CN115577440B - Bayesian-based shield tunnel face instability early warning method and system - Google Patents

Bayesian-based shield tunnel face instability early warning method and system Download PDF

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CN115577440B
CN115577440B CN202211577967.7A CN202211577967A CN115577440B CN 115577440 B CN115577440 B CN 115577440B CN 202211577967 A CN202211577967 A CN 202211577967A CN 115577440 B CN115577440 B CN 115577440B
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邱睿哲
刘凯文
高军
宁玻
方勇
倪芃芃
袁冉
陶杰
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Abstract

The invention provides a shield tunnel face instability early warning method and system based on Bayes, comprising the following steps: step 1: establishing a three-dimensional finite element model of the target tunnel under the current construction progress; step 2: collecting an existing field data set and a target tunnel field data set; step 3: determining existing information and current constraint information; step 4: the method comprises the steps of calculating super parameters of existing information by adopting a Markov chain Monte Carlo method; step 5: calculating the parameters of the target tunnel random field 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; step 7: calculating the instability probability of the face, outputting alarm information when the instability probability exceeds an alarm threshold, and exiting if not. According to the invention, the space variability of soil parameters and the specific site characteristics are considered, and the advanced early warning is carried out on the stability of the tunnel face of the shield tunnel by adopting a Bayesian method, so that the safety of shield construction is ensured.

