CN115577440A - Bayes-based shield tunnel face instability early warning method and system - Google Patents
Bayes-based shield tunnel face instability early warning method and system Download PDFInfo
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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
Technical Field
The invention relates to the field of tunnel engineering construction safety, in particular to a Bayesian-based shield tunnel face instability early warning method and system.
Background
The shield method tunnel construction is applied in large scale in China, and tunnel face instability accidents occur in the tunneling process of shield construction of some tunnels. The tunnel face instability not only affects the construction progress but also can cause the earth surface to deform or even collapse, seriously harms the life and property safety of people, and the problem of urgent need to be solved in the tunnel engineering construction safety field by predicting and avoiding the accidents.
Due to the difference between different fields and the natural variability of soil parameters in the same field, the robustness for analyzing the stability of the tunnel face by adopting the traditional deterministic method is poor. Although some methods already consider the variability of soil parameters and apply an uncertainty method to the tunnel face stability analysis, the error of predicting the tunnel face stability is larger by adopting a method based on a certain region or a certain type of soil samples without considering the soil characteristics of a specific field. Therefore, a shield tunnel face instability early warning method and system based on Bayes are urgently needed.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method solves the problem that the space variability of soil parameters and the characteristics of a specific field are ignored when the instability probability of the tunnel face is predicted in the prior art.
The technical solution of the invention is as follows: a shield tunnel face instability early warning method based on Bayes comprises the following steps:
step 1: and establishing a three-dimensional finite element model of the target tunnel at the current construction progress, wherein the direction vertical to the tunnel face is the x direction, the direction along the gravity is the z direction, and the direction vertical to the xz plane is the y direction, and acquiring the coordinates of the grid nodes.
Step 2: and acquiring an existing field data set A and a target tunnel field data set B.
And 3, step 3: determining existing information based on the data set A, wherein the existing information comprises each existing field parameter sample, point estimation of parameter mean and point estimation of covariance matrix among parameters; and determining current constraint information based on the data set B, wherein the current constraint information comprises target tunnel field parameter samples, point estimation of parameter mean values and point estimation of covariance matrixes among parameters.
And 4, step 4: adopting a Markov chain Monte Carlo method (MCMC method), alternately sampling the parameter mean value, the parameter covariance matrix and H based on the existing information, the distribution family of the parameter mean value, the distribution family of the parameter covariance matrix and the distribution family of the hyperparameter H in the step 3, taking the sample of the H sampled for the t + Deltat +1 times as the hyperparameter H of the existing information when the sample distribution of the H sampled for the current t times is the same as the H distribution sampled for the previous t + Deltat times 1 。
And 5: based on the current constraint information and H in step 3 by adopting an MCMC method 1 And the parameter mean value, the parameter covariance matrix and the H are alternately sampled, and the parameter mean value and the parameter covariance matrix of the T + DeltaT +1 th sampling are taken as the random field parameters of the target tunnel field when the sample distribution of the H obtained by the current T-time sampling is the same as the H distribution obtained by the previous T + DeltaT-time sampling.
And 6: generating n based on the random field parameters of step 5 3 A random field is given to a corresponding grid of the three-dimensional finite element model, and n is obtained 3 And (3) obtaining a three-dimensional random finite element model of the target tunnel at the current construction progress.
And 7: applying normal supporting force to the tunnel face, and calculating the tunnel face instability probability p under the current construction progress of the target tunnel f When p is f When the alarm threshold value p is exceeded, alarm information is output; if not, exiting.
Further, it is characterized byIn the step 2, the existing site data set A and the target tunnel site data set B both comprise five types of parameters: cohesion, friction angle, autocorrelation length in x direction θ 1 Y autocorrelation length θ 3 And the autocorrelation length theta in the z direction 2 。
Further, the hyperparameters H in the step 4 comprise four types of hyperparameters: the system comprises a generalized mean, a generalized covariance matrix, a scale matrix and a degree of freedom, wherein the generalized mean and the generalized covariance matrix control the distribution of parameter mean values, and the scale matrix and the degree of freedom control the distribution of covariance matrices among parameters.
Further, n is generated in the step 6 3 The process of the random field is as follows:
calculating a grid central point coordinate according to the finite element model grid node coordinate, and importing the finite element model grid central point coordinate into a Matlab script;
and generating a correlation coefficient rho of the coordinate positions of any two grid central points by adopting a three-dimensional index cosine type autocorrelation function, and generating a random field by combining random field parameters.
