CN113128108B - Method for determining diameter of jet grouting pile based on differential evolution artificial intelligence - Google Patents
Method for determining diameter of jet grouting pile based on differential evolution artificial intelligence Download PDFInfo
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Abstract
The invention discloses a method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence, which comprises the following steps: collecting construction parameters, stratum parameters and corresponding diameters of the jet grouting piles and preprocessing; dividing the preprocessed data set into a training set and a testing set, and carrying out normalization processing on the data set; initializing a differential evolution artificial neural network; inputting a training set into the differential evolution artificial neural network, and performing iterative training by using an N-Adam method optimization algorithm; performing mutation, recombination and selection of a differential evolution artificial neural network to obtain next generation population individuals; repeating the training step until the evolution algebra reaches a threshold value or the accuracy of the training set reaches the requirement, ending the training, and storing the differential evolution artificial neural network at the moment; and inputting the jet grouting pile data set into a differential evolution artificial neural network to obtain the diameter of the jet grouting pile. According to the invention, the accuracy of calculation is improved by utilizing the differential evolution artificial neural network, and the efficient and accurate prediction of the diameter of the jet grouting pile is realized.
Description
Technical Field
The invention relates to the field of constructional engineering, in particular to a method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence.
Background
The jet grouting pile is one of the most commonly used foundation treatment technologies at present, and is widely applied to underground engineering construction such as subways. In construction, cement slurry is injected into soil layer through a high-pressure rotary nozzle and mixed with soil, and the cement reinforcing body is formed after solidification. Because the construction operation of the high-pressure jet grouting pile is relatively simple, the high-pressure jet grouting pile is widely applied to engineering such as tunnels, foundation pits and the like. However, the construction results in different pile diameters due to the grouting operation in soil layers with different properties. How to determine the diameter of the jet grouting pile in different soil layers in the construction process has been a key problem in the design and construction of high-pressure jet grouting piles. Currently, methods for determining jet grouting pile diameter can be broadly divided into two categories: (1) a semi-theoretical semi-empirical method; (2) artificial intelligence methods. Due to the complexity of jet flow damage mechanisms and the limitation of time effect of jet grouting pile construction, the semi-theoretical semi-empirical method cannot accurately determine the analysis solution of the diameter of the jet grouting pile, so that the analysis result is inaccurate. The existing artificial intelligence method can directly obtain the nonlinear relation between the diameter of the jet grouting pile and the soil body and the construction parameters from the jet grouting construction data, a specific mechanism and theoretical assumption of soil body damage do not need to be considered, the method is more flexible, but the calculation efficiency is low, the time sequence analysis cannot be predicted, and the result error is large.
After searching the existing literature, the patent with the patent publication number of CN201410452452.3 discloses a method for determining the diameter of the high-pressure jet grouting pile by considering all construction parameters and soil characteristics, wherein a turbulent jet theory model is adopted, and construction data and soil characteristics are combined to determine the diameter of the high-pressure jet grouting pile. However, the related construction parameters and soil parameters are difficult to determine, so that the calculation result is incorrect. In addition, the artificial intelligence methods adopted at present are mainly Artificial Neural Networks (ANNs) and Support Vector Machines (SVMs). The Ochma ń ski is equal to Prediction of the diameter of jet grouting columns with artificial neural networks published in Soils and Foundations in 2015, and the prediction result is good by predicting the diameter of a jet grouting pile by adopting ANN. However, the method needs to determine the optimal network structure and parameters of the ANN through multiple pre-test training, and the time cost is high. In addition, the model is prone to over-fitting problems resulting in increased errors. Tinoco is equal to Jet grouting column diameter prediction based on a data-drive app reach published in European Journal of Environmental and Civil Engineering in 2016, SVM is adopted to predict the diameter of a jet grouting pile, the prediction result is good in accuracy, but the selection process is complex, and the time cost is high. Accordingly, there is a need for a more efficient and artificial intelligence method of determining the diameter of a jet grouting pile that increases the efficiency and accuracy of determining the diameter of the pile.
Disclosure of Invention
The invention provides a method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence, which overcomes the defects of difficult determination of construction parameters, low algorithm prediction efficiency, large deviation and the like in the existing method and realizes efficient and accurate prediction of the diameter of the jet grouting pile.
