CN114818418A - Slope reliability analysis method based on active learning multivariate self-adaptive regression spline - Google Patents
Slope reliability analysis method based on active learning multivariate self-adaptive regression spline Download PDFInfo
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Abstract
The invention provides a slope reliability analysis method, which comprises the following steps: acquiring slope parameters of a target object; constructing a slope analysis model by using simulation calculation software and slope parameters, and preprocessing the slope analysis model to obtain a stability file; determining a random field statistical index, and obtaining an independent standard normal distribution sample and an independent standard normal distribution sample pool by utilizing an LHS method and the random field statistical index; dispersing by using a KL series expansion method according to each independent standard normal distribution sample, each independent standard normal distribution sample pool and the stability file to obtain a sample matrix; calculating each sample matrix by using simulation calculation software to obtain a corresponding slope safety coefficient; constructing a multivariate self-adaptive regression model by using the slope safety coefficient, and verifying the accuracy of the multivariate self-adaptive regression model; and if the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, calculating the multivariate self-adaptive regression model by adopting an MCS method to obtain the slope failure probability.
Description
Technical Field
The application relates to the technical field of slope engineering, in particular to a slope reliability analysis method based on an active learning multivariate self-adaptive regression spline.
Background
Due to the complex deposition process of natural soil, the nature of the soil often shows spatial variability in space. Even if various exploration and test methods are available, the characteristics of the obtained soil body still have uncertainty, and the main reason is that the formation of the soil body is a complex process and is influenced by geology, environment and physicochemical processes. Therefore, the traditional method for obtaining the safety coefficient is usually calculated by a group of determined soil characteristic parameters, and the slope stability analysis cannot be accurately carried out. For this reason, in recent years, researchers have conducted a great deal of research into the spatial variability of slopes.
For slope reliability analysis, many methods have been proposed in previous studies, and the simplest method is direct Monte Carlo Simulation (MCS for short), which has the advantage that a higher-precision unbiased estimation value of failure probability can be obtained under the condition that the number of samples is sufficient. However, the method is huge in calculation amount, and when finite element/finite difference intensity reduction method is used, the calculation cost is high by adopting the MCS method. E.g. in the face of failure probability p f 1% of COV pf 10%, at least 10 4 One sample can achieve an estimation error below 0.1. Especially for the case of small failure probability, ten thousand times of numerical simulation calculation is often needed, so that the workload is too large to meet the requirement of practical application.
Disclosure of Invention
The embodiment of the application provides a slope reliability analysis method based on an active learning multivariate self-adaptive regression spline, so as to at least solve the defects in the related technology.
The embodiment of the application provides a slope reliability analysis method based on an active learning multivariate self-adaptive regression spline, which comprises the following steps:
the method comprises the following steps: acquiring slope parameters of a target object, wherein the slope parameters at least comprise slope size and soil characteristic parameters;
step two: constructing a corresponding slope analysis model by using preset simulation calculation software, the slope size and the soil characteristic parameters, and preprocessing the slope analysis model to obtain a stability file;
step three: determining a random field statistical index, and obtaining a plurality of independent standard normal distribution samples and independent standard normal distribution sample pools by using an LHS method and the random field statistical index;
performing dispersion by using a KL series expansion method according to each independent standard normal distribution sample, each independent standard normal distribution sample pool and the stability file to obtain a plurality of sample matrixes;
step four: calculating each sample matrix by using the simulation calculation software to obtain a corresponding slope safety coefficient;
step five: constructing a multivariate self-adaptive regression model by using the slope safety coefficient, and verifying the accuracy of the multivariate self-adaptive regression model;
step six: and if the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, calculating the multivariate self-adaptive regression model by adopting an MCS method to obtain the slope failure probability.
Further, the method further comprises:
step eight: if the accuracy of the multivariate self-adaptive regression model does not meet the preset accuracy requirement, calling a preset active learning function, selecting the optimal sample in each independent standard normal distribution sample pool, and constructing a new sample matrix according to the optimal sample and the sample matrix;
step nine: and re-executing the fourth step and the fifth step according to the new sample matrix until the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, and calculating the multivariate self-adaptive regression model meeting the requirement by adopting an MCS method to obtain the slope failure probability.
Further, the simulation calculation software adopts FLAC3D software, and the second step includes:
using FLAC3D software, the slope size and the soil characteristic parametersConstructing a corresponding slope analysis model, and extracting the centroid coordinates (x) of each finite element unit in the slope analysis model i ,y i ) Wherein, i is 1, 2 … m, and m is the number of units;
and calculating to obtain the stability file according to the centroid coordinates and the intensity reduction method in the finite difference method.
