CN116611002A - Slope safety coefficient prediction method based on whale algorithm optimization support vector machine - Google Patents
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Abstract
The invention relates to a whale algorithm-based slope safety coefficient prediction method based on an optimization support vector machine, and belongs to the technical field of slope engineering. According to the invention, slope parameter data information such as the volume weight, cohesive force, friction angle, slope height, pore water pressure, slope safety coefficient and the like of a slope are collected to form a slope sample original data set, and the slope sample data set is obtained through normalization processing and is divided into a training set and a test sample set; establishing a support vector machine model, and determining a kernel function width factor and a penalty coefficient of the support vector machine through a whale optimization algorithm to obtain the support vector machine model after whale algorithm optimization; and predicting the safety coefficient of the side slope in the test sample set by using the model, comparing and analyzing the predicted safety coefficient with the actual safety coefficient, and evaluating the prediction accuracy of the model. The prediction method can rapidly and effectively predict the safety coefficient of the side slope, has high prediction precision, and can provide important basis for slope design and safety coefficient prediction in actual engineering.
Description
Technical Field
The invention relates to a whale algorithm-based slope safety coefficient prediction method based on an optimization support vector machine, and belongs to the technical field of slope engineering.
Background
Once the slope is deformed and unstably damaged, the disaster is destroyed, and the life and property safety of personnel in the surrounding area is greatly endangered, and the economic loss is very serious. Therefore, it is important to predict the safety coefficient of the side slope. The safety coefficient of the side slope is the ratio of the anti-sliding force to the downward sliding force of the side slope, the stability state of the side slope can be judged according to the ratio, and when the safety coefficient is greater than 1, the side slope can be judged to be in the stable state; when the safety coefficient is smaller than 1, the risk of landslide on the side slope can be judged.
At present, the stable state of the side slope is widely analyzed at home and abroad by gradient, slope height, gravity, initial saturation, pore water pressure ratio, water permeability coefficient, internal friction angle, cohesion, water content, side slope safety coefficient and the like. The common slope safety coefficient evaluation methods include engineering geology analogy method, limit balance analysis method and numerical analysis method. The engineering geology analogy method is a method for evaluating engineering geology according to the comparison of the obtained slope exploration data and the slope data of the current research; the limit balance analysis method does not consider the influence of the deformation of the rock-soil body on the stability of the side slope, presumes the sliding of the side slope, establishes a force balance equation and solves the safety coefficient. The numerical simulation method is realized by a computer platform, and can be simulated according to the actual condition of the side slope. However, when the method is used for judging the stability of the slope, certain theoretical knowledge of the slope instability is required, and the factors influencing the stability of the slope are more, so that the essential relation between the influencing factors and the safety coefficient of the slope cannot be revealed.
Disclosure of Invention
Aiming at the problem that the essential relation between the influence factors and the slope safety coefficients cannot be revealed in the existing slope safety coefficient analysis method, the invention provides a slope safety coefficient prediction method based on a whale algorithm optimization support vector machine, namely, a support vector machine model is established, the kernel function width factors and penalty coefficients of the support vector machine are determined through the whale optimization algorithm, the model is trained by adopting actual slope parameter data, and then the model precision is evaluated; the model can rapidly and effectively predict the safety coefficient of the side slope, has high prediction precision, and can provide important basis for slope design and safety coefficient prediction in actual engineering.
