A method and system for determining the total thrust of a composite earth pressure balance shield machine

A composite earth pressure balance shield tunneling total thrust prediction model, established through dimensionless calculation and machine learning algorithms, has solved the problem of predicting total thrust in geological strata with different degrees of weathering, achieving higher prediction accuracy and construction support.

CN115017790BActive Publication Date: 2025-02-28TIANJIN UNIV +1
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Patent Information

Application Number
CN202110239557.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2021-03-04
Publication Date
2025-02-28
Estimated Expiration
2041-03-04

AI Technical Summary

Technical Problem

Existing technologies lack specificity and applicability for predicting the total thrust of composite earth pressure balance tunnel boring machines in rock strata with different degrees of weathering, which increases the difficulty of construction.

Method used

A predictive model for the total thrust of a composite earth pressure balance shield tunneling machine was established by employing a dimensionless calculation method and a decimal scaling normalization method, combined with the Lasso regression algorithm. By determining the characteristic parameters affecting the total thrust, dimensionless processing, normalization processing, and model training were performed to obtain the predicted value of the total thrust.

Benefits of technology

It improves the relevance and applicability of determining the total thrust of composite earth pressure balance shield tunneling machines, provides effective support for construction decision-making, and enhances the accuracy and practicality of prediction.

✦ Generated by Eureka AI based on patent content.

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Abstract

The invention discloses a method for determining the total thrust of a composite earth pressure balance shield machine, the determination method comprising: determining characteristic parameters that affect the total thrust; determining the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter according to a dimensionless calculation method; performing dimensionless processing and normalization processing on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust; training each coefficient of the dimensionless input function according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust; performing normalization and dimension reduction on the dimensionless prediction model to obtain a total thrust determination model; obtaining the current engineering data of the characteristic parameters, and inputting the total thrust determination model into the prediction. The invention targets composite geology of rock strata with different weathering degrees, determines the dimensionless characteristic parameters reflecting the common law of the working condition by applying dimension analysis on the basis of mechanical analysis, combines it with the machine learning algorithm training modeling, and improves the pertinence, practicality and accuracy of the method.
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Description

Technical Field

[0001] The invention relates to the technical field of tunnel excavation equipment, and in particular to a method and system for determining the total excavation thrust of a composite earth pressure balance shield machine. Background Art

[0002] The composite earth pressure balance shield machine is a tunnel excavation equipment suitable for tunneling with various composite strata with large strength differences in the excavation face. Its total thrust is an important performance parameter to ensure the normal advancement and construction of the equipment. The key to estimating the total thrust of the composite earth pressure balance shield machine is to establish a method that can be applied to composite geology of various strata. In many tunnel projects constructed by composite earth pressure balance shield machines, composite geology composed of different types of rock strata with different weathering degrees, such as fully weathered mixed rock, fully weathered granite, strongly weathered sandstone, strongly weathered mixed rock, and strongly weathered granite, is often encountered. However, the existing shield excavation total thrust estimation methods still lack a method that specifically considers the common influencing parameters of the total thrust during excavation in such rock strata with different weathering degrees, so as to establish a more targeted and applicable total thrust estimation model. How to improve the pertinence and applicability of determining the total thrust of the composite earth pressure balance shield machine has become a technical problem that needs to be solved urgently. Summary of the invention

[0003] The object of the present invention is to provide a method and system for determining the total thrust of a composite earth pressure balance shield machine, so as to improve the pertinence and applicability of determining the total thrust of a composite earth pressure balance shield machine.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] The present invention provides a method for determining the total thrust of a composite earth pressure balance shield machine, the method comprising the following steps:

[0006] Determine characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include structural parameters, operating parameters and geological parameters, the structural parameters include cutter head diameter, tunneling speed, cutter head rotation speed, soil bin pressure; the operating parameters include: tunneling speed, cutter head rotation speed, soil bin pressure, the geological parameters include: geological density, shear modulus, Poisson's ratio, cohesion, internal friction coefficient, static earth pressure coefficient, bearing capacity characteristic value, burial depth;

[0007] According to the dimensionless calculation method, the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling are determined;

[0008] According to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling are dimensionlessly processed to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling;

[0009] The decimal calibration normalization method is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling;

[0010] The coefficients of the dimensionless input function for determining the total thrust of tunneling are trained according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and the dimensionless input function after the coefficients are determined is obtained as a dimensionless estimation model;

[0011] The dimensionless estimation model is normalized and dimensionally reduced to obtain a total thrust determination model;

[0012] The current engineering data of characteristic parameters are obtained, and the current engineering parameters are input into a total excavation thrust determination model to obtain a predicted value of the total excavation thrust.