Further, the third step includes:
determining random field statistical indexes including a mean value, a variation coefficient, a distribution type and a correlation coefficient;
determining a correlation function and a correlation distance according to the mean value, the variation coefficient, the distribution type and the correlation coefficient;
performing geotechnical test on the position of the target object, and determining soil shear strength parameters of the target object, wherein the soil shear strength parameters comprise cohesive force c and an internal friction angle phi of the target object;
taking the correlation function as the spatial autocorrelation of the soil shear strength parameter:
in the formula, delta h And delta v Respectively, a horizontal correlation distance and a vertical correlation distance; l is a radical of an alcohol m And L n Respectively, the difference between the coordinates of the two centroids.
Further, the expression of the shear strength parameter-dependent log random field is as follows:
in the formula, n is the number of truncation terms; lambda [ alpha ] j The characteristic value corresponding to the autocorrelation function; f. of j (x, y) is a characteristic function corresponding to the autocorrelation function; mu.s lni And σ lni The mean and standard deviation of the corresponding normal distribution parameter lni, respectively; chi shape i,j Is a related standard normal random variableAnd the matrix is obtained by converting an independent standard normal random sample matrix.
Further, the mu lni And σ lni The calculation formulas of (A) and (B) are respectively as follows:
in the formula, ln i The method is a cross-correlation random variable which obeys log-normal distribution and is used for describing the distribution of a slope soil characteristic parameter random field.
Further, the expression for the kth row of the random sample matrix is:
in the formula, xi is a matrix of independent standard normal distribution samples, and is obtained by adopting an LHS method; rho c,φ Is the cross-correlation coefficient between the cohesion c of the target object and the internal friction angle phi of the target object.
Further, the fourth step includes:
and calculating the stability files in the sample matrixes by using FLAC3D software and a fish language to obtain the corresponding slope safety factors.
Further, the expression of the active learning function is:
in the formula, argmin () is an optimal parameter with the minimum function value in the return solving process;
proxy the model for the function; u. of T Is a sample point, i.e. a variable parameter; u. of c Selecting the sample point of the optimal sample from an independent standard normal distribution sample pool; d (u) T S) represents the u in the sample concentration point and the independent standard normal space T A minimum distance therebetween; d (S) is a minimum distance limit.
Further, the expression of the minimum distance limit is:
wherein λ is a constant coefficient term, between 0.1 and 0.5;
wherein, X i Is the ith random variable, U i Is the ith normal random variable, u i And x i Is the value of a random variable, F xi (. and F) Ui (. is a probability cumulative distribution function;
m-dimensional samples generated for a standard normal distribution.
Compared with the related technology, the slope reliability analysis method based on the active learning multivariate self-adaptive regression spline provided by the embodiment of the application comprises the steps of firstly adopting a KL series expansion method to disperse soil body parameters, calculating the slope safety coefficient based on a finite difference intensity reduction method, selecting an optimal point through an active learning function and combining with a training sample to construct an AMARS model, and adopting a Monte Carlo simulation method to carry out slope reliability analysis.
The details of one or more embodiments of the application are set forth in the accompanying drawings and the description below to provide a more concise and understandable description of the application, and features, objects, and advantages of the application.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the application and together with the description serve to explain the application and not to limit the application. In the drawings:
FIG. 1 is a flowchart of a slope reliability analysis method based on active learning multivariate adaptive regression spline according to a first embodiment of the present invention;
FIG. 2 is a flowchart illustrating a slope reliability analysis calculation based on an active learning multivariate adaptive regression spline according to a first embodiment of the present invention;
FIG. 3 is a schematic view of a slope model according to a first embodiment of the present invention;
FIG. 4 is a graph illustrating a comparison of values predicted by the AMARS model and actual response values according to a first embodiment of the present invention;
FIG. 5 is a mesh diagram of a slope model according to a second embodiment of the present invention;
FIG. 6 is a schematic diagram illustrating a comparison between a predicted safety factor and a calculated safety factor in a second embodiment of the present invention;
FIG. 7 is a diagram illustrating the variation of pf with the number of training samples according to the second embodiment of the present invention.
The following detailed description will further illustrate the invention in conjunction with the above-described figures.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application will be described and illustrated below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present application and are not intended to limit the present application. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments provided in the present application without any inventive step are within the scope of protection of the present application.
It is obvious that the drawings in the following description are only examples or embodiments of the present application, and that it is also possible for a person skilled in the art to apply the present application to other similar contexts on the basis of these drawings without inventive effort. Moreover, it should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers' specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another.