A slope safety coefficient prediction method based on whale algorithm optimization support vector machine comprises the following specific steps:
s1, collecting slope parameter data information to form a slope sample original data set, wherein the slope parameter data information comprises volume weight, cohesion, friction angle, slope height, pore water pressure and slope safety coefficient of a slope;
s2, carrying out normalization processing on the slope parameter data information of the slope sample original data set, mapping the slope parameter data information into a range of [0,1] to obtain a slope sample data set, and randomly dividing the normalized slope parameter data information in the slope sample data set into a training set and a test sample set;
s3, establishing a support vector machine model, setting parameters of a whale optimization algorithm, and determining a kernel function width factor and a penalty coefficient of the support vector machine through the whale optimization algorithm to obtain the support vector machine model after whale algorithm optimization;
s4, taking the data of the volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the training set as the input of a whale algorithm optimized support vector machine prediction algorithm, taking the corresponding slope safety coefficient in the training set as the output of the whale algorithm optimized support vector machine algorithm, and training the whale algorithm optimized support vector machine model to obtain a whale algorithm optimized support vector machine prediction model;
s5, carrying data of volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the test sample set into a support vector machine prediction model optimized by a whale algorithm for calculation, and obtaining a corresponding slope safety prediction coefficient;
s6, comparing and analyzing the slope safety prediction coefficient with the actual slope safety coefficient in the test sample set, and calculating the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE) and the correlation coefficient (R) of model prediction 2 ) Setting an error threshold of a prediction model, and verifying the accuracy of the model; if the root mean square error of the model is larger than the error threshold of the prediction model, collecting more slope original data sets, and training the model until the root mean square error of the model is not larger than the set error threshold;
s7, predicting the slope safety coefficient of the slope to be predicted by adopting a whale algorithm-optimized support vector machine prediction model after evaluating the accuracy of the model.
In the step S2, the slope parameter data information of the slope sample original data set is normalized by adopting a dispersion standardization method, and the calculation formula is as follows:
wherein x is i For a value normalized by certain data, x is a data value before data normalization, x min Is the minimum value in the sample data, x max Is the maximum value in the sample data.
The specific method for establishing the support vector machine model in the step S3 is as follows
(1) Establishing a slope safety coefficient regression prediction objective function:
y i ＝f(x i )
wherein the sample set d= { (x) 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 ),…(x n ,y n ) -where m is sample size, y i Is the value of the safety coefficient, x i An input vector for affecting the slope safety 4 coefficients;
(2) Slope safety coefficient input directionSample data between the quantity and the safety coefficient value is in nonlinear relation, and the support vector machine is mapped through nonlinearityInput data x i Mapping to a high-dimensional space and constructing a linear regression function in the high-dimensional space, i.e
Wherein ω is a weight vector,representing some non-linear mapping, b being the bias;
converting the regression problem of the support vector machine into:
wherein C is a penalty factor, ε i ，Is a relaxation variable;
introduction of Lagrangian multiplier mu i ≥0,α i ≥0,/>Converting the above problem into dual problem and solving
In the method, in the process of the invention,is a kernel function;
(3) The radial basis function RBF is used as a kernel function of a support vector machine, and the structure is as follows:
where σ is a parameter of the kernel function, and |x-y|| represents the distance from x to y.
The specific steps of the whale optimization algorithm in the step S3 are as follows:
the whale optimizing algorithm is one kind of optimizing algorithm set forth by observing hunting behavior of whale in the head, and the whale predation includes three steps of surrounding hunting, foaming net attack and searching predation,
s31, surrounding a prey: setting parameters of a whale algorithm, wherein the parameters comprise initial whale scale, iteration times, variable dimension and variable upper and lower limits, whale finds out the position of a prey, randomly selecting one whale individual as a navigation target to perform predation, gradually gathering the rest whales towards the whale individual, leading the best predation position in space to have uncertainty, supposing that the optimal spatial position is close to the prey, updating the position of the whale, and updating the formula to be
D＝|CX * (t)-X(t)|
X(t+1)＝X * (t)-AD
Wherein t is the current iteration number, A and C are coefficient vectors, X * (t) is the best solution of the position of whales in the space so far, X (t) is the current position vector of whales, and D is the distance between whales and the prey;
if a more optimal whale spatial position solution appears in each iteration, updating X * (t) the calculation formula is:
A＝2a·r-a
C＝2r
wherein r is a random vector between [0, 1]; a is a convergence factor, and as the number of iterations increases, the value linearly decreases from 2 to 0, and the calculation formula is:
wherein T is max Representing the maximum number of iterations;
s32, foam net attack: whale found prey, selecting spiral or shrink wrap spit bubbles to predate;
if predation is performed in a manner of contracting and surrounding the spitting air bubble, the rest whales approach to the optimal whale position in the current space position, and the mathematical model is as follows:
X(t+1)＝X * (t)-AD
wherein, the value range of the coefficient vector A is [ -1,1];
if predated in a spiral fashion, the mathematical model can be expressed as:
X(t+1)＝X * De bq csc(2πl)+X * (t)
wherein p is a random number between [0,1], b is a constant coefficient, and q is a random number between [ -1,1];
assuming that the probability of capturing a prey by spiral or shrink wrapping is 0.5, the mathematical model of the whale optimization algorithm is:
s33, searching predation: the search enclosure is that the value range of the coefficient vector A is [ -1,1]; if the value range of the coefficient vector A is not within [ -1,1], the rest whales are randomly selected to be close to one whale individual, and the mathematical model is as follows:
D＝|CX rand -X(t)|
X(t+1)＝X rand -AD
wherein X is rand Representing the random position of whales, the vector coefficient |A|>1。
Preferably, in step S3, the libsvm toolkit in matlab is used to train the support vector machine model, and the penalty coefficient C of the support vector machine and the g value of the kernel function are determined by adopting a cross-validation and grid search method.