[0013] Optionally, the dimensionless calculation formula for each characteristic parameter and the dimensionless calculation formula for the total thrust parameter of tunneling are determined according to the dimensionless calculation method, specifically including:

[0014] Classify each characteristic parameter according to basic dimensions;

[0015] From the characteristic parameters of each category, select constant parameters or parameters with greater impact on the total thrust of tunneling or parameters with relatively simple dimensions as the basic quantities of each category;

[0016] According to each type of basic quantity, dimensionless calculation is performed on each characteristic parameter and total excavation thrust parameter except the basic quantity, and the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total excavation thrust parameter are determined.

[0017] Optionally, the decimal calibration normalization method is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, specifically including:

[0018] Using the decimal calibration normalization method, using the formula Normalizing the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling;

[0019] Where, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π' i are the dimensionless engineering data of the ith characteristic parameter and the normalized engineering data of the ith characteristic parameter, respectively, F and π' F are the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π' i )<10.

[0020] Optionally, the training of each coefficient of the dimensionless input function for determining the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling to obtain the dimensionless input function after the coefficients are determined as the dimensionless estimation model specifically includes:

[0021] Based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, the hyperparameters of the Lasso regression algorithm are determined by using the LassoCV algorithm;

[0022] The Lasso regression algorithm after hyperparameters are determined is used to train the coefficients of the dimensionless input function used to determine the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and the dimensionless input function after coefficients are determined is obtained as the dimensionless estimation model.

[0023] A system for determining the total thrust of a composite earth pressure balance shield machine, the system comprising:

[0024] The characteristic parameter determination module is used to determine the characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include structural parameters, operating parameters and geological parameters, the structural parameters include cutter head diameter, tunneling speed, cutter head rotation speed, soil bin pressure; the operating parameters include: tunneling speed, cutter head rotation speed, soil bin pressure, the geological parameters include: geological density, shear modulus, Poisson's ratio, cohesion, internal friction coefficient, static earth pressure coefficient, bearing capacity characteristic value, burial depth;

[0025] A dimensionless calculation formula determination module is used to determine the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling according to the dimensionless calculation method;

[0026] A dimensionless processing module is used to perform dimensionless processing on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling according to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, respectively, to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling;

[0027] A normalization processing module is used to perform normalization processing on the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling by using a decimal calibration normalization method, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling;

[0028] A model coefficient training module is used to train various coefficients of a dimensionless input function for determining the total thrust of tunneling according to the normalized engineering data of various characteristic parameters and the normalized engineering data of the total thrust of tunneling, and obtain the dimensionless input function after the coefficients are determined as a dimensionless estimation model;

[0029] A model restoration module is used to perform normalization and dimensional restoration on the dimensionless estimation model to obtain a total thrust determination model;

[0030] The total thrust prediction module is used to obtain the current engineering data of characteristic parameters, input the current engineering parameters into the total thrust determination model, and obtain the predicted value of the total thrust.

[0031] Optionally, the dimensionless calculation formula determination module specifically includes:

[0032] A classification submodule is used to classify each characteristic parameter according to the basic dimension;

[0033] The basic quantity determination submodule is used to select constant parameters or parameters with a greater impact on the total thrust of tunneling or parameters with relatively simple dimensions from the characteristic parameters of each category as the basic quantity of each category;

[0034] The dimensionless calculation formula determination submodule is used to perform dimensionless calculations on various characteristic parameters and total excavation thrust parameters other than the basic quantities according to each type of basic quantity, and determine the dimensionless calculation formulas of various characteristic parameters and the dimensionless calculation formulas of the total excavation thrust parameters.

[0035] Optionally, the normalization processing module specifically includes:

[0036] The normalization processing submodule is used to adopt the decimal calibration normalization method, using the formula Normalizing the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling;

[0037] Where, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π' i are the dimensionless engineering data of the ith characteristic parameter and the normalized engineering data of the ith characteristic parameter, respectively, F and π' Fare the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π' i )<10.

[0038] Optionally, the model coefficient training module specifically includes:

[0039] A hyperparameter determination submodule is used to determine the hyperparameters of the Lasso regression algorithm using the LassoCV algorithm based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling;

[0040] The model coefficient training submodule is used to adopt the Lasso regression algorithm after the hyperparameters are determined, and to train the coefficients of the dimensionless input function used to determine the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, so as to obtain the dimensionless input function after the coefficients are determined as the dimensionless estimation model.