Reference in the specification to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the specification. The appearances of the phrase in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Those of ordinary skill in the art will explicitly and implicitly appreciate that the embodiments described herein may be combined with other embodiments without conflict.
Unless defined otherwise, technical or scientific terms referred to herein shall have the ordinary meaning as understood by those of ordinary skill in the art to which this application belongs. Reference to "a," "an," "the," and similar words throughout this application are not to be construed as limiting in number, and may refer to the singular or the plural. The present application is directed to the use of the terms "including," "comprising," "having," and any variations thereof, which are intended to cover non-exclusive inclusions; for example, a process, method, system, article, or apparatus that comprises a list of steps or modules (elements) is not limited to the listed steps or elements, but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus. Reference to "connected," "coupled," and the like in this application is not intended to be limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The term "plurality" as referred to herein means two or more. "and/or" describes an association relationship of associated objects, meaning that three relationships may exist, for example, "A and/or B" may mean: a exists alone, A and B exist simultaneously, and B exists alone. The character "/" generally indicates that the former and latter associated objects are in an "or" relationship. Reference herein to the terms "first," "second," "third," and the like, are merely to distinguish similar objects and do not denote a particular ordering for the objects.
Firstly, it should be noted that slope reliability analysis in spatially variable soil often faces huge computational burden. In order to effectively reduce the number of numerical models in reliability analysis and relieve the calculation pressure, the application aims to provide an active learning Multivariate Adaptive Regression Spline (MARS) method for performing reliability analysis on a spatial variation slope. First, an initial training sample is obtained by latin hypercube sampling. And then searching a new training sample near the extreme state surface by using the active learning function to update the MARS proxy model. After an accurate proxy model is obtained, the damage probability of the slope can be obtained through Monte Carlo simulation.
Example one
Referring to fig. 1, a slope reliability analysis method based on an active learning multivariate adaptive regression spline in a first embodiment of the present invention is shown, and the method specifically includes steps S101 to S108:
s101, acquiring slope parameters of a target object, wherein the slope parameters at least comprise slope size and soil characteristic parameters;
s102, constructing a corresponding slope analysis model by utilizing preset simulation calculation software, the slope size and the soil characteristic parameters, and preprocessing the slope analysis model to obtain a stability file;
s103, determining a random field statistical index, and obtaining a plurality of independent standard normal distribution samples and independent standard normal distribution sample pools by using an LHS method and the random field statistical index;
performing dispersion by using a KL series expansion method according to each independent standard normal distribution sample, each independent standard normal distribution sample pool and the stability file to obtain a plurality of sample matrixes;
in specific implementation, the soil property parameter spatial variability simulation based on a KL series expansion method is adopted in the method:
the shear strength parameters (i.e. cohesion c and internal friction angle phi) of the soil body are particularly important in slope stability analysis. The soil body is influenced by geology and physicochemical action in the forming process, so the shear strength parameter of the soil body shows spatial variability. The shear strength parameter is a positive value, and negative correlation exists among the parameters, and for this reason, the coherent force c and the spatial variability of the internal friction angle phi are represented by a correlated logarithmic random field. The KL series expansion method (the Karhunen-Loeve method) needs less random variables during expansion and use, and has higher calculation precision and efficiency. Therefore, the method is adopted to disperse the random field, and the shear strength parameter-dependent logarithmic random field can be expressed as follows:
in the formula, n is the number of truncation terms; lambda [ alpha ] j The characteristic value corresponding to the autocorrelation function; f. of j (x, y) is a characteristic function corresponding to the autocorrelation function; mu.s lni And σ lni The mean and standard deviation of the corresponding normal distribution parameter lni, respectively; chi shape i,j The random variable is a related standard normal random variable and is obtained by converting an independent standard normal random sample matrix. Wherein mu lni And σ lni The calculation formulas are respectively as follows:
it should be noted that autocorrelation exists between any two points in space, autocorrelation presents an inverse trend along with the distance between the two points, and only limited field test data can be used to establish an autocorrelation function of the soil parameter spatial autocorrelation, so a theoretical autocorrelation function is often used to replace a real autocorrelation function. Common autocorrelation functions are exponential, gaussian, second-order autoregressive, exponential cosine and triangular, etc. In view of the fact that the Gaussian correlation function is good in continuity and continuous in derivation everywhere, the Gaussian correlation function is selected as the soil parameter space autocorrelation:
in the formula: delta h And delta v Respectively horizontal and vertical relative distances; l is m And L n Respectively are the difference values of the coordinates corresponding to two points in the soil body space. Chi shape i,j The random sample matrix is a related standard normal random variable and is obtained by converting an independent standard normal random sample matrix, wherein the kth row of the random sample matrix can be expressed as:
in the formula: ξ is the independent standard normal sample matrix,
can be obtained by adopting Latin Hypercube Sampling (LHS); rho c,φ Is the cross correlation coefficient between c and phi.
