A three-dimensional displacement prediction method for open-pit mine slope based on improved stacking ensemble learning
By using an improved Stacking ensemble learning method, combined with multiple regression algorithms and data preprocessing techniques, the problem of insufficient accuracy in three-dimensional displacement prediction of open-pit mine slopes was solved, achieving high-precision and stable prediction in small sample environments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA COAL TECH & ENG GRP SHENYANG ENG CO
- Filing Date
- 2026-02-06
- Publication Date
- 2026-06-12
AI Technical Summary
Existing technologies suffer from poor adaptability and insufficient accuracy in predicting three-dimensional displacement of open-pit mine slopes. In particular, they are difficult to reliably extract the potential spatiotemporal patterns in displacement sequences under small sample and high noise conditions. Traditional single-model methods perform poorly in short- to medium-term predictions.
An improved Stacking ensemble learning method is adopted, which combines Support Vector Regression (SVR), Robust (Huber) Regression and LightGBM Regression as base learners, and performs relearning through Ridge Regression. The data is then processed by IQR anomaly detection, Akima interpolation and Savitzky-Golay filtering to construct a three-dimensional displacement prediction model.
It improves prediction accuracy in terms of nonlinearity and robustness, reduces model bias and variance, ensures data continuity and stability, and has good engineering usability and promotion potential.
Smart Images
Figure CN122199841A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of mine slope monitoring and surface deformation prediction technology, and specifically provides a method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning. Background Technology
[0002] The deformation evolution of open-pit mine slopes is influenced by multiple factors, including geological structure, mining disturbance, and meteorological conditions, exhibiting significant nonlinearity, time-varying characteristics, and uncertainties. Traditional single-model methods suffer from poor adaptability and insufficient accuracy in short- to medium-term displacement prediction. To improve prediction accuracy and robustness, ensemble learning is increasingly being used for time-series prediction tasks.
[0003] Existing research on GNSS data for slopes mostly focuses on single models (such as gray models, neural networks, or single-class tree models). However, in the task of predicting three-dimensional displacement of slopes, the data has the characteristics of strong nonlinearity, large noise disturbance, and complex change patterns. At the same time, due to the limitations of actual observation conditions, the number of available historical samples is relatively limited. In small sample and high noise environments, single models often have difficulty in stably extracting the potential spatiotemporal patterns in displacement sequences.
[0004] Existing research has shown that Stacking ensemble models have demonstrated excellent performance in time series forecasting, earthquake early warning, and hydrological simulation. In particular, their fusion effect is more significant in task scenarios where data quality is limited and model uniformity is obvious. However, there are still relatively few studies on systematically introducing the Stacking method into the three-dimensional displacement prediction task of open-pit mine slopes. Existing work is mostly limited to comparative experiments.
[0005] Furthermore, the traditional Stacking ensemble strategy consists of four steps: base model training, constructing a meta-dataset, meta-model training, and prediction during the testing phase. Its core idea is that different models have varying learning abilities on data. By combining the outputs of multiple models, bias and variance can be reduced, thereby improving the model's generalization ability to unknown data. While the base learner must use cross-validation for prediction when constructing meta-features, there is still significant room for improvement in prediction accuracy and stability in environments with small to medium sample sizes. Summary of the Invention
[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a three-dimensional displacement prediction method for open-pit mine slopes based on improved Stacking ensemble learning, comprising the following steps: Step 1: Collect raw three-dimensional displacement monitoring data to construct multi-dimensional time series data; Step 2, preprocessing the raw three-dimensional displacement monitoring data, the specific process includes: Step 2.1: Identify and remove outliers; Step 2.2, fill in missing values; Step 2.3: Calculate the three-dimensional composite displacement, orientation angle, tilt angle, and displacement rate; Step 2.4: Perform Savitzky-Golay filtering on the processed data; Step 3: Construct the Stacking ensemble learning prediction model. The base learner of the Stacking ensemble learning prediction model integrates support vector regression (SVR), robust regression (Huber) and lightGBM regression. The meta-learner introduces ridge regression to relearn the output of the base learner. The loss function for ridge regression is defined as: ; In the formula: y i The true value of the sample; These are the model's predicted values; w is the regression coefficient weight vector; λ is the regularization coefficient, used to control model complexity; n is the number of samples; Step 4: Perform short-to-medium-term predictions on the three-dimensional synthetic displacement and output the displacement trend curve for a future period.
