Slope stability evaluation method based on BEO-XGBoost algorithm

Abstract

The application discloses a kind of based on BEO-XGBoost algorithm's side slope stability evaluation method, and the invention includes the following steps: S1, the factor that influences side slope stability is analyzed, determines the parameter for being used for analyzing side slope stability, constructs side slope dataset;S2, the data distribution situation is analyzed, and data set is handled;S3, establishes XGBoost model, and data set is divided into training set and test set;S4, constructs BEO model and optimizes XGBoost;S5, BEO-XGBoost model is trained and tested.The BEO algorithm used in the application is a powerful heuristic algorithm developed based on the biological behavior of black eagles, which simulates the hunting, migration and breeding behavior of black eagles.Through simulating these behaviors of black eagles, BEO can gradually find the optimal solution from a complex search space, which makes BEO suitable for optimizing complex nonlinear problems such as machine learning models.XGBoost is an ensemble algorithm based on decision trees, which uses gradient descent to optimize the residual error of each tree, thereby continuously improving the accuracy of the model.Using the BEO-XGBoost model to predict the stability of the slope provides a new and highly adaptable hyperparameter optimization strategy that combines the global and local search mechanisms of BEO and significantly improves the accuracy of slope stability prediction through dynamic adaptive search.

Description

Technical Field

[0001] This invention relates to the field of slope engineering technology, and specifically to a slope stability evaluation method based on the BEO-XGBoost algorithm. Background Technology

[0002] Slope engineering is one of the most critical engineering projects in geotechnical engineering. The economic losses and accidents caused by slope instability are enormous. Therefore, accurately evaluating slope stability is a crucial task in slope engineering. Machine learning methods can analyze the relationship between slope stability and slope parameters from numerous slope case studies, thereby accurately evaluating the stability of unknown slopes. However, the accuracy of machine learning methods depends on appropriate hyperparameter combinations; therefore, exploring suitable hyperparameter combinations is a vital step in machine learning's evaluation of slope stability. Summary of the Invention

[0003] To address the aforementioned issues, this invention optimizes the XGBoost algorithm using the Black Hawk Algorithm (BEO), thereby proposing a slope stability evaluation method based on the BEO-XGBoost algorithm, which improves the accuracy of slope stability evaluation.

[0004] To achieve the above objectives, the present invention proposes a slope stability evaluation method based on the BEO-XGBoost algorithm, comprising the following steps:

[0005] S1. Analyze the factors affecting slope stability, determine the parameters used for slope stability analysis, and construct a slope dataset;

[0006] S2. Analyze the data distribution and process the dataset;

[0007] S3. Build an XGBoost model and divide the dataset into training and test sets;

[0008] S4. Construct a BEO model to optimize XGBoost;

[0009] S5. Train and test the BEO-XGBoost model.

[0010] According to the above scheme, the slope dataset in S1 includes parameters such as slope height, slope angle, pore water pressure ratio, unit weight, cohesion, and internal friction angle.

[0011] According to the above scheme, the XGBoost algorithm in S3 is a machine learning algorithm based on gradient boosting decision trees, which has the characteristics of high efficiency, flexibility, and high accuracy. XGBoost trains multiple trees in a stepwise optimization manner, with each tree improving the previous model, thereby improving the accuracy of the model.

[0012] According to the above scheme, the Black Hawk Algorithm (BEO) in S4 is a metaheuristic optimization algorithm based on the biological behavior of the black hawk. This algorithm simulates the black hawk's predation, migration, and reproductive behaviors, where predation includes tracking, circling, capturing, ambush, and vigilance, and reproductive behaviors include courtship and incubation. The specific steps of BEO are as follows:

[0013] In the BEO algorithm, the Black Hawk population can be represented by the following matrix:

[0014]

[0015] In the formula, n represents the total number of Black Hawk individuals, d represents the dimension of the variable to be optimized, and in this invention, d represents the number of hyperparameters that XGBoost needs to optimize.

[0016] The initial position of each black hawk in the population is given by the following formula:

[0017] X j =lb+rand·(ub-lb),j=1,2,...,n

[0018] In the formula, lb and ub represent the lower and upper bounds of the search space, respectively, and rand is a random number with a value range of (0,1).

[0019] BEO assesses the fit of each Black Hawk individual with the objective function through fitness, which in this invention is the evaluation index value of XGBoost.

[0020] BEO simulates the Black Hawk's tracking behavior using the following formula:

[0021]

[0022]

[0023]

[0024]

[0025] In the formula X r It is a random location in the search space, which is random X. k The location of the individual Black Hawk, X best D is the current optimal position; D is X best The furthest search boundary; r1 is a random number between 0 and 1; t1 is a random number generated by the tent mapping. The tracking behavior simulates the process of a black hawk observing and tracking its prey from a high altitude. Through this process, the algorithm can extensively explore the search space in order to find potential optimal solutions globally.

