CN112365044A - Tunnel face failure probability prediction method based on k nearest neighbor algorithm and support vector machine - Google Patents
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Abstract
The invention provides a tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine. The method can be used in tunnel engineering design to quickly predict the failure probability of tunnel face under a large number of different working conditions, provides basis for the support design and construction of the face, and can be used for expanding to other similar geotechnical engineering application fields.
Description
Technical Field
The invention relates to the technical field of tunnel engineering design and construction, in particular to a tunnel face failure probability prediction method based on a k nearest neighbor algorithm and a support vector machine.
Background
In the tunnel construction process, the stability of the tunnel face of the tunnel is one of the most important problems. The tunnel face collapse seriously threatens the safety of constructors and mechanical equipment. Therefore, in the design stage or the construction stage, it is necessary to predict the stability of the tunnel face of the tunnel, and for the working condition or the section where the stability does not meet the requirement, a support measure is needed to ensure the stability.
The existing palm surface failure probability prediction methods comprise a first-order second-order moment method, a data table method, a response surface method, a Monte Carlo method and the like. The first-order second-order moment method, the data table method and the response surface method are used for firstly calculating the reliability index of the stability of the tunnel face and then converting the reliability index into failure probability. The Monte Carlo method is to generate a certain number of samples according to the statistic value of the parameters, convert the uncertainty problem into a certain number of certainty problems, and determine the failure probability by counting the number of failure samples and calculating the proportion of the failure samples to the total samples.
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:
the existing methods usually need to determine a function related to tunnel face stability through a large amount of numerical calculation, and calculate the reliability index through an iterative algorithm, so that the time consumption is long, and the efficiency is low. In addition, in actual engineering, statistical parameters of rock-soil mass such as weight, cohesive force and friction angle are changed along with different positions, so that even if the same tunnel is used, the same tunnel needs to be divided into a plurality of working conditions according to the parameters for prediction, and the workload is extremely high and the difficulty is very high by adopting the conventional method.
Therefore, the method in the prior art has the technical problems of low prediction efficiency and long time consumption.
Disclosure of Invention
The invention provides a tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine, which is used for solving or at least partially solving the technical problems of low prediction efficiency and long time consumption of the method in the prior art.
In order to solve the technical problem, the invention provides a tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine, which comprises the following steps:
s1: determining the influence parameters of the tunnel face stability, wherein the influence parameters of the tunnel face stability comprise earth surface load, tunnel diameter, burial depth, soil mass cohesion, internal friction angle and gravity;
s2: determining the value range of each influence parameter, and equally dividing the value range of each influence parameter according to a preset quantity interval;
s3: determining influence parameter combinations by adopting an orthogonal experiment design method for the determined influence parameters and the equally divided value conditions, wherein each influence parameter combination corresponds to one working condition, and each working condition is used for expressing the condition of the tunnel face;
s4: performing intensity reduction calculation on the calculation working condition corresponding to each influence parameter combination, and determining the stable state condition of the tunnel face corresponding to the calculation working condition according to the intensity reduction calculation result;
s5: calibrating all training samples according to the determined stable state condition of the tunnel face, and obtaining a total training set, wherein one training sample corresponds to one influence parameter combination;
s6: carrying out Monte Carlo simulation on the tunnel face to be predicted according to the statistical parameters to generate n prediction samples, wherein n is an integer greater than or equal to 2;
s7: for each prediction sample, calculating the distance between the prediction sample and each training sample in a total training set, selecting k unstable samples and k stable samples which are closest to the prediction sample by adopting a k-nearest neighbor algorithm, and forming a personalized training set corresponding to the prediction sample, wherein k is an integer greater than or equal to 1;
s8: fitting an individualized decision function to the prediction samples by adopting a support vector machine, and classifying the prediction samples based on the individualized decision function, wherein the classification result comprises stability and instability;
s9: repeatedly executing the steps S7 and S8 until all the generated n prediction samples are classified;
s10: and counting the number of the unstable prediction samples according to the classification results of the n prediction samples, and calculating the failure probability of the tunnel face to be predicted according to the ratio of the unstable prediction samples to the total prediction sample number.
