Prediction method for maximum rushing-out distance of debris flow based on PCA-GPR

Abstract

The invention relates to a method for predicting the maximum debris flow rushing-out distance based on PCA-GPR. The method comprises the steps of obtaining an influence factor of the maximum debris flow rushing-out distance in a target area; the influence factors are input into a debris flow maximum rushing-out distance prediction model, the probability distribution prediction result of the debris flow maximum rushing-out distance is obtained, the debris flow maximum rushing-out distance prediction model is constructed based on a Gaussian process regression model GPR and is obtained through training of a training set, and the probability distribution prediction result of the debris flow maximum rushing-out distance is obtained. The training set is a data set comprising factors influencing the maximum rushing length of the debris flow and the corresponding maximum rushing distance, and dimension reduction processing is performed on the factors influencing the maximum rushing length of the debris flow before training. According to the debris flow maximum rushing-out distance prediction method based on the GPR model, the uncertainty in prediction is quantified through the prediction result in a probability distribution form, and the defect that a conventional model explains and evaluates the uncertainty in the prediction result is overcome.

Description

Technical Field

[0001] The invention relates to the technical field of debris flow disaster risk assessment, and in particular to a method for predicting a maximum discharge distance of a debris flow based on PCA-GPR. Background Art

[0002] At present, the methods for predicting the maximum outflow distance of debris flows are mainly empirical statistics, numerical simulation and machine learning. The empirical statistical method is based on a large amount of historical data and statistical analysis principles to establish a mathematical relationship between the maximum outflow distance of debris flows and various influencing factors. ZHOU et al. established two empirical relationships based on single variable and multivariate methods to predict the maximum outflow distance of debris flows in earthquake zones; RICKENMANN established a mathematical relationship function between the maximum outflow distance and the volume of the accumulation fan based on the history of debris flow development and basic data obtained from experiments through statistical analysis; in addition, SIMONI proposed that the uncertainty of the empirical relationship must be evaluated before the empirical statistical relationship is applied. The numerical simulation method uses mathematical models to describe the physical dynamic process of debris flows in the study area, and uses numerical solution methods to obtain the maximum outflow distance of debris flows, thereby conducting effective hazard range and hazard assessment [6]; numerical models based on physical equations have the advantage of estimating the maximum outflow distance of debris flows by using correct parameters, and can provide additional debris flow dynamic parameters, such as debris flow rate and velocity. However, due to the lack of experimental or observational data and insufficient understanding of the physical dynamics of debris flows during the simulation process, theoretical models often find it difficult to accurately describe the complex movement and accumulation process of debris flows, resulting in large deviations and uncertainties in the prediction of the maximum discharge distance of debris flows.

[0003] With the continuous development of computer technology and machine learning algorithms, more and more studies have begun to try to apply machine learning algorithms to geological disaster risk assessment, prediction of rock and soil mechanical properties, etc. KENNDY et al. developed a machine learning prediction model based on FOS, which was trained by metaheuristic techniques to predict the susceptibility of debris flows. Hou Runing et al. used the stacking ensemble algorithm to evaluate the susceptibility of debris flow disasters in the Tianshan area, and compared the prediction performance of the stacking ensemble algorithm with that of independent heterogeneous algorithms; Guo Pengning et al. applied deep fully connected neural networks to the evaluation of debris flow susceptibility in Ya'an City, Sichuan Province, and compared them with models such as gradient boosting tree, random forest and Bayesian network; KERN AN used naive Bayes, hybrid discriminant analysis, classification tree and other machine learning methods to establish a new prediction model for debris flow caused by wildfires; XIAO et al. used a deep trust network (DBN) composed of BP neural network and restricted Boltzmann machine to establish a risk assessment system for sudden debris flow and realized the hazard zoning of sudden debris flow; WANG et al. proposed a new hybrid generalized regression neural network (GRNN) model to predict the hazard range of debris flow; XU et al. used 7 data mining techniques such as CRT, CHAID and Boosting tree to predict the outburst distance of shallow and loess-bedrock landslides.