S6, a root mean square error RMSE calculation formula is as follows:
the mean absolute error MAE calculation formula is:
correlation coefficient R 2 The calculation formula is as follows:
wherein n is the data length, Y i Is the predicted value of the slope stability state at the ith moment, y i Is the true value of the slope stability state at the ith moment,is the average of the actual samples.
The beneficial effects of the invention are as follows:
(1) The method comprises the steps of establishing a support vector machine model, determining a kernel function width factor and a penalty coefficient of the support vector machine through a whale optimization algorithm, training the model by adopting actual side slope parameter data, and then evaluating the model accuracy; the model can rapidly and effectively predict the safety coefficient of the side slope, has high prediction precision, and can provide important basis for slope design and safety coefficient prediction in actual engineering.
(2) The invention provides a rapid and efficient method for predicting slope stability, which is characterized in that the calculation process required by the current method for judging whether the slope is stable consumes more time, the modeling process of a digital simulation method is more complicated, and a great amount of engineering data is required to be collected by an engineering geological analogy method; the method has the advantages that the model is trained, the time consumed in the model training process is saved, and therefore, the prediction result can be rapidly output only by inputting parameters of the factors of the slope, such as the gravity, the cohesive force, the internal friction angle, the slope height and the pore water pressure into the model, the working efficiency of predicting the stability of the slope can be improved, the time cost is saved, and a new research method and thinking are provided for slope stability prediction.
Drawings
FIG. 1 is a flow chart of a method for predicting slope stability based on a whale algorithm optimized support vector machine;
FIG. 2 is a flowchart of a whale optimization algorithm;
FIG. 3 is a graph of the prediction result of the slope safety coefficient of the training set of the support vector machine model after optimization of the whale algorithm in example 1;
fig. 4 is a graph of the prediction result of the slope safety coefficient of the support vector machine model test set after optimization of the whale algorithm in example 1.
Detailed Description
The invention will be described in further detail with reference to specific embodiments, but the scope of the invention is not limited to the description.
Algorithms currently related to slope stability studies fall into two general categories: dividing the side slope according to a new stable state, and classifying and predicting the new side slope stability by using an algorithm; and secondly, predicting the safety coefficient of the side slope by using an algorithm. Therefore, the invention aims to establish a slope safety coefficient prediction method based on a whale algorithm optimization Support Vector Machine (SVM) through a machine learning method and through learning of collected historical data.
