CN113222273A - TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm - Google Patents

TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm Download PDF

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CN113222273A
CN113222273A CN202110577145.8A CN202110577145A CN113222273A CN 113222273 A CN113222273 A CN 113222273A CN 202110577145 A CN202110577145 A CN 202110577145A CN 113222273 A CN113222273 A CN 113222273A
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张海波
杨海清
曹科
靳晓光
宋康磊
杜传奇
曾绍毅
种攀攀
周波
许天珍
安龙飞
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Tunnel Engineering Co Ltd of China Railway 18th Bureau Group Co Ltd
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Abstract

The invention relates to a TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm, which comprises the following steps: s1: acquiring TBM machine operation record data, and constructing a sample data set; s2: constructing an FW-MKL-SVR model; s3: optimizing and training parameters in the FW-MKL-SVR model by using an GWO algorithm and sample data to obtain a TBM tunneling rate prediction model based on GWO-FW-MKL-SVR; s4: testing the prediction accuracy of the GWO-FW-MKL-SVR model; if the preset TBM tunneling prediction accuracy is not met, returning to S3 to select parameters and train the model again; and if the set precision requirement is met, inputting the operation data of the unknown TBM machine, the soil body mechanical data and the rock mechanical data into the model to obtain an unknown TBM tunneling rate predicted value.

Description

TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm
Technical Field
The invention relates to the technical field of TBM tunneling rate prediction, in particular to a TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm.
Background
A Tunnel Boring Machine (TBM) is a large-scale boring apparatus with a high degree of automation and a high speed, which is 3-10 times more efficient and faster than conventional methods such as drilling and blasting. At present, the application of the TBM in tunnel construction is more and more extensive, especially for hard rock and long and large tunnels, but the adaptability of the TBM to site geological conditions is poor, and the problems of tunnel construction efficiency, rock burst, water inrush and the like are seriously influenced. Currently, a plurality of prediction methods for applying the support vector regression SVR algorithm to the prediction of the TBM tunneling rate also appear, and the cost of the TBM project can be effectively reduced by accurately predicting the tunneling rate and selecting a proper construction method.
The prior art has the following defects: in the actual tunnel boring engineering of the TBM, tunnel geological conditions are variable, and more boring parameters need to be input, so that the prediction precision of the existing SVR model is low, therefore, the intelligent prediction method is provided for accurately predicting the tunnel boring efficiency, and is very important for saving the construction cost of the tunnel engineering and controlling the risk of the construction progress.
Disclosure of Invention
Aiming at the problems in the prior art, the technical problems to be solved by the invention are as follows: and optimizing and improving the SVR algorithm by adopting a reasonable method, and improving the prediction precision of the TBM tunneling rate.
In order to solve the technical problems, the invention adopts the following technical scheme: a TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm comprises the following steps:
s100: constructing a sample data set, wherein the sample data set comprises: the method comprises the following steps that a plurality of TBM machines run and record data, soil body mechanics data and rock mechanics data and corresponding actual tunneling rate values of the TBMs;
s200: constructing an FW-MKL-SVR model;
s210: improving the kernel function of the SVR model to obtain an FW-MKL-SVR model kernel function, carrying out dual processing on the FW-MKL-SVR model kernel function, and then obtaining the FW-MKL-SVR model;
s300: constructing GWO-FW-MKL-SVR prediction model, wherein the specific steps are as follows:
s310: randomly selecting part of samples in the sample data set to form a training set, and forming the other sample into a test set;
s320: randomly initializing parameter values of parameters [ P, lambda, d, r, gamma ] in the FW-MKL-SVR model;
s330: setting the maximum iteration times, inputting all data in a training set as data of an FW-MKL-SVR model, calculating and updating the parameters by using an GWO Hui wolf optimization algorithm, and outputting the optimal parameters after the training reaches the maximum iteration times;
s340: substituting the optimal parameters into the FW-MKL-SVR model to obtain an GWO-FW-MKL-SVR prediction model;
s400: the accuracy of prediction of the GWO-FW-MKL-SVR model is checked by using the test set data, the test set data is input into the GWO-FW-MKL-SVR prediction model obtained in the step S340 to obtain a predicted value, and the predicted value and the driving speed of the TBM are calculatedRate measured value calculation performance index R2If R is2The method comprises the following steps of meeting the set TBM tunneling prediction accuracy requirement, carrying out the next step, and setting an GWO-FW-MKL-SVR prediction model as a final model; if the preset TBM tunneling prediction precision requirement is not met, repeating the steps S320-S340 to perform model training and parameter optimization again;
s500: and (3) predicting the unknown TBM tunneling rate: and substituting the machine operation record data, the soil body mechanical data and the rock mechanical data of the unknown TBM into the final model to obtain the tunneling rate predicted value of the unknown TBM.
