CN112182729A - Tunnel face stability rapid determination method based on naive Bayes - Google Patents
Tunnel face stability rapid determination method based on naive Bayes Download PDFInfo
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Abstract
The invention discloses a tunnel face stability rapid judgment method based on naive Bayes, which comprises the steps of designing a combined sample through a comprehensive experiment in a conventional parameter distribution range, calibrating according to a numerical calculation result, obtaining statistical characteristics of parameters on the basis, calculating posterior probability of each new sample based on a naive Bayes principle, and predicting the face stability. The method can be used for quickly predicting the tunnel face stability under the influence of different parameters in the tunnel engineering design and construction process.
Description
Technical Field
The invention relates to the technical field of tunnel engineering construction safety analysis, in particular to a method for quickly judging stability of a tunnel face based on naive Bayes.
Background
In the tunnel construction process, the tunnel face stability problem of the tunnel is of great importance. Once the instability collapse of the tunnel face occurs, the life safety of constructors near the tunnel face and the safety of excavation mechanical equipment are greatly threatened, and after the instability collapse, excavation construction needs to be recovered for a long time, so that the influence on the construction progress is very large.
In the design stage or the construction stage, it is very necessary to analyze the tunnel face of the tunnel. For stable conditions, excavation can be performed directly through the full face. For unstable conditions, advanced reinforcement technology, step-by-step excavation method and other methods are needed to improve the stability of the face and avoid the face from collapsing.
In the prior art, the stability problem of the tunnel face is generally analyzed by methods such as model experiment, theoretical analysis, numerical calculation and the like. Wherein, the accuracy of the model experiment is higher, but the cost is expensive and the time consumption is longer; theoretical analysis is fast to calculate, but is based on an assumed failure surface, and is easy to cause errors. The numerical calculation is more commonly used, but is usually suitable for the working condition with single geometric parameters and geological conditions.
The inventor of the present application finds that the method of the prior art has at least the following technical problems in the process of implementing the present invention:
in practical engineering, parameters affecting the stability of tunnel faces, such as tunnel diameter, buried depth, soil mass cohesion and friction angle, often change continuously with different locations. However, one numerical calculation can only be performed for a given set of parameters, and if a large number of different parameter combinations need to be analyzed, the time consumption is long. In addition, since both numerical modeling and calculation require a certain technology and time, in practical application, especially in the construction process, it is often difficult to analyze the stability of the tunnel face by means of numerical calculation because the timeliness is too low.
Therefore, the method in the prior art has the technical problem of long time consumption.
Disclosure of Invention
The invention provides a naive Bayes-based tunnel face stability rapid determination method, which is used for solving or at least partially solving the technical problem of long time consumption of the prior art.
In order to solve the technical problem, the invention provides a method for quickly judging stability of a tunnel face based on naive Bayes, which comprises the following steps:
s1: determining n tunnel face surfaces according to influence factors of the stability of the tunnel face surfaces, wherein the influence factors of the stability of the tunnel face surfaces comprise tunnel buried depth, tunnel diameter, soil mass cohesive force and soil mass friction angle, and n is a positive integer greater than 1;
s2: performing numerical calculation on the determined n tunnel faces by adopting an intensity reduction method to obtain an intensity reduction coefficient of each tunnel face, wherein when the numerical value of the intensity reduction coefficient is more than or equal to 1, the tunnel face is in a stable state, otherwise, the tunnel face is in an unstable state;
s3: dividing n tunnel faces into n according to whether the calculated intensity reduction coefficient is more than or equal to 11Unstable tunnel face and n2A stable tunnel face, wherein n1+n2＝n；
S4: respectively calculating the prior probability of an unstable tunnel face and the prior probability of a stable tunnel face, wherein the prior probability of the unstable tunnel face is the proportion of the number of the unstable tunnel faces in n tunnel faces, the prior probability of the stable tunnel face is the proportion of the number of the stable tunnel faces in n tunnel faces, and calculating the probability density function of each influence factor in the unstable tunnel face and the probability density function of each influence factor in the stable tunnel face;
s5: for the tunnel face to be determined, calculating prior probability and probability density function in an unstable state and a stable state according to the method in the step S4, calculating unstable probability of the tunnel face to be determined according to the prior probability and the probability density function in the unstable state, and calculating stable probability of the tunnel face to be determined according to the prior probability and the probability density function in the stable state;
s6: and judging the stability of the tunnel face to be judged according to the relation between the instability probability and the stability probability of the tunnel face to be judged.