The formula of the three-dimensional exponential cosine type autocorrelation function is as follows:
in the formula
The correlation coefficient rho, tau of the coordinate positions of any two grid central points of the finite element model under the current construction progress of the target tunnel x 、τ y And τ z Corresponding to the absolute distance theta in the x, y and z directions of the coordinate positions of the center points of any two grids 1 、θ 3 And theta 2 Corresponding to the autocorrelation lengths in the x, y and z directions and theta 1 =θ 3 。
Further, in the step 7, the tunnel face instability probability p under the current construction progress of the target tunnel f The acquisition method comprises the following steps:
applying normal supporting force to the tunnel face, and calculating n 3 A random number ofLimiting element model, when the displacement of the face exceeds the specified safety threshold value, judging the instability of the face, counting the number e of random finite element models with the instability of the face and the instability probability p of the face f =e/ n 3 ；
A shield tunnel face instability early warning system based on Bayesian comprises an information acquisition module, a processing module and an attitude adjustment module;
the information acquisition module is used for acquiring an existing site data set A and a target tunnel site data set B;
the processing module is used for calculating the existing information and the current constraint information according to the data set A and the data set B acquired by the information acquisition module; obtaining the hyper-parameter H of the existing information by MCMC method based on the existing information 1 (ii) a Acquiring random field parameters of a target tunnel field by an MCMC method based on current constraint information; obtaining n based on random field parameters 3 Sampling random fields and establishing corresponding finite element models; and applying normal supporting force to the tunnel face, and calculating the displacement of the tunnel face under the current construction progress of the target tunnel.
The early warning module is used for judging whether the tunnel face displacement exceeds a specified safety threshold value or not, and if the tunnel face displacement exceeds the specified safety threshold value, the model is judged to be unstable; and judging whether the tunnel face instability probability under the current construction progress of the target tunnel exceeds a set threshold, outputting early warning information if the tunnel face instability probability exceeds the set threshold, and quitting if the tunnel face instability probability does not exceed the set threshold.
Compared with the prior art, the invention has the advantages that:
according to the scheme provided by the embodiment of the invention, the instability probability of the tunnel face of the shield tunnel is quantified by considering the space variability of soil parameters and the characteristics of a specific site and adopting a Bayes theory, an analytic hierarchy process and a random finite element method. The method provides powerful means for early warning of instability of the tunnel face of the shield tunnel; the analysis method has clear flow and strong reliability.
Drawings
Fig. 1 is a schematic flow chart of a shield tunnel face instability early warning method based on bayes according to an embodiment of the present invention.
Detailed Description
Those skilled in the art will appreciate that those matters not described in detail in the present specification are well known in the art.
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a shield tunnel face instability early warning method based on bayes provided by an embodiment of the present invention is shown, which includes the following steps:
s101: and establishing a three-dimensional finite element model of the target tunnel at the current construction progress, wherein the direction vertical to the tunnel face is the x direction, the direction along the gravity is the z direction, and the direction vertical to the xz plane is the y direction, and acquiring grid node coordinates.
S102: and acquiring an existing field data set A and a target tunnel field data set B. The existing site data set A and the target tunnel site data set B comprise five types of parameters: cohesion, friction angle, autocorrelation length in x-direction θ 1 Y autocorrelation length θ 3 And the autocorrelation length theta in the z direction 2 。
S103: determining existing information based on the data set A, wherein the existing information comprises parameter samples of five types of parameters of each existing field, point estimation of parameter mean values of the five types of parameters, and point estimation of covariance matrixes among the five types of parameters; and determining current constraint information based on the data set B, wherein the current constraint information comprises parameter samples of five types of parameters of the target tunnel field, point estimation of parameter mean values of the five types of parameters, and point estimation of covariance matrixes among the five types of parameters. The parameter samples are obtained through in-situ test, the point estimation of the mean value of the five types of parameters of each field is obtained through calculation of the parameter samples of the five types of parameters of each existing field, the autocorrelation length of each existing field in the x direction, the y direction and the z direction is only one, and the point estimation of the mean value of the autocorrelation length in the x direction, the y direction and the z direction is the numerical value of the parameter samples.
S104: the four classes of hyperparameters H include the generalizedMean, generalized covariance matrix, scale matrix and degree of freedom, the respective distribution families are: the generalized mean value obeys normal distribution, the generalized covariance matrix obeys inverse Weishatt distribution, the scale matrix obeys Weishatt distribution, and the degree of freedom obeys uniform distribution. The distribution family of the parameter mean value and the covariance matrix among the five types of parameters is as follows: the parameter mean value follows normal distribution, and the parameter covariance matrix follows inverse Weishate distribution. The initial values of the four types of hyper-parameters, the parameter mean value of the five types of parameters and the covariance matrix among the parameters are random values, a Markov chain Monte Carlo method (MCMC method) is adopted, based on the existing information in S103, the distribution family of the parameter mean value of the five types of parameters and the covariance matrix among the parameters and the distribution family of the four types of hyper-parameters H, the parameter mean value of the five types of parameters, the covariance matrix among the parameters and the four types of hyper-parameters H are alternately sampled, the sample distribution of H obtained by current t-time sampling is the same as the H distribution obtained by previous t + delta t-time sampling, and the sample of H obtained by t + delta-t + 1-time sampling is taken as the hyper-parameters H of the existing information 1 。
S105: adopting MCMC method based on current constraint information and H in S103 1 The method comprises the steps of alternately sampling the parameter mean value and the parameter covariance matrix of five types of parameters and the four types of hyperparameters H, and taking the parameter mean value and the parameter covariance matrix of the five types of parameters sampled at the T + DeltaT +1 th time as random field parameters of a target tunnel field when the sample distribution of the five types of parameters obtained by sampling at the current T times is the same as the parameter mean value and the parameter covariance matrix of the five types of parameters obtained by sampling at the previous T + DeltaT times and the four types of hyperparameters H.