[0007] Further, in step 1, the raw monitoring data of three-dimensional displacement is collected based on GNSS (Global Navigation Satellite System).
[0008] Further, in step 2.1, outliers are identified and removed using IQR (interquartile range). The decision interval is x < Q1 - 1.5IQR or x > Q3 + 1.5IQR; In the formula, x represents the observed value in the table; Q1 is the first quartile; Q3 is the third quartile; IQR is the interquartile range, IQR = Q3 - Q1.
[0009] Further, in step 2.2, the missing value interpolation method adopted is Akima interpolation.
[0010] Further, step 2.3, The three-dimensional composite displacement S is: ; In the formula: The orientation angle α and the tilt angle β are respectively: ; ; The displacement rate v is: ; In the formula, x is the displacement value in the X direction; y represents the displacement value in the Y direction; z is the displacement value in the Z direction; s t This represents the current three-dimensional composite displacement value. s t-1 The table shows the three-dimensional composite displacement values at the previous moment; △t represents the time interval between adjacent monitoring times.
[0011] Further, in step 3, support vector regression uses a radial basis function kernel, and the prediction function has the following form: ; In the formula: f(x) is the predicted output of the support vector regression model for the input sample x; α i and α i * They are Lagrange multipliers; K(x i (x) is the kernel function, which uses radial basis functions (RBF). x i These are support vectors; b is the bias term; n is the number of support vectors.
[0012] Furthermore, step 3, the robust regression process includes: initializing model parameters, calculating residuals, calculating loss function, optimizing the problem, and updating parameters; The loss function formula for robust regression is as follows: ; In the formula, r is the residual of the model, which is the difference between the predicted value and the actual value; δ is the Huber threshold, which controls when the loss changes from quadratic loss (squared error) to linear loss (absolute error). The formula for minimizing the total loss is: .
[0013] Furthermore, in step 3, LightGBM regression is an efficient distributed decision tree algorithm based on the gradient boosting framework. It is based on the traditional GBDT (Gradient Boosting Decision Tree) and introduces two optimizations: gradient-based unilateral sampling and mutually exclusive feature binding. It adopts a leaf-first tree growth strategy, selecting the leaf node with the largest gain for splitting each time. This method can reduce errors faster than the traditional layer-by-layer growth strategy. The commonly used loss function in LightGBM regression is the Mean Squared Error (MSE), as shown in the following formula: ; In the formula, y i The true value of the sample; These are the model's predicted values; θ is the set of model parameters.
[0014] The beneficial effects of using this invention are: The base learner of the Stacking ensemble learning prediction model combines support vector regression (SVR), robust regression (Huber) and LightGBM regression, complementing each other in terms of nonlinear representation, robustness and feature modeling, and reducing bias and variance. Ridge meta-learners alleviate multicollinearity and overfitting in small sample sizes; IQR anomaly detection, Akima interpolation, and SG filtering constitute a reproducible data engineering process to ensure sequence continuity and stability; It possesses good engineering usability and promotion potential. Attached Figure Description
[0015] Figure 1 This is a schematic diagram of the present invention; Figure 2 This is a schematic diagram of the support vector regression algorithm of the present invention; Figure 3 This is a schematic diagram of the Huber regression algorithm of the present invention; Figure 4 This is a schematic diagram of the LightGBM regression algorithm of the present invention; Figure 5 This is a graph showing the change of engineering indicators over time in Embodiment 1 of the present invention; Figure 6 This is a comparison curve of the predicted monitoring point results and the actual values in Embodiment 1 of the present invention; Figure 7 This table compares the effects of filling missing values obtained by applying four interpolation methods in this invention. Detailed Implementation
[0016] The present invention will now be described in detail with reference to the accompanying drawings.
[0017] Reference Figure 1 A method for predicting the three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning includes the following steps: Step 1: Collect raw three-dimensional displacement monitoring data to construct multi-dimensional time series data; Step 2, preprocessing the raw three-dimensional displacement monitoring data, the specific process includes: Step 2.1: Identify and remove outliers; Step 2.2, fill in missing values; Step 2.3: Calculate the three-dimensional composite displacement, orientation angle, tilt angle, and displacement rate; Step 2.4: Perform Savitzky-Golay filtering on the processed data.