Example 1: a slope safety coefficient prediction method based on whale algorithm optimization support vector machine comprises the following specific steps:
s1, collecting slope parameter data information to form a slope sample original data set, wherein the slope parameter data information comprises volume weight, cohesion, friction angle, slope height, pore water pressure and slope safety coefficient of a slope; in this example 60 sets of side slope data were collected as shown in table 1;
table 1 side slope parameter data information
S2, carrying out normalization processing on slope parameter data information of an original slope sample data set by adopting a dispersion normalization method (MinMax), mapping the slope parameter data information into a range of [0,1] to obtain a slope sample data set (part of data is shown in Table 2), and randomly dividing the normalized slope parameter data information in the slope sample data set into a training set and a test sample set, wherein the training set accounts for 75% and the test sample set accounts for 25%; the calculation formula of the normalization process is as follows:
wherein x is i For a value normalized by certain data, x is a data value before data normalization, x min Is the minimum value in the sample data, x max Is the maximum value in the sample data;
table 2 normalized partial data
S3, establishing a support vector machine model, setting parameters of a whale optimization algorithm, and determining a kernel function width factor and a penalty coefficient of the support vector machine through the whale optimization algorithm to obtain the support vector machine model after whale algorithm optimization;
the specific method for establishing the support vector machine model comprises the following steps of
(1) Establishing a slope safety coefficient regression prediction objective function:
y i ＝f(x i ) (1)
wherein the sample set d= { (x) 1 ,y 1 ),(x 2 ,y 2 ),(x 3 ,y 3 ),…(x n ,y n ) -where m is sample size, y i Is the value of the safety coefficient, x i An input vector for affecting the slope safety 4 coefficients;
(2) Sample data between the slope safety coefficient input vector and the safety coefficient value is in a nonlinear relation, and a support vector machine is mapped through nonlinearityInput data x i Mapping to a high-dimensional space and constructing a linear regression function in the high-dimensional space, i.e
Wherein ω is a weight vector,representing some non-linear mapping, b being the bias;
converting the regression problem of the support vector machine into:
wherein C is a penalty factor, ε i ，Is a relaxation variable;
introduction of Lagrangian multiplier mu i ≥0,α i ≥0,/>Converting the above problem into dual problem and solving
In the method, in the process of the invention,is a kernel function; the kernel functions include Sigmoid kernel function, radial basis kernel function (RBF)Polynomial kernel function (poly), etc., preferably Radial Basis Function (RBF)
(3) The Radial Basis Function (RBF) is taken as a kernel function of the support vector machine, and the structure is as follows:
where σ is a parameter of the kernel function, and |x-y|| represents the distance from x to y.
Training a support vector machine model by using a libsvm tool package in matlab, and determining a penalty coefficient C and a g value of a kernel function of the support vector machine by adopting a cross validation and grid search method;
in the embodiment, the initial whale scale of the whale algorithm is set to be 30, the maximum iteration number is 100, the variable dimension is 2, the upper and lower limits of the penalty factor coefficient c are [0.01,1], and the upper and lower limits of the kernel function parameter g are [10,100];
as shown in fig. 2, the specific steps of the whale optimization algorithm are as follows:
the whale prey comprises three steps of surrounding prey, foaming net attack and searching prey,
s31, surrounding a prey: setting parameters of a whale algorithm, wherein the parameters comprise initial whale scale, iteration times, variable dimension and variable upper and lower limits, whale finds out the position of a prey, randomly selecting one whale individual as a navigation target to perform predation, gradually gathering the rest whales towards the whale individual, leading the best predation position in space to have uncertainty, supposing that the optimal spatial position is close to the prey, updating the position of the whale, and updating the formula to be
D＝|CX * (t)-X(t)| (5)
X(t+1)＝X * (t)-AD (6)
Wherein t is the current iteration number, A and C are coefficient vectors, X * (t) is the best solution of the position of whales in the space so far, X (t) is the current position vector of whales, and D is the distance between whales and the prey;
if a more optimal whale spatial position solution appears in each iteration, updatingX * (t) the calculation formula is:
A＝2a·r-a (7)
C＝2r (8)
wherein r is a random vector between [0, 1]; a is a convergence factor, and as the number of iterations increases, the value linearly decreases from 2 to 0, and the calculation formula is:
wherein T is max Representing the maximum number of iterations;
s32, foam net attack: whale found prey, selecting spiral or shrink wrap spit bubbles to predate;
if predation is performed in a manner of contracting and surrounding the spitting air bubble, the rest whales approach to the optimal whale position in the current space position, and the mathematical model is as follows:
X(t+1)＝X * (t)-AD (10)
wherein, the value range of the coefficient vector A is [ -1,1];
if predated in a spiral fashion, the mathematical model can be expressed as:
X(t+1)＝X * De bq csc(2πl)+X * (t) (11)
wherein p is a random number between [0,1], b is a constant coefficient, and q is a random number between [ -1,1];
assuming that the probability of capturing a prey by spiral or shrink wrapping is 0.5, the mathematical model of the whale optimization algorithm is:
