CN113033108A - Side slope reliability judgment method based on AdaBoost algorithm - Google Patents

Side slope reliability judgment method based on AdaBoost algorithm Download PDF

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CN113033108A
CN113033108A CN202110421163.7A CN202110421163A CN113033108A CN 113033108 A CN113033108 A CN 113033108A CN 202110421163 A CN202110421163 A CN 202110421163A CN 113033108 A CN113033108 A CN 113033108A
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张科
张凯
保瑞
齐飞飞
蔡晨曦
叶锦明
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Abstract

The invention discloses a slope reliability judging method based on an AdaBoost algorithm. The method can more reliably and effectively analyze and judge the slope stability degree, obtain the failure probability of the slope, provide basis for the decision of the slope engineering and better ensure the safety of the slope engineering.

Description

Side slope reliability judgment method based on AdaBoost algorithm
Technical Field
The invention relates to the technical field of slope soil safety detection, in particular to a slope reliability judging method based on an AdaBoost algorithm.
Background
The slope reliability is the possibility of maintaining the stability of the slope under the action of instability factors.
The side slopes are divided into natural slopes and artificial slopes, and the latter are divided into excavation side slopes, dam side slopes and the like. Unstable natural slopes and artificial slopes with too large design slope angles are frequently damaged by sliding or collapsing under the action of gravity, water pressure, vibration force and other external forces of rocks and soil bodies. Large-scale damage of the rock and soil bodies on the side slopes can cause traffic interruption, building collapse, river blockage and reservoir silting, and bring huge losses to the lives and properties of people. Therefore, the research on the instability of the side slope is of great significance.
The existing patents related to slope stability are mostly technologies for predicting or monitoring slope stability. Monitoring is usually achieved by embedding sensors in the slope soil or by arranging cameras above the slope. For example, CN207335617U discloses a monitoring structure for stability of an existing roadbed and a slope, and CN112432661A discloses a slope stability monitoring system based on a BIM platform. For example, CN101718876B discloses a slope stability monitoring and instability prediction method based on rock-soil mass strain state mutation; CN103163563B discloses a three-dimensional slope stability prediction method.
All the patents mentioned above are to detect and control or predict slope stability, and belong to a scheme based on a deterministic analysis method, that is, all parameters of the slope to be analyzed are determined fixed values, and then whether the slope is stable is determined, but the slope stability determination factors in practice have a large amount of uncertainty, including variability and randomness of calculation parameters, so that the deterministic analysis method is difficult to reflect the actual stability condition of the slope.
Therefore, how to judge the stability degree and the stability maintaining probability of the side slope by considering the uncertainty of each factor of the side slope is more practical and becomes a problem to be considered and solved in the field.
In the prior art, some patents also disclose slope stability calculation methods considering uncertainty of slope factors, for example, a slope failure probability calculation method based on a support vector machine SVM disclosed in CN 111428363A. However, in this calculation method, how to obtain the training samples is specified and the accuracy and reliability of the model can be better supported, and is not described in detail. Meanwhile, the feasibility of the selected algorithm and the calculation result is not verified and evaluated. Therefore, the accuracy, reliability and validity of the final calculation result cannot be better guaranteed.
Content of Ming dynasty
Aiming at the defects of the prior art, the technical problems to be solved by the invention are as follows: how to provide a slope reliability judging method which is more reliable and effective and can judge the slope stability degree based on an AdaBoost algorithm.
In order to solve the technical problems, the invention adopts the following technical scheme:
a slope reliability judging method based on an AdaBoost algorithm is characterized by comprising the following steps:
1. determining factors influencing the slope stability, acquiring an actual data set of the influencing factors of small sample size, determining probability distribution of the actual data set, and generating a data set of the influencing factors of large sample size by using a uniform test;
2. constructing a side slope model according to the side slope to be predicted and utilizing FLAC3DSoftware inputs a data set of influencing factors, and the safety coefficient K corresponding to each group of index parameters is solved by adopting an intensity reduction method;
3. comparing the calculated safety coefficient K with the allowable safety coefficient [ K ] to obtain a slope stability result corresponding to the corresponding influence factor, and further constructing a data set of judgment index influence factors and corresponding stability results;
4. constructing an AdaBoost classifier through an AdaBoost algorithm and the training samples, and establishing a mapping relation between whether the side slope is stable and the influence factors;
5. and substituting a large amount of random variable data generated by Monte Carlo simulation into the trained AdaBoost algorithm model to obtain a corresponding stability judgment result, and further solving the slope failure probability and the reliability index to realize reliability judgment.
