CN111024929A - Self-compacting concrete strength prediction method based on radial basis function neural network - Google Patents

Self-compacting concrete strength prediction method based on radial basis function neural network Download PDF

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CN111024929A
CN111024929A CN201911187769.8A CN201911187769A CN111024929A CN 111024929 A CN111024929 A CN 111024929A CN 201911187769 A CN201911187769 A CN 201911187769A CN 111024929 A CN111024929 A CN 111024929A
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radial basis
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孙振平
赵一鹤
冀言亮
黎碧云
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Abstract

The invention relates to a self-compacting concrete strength prediction method based on a radial basis function neural network, which comprises the following steps: s1, collecting sample data, wherein the sample data comprises N groups of original input vectors and corresponding original output vectors, wherein N is more than 50; s2, initializing the original input vector to obtain an initialized input vector; s3, constructing a radial basis function model based on the initialized input vector and the original output vector; s4, training the radial basis function model based on the sample data to obtain a trained radial basis function model; and S5, arbitrarily setting an actual input vector, and substituting the actual input vector into the trained radial basis function model to obtain a corresponding self-compacting concrete strength predicted value. Compared with the prior art, the method utilizes the radial basis function to nonlinearly map the input vector to the output vector, and combines the Gaussian function as the nonlinear kernel function, so that the global optimal solution can be rapidly obtained through convergence, and the prediction efficiency and the prediction accuracy are improved.