s33, searching predation: the search enclosure is that the value range of the coefficient vector A is [ -1,1]; if the value range of the coefficient vector A is not within [ -1,1], the rest whales are randomly selected to be close to one whale individual, and the mathematical model is as follows:
D＝|CX rand -X(t)| (13)
X(t+1)＝X rand -AD (14)
wherein X is rand Representing the random position of whales, the vector coefficient |A|>1；
Determining a punishment coefficient C of the support vector machine and a g value of a kernel function by adopting a whale optimization algorithm to obtain an optimal value of the punishment coefficient C of the support vector machine as 3.9316, and an optimal value of the g value of the kernel function as 1.5033; after the parameters are determined, the prediction result of the training set is shown in fig. 3;
s4, taking the data of the volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the training set as the input of a whale algorithm optimized support vector machine prediction algorithm, taking the corresponding slope safety coefficient in the training set as the output of the whale algorithm optimized support vector machine algorithm, and training the whale algorithm optimized support vector machine model to obtain a whale algorithm optimized support vector machine prediction model;
s5, carrying data of volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the test sample set into a support vector machine prediction model optimized by a whale algorithm for calculation to obtain a corresponding slope safety prediction coefficient (see figure 4);
s6, comparing and analyzing the slope safety prediction coefficient with the actual slope safety coefficient in the test sample set, and calculating the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE) and the correlation coefficient (R) of model prediction 2 ) Setting an error threshold of a prediction model, and verifying the accuracy of the model; if the root mean square error of the model is larger than the error threshold of the prediction model, collecting more slope original data sets, and training the model until the root mean square error of the model is not larger than the set error threshold;
the root mean square error RMSE calculation formula is as follows:
the mean absolute error MAE calculation formula is:
correlation coefficient R 2 The calculation formula is as follows:
wherein n is the data length, Y i Is the predicted value of the slope stability state at the ith moment, y i Is the true value of the slope stability state at the ith moment,is the average value of the actual samples;
the smaller the RMSE and MAE values of the model, the R 2 The larger the value is, the better the prediction effect of the model is proved, in the embodiment, the error threshold rmse=0.3 and mae=0.3 of the model are set, the calculated RMSE is 0.0963, the error value of the mae pair is 0.0572, and the model is smaller than the set error threshold, so that the model is applicable, and the prediction of the slope safety coefficient can be performed based on the model;
in addition, for the same samples and test results, predictions were made using Random Forest (RF), basis function neural network (RBF) and Support Vector Machine (SVM) only for comparison with the B support vector machine algorithm (SVM) prediction results optimized using whale optimization algorithm, as shown in table 3;
TABLE 3 statistics of predicted results
| Model | RMSE | MAE | R 2 |
| RF | 0.123 | 0.828 | 0.709 |
| BP | 0.282 | 0.206 | 0.533 |
| SVM | 0.115 | 0.066 | 0.901 |
| WOA-SVM | 0.0963 | 0.0572 | 0.938 |
As can be seen from table 3, the root mean square error of the support vector machine is 0.0963, the average absolute error value is 0.0572, the correlation coefficient is 0.938, which is the smallest of the four models, and the reliability of the model is verified, and the model can be used for predicting the slope safety coefficient;
s7, predicting the slope safety coefficient of the slope to be predicted by adopting a whale algorithm-optimized support vector machine prediction model after evaluating the accuracy of the model;
establishing a support vector machine model, determining a kernel function width factor and a penalty coefficient of the support vector machine through a whale optimization algorithm, training the model by adopting actual side slope parameter data, and then evaluating the model accuracy; the model can rapidly and effectively predict the safety coefficient of the side slope, has high prediction precision, and can provide important basis for slope design and safety coefficient prediction in actual engineering.
Example 2: in the embodiment, a whale algorithm optimized support vector machine prediction model after model accuracy evaluation in embodiment 1 is used for predicting the side slope safety coefficient of reservoir side slopes in Kong in Gansu province [ Yao Yi, wang Xiaomin ], a side slope stability analysis model based on PCA-ERBF-SVM [ J ]]Disaster science, 2022,37 (3): 43-50.]The predicted sample data are shown in table 4; the slope angle of the side slope of the embodiment is about 30-50 degrees, the relative height difference of the side slopes at two sides of the reservoir is 400-500 m, the annual average rainfall of the reservoir is about 680mm, and the water accumulation area of the reservoir is controlled to be about 602km 2 ；
Table 4 predictive sample data
Carrying out normalization processing on the predicted sample data, and predicting by adopting a whale algorithm optimized support vector machine predicted model after the accuracy of the model is trained and evaluated in the embodiment 1; and the prediction samples are respectively predicted by using RF, BP and SVM, and compared and analyzed with the prediction results of the WOA-SVM model, and the prediction values and relative errors of the 4 prediction models are compared as shown in Table 5.