In order to solve the technical problems, the technical scheme of the invention is as follows:
a method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence comprises the following steps:
s1: collecting construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s2: preprocessing the collected construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s3: dividing a data set formed by construction parameters, stratum parameters and corresponding jet grouting pile diameters of the preprocessed jet grouting pile into a training set and a testing set, and carrying out normalization processing on the data set;
s4: initializing a differential evolution artificial neural network;
s5: inputting a training set into the differential evolution artificial neural network, and performing iterative training by using an N-Adam method optimization algorithm;
s6: performing mutation, recombination and selection of a differential evolution artificial neural network to obtain next generation population individuals;
s7: repeating the steps S5 to S6 until the evolution algebra reaches a threshold value or the accuracy of the training set reaches the requirement, ending training, and storing the differential evolution artificial neural network at the moment;
s8: and (3) inputting the jet grouting pile data set into the differential evolution artificial neural network obtained in the step (S7) to obtain the diameter of the jet grouting pile.
Preferably, the construction parameters of the jet grouting pile in the step S1 comprise jet flow Q, jet pressure F, nozzle number M and lifting rate v s Water-cement ratio W, rotational speed N and nozzle diameter d o The stratum parameters are geological parameters obtained by physical and mechanical tests on the soil layer crossing of the jet grouting area or the jet grouting pile, and comprise drainage/non-drainage shear strength s and dry weight r d 。
Preferably, the preprocessing in step S2 includes removing outliers, sampling minimum, maximum, standard deviation and average, specifically:
removing abnormal values refers to removing abnormal data which are larger than or smaller than the corresponding average value by more than 3 times of standard deviation from each operation parameter of each sampling point;
the stratum parameter average value refers to an average value of soil layer sample parameters of perforation sampling of each jet grouting pile;
the construction parameter average value of the jet grouting pile refers to the average value of the construction parameters of each grouting jet grouting pile.
Preferably, the data set in step S3 is used as input data and output results of training the artificial neural network, wherein the input data are construction parameters and stratum parameters of the jet grouting pile, and the output results are corresponding jet grouting pile diameters.
Preferably, the normalization in step S3 is to perform dimensionless processing on the input data, map the data to a (0, 1) range, and normalize equation (1) as follows:
wherein X is n,min And X n,max Respectively the minimum value and the maximum value of X, wherein X is one of construction parameters and stratum parameters of the jet grouting pile, and X n The value normalized by X.
Preferably, in step S4, the differential evolution artificial neural network specifically includes:
obtaining N population individuals by utilizing a differential evolution algorithm, wherein the population individuals represent a possible parameter combination of an artificial neural network, and the parameter combination comprises a hidden layer number gamma of the artificial neural network, a node unit number phi of each layer, a regularization coefficient psi and iteration times omega, wherein:
the artificial neural network is a data network composed of a plurality of layered node units which are connected with each other and a weight w, wherein the weight w is a weight value connected with the node units;
the hidden layer number gamma is the layer number of each layer except the input layer and the output layer of the artificial neural network;
the regularization coefficient psi is a coefficient of a regularization term in a cost function of the artificial neural network;
the iteration times omega means that the weight and the deviation are reversely adjusted, so that the times of the cost function are optimized.
Preferably, the initializing the differential evolution artificial neural network in step S4 specifically includes:
weights w for artificial neural networks G Population individuals x of differential evolution algorithm i,G Giving an initial value, and enabling G to represent an nth generation iteratively generated by an ANN-DE method; when g=0, the representation model is in the initialized state, resulting in an initial weight w 0 And primary population individuals x i,0 The initial value is shown in the following formula:
x i,0 ＝[x 1,i,0 ,x 2,i,0 ,...,x D,i,0 ]i＝1,2,...,N；G＝0 (2)
wherein D is a parameter which needs differential evolution optimization, and specifically refers to four parameters (Γ, phi, ψ, omega) contained in population individuals; n is the number of iterations comprising the population of individuals.
Preferably, the N-adam optimization algorithm in step S5 is trained iteratively:
the N-Adam optimization algorithm comprises the following steps:
(a) Calculating weight parameter gradient
(b) Updating gradients
(c) Calculating first order momentum m t ←μ·m t-1 +(1-μ)g t
(d) Calculating a first order momentum correction term
(e) Calculating second order momentum
(f) Calculating a second order momentum correction term
(g) Calculating updated weight parameters
Wherein v and μ are momentum exponential decay parameters, defaults to 0.9 and 0.999; coefficient epsilon of 1e -8 The method comprises the steps of carrying out a first treatment on the surface of the η is the step size, defaulting to 0.002; w (w) t-1 Weight matrix and vector representing one-step iteration of differential evolution model, w t Refers to the updated weight matrix and vector.