[0004] However, existing machine learning methods for predicting the maximum distance of debris flow can often only provide deterministic numerical prediction results. When making predictions, these models ignore the fact that debris flow disasters are often affected by multiple factors, and there is still a lack of explanation for the uncertainty in the predictions. Summary of the invention

[0005] The purpose of the present invention is to provide a prediction method for the maximum rushing distance of a debris flow based on PCA-GPR, which can accurately predict the maximum rushing distance of a debris flow.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] The first aspect provides a prediction method for the maximum discharge distance of debris flow based on PCA-GPR, including:

[0008] Obtain the influencing factors of the maximum outflow distance of debris flow in the target area;

[0009] The influencing factors are input into a debris flow maximum rushing out distance prediction model to obtain a probability distribution prediction result of the debris flow maximum rushing out distance, wherein the debris flow maximum rushing out distance prediction model is constructed based on a Gaussian process regression model GPR and is obtained through training with a training set, wherein the training set is a data set including factors affecting the maximum rushing out length of the debris flow and the corresponding maximum rushing out distance, and before training, the factors affecting the maximum rushing out length of the debris flow are subjected to dimensionality reduction processing.

[0010] Optionally, the influencing factors include watershed area, watershed elevation difference, material source reserves, and average longitudinal slope.

[0011] Optionally, before the dimensionality reduction processing is performed on the factors affecting the maximum flushing length of the debris flow, the method also includes: cleaning the factors affecting the maximum flushing length of the debris flow, processing missing values ​​and abnormal values, and obtaining pre-processed data.

[0012] Optionally, performing dimensionality reduction processing on the factors that affect the maximum flushing length of the debris flow includes: performing principal component analysis PCA on the preprocessed data to obtain the feature data set after dimensionality reduction.

[0013] Optionally, performing principal component analysis (PCA) on the preprocessed data includes:

[0014] Performing standardization on the preprocessed data to obtain standardized data;

[0015] Calculating a covariance matrix according to the standardized data, and performing eigenvalue decomposition according to the covariance matrix to obtain eigenvalues;

[0016] The first several principal components are selected according to the eigenvalues ​​and contribution rates, and the preprocessed data are projected into the principal component space to obtain a feature data set after dimensionality reduction.

[0017] Optionally, the process of training the debris flow maximum flushing distance prediction model through a training set includes: obtaining the best hyperparameter combination through grid search combined with cross validation.

[0018] Optionally, the kernel function of the Gaussian process regression model is a GPRMatérn_3 / 2 kernel function.

[0019] A second aspect provides a storage medium, the storage medium comprising a stored program, wherein the program executes a prediction method when executed.

[0020] A third aspect provides a processor, which is used to run a program, wherein the program executes a prediction method when running.

[0021] The beneficial effects of the present invention are as follows: the method of the present invention combines the dimensionality reduction capability of the PCA method for multi-dimensional data, and uses the GPR method to train the data after dimensionality reduction to obtain a prediction model for the maximum flushing distance of debris flows. The PCA method avoids the redundancy between factors in the process of predicting the maximum flushing distance of debris flows, making the model prediction more accurate. The GPR prediction model based on the PCA method is better than the single GPR prediction model. The posterior probability distribution results of the maximum flushing distance prediction method of debris flows based on the GPR model break through the single numerical prediction of conventional machine learning algorithms, and quantify the uncertainty in the prediction in the form of probability distribution, making up for the lack of conventional models in explaining and evaluating the uncertainty in the prediction results. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0023] Figure 1 It is a flowchart of a method for predicting the maximum flushing distance of a debris flow based on PCA-GPR according to an embodiment of the present invention;

[0024] Figure 2 A schematic diagram of a 5-fold cross validation method according to an embodiment of the present invention;

[0025] Figure 3 is a posterior distribution probability (Matérn_3 / 2) distribution diagram of the test set of an embodiment of the present invention;