TABLE 5 prediction model predictors and relative error comparisons
Based on the prediction results, calculating average absolute error (MAE) and Root Mean Square Error (RMSE) of the 4 models, respectively, the calculation results being shown in table 6;
table 6 predictive model predictive evaluation index
| Model | RMSE | MAE | Model | RMSE | MAE |
| RF | 0.101 | 0.073 | SVM | 0.090 | 0.081 |
| BP | 0.189 | 0.149 | WOA-SVM | 0.063 | 0.062 |
As can be seen from table 6, the RMSE and MAE predictors for the WOA-SVM model are minimal compared to the RF, BP and SVM models, indicating that the WOA-SVM model can predict the side slope stability factor more accurately.
While the specific embodiments of the present invention have been described in detail, the present invention is not limited to the above embodiments, and various changes may be made without departing from the spirit of the present invention within the knowledge of those skilled in the art.
Claims (5)
1. A whale algorithm-based slope safety coefficient prediction method for optimizing a support vector machine is characterized by comprising the following specific steps:
s1, collecting slope parameter data information to form a slope sample original data set, wherein the slope parameter data information comprises volume weight, cohesion, friction angle, slope height, pore water pressure and slope safety coefficient of a slope;
s2, carrying out normalization processing on the slope parameter data information of the slope sample original data set, mapping the slope parameter data information into a range of [0,1] to obtain a slope sample data set, and randomly dividing the normalized slope parameter data information in the slope sample data set into a training set and a test sample set;
s3, establishing a support vector machine model, setting parameters of a whale optimization algorithm, and determining a kernel function width factor and a penalty coefficient of the support vector machine through the whale optimization algorithm to obtain the support vector machine model after whale algorithm optimization;
s4, taking the data of the volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the training set as the input of a whale algorithm optimized support vector machine prediction algorithm, taking the corresponding slope safety coefficient in the training set as the output of the whale algorithm optimized support vector machine algorithm, and training the whale algorithm optimized support vector machine model to obtain a whale algorithm optimized support vector machine prediction model;
s5, carrying data of volume weight, cohesion, friction angle, slope height and pore water pressure of the slope in the test sample set into a support vector machine prediction model optimized by a whale algorithm for calculation, and obtaining a corresponding slope safety prediction coefficient;
s6, comparing and analyzing the slope safety prediction coefficient with the actual slope safety coefficient in the test sample set, and calculating the Root Mean Square Error (RMSE), the Mean Absolute Error (MAE) and the correlation coefficient R of model prediction 2 Setting an error threshold of a prediction model, and evaluating the accuracy of the model; if the root mean square error of the model is larger than the error threshold of the prediction model, collecting more slope original data sets, and training the model until the root mean square error of the model is not larger than the set error threshold;
s7, predicting the slope safety coefficient of the slope to be predicted by adopting a whale algorithm-optimized support vector machine prediction model after evaluating the accuracy of the model.
2. The method for predicting the slope safety coefficient based on whale algorithm optimization support vector machine according to claim 1, wherein the method is characterized by comprising the following steps of: in the step S2, slope parameter data information of the slope sample original data set is normalized by adopting a dispersion standardization method, and a calculation formula is as follows:
wherein x is i For a value normalized by certain data, x is a data value before data normalization, x min Is the minimum value in the sample data, x max Is the maximum value in the sample data.