S106: generating n based on random field parameters of the target tunnel site in S105 3 A random field is given to the corresponding grid of the three-dimensional finite element model, and n is obtained 3 Generating n by using a three-dimensional random finite element model under the current construction progress of the target tunnel 3 The process of the random field is as follows:
calculating the grid central point coordinates according to the grid node coordinates of the finite element model, and importing the grid central point coordinates of the finite element model into a Matlab script;
and generating a correlation coefficient rho of the coordinate position of any two grid central points by adopting a three-dimensional index cosine type autocorrelation function, and generating a random field by combining random field parameters. The formula of the three-dimensional exponential cosine type autocorrelation function is as follows:
in the formula
A correlation coefficient tau between any two grid central points of the finite element model under the current construction progress of the target tunnel x 、τ y And τ z Corresponding to the absolute distance in the x, y and z directions between the center points of any two grids, theta 1 、θ 3 And theta 2 Corresponding to the autocorrelation lengths in the x, y and z directions and theta 1 =θ 3 。
S107: applying normal supporting force to the tunnel face, and calculating n 3 A random finite element model, when the displacement of the face exceeds the specified safety threshold value, the instability of the face is judged, the number e of the random finite element models with the instability of the face and the instability probability p of the face are counted f =e/ n 3 . Setting a tunnel face instability alarm threshold value p when p is f When the alarm threshold value p is exceeded, alarm information is output; if not, exiting.
According to the scheme provided by the embodiment of the invention, the space variability of soil body parameters and the characteristics of a specific site are considered, and the instability probability of the tunnel face of the shield tunnel is quantitatively predicted by adopting a Bayes theory, an analytic hierarchy process and a random finite element method. The method provides powerful means for early warning of tunnel face instability of the shield tunnel, and is beneficial to guaranteeing tunnel construction safety.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrases "comprising a component of' 8230; \8230;" does not exclude the presence of another like element in a process, method, article, or apparatus that comprises the element.
While the present invention has been described with reference to the particular illustrative embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, but is intended to cover various modifications, equivalent arrangements, and equivalents thereof, which may be made by those skilled in the art without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (7)
1. A shield tunnel face instability early warning method based on Bayes is characterized by comprising the following steps:
step 1: establishing a three-dimensional finite element model of the target tunnel at the current construction progress, wherein the direction vertical to a tunnel face is the x direction, the direction along the gravity is the z direction, and the direction vertical to an xz plane is the y direction, and acquiring grid node coordinates;
step 2: acquiring an existing field data set A and a target tunnel field data set B;
and 3, step 3: determining existing information based on the data set A, wherein the existing information comprises each existing field parameter sample, point estimation of parameter mean and point estimation of covariance matrix among parameters; determining current constraint information based on the data set B, wherein the current constraint information comprises a target tunnel field parameter sample, point estimation of a parameter mean value and point estimation of a covariance matrix among parameters;
and 4, step 4: adopting a Markov chain Monte Carlo method (MCMC method), alternately sampling the parameter mean value, the parameter covariance matrix and H based on the existing information, the distribution family of the parameter mean value, the distribution family of the parameter covariance matrix and the distribution family of the hyperparameter H in the step 3, taking the sample of the H sampled for the t + Deltat +1 times as the existing sample when the sample distribution of the H sampled for the current t times is the same as the H distribution obtained by the previous t + Deltat timesHyper-parameter H of information 1 ；
And 5: based on the current constraint information and H in step 3 by adopting an MCMC method 1 The parameter mean value, the parameter covariance matrix and the H are alternately sampled, the sample distribution of the H obtained by the current T-time sampling is the same as the H distribution obtained by the previous T + Delta T-time sampling, and the parameter mean value and the parameter covariance matrix of the T + Delta T + 1-time sampling are taken as random field parameters of a target tunnel field;
and 6: generating n based on the random field parameters of step 5 3 A random field is given to the corresponding grid of the three-dimensional finite element model, and n is obtained 3 A three-dimensional random finite element model of the target tunnel at the current construction progress;
and 7: applying normal supporting force to the tunnel face, and calculating the instability probability p of the tunnel face under the current construction progress of the target tunnel f When p is f When the alarm threshold value p is exceeded, alarm information is output; if not, exiting.
