the prediction result and verify the prediction accuracy of the RF model during model performance evaluation, two indexes are selected: root mean square error RMSE and goodness of fit R2To evaluate, wherein the smaller the RMSE, the smaller the R2The closer to 1, the higher the model accuracy and the better the performance. The calculation model of the root mean square error RMSE is as follows:
Figure BDA0002622474030000101
the calculation model of the goodness of fit R2 is as follows:
Figure BDA0002622474030000111
wherein, yobsSample data observations, y, in the original sample setpredIs the predicted value of the random forest prediction model,
Figure BDA0002622474030000112
the average value of all sample data observed values in the original sample set is obtained, and n is the number of samples.
And step three, taking the two random forest prediction models as an objective function for optimizing the mix proportion of the concrete, constructing an NSGA-II model by taking the value range of the concrete material and the mix proportion relation among the materials as constraint conditions, and performing multi-target global optimization on the durable concrete mix proportion according to a set iteration termination condition to generate a Pareto optimal solution of the objective function.
(1) Determining an objective function
The concrete freezing resistance and impermeability RF regression prediction algorithm is introduced to replace the traditional mathematical relation as a fitness function in the multi-target genetic algorithm, and the complex nonlinear relation between the concrete mixing ratio influence factors and the output target can be clearly reflected. Constructing an objective function for optimizing the concrete mixing ratio based on two random forest prediction models:
Figure BDA0002622474030000113
wherein x is1Is the ratio of water to glue, x2Is the cement strength, x3Is the amount of cement, x4Is fly ash, x5Is a fine aggregate, x6As coarse aggregate, x7Is a water reducing agent;
(2) determining a range of constraints
According to the invention, a reasonable value range of the mix proportion parameter is determined according to the requirements of specifications, engineering practice and the like and is used as a constraint condition for mix proportion optimization. Constructing constraint conditions based on the value range of the concrete material and the mixing proportion relation among the materials; according to the actual engineering situation and the relevant standard requirements, limiting the value range of each material of the concrete and the mixing ratio of the materials, thereby constructing the constraint condition of the NSGA-II model, wherein the calculation model of the constraint condition is as follows:
Figure BDA0002622474030000121
wherein x is1Is the ratio of water to glue, x2Is the cement strength, x3Is the amount of cement, x4Is fly ash, x5Is a fine aggregate, x6As coarse aggregate, x7Is a water reducing agent, fcu,kThe standard value of the cubic compressive strength of the concrete.
(3) And constructing an NSGA-II model according to the objective function for optimizing the concrete mixing ratio and the constraint conditions, and performing multi-objective optimization on the concrete mixing ratio according to the set iteration termination condition to generate a Pareto optimal solution of the concrete durability objective function.
More specifically, firstly, an NSGA-II model is constructed according to an objective function for optimizing the mixing proportion of the concrete and constraint conditions, and then the mixed NSGA-II model is subjected to parameter definition and initialization according to each variable forming a concrete durability index system.
Then, Y concrete durability index systems are defined as an initial population Y with a population size of Y, each concrete durability index system constitutes an individual of the initial population Y, the influencing factors and the durability evaluation indexes constitute chromosomes of the individual, and variables in the influencing factors and the durability evaluation indexes constitute genes of the chromosomes, and the individuals are initialized.
Then, fitness values of the individuals in the initial population y are calculated, non-dominant ranking levels of the individuals in the initial population y are obtained according to the fitness values, mating individuals are selected according to the non-dominant ranking levels and crowdedness of the individuals, and a mating pool is formed. Screening each individual in the initial population y by adopting a binary tournament, wherein for different fitness values, the individual with a large fitness value is selected and added into a mating pool; and comparing the crowdedness of the individuals with the same fitness value, selecting the individual with the high crowdedness to add into the mating pool, and otherwise, randomly selecting one individual to add into the mating pool until the capacity of the mating pool is reached.
Next, genes of chromosomes of individuals in the mating pool are crossed and mutated according to the crossing probability and mutation probability defined in the NSGA-II model to form new individuals.