The tunneling parameters of the TBM are adjusted in real time according to the obtained tunneling rate predicted value, and then the current parameters are optimized and adjusted to achieve the purpose of safe and efficient tunneling of the TBM.
Preferably, the method for constructing the sample data set in step S100 includes the specific steps of:
acquiring TBM machine operation record data: the device comprises a chamber soil pressure CEP, a total thrust TH, a cutter head torque CT and a cutter head rotating speed CS;
confirm soil body mechanics data and rock mechanics data through normal position experiment and indoor experiment, soil body mechanics data include: the parameters of the composite stratum comprise cohesive force c, an internal friction angle psi and a compression modulus Es; rock mechanics data include: the pebble ratio RB, the uniaxial compressive strength UCS and the rock quality index RQD.
The TBM tunneling rate influencing factors are various, and mainly comprise rock and soil mass indexes and tunneling parameters. Research and practice show that the common influencing factors and indexes for predicting the TBM tunneling rate mainly comprise rock uniaxial compressive strength UCS, rock quality index RQD, pebble ratio RB, rock integrity coefficient, cohesion c, internal friction angle psi, compression modulus Es and the like.
The selection of the model parameters is determined by comprehensively considering the principles of parameter availability, prediction accuracy, model complexity, use frequency of previous research and the like; the rock uniaxial compressive strength UCS, the rock quality index RQD, the rock integrity coefficient, the cohesion force c, the internal friction angle psi, the compression modulus Es and other soil mechanical data and rock mechanical data can be obtained through in-situ experiments and indoor experiments; and for machine operation record data of the TBM such as soil bin pressure CEP, total cutter head thrust TH, cutter head torque CT, cutter head rotating speed CS and the like, acquiring TBM machine operation records according to on-duty daily reports of a tunnel construction site.
Preferably, the specific steps of obtaining the FW-MKL-SVR model in step S210 are as follows:
s211: improving the kernel function of the SVR model to obtain a FW-MKL-SVR model kernel function;
the kernel function of the SVR model is represented as follows:
Figure BDA0003084743630000031
the kernel function of the FW-MKL-SVR model is as follows:
Figure BDA0003084743630000032
wherein, P is the weight of input characteristic, λ is the weight of polynomial kernel function, 1- λ is the weight of radial basis kernel function, d, r are the parameters of polynomial kernel function, γ is the parameters of radial basis kernel function;
s212: and (3) expressing the kernel function of the FW-MKL-SVR model by using an SVR dual problem, substituting the SVR dual problem into a function f (x) to obtain the FW-MKL-SVR model, wherein the formula is expressed as follows:
Figure BDA0003084743630000033
preferably, the TBM tunneling rate prediction model of GWO-FW-MKL-SVR obtained in step S330 comprises the following specific steps:
s231: setting the maximum iteration times, setting the number of grey wolves in a grey wolves optimization algorithm, and randomly initializing parameter values of parameters [ P, lambda, d, r and gamma ] in an FW-MKL-SVR model, namely initial values of grey wolves, wherein the position of each wolf is represented by the parameters [ P, lambda, d, r and gamma ] in the FW-MKL-SVR model;
s232: calculating the fitness value of each wolf according to the training set, wherein the fitness value is the mean square error of a TBM rate predicted value and a rate true value, the larger the fitness value is, the better the model training is, sorting the fitness values according to the sizes of the fitness values, and selecting the first three optimal position fitness values to guide and complete the selection of the optimal related parameters;
s233: updating the positions of all the gray wolves by calculating the distances between the gray wolves omega except the optimal gray wolves and the three optimal gray wolves, and updating the coefficient vector value of the gray wolves optimization algorithm;
s234: and stopping when the iterative updating reaches the maximum value, outputting the gray wolf with the best fitness, namely outputting the position [ P, lambda, d, r, gamma ] of the best gray wolf, and establishing a TBM tunneling rate prediction model of GWO-FW-MKL-SVR.