Description

Self-compacting concrete strength prediction method based on radial basis function neural network
Technical Field
The invention relates to the technical field of concrete strength prediction methods, in particular to a method for predicting the strength of an auto power number based on a radial basis function neural network.
Background
Self-compacting concrete has good properties in terms of flowability, deformability and segregation resistance, and is able to flow and fill the framework and structural voids by itself. The development and application of the self-compacting concrete reduces labor cost and improves the strength and durability of the concrete structure. Because the strength design of the self-compacting concrete relates to different materials (such as cement, filler, aggregate, admixture and the like) and the dosage thereof, the composition of the materials has interaction with each other to different degrees. Particularly, the self-compacting concrete cementing material has large using amount, the water reducing agent has large mixing amount, the intensity fluctuation conditions corresponding to different mixing ratios are complex, and if the traditional method is adopted, a large amount of manual experiments are needed to obtain the optimal mixing ratio.
Different from the traditional linear function expression with the water cement ratio as a single factor, the self-compacting concrete can be ensured to obtain the optimal performance by optimizing the mixing ratio of the self-compacting concrete through a large amount of experiments. However, the manual test has a large workload and a long period, so that the strength of the self-compacting concrete needs to be predicted.
In the prior art, the concrete strength is mostly predicted by adopting a neural network method, such as: chinese patent CN104034865A discloses a method for predicting concrete strength, it utilizes a nonlinear support vector machine regression method and a neural network method, combines sample data training to obtain a concrete strength prediction model, Chinese patent CN106568647A provides a concrete strength prediction method based on the neural network, the method predicts the concrete strength value of the coring method by introducing an artificial neural network system and analyzing the concrete strength values of a compression test method and a rebound method of a standard test piece, and Chinese patent CN107133446A discloses a method for predicting the compression strength of ultra-early-strength concrete, the method maps a sample space into a high-dimensional characteristic space through nonlinear mapping, and simultaneously a support vector machine converts inner product operation in the high-dimensional space into kernel function operation in an original space through defining a kernel function, so that the compressive strength of the ultra-early-strength concrete is predicted finally.
The methods all use a support vector machine or a back propagation learning algorithm (BP neural network), the training samples are limited in quantity, a large database cannot be processed, the problems of low convergence speed and local optimal solution falling into the prediction process easily occur, and therefore prediction efficiency is low and prediction results are inaccurate.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provide a self-compacting concrete strength prediction method based on a radial basis function neural network, which utilizes the radial basis function neural network to search a global optimal solution and accelerate the convergence rate, thereby effectively improving the prediction efficiency and the prediction accuracy.
The purpose of the invention can be realized by the following technical scheme: a self-compacting concrete strength prediction method based on a radial basis function neural network comprises the following steps:
s1, collecting sample data, wherein the sample data comprises N groups of original input vectors and corresponding original output vectors, wherein N is more than 50;
s2, initializing the original input vector to obtain an initialized input vector;
s3, constructing a radial basis function model based on the initialized input vector and the original output vector;
s4, training the radial basis function model based on the sample data to obtain a trained radial basis function model;
and S5, arbitrarily setting an actual input vector, and predicting the actual input vector by the trained radial basis function model to obtain a corresponding self-compacting concrete strength predicted value.
Furthermore, the input vector is the self-compacting concrete mix proportion, and the output vector is the self-compacting concrete strength.
Further, the self-compacting concrete comprises the following components in proportion of cement, filler, water, coarse aggregate, fine aggregate and an additive, wherein the cement and the filler jointly form a cementing material.
Further, the specific method for initializing the original input vector in step S2 is as follows: converting the mass of each component of the self-compacting concrete mixing ratio into the mass ratio of each component to the cementing material.
Further, the radial basis function model in step S3 is specifically:
Figure BDA0002292817180000021
Figure BDA0002292817180000022
Figure BDA0002292817180000031
where y is the output vector, N is the number of groups of input vectors, ωiIs the weight of the i-th set of input vectors, phiiFor the non-linear mapping between the i-th set of input vectors to the corresponding output vectors, x is the input vector with dimension N x N, N is the number of component classes of the input vector minus 1, ciIs the center vector and is initially the zero vector.
Further, the non-linear mapping between the input vectors to the corresponding output vectors employs a gaussian function:
Figure BDA0002292817180000032
Figure BDA0002292817180000033
where t is the independent variable, δiGiven a coefficient.
Further, the step S4 specifically includes the following steps:
s41, substituting the original input vector of the sample data into the constructed radial basis function model to obtain a corresponding sample predicted value;
s42, comparing the predicted value of the sample with the corresponding original output vector in the sample data to judge whether the radial basis function model meets the prediction precision condition, if so, the radial basis function model is the trained radial basis function model, otherwise, executing the step S43;
s43, adjusting the weight in the radial basis function model, and then returning to the step S41.
Further, the prediction accuracy condition in step S42 is specifically:
Figure BDA0002292817180000034
wherein, ykIs a sample prediction value, yaAnd epsilon is the original output vector and is the preset prediction precision.
Compared with the prior art, the self-compacting concrete strength prediction model has the advantages that a large number of self-compacting concrete mixing ratio parameters are collected, the input vector is nonlinearly mapped to the corresponding output vector by using the radial basis function, the Gaussian function is used as the nonlinear sum function, the weight is adjusted, the prediction precision of the prediction model is guaranteed, and the corresponding strength prediction value can be accurately obtained by adopting the self-compacting concrete strength prediction model provided by the invention for any given input vector. The invention has the advantages of large training sample amount and high training precision, saves a large amount of manpower, materials and time cost, and effectively improves the prediction efficiency and the prediction accuracy.