[0018] Step 3: Construct the Stacking ensemble learning prediction model. The base learner of the Stacking ensemble learning prediction model integrates support vector regression (SVR), robust regression (Huber) and lightGBM regression. The meta-learner introduces ridge regression to relearn the output of the base learner. The loss function for ridge regression is defined as: ; In the formula: y i The true value of the sample; These are the model's predicted values; w is the regression coefficient weight vector; λ is the regularization coefficient, used to control model complexity; n is the number of samples.
[0019] Step 4: Perform short-to-medium-term predictions on the three-dimensional synthetic displacement and output the displacement trend curve for a future period.
[0020] Preferably, in step 1, the raw three-dimensional displacement monitoring data is collected based on GNSS (Global Navigation Satellite System).
[0021] The specific categories of multidimensional time series data include the X direction, Y direction, uplift direction, and subsidence direction.
[0022] Preferably, in step 2.1, outliers are identified and removed using IQR (interquartile range). The decision interval is x < Q1 - 1.5IQR or x > Q3 + 1.5IQR; In the formula, x represents the observed value in the table; Q1 is the first quartile; Q3 is the third quartile; IQR is the interquartile range, IQR = Q3 - Q1.
[0023] Preferably, in step 2.2, the missing value interpolation method is Akima interpolation.
[0024] Specifically, the four commonly used missing value interpolation methods in engineering are linear interpolation, spline interpolation, polynomial interpolation, and Akima interpolation. These four methods are used to interpolate missing values for the time series characteristics of GNSS displacement monitoring data. After calculating the above indicators based on different interpolation results for each monitoring point, a comprehensive ranking is performed according to the principle of "optimal smoothness and stability." This ranking primarily uses three indicators: MAD_diff (a robust measure of dispersion based on median absolute deviation (MAD) used to measure data variability), maximum jump value, and third-order difference variance, combined with... The ability to maintain trends and make weighted decisions; Reference Figure 7 The third difference variance of the data in the table is 5.760795. Akima interpolation has the best smoothness and trend consistency, so Akima interpolation is adopted as the missing value interpolation method.
[0025] Preferably, step 2.3, The three-dimensional composite displacement S is: ; In the formula: The orientation angle α and the tilt angle β are respectively: ; ; The displacement rate v is: ; In the formula, x is the displacement value in the X direction; y represents the displacement value in the Y direction; z is the displacement value in the Z direction; s t This represents the current three-dimensional composite displacement value. s t-1 The table shows the three-dimensional composite displacement values at the previous moment; △t represents the time interval between adjacent monitoring times.
[0026] Step 2.4: The Savitzky-Golay filter is used to smooth the time series, which can reduce random noise and short-term fluctuations in GNSS observation data, make the changing trends of various engineering indicators over time clearer, and enhance their engineering interpretability. Reference Figure 5 The time history of typical engineering indicators after filtering.
[0027] Furthermore, it should be noted that, considering the potential for look-ahead bias in time series forecasting, the order of SG filtering was strictly controlled during the data preprocessing stage. Specifically, the raw monitoring data was first divided into training and test sets according to time sequence, and then SG filtering was performed independently within each set. Throughout this process, the calculation scope of SG filtering was always limited to the corresponding data subset, without involving future observation information from the testing phase. This avoided the information leakage risk associated with bidirectional filtering and ensured the rigor and reproducibility of the model training and prediction validation process.
[0028] Specifically, refer to Figure 2 Step 3, Support Vector Regression uses a radial basis function kernel, and the prediction function has the following form: ; In the formula: f(x) is the predicted output of the support vector regression model for the input sample x; α i and α i * They are Lagrange multipliers; K(x i (x) is the kernel function, which uses radial basis functions (RBF). x i These are support vectors; b is the bias term; n is the number of support vectors; Furthermore, the loss function formula for support vector regression is as follows: ; In the formula, w is the weight vector, which determines the direction and position of the regression hyperplane; b is the bias, which determines the offset of the regression hyperplane; ξ i Let be a slack variable, representing the error of the i-th sample, which allows some samples to go outside the ε region; C is the penalty coefficient, used to measure the complexity and error tolerance of the model; ||w|| 2 This is a regularization term that controls the complexity of the model; n is the number of training samples; To ensure that the error is within acceptable limits, support vector regression uses constraints to ensure that each data point y is within acceptable limits. i The distance from the regression hyperplane does not exceed a specified threshold ε (i.e., the maximum permissible error), as shown in the following formula: ; In the formula, y i This represents the true value of the i-th sample. x i Let be the feature vector of the i-th sample; w T x i +b represents the predicted values from the regression model; By constructing the loss function and constraints, a regression hyperplane is found that makes most sample points as close to the hyperplane as possible, while slack variables allow some sample points to deviate from the hyperplane. After balancing the regularization and error terms, support vector regression can perform regression predictions on complex datasets.