In one embodiment, step S2 includes:
s2.1: combining the influence factors according to the magnitude of the influence factors;
s2.2: the tunnel face subjected to factor combination is subjected to numerical calculation by adopting an intensity reduction method to obtain a corresponding intensity reduction coefficient, and the calculation method comprises the following steps:
wherein c and
representing the soil mass cohesive force and the soil mass friction angle corresponding to the tunnel face, ccrAnd
the method is characterized by comprising the following steps of representing the critical cohesive force and the critical internal friction angle when the tunnel face is in a limit state, indicating that the initial state of the tunnel face is a stable state when the calculated intensity reduction coefficient is larger than or equal to 1, and indicating that the initial state of the tunnel face is an unstable state when the calculated intensity reduction coefficient is smaller than 1.
In one embodiment, S4 includes:
s4.1: calculating the prior probability of the unstable tunnel face and the prior probability of the stable tunnel face, wherein the calculation formula is as follows:
p (stable) ═ n2/(n1+n2) P (unstable) ═ n1/(n1+nP)
Where P (stable) represents the prior probability of a stable tunnel face, P (unstable (represents the prior probability of an unstable tunnel face;
s4.2: and calculating the probability density function of each influencing factor in the unstable tunnel face according to the standard deviation and the variance of the unstable tunnel face, and calculating the probability density function of each influencing factor in the stable tunnel face according to the standard deviation and the variance of the stable tunnel face.
In one embodiment, step S5 includes:
s5.1: calculating the instability probability of the tunnel face to be judged according to the prior probability and the probability density function in the unstable state, wherein the calculation formula is as follows:
p, wherein the content of the compound is,
the instability probability of the tunnel face is shown, the posterior probability is shown, P (stable) shows the prior probability of the unstable tunnel face, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel burial depth, P (D | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel diameter, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the soil body cohesion,
representing a probability density function when the influence factor in the unstable tunnel face is the soil friction angle;
s5.2: calculating the stability probability of the tunnel face to be judged according to the prior probability and the probability density function in the stable state,
wherein the content of the first and second substances,
the stability probability of the tunnel face is represented as posterior probability, P (stability) represents the prior probability of the stable tunnel face, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel burial depth, P (Dstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel diameter, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the soil mass cohesion,
show steadyAnd determining the influence factor in the tunnel face of the tunnel as a probability density function when the soil body friction angle is determined.
In one embodiment, step S6 includes:
and (3) adopting a maximum posterior probability criterion as a decision criterion, if the stability probability of the tunnel face to be judged is greater than the instability probability, judging the tunnel face to be judged to be in a stable state, and otherwise, judging the tunnel face to be judged to be in an unstable state.
One or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:
the invention provides a naive Bayes-based tunnel face stability rapid determination method, which comprises the steps of carrying out numerical calculation on n selected tunnel faces by adopting an intensity reduction method, dividing the n selected tunnel faces into a plurality of unstable tunnel faces and stable tunnel faces according to the calculation result of an intensity reduction coefficient, then calculating the prior probability of each tunnel face and the probability density function of an influence factor, respectively calculating the prior probability and the probability density function in an unstable state and a stable state, calculating the prior probability and the probability density function in the stable state and the stable state for the tunnel faces to be determined, and then calculating the posterior probability according to the prior probability and the probability density function so as to carry out rapid determination on the stability.