[0026] Figure 4 This is a graph showing the prediction results of the GPR model for the maximum discharge distance of debris flows in the test set under the Matérn_3 / 2 kernel function of an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0029] This embodiment provides a method for predicting the maximum discharge distance of a debris flow based on PCA-GPR, including:

[0030] Obtain the influencing factors of the maximum outflow distance of debris flow in the target area;

[0031] The influencing factors are input into the maximum outflow distance prediction model of debris flow to obtain the maximum outflow distance of debris flow. The maximum outflow distance prediction model of debris flow is constructed based on the Gaussian process regression model GPR and is obtained through training with a training set. The training set is a data set including factors affecting the maximum outflow length of debris flow and the corresponding maximum outflow distance. Before training, the factors affecting the maximum outflow length of debris flow are subjected to dimensionality reduction processing.

[0032] Furthermore, the influencing factors include watershed area, watershed elevation difference, material source reserves, and average longitudinal slope.

[0033] Specifically, the selection of input variables is critical for the prediction of the maximum outflow distance of debris flow. The input variables should be combined with the real physical process of debris flow activities, and the factors with the greatest influence on the maximum outflow distance of debris flow should be selected. The basin area (A) indicates the potential water source gathering conditions, which affects the occurrence and intensity of debris flow; the average longitudinal slope (J) indicates the slope conditions and water flow dynamic conditions of the debris flow ditch. The greater longitudinal slope gives the debris flow greater speed and energy. The basin height difference H is a characteristic of the elevation of the debris flow basin, which can explain the dynamic conditions for the occurrence and movement of debris flow; the material reserve V represents the volume of solid debris in the debris flow ditch, and explains the material supply conditions for the formation of the accumulation fan by the debris flow.

[0034] Furthermore, before the dimensionality reduction processing is performed on the factors that affect the maximum flushing length of the debris flow, the following steps are also included: cleaning the factors that affect the maximum flushing length of the debris flow, processing missing values ​​and abnormal values, and obtaining pre-processed data.

[0035] Furthermore, the dimension reduction processing of the factors affecting the maximum flushing length of the debris flow includes: performing principal component analysis PCA on the preprocessed data to obtain a feature data set after dimension reduction.

[0036] Specifically, principal component analysis (PCA) is a data dimensionality reduction algorithm. Its main idea is to map high-dimensional data to low-dimensional space through mathematical transformation, while retaining the structural variation characteristics in the data as much as possible, achieving dimensionality reduction of data features, thereby simplifying the data analysis process and reducing computational complexity.

[0037] Furthermore, the principal component analysis (PCA) of the preprocessed data includes:

[0038] Performing standardization on the preprocessed data to obtain standardized data;

[0039] Calculate the covariance matrix based on the standardized data, and perform eigenvalue decomposition based on the covariance matrix to obtain the eigenvalue;

[0040] According to the eigenvalue and contribution rate, the first several principal components are selected, and the preprocessed data are projected into the principal component space to obtain the feature data set after dimensionality reduction.

[0041] Furthermore, the process of training the maximum discharge distance prediction model of debris flow through the training set includes: obtaining the best hyperparameter combination through grid search combined with cross validation.

[0042] Specifically, select the appropriate kernel function and set the initial hyperparameters, use the reduced feature set and the corresponding maximum exit distance for training, set grid search and cross-validation to optimize the hyperparameters, search and evaluate the best hyperparameter combination, find the best hyperparameter combination, and select the best model configuration.

[0043] In this embodiment, the kernel function of the Gaussian process regression model is the GPRMatérn_3 / 2 kernel function.

[0044] The present invention is further described below with the river valley area located in the southeastern Qinghai-Tibet Plateau and the middle reaches of the Yarlung Zangbo River, between the Nyainqentanglha Mountains and the Himalayas as the research area. The area has a typical alpine canyon landform.