In one embodiment, when the image parameter is the tunnel diameter in step S2, the method includes:
determining the value range of the tunnel diameter to be 4-15 m;
the value ranges are equally divided according to the number interval of 1, the tunnel diameter parameters are 12 in total, and the value ranges are 12, namely 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m and 15 m.
In one embodiment, S4 includes:
s4.1: and (3) intensity reduction calculation is carried out on the calculation working condition corresponding to each influence parameter combination by adopting preset calculation software to obtain an intensity reduction coefficient, namely a safety coefficient, and the formula is as follows:
in the formula, c and
representing the cohesion and internal friction angle of each influencing parameter combination input, ccrAnd
representing the critical cohesive force and the critical internal friction angle when the tunnel face is in the limit state,
s4.2: when the safety factor FsWhen the tunnel face is less than 1, the tunnel face is in an unstable state, and when the safety factor F is less thansWhen the tunnel face is more than or equal to 1, the tunnel face is in a stable state.
In one embodiment, step S5 includes:
using the ith training sample as a vector
Indicating if a safety factor F is obtainedsIf the training sample is greater than or equal to 1, the training sample is marked as yiIf a safety factor F is obtained ═ 1sIf less than 1, the training sample is designated as yi＝-1；
And combining all the calibrated training samples into a total training set D.
In one embodiment, the statistical parameter comprises a cumulative probability distribution function, and step S6 comprises:
and for the tunnel face to be predicted, carrying out Monte Carlo simulation according to the statistical parameters, and generating n prediction samples by using the inverse function of the cumulative probability distribution function of each influence parameter.
In one embodiment, the method for calculating the failure probability of the tunnel face to be predicted in step S10 includes:
wherein p isfRepresenting the failure probability of the tunnel face to be predicted, n-Representing the number of unstable prediction samples, n+Represents the number of stable prediction samples, and n-+n+＝n。
One or more technical solutions in the embodiments of the present application have at least one or more of the following technical effects:
the tunnel face failure probability prediction method based on the k-nearest neighbor algorithm and the support vector machine obtains a training sample set through numerical calculation on the basis of an orthogonal experiment, and fits a decision boundary by combining the k-nearest neighbor algorithm and the support vector machine, so that the stability of a new prediction sample generated by Monte Carlo simulation is predicted, and the tunnel face failure probability to be predicted is counted. The training samples in the conventional value range are acquired through the steps S1-S5 of the method, for the tunnel face to be predicted, only parameters corresponding to working conditions need to be input, the steps S6-S10 are completed through running programs, the failure probability of the tunnel face to be predicted can be rapidly calculated within tens of seconds, the calculation efficiency and the convenience are far superior to those of the conventional method, and the prediction efficiency is improved. The method can provide a basis for the design and construction of the tunnel face support in specific application, and can be used for expanding other similar geotechnical engineering application fields.
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 technical route diagram of a tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine according to the present invention;
FIG. 2 is a schematic diagram showing a comparison of the combination of the full experiment and the orthogonal experiment in the embodiment;
FIG. 3 is a block diagram illustrating the determination of a personalized training set D using k-nearest neighbor algorithm in an exemplary embodiment*A schematic diagram of (a);
FIG. 4 is a schematic diagram of a classification principle of a support vector machine;
FIG. 5 is a diagram illustrating the calculation of a face failure probability in an exemplary embodiment;
FIG. 6 is a diagram of a numerical model of an application example;
FIG. 7 is a diagram illustrating the calculated reduction in intensity coefficients for 144 orthogonally combined samples in an exemplary embodiment;
FIG. 8 is a schematic diagram of 1000 Monte Carlo simulation samples in an exemplary embodiment;
FIG. 9 is a diagram illustrating the values of decision functions in ascending order according to an exemplary embodiment;
FIG. 10 is a diagram illustrating a comparison of predicted results and response surface method calculations in an exemplary embodiment;
FIG. 11 is a schematic diagram of 1000 Monte Carlo simulation samples in an exemplary embodiment;
FIG. 12 is a diagram illustrating a comparison between the predicted result and the calculated result of the response surface method in the embodiment.