The iterative training refers to iteratively updating the weight w of the artificial neural network to minimize the cost function C of the artificial neural network;
the cost function C satisfies the formula (3):
where n is the number of samples,
model output value for the ith sample, p i For the target value of the ith sample, ψ is the regularization coefficient, w is the assigned weight, and the weight and bias update procedure satisfies equation (4):
where δ represents the learning rate, n is the number of samples, and w is the assigned weight.
Preferably, in step S6, mutation, recombination and selection of the differential evolution artificial neural network are performed to obtain a next generation population individual, which specifically includes:
the mutation refers to a mutation ofA given population individual vector x i,G ＝[x 1,i,G ,x 2,i,G ,x 3,i,G ]Adding the weighted difference of the two vectors to the third vector yields a new vector, as shown in equation (5):
v i,G ＝x 1,i,G-1 +F(x 2,i,G-1 -x 3,i,G-1 ) (5)
wherein v is i,G Is donor vector, F is mutation factor, F E [0,2 ]]；
The recombination refers to the test vector u i,G From the target vector x i,G-1 And donor vector v i,G Is u, assuming that the elements of the donor vector enter the trial vector with probability CR i,G The j-th component u of (2) j,i,G The expression of (2) is as shown in formula (6):
wherein rand is j,i ～U[0,1]And I rand [1,2,...,D]V for assurance i,G ≠x i,G-1 A range of random integers;
the selection refers to the target vector x i,G-1 And test vector v i,G The comparison is then performed, and the target vector corresponding to the minimum function value is selected for the next generation, as shown in formula (7):
preferably, the accuracy in step S7 is the standard deviation RMSE of the prediction error, as shown in equation (8):
where N is the number of data points, Y obs Is the actual jet grouting pile diameter, Y pred And D, predicting the diameter of the jet grouting pile of the artificial neural network for differential evolution.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that:
aiming at the defects of difficult construction parameter determination, low algorithm prediction efficiency, large deviation and the like in the existing method, the method improves the calculation efficiency by utilizing an N-Adam method optimization algorithm, improves the calculation accuracy by utilizing a differential evolution artificial neural network, and realizes the efficient and accurate prediction of the diameter of the jet grouting pile without assuming a model theory.
Drawings
FIG. 1 is a schematic flow chart of the method of the present invention.
FIG. 2 is a graph showing the comparison of the predicted results and the measured results of the present invention in the examples.
Detailed Description
The drawings are for illustrative purposes only and are not to be construed as limiting the present patent;
for the purpose of better illustrating the embodiments, certain elements of the drawings may be omitted, enlarged or reduced and do not represent the actual product dimensions;
it will be appreciated by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The technical scheme of the invention is further described below with reference to the accompanying drawings and examples.
Example 1
The embodiment provides a method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence, which comprises the following steps of:
s1: collecting construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s2: preprocessing the collected construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s3: dividing a data set formed by construction parameters, stratum parameters and corresponding jet grouting pile diameters of the preprocessed jet grouting pile into a training set and a testing set, and carrying out normalization processing on the data set;
s4: initializing a differential evolution artificial neural network;
s5: inputting a training set into the differential evolution artificial neural network, and performing iterative training by using an N-Adam method optimization algorithm;
s6: performing mutation, recombination and selection of a differential evolution artificial neural network to obtain next generation population individuals;
s7: repeating the steps S5 to S6 until the evolution algebra reaches a threshold value or the accuracy of the training set reaches the requirement, ending training, and storing the differential evolution artificial neural network at the moment;
s8: and (3) inputting the jet grouting pile data set into the differential evolution artificial neural network obtained in the step (S7) to obtain the diameter of the jet grouting pile.
The construction parameters of the jet grouting pile in the step S1 comprise jet flow Q (X 1 ,m 3 /s), injection pressure F (X) 2 kN), number of nozzles M (X 3 ) Rate of lift v s (X 4 M/s), water-cement ratio W (X) 5 ) Rotational speed N (X) 6 Rpm) and nozzle diameter d o (X 7 M), the stratum parameters are geological parameters obtained by physical and mechanical tests on the soil layer penetrated by the jet grouting area or the jet grouting pile, and comprise drainage/non-drainage shear strength s (X) 8 kPa) and dry weight r d (X 9 ,kN/m 3 )。
Geological survey refers to taking soil from a region to be reinforced on a construction site, arranging exploratory holes according to the geotechnical engineering survey Specification GB 50021, wherein the exploratory holes are controlled holes in a ratio of 12-35 m, the controlled holes penetrate through the thickness of a compression layer below the pile end plane, and the general exploratory holes are expected to be deeper than the pile end plane by 3-5 times the designed diameter of the pile body and not less than 3m.