The position [ P, lambda, d, r, gamma ] of the optimal wolf is the optimal parameter to be obtained, and the obtained optimal parameter is led into the FW-MKL-SVR model, so that the GWO-FW-MKL-SVR prediction model can be obtained.
Preferably, the accuracy of the GWO-FW-MKL-SVR model prediction tested in step S400 is specifically as follows:
using test set, R2Index evaluation model prediction model performance, R2The calculation formula of (2) is as follows:
Figure BDA0003084743630000041
wherein n is the number of samples; y isiRepresents an actual measurement value, y'iRepresenting a predicted value;
Figure BDA0003084743630000042
which represents the mean of the measured values and,
Figure BDA0003084743630000043
means representing the predicted values; 1,2, … n; r requiring a predicted tunneling rate for a TBM2Up to over 0.85.
Compared with the prior art, the invention has at least the following advantages:
1. the method adopts a mixed algorithm of a gray wolf optimization algorithm (GWO) and a feature weighted multi-core support vector regression (FW-MKL-SVR) to predict the tunneling rate of the TBM (tunnel boring machine), and the algorithm has rich data types and flexible expression mode, and can effectively improve the prediction precision of the tunneling rate of the TBM.
2. The invention adopts a reasonable method to optimize and improve the SVR algorithm, the proposed TBM tunneling rate prediction model has obvious advantages in the aspects of parameter optimization processing and prediction precision, parameter redundancy can be reduced on the premise of ensuring the prediction precision, and the method is suitable for tunnel construction environments with complicated geological environments.
3. In the actual tunneling construction process, the intelligent prediction method provided by the invention can more accurately predict the tunneling rate of the TBM, so that reference is provided for the actual engineering, and the intelligent prediction method has very obvious guiding effects on reducing the tunneling construction cost, prolonging the service life of equipment, controlling the construction progress risk and improving the engineering quality.
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FIG. 1 is a flow chart of the operation of the present invention.
FIG. 2 shows the parameter results obtained by training the GWO-FW-MKL-SVR algorithm in the present invention.
FIG. 3 is an input feature weight distribution of the GWO-FW-MKL-SVR model in the present invention.
FIG. 4 is a diagram of TBM PR prediction data during the training phase of the present invention.
FIG. 5 is a diagram of the TBM PR prediction data at the test stage of the present invention.
Detailed Description
The present invention is described in further detail below.
The invention relates to a hybrid intelligent prediction technology based on SVR algorithm improvement, which adopts a hybrid algorithm of a gray wolf optimization algorithm (GWO) and a feature weighted multi-core support vector regression (FW-MKL-SVR) to predict the tunneling rate of a TBM (tunnel boring machine), and the algorithm can effectively improve the prediction precision of the tunneling rate of the TBM.