Description

Bayesian-based shield tunnel face instability early warning method and system
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 tunnel construction is applied in large scale in China, wherein tunnel face instability accidents occur in the tunneling process of the shield tunnel construction. The instability of the tunnel face not only affects the construction progress, but also causes deformation and even collapse of the earth surface, seriously endangers the life and property safety of people, and how to predict and avoid the occurrence of such accidents is a problem to be solved urgently in the field of tunnel engineering construction safety.
Because of the differences among different sites and the natural variability of soil parameters in the same site, the robustness of analyzing the stability of the face by adopting the traditional deterministic method is poor. Although some methods have considered variability in soil parameters and applied uncertainty methods to face stability analysis, the use of soil samples based on a region or class without regard to site-specific soil characteristics results in greater errors in predicting face stability. Therefore, a shield tunnel face instability early warning method and system based on Bayes are urgently needed.
Disclosure of Invention
The invention solves the technical problems that: the problem that the space variability of soil parameters and the specific field characteristics are ignored when the instability probability of the face is predicted in the prior art is solved.
The technical scheme of the invention is as follows: a Bayesian-based shield tunnel face instability early warning method comprises the following steps:
step 1: and establishing a three-dimensional finite element model of the target tunnel under the current construction progress, wherein the direction of the vertical tunnel face is the x direction, the direction of the gravity is the z direction, and the vertical xz plane is the y direction, and acquiring grid node coordinates.
Step 2: existing site dataset a and target tunnel site dataset B are collected.
Step 3: determining existing information based on the data set A, wherein the existing information comprises each existing field parameter sample, point estimation of a parameter mean value and point estimation of an inter-parameter covariance matrix; and 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 an inter-parameter covariance matrix.
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 superparameter H in the step 3, and performing current t times of pumpingWhen the sample distribution of H obtained by sampling is the same as that obtained by sampling the previous t+Deltat times, taking the sample of H sampled by the t+Deltat+1st times as the super-parameter H of the existing information 1 。
Step 5: the MCMC method is adopted, and based on the current constraint information and H in the step 3 1 And alternately sampling the parameter mean value, the inter-parameter covariance matrix and H, and taking the parameter mean value and the inter-parameter covariance matrix of the T+DeltaT+1st sampling as random field parameters of the target tunnel field when the sample distribution of the H obtained by the current T sampling is the same as the H distribution obtained by the previous T+DeltaT sampling.
Step 6: generating n based on the random field parameters of step 5 3 The random field is endowed with a grid corresponding to the three-dimensional finite element model, and n is obtained altogether 3 And a three-dimensional random finite element model under the current construction progress of each target tunnel.
Step 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, the method exits.
Further, in the step 2, the existing field data set a and the target tunnel field data set B each include five types of parameters: cohesion, friction angle, autocorrelation length in x-direction θ 1 Length of autocorrelation theta in y direction 3 And an autocorrelation length θ in the z-direction 2 。
Further, the super parameter H in the step 4 includes four types of super parameters: the system comprises a generalized mean value, a generalized covariance matrix, a scale matrix and a degree of freedom, wherein the generalized mean value and the generalized covariance matrix control the distribution of parameter mean values, and the covariance matrix distribution between the scale matrix and the degree of freedom control parameters.
Further, n is generated in the step 6 3 The procedure of the individual random fields is:
calculating grid center point coordinates according to the grid node coordinates of the finite element model, and importing the grid center point coordinates of the finite element model into a Matlab script;
and generating a coordinate position correlation coefficient rho of the central points of any two grids by adopting a three-dimensional exponential residual string type autocorrelation function, and generating a random field by combining random field parameters.
The three-dimensional exponential and cosine type autocorrelation function formula is as follows:
Figure 590756DEST_PATH_IMAGE001
in the middle of
Figure 773475DEST_PATH_IMAGE002
The method is characterized in that the method is used for obtaining the correlation coefficient rho tau of the coordinate position of the central point of any two grids of the finite element model under the current construction progress of the target tunnel x 、τ y And τ z Absolute distance, θ, in x, y and z directions corresponding to 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 θ 1 =θ 3 。
Further, the tunnel face instability probability p of the target tunnel in the step 7 under the current construction progress f The acquisition method comprises the following steps:
applying normal supporting force to the face, and calculating n 3 Judging the face instability when the face displacement exceeds a specified safety threshold, counting the number e of the random finite element models with the face instability, and the face instability probability p f =e/ n 3 ；
The shield tunnel face instability early warning system based on Bayes comprises an information acquisition module, a processing module and a gesture 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 existing information and current constraint information according to the data set A and the data set B acquired by the information acquisition module; based on the existing information, acquiring super parameter H of the existing information by an MCMC method 1 The method comprises the steps of carrying out a first treatment on the surface of the Acquiring random field parameters of a target tunnel field by an MCMC method based on current constraint information; random field based parameter acquisitionn 3 The random field samples are subjected to random field sampling and a corresponding finite element model is established; 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 displacement of the face exceeds a specified safety threshold, and judging that the model is unstable if the displacement exceeds the specified safety threshold; judging whether the tunnel face instability probability of the target tunnel under the current construction progress exceeds a set threshold, outputting early warning information if the tunnel face instability probability exceeds the set threshold, and exiting if the tunnel face instability probability exceeds 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 probability of instability of the tunnel face of the shield tunnel is quantized by adopting a Bayesian theory, an analytic hierarchy process and a random finite element method in consideration of the space variability of soil parameters and specific field characteristics. The invention provides a powerful means for the early warning of the tunnel face instability of the shield tunnel; the analysis method has clear flow and strong reliability.