[0029] Reference Figure 3 The process of robust regression includes: initializing model parameters, calculating residuals, calculating loss function, optimizing the problem, and updating parameters; The loss function formula for robust regression is as follows: ; In the formula, r is the residual of the model, which is the difference between the predicted value and the actual value; δ is the Huber threshold, which controls when the loss changes from quadratic loss (squared error) to linear loss (absolute error).
[0030] The formula for minimizing the total loss is: .
[0031] Reference Figure 4 LightGBM regression is an efficient distributed decision tree algorithm based on the gradient boosting framework. It is based on the traditional GBDT (Gradient Boosting Decision Tree) and introduces two optimizations: gradient-based unilateral sampling and mutually exclusive feature binding. It adopts a leaf-first tree growth strategy, selecting the leaf node with the largest gain for splitting each time. This approach can reduce errors faster than the traditional layer-by-layer growth strategy. The commonly used loss function in LightGBM regression is the Mean Squared Error (MSE), as shown in the following formula: ; In the formula, y i The true value of the sample; These are the model's predicted values; θ is the set of model parameters; In each iteration, the model fits the residual from the previous iteration, i.e., the negative gradient, as shown in the following formula: ; In the formula, g i (t) The negative gradient (i.e., residual) of the i-th sample in the t-th iteration represents the direction of the fitting error of the current model at that sample point; L(·) is the loss function; It is the model's prediction of the i-th sample in the (t-1)-th iteration; To obtain the partial derivative with respect to the predicted value; Train a new regression tree to fit this gradient and update the model, as shown in the following formula: ; In the formula, η is the learning rate, which controls the degree of influence of each round of the tree model on the final prediction; f t (x i ) represents the t-th regression tree in sample x i The output value (used to fit the residual).
[0032] Evaluation metrics for prediction results include mean absolute error (MAE), root mean square error (RMSE), and coefficient of determination (R²). 2 ), respectively defined as: ; ; ; In the formula: R 2 The coefficient of determination reflects the goodness of fit of the model to the data; y i The true value of the sample; These are the model's predicted values; The average of the true values; n is the number of samples.
[0033] Example 1
[0034] The Heishantou open-pit mine in Xinjiang was used as the test site; GNSS monitoring data were selected from the eastern slope of the Heishantou open-pit mine in Xinjiang, with a sampling interval of once per day; The time range is from February 17, 2024 to August 30, 2024, a total of 195 days; The sample contains triaxial displacement components and timestamps; The ratio of training set to prediction set is set to 8:2.
[0035] Suppose the original dataset for a certain monitoring indicator is: After sorting the data in ascending order, calculate its 25th percentile (first quartile Q1) and 75th percentile (third quartile Q3). Based on statistical experience, if a certain observed value x i A point is considered an outlier if one of the following conditions is met: x < Q1 - 1.5IQR or x > Q3 + 1.5IQR; The coefficient 1.5 is a commonly used empirical threshold, used to balance the sensitivity and stability of anomaly detection.
[0036] Reference Figure 5 After preprocessing in step 2, the curves of three-dimensional composite displacement, orientation angle, tilt angle and displacement rate as a function of time are obtained.
[0037] Step 3 involves constructing a Stacking ensemble learning model and then calculating the prediction dataset based on the constructed model. Reference Figure 6 The predicted curves and the measured curves maintain a high degree of consistency in the main evolutionary stages.
[0038] The prediction results were evaluated. On the test set, the model's mean absolute error (MAE) was 0.309 mm, the root mean square error (RMSE) was 0.486 mm, and the coefficient of determination R0 was [value missing]. 2 The accuracy reached 0.961, indicating that the model has high prediction accuracy overall. The maximum absolute error was 2.19 mm, which occurred at prediction time 36 of the test set (corresponding to the date 2024-08-28). At this time, the model underestimated the measured displacement value to a certain extent, but did not change the overall trend judgment of displacement evolution.