According to the method, firstly, a large-sample-size data set is generated for training through a uniform test according to the actual data of the influence factors of small sample sizes to obtain a mapping relation between the influence factors and stability results, then, a large amount of random variable data generated through Monte Carlo simulation is brought into a model of the mapping relation, and failure probability and reliability indexes are solved. The step flow is simpler and more reliable. The large sample data is generated by adopting the uniform test, so that the generated test points can be uniformly dispersed in a high-dimensional space, the limited data can have wide representativeness, and the test times are reduced; using FLAC3DThe software can more conveniently and simply use the intensity reduction method to solve the slope safety coefficient corresponding to each group of influence factor index parameters. The training calculation is performed through an AdaBoost algorithm, because AdaBoost is an important algorithm in the field of machine learning and data mining, compared with methods such as KNN and SVM, the AdaBoost has the following advantages: (1) the weak classifier can be used as a computing frame and constructed by combining different computing methods, and when the complexity of a weak classifier model is lower, the overfitting phenomenon is less likely to occur; (2) the method is very suitable for solving the classification problem, the parameters do not need to be manually adjusted in the process of using the method, and the data set can be classified with high efficiency under the condition that the data characteristics are not much; (3) the training samples can be repeatedly trained, so that the efficiency of the classifier is improved, and a better classification effect can be realized under the condition of less data volume in a data set; (4) the weak classifier of Adaboost has a simple structure and does not need to search a proper kernel function.
Further, in step 1, the small sample size is usually in the range of 30 sets, and the large sample size needs to exceed 30 sets.
Small and large sample sizes generally have no absolute criteria. The small sample size is determined according to the actual engineering conditions, and the sample size exceeding 30 groups is generally regarded as the large sample size, and of course, the larger the large sample size, the better.
Further, in the step 1, the influence factors are divided into quantitative influence factors and variable influence factors, and actual data of the variable influence factors are obtained through geological exploration and geotechnical experiments after points are taken at different positions of the side slope.
Therefore, influence factors are distinguished, the factor with larger change has larger influence on the slope stability change condition, and the reliability of the final calculation result can be better ensured by taking actual exploration values of a plurality of positions as the basis of research. The factors with small changes have small influence on the slope stability change condition, the factors are considered as quantitative influence factors, the fixed value is taken as a subsequent data sample, and the data can be obtained by obtaining the value at a single position of the slope through geological exploration and geotechnical experiments or calculating the mean value after the values of a few positions are obtained. Therefore, under the condition of greatly reducing the practical application difficulty of the method, the reliability of the calculation result can be ensured to the maximum extent, meanwhile, the influence on the slope stability can be reduced to the maximum extent, and the calculation judgment is realized on the basis of better maintaining the slope stability.
Further, in step 1, for homogeneous soil slope, the selected variable influence factors are cohesive force c and internal friction angle
Figure BDA0003027892740000031
Wherein the variable influencing factors are cohesive force c and internal friction angle
Figure BDA0003027892740000032
Because of the homogeneous slope of the earth, c and
Figure BDA0003027892740000033
the variation is large and the influence on the stability variation of the slope is large, and generally speaking, the variation is mutually independent random variables which are subject to normal distribution. Therefore, on the basis of uniform test design, the 3 sigma criterion and the interpolation method are combined, training data with large sample size can be generated better, enough similarity with real data is guaranteed, meanwhile, the influence of relevance among factors on the accuracy of a calculation result can be avoided, and the reliability of the generated data with large sample size is enhanced. The specific data acquisition means is the prior art and is not described in detail here. The quantitative influence factors can be parameters including slope height, slope angle, pore water pressure ratio, rock mass volume weight and the like, and can be obtained by taking a fixed value after one-time measurement or taking homogeneity as the fixed value after several times of measurement and bringing the fixed value into subsequent calculation. The specific survey measurement method is prior art and will not be described in detail herein.
Further, in step 1, the specific steps of generating a data set of the influencing factors of the large sample size by using the homogeneous test are as follows:
assuming that the number of training samples is set as x groups, a uniform table is selected
Figure BDA0003027892740000034
Conducting a numerical test in which U*Representing a uniform table with better uniformity, wherein x is a horizontal number, namely x groups of data are generated, and y represents the number of variable influence factors, namely the table can represent a numerical test containing y variable influence factors at most; (since the variables of the foregoing choices influence c and
Figure BDA0003027892740000035
therefore, y is 2; )
Wherein, due to c and
Figure BDA0003027892740000036
the value follows normal distribution, so the value range determines the upper and lower limits according to the 3 sigma criterion, namely [ mu-3 sigma, mu +3 sigma]Where μ is the mean and σ is the standard deviation, the 2 columns of data are converted to c and
Figure BDA0003027892740000037
a value within the true range; and then, supplementing the values of the quantitative influence factors with fixed values to obtain a data set of the influence factors with large sample size.
Thus, sample data c and c are generated using a uniform design
Figure BDA0003027892740000041
The uniform design is a test design method considering that test points are uniformly distributed in a test range; the test points generated by the method are uniformly dispersed in a high-dimensional space, and the generated data has wide representativeness and can greatly reduce the number of experiments. Because the uniform test design considers the test points selected by uniformly spreading the test points in the test range, each level of each factor can be tested only once, and when the number of levels (namely, the influence factors) is increased, the test frequency is increased along with the increase of the number of levels, compared with the traditional orthogonal test design (the test frequency is increased along with the square number of the number of levels), the test frequency can be greatly reduced. And a value range is determined by further combining a 3 sigma criterion and an interpolation method, so that the data distribution is in normal distribution and is close to the real data. Compared with other methods, the method for generating the large sample data has the advantages of simple principle and easy operation.