Detailed Description
The tunnel face stability problem of the tunnel is one of the most important problems in the tunnel construction process. In actual engineering, the parameters of the rock-soil mass often have large uncertainty, so the tunnel face stability is a probability between 0 and 1. The lower the probability of failure, the more stable the tunnel face.
The inventor of the application finds out through a great deal of research and practice that:
in the existing research, the failure probability or reliability index of the tunnel face is generally calculated by a response surface method, a monte carlo method, a first-order second-order moment method and other methods. However, such methods often require a large number of numerical simulations, are time consuming, inefficient, and complex to calculate. In addition, in actual engineering, statistical parameters of rock-soil mass such as weight, cohesive force and friction angle are changed along with different positions, so that even if the same tunnel is used, the same tunnel needs to be divided into a plurality of working conditions according to the parameters for prediction, and the workload is extremely high and the difficulty is very high by adopting the conventional method. Therefore, the predictive analysis of the stability of the working face is not widely carried out in the actual engineering, and usually, the stability of the working face is estimated according to experience and corresponding stabilizing measures are taken.
Based on the background, a rapid tunnel face failure probability prediction method is urgently needed at present, and is used for predicting the face failure probability in a design stage and a construction stage and making support measures of corresponding levels according to the size of the failure probability.
In order to achieve the above object, the main inventive concept of the present invention is as follows:
on the basis of orthogonal experiments, training samples are obtained through numerical calculation, decision boundaries are fitted by combining a k-nearest neighbor method and a support vector machine, so that the stability of new samples generated by Monte Carlo simulation is predicted, and the failure probability is counted. The method can be used in tunnel engineering design to quickly predict the tunnel face failure probability of a large number of different working conditions (parameters), provides a basis for the face support design and construction, and can be used for expanding to other similar geotechnical engineering application fields.
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 predicting failure probability of a tunnel face based on a k-nearest neighbor algorithm and a support vector machine, including:
s1: determining the influence parameters of the tunnel face stability, wherein the influence parameters of the tunnel face stability comprise earth surface load, tunnel diameter, burial depth, soil mass cohesion, internal friction angle and gravity;
s2: determining the value range of each influence parameter, and equally dividing the value range of each influence parameter according to a preset quantity interval;
s3: determining influence parameter combinations by adopting an orthogonal experiment design method for the determined influence parameters and the equally divided value conditions, wherein each influence parameter combination corresponds to one working condition, and each working condition is used for expressing the condition of the tunnel face;
s4: performing intensity reduction calculation on the calculation working condition corresponding to each influence parameter combination, and determining the stable state condition of the tunnel face corresponding to the calculation working condition according to the intensity reduction calculation result;
s5: calibrating all training samples according to the determined stable state condition of the tunnel face, and obtaining a total training set, wherein one training sample corresponds to one influence parameter combination;
s6: carrying out Monte Carlo simulation on the tunnel face to be predicted according to the statistical parameters to generate n prediction samples, wherein n is an integer greater than or equal to 2;
s7: for each prediction sample, calculating the distance between the prediction sample and each training sample in a total training set, selecting k unstable samples and k stable samples which are closest to the prediction sample by adopting a k-nearest neighbor algorithm, and forming a personalized training set corresponding to the prediction sample, wherein k is an integer greater than or equal to 1;
s8: fitting an individualized decision function to the prediction samples by adopting a support vector machine, and classifying the prediction samples based on the individualized decision function, wherein the classification result comprises stability and instability;
s9: repeatedly executing the steps S7 and S8 until all the generated n prediction samples are classified;
s10: and counting the number of the unstable prediction samples according to the classification results of the n prediction samples, and calculating the failure probability of the tunnel face to be predicted according to the ratio of the unstable prediction samples to the total prediction sample number.