[0041] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0042] The invention discloses a method for determining the total thrust of a composite earth pressure balance shield machine. The method comprises the following steps: determining characteristic parameters that affect the total thrust; determining the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter according to a dimensionless calculation method; performing dimensionless processing on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust according to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, respectively, to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust; using a decimal calibration normalization method to normalize the dimensionless engineering data of each characteristic parameter. The dimensionless engineering data of the characteristic parameters and the total thrust of the tunneling are normalized to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of the tunneling; the coefficients of the dimensionless input function used to determine the total thrust of the tunneling are trained according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of the tunneling, and the dimensionless input function after the coefficient is determined is obtained as a dimensionless prediction model; the dimensionless prediction model is normalized and dimensionally reduced to obtain the total thrust determination model; the current engineering data of the characteristic parameters are obtained, and the current engineering parameters are input into the total thrust determination model to obtain the predicted value of the total thrust of the tunneling. The present invention is aimed at composite geology of rock strata with different weathering degrees, and by applying dimensional analysis on the basis of mechanical analysis, the dimensionless characteristic parameters reflecting the common laws of the working conditions are determined, and the dimensionless characteristic parameters are combined with the machine learning algorithm training modeling, thereby improving the pertinence, practicality and accuracy of the method, and providing effective decision support for the construction adjustment of the total thrust of the composite earth pressure balance shield machine. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0044] Figure 1 The present invention provides a flow chart of a method for determining the total thrust of a composite earth pressure balance shield machine. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] The object of the present invention is to provide a method and system for determining the total thrust of a composite earth pressure balance shield machine, so as to improve the pertinence and applicability of determining the total thrust of a composite earth pressure balance shield machine.

[0047] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0048] like Figure 1 As shown, the present invention provides a method for determining the total thrust of a composite earth pressure balance shield machine, and the determination method comprises the following steps:

[0049] Step 101, determine the characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include: structural parameters: cutter head diameter D (m), operating parameters: tunneling speed v (m / s), cutter head speed w (r / min), soil bin pressure Pe (MPa), geological parameters: geological density ρ (g / cm 3 ), shear modulus G (MPa), Poisson's ratio μ, cohesion c (kPa), internal friction coefficient Static earth pressure coefficient K0, bearing capacity characteristic value W (kPa), burial depth H (m).

[0050] Step 102, according to the dimensionless calculation method, determine the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling.

[0051] In step 102, the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling are determined according to the dimensionless calculation method, which specifically includes:

[0052] Classify each characteristic parameter according to the basic dimensions. Specifically, classify the parameters described in step 1 according to the basic dimensions M, L, and T involved in the mechanical problem and list their dimensions. The classification method is to classify the parameters containing the basic dimension M into one category, the parameters containing the basic dimension L into one category, and the parameters containing the basic dimension T into one category. The classification results are shown in Tables 1-3.

[0053] Table 1 contains the parameters of the basic dimension M and their dimension list

[0054]

[0055]

[0056] Table 2 contains the parameters of the basic dimension L and their dimension list

[0057] parameter D v ρ c <![CDATA[K0]]> P W G dimension L <![CDATA[LT -1 ]]> <![CDATA[ML -3 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -2 T -2 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -1 T -2 ]]>

[0058] Table 3 contains the parameters of the basic dimension T and their dimension list

[0059] parameter ω v G <![CDATA[K0]]> c P W dimension <![CDATA[T -1 ]]> <![CDATA[LT -1 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -2 T -2 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -1 T -2 ]]> <![CDATA[ML -1 T -2 ]]>

[0060] In each category of characteristic parameters, constant parameters or parameters with a greater impact on the total thrust of tunneling or parameters with relatively simple dimensions are selected as the basic quantities of each category; specifically, for each characteristic parameter in each category, basic quantities are selected according to the principle of "giving priority to constant parameters, parameters with relatively simple dimensions, and parameters that have a key impact on the target quantity", and the selected basic quantities must meet the following conditions: only one parameter must be selected as the basic quantity in each category of parameters; the dimensions of the three basic quantities must be independent of each other. The basic quantity selected in the parameters containing the basic dimension M is: G, the basic quantity selected in the parameters containing the basic dimension L is: D; the basic quantity selected in the parameters containing the basic dimension T is: ω.

[0061] According to each type of basic quantity, dimensionless calculation is performed on each characteristic parameter and total thrust parameter other than the basic quantity, and the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter are determined;

[0062] Specifically, based on the selected basic quantity, the remaining influencing parameters and the excavation thrust are dimensionless, and the dimensionless calculation formulas of the characteristic parameters and the dimensionless calculation formula of the total excavation thrust parameters of the composite earth pressure balance shield machine during the excavation process are determined, including: π3=μ, π8=K0、

[0063] Among them, π1, π2, π3, π4, π5, π6, π7, π8, and π9 are characteristic parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c(kPa), internal friction coefficient The nine dimensionless characteristic π quantities after the dimensionless conversion of the bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, and burial depth H (m), π F It is the dimensionless value of the target total excavation thrust F (kN).

[0064] Step 103, dimensionless processing is performed on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling according to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, so as to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling.

[0065] Step 104, using a decimal calibration normalization method, normalizes the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling, and obtains the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling.

[0066] In step 104, the decimal calibration normalization method is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, which specifically includes:

[0067] Using the decimal calibration normalization method, using the formula The dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling are normalized to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling.

[0068] Where, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π' i are the dimensionless engineering data of the ith characteristic parameter and the normalized engineering data of the ith characteristic parameter, respectively, F and π' F are the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π' i )<10.