S104, calculating each sample matrix by using the simulation calculation software to obtain a corresponding slope safety coefficient;
s105, constructing a multivariate self-adaptive regression model by using the slope safety coefficient, and verifying the accuracy of the multivariate self-adaptive regression model;
in specific implementation, the method adopts a multivariate self-adaptive regression spline method:
compared with other methods, the MARS method has the characteristics of stronger adaptability and higher model prediction precision, and the method takes the tensor product of the spline function as a base function. The MARS method has the advantage of multidimensional large sample data processing, and the method is easy to determine the accumulated contribution of each variable and the interaction of a plurality of different variables. Variable set x ═ of input variables in the system (x) 1 ,x 2 ,...,x p ) Set of variables with output variable, y ═ y (y) 1 ,y 2 ,...,y p ) The relationship exists as follows:
y i ＝f i (x 1 ,x 2 ,...,x p )+ε j (6)
wherein
Is a function of the degree of certainty,
is a set of random variables that reflects the random disturbance of the system, and the expected value is set to zero. The goal of MARS is to approximate the training data to obtain a true function that can be used instead of the original function. According to MARS, the true function f (ξ) can be expressed as follows:
wherein
A predicted value output for the MARS model; xi ═ xi (xi) 1 ,ξ 2 ,...,ξ p ) Is a set of input variables; a is m Is the coefficient of the m-th basis function, coefficient a m The least squares fit through the training samples can yield:
B m (x n1 ,x n2 ,...,x np ) Is the mth basis function or spline function, and has the following form:
in the formula B m (x n1 ,x n2 ,...,x np ) B is formed by km Is multiplied by an input variable x v(k,m) And parameter set P km Determining; k is a radical of m Is b is km Number of (·); b km (. cndot.) is a spline basis function; wherein b is km The form of (A) is as follows:
b km (x|s,t)＝[s(x-t)] + (10)
where the subscripts represent the positive part, i.e.:
the parameters in the formula (10) are 11- ∞ ≦ t ≦ infinity + ∞ of the node position of the basis function and 12s ≦ 1 in the stage direction, i.e., P in the formula (9) km ＝(s km ，t km )。
In the formula: s k,m A truncation direction with a value of +1 or-1; eta v(k,m) An input variable corresponding to the kth truncated spline basis function in the mth term in equation (1); t is t k,m Is the node position; q is the power of the spline basis function.
The MARS algorithm is implemented in two processes, namely forward selection and backward pruning. The forward process algorithm is to only contain one constant term basis function B 0 (x) Starting at 1, each iteration generates two new basis functions, and then identifies the new basis functions, resulting in an approximate model. The model updated for each iteration is of the form:
in the formula:
and
least squares fit calculations can be performed on the training samples; b is i (xi) isThe previously determined basis function, l is 0 ≦ M. Generally, the forward process algorithm will generate an over-fit model, and since the MARS algorithm allows new basis functions to be constructed using previous basis functions, resulting in a reduced contribution of the original basis functions, a backward process algorithm is used to improve the model prediction capability.
The backward process algorithm adopts each cycle, deletes the original basis function to obtain the sub-model, uses the Generalized Cross-validation (GCV), and the specific form is as follows:
wherein:
is at sample point x i Corresponding predicted values; d is a penalty factor, which is between 2 and 4, and is generally 3; c (m) trace (B) T B) -1 B T )+1+dM；trace(B(B T B) -1 B T ) +1 is the number of significant coefficients of the model.
S106, if the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, calculating the multivariate self-adaptive regression model by adopting an MCS method to obtain the slope failure probability;
s107, if the accuracy of the multivariate adaptive regression model does not meet the preset accuracy requirement, calling a preset active learning function, selecting the optimal sample in each independent standard normal distribution sample pool, and constructing a new sample matrix according to the optimal sample and the sample matrix;
in specific implementation, after the initial sample point is determined, iterative updating of the proxy model is performed, the active learning function is based on the currently selected MARS model, and an optimal sample point (obtained by using the result of each simulation calculation analysis) is selected and added into the training sample set each time, so that the purpose of iteratively updating the MARS model is achieved. For the selection of the optimal sample point, a Monte Carlo-based sample is adoptedA sampling method of a pool. Compared with other optimization algorithms, the sample cell method has the advantages of simpler and easier-to-understand concept, simpler and more convenient operation and easy realization. The method comprises the steps of generating a large sample pool T by MCS sampling, and calculating p during model iteration f And selecting the optimal sample point are based on the sample pool T.