Specifically, the invention aims to provide a tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine, wherein parameters of working conditions are given, and the tunnel face failure probability of the corresponding working conditions can be rapidly calculated through a written program, so that the problems of low efficiency and long time consumption of a traditional method aiming at a large number of different working conditions are solved. In order to solve the above technical problems, a technical route of the failure probability prediction method provided by the invention is shown in fig. 1.
In step S3, if a comprehensive experimental design method is adopted, each value of each influence parameter needs to be combined with all values of all other influence parameters, and the number of obtained combinations is too large, which is difficult to calibrate by a numerical method and difficult to fit by a support vector machine. And an orthogonal experiment method is adopted for design, each value of each influence parameter is only combined once, and the number of combinations can be greatly reduced. Fig. 2 is a comparison of a three-factor three-level (valued) combination of a full experiment, which requires 27 combinations, and an orthogonal experiment, which requires only 9 combinations.
In one embodiment, when the image parameter is the tunnel diameter in step S2, the method includes:
determining the value range of the tunnel diameter to be 4-15 m;
the value ranges are equally divided according to the number interval of 1, the tunnel diameter parameters are 12 in total, and the value ranges are 12, namely 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m and 15 m.
In one embodiment, S4 includes:
s4.1: and (3) intensity reduction calculation is carried out on the calculation working condition corresponding to each influence parameter combination by adopting preset calculation software to obtain an intensity reduction coefficient, namely a safety coefficient, and the formula is as follows:
in the formula, c and
representing the cohesion and internal friction angle of each influencing parameter combination input, ccrAnd
representing the critical cohesive force and the critical internal friction angle when the tunnel face is in the limit state,
s4.2: when the safety factor FsWhen the tunnel face is less than 1, the tunnel face is in an unstable state, and when the safety factor F is less thansWhen the tunnel face is more than or equal to 1, the tunnel face is in a stable state.
Specifically, according to the value of the influence parameter, an orthogonal experimental design is adopted, a plurality of groups of different parameter combinations are obtained, each group of parameter combination represents a group of working conditions, the strength reduction method carried by OptomG 2 software is adopted for each group of working conditions to carry out numerical calculation, and the strength reduction coefficient is the safety coefficient.
In one embodiment, step S5 includes:
using the ith training sample as a vector
Indicating if a safety factor F is obtainedsIf the training sample is greater than or equal to 1, the training sample is marked as yiIf a safety factor F is obtained ═ 1sIf less than 1, the training sample is designated as yi＝-1；
And combining all the calibrated training samples into a total training set D.
In particular, the present invention relates to a method for producing,
respectively showing the tunnel diameter, burial depth, surface load, gravity, cohesive force and internal friction angle of soil body, y of the ith training sampleiA label representing the ith training sample; all training samples can be divided into two types of stable training samples and unstable training samples through the method, and a total training set D is formed.
The steps S1-S5 are performed only once to obtain the total training sample set. In practical applications, all predictions may use this set of samples, so that the prediction of the failure probability for different conditions only needs to start from step S6.
In one embodiment, the statistical parameter comprises a cumulative probability distribution function, and step S6 comprises:
and for the tunnel face to be predicted, carrying out Monte Carlo simulation according to the statistical parameters, and generating n prediction samples by using the inverse function of the cumulative probability distribution function of each influence parameter.
The number of prediction samples generated may be determined according to actual conditions, for example, n is 1000.
In the implementation of step S7, the higher the similarity between the prediction sample and the training sample (i.e., the closer the distance in the parameter space), the more accurate the prediction thereof. Because a large number of training samples are possibly in the total training set, the similarity between some training samples and the prediction sample is small (the distance is far), negative influence is possibly generated on prediction, and the calculation efficiency is possibly influenced by too many samples, the method selects some training samples close to the prediction sample to form the personalized training set by using a k-nearest neighbor algorithm (KNN), so that the prediction precision and efficiency are improved.