By the method, for a tunnel face to be judged, the stable and unstable posterior probability of the tunnel face can be calculated through the determined prior probabilities of two states and the likelihood function of each variable (the probability density function of each influence factor), the stability of the tunnel face can be quickly judged through the given maximum posterior probability criterion, and complicated modeling calculation or theoretical analysis is not needed, so that the calculation and judgment time is greatly shortened, and the judgment efficiency is improved. The method is very suitable for preliminarily judging the stability of the tunnel face by construction managers during field construction.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a method for rapidly determining stability of a tunnel face based on naive Bayes in the present invention;
FIG. 2 is a diagram of a technical framework for a decision-making method in an embodiment;
FIG. 3 is a diagram of a numerical model in an embodiment;
FIG. 4 is a calibration of 750 test specimens in an example embodiment;
FIG. 5 is a probability density function of a sample in a specific embodiment;
FIG. 6 is an intensity reduction calculation model for an application example;
FIG. 7 is an error estimation of a prediction model according to an embodiment;
FIG. 8 is a prediction and determination of a new sample in an embodiment;
FIG. 9 illustrates 802 sample calibrations in an exemplary embodiment;
FIG. 10 is a probability density function of samples in example two;
FIG. 11 is an error estimation of the prediction model in the second embodiment;
FIG. 12 prediction and decision of new samples.
Detailed Description
In the tunnel construction process, instability of the tunnel excavation surface may occur, thereby endangering the safety of constructors and construction equipment. Therefore, in both the tunnel design stage and the construction stage, the stability of the tunnel face needs to be judged according to the actual surrounding rock conditions so as to determine whether a supporting means is adopted or not and improve the stability of the excavation face
The inventor of the application finds out through a great deal of research and practice that:
the tunnel face stability analysis method is suitable for single or small evaluation conditions, but in actual engineering, parameters of tunnel surrounding rocks are often changed continuously, even if the tunnel is the same, the tunnel face stability sometimes has great difference, and a large amount of predictions need to be carried out according to different parameters.
Based on the above background, there is a need for a method for rapidly predicting the stability of a working face, which can preliminarily predict the stability of the working face by simple calculation under the condition of a given set of parameters. Therefore, the invention develops a tunnel face stability rapid determination method based on naive Bayes, in a conventional parameter distribution range, a combined sample is designed through comprehensive experiments, calibration is carried out according to numerical calculation results, statistical characteristics of parameters are obtained on the basis, and finally, posterior probability of each new sample is calculated based on the naive Bayes principle, and the tunnel face stability is predicted.
In order to achieve the above object, the main inventive concept of the present invention is as follows:
the method comprises the steps of carrying out numerical calculation on n selected tunnel faces by adopting an intensity reduction method, dividing the n selected tunnel faces into a plurality of unstable tunnel faces and stable tunnel faces according to a calculation result, then calculating prior probability of each tunnel face and a probability density function of an influence factor, calculating prior probability and a probability density function under an unstable state and a stable state respectively for the tunnel faces to be judged, calculating prior probability and a probability density function under the stable state and the stable state respectively, calculating posterior probability according to the prior probability and the probability density function, and further carrying out rapid judgment on stability.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, 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 to 12, an embodiment of the present invention provides a method for quickly determining stability of a tunnel face based on naive bayes, including:
s1: determining n tunnel face surfaces according to influence factors of the stability of the tunnel face surfaces, wherein the influence factors of the stability of the tunnel face surfaces comprise tunnel buried depth, tunnel diameter, soil mass cohesive force and soil mass friction angle, and n is a positive integer greater than 1;
s2: performing numerical calculation on the determined n tunnel faces by adopting an intensity reduction method to obtain an intensity reduction coefficient of each tunnel face, wherein when the numerical value of the intensity reduction coefficient is more than or equal to 1, the tunnel face is in a stable state, otherwise, the tunnel face is in an unstable state;
s3: dividing n tunnel faces into n according to whether the calculated intensity reduction coefficient is more than or equal to 11Unstable tunnel face and n2A stable tunnel face, wherein n1+n2＝n；
S4: respectively calculating the prior probability of an unstable tunnel face and the prior probability of a stable tunnel face, wherein the prior probability of the unstable tunnel face is the proportion of the number of the unstable tunnel faces in n tunnel faces, the prior probability of the stable tunnel face is the proportion of the number of the stable tunnel faces in n tunnel faces, and calculating the probability density function of each influence factor in the unstable tunnel face and the probability density function of each influence factor in the stable tunnel face;
s5: for the tunnel face to be determined, calculating prior probability and probability density function in an unstable state and a stable state according to the method in the step S4, calculating unstable probability of the tunnel face to be determined according to the prior probability and the probability density function in the unstable state, and calculating stable probability of the tunnel face to be determined according to the prior probability and the probability density function in the stable state;
s6: and judging the stability of the tunnel face to be judged according to the relation between the instability probability and the stability probability of the tunnel face to be judged.