The preprocessing in step S2 includes removing outliers, and calculating minimum, maximum, standard deviation and average values of the samples, specifically:
removing abnormal values refers to removing abnormal data which are larger than or smaller than the corresponding average value by more than 3 times of standard deviation from each operation parameter of each sampling point;
the stratum parameter average value refers to an average value of soil layer sample parameters of perforation sampling of each jet grouting pile;
the construction parameter average value of the jet grouting pile refers to the average value of the construction parameters of each grouting jet grouting pile.
In the present embodiment, the number of nozzles M (X 3 ) The maximum value is 2, and the minimum value is 1; rate of rise v s (X 4 M/s) maximum value of 0.0103m/s and minimum value of 0.0020m/s; water to ash ratio W (X) 5 ) Maximum value is 0.0103 and minimum value is 0.8; rotation speed N (X) 6 Rpm) maximum of 1.5rpm, minimum of 0.8; nozzle diameter d o (X 7 M) maximum value of 0.008m and minimum value of 0.0018m; shear strength s (X) 8 kPa) maximum value of 212.00kPa and minimum value of 42.70kPa; dry weight r d (X 9 ,kN/m 3 ) Maximum value of 16.11kN/m 3 Minimum value of 13.70kN/m 3 ；
In the present embodiment, the number of nozzles M (X 3 ) Standard deviation of 0.47, lifting rate v s (X 4 M/s) standard deviation of 0.0014m/s, water-cement ratio W (X) 5 ) The standard deviation is 1.181, and the rotation speed N (X 6 Rpm) standard deviation of 0.18rpm, nozzle diameter d o (X 7 M) standard deviation of 0.0009m, drainage/non-drainage shear strength s (X) 8 kPa) standard deviation of 33.1kPa, dry weight r d (X 9 ,kN/m 3 ) Standard deviation of 0.63kN/m 3 ；
In this embodiment, the drainage/non-drainage shear strength s (X 8 kPa) average value of 119.88kPa, dry weight r d (X 9 ,kN/m 3 ) Average value of 15.236kN/m 3 ；
In the present embodiment, the number of nozzles M (X 3 ) Average value of 1.31, lifting rate v s (X 4 M/s) average value of 0.0053m/s, water-ash ratio W (X) 5 ) The average value is 1.006, the rotational speed N (X) 6 Rpm) average value of 1.01rpm, nozzle diameter d o (X 7 M) average value was 0.0031m.
And step S3, the data set is used as input data and output results of training the artificial neural network, wherein the input data are construction parameters and stratum parameters of the jet grouting pile, and the output results are corresponding jet grouting pile diameters.
In the step S3, the normalization process is to perform dimensionless processing on the input data, map the data to a (0, 1) range, and normalize the formula (1) as follows:
wherein X is n,min And X n,max Respectively the minimum value and the maximum value of X, wherein X is one of construction parameters and stratum parameters of the jet grouting pile, and X n The value is normalized by X;
in the present embodiment, the number of nozzles X 3,max Is 2, X 3,min 1 is shown in the specification; rate of rise X 4,max 0.0103, X 4 , min 0.0020; water to ash ratio X 5,max 0.0103, X 5,min 0.8; rotational speed X 6,max 1.5rpm, X 6,min 0.8; nozzle diameter X 7,max 0.008m, X 7,min 0.0018m; shear strength X of drainage/non-drainage 8,max 212.00kPa, X 8,min 42.70kPa; dry weight X 9,max 16.11kN/m 3 ，X 9,min 13.70kN/m 3 。
The differential evolution artificial neural network in the step S4 specifically comprises the following steps:
obtaining N population individuals by utilizing a differential evolution algorithm, wherein the population individuals represent a possible parameter combination of an artificial neural network, and the parameter combination comprises a hidden layer number gamma of the artificial neural network, a node unit number phi of each layer, a regularization coefficient psi and iteration times omega, wherein:
the artificial neural network is a data network composed of a plurality of layered node units which are connected with each other and a weight w, wherein the weight w is a weight value connected with the node units;
the hidden layer number gamma is the layer number of each layer except the input layer and the output layer of the artificial neural network;
the regularization coefficient psi is a coefficient of a regularization term in a cost function of the artificial neural network;
the iteration times omega means that the weight and the deviation are reversely adjusted, so that the times of the cost function are optimized.