Further, in step 2, FLAC3DThe process of solving the safety coefficient K of the slope model by adopting a strength reduction method mainly comprises the following steps:
(1) establishing a corresponding homogeneous slope model in the CAD, and outputting a format file (such as a star sat format) which can be identified by engineering simulation software;
(2) then, importing the format file into engineering simulation software ANSYS, carrying out grid division according to requirements, generating a grid-containing model, and setting local coordinates in the ANSYS to enable the local coordinates to be matched with FLAC3DThe coordinate systems are the same, and files with the format of FLAC3D are output;
(3) determining boundary conditions, wherein the left side and the right side of the boundary conditions are generally horizontally constrained, the lower part of the boundary conditions is fixed, the upper part of the boundary conditions is a free boundary, and the initial ground stress is selected as a self-weight ground stress field;
(4) in FLAC3DAnd inputting a sample data set of influencing factors, and solving the safety coefficient K by adopting an intensity reduction method.
In this way, the strength reduction method adopted in step 2 does not need to assume the position and shape of the sliding surface, and the assumed conditions for calculation are less, and the calculation formula of the cohesive force and the internal friction angle after the strength reduction is as follows:
cF＝c/F*
Figure BDA0003027892740000042
in the formula: c. CF、
Figure BDA0003027892740000043
Respectively the reduced cohesion and internal friction angle, F*The reduction coefficient is the ratio of the strength index of the slope reaching the critical failure state to the original strength index of the rock-soil body, namely the safety coefficient K of the slope to be solved.
Thus, FLAC is employed3DWhen the software calculates the safety coefficient, a built-in solution FOS command is usually adopted for solving, namely the slope stability is analyzed by repeatedly adjusting the strength indexes c and phi of the rock-soil body through continuously increasing the strength reduction coefficient until the critical damage is reached, and the strength reduction coefficient is the safety coefficient at the moment. Therefore, by using the software, the stress and the deformation of the soil body can be reflected while the error caused by artificial assumption is avoided.
Further, in step 3, an allowable safety factor [ K ] of 1.3 is selected.
Because the allowable safety factor of the side slope is generally between 1.10 and 1.35 according to the standard of the allowable safety factor of the side slope stability in the technical Specification for building slope engineering GB50330-2013, a larger safety factor is preferably selected in the scheme, namely 1.30 is selected, and the safety can be better ensured.
Further, in step 3, the calculated safety factor K is compared with the allowable safety factor [ K ], and if K ≧ K ] is considered stable, it is represented by G ═ 1, and K < [ K ] is considered unstable, and is represented by G ═ 1.
Thus, subsequent calculation can be better facilitated.
Further, in step 4, an AdaBoost classifier is constructed, which mainly comprises the following steps:
(1) initializing weight distribution of training data; each training sample is initially given the same weight: 1/N;
D1＝(w11,w12,...,w1i,...,w1N),w1i＝1/N,i＝1,2,...,N (1)
(2) performing m iterations with Gm(x) Classifier representing current m iterations, emRepresenting the current classification error, amRepresents a sum coefficient, wherein:
A. using a weight distribution DmLearning the training data set to obtain a basic classifier:
Gm(x):x→{-1,+1}(2)
B. calculation of Gm(x) Classification error rate on training set:
Figure BDA0003027892740000051
C. calculation of Gm(x) Coefficient of (a)mRepresents Gm(x) Degree of importance in the final classifier:
Figure BDA0003027892740000052
from the above formula, emWhen the content is less than or equal to 0.5, amIs not less than 0, and amWith emIs increased, meaning that the smaller the classification error rate, the more the basic classifier plays a role in the final classifier;
D. the weight distribution of the training data set is updated (for the purpose of obtaining a new weight distribution of the samples) for the next iteration:
Figure BDA0003027892740000053
wherein:
Figure BDA0003027892740000054
so as to be classified by the basic classifier Gm(x) The weight of the misclassified samples is increased, while the weight of the correctly classified samples is decreased; (thus, in this manner, the AdaBoost algorithm can "focus" or "focus" on those samples that are less readily distinguishable.)
(3) Combining the classifiers:
Figure BDA0003027892740000061
the final classifier is:
Figure BDA0003027892740000062
further, in step 4, after the AdaBoost classifier is established, the training sample is brought into the established AdaBoost classifier, and whether the error rate of the classification result is less than the precision error threshold value [ error ] is judged]If error < [ error < >]If yes, ending the test; if error is not less than [ error ≥ error]Iteration is carried out until the iteration times are reached; taking the finally obtained AdaBoost classifier as the mapping relation between whether the slope is stable or not and the random variable
Figure BDA0003027892740000063
The iteration times T of the AdaBoost classifier can be set to be 50 times according to experience, wherein T is too large, the model is easy to be over-fitted, T is too small, and the model is easy to be under-fitted; the accuracy error threshold error may be 0.01. Therefore, the AdaBoost algorithm can be used for reliably and stably establishing the mapping relation between whether the slope is stable and the random variable.