2. The Bayesian-based shield tunnel face instability early warning method according to claim 1, wherein the existing site data set A and the target tunnel site data set B in the step 2 both include five types of parameters: cohesion, friction angle, autocorrelation length in x direction θ 1 Y autocorrelation length θ 3 And the autocorrelation length theta in the z direction 2 。
3. The Bayesian-based shield tunnel face instability early warning method according to claim 1, wherein the hyperparameter H in the step 4 comprises four types of hyperparameters: the system comprises a generalized mean, a generalized covariance matrix, a scale matrix and a degree of freedom, wherein the generalized mean and the generalized covariance matrix control the distribution of mean values of parameters, and the covariance matrix distribution between the scale matrix and the degree of freedom control parameters.
4. The Bayesian-based shield tunnel face instability prediction method of claim 1Police method, characterized in that n is generated in the step 6 3 The process of the random field is as follows:
calculating the grid central point coordinates according to the grid node coordinates of the finite element model, and importing the grid central point coordinates of the finite element model into a Matlab script;
and generating a correlation coefficient rho of the coordinate position of any two grid central points by adopting a three-dimensional index cosine type autocorrelation function, and generating a random field by combining random field parameters.
5. The Bayesian-based shield tunnel face instability early warning method of claim 4, wherein the three-dimensional exponential cosine type autocorrelation function formula is as follows:
in the formula
The correlation coefficients rho, tau of the coordinate positions of any two grid central points of the finite element model under the current construction progress of the target tunnel x 、τ y And τ z Corresponding to the absolute distance theta in the x, y and z directions of the coordinate positions of the center points of any two grids 1 、θ 3 And theta 2 Corresponding to the autocorrelation lengths in the x, y and z directions and theta 1 =θ 3 。
6. The Bayesian-based shield tunnel face instability early warning method according to claim 1, wherein in the step 7, the face instability probability p under the current construction progress of the target tunnel f The acquisition method comprises the following steps:
applying normal supporting force to the tunnel face, and calculating n 3 A random finite element model, when the displacement of the face exceeds the specified safety threshold value, the instability of the face is judged, the number e of the random finite element models with the instability of the face and the instability probability p of the face are counted f =e/ n 3 。
7. The Bayesian-based shield tunnel face instability early warning system as recited in any one of claims 1 to 8, comprising an information acquisition module, a processing module and an attitude adjustment module;
the information acquisition module is used for acquiring an existing field data set A and a target tunnel field data set B;
the processing module is used for calculating the existing information and the current constraint information according to the data set A and the data set B acquired by the information acquisition module; obtaining the hyperparameter H of the existing information by MCMC method based on the existing information 1 (ii) a Based on the current constraint information, acquiring random field parameters of a target tunnel field by an MCMC method; obtaining n based on random field parameters 3 Sampling random fields and establishing corresponding finite element models; applying normal supporting force to the tunnel face, and calculating the displacement of the tunnel face under the current construction progress of the target tunnel;
the early warning module is used for judging whether the tunnel face displacement exceeds a specified safety threshold value or not, and if the tunnel face displacement exceeds the specified safety threshold value, the model is judged to be unstable; and judging whether the tunnel face instability probability under the current construction progress of the target tunnel exceeds a set threshold, outputting early warning information if the tunnel face instability probability exceeds the set threshold, and quitting if the tunnel face instability probability does not exceed the set threshold.
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| CN112365044A (en) * | 2020-11-09 | 2021-02-12 | 武汉理工大学 | Tunnel face failure probability prediction method based on k nearest neighbor algorithm and support vector machine |
| CN115688307A (en) * | 2022-10-24 | 2023-02-03 | 武汉大学 | Tunnel face instability risk assessment method considering soil body strength uncertainty |
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| CN106570287A (en) * | 2016-11-10 | 2017-04-19 | 中国人民解放军理工大学 | Method for predicting water inflow of tunnel based on three-dimensional discrete fracture network |
| CN112182729A (en) * | 2020-10-26 | 2021-01-05 | 武汉理工大学 | Tunnel face stability rapid determination method based on naive Bayes |
| CN112365044A (en) * | 2020-11-09 | 2021-02-12 | 武汉理工大学 | Tunnel face failure probability prediction method based on k nearest neighbor algorithm and support vector machine |
| CN115688307A (en) * | 2022-10-24 | 2023-02-03 | 武汉大学 | Tunnel face instability risk assessment method considering soil body strength uncertainty |
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