In the step S4, the differential evolution artificial neural network is initialized, specifically:
weights w for artificial neural networks G Population individuals x of differential evolution algorithm i,G Giving an initial value, and enabling G to represent an nth generation iteratively generated by an ANN-DE method; when g=0, the model is in the initialized state, and in this embodiment, the hidden layer number Γ is [1,2 ]]The number of node units per layer phi is [1,8]Regularized coefficient ψ is [0.0,0.4 ]]The iteration number omega is [1000,3000]. Obtaining an initial weight w 0 And primary population individuals x i,0 The initial value is shown in the following formula:
x i,0 ＝[x 1,i,0 ,x 2,i,0 ,...,x D,i,0 ]i＝1,2,...,N；G＝0 (2)
wherein D is a parameter which needs differential evolution optimization, and specifically refers to four parameters (Γ, phi, ψ, omega) contained in population individuals; n is the number of iterations comprising the population of individuals, n=50 in this example.
In the step S5, the N-Adam optimization algorithm is trained iteratively:
the N-Adam optimization algorithm comprises the following steps:
(a) Calculating weight parameter gradient
(b) Updating gradients
(c) Calculating first order momentum m t ←μ·m t-1 +(1-μ)g t
(d) Calculating a first order momentum correction term
(e) Calculating second order momentum
(f) Calculating a second order momentum correction term
/>
(g) Calculating updated weight parameters
Wherein v and μ are momentum exponential decay parameters, defaults to 0.9 and 0.999; coefficient epsilon of 1e -8 The method comprises the steps of carrying out a first treatment on the surface of the η is the step size, defaulting to 0.002; w (w) t-1 Weight matrix and vector representing one-step iteration of differential evolution model, w t Refers to the updated weight matrix and vector.
The iterative training refers to iteratively updating the weight w of the artificial neural network to minimize the cost function C of the artificial neural network;
the cost function C satisfies the formula (3):
where n is the number of samples,
model output value for the ith sample, p i For the target value of the ith sample, ψ is the regularization coefficient, w is the assigned weight, and the weight and bias update procedure satisfies equation (4):
where δ represents the learning rate, n is the number of samples, and w is the assigned weight.
In the step S6, mutation, recombination and selection of the differential evolution artificial neural network are carried out to obtain the next generation population individuals, which are specifically as follows:
the mutation refers to the vector x of individuals in a given population i,G ＝[x 1,i,G ,x 2,i,G ,x 3,i,G ]Adding two vectorsThe weight difference is added to the third vector to obtain a new vector, as shown in equation (5):
v i,G ＝x 1,i,G-1 +F(x 2,i,G-1 -x 3,i,G-1 ) (5)
wherein v is i,G Called donor vector, F is a mutation factor, F.epsilon.0, 2]；
The recombination refers to the test vector u i,G From the target vector x i,G-1 And donor vector v i,G Is u, assuming that the elements of the donor vector enter the trial vector with probability CR i,G The j-th component u of (2) j,i,G The expression of (2) is as shown in formula (6):
wherein rand is j,i ～U[0,1]And I rand [1,2,...,D]V for assurance i,G ≠x i,G-1 A range of random integers;
the selection refers to the target vector x i,G-1 And test vector v i,G The comparison is then performed, and the target vector corresponding to the minimum function value is selected for the next generation, as shown in formula (7):
the accuracy in step S7 is the standard deviation RMSE of the prediction error, as shown in equation (8):
where N is the number of data points, Y obs Is the actual jet grouting pile diameter, Y pred And D, predicting the diameter of the jet grouting pile of the artificial neural network for differential evolution.
Maximum number of evolution iterations G specified in advance max ＝100。
The test model results show that compared with the traditional optimized neural network and the theoretical model, the proposed differential evolution artificial neural network (ANN-DE) can achieve higher accuracy while guaranteeing the reliability and efficiency of the training process. In this case, when g=27, the optimal super-parameters can be extracted; at this time, the hidden layer Γ=2, the node unit number Φ=8 of each layer, the regularization coefficient ψ= 0.24469, and the iteration number Ω=2995. The results show that the standard deviation rmse= 0.05339 obtained by training and the standard deviation rmse= 0.04238 obtained by testing.