In particular, the influencing factor of the tunnel face stability can be selected according to practical situations, including but not limited to the several situations listed in the present application. The probability density function of each influencing factor of S4 is a likelihood function. In S5, for the tunnel face to be judged, the prior probability and the probability density function in each state are respectively calculated, the posterior probability can be further calculated according to the prior probability and the probability density function, and finally the posterior probability in the two states is judged through the step S6, so that the rapid judgment of the stability of the tunnel face is realized.
In one embodiment, step S2 includes:
s2.1: combining the influence factors according to the magnitude of the influence factors;
s2.2: the tunnel face subjected to factor combination is subjected to numerical calculation by adopting an intensity reduction method to obtain a corresponding intensity reduction coefficient, and the calculation method comprises the following steps:
wherein c and
representing the soil mass cohesive force and the soil mass friction angle corresponding to the tunnel face, ccrAnd
the method is characterized by comprising the following steps of representing the critical cohesive force and the critical internal friction angle when the tunnel face is in a limit state, indicating that the initial state of the tunnel face is a stable state when the calculated intensity reduction coefficient is larger than or equal to 1, and indicating that the initial state of the tunnel face is an unstable state when the calculated intensity reduction coefficient is smaller than 1.
In one embodiment, S4 includes:
s4.1: calculating the prior probability of the unstable tunnel face and the prior probability of the stable tunnel face, wherein the calculation formula is as follows:
p (stable (═ n)2/(n1+n2) P (unstable) ═ n1/(n1+n2)
Wherein, P (stable) represents the prior probability of the stable tunnel face, and P (unstable) represents the prior probability of the unstable tunnel face;
s4.2: and calculating the probability density function of each influencing factor in the unstable tunnel face according to the standard deviation and the variance of the unstable tunnel face, and calculating the probability density function of each influencing factor in the stable tunnel face according to the standard deviation and the variance of the stable tunnel face.
In one embodiment, step S5 includes:
s5.1: calculating the instability probability of the tunnel face to be judged according to the prior probability and the probability density function in the unstable state, wherein the calculation formula is as follows:
p, wherein the content of the compound is,
the instability probability of the tunnel face is shown, the posterior probability is shown, P (stable) shows the prior probability of the unstable tunnel face, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel burial depth, P (D | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel diameter, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the soil body cohesion,
representing a probability density function when the influence factor in the unstable tunnel face is the soil friction angle;
s5.2: calculating the stability probability of the tunnel face to be judged according to the prior probability and the probability density function in the stable state,
wherein the content of the first and second substances,
the stability probability of the tunnel face is represented as posterior probability, P (stability) represents the prior probability of the stable tunnel face, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel burial depth, P (Dstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel diameter, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the soil mass cohesion,
and representing the probability density function when the influencing factor in the stable tunnel face is the soil friction angle.
Specifically, for the tunnel face needing to be judged, the stable probability and the unstable probability of the tunnel face are calculated according to the naive Bayes theory, if the stable probability is greater than the unstable probability, the tunnel face can be judged to be in a stable state, and if not, the tunnel face is judged to be in an unstable state.