To achieve this, assume x*Respectively and sequentially calculating the distance D between the first sample in the n prediction samples and each training sample in the unstable sample set and the stable sample set in the total training set D through cyclic controlj＝||x*-xjAnd selecting the distance x according to the principle of a k-nearest neighbor algorithm (KNN)*The nearest k unstable training samples and k training stable samples, which are formed for x*Personalized training set D of*. FIG. 3 shows that when k is 4, 4 unstable samples and 4 stable samples are selected, and the corresponding personalized training set D is obtained*Is a set containing these 8 training samples.
In determining the personalized training set D*Then, the decision boundary can be fitted through the support vector machine, and the vector x to be predicted is obtained*And (6) classifying. The classification principle of the support vector machine is shown in fig. 4.
In the parameter space, for selected training data, the support vector machine method aims to fit a maximally spaced hyperplane (decision boundary), separate the stationary and unstable samples, and maximize the distance between the stationary and unstable samples. The mathematical expression of the decision boundary is:
in the formula
Representing a vector perpendicular to the hyperplane,
a vector representing the sample, b being a constant, normalized form thereof
Representing the hyperplane from the origin along its normal vector
The offset in direction. In addition, there are two parallel hyperplanes in the parameter space, whose expression is:
and
these
I.e. support vectors lying on two parallel hyperplanes. The distance between two parallel hyperplanes being
Maximizing the distance, i.e. equivalently, will
And (4) minimizing.
For a stable sample, the constraints are:
for unstable samples, the constraints are:
these two conditions can be combined into one:
solving given a constraint (equation 7)
Is a convex optimization problem, and to solve this problem, a series of lagrange multipliers (α ═ α can be introduced1，α2，...αm)，αi≧ 0) defining an auxiliary function:
and applying the function to the variables
The partial derivative of b is taken to be zero:
thereby obtaining a group
And the value of b. Thus, a new sample
The decision function value of (a) can be calculated by:
if the value of the function is positive, a new sample may be taken
Due to stable analogy, if the value of the function is negative, the new sample can be classified as unstable.
S9: steps S7 and S8 are performed on the first sample x in the n sample sets generated in the Monte Carlo simulation*Fitting a personalized decision function and applying to x*Classification is performed. Similarly, steps S7 and S8 are repeated for the other n-1 samples, and n-1 additional decision functions are fitted to perform n-1 classification (calculating decision function values).
In one embodiment, the method for calculating the failure probability of the tunnel face to be predicted in step S10 includes:
wherein p isfRepresenting the failure probability of the tunnel face to be predicted, n-Representing the number of unstable prediction samples, n+Represents the number of stable prediction samples, and n-+n+＝n。
FIG. 5 is a schematic illustration of calculating the probability of failure. It should be noted that the decision boundaries in this figure are only schematic diagrams, and there are actually n different decision boundaries in the prediction process.
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 OptumG2, other numerical software with intensity reduction may be used; the steps and methods involved are conventional, unless otherwise indicated.
The first embodiment is as follows: a circular tunnel with the diameter D of 4m and the buried depth C of 20m, the ground surface load of 0kPa and the soil body gravity of 19kN/m3The cohesive force and the internal friction are normally distributed variables, and the average values are respectively as follows: the failure probabilities were predicted at 20kPa and 22 deg., with standard deviations of 4kPa and 5 deg., respectively. The specific implementation steps are as follows:
s1: determining the main influencing parameters of the face stability, including the earth surface load σsDiameter D of tunnel, depth of burial H, cohesive force c of soil body, and internal friction angle
And a severity γ.
S2: determining the conventional value range of each parameter, and equally dividing each parameter into 12 levels, wherein the values are shown in table 1:
TABLE 1 twelve levels of six influencing factors
S3: the combination is carried out by adopting an orthogonal experimental design method, wherein the 6-factor 12 horizontal common combination is 122144 as shown in table 2.
S4: for each combination, an Optum G2 was used to build a two-dimensional numerical model for the intensity reduction calculation, where the numerical model is schematically shown in FIG. 6. Wherein, the distance H between the bottom of the tunnel and the bottom of the model1Distance of tunnel face from left and right sides of model (L)1And L2) The constant is set, and the selected values are all larger than the maximum value (45m) of the 3 times hole diameter, and the main purpose is to prevent the influence of the boundary effect on the stability of the tunnel face. The left side and the right side of the numerical model are normal constraint, and the bottom of the model is full constraint.