[0069] Step 105, training each coefficient of the dimensionless input function for determining the total excavation thrust according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total excavation thrust, and obtaining the dimensionless input function after the coefficients are determined as the dimensionless estimation model.

[0070] Before step 105, the method further includes: based on the dimensionless characteristic π in step 102 and the dimensionless total tunneling thrust, according to the general theoretical influence relationship of linear positive correlation between each characteristic quantity and the tunneling thrust, determining the dimensionless input function as follows:

[0071] π F =k1π1+k2π2+k3π3+k4π4+k5π5+k6π6+k7π7+k8π8+k9π9

[0072] Among them, k i ,i=1,2,3...,9 are dimensionless characteristic π quantities π i , the unknown coefficients corresponding to i=1,2,3...,9.

[0073] π1, π2, π3, π4, π5, π6, π7, π8, and π9 are characteristic parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c (kPa), internal friction coefficient tanφ, bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, burial depth H (m) after dimensionless conversion, π F It is the dimensionless value of the target total excavation thrust F (kN).

[0074] According to the normalization process in step 104, the dimensionless input function of the present invention is rewritten as follows:

[0075] π F '=k1π1'+k2π2'+k3π3'+k4π4'+k5π5'+k6π6'+k7π7'+k8π8'+k9π9'.

[0076] Among them, k i ,i=1,2,3...,9 are dimensionless characteristic π quantities π' of each characteristic parameter i ,i=1,2,3...,9 corresponding to the undetermined coefficients. π′1, π′2, π′3, π′4, π′5, π′6, π′7, π′8, π′9 are the characteristic parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c(kPa), internal friction coefficient The dimensionless characteristic π values ​​of the bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, and burial depth H (m): π1, π2, π3, π4, π5, π6, π7, π8, π9, and the normalized nine dimensionless characteristic π values, π′ F is the dimensionless quantity π of the target total thrust F (kN) F The dimensionless π quantity after normalization.

[0077] Step 105 is to train each coefficient of the dimensionless input function for determining the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and obtain the dimensionless input function after the coefficient is determined as the dimensionless estimation model, which specifically includes:

[0078] Based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, the hyperparameters of the Lasso regression algorithm are determined by using the LassoCV algorithm;

[0079] Specifically, the processed data is imported into the LassoCV algorithm to implement a ten-fold crossover calculation to identify the undetermined coefficients under different hyperparameter values, and the change law of the predicted mean square error of its dimensionless input function with the hyperparameter value is obtained. Then, based on this change law, the principle of "stabilizing the mean square error (MSE) at a low level" is followed to determine the value range of the hyperparameter:

[0080] α≤10 -n

[0081] Where α is a hyperparameter and n is the maximum integer that makes the MSE no longer decrease. -n Based on experience, we select 2 to 3 values ​​near to set the hyperparameter values ​​accordingly and perform multiple random sampling trials. When the coefficient changes relatively stably with the sampling, the corresponding hyperparameter value is used as the hyperparameter setting for Lasso regression modeling of the project data. It should be noted that when modeling data for different projects, the applicable hyperparameters must be determined by this method.

[0082] The Lasso regression algorithm after the hyperparameters are determined is used to train the coefficients of the dimensionless input function used to determine the total thrust of the tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of the tunneling, and the dimensionless input function after the coefficients are determined is obtained as the dimensionless estimation model;

[0083] Specifically, based on the determined hyperparameter settings, the engineering data is trained through the Lasso regression algorithm and the identification coefficients corresponding to each π quantity are output. The coefficients are substituted into the dimensionless input function to obtain the dimensionless estimation model.

[0084] Step 106, normalizing and dimensionalizing the dimensionless estimation model to obtain a total tunneling thrust determination model.

[0085] The total thrust determination model is:

[0086]

[0087] Among them, k i ,i=1,2,3...,9 are dimensionless characteristic π quantities π i ',i=1,2,3...,9 corresponding to the undetermined coefficient. v is the excavation speed, unit: (m / s); Pe is the soil bin pressure, unit: (MPa); μ is the Poisson's ratio; ρ is the geological density, unit: (g / cm 3 ); c is cohesion, unit: (kPa); is the internal friction coefficient; W is the characteristic value of bearing capacity, unit: (kPa); K0 is the static earth pressure coefficient; H is the burial depth, unit: (m); G is the shear modulus, unit: (MPa); w is the cutterhead speed, unit: (r / min); D is the cutterhead diameter, unit: (m). The nine dimensionless characteristic π quantities after dimensionless conversion, F is the total thrust of excavation, unit: (kN).

[0088] It should be noted that in specific projects, there will be many coefficients of 0, thus screening out the main parameters that affect the total thrust of the composite earth pressure balance shield machine in the specific project, and the final model is very simple.

[0089] Step 107, obtaining current engineering data of characteristic parameters, inputting the current engineering parameters into a total excavation thrust determination model, and obtaining a predicted value of the total excavation thrust.