Further, step 5 specifically includes the following steps:
5.1 adopting Monte Carlo simulation method, when c, which influences the slope stability,
Figure BDA0003027892740000067
When the probability distribution function of the variable is known, a computer is utilized to generate n groups of random numbers (n is large enough and is generally larger than 50000 groups, because the slope failure probability obtained by calculation with more quantity is more accurate, generally, when n is larger than 50000, the variation coefficient of the failure probability is smaller and is about 10 percent, and basically tends to be stable, in order to make the result more accurate and take precision and efficiency into consideration, 100000 groups of random parameter samples can be specifically selected for slope reliability analysis during implementation), the random numbers are respectively substituted into a limit state equation G, wherein G is-1 or 1, namely the final classifier of AdaBoost, if M is-1, the Bernoulli's large number theorem can know that the failure probability is-1
Pf＝P{G＝-1}＝M/n (9)
For n G1,G2,…,GnMean value of μGSum mean square error σGThe estimators of (a) are:
Figure BDA0003027892740000064
Figure BDA0003027892740000065
the reliability index is then:
Figure BDA0003027892740000066
when the basic variable is normally distributed, the corresponding reliability index is:
β＝-Φ-1(Pf)＝Φ-1(1-Pf) (14)
in the formula: Φ is the standard normal distribution.
5.2 generating a plurality of groups of the c, c and c by using a norm function in Matlab software,
Figure BDA0003027892740000073
Random sample data for variables, typically larger than 100000 sets (the more accurate the more), is brought into the established mapping
Figure BDA0003027892740000071
Solving is carried out to obtain the number of samples of slope instability G-1 and slope stability G-1, and the failure probability P is solved according to the Bernoulli's theorem, namely the formula (9)f；
5.3 failure probability P obtained by solvingfThe slope reliability β is solved by substituting in equation (14).
Therefore, the stability and instability of the side slope can be known according to the failure probability and reliability. And thus as an evaluation basis for how the slope should be maintained and whether the construction of the building, etc., can be renovated. The construction of the related engineering of the side slope is guided better, and the safety is improved.
Further, in step 5, solving the reliability β of the slope corresponding to each group of sample data by using a direct monte carlo method1Judging beta and beta1If the relative error rate is within 5.0%, this indicates that the method is feasible.
Therefore, the feasibility of the method can be better verified, generally, the slope reliability obtained by the direct Monte Carlo method is more accurate, and the slope reliability is taken as a comparison group, and the calculated relative error rate is generally considered to be feasible within 5.0%, and is considered to be higher in precision within 3.0%.
Therefore, the method introduces an intelligent algorithm into reliability analysis, constructs a mapping relation between corresponding influence parameters and slope stability by using the strong data mining capability of the intelligent algorithm, solves the problem of large calculated amount of a direct Monte Carlo method by combining a uniform test and Monte Carlo simulation to solve the failure probability and reliability index of the slope, provides a new approach for slope reliability theory and engineering practice, and has wide application prospect.In addition, the method mainly aims at the homogeneous soil slope, but is not limited to the homogeneous soil slope, and can also be applied to a composite slope, and corresponding influence parameters are not limited to c,
Figure BDA0003027892740000072
Corresponding screening can be carried out according to conditions.
In conclusion, the method and the device can more reliably and effectively analyze and judge the slope stability degree, obtain the failure probability, provide a basis for the decision of the slope engineering and better ensure the safety of the slope engineering.
Drawings
FIG. 1 is a schematic flow chart of the present invention.
Fig. 2 is a schematic structural diagram of the AdaBoost algorithm in the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments.
The specific implementation mode is as follows: referring to fig. 1 and 2, a slope reliability determination method based on an AdaBoost algorithm includes the following steps:
1. determining factors influencing the slope stability, acquiring an actual data set of the influencing factors of small sample size, determining probability distribution of the actual data set, and generating a data set of the influencing factors of large sample size by using a uniform test;
2. constructing a side slope model according to the side slope to be predicted and utilizing FLAC3DSoftware inputs a data set of influencing factors, and the safety coefficient K corresponding to each group of index parameters is solved by adopting an intensity reduction method;
3. comparing the calculated safety coefficient K with the allowable safety coefficient [ K ] to obtain a slope stability result corresponding to the corresponding influence factor, and further constructing a data set of judgment index influence factors and corresponding stability results;
4. constructing an AdaBoost classifier through an AdaBoost algorithm and the training samples, and establishing a mapping relation between whether the side slope is stable and the influence factors;
5. and substituting a large amount of random variable data generated by Monte Carlo simulation into the trained AdaBoost algorithm model to obtain a corresponding stability judgment result, and further solving the slope failure probability and reliability index.
According to the method, firstly, a large-sample-size data set is generated for training through a uniform test according to the actual data of the influence factors of small sample sizes to obtain a mapping relation between the influence factors and stability results, then, a large amount of random variable data generated through Monte Carlo simulation is brought into a model of the mapping relation, and failure probability and reliability indexes are solved. The step flow is simpler and more reliable. The large sample data is generated by adopting the uniform test, so that the generated test points can be uniformly dispersed in a high-dimensional space, the limited data can have wide representativeness, and the test times are reduced; using FLAC3DThe software can more conveniently and simply use the intensity reduction method to solve the slope safety coefficient corresponding to each group of influence factor index parameters. The training calculation is performed through an AdaBoost algorithm, because AdaBoost is an important algorithm in the field of machine learning and data mining, compared with methods such as KNN and SVM, the AdaBoost has the following advantages: (1) the weak classifier can be used as a computing frame and constructed by combining different computing methods, and when the complexity of a weak classifier model is lower, the overfitting phenomenon is less likely to occur; (2) the method is very suitable for solving the classification problem, the parameters do not need to be manually adjusted in the process of using the method, and the data set can be classified with high efficiency under the condition that the data characteristics are not much; (3) the training samples can be repeatedly trained, so that the efficiency of the classifier is improved, and a better classification effect can be realized under the condition of less data volume in a data set; (4) the weak classifier of Adaboost has a simple structure and does not need to search a proper kernel function.