The expression of Bayesian theory is as follows:
where A and B represent two events, and P (A | B) represents the probability of event A occurring when event B occurs. P (A) and P (A | B) refer to prior and posterior probabilities, respectively. P (B | a) is a likelihood function that characterizes the parameters of the unknown model given the observed data. Event A can be divided into N mutually independent events, A1，A2，…ANThe posterior probability can be expressed as:
for the stability problem of the tunnel face, the event a can be simply divided into two mutually exclusive events, namely a stable state and an unstable state. The event B is a main parameter (influencing factor) influencing the stability of the tunnel face of the tunnel, and comprises the buried depth, the diameter of the tunnel, the cohesive force of soil and an internal friction angle. Naive bayes is a conditional probability model that can be used to build classifiers. The assumption is that the parameters are independent of each other. Thus, the posterior probability of an event a can be expressed as:
P(An|B1，B2，…Bn) (3)
wherein B ═ B1，B2，…Bn) Representing vectors formed of variables assumed to be independent of each other, AnBased on Bayesian theory, the conditional probability can be expressed as:
using bayesian terminology, the above formula can be rewritten as:
if selected, the
As vectors affecting the stability of the tunnel face, the posterior probabilities of tunnel stability and instability can be expressed as:
wherein, the normalization factor can be expressed as:
a naive bayes classifier can be composed of a naive bayes probability model and a decision criterion. A common decision criterion is the maximum a posteriori probability criterion (MAP). Under the criterion, the stability of the tunnel face can be predicted by comparing the two posterior probabilities. Such as
The palm surface is in a stable state, otherwise, the palm surface is in an unstable state.
With a normalization factor, the sum of the posterior probabilities of the steady state and the unstable state is 1. Combined with the maximum a posteriori probability criterion, then
When the tunnel face is in a stable state
The palm surface is unstable.
By n1And n2Representing the number of unstable and stable samples, respectively, the prior probability of both probabilities can be expressed as:
p (stable) ═ n2/(n1+n2) P (unstable) ═ n1/(n1+n2) (10)
Based on the above conclusions, a tunnel face to be judged is given, namely the stable posterior probability and the unstable posterior probability of the tunnel face can be calculated through the determined prior probabilities of the two states and the likelihood function of each variable, and the stability of the tunnel face is rapidly judged through the given maximum posterior probability criterion.
The judging method can be widely applied to the classification problems (such as stability or deformation with a limited fixed value) of various geotechnical engineering, such as the problem of slope stability, the problem of foundation pit stability, the problem of surface subsidence and the like.
In one embodiment, step S6 includes:
and (3) adopting a maximum posterior probability criterion as a decision criterion, if the stability probability of the tunnel face to be judged is greater than the instability probability, judging the tunnel face to be judged to be in a stable state, and otherwise, judging the tunnel face to be judged to be in an unstable state.
Compared with the prior art, the invention has the main beneficial technical effects that:
the judging method provided by the invention can be used for extremely quickly predicting the tunnel face stability of the tunnel under different parameter combination working conditions of the tunnel face through the calculated posterior probability. Compared with the traditional method, the method only needs to calculate the prior probability and the likelihood function, and does not need complex modeling calculation or theoretical analysis, so that the method is very suitable for preliminarily judging the stability of the tunnel face by construction managers during field construction. In addition, the number of unstable samples in the training samples can be increased, so that the safety of the judging method is improved, namely, the stable situation is predicted to be the unstable situation, and the safety of a construction site is favorably ensured.
The following examples are intended to illustrate the present invention in detail and should not be construed as limiting the scope of the present invention in any way.
The analysis software referred to in the following examples is conventional application software unless otherwise specified; the steps and methods involved are conventional, unless otherwise indicated.