3. The method for predicting the slope safety coefficient based on whale algorithm optimization support vector machine according to claim 1, wherein the method is characterized by comprising the following steps of: s3, establishing a support vector machine model by the following specific method
(1) Establishing a slope safety coefficient regression prediction objective function:
y i ＝f(x i )
wherein the sample set d= { (x) 1 ，y 1 )，(x 2 ，y 2 )，(x 3 ，y 3 )，...(x n ，y n ) -where m is sample size, y i Is the value of the safety coefficient, x i An input vector for affecting the slope safety 4 coefficients;
(2) Sample data between the slope safety coefficient input vector and the safety coefficient value is in a nonlinear relation, and a support vector machine is mapped through nonlinearityInput data x i Mapping to a high-dimensional space and constructing a linear regression function in the high-dimensional space, i.e
Wherein ω is a weight vector,representing some non-linear mapping, b being the bias;
converting the regression problem of the support vector machine into:
wherein C is a penalty factor, ε i ，Is a relaxation variable;
introduction of Lagrangian multiplier mu i ≥0，α i ≥0，/>Converting the above problem into dual problem and solving
In the method, in the process of the invention,is a kernel function;
(3) The radial basis function RBF is used as a kernel function of a support vector machine, and the structure is as follows:
where σ is a parameter of the kernel function, the expression x-y represents the distance from x to y.
4. The slope safety coefficient prediction method based on whale algorithm optimization support vector machine according to claim 3, wherein the method is characterized by comprising the following steps: the specific steps of the whale optimization algorithm in the step S3 are as follows:
the whale prey comprises three steps of surrounding prey, foaming net attack and searching prey,
s31, surrounding a prey: setting parameters of a whale algorithm, wherein the parameters comprise initial whale scale, iteration times, variable dimension and variable upper and lower limits, whale finds out the position of a prey, randomly selecting one whale individual as a navigation target to perform predation, gradually gathering the rest whales towards the whale individual, leading the best predation position in space to have uncertainty, supposing that the optimal spatial position is close to the prey, updating the position of the whale, and updating the formula to be
D＝|CX * (t)-X(t)|
X(t+1)＝X * (t)-AD
Wherein t is the current iteration number, A and C are coefficient vectors, X * (t) is the best solution of the position of whales in the space so far, X (t) is the current position vector of whales, and D is the distance between whales and the prey;
if a more optimal whale spatial position solution appears in each iteration, updating X * (t) the calculation formula is:
A＝2a·r-a
C＝2r
wherein r is a random vector between [0, 1]; a is a convergence factor, and as the number of iterations increases, the value linearly decreases from 2 to 0, and the calculation formula is:
wherein T is max Representing the maximum number of iterations;
s32, foam net attack: whale found prey, selecting spiral or shrink wrap spit bubbles to predate;
if predation is performed in a manner of contracting and surrounding the spitting air bubble, the rest whales approach to the optimal whale position in the current space position, and the mathematical model is as follows:
X(t+1)＝X * (t)-AD
wherein, the value range of the coefficient vector A is [ -1,1];
if predated in a spiral fashion, the mathematical model can be expressed as:
X(t+1)＝X * De bq csc(2πl)+X * (t)
wherein p is a random number between [0,1], b is a constant coefficient, and q is a random number between [ -1,1];
assuming that the probability of capturing a prey by spiral or shrink wrapping is 0.5, the mathematical model of the whale optimization algorithm is:
s33, searching predation: the search enclosure is that the value range of the coefficient vector A is [ -1,1]; if the value range of the coefficient vector A is not within [ -1,1], the rest whales are randomly selected to be close to one whale individual, and the mathematical model is as follows:
D＝|CX rand -X(t)|
X(t+1)＝X rand -AD
wherein X is rand Representing the random position of whales, the vector coefficient |A| > 1.
5. The method for predicting the slope safety coefficient based on whale algorithm optimization support vector machine according to claim 1, wherein the method is characterized by comprising the following steps of: s4, a root mean square error RMSE calculation formula is as follows:
the mean absolute error MAE calculation formula is:
correlation coefficient R 2 The calculation formula is as follows:
wherein n is the data length, Y i Is the predicted value of the slope stability state at the ith moment, y i Is the true value of the slope stability state at the ith moment,is the average of the actual samples.
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| CN116955966A (en) * | 2023-09-20 | 2023-10-27 | 山东科技大学 | Method for judging water-rich grade of mine roof |
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| CN116955966A (en) * | 2023-09-20 | 2023-10-27 | 山东科技大学 | Method for judging water-rich grade of mine roof |
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| CN117574255A (en) * | 2023-12-15 | 2024-02-20 | 昆明理工大学 | Slope safety coefficient prediction method based on pelican algorithm and support vector machine |
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