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Fig. 1 is a flow chart of a method for early warning of tunnel face instability of a shield tunnel based on bayesian.
Detailed Description
What is not described in detail in the present specification is a well known technology to those skilled in the art.
The following description of the embodiments of the present invention will be made clearly and fully with reference to the accompanying drawings, in which it is evident that the embodiments described are some, but not all embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
Referring to fig. 1, a method for early warning of tunnel face instability of a shield tunnel based on bayesian, provided by the embodiment of the invention, includes the following steps:
s101: and establishing a three-dimensional finite element model of the target tunnel under the current construction progress, wherein the direction of the vertical tunnel face is the x direction, the direction of the gravity is the z direction, and the vertical xz plane is the y direction, and acquiring grid node coordinates.
S102: existing site dataset a, and target tunnel site dataset B are collected. Existing field data set a and target tunnel field data set B contain five types of parameters: cohesion, friction angle, autocorrelation length in x-direction θ 1 Length of autocorrelation theta in y direction 3 And an autocorrelation length θ in the z-direction 2 。
S103: determining existing information based on the data set A, wherein the existing information comprises a parameter sample of five types of parameters of each existing field, point estimation of a parameter mean value of the five types of parameters, and point estimation of a covariance matrix among the parameters of 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 parameters of the five types of parameters. The parameter samples are obtained through in-situ tests, the point estimation of the average value of five types of parameters of each field is obtained through calculation of the parameter samples of five types of parameters of each existing field, the autocorrelation length of each existing field in the x, y and z directions is only one, and the point estimation of the average value of the autocorrelation length in the fixed x, y and z directions is the value of the parameter sample.
S104: the four types of super parameters H comprise a generalized mean value, a generalized covariance matrix, a scale matrix and degrees of freedom, and the distribution families of the four types of super parameters H are as follows: the generalized mean value is subjected to normal distribution, the generalized covariance matrix is subjected to inverse Weisal distribution, the scale matrix is subjected to Weisal distribution, and the degree of freedom is subjected to uniform distribution. The distribution families of the parameter mean values and the inter-parameter covariance matrix of the five types of parameters are as follows: the parameter mean obeys normal distribution and the covariance matrix among the parameters obeys inverse Weisauter distribution. The initial values of the parameter mean values of the four types of super parameters and the five types of parameters and the covariance matrix between the parameters are random values, a Markov chain Monte Carlo method (MCMC method) is adopted, and based on the existing information in S103, the parameter mean values of the five types of parameters and the covariance matrix between the parameters, the distribution family of the four types of super parameters H, the parameter mean values of the five types of parameters, the covariance matrix between the parameters and the four types of super parameters H are alternately sampled, and the sample distribution of the H obtained by sampling for the current t times and the previous t times are alternately sampledWhen the H distribution obtained by sampling at times of delta t is the same, taking a sample of H sampled at times of delta t+1 as a super-parameter H of the existing information 1 。
S105: based on the current constraint information in S103 and H by adopting an MCMC method 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 parameter mean value and the parameter covariance matrix of four types of super parameters H, and taking the parameter mean value and the parameter covariance matrix of the five types of parameters obtained by sampling the current T times as random field parameters of a target tunnel field when the sample distribution of the four types of super parameters H is the same as the parameter mean value and the parameter covariance matrix of the five types of parameters obtained by sampling the previous T+DeltaT times and the parameter mean value and the parameter covariance matrix of the four types of super parameters H.
S106: generating n based on random field parameters of the target tunnel site in S105 3 The random field is endowed with a grid corresponding to the three-dimensional finite element model, and n is obtained altogether 3 Generating n by using a three-dimensional random finite element model under the current construction progress of each target tunnel 3 The procedure of the individual random fields is:
calculating grid center point coordinates according to the grid node coordinates of the finite element model, and importing the grid center point coordinates of the finite element model into a Matlab script;
and generating a coordinate position correlation coefficient rho of the central points of any two grids by adopting a three-dimensional exponential residual string type autocorrelation function, and generating a random field by combining random field parameters. The three-dimensional exponential and tailed autocorrelation function formula is:
Figure 818792DEST_PATH_IMAGE004
in the middle of
Figure 479580DEST_PATH_IMAGE006
Is the correlation coefficient between any two grid center points of the finite element model under the current construction progress of the target tunnel, and tau x 、τ y And τ z Corresponding to any two grid center pointsAbsolute distance, θ, in the x, y and z directions between 1 、θ 3 And theta 2 Corresponding to the autocorrelation lengths in the x, y and z directions and θ 1 =θ 3 。
S107: applying normal supporting force to the face, and calculating n 3 Judging the face instability when the face displacement exceeds a specified safety threshold, counting the number e of the random finite element models with the face instability, and the face instability probability p f =e/ n 3 . Setting a tunnel face instability alarm threshold p, and when p is f When the alarm threshold value p is exceeded, alarm information is output; if not, the method exits.
According to the scheme provided by the embodiment of the invention, the space variability of the soil parameters and the specific field characteristics are considered, and the probability of instability of the tunnel face of the shield tunnel is predicted in a quantification mode by adopting a Bayesian theory, an analytic hierarchy process and a random finite element method. The invention provides powerful means for early warning of tunnel face instability of the shield tunnel, and is helpful for 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 phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or apparatus that comprises the element.
The embodiments of the present invention have been described above with reference to the accompanying drawings, but the present invention is not limited to the above-described embodiments, which are merely illustrative and not restrictive, and many forms may be made by those having ordinary skill in the art without departing from the spirit of the present invention and the scope of the claims, which are to be protected by the present invention.