[0045] This embodiment selects the basic data of 31 debris flow gullies in the Milin section of the Yarlung Zangbo River as the research object, and uses the PCA-GPR model of this embodiment, i.e., the maximum outflow distance prediction model of the debris flow, to predict the dangerous range of the debris flow, i.e., the maximum outflow distance of the debris flow. Table 1 presents the basic data of each selected debris flow.

[0046] Table 1

[0047]

[0048] The calculation process of the maximum outflow distance prediction model of debris flow is as follows: Figure 1 As shown in the figure, the calculation process includes three basic steps: 1. Dimension reduction and principal component extraction of the original data set based on principal component analysis; 2. Training the preprocessed data set based on Gaussian process regression to obtain a prediction model for predicting the maximum flushing distance of debris flow; 3. PCA-GPR model prediction performance evaluation. The specific process is as follows:

[0049] 1) Data collection and preprocessing

[0050] Basic data of debris flow areas (including watershed area, watershed elevation difference, material reserve, average longitudinal slope, etc.) were collected, and variables that may affect the maximum length of debris flow were selected. The data were randomly divided into 80% training data sets and 20% test data sets. The data were cleaned, missing values ​​and outliers were processed to ensure data quality.

[0051] The premise of ensuring the performance of the maximum outflow distance prediction model of debris flow is that there must be sufficient correlation conditions between the target variable and the influencing factors, and whether it is reasonable. Therefore, it is necessary to test the correlation between the influencing factors. In order to verify the degree of correlation between the selected influencing factors and the maximum outflow distance of debris flow, the traditional grey correlation method, entropy method, and Person Pearson correlation coefficient method were adopted. The maximum outflow distance data of 31 debris flow gullies in the original data set were used as samples to analyze the correlation between each influencing factor and the maximum outflow distance of debris flow. In order to eliminate the dimension effect, the data in the sample were normalized, and the resolution coefficient was taken as ζ = 0.5 in the grey correlation calculation. The calculation results are shown in Table 2. It can be seen from Table 2 that in the grey correlation analysis, the values ​​of the four factors are all greater than 0.7, and it can be considered that the four influencing factors have a strong correlation with the maximum outflow distance of debris flow. In the entropy method analysis, the weight difference of the four influencing factors is very small, and it can be considered that each influencing factor will have different degrees of effect on the maximum outflow distance of debris flow. Based on Person's correlation analysis, it can be determined that the three factors of basin relative height difference, material source storage and average longitudinal slope have obvious correlation with the maximum outflow distance of debris flow. The three methods verify each other, indicating that the selected influencing factors are reasonable and have different degrees of correlation with the maximum outflow distance of debris flow.

[0052] Table 2

[0053]

[0054]

[0055] Note: ** indicates significant correlation at the 0.01 level (two-sided)

[0056] The results of Person analysis between the four influencing factors can be seen from Table 3. The Person correlation values ​​between the basin area and the source reserves, and the source reserves and the average longitudinal slope are large, and the Person correlation coefficients between the other influencing factors are all less than 0.5577, and the correlation is weak. Therefore, when selecting influencing factors that are as objective as possible, the principal component analysis method is used to reduce the impact of the correlation between the influencing factors. In addition, there are many factors that affect the maximum outflow distance of debris flows, such as debris flow velocity, topographic morphology of the accumulation area, etc. If the information of these parameters can be obtained, they can be considered as input parameters in the machine learning model, so as to reconstruct the maximum outflow distance prediction model of debris flows.

[0057] Table 3

[0058]

[0059] 2) Feature Dimensionality Reduction (PCA)

[0060] Based on the principal component analysis method, the selected data set is standardized to make its mean 0 and variance 1, the covariance matrix is ​​calculated, the eigenvalue decomposition is performed, and the first few principal components are selected. Usually, the components that can explain 85%-95% of the variance are selected. The original characteristic data (pre-processed basin area, basin elevation difference, material source reserves, average longitudinal slope drop) are projected into the principal component space to obtain the characteristic data set after dimensionality reduction.