In step 1, the small sample size is in the range of 30 groups, and the large sample size needs to exceed 30 groups.
Small and large sample sizes generally have no absolute criteria. The small sample size is determined according to the actual engineering conditions, and the sample size exceeding 30 groups is generally regarded as the large sample size, and of course, the larger the large sample size, the better.
In the step 1, the influence factors are divided into quantitative influence factors and variable influence factors, and actual data of the variable influence factors are obtained through geological exploration and geotechnical experiments after points are taken at different positions of the side slope.
Therefore, influence factors are distinguished, the factor with larger change has larger influence on the slope stability change condition, and the reliability of the final calculation result can be better ensured by taking actual exploration values of a plurality of positions as the basis of research. The factors with small changes have small influence on the slope stability change condition, the factors are considered as quantitative influence factors, the fixed value is taken as a subsequent data sample, and the data can be obtained by obtaining the value at a single position of the slope through geological exploration and geotechnical experiments or calculating the mean value after the values of a few positions are obtained. Therefore, under the condition of greatly reducing the practical application difficulty of the method, the reliability of the calculation result can be ensured to the maximum extent, meanwhile, the influence on the slope stability can be reduced to the maximum extent, and the calculation judgment is realized on the basis of better maintaining the slope stability.
In the present embodiment, the homogeneous soil slope is subjected to step 1, and the selected variable influencing factors are the cohesive force c and the internal friction angle
Figure BDA0003027892740000091
Wherein the variable influencing factors are cohesive force c and internal friction angle
Figure BDA0003027892740000092
Because of the homogeneous slope of the earth, c and
Figure BDA0003027892740000095
the variation is large and the influence on the stability variation of the slope is large, and generally speaking, the variation is mutually independent random variables which are subject to normal distribution. Therefore, on the basis of uniform test design, the 3 sigma criterion and the interpolation method are combined, training data with large sample size can be generated better, enough similarity with real data is guaranteed, meanwhile, the influence of relevance among factors on the accuracy of a calculation result can be avoided, and the reliability of the generated data with large sample size is enhanced. It is concretelyThe data acquisition means of (2) is prior art and will not be described in detail here. The quantitative influence factors can be parameters including slope height, slope angle, pore water pressure ratio, rock mass volume weight and the like, and can be obtained by taking a fixed value after one-time measurement or taking homogeneity as the fixed value after several times of measurement and bringing the fixed value into subsequent calculation. The specific survey measurement method is prior art and will not be described in detail herein.
In step 1, the specific steps of generating a data set of the influencing factors of large sample size by using a uniform test are as follows:
assuming that the number of training samples is set as x groups, a uniform table is selected
Figure BDA0003027892740000093
Conducting a numerical test in which U*Representing a uniform table with better uniformity, wherein x is a horizontal number, namely x groups of data are generated, and y represents the number of variable influence factors, namely the table can represent a numerical test containing y variable influence factors at most; (since the variables of the foregoing choices influence c and
Figure BDA0003027892740000094
therefore, y is 2; )
Wherein, due to c and
Figure BDA0003027892740000096
the value follows normal distribution, so the value range determines the upper and lower limits according to the 3 sigma criterion, namely [ mu-3 sigma, mu +3 sigma]Where μ is the mean and σ is the standard deviation, the 2 columns of data are converted to c and
Figure BDA0003027892740000097
a value within the true range; and then, supplementing the values of the quantitative influence factors with fixed values to obtain a data set of the influence factors with large sample size.
Thus, sample data c and c are generated using a uniform design
Figure BDA0003027892740000101
The uniform design is a test design method considering that test points are uniformly distributed in a test range; from the aboveThe test points generated by the method are uniformly dispersed in a high-dimensional space, and the generated data has wide representativeness and can greatly reduce the experiment times. Because the uniform test design considers the test points selected by uniformly spreading the test points in the test range, each level of each factor can be tested only once, and when the number of levels (namely, the influence factors) is increased, the test frequency is increased along with the increase of the number of levels, compared with the traditional orthogonal test design (the test frequency is increased along with the square number of the number of levels), the test frequency can be greatly reduced. And a value range is determined by further combining a 3 sigma criterion and an interpolation method, so that the data distribution is in normal distribution and is close to the real data. Compared with other methods, the method for generating the large sample data has the advantages of simple principle and easy operation.