Claims (7)

1. A Bayesian-based shield tunnel face instability early warning method is characterized by comprising the following steps:
step 1: establishing a three-dimensional finite element model of a target tunnel under the current construction progress, wherein the direction of a vertical tunnel face is x-direction, the direction of gravity is z-direction, and the direction of a vertical xz plane is y-direction, and acquiring grid node coordinates;
step 2: collecting an existing field data set A and a target tunnel field data set B;
step 3: determining existing information based on the data set A, wherein the existing information comprises each existing field parameter sample, point estimation of a parameter mean value and point estimation of an inter-parameter covariance matrix; 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 an inter-parameter covariance matrix;
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 in the step 3, the distribution family of the parameter mean value, the distribution family of the parameter covariance matrix and the distribution family of the superparameter H, and taking the sample of the H sampled at the t+Deltat+1st time as the superparameter H of the existing information when the sample distribution of the H sampled at the current t time is the same as the H distribution obtained by the previous t+Deltat time 1 ；
Step 5: the MCMC method is adopted, and based on the current constraint information and H in the step 3 1 Alternately sampling the parameter mean value, the inter-parameter covariance matrix and H, and taking the parameter mean value and the inter-parameter covariance matrix of the T+DeltaT+1st sampling as random field parameters of the target tunnel field when the sample distribution of the H obtained by the current T sampling is the same as the H distribution obtained by the previous T+DeltaT sampling;
step 6: generating n based on the random field parameters of step 5 3 The random field is endowed with a grid corresponding to the three-dimensional finite element model, and n is obtained altogether 3 Three-dimensional random finite element models of the target tunnels under the current construction progress;
step 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, the method exits.
2. The method for early warning of tunnel face instability of a shield tunnel based on Bayesian as claimed in claim 1, wherein the existing field data set A and the target tunnel field data set B in the step 2 comprise five types of parameters: cohesion, friction angle, autocorrelation length in x-direction θ 1 Length of autocorrelation theta in y direction 3 And an autocorrelation length θ in the z-direction 2 。
3. The method for early warning of tunnel face instability of a shield tunnel based on Bayes according to claim 1, wherein the super-parameters H in the step 4 comprise four types of super-parameters: the system comprises a generalized mean value, a generalized covariance matrix, a scale matrix and a degree of freedom, wherein the generalized mean value and the generalized covariance matrix control the distribution of parameter mean values, and the covariance matrix distribution between the scale matrix and the degree of freedom control parameters.
4. The method for early warning of tunnel face instability of a shield tunnel based on Bayes as claimed in claim 1, wherein n is generated in the step 6 3 The procedure of the individual random fields is: calculating grid center point coordinates according to the grid node coordinates of the finite element model, and importing the grid center point coordinates of the finite element model into a Matlab script;
and generating a coordinate position correlation coefficient rho of the central points of any two grids by adopting a three-dimensional exponential residual string type autocorrelation function, and generating a random field by combining random field parameters.
5. The shield tunnel face instability early warning method based on Bayes according to claim 4, wherein the three-dimensional exponential residual string type autocorrelation function formula is as follows:
Figure FDA0004261250210000021
wherein ρ is the correlation coefficient ρ, τ of the coordinate positions of the central points of any two grids of the finite element model under the current construction progress of the target tunnel x 、τ y And τ z Absolute distance, θ, in x, y and z directions corresponding to 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 θ 1 ＝θ 3 。
6. The method for early warning of tunnel face instability of shield tunnel based on Bayes as claimed in claim 1, wherein the tunnel face instability probability p of the target tunnel under the current construction progress in the step 7 is characterized in that f The acquisition method comprises the following steps: applying normal supporting force to the face, and calculating n 3 Judging the face instability when the face displacement exceeds a specified safety threshold, counting the number e of the random finite element models with the face instability, and the face instability probability p f ＝e/n 3 。
7. A Bayesian-based shield tunnel face instability early-warning system, which uses the Bayesian-based shield tunnel face instability early-warning method according to any one of claims 1-6, and is characterized by comprising an information acquisition module, a processing module and a gesture 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 existing information and current constraint information according to the data set A and the data set B acquired by the information acquisition module; based on the existing information, acquiring super parameter H of the existing information by an MCMC method 1 The method comprises the steps of carrying out a first treatment on the surface of the Acquiring random field parameters of a target tunnel field by an MCMC method based on current constraint information; acquiring n based on random field parameters 3 The random field samples are subjected to random field sampling and a corresponding finite element model is established; 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 displacement of the face exceeds a specified safety threshold, and judging that the model is unstable if the displacement exceeds the specified safety threshold; judging whether the tunnel face instability probability of the target tunnel under the current construction progress exceeds a set threshold, outputting early warning information if the tunnel face instability probability exceeds the set threshold, and exiting if the tunnel face instability probability exceeds the set threshold.
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