Example (b): a TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm comprises the following steps:
s100: sample data collection: the method comprises the steps of obtaining TBM machine operation record data, determining soil and rock mechanical data through in-situ experiments and indoor experiments, and constructing a sample data set, wherein the sample data set comprises the following components: running the plurality of TBM machines to record data, soil body mechanics data and rock mechanics data and corresponding actual measurement values of the tunneling rates of the TBMs;
s200: constructing an FW-MKL-SVR model;
s210: improving an SVR model, wherein the SVR model is a kernel function of an existing model to obtain an FW-MKL-SVR model kernel function, and performing dual processing on the FW-MKL-SVR model kernel function to obtain an FW-MKL-SVR model;
s300: constructing GWO-FW-MKL-SVR prediction model, wherein the specific steps are as follows:
s310: randomly selecting part of samples in the sample data set to form a training set, and forming the other sample into a test set;
s320: randomly initializing parameter values of parameters [ P, lambda, d, r, gamma ] in the FW-MKL-SVR model;
s330: setting the maximum iteration times, inputting all data in a training set as data of an FW-MKL-SVR model, calculating and updating the parameters by using an GWO Hui wolf optimization algorithm, and outputting the optimal parameters after the training reaches the maximum iteration times; GWO the gray wolf optimization algorithm is the existing technology, in the iterative process, the gray wolf optimization algorithm will screen the output related parameters, always selects the optimal group of related parameters as the output; the GWO algorithm is an optimization searching method which is inspired by the predation activity of the wolf, and is used for quickly searching a global optimization solution, and the GWO-FW-MKL-SVR model is a feature-weighted multi-core support vector regression (FW-MKL-SVR) mixed algorithm model optimized based on the wolf optimization algorithm (GWO);
s340: substituting the optimal parameters into the FW-MKL-SVR model to obtain an GWO-FW-MKL-SVR prediction model;
s400: the accuracy of prediction of the GWO-FW-MKL-SVR model is verified by using the data of the test set, the data of the test set is input into the GWO-FW-MKL-SVR prediction model obtained in the step S340 to obtain a predicted value, and the performance index R is calculated according to the predicted value and the actual measurement value of the tunneling rate of the TBM2If R is2TBM tunneling prediction essence meeting settingWhen the degree is required, the next step is carried out, and the GWO-FW-MKL-SVR prediction model is set as a final model; if the preset TBM tunneling prediction precision requirement is not met, repeating S320-S340 to perform model training and parameter optimization again;
s500: and (3) predicting the unknown TBM tunneling rate: and substituting the machine operation record data, the soil body mechanical data and the rock mechanical data of the unknown TBM into the final model to obtain the tunneling rate predicted value of the unknown TBM. TBM tunneling rate (PR) prediction result data for the training and testing phase are shown in fig. 4 and 5.
In the specific implementation: the specific steps for constructing the sample data set are as follows:
acquiring TBM machine operation record data: the mutual action of the machine parameters and geological conditions jointly determines the tunneling rate PR of the TBM, and the TBM records the machine parameters including the soil bin pressure CEP, the total thrust TH, the cutter torque CT and the cutter rotation speed CS;
confirm soil body mechanics data and rock mechanics data through in situ experiment and indoor experiment, because the weathering degree of composite formation is high, intensity is low, can use the parameter of soil body mechanics: the parameters of the composite stratum comprise cohesive force c, an internal friction angle psi and a compression modulus Es; the pebble lithology is slightly weathered granite with complete surface and high hardness, and the rock mechanics data comprise: the pebble ratio RB, the uniaxial compressive strength UCS and the rock quality index RQD; through drilling and indoor tests, the parameters of the composite stratum and the round stone are obtained, and the distribution of the stratum among the drill holes can be deduced from the drilling data.
The TBM tunneling rate is predicted and a database of 503 data samples is built for modeling the TBM tunneling rate PR. In artificial intelligence and machine learning research, the entire database is typically divided into two groups; one group develops AI and ML models using a training data set and one group evaluates the developed models using a test data set. Given the existing relevant studies, 20% -30% of the data set can be allocated for testing. Thus, in the present embodiment, 350 sample sets are used in the training phase and the remaining 153 sample sets are used in the model evaluation or testing phase. Some basic statistical details of the parameters used as model inputs/outputs are given in the table of fig. 2.