[0026] BEO simulates the circling behavior of the Black Hawk using the following formula:

[0027]

[0028]

[0029] In the formula, m is a hovering matrix, a = r²·2π, where a is the hovering angle and r² is a random number between 0 and 1. The circling behavior simulates the black hawk constantly adjusting its position as it approaches its prey, allowing the algorithm to further search within the optimal solution range determined by the tracking behavior.

[0030] BEO simulates the Black Hawk's hunting behavior using the following formula:

[0031]

[0032]

[0033]

[0034]

[0035] In the formula, D1 and D2 are two position adjustment factors, and s0 is a column vector of dimension d with elements between 0.5 and 1.

[0036] BEO simulates the Black Hawk's grasping behavior using the following formula:

[0037]

[0038] In the formula, r3 is a random vector of dimension d, and the value of each element in each dimension conforms to a normal distribution.

[0039] BEO simulates the Black Hawk's warning behavior using the following formula:

[0040]

[0041]

[0042] P(j)=λ j / j! e -λ

[0043] λ=-10(d si -d smin ) / (d smax -d smin +15

[0044]

[0045] λ n = (λ-5) / 10

[0046] In the formula, dsi is The distances from the center of the search space, dsmin and dsmax, are the minimum and maximum values ​​of dsi, respectively. It is X t According to The position matrix after rearranging the distances.

[0047] BEO simulates the migration behavior of black hawks using the following formula:

[0048]

[0049]

[0050] In the formula, fbest is the current best fitness value, fj is the fitness value of the j-th individual, s1 is a column vector of dimension d, whose value ranges from -1 to 1, and t2 is a random number between 0.4 and 1 generated by the tent mapping.

[0051] BEO simulates the courtship behavior of black hawks using the following formula:

[0052]

[0053]

[0054] In the formula, k is a step factor, r4 and r6 are random numbers between 0 and 1, and r5 and r7 are column vectors of dimension d whose elements follow a normal distribution.

[0055] BEO simulates the incubation behavior of the Black Hawk using the following formula:

[0056]

[0057] In the formula, R is an array of normally distributed data, and Xd is the population position matrix arranged according to... The population position matrix is ​​rearranged from closest to furthest.

[0058] A slope stability evaluation method based on the BEO-XGBoost algorithm is proposed. This method optimizes the XGBoost model using the BEO algorithm, and then uses the optimized model to learn and test slope data, thereby constructing a slope stability prediction model and achieving accurate and rapid prediction of slope stability. The process of optimizing XGBoost using the BEO algorithm is as follows:

[0059] First, a machine learning model is established. Then, the BEO algorithm randomly generates an initial population. The position of each black hawk individual in the initial population determines the initial hyperparameter combination of the XGBoost model. After obtaining the initial hyperparameter combination, the XGBoost model is trained, tested, and evaluated. The evaluation metric value is passed to the initial population as fitness. The BEO algorithm updates the initial population based on individual fitness, simulating black hawk predation, migration, and reproduction. Updating the black hawk population means updating the XGBoost hyperparameter combination, which the XGBoost model then uses for training, testing, and evaluation. This population update process is repeated until the maximum number of iterations is reached. The position of the individual with the highest fitness during this process is the optimal hyperparameter combination.

[0060] The beneficial effects of this invention are: 1. This model uses the BEO algorithm to optimize the XGBoost model, providing a novel and highly adaptive hyperparameter optimization strategy. It comprehensively utilizes the global and local search mechanisms of BEO and significantly improves the accuracy of slope stability prediction through dynamic adaptive search.

[0061] 2. This method uses six factors that affect slope stability to construct a slope dataset and explores the influence of three aspects on slope stability: slope geometry, the physical and mechanical properties of the soil and rock mass itself, and factors that induce slope instability.

[0062] Description of attached figures and tables

[0063] Figure 1 This is the workflow of this patent.

[0064] Figure 2 The working principle of the BEO algorithm in optimizing the XGBoost model

[0065] Figure 3 These are the prediction results from the BEO-XGBoost model.

[0066] Figure 4 This is a comparison of XGBoost metrics before and after optimization. Specific implementation methods

[0067] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0068] S1. Analyze the factors affecting slope stability, determine the parameters used for slope stability analysis, and construct a slope dataset;

[0069] In this example, we consider three aspects: slope geometry, slope's own physical and mechanical parameters, and external inducing factors. We select the following parameters: unit weight γ, cohesion C, internal friction angle φ, slope angle β, slope height H, and pore water pressure ratio ru.