The number of parameters and levels used in the following examples are only selected to illustrate the implementation steps of the method, and may be extended to improve accuracy. Theoretically, the larger the range of parameters, the higher the applicability of the prediction model, and the more levels of parameters, the higher the accuracy of the prediction.
In the embodiment, the two-dimensional numerical calculation result is adopted to calibrate the sample. For most models, the classification result is consistent with the three-dimensional calculation result, namely, the classification result is in a stable state or an unstable state, so that the influence on the prediction accuracy of the model is small, and in order to improve the prediction accuracy (judgment accuracy), the sample can be calibrated by using the three-dimensional calculation result.
The first embodiment is as follows:
and carrying out comprehensive experimental combination based on the selected parameters, and obtaining the safety coefficient of the combined sample through numerical calculation to obtain the statistical parameters of the stable sample and the unstable sample. For a given prediction sample, the posterior probability of stability and instability is predicted according to the naive Bayes principle, and the prediction is completed. Referring to fig. 2, a technical framework diagram of a determination method in an embodiment includes the following steps:
(1) selecting four main parameters influencing the stability of the tunnel face of the tunnel to combine, wherein the buried depth is set to six levels which are sequentially as follows: 5m, 10m, 15m, 20m, 25m, 30 m; the tunnel diameter sets up to five levels, does in proper order: 5m, 7.5m, 10m, 12.5m, 15 m; the cohesive force is set at five levels, which are sequentially as follows: 5kPa, 10kPa, 15kPa, 20kPa, 25 kPa; the internal friction angle is set to five levels, which are sequentially as follows: 5 °, 10 °, 15 °, 20 °, 25 °. A schematic diagram of the numerical calculation model is shown in FIG. 3. The other geometric parameters are set to be constant in order to avoid the influence of the boundary effect on the tunnel face stability during calculation.
(2) Since there are 30 combinations of geometric parameters in total, 6 × 5 is set depending on the combination of setting variables (influencing factors), the number of models to be created is also 30. For each set of models, the mechanical parameters are combined to be 5 × 5-25, and all the models are based on a comprehensive experimental design method, and the total number of samples is as follows:
n＝30×5×5＝750 (11)
(3) the intensity reduction calculation module embedded in the finite element limit analysis software OptunG 2 is adopted to carry out numerical calculation on each experimental sample, and the intensity reduction coefficient of each sample is obtained and is defined as:
in the formula c and
representing the cohesion and internal friction angle of the sample input, ccrAnd
indicating the critical cohesion and critical internal friction angle of the tunnel face in the limit state. If the calculated intensity reduction coefficient is larger than or equal to 1, the initial state of the tunnel face is a stable state, and if the intensity reduction coefficient is smaller than 1, the initial state of the tunnel face is an unstable state. Therefore, the tunnel face can be divided into two types of stable state and unstable state. The calculation results of the first set of numerical models for 25 operating conditions with a burial depth of 5m and a diameter of 5m are shown in table 1:
TABLE 1 calculation of the intensity reduction factor (C5 m; D5 m)
The calculated intensity reduction factor for 750 samples is shown in fig. 4. The red dotted line in the figure indicates the case where the intensity reduction factor is 1.0, and according to this boundary, 750 experimental samples can be divided into 45 stable samples and 705 unstable samples.
(4) According to the classification result, the prior probabilities of the stable samples and the unstable samples can be obtained:
in addition, the distribution statistical parameters of the stable samples and the unstable samples are obtained,
TABLE 2 statistical parameters of probability density functions for stationary and non-stationary samples
(5) Assuming that the parameters are all in accordance with the positive distribution, the probability density functions of the tunnel burial depths in the stable sample and the unstable sample are respectively as follows:
from the probability density function, a probability density function graph for each variable can be obtained as shown in fig. 5:
(6) and predicting through the established classifier. Considering the working condition of the parameters as C-12 m, D-6 m,
for the case of a buried depth of C-12 m, the probabilities of both stable and unstable cases, calculated from their probability density functions, are:
similarly, the probabilities for the other three parameters are:
p (D6 m stable) 0.3487, P (D6 m unstable) 0.0533 (19)
P (c 24kPa unstable) 0.0795, P (c 24kPa unstable) 0.0229 (20)
The normalization factor is:
normalization factor 2.44 × 10-6+2.18×10-6＝4.62×10-6(22) The posterior probability for a given parameter steady state is then:
the posterior probability of an unstable state is:
according to the maximum posterior probability criterion, the stability probability is greater than the instability probability, and the tunnel face of the group of parameter tunnels can be judged to be in a stable state.