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FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic flowchart of the working procedure for obtaining the prediction model in the embodiment.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
As shown in fig. 1, a method for predicting the strength of self-compacting concrete based on a radial basis function neural network includes the following steps:
s1, collecting sample data, wherein the sample data comprises N groups of original input vectors and corresponding original output vectors, wherein N is more than 50;
s2, initializing the original input vector to obtain an initialized input vector;
s3, constructing a radial basis function model based on the initialized input vector and the original output vector;
s4, training the radial basis function model based on the sample data to obtain a trained radial basis function model;
and S5, arbitrarily setting an actual input vector, and predicting the actual input vector by the trained radial basis function model to obtain a corresponding self-compacting concrete strength predicted value.
The specific working flow of obtaining the prediction model by applying the method to practice is shown in fig. 2:
1. collecting input vectors;
2. initializing an input vector;
3. building a radial basis function model;
4. predicting according to the radial basis function model;
5. and (4) judging whether the precision of the prediction result meets the precision requirement of the prediction, if not, adjusting the weight and repeating the step (4), and if so, outputting the prediction result.
The quantity of the collected input vectors in the step 1 is more than 50 groups, and the input vectors are the component mixing ratio of the self-compacting concrete, wherein the components of the self-compacting concrete comprise but are not limited to cement, fillers, coarse aggregates, fine aggregates, water and additives.
The initialization method in the step 2 comprises the following steps: converting the mass of each component in the mixing ratio into the ratio of the mass of the cementing material to the total mass of the cement and the filler, wherein the initialized input vector in the embodiment comprises the water cement ratio (x)1) Water to gel ratio (x)2) The ratio of coarse aggregate to cementitious material (x)3) The ratio of fine aggregate to cementitious material (x)4) The ratio of the admixture to the cementitious material (x)5)。
The radial basis function model used in step 3 is as follows:
Figure BDA0002292817180000051
in the formula (1), y is the output vector, N is the number of groups of input vectors, and ω isiIs the weight of the i-th set of input vectors, phiiFor the non-linear mapping between the i-th set of input vectors to the corresponding output vectors, x being the input vector, ciIs a central vector, andinitially a zero vector.
The input vector x and the output vector y are respectively:
Figure BDA0002292817180000052
in the formula (2), x represents data with different mix ratios, the number of dimensions is x (number of component types-1) for the data set, N is the number of sample data sets, N is 10 in the present embodiment, N is the number of dimensions of the variable x, and considering that the number of types of components of the self-compacting concrete is 6, N is 5, and y is the strength of the self-compacting concrete.
The non-linear mapping used in equation (1) is a gaussian function:
Figure BDA0002292817180000053
in the formula (3), δiFor a given coefficient, t is an argument, in this example the norm of x-c.
For the
Figure BDA0002292817180000054
In this example, a circulating part is added
Figure BDA0002292817180000055
Taking values in 0.0001 step size between 0 and 1 to determine delta for minimizing prediction errori。
And (3) comparing the predicted value obtained by calculation of the formula (1) with the actual output vector, and if the predicted value does not reach the precision, adjusting the weight until a predicted precision condition is met:
Figure BDA0002292817180000056
in the formula (4), ykIs a sample prediction value, yaLet ε be the precision of the actual output vector in the sample data, and in this example, ε is taken to be 10-4。
The radial basis function neural network model meeting the prediction accuracy condition after training is a prediction model for predicting the strength of the self-compacting concrete, any input vector can be taken, a prediction result is obtained through the formula (1), the prediction result is compared with an actual result, and the prediction accuracy of the method provided by the invention can be verified.
For space reasons, the embodiment takes 10 sets of input vector data as an example (as shown in table 1) to compare and verify the prediction accuracy, and in practical applications, the greater the number of input vectors, the higher the training accuracy.
TABLE 1
Number of groups Cement/kg m-3 Water/kg m-3 Fillers/kg m-3 Fine aggregate/kg m-3 Coarse aggregate/kg m-3 Additive/% of
1 325 211.75 60 899 850 0.51
2 325 211.75 60 899 850 0.51
3 325 244.75 120 755 850 0.59
4 249 169.95 60 1079 850 0.53
5 325 277.2 60 722 850 0.51
6 370 209.7 96 833 850 0.31
7 400 253 60 718 850 0.49
8 325 211.75 60 899 850 0.51
9 280 136.8 24 1172 850 0.67
10 370 256.1 24 770 850 0.66
The self-compacting concrete mixing ratio data in the table 1 are taken as input vectors and substituted into the prediction model provided by the invention to obtain corresponding predicted values as shown in the table 2, and the predicted values and actual values are compared to verify the prediction precision of the method, as shown in the table 2, the relative errors of the predicted values and the actual values in the embodiment are below 2.5%, and the mean square error is 0.55.
TABLE 2
Figure BDA0002292817180000061
Similarly, the strength values of the self-compacting concrete were predicted by using the neural network prediction methods of chinese patents CN104034865A, CN106568647A and CN107133446 with the self-compacting concrete mix ratio data in table 1 as input vectors, and compared with the prediction results obtained in example 1, and the comparison results are shown in table 3.
TABLE 3
Figure BDA0002292817180000071
In this embodiment, the standard deviations of the predicted values obtained by the support vector machine prediction methods adopted in patents CN104034865A and CN107133446A are 7.08 and 3.60, respectively, which are both greater than the standard deviation of the prediction of the present invention, which is 0.55. Among them, the standard deviation of patent CN104034865A is larger, and the relative error between group 7 and group 9 is even larger than 10%, because the nonlinear kernel function of the algorithm core is a polynomial kernel function or Sigmoid kernel function, and the fitting radius is smaller than the gaussian function used in the present invention, so the error is larger.
In this embodiment, the mean square error of the predicted value of CN106568647A is as high as 22.79, where the relative error of group 1 is 26.62%, and the relative error of group 9 is 71.95%, because the BP neural network prediction method adopted in this patent is prone to fall into a local optimal solution with respect to the radial basis function neural network used in the present invention, so that the error of partial results is large.
The embodiment proves that the method has the advantages of high-efficiency and high-precision prediction effect, labor, material and time cost saving compared with the traditional strength prediction method, smaller error compared with other similar neural network prediction methods, and great significance for the research of the self-compacting concrete strength prediction.