[0070] S2. Analyze the data distribution and process the dataset;

[0071] In this example, the statistical information of the dataset was calculated, and the results are shown in Table 1. The minimum values ​​of cohesion, internal friction angle, and slope height are 0, indicating that some data for these three characteristic parameters are missing. These missing values ​​need to be preprocessed before building the model. The minimum and maximum values ​​of cohesion and slope height differ significantly, and the mean and median also have large differences, indicating that there are many outliers in the cohesion and slope height data, and the data are mainly concentrated on the smaller side. Table 1. Statistical Information of the Dataset

[0072] S3. Build an XGBoost model and divide the dataset into training and test sets;

[0073] In this example, the dataset is divided into a training set and a test set in a 7:3 ratio.

[0074] S4. Construct a BEO model to optimize XGBoost;

[0075] In this example, the Black Hawk Algorithm (BEO) is a metaheuristic optimization algorithm based on the biological behaviors of the black hawk. This algorithm simulates the black hawk's predation, migration, and reproductive behaviors, where predation includes tracking, circling, capturing, ambush, and vigilance, and reproductive behaviors include courtship and incubation. The specific steps of BEO are as follows:

[0076] In the BEO algorithm, the Black Hawk population can be represented by the following matrix:

[0077]

[0078] In the formula, n represents the total number of Black Hawk individuals, d represents the dimension of the variable to be optimized, and in this invention, d represents the number of hyperparameters that XGBoost needs to optimize.

[0079] The initial position of each black hawk in the population is given by the following formula:

[0080] X j =lb+rand·(ub-lb),j=1,2,...,n

[0081] In the formula, lb and ub represent the lower and upper bounds of the search space, respectively, and rand is a random number with a value range of (0,1).

[0082] BEO assesses the fit of each Black Hawk individual with the objective function through fitness, which in this invention is the evaluation index value of XGBoost.

[0083] BEO simulates the Black Hawk's tracking behavior using the following formula:

[0084]

[0085]

[0086]

[0087]

[0088] In the formula X r It is a random location in the search space, which is random X. k The location of the individual Black Hawk, X best D is the current optimal position; D is X best The furthest search boundary; r1 is a random number between 0 and 1; t1 is a random number generated by the tent mapping. The tracking behavior simulates the process of a black hawk observing and tracking its prey from a high altitude. Through this process, the algorithm can extensively explore the search space in order to find potential optimal solutions globally.

[0089] BEO simulates the circling behavior of the Black Hawk using the following formula:

[0090]

[0091]

[0092] In the formula, m is a hovering matrix, a = r²·2π, where a is the hovering angle and r² is a random number between 0 and 1. The circling behavior simulates the black hawk constantly adjusting its position as it approaches its prey, allowing the algorithm to further search within the optimal solution range determined by the tracking behavior.

[0093] BEO simulates the Black Hawk's hunting behavior using the following formula:

[0094]

[0095]

[0096]

[0097]

[0098] In the formula, D1 and D2 are two position adjustment factors, and s0 is a column vector of dimension d with elements between 0.5 and 1.

[0099] BEO simulates the Black Hawk's grasping behavior using the following formula:

[0100]

[0101] In the formula, r3 is a random vector of dimension d, and the value of each element in each dimension conforms to a normal distribution.

[0102] BEO simulates the Black Hawk's warning behavior using the following formula:

[0103]

[0104]

[0105] P(j=λ) j / j! e -λ

[0106] λ=-10(d si -d smin ) / (d smax -d smin +15

[0107]

[0108] λ n =(λ-5) / 10

[0109] In the formula, dsi is The distances from the center of the search space, dsmin and dsmax, are the minimum and maximum values ​​of dsi, respectively. It is X t According to The position matrix after rearranging the distances.

[0110] BEO simulates the migration behavior of black hawks using the following formula:

[0111]

[0112]

[0113] In the formula, fbest is the current best fitness value, fj is the fitness value of the j-th individual, s1 is a column vector of dimension d, whose value ranges from -1 to 1, and t2 is a random number between 0.4 and 1 generated by the tent mapping.

[0114] BEO simulates the courtship behavior of black hawks using the following formula:

[0115]

[0116]

[0117] In the formula, k is a step factor, r4 and r6 are random numbers between 0 and 1, and r5 and r7 are column vectors of dimension d whose elements follow a normal distribution.

[0118] BEO simulates the incubation behavior of the Black Hawk using the following formula:

[0119]

[0120] In the formula, R is an array of normally distributed data, and Xd is the population position matrix arranged according to... The population position matrix is ​​rearranged from closest to furthest.

[0121] S5. Train and test the BEO-XGBoost model.