In this example, the average value of the predicted values of the diameter of the jet grouting piles is 0.65071m.
The prediction results are shown in fig. 2, wherein the square blocks in the figure are the calculation results of the ANN-DE method, and the forked points are the calculation results of the theoretical method. The distribution of points on the graph can obtain better fitting degree and correlation R of the ANN-DE method 2 0.97 for the ANN-DE process is higher than 0.93 for the theoretical process. Meanwhile, the model performance of the RMSE and the coefficient determination mapping shows that the deviation of the ANN-DE method and the theoretical method RMSE is 0.02818, and the deviation of the coefficient determination is 0.04, so that the ANN-DE method can achieve higher accuracy while guaranteeing the reliability and efficiency of the training process.
The same or similar reference numerals correspond to the same or similar components;
the terms describing the positional relationship in the drawings are merely illustrative, and are not to be construed as limiting the present patent;
it is to be understood that the above examples of the present invention are provided by way of illustration only and not by way of limitation of the embodiments of the present invention. Other variations or modifications of the above teachings will be apparent to those of ordinary skill in the art. It is not necessary here nor is it exhaustive of all embodiments. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the invention are desired to be protected by the following claims.
Claims (9)
1. The method for determining the diameter of the jet grouting pile based on the differential evolution artificial intelligence is characterized by comprising the following steps of:
s1: collecting construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s2: preprocessing the collected construction parameters, stratum parameters and corresponding diameters of the jet grouting piles;
s3: dividing a data set formed by construction parameters, stratum parameters and corresponding jet grouting pile diameters of the preprocessed jet grouting pile into a training set and a testing set, and carrying out normalization processing on the data set;
s4: initializing a differential evolution artificial neural network;
s5: inputting a training set into the differential evolution artificial neural network, and performing iterative training by using an N-Adam method optimization algorithm;
s6: performing mutation, recombination and selection of a differential evolution artificial neural network to obtain next generation population individuals;
s7: repeating the steps S5 to S6 until the evolution algebra reaches a threshold value or the accuracy of the training set reaches the requirement, ending training, and storing the differential evolution artificial neural network at the moment;
s8: inputting the jet grouting pile data set into the differential evolution artificial neural network obtained in the step S7 to obtain the diameter of the jet grouting pile;
the N-Adam optimization algorithm in the step S5 comprises the following steps:
(a) Calculating weight parameter gradient
(b) Updating gradients
(c) Calculating first order momentum m t ←μ·m t-1 +(1-μ)g t
(d) Calculating a first order momentum correction term
(e) Calculating second order motionMeasuring amount
(f) Calculating a second order momentum correction term
(g) Calculating updated weight parameters
Wherein v and μ are momentum exponential decay parameters, defaults to 0.9 and 0.999; coefficient epsilon of 1e -8 The method comprises the steps of carrying out a first treatment on the surface of the η is the step size, defaulting to 0.002; w (w) t-1 Weight matrix and vector representing one-step iteration of differential evolution model, w t The updated weight matrix and vector are referred;
the iterative training refers to iteratively updating the weight w of the artificial neural network to minimize the cost function C of the artificial neural network;
the cost function C satisfies the formula (3):
where n is the number of samples,
model output value for the ith sample, p i For the target value of the ith sample, ψ is the regularization coefficient, w is the assigned weight, and the weight and bias update procedure satisfies equation (4):
where δ represents the learning rate, n is the number of samples, and w is the assigned weight.
2. The method for determining the diameter of the jet grouting pile based on the differential evolution artificial intelligence according to claim 1, wherein the construction parameters of the jet grouting pile in the step S1 comprise jet flow Q, jet pressure F, nozzle number M and lifting rate v s Water-cement ratio W, rotational speed N and nozzle diameter d o The stratum parameters are geological parameters obtained by physical and mechanical tests on the soil layer crossing of the jet grouting area or the jet grouting pile, and comprise drainage shear strength s or non-drainage shear strength s u And dry weight r d 。
3. The method for determining the diameter of a rotary jetting tool based on differential evolution artificial intelligence according to claim 1, wherein the preprocessing in step S2 comprises removing outliers, sampling minimum, maximum, standard deviation and average, in particular:
removing abnormal values refers to removing abnormal data which are larger than or smaller than the corresponding average value by more than 3 times of standard deviation from each operation parameter of each sampling point;
the stratum parameter average value refers to an average value of soil layer sample parameters of perforation sampling of each jet grouting pile;
the construction parameter average value of the jet grouting pile refers to the average value of the construction parameters of each grouting jet grouting pile.