The active learning function plays a significant role in the iterative process, especially in model convergence, so that the following principle is satisfied when selecting an optimal sample point: the sample point is located at the junction of the failure domain and the security domain, and more effective information can be provided, so that the model is converged, and the calculation accuracy can be effectively improved. Secondly, the optimal sample points need to be far away from each other, repeated sampling is avoided, and the sampling space is conveniently and quickly traversed, so that the model is quickly converged.
If the agent model can obtain a standard index such as variance of the model prediction value, an active learning function can be conveniently constructed. For example, a simple and efficient active learning function is provided by fully utilizing the predicted value and variance information:
in the formula, argmin (·) returns the optimal parameter with the minimum function value in the solving process, and at the moment, the sample point u T The parameters are regarded as variable parameters and need to be subjected to traversal calculation; u. of c Representing the optimal sample point selected from the pool.
Because the construction of the active learning function is a difficulty which always exists, based on the above formula (15), an efficient active learning function considering the distance penalty term is provided:
in the formula (I), the compound is shown in the specification,
is a function proxy model, and only gives a prediction result for a classifierFruit rather than numeric value, in which case F (u) may be substituted
For the other models, the model is,
no changes are required; d (u) T S) represents the sample concentration point and u in the independent standard normal space T A minimum distance therebetween; d (S) is a minimum distance limit, which varies and can be calculated according to the following equation:
wherein λ is a constant coefficient term, between 0.1 and 0.5;
wherein, X i Is the ith random variable, U i Is the ith normal random variable, u i And x i Is the value of a random variable, F xi (. and F) Ui (. is a probability cumulative distribution function;
m-dimensional samples generated for a standard normal distribution. And a distance limit value is introduced, so that the condition that the local sampling of a sampling space is too dense is avoided.
And S108, re-executing the step S104 and the step S105 according to the new sample matrix until the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, and calculating the multivariate self-adaptive regression model meeting the requirement by adopting an MCS method to obtain the slope failure probability.
In specific implementation, please refer to fig. 2, which shows a flowchart of the slope reliability analysis method based on the active learning multivariate adaptive regression spline in this embodiment, and the specific steps are as follows:
1. firstly, determining the size of a slope of a researched object, collecting related materials to obtain soil body characteristic parameters required by calculation, such as mean deviation, standard deviation, fluctuation range and the like;
2. in the FLAC3D software, corresponding models were built from the collected material and the centroid coordinates (x) of each finite element of the model were extracted i ,y i ) I is 1, 2 … m, m is the number of units. A strength reduction method program for the finite difference method was written and saved as stability. In the file, the parameter values (such as cohesive force and internal friction angle) of each unit need to be input;
3. obtaining a small amount of independent standard normal distribution sample matrix xi and a large amount of random sample pool X by using a Latin hypercube method;
4. dispersing by using a KL series expansion method according to the obtained information to obtain Nsim new Stability.dat files;
5. and calling the stability.dat of the number of the sample matrixes by using the fish language to calculate to obtain the corresponding FS.
6. Constructing a MARS model by using the obtained FS, and verifying the accuracy of the model;
7. if the model precision is poor, calling an active learning function, selecting an optimal point in a sample pool, substituting the optimal point into a sample matrix to obtain a new sample matrix, and constructing the MARS model again;
8. and when the precision meets the requirement, calculating the failure probability of the slope by adopting an MCS method.
In the embodiment, a rock slope and slope stability analysis model is adopted as shown in fig. 3, and the calculation of the slope safety factor is simplified in order to obtain an explicit expression of the safety factor. The specific content assumed is as follows: in the calculation, the trend of the sliding surface and the open cracks is supposed to be parallel to the slope surface, only one open crack is arranged, the open crack is vertical, water enters the sliding surface along the bottom of the open crack to leak, the water pressure in the length between the bottom of the open crack and the toe of the slope is changed to 0 (triangular distribution) according to the linearity, and the like. The block safety coefficient calculation method adopts a rigid body limit balance method. The deterministic variables in the slope take the following values: the volume weight of the rock and the water is respectively 26kN/m 3 、γ w ＝10kN/m 3 Slope angle psi f 50 degrees of crack inclinationψ p 35 °, anchor force and its angle T0, θ 0, and slope height H60 m. The statistical characteristics of the basic variables are shown in tables 1-2.