In step 2, in FLAC3DThe process of solving the safety coefficient K of the slope model by adopting a strength reduction method mainly comprises the following steps:
(1) establishing a corresponding homogeneous slope model in the CAD, and outputting a format file (such as a star sat format) which can be identified by engineering simulation software;
(2) then, importing the format file into engineering simulation software ANSYS, carrying out grid division according to requirements, generating a grid-containing model, and setting local coordinates in the ANSYS to enable the local coordinates to be matched with FLAC3DThe coordinate systems are the same, and files with the format of FLAC3D are output;
(3) determining boundary conditions, wherein the left side and the right side of the boundary conditions are generally horizontally constrained, the lower part of the boundary conditions is fixed, the upper part of the boundary conditions is a free boundary, and the initial ground stress is selected as a self-weight ground stress field;
(4) in FLAC3DAnd inputting a sample data set of influencing factors, and solving the safety coefficient K by adopting an intensity reduction method.
In this way, the strength reduction method adopted in step 2 does not need to assume the position and shape of the sliding surface, and the assumed conditions for calculation are less, and the calculation formula of the cohesive force and the internal friction angle after the strength reduction is as follows:
cF＝c/F*
Figure BDA0003027892740000102
in the formula: c. CF、
Figure BDA0003027892740000103
Respectively the reduced cohesion and internal friction angle, F*The reduction coefficient is the ratio of the strength index of the slope reaching the critical failure state to the original strength index of the rock-soil body, namely the safety coefficient K of the slope to be solved. Thus, FLAC is employed3DWhen the software calculates the safety coefficient, a built-in solution FOS command is usually adopted for solving, namely the slope stability is analyzed by repeatedly adjusting the strength indexes c and phi of the rock-soil body through continuously increasing the strength reduction coefficient until the critical damage is reached, and the strength reduction coefficient is the safety coefficient at the moment. Therefore, by using the software, the stress and the deformation of the soil body can be reflected while the error caused by artificial assumption is avoided.
In step 3, an allowable safety factor [ K ] of 1.3 is selected.
Because the allowable safety factor of the side slope is generally between 1.10 and 1.35 according to the standard of the allowable safety factor of the side slope stability in the technical Specification for building slope engineering GB50330-2013, a larger safety factor is preferably selected in the scheme, namely 1.30 is selected, and the safety can be better ensured.
In step 3, the calculated safety factor K is compared with the allowable safety factor [ K ], and if K ≧ K ] is considered stable, it is represented by G ═ 1, and K < [ K ] is considered unstable, and is represented by G ═ 1.
Thus, subsequent calculation can be better facilitated.
In step 4, an AdaBoost classifier is constructed, which mainly comprises the following steps:
(1) initializing weight distribution of training data; each training sample is initially given the same weight: 1/N;
D1＝(w11,w12,...,w1i,...,w1N),w1i＝1/N,i＝1,2,...,N (1)
(2) perform m iterationsInstead, with Gm(x) Classifier representing current m iterations, emRepresenting the current classification error, amRepresents a sum coefficient, wherein:
A. using a weight distribution DmLearning the training data set to obtain a basic classifier:
Gm(x):x→{-1,+1}(2)
B. calculation of Gm(x) Classification error rate on training set:
Figure BDA0003027892740000111
C. calculation of Gm(x) Coefficient of (a)mRepresents Gm(x) Degree of importance in the final classifier:
Figure BDA0003027892740000112
from the above formula, emWhen the content is less than or equal to 0.5, amIs not less than 0, and amWith emIs increased, meaning that the smaller the classification error rate, the more the basic classifier plays a role in the final classifier;
D. the weight distribution of the training data set is updated (for the purpose of obtaining a new weight distribution of the samples) for the next iteration:
Figure BDA0003027892740000113
wherein:
Figure BDA0003027892740000114
so as to be classified by the basic classifier Gm(x) The weight of the misclassified samples is increased, while the weight of the correctly classified samples is decreased; (thus, in this manner, the AdaBoost algorithm can "focus" or "focus" on samples that are less readily distinguishable。)
(3) Combining the classifiers:
Figure BDA0003027892740000121
the final classifier is:
Figure BDA0003027892740000122
in step 4, after the AdaBoost classifier is established, the training sample is brought into the established AdaBoost classifier, and whether the error rate of the classification result is less than the precision error threshold value [ error [ ]]If error < [ error < >]If yes, ending the test; if error is not less than [ error ≥ error]Iteration is carried out until the iteration times are reached; taking the finally obtained AdaBoost classifier as the mapping relation between whether the slope is stable or not and the random variable
Figure BDA0003027892740000123
The iteration times T of the AdaBoost classifier can be set to be 50 times according to experience, wherein T is too large, the model is easy to be over-fitted, T is too small, and the model is easy to be under-fitted; the accuracy error threshold error may be 0.01. Therefore, the AdaBoost algorithm can be used for reliably and stably establishing the mapping relation between whether the slope is stable and the random variable.