4. The method for determining the diameter of the jet grouting pile based on the differential evolution artificial intelligence according to claim 2, wherein the data set in the step S3 is used as input data and output results of training an artificial neural network, wherein the input data are construction parameters and stratum parameters of the jet grouting pile, and the output results are corresponding diameters of the jet grouting pile.
5. The method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence according to claim 4, wherein the normalization process in step S3 is a dimensionless process of input data, mapping the data to a (0, 1) range, and the normalization formula (1) is as follows:
wherein X is n,min And X n,max Respectively the minimum value and the maximum value of X, wherein X is one of construction parameters and stratum parameters of the jet grouting pile, and X n The value normalized by X.
6. The method for determining a diameter of a jet grouting pile based on differential evolution artificial intelligence according to claim 5, wherein the differential evolution artificial neural network in step S4 is specifically:
obtaining N population individuals by utilizing a differential evolution algorithm, wherein the population individuals represent a possible parameter combination of an artificial neural network, and the parameter combination comprises a hidden layer number gamma of the artificial neural network, a node unit number phi of each layer, a regularization coefficient psi and iteration times omega, wherein:
the artificial neural network is a data network composed of a plurality of layered node units which are connected with each other and a weight w, wherein the weight w is a weight value connected with the node units;
the hidden layer number gamma is the layer number of each layer except the input layer and the output layer of the artificial neural network;
the regularization coefficient psi is a coefficient of a regularization term in a cost function of the artificial neural network;
the iteration times omega means that the weight and the deviation are reversely adjusted, so that the times of the cost function are optimized.
7. The method for determining a diameter of a jet grouting pile based on differential evolution artificial intelligence according to claim 6, wherein the initializing the differential evolution artificial neural network in step S4 comprises:
weights w for artificial neural networks G Population individuals x of differential evolution algorithm i,G Giving an initial value, and enabling G to represent an nth generation iteratively generated by an ANN-DE method; when g=0, the representation model is in the initialized state, resulting in an initial weight w 0 And primary population individuals x i,0 The initial value is shown in the following formula:
x i,0 ＝[x 1,i,0 ,x 2,i,0 ,...,x D,i,0 ] i＝1,2,...,N； G＝0 (2)
wherein D is a parameter which needs differential evolution optimization, and specifically refers to four parameters (Γ, phi, ψ, omega) contained in population individuals; n is the number of iterations comprising the population of individuals.
8. The method for determining the diameter of a jet grouting pile based on differential evolution artificial intelligence according to claim 7, wherein in the step S6, mutation, recombination and selection of the differential evolution artificial neural network are performed to obtain next generation population individuals, specifically:
the mutation refers to the vector x of individuals in a given population i,G ＝[x 1,i,G ,x 2,i,G ,x 3,i,G ]Adding the weighted difference of the two vectors to the third vector yields a new vector, as shown in equation (5):
wherein v is i,G Is donor vector, F is mutation factor, F E [0,2 ]]；
v i,G ＝x 1,i,G-1 +F(x 2,i,G-1 -x 3,i,G-1 ) (5)
The recombination refers to the test vector u i,G From the target vector x i,G-1 And donor vector v i,G Is u, assuming that the elements of the donor vector enter the trial vector with probability CR i,G The j-th component u of (2) j,i,G The expression of (2) is as shown in formula (6):
wherein v is j,i,G For the donor vector v i,G The j-th component, x j,i,G-1 For the target vector x i,G-1 The j-th component, rand j,i ～U[0,1]And I rand [1,2,...,D]V for assurance i,G ≠x i,G-1 A range of random integers;
the selection refers to the target vector x i,G-1 And test vector v i,G The comparison is then performed, and the target vector corresponding to the minimum function value is selected for the next generation, as shown in formula (7):
9. the method for determining a diameter of a rotary jetting tool based on differential evolution artificial intelligence as claimed in claim 8, wherein the accuracy in step S7 is a standard deviation RMSE with prediction error, as shown in formula (8):
where N is the number of data points, Y obs Is the actual jet grouting pile diameter, Y pred And D, predicting the diameter of the jet grouting pile of the artificial neural network for differential evolution.
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