[0039] This demonstrates that the model, during the testing phase, can maintain its overall trend discrimination capability while effectively controlling the prediction error within a small range, exhibiting good stability and reliability in the short to medium term prediction of GNSS three-dimensional displacement.
[0040] The above content is only a preferred embodiment of the present invention. For those skilled in the art, many changes can be made in the specific implementation and application scope based on the concept of the present invention. As long as these changes do not depart from the concept of the present invention, they all fall within the protection scope of the present invention.
Claims
1. A method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning, characterized in that, Includes the following steps: Step 1: Collect raw three-dimensional displacement monitoring data to construct multi-dimensional time series data; Step 2, preprocessing the raw three-dimensional displacement monitoring data, the specific process includes: Step 2.1: Identify and remove outliers; Step 2.2, fill in missing values; Step 2.3: Calculate the three-dimensional composite displacement, orientation angle, tilt angle, and displacement rate; Step 2.4: Perform Savitzky-Golay filtering on the processed data; Step 3: Construct the Stacking ensemble learning prediction model. The base learner of the Stacking ensemble learning prediction model integrates support vector regression (SVR), robust regression (Huber) and lightGBM regression. The meta-learner introduces ridge regression to relearn the output of the base learner. The loss function for ridge regression is defined as: ； In the formula: y i The true value of the sample; These are the model's predicted values; w is the weight vector of the regression coefficients; λ is the regularization coefficient, used to control model complexity; n is the number of samples; Step 4: Perform short-to-medium-term predictions on the three-dimensional synthetic displacement and output the displacement trend curve for a future period.
2. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 1: Collect raw three-dimensional displacement monitoring data based on GNSS (Global Navigation Satellite System).
3. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 2.1: Use IQR (interquartile range) to identify and remove outliers; The decision interval is x < Q1 - 1.5IQR or x > Q3 + 1.5IQR; In the formula, x represents the observed value in the table; Q1 is the first quartile; Q3 is the third quartile; IQR is the interquartile range, IQR = Q3 - Q1.
4. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 2.2: The missing value interpolation method used is Akima interpolation.
5. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 2.3, The three-dimensional composite displacement S is: ； In the formula: The orientation angle α and the tilt angle β are respectively: ； ； The displacement rate v is: ； In the formula, x is the displacement value in the X direction; y represents the displacement value in the Y direction; z is the displacement value in the Z direction; s t This represents the current three-dimensional composite displacement value. s t-1 The table shows the three-dimensional composite displacement values at the previous moment; △t represents the time interval between adjacent monitoring times.
6. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 3, Support Vector Regression uses a radial basis function kernel, and the prediction function has the following form: ； In the formula: f(x) is the predicted output of the support vector regression model for the input sample x; α i and α i * They are Lagrange multipliers; K(x i (x) is the kernel function, which uses radial basis functions (RBF). x i These are support vectors; b is the bias term; n is the number of support vectors.
7. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 3, the robust regression process includes: initializing model parameters, calculating residuals, calculating loss function, optimizing the problem, and updating parameters; The loss function formula for robust regression is as follows: ； In the formula, r is the residual of the model, which is the difference between the predicted value and the actual value; δ is the Huber threshold, which controls when the loss changes from quadratic loss (squared error) to linear loss (absolute error). The formula for minimizing the total loss is: 。 8. The method for predicting three-dimensional displacement of open-pit mine slopes based on improved Stacking ensemble learning as described in claim 1, characterized in that: Step 3: LightGBM regression is an efficient distributed decision tree algorithm based on the gradient boosting framework. It is based on the traditional GBDT (Gradient Boosting Decision Tree) and introduces two optimizations: gradient-based unilateral sampling and mutually exclusive feature binding. It adopts a leaf-first tree growth strategy, selecting the leaf node with the largest gain for splitting each time. This method can reduce errors faster than the traditional layer-by-layer growth strategy. The commonly used loss function in LightGBM regression is the Mean Squared Error (MSE), as shown in the following formula: ； In the formula, y i The true value of the sample; These are the model's predicted values; θ is the set of model parameters.