CN115577440A - Bayes-based shield tunnel face instability early warning method and system - Google Patents

Abstract

The invention provides a shield tunnel face instability early warning method and a shield tunnel face instability early warning system based on Bayes, which comprise the following steps: step 1: establishing a three-dimensional finite element model of the target tunnel at the current construction progress; step 2: collecting an existing field data set and a target tunnel field data set; and step 3: determining existing information and current constraint information; and 4, step 4: calculating the hyper-parameters of the existing information by adopting a Markov chain Monte Carlo method; and 5: calculating the random field parameters of the target tunnel by adopting a Markov chain Monte Carlo method; step 6: generating a random field based on the random field parameters, and establishing a three-dimensional random finite element model; and 7: and calculating the instability probability of the tunnel face, outputting alarm information when the instability probability exceeds an alarm threshold value, and quitting if not. According to the method, the spatial variability of soil body parameters and the characteristics of a specific field are considered, the Bayesian method is adopted to perform advanced early warning on the tunnel face stability of the shield tunnel, and the shield construction safety is guaranteed.

Description

A method and system for early warning of face instability of shield tunnel based on Bayesian

technical field

The invention relates to the field of tunnel engineering construction safety, in particular to a Bayesian-based early warning method and system for face instability of a shield tunnel face.

Background technique

The shield tunneling method has been widely used in my country, and some tunnel face instability accidents occurred during the tunneling process of shield tunneling. Face instability not only affects the construction progress but also causes surface deformation or even collapse, which seriously endangers the safety of people's lives and properties. How to predict and avoid such accidents has become an urgent problem in the field of tunnel engineering construction safety.

Due to the differences between different sites and the natural variability of soil parameters in the same site, the robustness of using traditional deterministic methods to analyze face stability is poor. Although some methods have considered the variability of soil parameters and applied the uncertainty method to the face stability analysis, the methods based on a certain area or a certain type of soil samples without considering the specific site soil characteristics, This leads to a large error in predicting the stability of the face. Therefore, there is an urgent need for a Bayesian-based face instability warning method and system for shield tunnels.

Contents of the invention

The technical problem solved by the invention is to overcome the problem of ignoring the spatial variability of soil parameters and specific site characteristics when predicting the instability probability of the face in the prior art.

The technical solution of the present invention is: a Bayesian-based method for early warning of face instability of a shield tunnel, comprising the following steps:

Step 1: Establish a 3D finite element model of the target tunnel under the current construction progress. The direction vertical to the tunnel face is the x direction, the gravity direction is the z direction, and the vertical xz plane is the y direction, and the grid node coordinates are obtained.

Step 2: Collect the existing site data set A and the target tunnel site data set B.

Step 3: Determine the existing information based on data set A. The existing information includes each existing site parameter sample, point estimation of the parameter mean, and point estimation of the covariance matrix between parameters; determine the current constraint information based on data set B. The current constraint The information includes samples of target tunnel site parameters, point estimates of parameter means, and point estimates of the covariance matrix between parameters.

Step 4: Using the Markov chain Monte Carlo method (MCMC method), based on the existing information in step 3, the distribution family of the parameter mean, the distribution family of the covariance matrix between parameters, and the distribution family of the hyperparameter H, the parameter mean value , inter-parameter covariance matrix, and H are alternately sampled. When the sample distribution of H obtained by the current t sampling is the same as the H distribution obtained by the previous t+△t sampling, the sample of H obtained by the t+△t+1 sampling is taken as Hyperparameter H ₁ with existing information.

Step 5: Based on the current constraint information, H ₁ , the distribution family of the parameter mean, the distribution family of the inter-parameter covariance matrix, and the distribution family of H in step 3, the MCMC method is used to carry out the parameter mean value, the inter-parameter covariance matrix and H Alternate sampling, when the sample distribution of H obtained by the current T sampling is the same as the H distribution obtained by the previous T+△T sampling, the mean value of the parameters and the covariance matrix between the parameters of the T+△T+1 sampling are taken as the target tunnel site. random field parameter.