S5: and obtaining a safety factor statistic value of 144 samples according to the calculation result of the intensity reduction method, as shown in fig. 7. The 144 combined samples can be divided into 49 stable samples (y ═ 1) and 95 unstable samples (y ═ 1) depending on whether the safety factor is greater than 1. The total training set of compositions is shown in table 2.
TABLE 2 Total training data set
S6: from the statistical parameters of cohesion and internal friction angle in this example, a monte carlo simulation was performed, and 1000 samples automatically generated by the program are shown in fig. 8.
S7: for the first sample of the 1000 samples, the nearest training sample is selected by using the k-nearest neighbor algorithm. Since there are 49 stable samples and 95 unstable samples in the total training set, to keep the balance between the two types of samples, the maximum value k is 49 in this example, and x is selected separately*The latest k stable samples and k unstable samples form an individualized training including 2k training samplesExercise Collection D*。
S8: for a given personalized training set D*Fitting a decision function using a support vector machine and calculating a prediction sample x*The value of the decision function. If the function value is greater than or equal to zero, the face is predicted to be stable, and if the function value is less than zero, the face is predicted to be unstable.
S9: steps S7 and S8 are repeated until all 1000 monte carlo samples are predicted.
S10: the decision function values for the 1000 samples are arranged in ascending order as shown in fig. 9. The decision function value of 153 samples is less than zero and is an unstable sample, and the decision function value of 847 samples is greater than zero and is a stable sample. The probability of failure for this condition can thus be calculated:
in order to verify the prediction result, the failure probability of the working condition is calculated by adopting a traditional Response Surface Method (RSM), and the calculated result is pf14.1%, which is in agreement with the prediction of the method of the invention. Because Monte Lo sampling has certain randomness and the sampling results are different, 10 Monte Carlo simulations are carried out by adopting the method (SVM-KNN) of the invention, the comparison between the prediction result and the response surface method is shown in figure 10, the two kinds of goodness of fit are higher, and the accuracy of the method is verified.
Example two: a circular tunnel with the diameter D of 4m and the buried depth C of 20m, the ground surface load of 0kPa and the soil body gravity of 19kN/m3The cohesive force and the internal friction are normally distributed variables, and the average values are respectively as follows: the failure probabilities were predicted at 15kPa and 20 deg., with standard deviations of 3kPa and 4 deg., respectively.
Since the total training set is already formed in the conventional parameter value range in the first embodiment, the second embodiment can skip the previous 5 steps, and directly start from S6, and the specific implementation steps are as follows:
s6: from the statistical parameters of cohesion and internal friction angle in this example, a monte carlo simulation was performed, and 1000 samples automatically generated by the program are shown in fig. 11.
The steps of S7-S10 are the same as those of the first embodiment, and the failure probability is calculated by running a programmed program, and the failure probability of the second embodiment is 54.2%, and similarly, referring to fig. 12, the failure probability of the working condition is calculated by a response surface method, and p is obtainedfThe result is compared with the result of 10 Monte Carlo simulations, the two goodness of fit are better, and the prediction of the method is more conservative and safer.
In the traditional method, for each working condition, a function is supposed, coefficients of the function are determined through a large number of numerical calculations, and then the reliability or the failure probability is calculated through an iterative method, so that the calculation time is long and the calculation process is complex. However, in the method of the present invention, since the steps S1-S5 in the first embodiment have completed the acquisition of the training samples within the conventional value range, for a general tunnel, only the parameters corresponding to the working conditions need to be input, and the steps S6-S10 are completed by running the program, so that the failure probability can be rapidly calculated within tens of seconds, and the calculation efficiency and convenience far exceed those of the conventional method.
The method can also be applied to similar prediction of the failure probability of engineering.