In the step 5, the method specifically comprises the following steps:
5.1 adopting Monte Carlo simulation method, when c, which influences the slope stability,
Figure BDA0003027892740000127
When the probability distribution function of the variable is known, n groups of random numbers (n is large enough and generally larger than 50000 groups because the slope failure probability calculated by the larger number is more accurate) conforming to the probability distribution of the corresponding basic variable are generated by a computer, generally, when n is larger than 50000, the variation coefficient of the failure probability is smaller and about 10 percent, and the probability basically tends to be stable, so that the result is more accurateConsidering both precision and efficiency, 100000 groups of random parameter samples can be specifically selected for slope reliability analysis) and are respectively substituted into a limit state equation G, wherein G is-1 or 1, namely the final classifier of AdaBoost, if M is-1, the probability of failure is known by Bernoulli's theorem
Pf＝P{G＝-1}＝M/n (9)
For n G1,G2,…,GnMean value of μGSum mean square error σGThe estimators of (a) are:
Figure BDA0003027892740000124
Figure BDA0003027892740000125
the reliability index is then:
Figure BDA0003027892740000126
when the basic variable is normally distributed, the corresponding reliability index is:
β＝-Φ-1(Pf)＝Φ-1(1-Pf) (14)
in the formula: Φ is the standard normal distribution.
5.2 generating a plurality of groups of the c, c and c by using a norm function in Matlab software,
Figure BDA0003027892740000133
Random sample data for variables, typically larger than 100000 sets (the more accurate the more), is brought into the established mapping
Figure BDA0003027892740000131
Solving is carried out to obtain the number of samples of slope instability G-1 and slope stability G-1, and the failure probability P is solved according to the Bernoulli's theorem, namely the formula (9)f；
5.3 failure probability P obtained by solvingfThe slope reliability β is solved by substituting in equation (14).
Therefore, the stability and instability of the side slope can be known according to the failure probability and reliability. And thus as an evaluation basis for how the slope should be maintained and whether the construction of the building, etc., can be renovated. The construction of the related engineering of the side slope is guided better, and the safety is improved.
In the implementation, step 5 may further include solving the reliability β of the slope corresponding to each group of sample data by using a direct monte carlo method1Judging beta and beta1If the relative error rate is within 5.0%, this indicates that the method is feasible.
Therefore, the feasibility of the method can be better verified, generally, the slope reliability obtained by the direct Monte Carlo method is more accurate, and the slope reliability is taken as a comparison group, and the calculated relative error rate is generally considered to be feasible within 5.0%, and is considered to be higher in precision within 3.0%.
Therefore, the method introduces an intelligent algorithm into reliability analysis, constructs a mapping relation between corresponding influence parameters and slope stability by using the strong data mining capability of the intelligent algorithm, solves the problem of large calculated amount of a direct Monte Carlo method by combining a uniform test and Monte Carlo simulation to solve the failure probability and reliability index of the slope, provides a new approach for slope reliability theory and engineering practice, and has wide application prospect. In addition, the method mainly aims at the homogeneous soil slope, but is not limited to the homogeneous soil slope, and can also be applied to a composite slope, and corresponding influence parameters are not limited to c,
Figure BDA0003027892740000132
Corresponding screening can be carried out according to conditions.

Claims (10)

1. A slope reliability judging method based on an AdaBoost algorithm is characterized by comprising the following steps:
determining factors influencing slope stability, acquiring an actual data set of the influencing factors of small sample size, determining probability distribution of the actual data set, and generating a data set of the influencing factors of large sample size by using a uniform test;
2 constructing a side slope model according to the side slope to be predicted and utilizing FLAC3DSoftware inputs a data set of influencing factors, and the safety coefficient K corresponding to each group of index parameters is solved by adopting an intensity reduction method;
comparing the calculated safety coefficient K with the allowable safety coefficient [ K ] to obtain a slope stability result corresponding to the corresponding influence factor, and further constructing a data set of judgment index influence factors and corresponding stability results;
4, constructing an AdaBoost classifier through an AdaBoost algorithm and the training samples, and establishing whether the side slope is stable and a mapping relation between influencing factors;
and 5, substituting a large amount of random variable data generated by Monte Carlo simulation into the trained AdaBoost algorithm model to obtain a corresponding stability judgment result, and further solving the slope failure probability and the reliability index to realize reliability judgment.
2. The method for judging the reliability of the side slope based on the AdaBoost algorithm according to claim 1, wherein in the step 1, the influence factors are divided into quantitative influence factors and variable influence factors, and the actual data of the variable influence factors are obtained through geological exploration and geotechnical experiments after points are taken at different positions of the side slope.
3. The method for judging the reliability of the side slope based on the AdaBoost algorithm according to claim 1, wherein in the step 1, for the homogeneous soil slope, the selected variable influence factors are cohesive force c and internal friction angle
Figure FDA0003027892730000011
4. The method for judging the slope reliability based on the AdaBoost algorithm according to claim 3, wherein in the step 1, the specific steps of generating the data set of the influencing factors with large sample size by using the uniform test are as follows:
assuming that the number of training samples is set as x groups, a uniform table is selected
Figure FDA0003027892730000012
Conducting a numerical test in which U*Representing a uniform table with better uniformity, wherein x is a horizontal number, namely x groups of data are generated, and y represents the number of variable influence factors, namely the table can represent a numerical test containing y variable influence factors at most;
wherein, due to c and
Figure FDA0003027892730000013
the value follows normal distribution, so the value range determines the upper and lower limits according to the 3 sigma criterion, namely [ mu-3 sigma, mu +3 sigma]Where μ is the mean and σ is the standard deviation, the 2 columns of data are converted to c and
Figure FDA0003027892730000014
a value within the true range; and then, supplementing the values of the quantitative influence factors with fixed values to obtain a data set of the influence factors with large sample size.