Step 6: Based on the random field parameters in step 5, generate n ₃ random fields, assign the random fields to the corresponding grids of the 3D finite element model, and obtain a total of n ₃ 3D random finite element models of the target tunnel under the current construction progress.

Step 7: Apply normal support force to the tunnel face, calculate the tunnel face instability probability p _f under the current construction progress of the target tunnel, and output an alarm message when p _f exceeds the alarm threshold p; otherwise, exit.

Further, in the step 2, both the existing site data set A and the target tunnel site data set B include five types of parameters: cohesion, friction angle, autocorrelation length θ ₁ in the x direction, and autocorrelation length θ in the y direction ₃ and the autocorrelation length θ ₂ in the z direction.

Further, the hyperparameter H in step 4 includes four types of hyperparameters: generalized mean, generalized covariance matrix, scale matrix and degrees of freedom, wherein the generalized mean and generalized covariance matrix control the distribution of parameter mean values, and the scale matrix and degrees of freedom control The covariance matrix distribution between parameters.

Further, the process of generating n3 random fields in the step ₆ is:

Calculate the grid center point coordinates according to the finite element model grid node coordinates, and import the finite element model grid center point coordinates into the Matlab script;

The three-dimensional exponential cosine type autocorrelation function is used to generate the correlation coefficient ρ of the center point coordinates of any two grids, and the random field is generated by combining the random field parameters.

The three-dimensional exponential cosine type autocorrelation function formula is:

为目标隧道当前施工进度下的有限元模型任意两网格中心点坐标位置相关 系数ρ，τ_x、τ_y和τ_z对应于任意两网格中心点坐标位置x、y和z方向上的绝对距离，θ₁、θ₃和θ₂对 应于x、y和z方向上自相关长度且θ₁=θ₃。 In the formula

is the correlation coefficient ρ of the coordinate positions of any two grid center points of the finite element model under the current construction progress of the target tunnel, and τ _x , τ _y and τ _z correspond to the absolute The distances, θ ₁ , θ ₃ and θ ₂ correspond to autocorrelation lengths in x, y and z directions and θ ₁ =θ ₃ .

Further, the method for obtaining the face instability probability _pf of the target tunnel under the current construction progress in step 7 is as follows:

Apply normal support force to the face, calculate n ₃ random finite element models, when the displacement of the face exceeds the specified safety threshold, it is judged that the face is unstable, and the stochastic finite element models of face instability are counted The number e, the face instability probability p _f =e/ n ₃ ;

A Bayesian-based face instability warning system for shield tunnels includes an information collection module, a processing module, and an attitude adjustment module;

The information collection module is used to collect the existing site data set A and the target tunnel site data set B;

The processing module is used to calculate the existing information and current constraint information according to the data set A and data set B collected by the information collection module; based on the existing information, obtain the hyperparameter H ₁ of the existing information through the MCMC method; based on the current constraint information, through The MCMC method obtains the random field parameters of the target tunnel site; obtains n ₃ random field samples based on the random field parameters and establishes the corresponding finite element model; applies the normal support force to the tunnel face, and calculates the tunnel tunnel under the current construction progress of the target tunnel surface displacement.

The early warning module is used to judge whether the displacement of the tunnel face exceeds the specified safety threshold. If it exceeds the specified safety threshold, it is determined that the model is unstable; it is judged whether the tunnel face instability probability under the current construction progress of the target tunnel exceeds the set threshold. If If it exceeds the set threshold, it will output a warning message, otherwise it will exit.

The advantages of the invention over the prior art are:

The solution provided by the embodiment of the present invention considers the spatial variability of soil parameters and specific site characteristics, and uses Bayesian theory, analytic hierarchy process and stochastic finite element method to quantify the instability probability of the face of a shield tunnel. The invention provides a powerful means for early warning of the face instability of the shield tunnel; the flow of the analysis method is clear and the reliability is strong.