[0090] The present invention also provides a system for determining the total thrust of a composite earth pressure balance shield machine, the system comprising:

[0091] The characteristic parameter determination module is used to determine the characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include structural parameters, operating parameters and geological parameters, the structural parameters include cutter head diameter, tunneling speed, cutter head rotation speed, soil bin pressure; the operating parameters include: tunneling speed, cutter head rotation speed, soil bin pressure, the geological parameters include: geological density, shear modulus, Poisson's ratio, cohesion, internal friction coefficient, static earth pressure coefficient, bearing capacity characteristic value, burial depth;

[0092] The dimensionless calculation formula determination module is used to determine the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling according to the dimensionless calculation method.

[0093] The dimensionless calculation formula determination module specifically includes: a classification submodule, which is used to classify each characteristic parameter according to the basic dimension; a basic quantity determination submodule, which is used to select constant parameters or parameters that have a greater impact on the total thrust of tunneling or parameters with relatively simple dimensions from the characteristic parameters of each category as the basic quantity of each category; a dimensionless calculation formula determination submodule, which is used to perform dimensionless calculation on each characteristic parameter and the total thrust parameter other than the basic quantity according to the basic quantity of each category, and determine the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter.

[0094] The dimensionless processing module is used to perform dimensionless processing on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling according to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, so as to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling.

[0095] The normalization processing module is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling by adopting the decimal calibration normalization method, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling.

[0096] The normalization processing module specifically includes: a normalization processing submodule for adopting a decimal calibration normalization method, using the formula The dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling are normalized to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; wherein, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π' i are the dimensionless engineering data of the ith characteristic parameter and the normalized engineering data of the ith characteristic parameter, respectively, F and π' F are the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π' i )<10.

[0097] The model coefficient training module is used to train the coefficients of the dimensionless input function used to determine the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and obtain the dimensionless input function after the coefficients are determined as a dimensionless estimation model.

[0098] The model coefficient training module specifically includes: a hyperparameter determination submodule, which is used to determine the hyperparameters of the Lasso regression algorithm using the LassoCV algorithm based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of the tunneling; a model coefficient training submodule, which is used to use the Lasso regression algorithm after the hyperparameters are determined, to train each coefficient of the dimensionless input function used to determine the total thrust of the tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of the tunneling, and obtain the dimensionless input function after the coefficients are determined as the dimensionless estimation model.

[0099] A model restoration module is used to perform normalization and dimensional restoration on the dimensionless estimation model to obtain a total thrust determination model;

[0100] The total thrust prediction module is used to obtain the current engineering data of characteristic parameters, input the current engineering parameters into the total thrust determination model, and obtain the predicted value of the total thrust.

[0101] The present invention also provides a specific implementation method to further illustrate the implementation process and effect of the method and system for determining the total thrust of the composite earth pressure balance shield machine of the present invention.

[0102] This example is based on a construction section of a subway project, which is a composite geology of fully and strongly weathered granite layers. The following will take the project data as an example to give the detailed steps of modeling the total thrust of the composite earth pressure balance shield machine:

[0103] The first step is to determine the characteristic parameters

[0104] Determine the characteristic parameters that affect the total thrust of tunneling, including: structural parameters: cutter head diameter D (m), operating parameters: tunneling speed v (m / s), cutter head speed w (r / min), soil bin pressure Pe (MPa), geological parameters: geological density ρ (g / cm 3 ), shear modulus G (MPa), Poisson's ratio μ, cohesion c (kPa), internal friction coefficient Static earth pressure coefficient K0, bearing capacity characteristic value W (kPa), burial depth H (m).

[0105] The second step is to classify the above characteristic parameters according to basic dimensions.

[0106] The parameters described in the first step are classified into basic dimensions including M, L, and T and their dimensions are listed as shown in Tables 1 to 3.

[0107] The third step is to select the basic quantities under each basic dimension based on the above classification.

[0108] For each type of parameter in the second step, the basic quantity is selected according to the principle of "giving priority to constant parameters, parameters with relatively simple dimensions, and parameters that have a key impact on the target quantity", and the selected basic quantities must meet the following conditions: only one parameter must be selected as the basic quantity in each type of parameter; the dimensions of the three basic quantities must be independent of each other. The basic quantity selected for the parameters containing the basic dimension M is: G, the basic quantity selected for the parameters containing the basic dimension L is: D; the basic quantity selected for the parameters containing the basic dimension T is: ω.

[0109] The fourth step is to calculate and determine the dimensionless characteristic parameters and dimensionless thrust based on the selected basic quantities.