And finally, outputting a genetic algorithm according to an iteration termination condition set in the NSGA-II model to iteratively generate a Pareto optimal solution of the objective function for optimizing the concrete mixing ratio. In the process of crossing genes of chromosomes of individuals in a mating pool, one or more genes at the same position of a certain same chromosome which forms two individuals are randomly selected to be interchanged, so that two new individuals are obtained. In the process of carrying out mutation on genes of chromosomes of individuals in the mating pool, other parameters are randomly selected to replace one or more gene segments of a certain chromosome of the individuals, and therefore new individuals are obtained.
Example 1
As shown in fig. 1, the method for optimizing the mix proportion of the durable concrete based on RF-NSGA-II provided in this embodiment mainly includes the following steps:
(1) data acquisition and preprocessing
The sample data of 71 group C40 concrete in engineering is collected by taking 7 influencing factors such as water-cement ratio, cement strength, cement dosage, fly ash, fine aggregate, coarse aggregate, water reducing agent and the like as input variables and taking the relative dynamic elastic modulus and chloride ion permeability coefficient of the concrete as two output variables, as shown in Table 1.
And (3) carrying out normalization processing on the samples, randomly extracting 56 groups of samples from all the samples to form a training set for training the model, and taking the remaining 15 groups of samples as a test set to verify the effect of the model in order to test the generalization performance of the model.
TABLE 1C 40 concrete sample data
Figure BDA0002622474030000131
Figure BDA0002622474030000141
(3) Optimizing model parameters
Because the selected training sample feature number is less, the maximum feature number max _ features of the decision tree parameter can be set to auto, and the maximum leaf node number max _ leaf _ nodes and the maximum depth max _ depth of the decision tree are not considered to be defaults; the minimum impure degree min _ impurity _ split of the node division is defaulted to 1 e-7.
Only n _ estimators need to be considered for parameter adjustment of random forest regression training, and the training performance evaluation index is a linear correlation coefficient R2. 0.2 of the number of samples in the data set is divided into a test set, and 0.8 is divided into a training set. As shown in FIG. 2, R is the distance between the true value and the predicted value of the training set2Curves with n _ estimators. As can be seen from (a) in FIG. 2, when n _ estimators is 59, R is2A maximum value of 0.9441; as can be seen from (b) in FIG. 2, when n _ estimators is 87, R is2The maximum value is 0.9358, which indicates that the model has higher generalization ability.
(4) Analysis of predicted results
And respectively establishing concrete frost resistance and impermeability prediction models according to the parameter optimization result, and obtaining regression fitting results of the training set and the test set as shown in fig. 3 and fig. 4.
As can be seen from (a) and (b) in fig. 3, the root mean square error of the concrete impermeability prediction model training set is 0.1404, the goodness of fit is 0.9441, the model fitting result is good, and the error between the predicted value and the actual value is very small. The root mean square error on the test set is 0.0409, the goodness of fit is 0.9850, and the verification shows that the prediction model has high precision and stable and good performance. The same analysis with reference to fig. 4 shows that the RF prediction model has a good effect on concrete impermeability. Therefore, it can be determined that the established concrete durability prediction model has a good prediction effect and excellent generalization ability.
(5) Determining objective function and variable constraint range
And taking the trained regression function of the relative dynamic elastic modulus and chloride ion permeability coefficient obtained by the established high-precision RF prediction model as a multi-objective function for optimizing the concrete mixing ratio, and respectively expressing the regression function and the chloride ion permeability coefficient as f1 and f 2:
f1＝max(randomforestregression(X1,X2,X3,X4,X5,X6,X7))
f2＝min(randomforestregression(X1,X2,X3,X4,X5,X6,X7))
determining a reasonable value range of the mix proportion parameters according to the requirements of specifications, engineering practice and the like, wherein the constraint conditions of mix proportion optimization are as follows:
Figure BDA0002622474030000151
(6) NSGA-II based multi-objective optimization
The established objective function and the constraint range form a fitness function of the NSGA-II algorithm, in the text, selection is carried out through random ergodic sampling, and a single-point crossover operator is used for crossover operation, wherein the crossover operator is 0.7, the mutation operator is 0.01, the initial population size is set to be 50, and the maximum evolution algebra and the stopping algebra are 60. According to the set parameters and the two objective functions of freezing resistance and impermeability, a pareto frontier solution set obtained by global optimization and solution is shown in fig. 5, and 50 groups of combination results of the mix proportion decision variables meeting the double objectives in the graph are shown in table 2.