Description of drawings

FIG. 1 is a schematic flowchart of a Bayesian-based method for early warning of face instability of a shield tunnel provided by an embodiment of the present invention.

detailed description

The content that is not described in detail in the description of the present invention belongs to the well-known technology of those skilled in the art.

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some of the embodiments of the present invention, but not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

Referring to Fig. 1, it shows a Bayesian-based method for early warning of face instability of shield tunnel face provided by an embodiment of the present invention, comprising the following steps:

S101: Establish a three-dimensional finite element model of the target tunnel under the current construction progress, the direction vertical to the tunnel face is the x direction, the gravity direction is the z direction, and the vertical xz plane is the y direction, and grid node coordinates are obtained.

S102: Collect the existing site data set A and the target tunnel site data set B. The existing site data set A and the target tunnel site data set B contain five types of parameters: cohesion, friction angle, autocorrelation length θ ₁ in the x direction, autocorrelation length θ ₃ in the y direction, and autocorrelation length θ in the z direction ₂ .

S103: Determine the existing information based on the data set A, the existing information includes parameter samples of the five types of parameters for each existing site, point estimates of the parameter mean values of the five types of parameters, and point estimates of the covariance matrix between the parameters of the five types of parameters; The current constraint information is determined based on the data set B. The current constraint information includes parameter samples of the five types of parameters of the target tunnel site, point estimates of the parameter mean values of the five types of parameters, and point estimates of the inter-parameter covariance matrix of the five types of parameters. Among them, the parameter samples are obtained through in-situ testing, and the point estimation of the mean value of the five types of parameters for each site is calculated through the parameter samples of the five types of parameters for each existing site, and the x, y, and z directions of each existing site There is only one correlation length, and the point estimation of the mean value of the autocorrelation length in the x, y, and z directions is the value of the parameter sample itself.

S104: The four types of hyperparameters H include generalized mean, generalized covariance matrix, scale matrix and degrees of freedom, and their respective distribution families are: generalized mean obeys normal distribution, generalized covariance matrix obeys inverse Wishart distribution, and scale matrix obeys Wishart The distribution and degrees of freedom obey the uniform distribution. The distribution family of the parameter mean value and inter-parameter covariance matrix of the five types of parameters is: the parameter mean value obeys the normal distribution, and the inter-parameter covariance matrix obeys the inverse Wishart distribution. The initial value of the parameter mean value of the four types of hyperparameters and the five types of parameters and the covariance matrix between parameters are random values, using the Markov chain Monte Carlo method (MCMC method), based on the existing information in S103 and the parameters of the five types of parameters The distribution family of the mean value and the inter-parameter covariance matrix, the distribution family of the four types of hyperparameters H, alternately sample the parameter mean values and inter-parameter covariance matrices of the five types of parameters, and the four types of hyperparameters H, and the H obtained by the current t sampling When the sample distribution of is the same as the H distribution obtained by the previous t+△t sampling, the H sample of the t+△t+1th sampling is taken as the hyperparameter H ₁ of the existing information.

S105: Using the MCMC method, based on the current constraint information in S103, H ₁ , the distribution family of the parameter mean value of the five types of parameters and the covariance matrix between parameters, and the distribution family of the four types of hyperparameters H, the parameter mean value and parameter value of the five types of parameters The inter-parameter covariance matrix and the four types of hyperparameters H are alternately sampled. The parameter mean and inter-parameter covariance matrix of the five types of parameters obtained by the current T sampling and the sample distribution of the four types of hyperparameters H are the same as those obtained by the previous T+△T sampling. When the parameter mean value and inter-parameter covariance matrix of the five types of parameters and the distribution of the four hyperparameters H are the same, the parameter mean value and the inter-parameter covariance matrix of the five types of parameters in the T+△T+1th sampling are taken as the random parameters of the target tunnel site. Airport parameters.