[0061] To ensure that each data is on the same scale, the original data set is standardized and then the PCA method is used to reduce the dimension of the data set. The main calculation formulas of PCA are shown in formulas (1) to (3):

[0062] 1) Data standardization: The purpose of standardization is to eliminate the dimensional effects of different features. A common method is to subtract the mean of each feature and then divide it by the standard deviation so that the mean of each feature is 0 and the variance is 1.

[0063]

[0064] Where: X is the original data; μ is the mean of each column feature; σ is the standard deviation of each column feature; X′ is the processed data.

[0065] 2) Calculate the covariance matrix: The covariance matrix can reflect the relationship between different features.

[0066]

[0067] Where: X′ is the standardized data; n is the number of samples.

[0068] 3) Eigenvalue decomposition: The eigenvalue represents the variance of each principal component, and the eigenvector represents the direction of the principal component.

[0069] Cv=λv (3)

[0070] Where: v is the eigenvector; λ is the eigenvalue.

[0071] 4) Select principal components: Select the first k principal components based on the eigenvalue and contribution rate. Usually, the number of principal components that can explain enough variance is selected, such as selecting principal components that can explain 80%-95% of the variance.

[0072] The eigenvalues ​​and variance contribution rates of each relevant principal component are calculated from the values ​​of the four influencing factors in the selected 31 debris flow gullies, as shown in Table 4. The cumulative contribution rate of the first two principal components is 85.99%, which is higher than the generally required 85%, so the first two principal components can be used to represent the four principal components for subsequent analysis. The two selected principal components are rotated by the maximum variance method so that the values ​​of each row in each principal component load matrix can be polarized to the possible extent (close to 0 or ±1), so that the actual significance of the principal component can be determined. The proportion of the load matrix obtained after rotating the principal component using the maximum variance method is shown in the data in Table 5. The data in Table 5 show that the basin height difference (0.5555), material source reserves (0.6251) and average longitudinal slope (0.5460) have a large contribution (load) value in the first principal component, which can be defined as the PC1 condition; the basin area (0.8102) and the average longitudinal slope (-0.4261) have a large contribution value to the second principal component PC2. Therefore, the corresponding principal component set is defined as PC = [PC1, PC2] and is used as the input variable of the GPR model. After applying principal component analysis to the original data, the dimension of the original data is reduced from 4 to 2, and the two principal components represent the information of all influencing factors.

[0073] Table 4

[0074]

[0075] Table 5

[0076]

[0077] In order to verify the effectiveness of the PCA dimensionality reduction method for the original data in this model, the data before and after the PCA dimensionality reduction process were used as the input data of the GPR prediction model, and the same training and verification were performed. The performance evaluation indicators of the GPR model before and after the data were processed were compared. From the comparison results in Table 6, it can be seen that through the PCA dimensionality reduction process, the GPR prediction model is improved from R 2The value, RMSE, MAE and test time all have different improvements, indicating that PCA's dimensionality reduction processing of the original data not only retains the main influencing factor information, but also avoids the "dimensionality disaster" caused by high-dimensional data, improves computing efficiency, and speeds up model training and prediction. The model prediction results show that before the data is input into the model, it is very necessary to reduce the dimensionality of the original data and extract the principal components to improve the accuracy and prediction ability of the subsequent model.

[0078] Table 6

[0079]

[0080] Note: The model calculation time is based on the python3.12 platform of Intel i5_13500HX, 16GB_DDR5 memory and windows11_64 bit system

[0081] 3) Model construction (GPR)

[0082] Select an appropriate kernel function and set the initial hyperparameters. Use the reduced feature set and the corresponding maximum exit distance to train the prediction model based on Gaussian process regression (GPR). Set grid search and cross-validation to optimize hyperparameters to search and evaluate the best hyperparameter combination. Find the best hyperparameter combination and select the best model configuration.