Wherein the safety factor of the slope can be represented by the following equation:
in the formula:
A＝(H-z)/sinψ p a represents the area of the bottom sliding surface (single width);
N'＝W(cosψ p -αsinψ p )-U-Vsinψ p + Tcos θ, N' represents the positive pressure acting on the bottom slip surface; ,
W＝0.5γH 2 ((1-(Z/H) 2 )cotψ p -cotψ f ) W represents the dead weight of the slide block;
U＝0.5γ w rzA U represents the resultant of the water pressure acting on the bottom slide surface;
V＝0.5γ w r 2 z 2 v represents the resultant of water pressure acting on the fracture surface;
TABLE 1 statistical characterization of the fundamental variables
This example is a slope problem with an explicit expression containing five random variables, assuming a correlation coefficient between the cohesion c and the internal friction angle phi of-0.5 and a correlation coefficient between the area z of the single broad fracture surface and the water depth coefficient r in the fracture of-0.5, to obtainThis begins the reliability analysis. Firstly, 1000000 groups of sample points are extracted by using the LHS to form a sample pool, and then 30 groups of sample points are extracted to obtain an independent standard normal sample matrix xi with the size of 60x 6. Selecting an optimal sample point X from a sample pool through an active learning function, and putting the X into an independent standard normal sample matrix xi to obtain a new sample matrix xi i Then, updating the sample pool, selecting the optimal sample point, and repeatedly operating to finally obtain an independent standard normal sample matrix xi with the size of 50x6 n And then, obtaining a random variable sample matrix χ through conversion, substituting the sample matrix χ into an equation (17), and calculating to obtain a safety factor FS, so as to obtain a functional function matrix G which is FS-1. The AMARS model is then constructed. In order to test the effectiveness of the model, a sample matrix U containing 100 independent standard normal sample points is randomly generated, a corresponding random variable sample matrix is obtained through transformation, and a response function value G of the random variable sample matrix is obtained 1 . Calling an AMARS model to predict according to the known sample matrix U to obtain a predicted function value G 2 . As can be seen from fig. 4, the function value predicted by the AMARS model and the real function value are substantially maintained on a 45 ° straight line, which illustrates the effectiveness of the established model.
After the appropriate AMARS model is established in the above manner, the MCS method is adopted to calculate the slope reliability, and the calculation result is compared with the direct MCS method, and is shown in Table 2. It can be seen from the table that the error of using the AMARS-MCS is only 1.3%, which shows the effectiveness of the present embodiment, and the number of sample points required by the method proposed in the present application is much less than that of the MCS method.
TABLE 2 correlation coefficient ρ c,φ ＝ρ z,r Calculated result of-0.5 hour reliability
In summary, in the slope reliability analysis method based on the active learning multivariate adaptive regression spline in the above embodiments of the present invention, the KL series expansion method is first adopted to discretize the soil parameters, the slope safety coefficient is calculated based on the finite difference intensity reduction method, the AMARS model is constructed by selecting the optimal point through the active learning function in combination with the training sample, and the monte carlo simulation method is adopted to perform the slope reliability analysis.
Example two
For a single layer in this embodiment
And analyzing the stability and reliability of the side slope.
Referring to fig. 5, a slope model in this embodiment is shown, where the height of the slope is 10m, the slope toe is 45 °, and the slope is a mean slope. The soil parameters of the probability stability analysis are shown in table 3, the embodiment only focuses on the spatial variability of the cohesive force and the internal friction angle of the soil, the cross-correlation coefficient is assumed to be-0.5, and other parameters are regarded as constants. According to known parameters, a model is preliminarily established by using FLAC3D, and the safety factor is calculated to be 1.228 by using intensity reduction, which is quite similar to 1.204 and 1.205 in the prior art, thereby indicating the correctness of the model.
TABLE 3 statistical characterization of soil parameters
As can be seen from fig. 5, the created model mesh partition case includes 1190 quadrilateral elements and 20 triangle elements. In order to compare with the calculation result of the prior art, the division condition of the grid is consistent with the division condition of the grid, random field dispersion is carried out on the grid under the assumption that the fluctuation range is 40m and 4m, and the data dispersed by the mass center of each random field unit can represent the soil shear strength of the unit, so that the spatial variability of the soil shear strength parameter is represented. Next, slope probability stability analysis will be performed using the above parameters and methods.
Referring to fig. 6, according to the statistical characteristics of the soil parameters, a K-L series expansion method is used to perform random field simulation, and the number of expansion terms is 14, so that 28 random variables are generated finally. The number of samples is a key factor influencing the accuracy of the proxy model, the sample size is large enough, the accuracy of the obtained calculation result is improved, and the calculation workload is increased. Therefore, it is necessary to prove that a higher accuracy result is obtained when the sample amount is sufficiently small. In this embodiment, an AMARS-MCS proxy model is constructed, and the accuracy of the model is evaluated by using the root mean square error, and the calculation formula is as follows:
in the formula (I), the compound is shown in the specification,
is a factor of safety, F, estimated by the proxy model i The safety coefficient is obtained by calculating an original slope model; n is a radical of t Is the number of samples tested.