[0110] Based on the basic quantities selected in the third step, the remaining parameters and the excavation thrust are dimensionless, and the dimensionless characteristic quantities and the dimensionless total excavation thrust of the composite earth pressure balance shield machine during excavation are determined, including: π3=μ, π8=K0、

[0111] Among them, π1, π2, π3, π4, π5, π6, π7, π8, and π9 are the influencing parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c(kPa), internal friction coefficient The nine dimensionless characteristic π quantities after the dimensionless conversion of the bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, and burial depth H (m), π F It is the dimensionless value of the target total excavation thrust F (kN).

[0112] Step 5: Determine the dimensionless input function

[0113] Based on the dimensionless characteristic quantities and the dimensionless total tunneling thrust in the fourth step, and according to the general theoretical influence relationship of linear positive correlation between each characteristic quantity and the tunneling thrust, the dimensionless input function is determined as follows:

[0114] π F =k1π1+k2π2+k3π3+k4π4+k5π5+k6π6+k7π7+k8π8+k9π9where, k i ,i=1,2,3...,9 are dimensionless characteristic π quantities π i ,i=1,2,3...,9 corresponding to the undetermined coefficients. π1, π2, π3, π4, π5, π6, π7, π8, π9 are the influencing parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c(kPa), internal friction coefficient The nine dimensionless characteristic π quantities after the dimensionless conversion of the bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, and burial depth H (m), π F It is the dimensionless value of the target total excavation thrust F (kN).

[0115] Step 6: Non-dimensionalize the engineering data based on dimensionless characteristic parameters and dimensionless thrust expressions

[0116] Based on the dimensionless characteristic parameters and dimensionless thrust expression in the fourth step, the construction section data is dimensionless, and each π quantity (π F ,π i ,i=1,2,3...,9)corresponding engineering data.

[0117] Step 7: Normalize dimensionless engineering data

[0118] The engineering data obtained in the sixth step are normalized. The specific method is to use the decimal calibration normalization method for the data corresponding to each π quantity. The calculation method is as follows:

[0119]

[0120] Where j is the value that makes max(π' i )<10, i=1,2,3...,9,F, the specific calculation formula of the construction data is as follows:

[0121]

[0122] At this point, the dimensionless input model in step 5 is rewritten as follows:

[0123] π F '=k1π1'+k2π2'+k3π3'+k4π4'+k5π5'+k6π6'+k7π7'+k8π8'+k9π9'

[0124] Among them, k i ,i=1,2,3...,9 are dimensionless characteristic π quantities π i ',i=1,2,3...,9 corresponding to the undetermined coefficients. π′1, π′2, π′3, π′4, π′5, π′6, π′7, π′8, π′9 are the influencing parameters: excavation speed v (m / s), soil bin pressure Pe (MPa), Poisson's ratio μ, geological density ρ (g / cm 3 ), cohesion c(kPa), internal friction coefficient The dimensionless characteristic π values ​​of the bearing capacity characteristic value W (kPa), static earth pressure coefficient K0, and burial depth H (m): π1, π2, π3, π4, π5, π6, π7, π8, and π9 are the nine dimensionless characteristic π values ​​after normalization; π′ F is the dimensionless quantity π of the target total thrust F (kN) F The dimensionless π quantity after normalization.

[0125] Step 8: Determine the hyperparameters of the Lasso regression algorithm

[0126] The data after normalization in step 7 is imported into the LassoCV algorithm to perform a ten-fold cross validation calculation to identify the undetermined coefficients under different hyperparameter values, and obtain the change law of the predicted mean square error of its dimensionless prediction model with the hyperparameter value. Then, based on this change law, the principle of "making MSE stable at a low level" is followed to determine the value range of the hyperparameter:

[0127] α≤10 -2

[0128] In the formula, α is a hyperparameter.

[0129] Then in less than 10 -2 Take 2 values ​​near 0.5×10 -2 and 1×10 -3 20 random sampling trials were performed as hyperparameters to obtain the coefficient variation with sampling. It was found that when α = 0.5 × 10 -2 The coefficient is relatively stable, so 0.5×10 -2 As the hyperparameter setting value for Lasso regression modeling of the construction section data of the project.

[0130] Step 9: Identify the coefficients of the dimensionless input model based on the Lasso regression algorithm

[0131] Based on the hyperparameter settings determined in step 8, the Lasso regression algorithm is used to randomly sample the engineering data for training and output the recognition coefficients corresponding to each π quantity. The coefficients are substituted into the dimensionless input function described in step 7 to obtain the dimensionless estimation model:

[0132] π F '=0.6626π4'+0.1056π8'

[0133] Among them, π′ F is the dimensionless quantity π of the target total thrust F (kN) F The dimensionless π quantity after normalization; π′4 and π′8 are the geological density ρ (g / cm 3 ) and the dimensionless characteristic π quantity of the static earth pressure coefficient K0: π4 and π8 are the normalized dimensionless characteristic π quantities.