(7) And as verification, directly inputting the group of parameters into a numerical model, and calculating the safety coefficient by adopting an intensity reduction method. The computational model is shown in figure 6. The safety factor obtained is FsThe tunnel face is in a stable state when the value is 1.047 > 1, which shows that the prediction result of the prediction model is correct.
(8) And inputting all the calculated sample parameters into a prediction model, predicting and calculating a prediction error. The resulting error estimate is shown in figure 7. It can be seen that all the unstable samples are predicted correctly, and some of the stable samples are predicted as unstable states, so that the prediction result of the prediction model is a conservative estimation of the stable state of the tunnel face.
(9) In the range class of the selected parameters, 50 groups of parameters (brand new samples) are randomly selected for prediction, and the prediction result is compared with the safety coefficient obtained by numerical calculation. It can be seen that most samples are correctly predicted, and only a small number of samples have been incorrectly predicted. As shown in particular in fig. 8.
Example two
The second embodiment expands the range of the cohesive force and the friction angle on the basis of the first embodiment, and comprises the following specific steps:
(1) increasing c to 30kPa and
and adding the newly added 52 stable samples in the combination to the previous data, ignoring the unstable samples in the combination. The obtained sample calibration results are shown in fig. 9.
(2) According to the classification result, the prior probabilities of the stable samples and the unstable samples in the second embodiment are obtained as follows:
in addition, the statistical parameters of the distribution of the stable samples and the unstable samples in the second embodiment are obtained as follows:
TABLE 2 statistical parameters of probability density functions for stationary and non-stationary samples
The probability density function graph of example two thus determined is shown in fig. 10.
(3) The new classifier is used for prediction, and the obtained error estimation result is shown in figure 11. It can be seen that most samples are correctly classified, and only a few samples are in prediction error
(4) When a series of samples randomly taken in the first embodiment are classified by a new classifier, the predicted result and the numerical calculation result are compared as shown in fig. 12, most of the results are correctly classified, and the prediction precision is better than that of the classifier in the first embodiment.
The specific embodiments described herein are merely illustrative of the methods and steps of the present invention. Those skilled in the art to which the invention relates may make various changes, additions or modifications to the described embodiments (i.e., using similar alternatives), without departing from the principles and spirit of the invention or exceeding the scope thereof as defined in the appended claims. The scope of the invention is only limited by the appended claims.
Claims (5)
1. A tunnel face stability rapid determination method based on naive Bayes is characterized by comprising the following steps:
s1: determining n tunnel face surfaces according to influence factors of the stability of the tunnel face surfaces, wherein the influence factors of the stability of the tunnel face surfaces comprise tunnel buried depth, tunnel diameter, soil mass cohesive force and soil mass friction angle, and n is a positive integer greater than 1;
s2: performing numerical calculation on the determined n tunnel faces by adopting an intensity reduction method to obtain an intensity reduction coefficient of each tunnel face, wherein when the numerical value of the intensity reduction coefficient is more than or equal to 1, the tunnel face is in a stable state, otherwise, the tunnel face is in an unstable state;
s3: dividing n tunnel faces into n according to whether the calculated intensity reduction coefficient is more than or equal to 11Unstable tunnel face and n2A stable tunnel face, wherein n1+n2＝n；
S4: respectively calculating the prior probability of an unstable tunnel face and the prior probability of a stable tunnel face, wherein the prior probability of the unstable tunnel face is the proportion of the number of the unstable tunnel faces in n tunnel faces, the prior probability of the stable tunnel face is the proportion of the number of the stable tunnel faces in n tunnel faces, and calculating the probability density function of each influence factor in the unstable tunnel face and the probability density function of each influence factor in the stable tunnel face;
s5: for the tunnel face to be determined, calculating prior probability and probability density function in an unstable state and a stable state according to the method in the step S4, calculating unstable probability of the tunnel face to be determined according to the prior probability and the probability density function in the unstable state, and calculating stable probability of the tunnel face to be determined according to the prior probability and the probability density function in the stable state;
s6: and judging the stability of the tunnel face to be judged according to the relation between the instability probability and the stability probability of the tunnel face to be judged.