Firstly, according to the statistical parameters of the random field and the centroid coordinates of the model, the parameters are dispersed to each centroid coordinate point, the spatial variability is simulated, and 60 groups of side slope models with the parameters are generated. And calculating the safety coefficient of the slope by using a finite difference intensity reduction method, repeatedly increasing the number of training samples according to an active learning function, and constructing an AMARS model by using the finally obtained training samples. Finally, Monte Carlo simulation is carried out on the basis of the established proxy model, and the number of samples is 1 multiplied by 10 6 Therefore, the calculation result of the slope reliability can be calculated and obtained, and is shown in table 4. The AMRAS-MCS method mentioned in this embodiment is calculated by the following method and 1 × 10 4 The secondary LHS calculation results are all kept highly consistent, and the accuracy of the method provided by the embodiment in the aspect of slope reliability calculation is shown. Moreover, the method proposed in this embodiment only needs to call the original slope stability model 60 times, and particularly proposes that the number of monte carlo calculations is set to 1 × 10 6 If higher accuracy is sought, for example, the Monte Carlo samples are set to 1 × 10 8 In the above, the memory occupation of the model will occupy more than 16GB of hardware memory capacity, and the time will exceed 1 × 10 5 Second, it shows that the method provided by the embodiment can effectively reduce the time cost in calculationThe method is as follows.
As shown in FIG. 7, p is measured after the number of samples reaches 60 f Has already stabilized and at the time of the sample number 60, the corresponding root mean square error is 0.0249, indicating that the constructed AMARS proxy model has been quite accurate.
TABLE 4 reliability calculation results corresponding to different methods
In summary, the slope reliability analysis method based on the active learning multivariate adaptive regression spline in the above embodiments of the present invention combines the advantages of the active learning function and the MARS. The AMARS model is used for a side slope with spatial variability, and the relation between the side slope shear strength parameter and the safety factor FS can be effectively established. For complex spatial variability slopes, the method can obtain a reliable calculation result with sufficient accuracy under the condition of low calculation cost. The spatial variation slope reliability analysis method based on AMARS-MCS provided by the invention provides an effective and practical approach for solving the problem of spatial variation slope reliability with small failure probability.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present application, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the concept of the present application, which falls within the scope of protection of the present application. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. A slope reliability analysis method based on an active learning multivariate self-adaptive regression spline is characterized by comprising the following steps:
the method comprises the following steps: acquiring slope parameters of a target object, wherein the slope parameters at least comprise slope size and soil characteristic parameters;
step two: constructing a corresponding slope analysis model by using preset simulation calculation software, the slope size and the soil characteristic parameters, and preprocessing the slope analysis model to obtain a stability file;
step three: determining a random field statistical index, and obtaining a plurality of independent standard normal distribution samples and independent standard normal distribution sample pools by using an LHS method and the random field statistical index;
performing dispersion by using a KL series expansion method according to each independent standard normal distribution sample, each independent standard normal distribution sample pool and the stability file to obtain a plurality of sample matrixes;
step four: calculating each sample matrix by using the simulation calculation software to obtain a corresponding slope safety coefficient;
step five: constructing a multivariate self-adaptive regression model by using the slope safety coefficient, and verifying the accuracy of the multivariate self-adaptive regression model;
step six: and if the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, calculating the multivariate self-adaptive regression model by adopting an MCS method to obtain the slope failure probability.
2. The slope reliability analysis method based on active learning multivariate adaptive regression spline according to claim 1, further comprising:
step seven: if the accuracy of the multivariate self-adaptive regression model does not meet the preset accuracy requirement, calling a preset active learning function, selecting the optimal sample in each independent standard normal distribution sample pool, and constructing a new sample matrix according to the optimal sample and the sample matrix;
step eight: and re-executing the fourth step and the fifth step according to the new sample matrix until the accuracy of the multivariate self-adaptive regression model meets the preset accuracy requirement, and calculating the multivariate self-adaptive regression model meeting the requirement by adopting an MCS method to obtain the slope failure probability.