[0134] Step 10: Restore the dimensionless estimation model to normalized dimensions

[0135] Based on the dimensionless estimation model obtained in step 9, its dimensions are restored and normalized, and the final load model is determined by the following formula:

[0136] F = 6.626 × 10 3 ρω 2 D 4 +1.056×10 -2 KDJ 2 (1)

[0137] Where ρ is the geological density, unit: (g / cm 3 ) ; K0 is the static earth pressure coefficient; G is the shear modulus, unit: (MPa); w is the cutter head speed, unit: (r / min); D is the cutter head diameter, unit: (m). The nine dimensionless characteristic π quantities after dimensionless conversion, F is the total thrust of excavation, unit: (kN).

[0138] The engineering data of the 180th ring are randomly selected, as shown in Table 4.

[0139] Table 4 Engineering data list of the 180th ring

[0140] parameter v w G ρ <![CDATA[K0]]> D F unit mm / min r / min Mpa <![CDATA[kg / m 3 ]]> 1 m kN Numeric 48 1.26 9.947 1832.731 0.489 6.28 11470

[0141] Substituting into formula (1), the total thrust F required for the composite earth pressure balance shield machine in this project section to excavate the 180th ring is as follows:

[0142] F=10355.400(kN)

[0143] The prediction error is less than 9.718%.

[0144] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0145] The present invention discloses a method and system for determining the total thrust of a composite earth pressure balance shield machine. Aiming at composite geology of rock strata with different weathering degrees, the present invention determines dimensionless characteristic parameters reflecting the common laws of the working conditions by applying dimensional analysis on the basis of mechanical analysis, and combines the parameters with machine learning algorithm training modeling, thereby improving the pertinence, practicality and accuracy of the method, and providing effective decision support for the construction adjustment of the total thrust of the composite earth pressure balance shield machine.

[0146] The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be referenced to each other.

[0147] The principles and implementation methods of the present invention are described in this article using specific examples. The description of the above embodiments is only used to help understand the method and core idea of ​​the present invention. At the same time, for those skilled in the art, according to the idea of ​​the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for determining the total thrust of a composite earth pressure balance shield machine, characterized in that: The determination method comprises the following steps: Determine characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include structural parameters, operating parameters and geological parameters, and the structural parameters include cutterhead diameter, tunneling speed, cutterhead rotation speed and soil bin pressure; The operating parameters include: excavation speed, cutter head rotation speed and soil bin pressure; the geological parameters include: geological density, shear modulus, Poisson's ratio, cohesion, internal friction coefficient, static earth pressure coefficient, bearing capacity characteristic value and burial depth; According to the dimensionless calculation method, the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling are determined; According to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling are dimensionlessly processed to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling; The decimal calibration normalization method is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; The coefficients of the dimensionless input function for determining the total thrust of tunneling are trained according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and the dimensionless input function after the coefficients are determined is obtained as a dimensionless estimation model; The dimensionless estimation model is normalized and dimensionally reduced to obtain a total thrust determination model; Obtaining current engineering data of characteristic parameters, inputting the current engineering parameters into a total excavation thrust determination model, and obtaining a predicted value of the total excavation thrust; The dimensionless calculation method is used to determine the dimensionless calculation formulas of the characteristic parameters and the dimensionless calculation formula of the total thrust parameter, which specifically includes: Classify each characteristic parameter according to basic dimensions; From the characteristic parameters of each category, select constant parameters or parameters with greater influence on the total thrust of tunneling or parameters with relatively simple dimensions as the basic quantities of each category; According to each type of basic quantity, dimensionless calculation is performed on each characteristic parameter and total thrust parameter other than the basic quantity, and the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter are determined; The decimal calibration normalization method is used to normalize the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling, and obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, which specifically includes: Using the decimal calibration normalization method, using the formula Normalizing the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; Where, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π i ' are the dimensionless engineering data of the i-th characteristic parameter and the normalized engineering data of the i-th characteristic parameter, π F and π' F are the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π i ')<10; Based on the selected basic quantity, the remaining influencing parameters and the excavation thrust are dimensionless, and the dimensionless calculation formulas of the characteristic parameters and the dimensionless calculation formulas of the total excavation thrust parameters of the composite earth pressure balance shield machine during the excavation process are determined, including: π3=μ, π8=K0、 Among them, π1, π2, π3, π4, π5, π6, π7, π8, and π9 are the nine dimensionless characteristic π quantities after the dimensionless transformation of characteristic parameters: excavation speed v, soil bin pressure Pe, Poisson's ratio μ, geological density ρ, cohesion c, internal friction coefficient tanφ, bearing capacity characteristic value W, static earth pressure coefficient K0, and burial depth H. F is the dimensionless value of the target total thrust F, G is the basic quantity selected from the parameters containing the basic dimension M, D is the basic quantity selected from the parameters containing the basic dimension L; ω is the basic quantity selected from the parameters containing the basic dimension T.