TABLE 2 optimal mix proportion combination solution set
Figure BDA0002622474030000152
Figure BDA0002622474030000161
It can be seen from fig. 5 that as the permeability coefficient of chloride ions increases, the relative dynamic elastic modulus increases, and the influence of the variation trend of the two indexes on the durability performance is opposite. According to the experience of freeze-thaw experiments, the relative dynamic elastic modulus of the concrete after 300 times of freeze-thaw cycles is more than 85 percent, and the 28d chloride ion permeability coefficient is 3.2 x 10-8cm2The engineering durability can be achieved only when the temperature is lower than s. Because the change range of the chloride ion permeability coefficient is small in the optimizing process and the influence on the performance of concrete is not large, according to experience, the solution with the largest relative dynamic elastic modulus is selected as the optimal mixing ratio from the mixing ratio combinations meeting the requirement of the chloride ion permeability coefficient, such as the 40 th solution in the table 2, the water-cement ratio of the concrete in unit volume is 0.40, the cement strength is 51.51MPa, the cement using amount is 357.64kg, the fly ash using amount is 62.46kg, the fine aggregate using amount is 816.00kg, the coarse aggregate using amount is 1115.27kg, and the water reducer using amount is 4.95%. The optimized mixing ratio of the C40-compliant concrete selected by the embodiment can meet the expected requirements in practical engineering application.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (10)

1. A durable concrete mixing proportion optimization method based on RF-NSGA-II is characterized by comprising the following steps:
s1, constructing a concrete durability index system according to the material and the mixing proportion factors which influence the frost resistance and the impermeability of the concrete, collecting sample data of each variable in the concrete durability index system, and establishing an original sample set according to the sample data;
s2, training the random forest regression calculation model by adopting the original sample set, and evaluating the trained random forest regression calculation model to respectively generate random forest prediction models of the relative dynamic elastic modulus and the chloride ion permeability coefficient of concrete;
s3, the two random forest prediction models are used as an objective function for optimizing the mix proportion of concrete, the value range of concrete materials and the mix proportion relation among the materials are used as constraint conditions, an NSGA-II model is constructed, and multi-objective global optimization of the mix proportion of the durable concrete is carried out according to set iteration termination conditions, so that a Pareto optimal solution of the objective function is generated.
2. The RF-NSGA-II durability-based concrete mixing proportion optimization method according to claim 1, wherein the concrete durability index system comprises influencing factors and durability evaluation indexes, the influencing factors comprise water-cement ratio, cement strength, cement using amount, fly ash, fine aggregates, coarse aggregates and a water reducing agent, and the influencing factors are input variables in the training process of a random forest regression calculation model;
the durability evaluation index comprises a concrete relative dynamic elastic modulus and a concrete chloride ion permeability coefficient, and the concrete relative dynamic elastic modulus and the concrete chloride ion permeability coefficient are output variables in the training process of the random forest regression calculation model respectively.
3. The method for optimizing the mix proportion of the durable concrete based on the RF-NSGA-II as claimed in claim 1, wherein the step S1 further comprises the steps of: after the original sample set is established, normalization processing is carried out on data in the original sample set, so that the dimensions of the data in the original sample set are uniform.
4. The method for optimizing the mix proportion of the durable concrete based on the RF-NSGA-II as claimed in claim 2, wherein the step S2 specifically comprises the following steps:
dividing an original sample set into K sub-sample sets by adopting a K-fold cross verification method, randomly taking a K-1 sub-sample set as a training subset, taking the rest sub-sample set as a verification subset, training a new decision tree of a random forest regression calculation model by adopting the K sub-sample sets, verifying the prediction precision of the new decision tree by adopting the verification subset, and selecting the new decision tree with the highest prediction precision as an optimal branch;
and taking the optimal branch as the input of the random forest regression calculation model, dividing the node into two branches according to the characteristics in the corresponding decision tree, then searching the characteristics with the classification effect meeting the requirement from the rest characteristics, and recursively constructing the branches of the decision tree so as to ensure that the decision tree fully grows without any cutting until the random forest regression calculation model can accurately classify and train subsets to complete the training of the random forest regression calculation model, thus respectively generating the random forest prediction models of the concrete relative dynamic elastic modulus and the chloride ion permeability coefficient.