In specific implementation, the specific steps for obtaining the FW-MKL-SVR model are as follows:
s211: improving the kernel function of the SVR model to obtain a FW-MKL-SVR model kernel function;
the kernel function of the SVR model is represented as follows:
Figure BDA0003084743630000061
the kernel function of the FW-MKL-SVR model is as follows:
Figure BDA0003084743630000062
wherein, P is the weight of input characteristic, λ is the weight of polynomial kernel function, 1- λ is the weight of radial basis kernel function, d, r are the parameters of polynomial kernel function, γ is the parameters of radial basis kernel function;
s212: the kernel function of the FW-MKL-SVR model is expressed by an SVR dual problem, the FW-MKL-SVR problem can be converted into a general optimization problem of the SVR, the FW-MKL-SVR model is solved by solving the SVR, and finally a function f (x) is substituted to obtain the FW-MKL-SVR model, wherein the formula is expressed as follows:
Figure BDA0003084743630000063
in specific implementation, the TBM tunneling rate prediction model of GWO-FW-MKL-SVR is established by the following specific steps:
s231: setting the maximum iteration times, setting the number of grey wolves in a grey wolves optimization algorithm, and randomly initializing parameter values of parameters [ P, lambda, d, r and gamma ] in an FW-MKL-SVR model, namely initial values of grey wolves, wherein the position of each wolf is represented by the parameters [ P, lambda, d, r and gamma ] in the FW-MKL-SVR model;
s232: calculating the fitness value of each wolf according to the training set, wherein the fitness value is the mean square error of a TBM rate predicted value and a rate true value, the larger the fitness value is, the better the model training is, sorting the fitness values according to the sizes of the fitness values, and selecting the first three optimal position fitness values to guide and complete the selection of the optimal related parameters;
s233: updating the positions of all the gray wolves by calculating the distances between the gray wolves omega except the optimal gray wolves and the three optimal gray wolves, and updating the coefficient vector value of the gray wolves optimization algorithm; GWO-FW-MKL-SVR algorithm was trained to obtain the parameter results as shown in FIG. 2.
S234: and stopping when the iterative updating reaches the maximum value, outputting the gray wolf with the best fitness, namely outputting the position [ P, lambda, d, r, gamma ] of the best gray wolf, and establishing a TBM tunneling rate prediction model of GWO-FW-MKL-SVR.
In specific implementation, the accuracy of the GWO-FW-MKL-SVR model prediction is tested as follows:
using test set, R2Index evaluation model prediction model performance, R2The calculation formula of (2) is as follows:
Figure BDA0003084743630000071
wherein n is the number of samples; y isiRepresents an actual measurement value, y'iRepresenting a predicted value;
Figure BDA0003084743630000072
which represents the mean of the measured values and,
Figure BDA0003084743630000073
means representing the predicted values; 1,2, … n; r requiring a predicted tunneling rate for a TBM2Up to over 0.85. GWO-FW-MKL-SVR model input feature weight distribution is shown in FIG. 3.
During specific implementation, unknown TBM machine operation data, soil body mechanical data and rock mechanical data are introduced into a final GWO-FW-MKL-SVR model, namely, model parameters such as soil bin pressure, total thrust, hob torque, hob rotating speed, rock mass cohesive force, internal friction angle, compression modulus, solitary stone ratio, uniaxial compressive strength and rock quality index are input, and then the tunneling rate of the TBM is predicted. TBM tunneling rate (PR) prediction result data in the training stage are shown in figure 4; TBM tunneling rate (PR) prediction results data for the test phase fig. 5.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (5)

1. A TBM tunneling rate prediction method based on GWO-FW-MKL-SVR algorithm is characterized by comprising the following steps: the method comprises the following steps:
s100: constructing a sample data set, wherein the sample data set comprises: the method comprises the following steps that a plurality of TBM machines run and record data, soil body mechanics data and rock mechanics data and corresponding actual tunneling rate values of the TBMs;
s200: constructing an FW-MKL-SVR model;
s210: improving the kernel function of the SVR model to obtain an FW-MKL-SVR model kernel function, carrying out dual processing on the FW-MKL-SVR model kernel function, and then obtaining the FW-MKL-SVR model;
s300: constructing GWO-FW-MKL-SVR prediction model, wherein the specific steps are as follows:
s310: randomly selecting part of samples in the sample data set to form a training set, and forming the other sample into a test set;
s320: randomly initializing parameter values of parameters [ P, lambda, d, r, gamma ] in the FW-MKL-SVR model;
s330: setting the maximum iteration times, inputting all data in a training set as data of an FW-MKL-SVR model, calculating and updating the parameters by using an GWO Hui wolf optimization algorithm, and outputting the optimal parameters after the training reaches the maximum iteration times;
s340: substituting the optimal parameters into the FW-MKL-SVR model to obtain an GWO-FW-MKL-SVR prediction model;
s400: the accuracy of prediction of the GWO-FW-MKL-SVR model is verified by using the test set data, and the test set data is input into the step S340 to obtainObtaining a predicted value in an GWO-FW-MKL-SVR prediction model, and calculating a performance index R through the predicted value and a tunneling rate measured value of the TBM2If R is2The method comprises the following steps of meeting the set TBM tunneling prediction accuracy requirement, carrying out the next step, and setting an GWO-FW-MKL-SVR prediction model as a final model; if the preset TBM tunneling prediction precision requirement is not met, repeating S320-S340 to perform model training and parameter optimization again;
s500: and (3) predicting the unknown TBM tunneling rate: and substituting the machine operation record data, the soil body mechanical data and the rock mechanical data of the unknown TBM into the final model to obtain the tunneling rate predicted value of the unknown TBM.