5. The method for determining the reliability of the side slope based on the AdaBoost algorithm as claimed in claim 1, wherein in step 2, FLAC is performed3DThe process of solving the safety coefficient K of the slope model by adopting a strength reduction method mainly comprises the following steps:
(1) establishing a corresponding homogeneous slope model in the CAD, and outputting the homogeneous slope model as a format file which can be identified by engineering simulation software;
(2) then, importing the format file into engineering simulation software ANSYS, carrying out grid division according to requirements, generating a grid-containing model, and setting local coordinates in the ANSYS to enable the local coordinates to be matched with FLAC3DThe coordinate systems are the same, and files with the format of FLAC3D are output;
(3) determining boundary conditions, wherein the left side and the right side of the boundary conditions are generally horizontally constrained, the lower part of the boundary conditions is fixed, the upper part of the boundary conditions is a free boundary, and the initial ground stress is selected as a self-weight ground stress field;
(4) in FLAC3DAnd inputting a sample data set of influencing factors, and solving the safety coefficient K by adopting an intensity reduction method.
6. The method for judging the reliability of the side slope based on the AdaBoost algorithm according to claim 1, wherein in the step 3, an allowable safety factor [ K ] is selected to be 1.3.
7. The method for judging the reliability of the slope based on the AdaBoost algorithm as claimed in claim 1, wherein in step 3, the calculated safety factor K is compared with the allowable safety factor [ K ], and if K ≧ K ] is considered stable, the method is represented by G ═ 1, and K < [ K ] is considered unstable, and is represented by G ═ 1.
8. The side slope reliability determination method based on the AdaBoost algorithm as claimed in claim 1, characterized in that: in step 4, an AdaBoost classifier is constructed, which mainly comprises the following steps:
(1) initializing weight distribution of training data; each training sample is initially given the same weight: 1/N;
D1＝(w11,w12,...,w1i,...,w1N),w1i＝1/N,i＝1,2,...,N (1)
(2) performing m iterations with Gm(x) Classifier representing current m iterations, emRepresenting the current classification error, amRepresents a sum coefficient, wherein:
A. using a weight distribution DmLearning the training data set to obtain a basic classifier:
Gm(x):x→{-1,+1} (2)
B. calculation of Gm(x) Classification error rate on training set:
Figure FDA0003027892730000021
C. calculation of Gm(x) Coefficient of (a)mRepresents Gm(x) Degree of importance in the final classifier:
Figure FDA0003027892730000022
from the above formula, emWhen the content is less than or equal to 0.5, amIs not less than 0, and amWith emIs increased, meaning that the smaller the classification error rate, the more the basic classifier plays a role in the final classifier;
D. updating the weight distribution of the training data set for the next iteration:
Figure FDA0003027892730000031
wherein:
Figure FDA0003027892730000032
so as to be classified by the basic classifier Gm(x) The weight of the misclassified samples is increased, while the weight of the correctly classified samples is decreased;
(3) combining the classifiers:
Figure FDA0003027892730000033
the final classifier is:
Figure FDA0003027892730000034
9. the method for determining the reliability of the side slope based on the AdaBoost algorithm as claimed in claim 8, wherein in the step 4, after the AdaBoost classifier is established, the training samples are brought into the establishmentA good AdaBoost classifier judges whether the error rate of the classification result is less than the precision error threshold value [ error]If error < [ error < >]If yes, ending the test; if error is not less than [ error ≥ error]Iteration is carried out until the iteration times are reached; taking the finally obtained AdaBoost classifier as the mapping relation between whether the slope is stable or not and the random variable
Figure FDA0003027892730000035
10. The method for judging the reliability of the side slope based on the AdaBoost algorithm as claimed in claim 1, wherein the step 5 specifically comprises the following steps:
5.1 adopting Monte Carlo simulation method, when c, which influences the slope stability,
Figure FDA0003027892730000036
When the probability distribution function of the variable is known, n groups of random numbers which accord with the probability distribution of the corresponding basic variable are generated by a computer and are respectively substituted into a limit state equation G, wherein G is-1 or 1, namely the final classifier of AdaBoost, if M values are-1, the probability of failure is known by Bernoulli's theorem
Pf＝P{G＝-1}＝M/n (9)
For n G1,G2,…,GnMean value of μGSum mean square error σGThe estimators of (a) are:
Figure FDA0003027892730000037
Figure FDA0003027892730000038
the reliability index is then:
Figure FDA0003027892730000039
when the basic variable is normally distributed, the corresponding reliability index is:
β＝-Φ-1(Pf)＝Φ-1(1-Pf) (14)
in the formula: phi is standard normal distribution;
5.2 generating a plurality of groups of the c, c and c by using a norm function in Matlab software,
Figure FDA0003027892730000041
Random sample data for variables, typically larger than 100000 sets (the more accurate the more), is brought into the established mapping
Figure FDA0003027892730000042
Solving is carried out to obtain the number of samples of slope instability G-1 and slope stability G-1, and the failure probability P is solved according to the Bernoulli's theorem, namely the formula (9)f；
5.3 failure probability P obtained by solvingfThe slope reliability β is solved by substituting in equation (14).
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