2. The method for determining the total thrust of a composite earth pressure balance shield machine according to claim 1, characterized in that: The method of training each coefficient of the dimensionless input function for determining the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling to obtain the dimensionless input function after the coefficients are determined as the dimensionless estimation model specifically includes: Based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, the hyperparameters of the Lasso regression algorithm are determined by using the LassoCV algorithm; The Lasso regression algorithm after hyperparameters are determined is used to train the coefficients of the dimensionless input function used to determine the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, and the dimensionless input function after coefficients are determined is obtained as the dimensionless estimation model.

3. A system for determining the total thrust of a composite earth pressure balance shield machine, characterized in that: The determination system comprises: The characteristic parameter determination module is used to determine the characteristic parameters that affect the total thrust of tunneling; the characteristic parameters include structural parameters, operating parameters and geological parameters, the structural parameters include cutter head diameter, tunneling speed, cutter head rotation speed, soil bin pressure; the operating parameters include: tunneling speed, cutter head rotation speed, soil bin pressure, the geological parameters include: geological density, shear modulus, Poisson's ratio, cohesion, internal friction coefficient, static earth pressure coefficient, bearing capacity characteristic value, burial depth; A dimensionless calculation formula determination module is used to determine the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter of tunneling according to the dimensionless calculation method; A dimensionless processing module is used to perform dimensionless processing on the historical engineering data of each characteristic parameter and the historical engineering data of the total thrust of tunneling according to the dimensionless calculation formula of each characteristic parameter and the dimensionless calculation formula of the total thrust parameter, respectively, to obtain the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling; A normalization processing module is used to perform normalization processing on the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling by using a decimal calibration normalization method, so as to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; A model coefficient training module is used to train various coefficients of a dimensionless input function for determining the total thrust of tunneling according to the normalized engineering data of various characteristic parameters and the normalized engineering data of the total thrust of tunneling, and obtain the dimensionless input function after the coefficients are determined as a dimensionless estimation model; A model restoration module is used to perform normalization and dimensional restoration on the dimensionless estimation model to obtain a total thrust determination model; A tunneling total thrust prediction module is used to obtain current engineering data of characteristic parameters, input the current engineering parameters into a tunneling total thrust determination model, and obtain a predicted value of the tunneling total thrust; The dimensionless calculation formula determination module specifically includes: A classification submodule is used to classify each characteristic parameter according to the basic dimension; The basic quantity determination submodule is used to select constant parameters or parameters with a greater impact on the total thrust of tunneling or parameters with relatively simple dimensions from the characteristic parameters of each category as the basic quantity of each category; A dimensionless calculation formula determination submodule is used to perform dimensionless calculations on various characteristic parameters and total excavation thrust parameters other than the basic quantities according to each type of basic quantity, and determine the dimensionless calculation formulas of various characteristic parameters and the dimensionless calculation formula of the total excavation thrust parameter; The standardization processing module specifically includes: The normalization processing submodule is used to adopt the decimal calibration normalization method, using the formula Normalizing the dimensionless engineering data of each characteristic parameter and the dimensionless engineering data of the total thrust of tunneling to obtain the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; Where, i=1,2,3...,9,F, when i=1,2,3...,9,π i and π i ' are the dimensionless engineering data of the i-th characteristic parameter and the normalized engineering data of the i-th characteristic parameter, π F and π' F are the dimensionless engineering data of the total thrust of tunneling and the normalized engineering data of the total thrust of tunneling, and j is the value that makes max(π i ')<10; Based on the selected basic quantity, the remaining influencing parameters and the excavation thrust are dimensionless, and the dimensionless calculation formulas of the characteristic parameters and the dimensionless calculation formulas of the total excavation thrust parameters of the composite earth pressure balance shield machine during the excavation process are determined, including: π3=μ, π8=K0、 Among them, π1, π2, π3, π4, π5, π6, π7, π8, and π9 are the nine dimensionless characteristic π quantities after the dimensionless transformation of characteristic parameters: excavation speed v, soil bin pressure Pe, Poisson's ratio μ, geological density ρ, cohesion c, internal friction coefficient tanφ, bearing capacity characteristic value W, static earth pressure coefficient K0, and burial depth H. F is the dimensionless value of the target total thrust F, G is the basic quantity selected from the parameters containing the basic dimension M, D is the basic quantity selected from the parameters containing the basic dimension L; ω is the basic quantity selected from the parameters containing the basic dimension T.

4. The system for determining the total thrust of a composite earth pressure balance shield machine according to claim 3, characterized in that: The model coefficient training module specifically includes: A hyperparameter determination submodule is used to determine the hyperparameters of the Lasso regression algorithm using the LassoCV algorithm based on the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling; The model coefficient training submodule is used to adopt the Lasso regression algorithm after the hyperparameters are determined, and to train the coefficients of the dimensionless input function used to determine the total thrust of tunneling according to the normalized engineering data of each characteristic parameter and the normalized engineering data of the total thrust of tunneling, so as to obtain the dimensionless input function after the coefficients are determined as the dimensionless estimation model.

Citation Information

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