S106: Based on the random field parameters of the target tunnel site in S105, generate n ₃ random fields, assign the random fields to the corresponding grids of the 3D finite element model, and obtain a total of n ₃ 3D random finite element models of the target tunnel under the current construction progress, The process of generating n ₃ random fields is:

Calculate the grid center point coordinates according to the finite element model grid node coordinates, and import the finite element model grid center point coordinates into the Matlab script;

The three-dimensional exponential cosine type autocorrelation function is used to generate the correlation coefficient ρ of the center point coordinates of any two grids, and the random field is generated by combining the random field parameters. The three-dimensional exponential cosine autocorrelation function formula is:

为目标隧道当前施工进度下的有限元模型任意两网格中心点间的相关系 数，τ_x、τ_y和τ_z对应于任意两网格中心点间x、y和z方向上的绝对距离，θ₁、θ₃和θ₂对应于x、y和 z方向上自相关长度且θ₁=θ₃。 In the formula

is the correlation coefficient between any two grid center points of the finite element model under the current construction progress of the target tunnel, τ _x , τ _y and τ _z correspond to the absolute distances in the x, y and z directions between any two grid center points, θ ₁ , θ ₃ and θ ₂ correspond to autocorrelation lengths in x, y and z directions and θ ₁ =θ ₃ .

S107: Apply normal support force to the tunnel face, calculate n ₃ random finite element models, when the displacement of the tunnel face exceeds the specified safety threshold, it is determined that the tunnel face is unstable, and the random finite element of the tunnel face instability is counted. The number of meta-models e, the face instability probability p _f =e/ n ₃ . Set the face instability alarm threshold p, when p _f exceeds the alarm threshold p, output an alarm message; otherwise, exit.

The scheme provided by the embodiment of the present invention considers the spatial variability of soil parameters and specific site characteristics, and adopts Bayesian theory, analytic hierarchy process and stochastic finite element method to quantify and predict the instability probability of the shield tunnel face. The invention provides a powerful means for pre-warning the instability of the face of the shield tunnel and helps to ensure the safety of tunnel construction.

It should be noted that, in this document, the term "comprising", "comprising" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article or apparatus comprising a set of elements includes not only those elements, It also includes other elements not expressly listed, or elements inherent in the process, method, article, or device. Without further limitations, an element defined by the phrase "comprising a ..." does not preclude the presence of additional identical elements in the process, method, article, or apparatus comprising that element.

Embodiments of the present invention have been described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementations, and the above-mentioned specific implementations are only illustrative, rather than restrictive. Those of ordinary skill in the art will Under the enlightenment of the present invention, many forms can also be made without departing from the gist of the present invention and the protection scope of the claims, all of which belong to the protection of the present invention.

Claims (7)