2. The method for rapidly determining the stability of a tunnel face according to claim 1, wherein step S2 includes:
s2.1: combining the influence factors according to the magnitude of the influence factors;
s2.2: the tunnel face subjected to factor combination is subjected to numerical calculation by adopting an intensity reduction method to obtain a corresponding intensity reduction coefficient, and the calculation method comprises the following steps:
wherein c and
representing the soil mass cohesive force and the soil mass friction angle corresponding to the tunnel face, ccrAnd
the method is characterized by comprising the following steps of representing the critical cohesive force and the critical internal friction angle when the tunnel face is in a limit state, indicating that the initial state of the tunnel face is a stable state when the calculated intensity reduction coefficient is larger than or equal to 1, and indicating that the initial state of the tunnel face is an unstable state when the calculated intensity reduction coefficient is smaller than 1.
3. The method for rapidly determining the stability of a tunnel face of claim 1, wherein S4 includes:
s4.1: calculating the prior probability of the unstable tunnel face and the prior probability of the stable tunnel face, wherein the calculation formula is as follows:
p (stable) ═ n2/(n1+n2) P (unstable) ═ n1/(n1+n2)
Wherein, P (stable) represents the prior probability of the stable tunnel face, and P (unstable) represents the prior probability of the unstable tunnel face;
s4.2: and calculating the probability density function of each influencing factor in the unstable tunnel face according to the standard deviation and the variance of the unstable tunnel face, and calculating the probability density function of each influencing factor in the stable tunnel face according to the standard deviation and the variance of the stable tunnel face.
4. The method for rapidly determining the stability of a tunnel face according to claim 1, wherein step S5 includes:
s5.1: calculating the instability probability of the tunnel face to be judged according to the prior probability and the probability density function in the unstable state, wherein the calculation formula is as follows:
p, wherein the content of the compound is,
the instability probability of the tunnel face is shown, the posterior probability is shown, P (stable) shows the prior probability of the unstable tunnel face, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel burial depth, P (unstable) shows the probability density function when the influence factor in the unstable tunnel face is the tunnel diameter, P (C | unstable) shows the probability density function when the influence factor in the unstable tunnel face is the soil body cohesion,
representing a probability density function when the influence factor in the unstable tunnel face is the soil friction angle;
s5.2: calculating the stability probability of the tunnel face to be judged according to the prior probability and the probability density function in the stable state,
wherein the content of the first and second substances,
the stability probability of the tunnel face is represented as posterior probability, P (stability) represents the prior probability of the stable tunnel face, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel burial depth, P (Dstabilized) represents the probability density function when the influence factor in the stable tunnel face is the tunnel diameter, P (Cstabilized) represents the probability density function when the influence factor in the stable tunnel face is the soil mass cohesion,
and representing the probability density function when the influencing factor in the stable tunnel face is the soil friction angle.
5. The method for rapidly determining the stability of a tunnel face according to claim 1, wherein step S6 includes:
and (3) adopting a maximum posterior probability criterion as a decision criterion, if the stability probability of the tunnel face to be judged is greater than the instability probability, judging the tunnel face to be judged to be in a stable state, and otherwise, judging the tunnel face to be judged to be in an unstable state.
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