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 (6)
1. A tunnel face failure probability prediction method based on a k-nearest neighbor algorithm and a support vector machine is characterized by comprising the following steps:
s1: determining the influence parameters of the tunnel face stability, wherein the influence parameters of the tunnel face stability comprise earth surface load, tunnel diameter, burial depth, soil mass cohesion, internal friction angle and gravity;
s2: determining the value range of each influence parameter, and equally dividing the value range of each influence parameter according to a preset quantity interval;
s3: determining influence parameter combinations by adopting an orthogonal experiment design method for the determined influence parameters and the equally divided value conditions, wherein each influence parameter combination corresponds to one working condition, and each working condition is used for expressing the condition of the tunnel face;
s4: performing intensity reduction calculation on the calculation working condition corresponding to each influence parameter combination, and determining the stable state condition of the tunnel face corresponding to the calculation working condition according to the intensity reduction calculation result;
s5: calibrating all training samples according to the determined stable state condition of the tunnel face, and obtaining a total training set, wherein one training sample corresponds to one influence parameter combination;
s6: carrying out Monte Carlo simulation on the tunnel face to be predicted according to the statistical parameters to generate n prediction samples, wherein n is an integer greater than or equal to 2;
s7: for each prediction sample, calculating the distance between the prediction sample and each training sample in a total training set, selecting k unstable samples and k stable samples which are closest to the prediction sample by adopting a k-nearest neighbor algorithm, and forming a personalized training set corresponding to the prediction sample, wherein k is an integer greater than or equal to 1;
s8: fitting an individualized decision function to the prediction samples by adopting a support vector machine, and classifying the prediction samples based on the individualized decision function, wherein the classification result comprises stability and instability;
s9: repeatedly executing the steps S7 and S8 until all the generated n prediction samples are classified;
s10: and counting the number of the unstable prediction samples according to the classification results of the n prediction samples, and calculating the failure probability of the tunnel face to be predicted according to the ratio of the unstable prediction samples to the total prediction sample number.
2. The method of claim 1, wherein when the image parameter is a tunnel diameter in step S2, the method comprises:
determining the value range of the tunnel diameter to be 4-15 m;
the value ranges are equally divided according to the number interval of 1, the tunnel diameter parameters are 12 in total, and the value ranges are 12, namely 4m, 5m, 6m, 7m, 8m, 9m, 10m, 11m, 12m, 13m, 14m and 15 m.
3. The method for predicting failure probability of tunnel face of claim 1, wherein S4 includes:
s4.1: and (3) intensity reduction calculation is carried out on the calculation working condition corresponding to each influence parameter combination by adopting preset calculation software to obtain an intensity reduction coefficient, namely a safety coefficient, and the formula is as follows:
in the formula, c and
representing the cohesion and internal friction angle of each influencing parameter combination input, ccrAnd
representing the critical cohesive force and the critical internal friction angle when the tunnel face is in the limit state,
s4.2: when the safety factor FsWhen the tunnel face is less than 1, the tunnel face is in an unstable state, and when the safety factor F is less thansWhen the tunnel face is more than or equal to 1, the tunnel face is in a stable state.
4. The method for predicting failure probability of tunnel face of claim 1, wherein step S5 includes:
using the ith training sample as a vector
Indicating if a safety factor F is obtainedsIf the training sample is greater than or equal to 1, the training sample is marked as yiIf a safety factor F is obtained ═ 1sIf less than 1, the training sample is designated as yi＝-1；
And combining all the calibrated training samples into a total training set D.
5. The method of predicting failure probability of tunnel face of claim 1, wherein the statistical parameters include cumulative probability distribution function, and step S6 includes:
and for the tunnel face to be predicted, carrying out Monte Carlo simulation according to the statistical parameters, and generating n prediction samples by using the inverse function of the cumulative probability distribution function of each influence parameter.
6. The method for predicting failure probability of tunnel face according to claim 1, wherein the method for calculating failure probability of tunnel face to be predicted in step S10 comprises:
wherein p isfRepresenting the failure probability of the tunnel face to be predicted, n-Representing the number of unstable prediction samples, n+Represents the number of stable prediction samples, and n-+n+＝n。
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