1. A Bayesian-based shield tunnel face instability early warning method is characterized in that, comprising the following steps: Step 1: Establish a three-dimensional finite element model of the target tunnel under the current construction progress, the direction vertical to the tunnel face is the x direction, the gravity direction is the z direction, and the vertical xz plane is the y direction, and the grid node coordinates are obtained; Step 2: Collect existing site data set A and target tunnel site data set B; Step 3: Determine the existing information based on data set A. The existing information includes each existing site parameter sample, point estimation of the parameter mean, and point estimation of the covariance matrix between parameters; determine the current constraint information based on data set B. The current constraint The information includes target tunnel site parameter samples, point estimates of parameter mean values, and point estimates of covariance matrices between parameters; Step 4: Using the Markov chain Monte Carlo method (MCMC method), based on the existing information in step 3, the distribution family of the parameter mean value, the distribution family of the covariance matrix between parameters, and the distribution family of the hyperparameter H, the parameter mean value , inter-parameter covariance matrix, and H are alternately sampled. When the sample distribution of H obtained by the current t sampling is the same as the H distribution obtained by the previous t+△t sampling, the sample of H obtained by the t+△t+1 sampling is taken as The hyperparameter H ₁ of the existing information; Step 5: Based on the current constraint information, H ₁ , the distribution family of the parameter mean, the distribution family of the inter-parameter covariance matrix, and the distribution family of H in step 3, the MCMC method is used to carry out the parameter mean value, the inter-parameter covariance matrix and H Alternate sampling, when the sample distribution of H obtained by the current T sampling is the same as the H distribution obtained by the previous T+△T sampling, the mean value of the parameters and the covariance matrix between the parameters of the T+△T+1 sampling are taken as the target tunnel site. random field parameters; Step 6: Based on the random field parameters in step 5, generate n ₃ random fields, assign the random fields to the corresponding grids of the 3D finite element model, and obtain a total of n ₃ 3D random finite element models of the target tunnel under the current construction progress; Step 7: Apply normal support force to the tunnel face, calculate the tunnel face instability probability p _f under the current construction progress of the target tunnel, and output an alarm message when p _f exceeds the alarm threshold p; otherwise, exit. 2. A kind of Bayesian-based shield tunnel face instability early warning method as claimed in claim 1, is characterized in that, in described step 2, existing site data set A and target tunnel site data set B all include Five types of parameters: cohesion, friction angle, autocorrelation length θ ₁ in x direction, autocorrelation length θ ₃ in y direction, and autocorrelation length θ ₂ in z direction. 3. A kind of Bayesian-based shield tunnel face instability early warning method as claimed in claim 1, is characterized in that, in the described step 4, hyperparameter H comprises four kinds hyperparameters: generalized mean value, generalized covariance matrix , scale matrix and degrees of freedom, where the generalized mean and generalized covariance matrix control the distribution of parameter means, and the scale matrix and degrees of freedom control the distribution of the covariance matrix between parameters. 4. a kind of shield tunnel face instability early warning method based on Bayesian as claimed in claim 1, is characterized in that, the process of generating n ₃ random fields in the described step 6 is: Calculate the grid center point coordinates according to the finite element model grid node coordinates, and import the finite element model grid center point coordinates into the Matlab script; The three-dimensional exponential cosine type autocorrelation function is used to generate the correlation coefficient ρ of the center point coordinates of any two grids, and the random field is generated by combining the random field parameters. 5. a kind of shield tunnel face instability early warning method based on Bayesian as claimed in claim 4, is characterized in that, described three-dimensional exponential cosine type autocorrelation function formula is:

In the formula

is the correlation coefficient ρ of the coordinate positions of any two grid center points of the finite element model under the current construction progress of the target tunnel, and τ _x , τ _y and τ _z correspond to the absolute The distances, θ ₁ , θ ₃ and θ ₂ correspond to autocorrelation lengths in x, y and z directions and θ ₁ =θ ₃ . 6. A Bayesian-based face-instability early warning method for shield tunnels as claimed in claim 1, wherein the face-instability probability _pf of the target tunnel under the current construction progress in said step 7 The method of obtaining is as follows: Apply normal support force to the face, calculate n ₃ random finite element models, when the displacement of the face exceeds the specified safety threshold, it is judged that the face is unstable, and the stochastic finite element models of face instability are counted The number e, the face instability probability p _f =e/n ₃ . 7. The system of any Bayesian-based shield tunnel face instability warning method as claimed in claims 1 to 8, is characterized in that, comprising an information collection module, a processing module and an attitude adjustment module; The information collection module is used to collect the existing site data set A and the target tunnel site data set B; The processing module is used to calculate the existing information and current constraint information according to the data set A and data set B collected by the information collection module; based on the existing information, obtain the hyperparameter H ₁ of the existing information through the MCMC method; based on the current constraint information, through The MCMC method obtains the random field parameters of the target tunnel site; obtains n ₃ random field samples based on the random field parameters and establishes the corresponding finite element model; applies the normal support force to the tunnel face, and calculates the tunnel tunnel under the current construction progress of the target tunnel surface displacement; The early warning module is used to judge whether the displacement of the tunnel face exceeds the specified safety threshold. If it exceeds the specified safety threshold, it is determined that the model is unstable; it is judged whether the tunnel face instability probability under the current construction progress of the target tunnel exceeds the set threshold. If If it exceeds the set threshold, it will output a warning message, otherwise it will exit.

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