2. The method for predicting the TBM tunneling rate based on the GWO-FW-MKL-SVR algorithm according to claim 1, wherein: constructing the sample data set in the step S100, specifically comprising the following steps:
acquiring TBM machine operation record data: the device comprises a soil bin pressure CEP, a total thrust TH, a cutter head torque CT and a cutter head rotating speed CS;
confirm soil body mechanics data and rock mechanics data through normal position experiment and indoor experiment, soil body mechanics data include: the parameters of the composite stratum comprise cohesive force c, an internal friction angle psi and a compression modulus Es; rock mechanics data include: the pebble ratio RB, the uniaxial compressive strength UCS and the rock quality index RQD.
3. The method for predicting the TBM tunneling rate based on the GWO-FW-MKL-SVR algorithm according to claim 2, wherein: the specific steps of obtaining the FW-MKL-SVR model in the step S210 are as follows:
s211: improving the kernel function of the SVR model to obtain a FW-MKL-SVR model kernel function;
the kernel function of the SVR model is represented as follows:
Figure FDA0003084743620000021
the kernel function of the FW-MKL-SVR model is as follows:
Figure FDA0003084743620000022
wherein, P is the weight of input characteristic, λ is the weight of polynomial kernel function, 1- λ is the weight of radial basis kernel function, d, r are the parameters of polynomial kernel function, γ is the parameters of radial basis kernel function;
s212: and (3) expressing the kernel function of the FW-MKL-SVR model by using an SVR dual problem, substituting the SVR dual problem into a function f (x) to obtain the FW-MKL-SVR model, wherein the formula is expressed as follows:
Figure FDA0003084743620000023
4. the method for predicting the TBM tunneling rate based on the GWO-FW-MKL-SVR algorithm according to claim 3, wherein: the TBM tunneling rate prediction model of the GWO-FW-MKL-SVR obtained in the step S330 comprises the following specific steps:
s231: setting the maximum iteration times, setting the number of grey wolves in a grey wolves optimization algorithm, and randomly initializing parameter values of parameters [ P, lambda, d, r and gamma ] in an FW-MKL-SVR model, namely initial values of grey wolves, wherein the position of each wolf is represented by the parameters [ P, lambda, d, r and gamma ] in the FW-MKL-SVR model;
s232: calculating the fitness value of each wolf according to the training set, wherein the fitness value is the mean square error of a TBM rate predicted value and a rate true value, the larger the fitness value is, the better the model training is, sorting the fitness values according to the sizes of the fitness values, and selecting the first three optimal position fitness values to guide and complete the selection of the optimal related parameters;
s233: updating the positions of all the gray wolves by calculating the distances between the gray wolves omega except the optimal gray wolves and the three optimal gray wolves, and updating the coefficient vector value of the gray wolves optimization algorithm;
s234: and stopping when the iterative updating reaches the maximum value, outputting the gray wolf with the best fitness, namely outputting the position [ P, lambda, d, r, gamma ] of the best gray wolf, and establishing a TBM tunneling rate prediction model of GWO-FW-MKL-SVR.
5. The method for predicting the TBM tunneling rate based on the GWO-FW-MKL-SVR algorithm according to claim 4, wherein: the accuracy of the test GWO-FW-MKL-SVR model prediction described in step S400 is specifically as follows:
using test set, R2Index evaluation model prediction model performance, R2The calculation formula of (2) is as follows:
Figure FDA0003084743620000031
wherein n is the number of samples; y isiRepresents an actual measurement value, y'iRepresenting a predicted value;
Figure FDA0003084743620000032
which represents the mean of the measured values and,
Figure FDA0003084743620000033
means representing the predicted values; 1,2, …, n; r requiring a predicted tunneling rate for a TBM2Up to over 0.85.
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