Claims (8)

1. A self-compacting concrete strength prediction method based on a radial basis function neural network is characterized by comprising the following steps:
s1, collecting sample data, wherein the sample data comprises N groups of original input vectors and corresponding original output vectors, wherein N is more than 50;
s2, initializing the original input vector to obtain an initialized input vector;
s3, constructing a radial basis function model based on the initialized input vector and the original output vector;
s4, training the radial basis function model based on the sample data to obtain a trained radial basis function model;
and S5, arbitrarily setting an actual input vector, and predicting the actual input vector by the trained radial basis function model to obtain a corresponding self-compacting concrete strength predicted value.
2. The method for predicting the strength of the self-compacting concrete based on the radial basis function neural network as claimed in claim 1, wherein the input vector is the mix proportion of the self-compacting concrete, and the output vector is the strength of the self-compacting concrete.
3. The method for predicting the strength of the self-compacting concrete based on the radial basis function neural network as claimed in claim 2, wherein the self-compacting concrete comprises cement, filler, water, coarse aggregate, fine aggregate and additives, wherein the cement and the filler together form a cementing material.
4. The method for predicting the strength of self-compacting concrete based on the radial basis function neural network as claimed in claim 3, wherein the specific method for initializing the original input vector in step S2 is as follows: converting the mass of each component of the self-compacting concrete mixing ratio into the mass ratio of each component to the cementing material.
5. The method for predicting the strength of self-compacting concrete based on the radial basis function neural network according to claim 1, wherein the radial basis function model in the step S3 specifically comprises:
Figure FDA0002292817170000011
Figure FDA0002292817170000012
Figure FDA0002292817170000021
where y is the output vector, N is the number of groups of input vectors, ωiIs the weight of the i-th set of input vectors, phiiFor the non-linear mapping between the i-th set of input vectors to the corresponding output vectors, x is the input vector with dimension N x N, N is the number of component classes of the input vector minus 1, ciIs the center vector and is initially the zero vector.
6. The self-compacting concrete strength prediction method based on the radial basis function neural network as claimed in claim 5, wherein the nonlinear mapping between the input vector and the corresponding output vector adopts a Gaussian function:
Figure FDA0002292817170000022
Figure FDA0002292817170000023
where t is the independent variable, δiGiven a coefficient.
7. The method for predicting the strength of self-compacting concrete based on the radial basis function neural network as claimed in claim 1, wherein the step S4 specifically comprises the following steps:
s41, substituting the original input vector of the sample data into the constructed radial basis function model to obtain a corresponding sample predicted value;
s42, comparing the predicted value of the sample with the corresponding original output vector in the sample data to judge whether the radial basis function model meets the prediction precision condition, if so, the radial basis function model is the trained radial basis function model, otherwise, executing the step S43;
s43, adjusting the weight in the radial basis function model, and then returning to the step S41.
8. The method for predicting the strength of self-compacting concrete based on the radial basis function neural network according to claim 7, wherein the prediction accuracy condition in the step S42 is specifically:
Figure FDA0002292817170000024
wherein, ykIs a sample prediction value, yaAnd epsilon is the original output vector and is the preset prediction precision.
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