3. The slope reliability analysis method based on active learning multivariate adaptive regression spline according to claim 1 or 2, characterized in that the simulation calculation software adopts FLAC3D software, and the second step comprises:
constructing a corresponding slope analysis model by using the FLAC3D software, the slope size and the soil characteristic parameters, and extracting the centroid coordinates (x) of each finite element unit in the slope analysis model i ,y i ) Wherein, i is 1, 2 … m, and m is the number of units;
and calculating according to the centroid coordinates and the intensity reduction in the finite difference method to obtain the stability file.
4. The slope reliability analysis method based on active learning multivariate adaptive regression spline according to claim 3, wherein the third step comprises:
determining random field statistical indexes including a mean value, a variation coefficient, a distribution type and a correlation coefficient;
determining a correlation function and a correlation distance according to the mean value, the variation coefficient, the distribution type and the correlation coefficient;
performing geotechnical test on the position of the target object, and determining soil shear strength parameters of the target object, wherein the soil shear strength parameters comprise cohesive force c and an internal friction angle phi of the target object;
taking the correlation function as the spatial autocorrelation of the soil shear strength parameter:
in the formula, delta h And delta v Respectively, a horizontal correlation distance and a vertical correlation distance; l is a radical of an alcohol m And L n Respectively, the difference between the coordinates of the two centroids.
5. The slope reliability analysis method based on active learning multivariate adaptive regression spline of claim 4, wherein the expression of the shear strength parameter-dependent log random field is:
in the formula, n is the number of truncation terms; lambda [ alpha ] j The characteristic value corresponding to the autocorrelation function; f. of j (x, y) is a characteristic function corresponding to the autocorrelation function; mu.s lni And σ lni The mean and standard deviation of the corresponding normal distribution parameter lni, respectively; chi shape i,j The random variable is a related standard normal random variable and is obtained by converting an independent standard normal random sample matrix.
6. The slope reliability analysis method based on active learning multivariate adaptive regression spline of claim 5, wherein the μ lni And σ lni The calculation formulas of (A) and (B) are respectively as follows:
in the formula, ln i The method is a cross-correlation random variable which obeys log-normal distribution and is used for describing the distribution of a slope soil characteristic parameter random field.
7. The slope reliability analysis method based on active learning multivariate adaptive regression spline of claim 5, wherein the expression for the K-th row of the random sample matrix is:
in the formula, xi is a matrix of independent standard normal distribution samples, and is obtained by adopting an LHS method; rho c,φ Is the cross-correlation coefficient between the cohesion c of the target object and the internal friction angle phi of the target object.
8. The slope reliability analysis method based on active learning multivariate adaptive regression spline according to claim 1, wherein the fourth step comprises:
and calculating the stability files in the sample matrixes by using FLAC3D software and a fish language to obtain the corresponding slope safety factors.
9. The slope reliability analysis method based on active learning multivariate adaptive regression spline of claim 2, wherein the expression of the active learning function is:
in the formula, argmin () is an optimal parameter with the minimum function value in the return solving process;
proxy the model for the function; u. of T Is a sample point, i.e. a variable parameter; u. of c Selecting the sample point of the optimal sample from an independent standard normal distribution sample pool; d (u) T S) represents the sample concentration point and u in the independent standard normal space T A minimum distance therebetween; d (S) is a minimum distance limit.
10. The slope reliability analysis method based on active learning multivariate adaptive regression spline of claim 9, wherein the expression of the minimum distance limit is:
wherein λ is a constant coefficient term, between 0.1 and 0.5;
wherein, X i Is the ith random variable, U i Is the ith normal random variable, u i And x i Is the value of a random variable, F xi (. and F) Ui (. is a probability cumulative distribution function;
m-dimensional samples generated for a standard normal distribution.
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| CN117113516A (en) * | 2023-10-23 | 2023-11-24 | 西南交通大学 | Limit bearing capacity prediction method and related device for strip foundation of adjacent side slope |
| CN117423000A (en) * | 2023-12-14 | 2024-01-19 | 江苏狄诺尼信息技术有限责任公司 | MARS-based intelligent road longitudinal section linear reconstruction method |
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| CN117113516A (en) * | 2023-10-23 | 2023-11-24 | 西南交通大学 | Limit bearing capacity prediction method and related device for strip foundation of adjacent side slope |
| CN117113516B (en) * | 2023-10-23 | 2024-01-26 | 西南交通大学 | Limit bearing capacity prediction method and related device for strip foundation of adjacent side slope |
| CN117423000A (en) * | 2023-12-14 | 2024-01-19 | 江苏狄诺尼信息技术有限责任公司 | MARS-based intelligent road longitudinal section linear reconstruction method |
| CN117423000B (en) * | 2023-12-14 | 2024-03-19 | 江苏狄诺尼信息技术有限责任公司 | MARS-based intelligent road longitudinal section linear reconstruction method |
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