[0122] In this example, the XGBoost model optimized using the BEO algorithm is used to predict slope stability, and the results are as follows: Figure 1 As shown in the figure. To better observe the effect of BEO on XGBoost optimization, various indicators before and after XGBoost optimization were calculated and compared, and the results are as follows. Figure 2 As shown, after BEO optimization, all indicators of XGBoost were improved, with the accuracy increasing from 78.48% to 89.83%, indicating that BEO has a significant optimization effect on XGBoost, and that BEO-XGBoost has high accuracy in predicting slope stability.

Claims

1. A slope stability evaluation method based on the BEO-XGBoost algorithm, characterized in that: Includes the following steps: S1. Analyze the factors affecting slope stability, determine the parameters used for slope stability analysis, and construct a slope dataset; S2. Analyze the data distribution and process the dataset; S3. Build an XGBoost model and divide the dataset into training and test sets; S4. Construct a BEO model to optimize XGBoost; S5. Train and test the BEO-XGBoost model.

2. The hyperparameters to be optimized for XGBoost according to claim 1 include: n_setimators, learning_rate, max_depth, subsample, min_child_weight and other parameters.

3. The steps of BEO according to claim 1 are as follows: In the BEO algorithm, the Black Hawk population can be represented by the following matrix: In the formula, n represents the total number of Black Hawk individuals, d represents the dimension of the variable to be optimized, and in this invention, d represents the number of hyperparameters that XGBoost needs to optimize. The initial position of each black hawk in the population is given by the following formula: X j =lb+rand·(ub-lb),j=1,2,...,n In the formula, lb and ub represent the lower and upper bounds of the search space, respectively, and rand is a random number with a value range of (0,1). BEO assesses the fit of each Black Hawk individual with the objective function through fitness, which in this invention is the evaluation index value of XGBoost. BEO simulates the Black Hawk's tracking behavior using the following formula: In the formula X r It is a random location in the search space, which is random X. k The location of the individual Black Hawk, X best D is the current optimal position; D is X best The furthest search boundary; r1 is a random number between 0 and 1; t1 is a random number generated by the tent mapping. The tracking behavior simulates the process of a black hawk observing and tracking its prey from a high altitude. Through this process, the algorithm can extensively explore the search space in order to find potential optimal solutions globally. BEO simulates the circling behavior of the Black Hawk using the following formula: In the formula, m is a hovering matrix, a = r²·2π, where a is the hovering angle and r² is a random number between 0 and 1. The circling behavior simulates the black hawk constantly adjusting its position as it approaches its prey, allowing the algorithm to further search within the optimal solution range determined by the tracking behavior. BEO simulates the Black Hawk's hunting behavior using the following formula: In the formula, D1 and D2 are two position adjustment factors, and s0 is a column vector of dimension d with elements between 0.5 and 1. BEO simulates the Black Hawk's grasping behavior using the following formula: In the formula, r3 is a random vector of dimension d, and the value of each element in each dimension conforms to a normal distribution. BEO simulates the Black Hawk's warning behavior using the following formula: P(j)=λ j / her -λ l n =(λ-5) / 10 In the formula, dsi is The distances from the center of the search space, dsmin and dsmax, are the minimum and maximum values ​​of dsi, respectively. It is X t According to The position matrix after rearranging the distances. BEO simulates the migration behavior of black hawks using the following formula: In the formula, fbest is the current best fitness value, fj is the fitness value of the j-th individual, s1 is a column vector of dimension d, whose value ranges from -1 to 1, and t2 is a random number between 0.4 and 1 generated by the tent mapping. BEO simulates the courtship behavior of black hawks using the following formula: In the formula, k is a step factor, r4 and r6 are random numbers between 0 and 1, and r5 and r7 are column vectors of dimension d whose elements follow a normal distribution. BEO simulates the incubation behavior of the Black Hawk using the following formula: In the formula, R is an array of normally distributed data, and Xd is the population position matrix arranged according to... The population position matrix is ​​rearranged from closest to furthest.

4. The slope stability evaluation method based on the BEO-XGBoost algorithm according to claim 3 is characterized in that: The process of optimizing XGBoost using the BEO algorithm is shown in Figure 1: First, a machine learning model is established. Then, the BEO algorithm randomly generates an initial population. The position of each black hawk individual in the initial population determines the initial hyperparameter combination of the XGBoost model. After obtaining the initial hyperparameter combination, the XGBoost model is trained, tested, and evaluated. The evaluation metric value is passed to the initial population as fitness. The BEO algorithm updates the initial population based on individual fitness, simulating black hawk predation, migration, and reproduction. Updating the black hawk population means updating the XGBoost hyperparameter combination, which the XGBoost model then uses for training, testing, and evaluation. This population update process is repeated until the maximum number of iterations is reached. The position of the individual with the highest fitness during this process is the optimal hyperparameter combination.

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