5. The method of claim 1, wherein the Root Mean Square Error (RMSE) and the goodness of fit (R) are used in step S22Evaluating a trained random forest regression calculation model, wherein the calculation model of the root mean square error RMSE is as follows:
Figure FDA0002622474020000021
the goodness of fit R2The calculation model of (a) is:
Figure FDA0002622474020000022
wherein, yobsSample data observations, y, in the original sample setpredIs the predicted value of the random forest prediction model,
Figure FDA0002622474020000023
the average value of all sample data observed values in the original sample set is obtained, and n is the number of samples.
6. The method for optimizing the mix proportion of the durable concrete based on the RF-NSGA-II as claimed in claim 1, wherein the step S3 specifically comprises the following steps:
s31, constructing an objective function for optimizing the concrete mixing ratio based on two random forest prediction models:
Figure FDA0002622474020000031
wherein x is1Is the ratio of water to glue, x2Is the cement strength, x3Is the amount of cement, x4Is fly ash, x5Is a fine aggregate, x6As coarse aggregate, x7Is a water reducing agent;
s32, constructing constraint conditions based on the value range of the concrete material and the mixing proportion relation among the materials;
s33, constructing an NSGA-II model according to the objective function of the optimized concrete mixing ratio and the constraint conditions, and performing multi-objective optimization on the concrete mixing ratio according to the set iteration termination conditions to generate a Pareto optimal solution of the concrete durability objective function.
7. The method for optimizing the mix proportion of the concrete based on the RF-NSGA-II durability of the claim 1, wherein in the step S32, the value ranges of the concrete materials and the mix proportion among the materials are limited according to the engineering practical situation and the relevant specification requirements, so as to construct the constraint condition of the NSGA-II model.
8. The RF-NSGA-II based durable concrete mixing proportion optimization method according to claim 3, wherein the step S33 specifically comprises the following steps:
s331, constructing an NSGA-II model according to an objective function for optimizing the mixing proportion of the concrete and constraint conditions, and then performing parameter definition and initialization on the mixed NSGA-II model according to each variable forming a concrete durability index system;
s332, defining Y concrete durability index systems as an initial population Y with a population scale of Y, enabling each concrete durability index system to form an individual of the initial population Y, enabling influencing factors and durability evaluation indexes to form chromosomes of the individual, enabling variables in the influencing factors and the durability evaluation indexes to form genes of the chromosomes, and initializing the individual;
s333, calculating the fitness value of each individual in the initial population y, acquiring the non-dominated sorting level of each individual in the initial population y according to the fitness value, and selecting mating individuals according to the non-dominated sorting level and the crowding degree of each individual to form a mating pool;
s334, crossing and mutating genes of chromosomes of individuals in a mating pool according to the crossing probability and the mutation probability defined in the NSGA-II model to form new individuals;
s335, outputting a genetic algorithm according to an iteration termination condition set in the NSGA-II model to iteratively generate a Pareto optimal solution of the objective function for optimizing the concrete mixing ratio.
9. The RF-NSGA-II durability concrete mix proportion optimization method according to the claim 8, wherein in the step S333, each individual in the initial population y is screened by binary tournament, wherein for different fitness values, the individual with larger fitness value is selected to be added into the mating pool; and comparing the crowdedness of the individuals with the same fitness value, selecting the individual with the high crowdedness to add into the mating pool, and otherwise, randomly selecting one individual to add into the mating pool until the capacity of the mating pool is reached.
10. The RF-NSGA-II based durable concrete mix proportion optimization method of claim 8, wherein in step S334, crossing genes of chromosomes of individuals in a mating pool specifically comprises the following steps: randomly selecting one or more genes at the same position of a certain same chromosome which forms two individuals for interchange to obtain two new individuals;
the mutation of the genes of the chromosomes of the individuals in the mating pool specifically comprises the following steps: other parameters are randomly selected to replace one or more gene segments of a chromosome that constitutes an individual, thereby resulting in a new individual.
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