[0083] Gaussian process is a random process defined on a continuous domain (such as time or space). Different from the traditional modeling method of directly determining the function form, when a function is defined by Gaussian process, a probability distribution is defined for the function, in which the joint probability distribution of any point is Gaussian distribution. In mathematical expression, Gaussian process can be completely determined by its mean function and covariance (kernel) function. The mean function describes the central tendency of the process, while the covariance function describes the similarity or correlation of the function values ​​between different input points. The calculation formulas of these functions are shown in equations (4) to (5):

[0084] 1) Mean function m(x): f(x) is the unknown function to be regressed, and m(x) is the mean of the function.

[0085]

[0086] 2) Covariance function k(x, x′): describes the correlation between the function at different input points x and x′, usually called the kernel function:

[0087] k(x,x′)=Cov(f(x),f(x′)) (5)

[0088] Gaussian process regression is a non-parametric Bayesian regression method that uses Gaussian processes to perform regression analysis on data. It uses the properties of Gaussian processes to model and predict input data through a specified kernel function. The prediction process of the GPR model involves calculating the posterior distribution of the function value of the new input data, and the posterior distribution is obtained through Bayesian updating based on the prior distribution and the training set data. Its mathematical expression is shown in equations (6) to (11):

[0089] Given a set of training data sets X = {x 1 , x 2 , ..., x n} and the corresponding output y={y 1 ,y 2 , ..., y n}, first define a Gaussian process prior distribution for f(x), and add Gaussian noise during observation:

[0090]

[0091] y=f(x)+ε (7)

[0092] Where: ε is the observation noise; it is usually assumed That is, it obeys the mean of 0 and the variance of Gaussian distribution.

[0093] Given training data X and its corresponding output y, we want to infer * The output y on * According to the Bayesian formula, the posterior distribution depends on the joint distribution of the prior distribution and the observed data. Therefore, the prior distribution of the training set can be obtained:

[0094]

[0095] Where: K(X, X) is the covariance matrix between training points; K(X, X * ) is the covariance matrix between the training points and the test points; K(X * , X * ) is the covariance matrix between the test points.

[0096] The output y can be calculated using the conditional Gaussian distribution * The posterior distribution of :

[0097]

[0098] Among them: Mean:

[0099]

[0100] variance:

[0101]

[0102] In Gaussian process regression, hyperparameters refer to the length scale that controls the smoothness of the kernel function and the variance of the noise term. The length scale in the kernel function changes the model's ability to fit the data, while the noise variance adjusts the model's bias and variance balance. The two hyperparameters jointly affect the model's final prediction accuracy and stability. In order to find the best hyperparameter combination for the GPR-based debris flow maximum outrush distance prediction model, a grid search combined with a cross-validation method was used to establish a hyperparameter grid, search for hyperparameter combinations, and evaluate model performance. The grid search creates a discrete value grid of hyperparameters, then traverses each combination to establish models with multiple different hyperparameter combinations, and uses cross-validation to evaluate the model performance of each hyperparameter combination. From the perspective of the algorithm principle, this grid search combined with the parameter optimization idea of ​​cross-validation can effectively explore the hyperparameter space to find the global optimal result, that is, the best hyperparameter combination, while avoiding falling into the local optimum. Through this systematic search, the model can be optimized in terms of generalization ability and comprehensive performance of reducing errors.

[0103] The 5-fold cross validation method is Figure 2 As shown in the figure, the specific process is as follows: Through 5-fold cross validation, the dataset is divided into 5 subsets. In each iteration, one subset is selected as the validation set and the rest as the training set. For each hyperparameter combination, the performance of the model on the validation set is calculated. Finally, the hyperparameter combination with the best performance among all folds is selected.

[0104] The performance of the GPR model depends on the length scale of the kernel function and the noise variance. Here, the RBF kernel function is taken as an example: In the grid search of this embodiment, a radial basis kernel (RBF) kernel function is set, and the length scale of the RBF kernel is 0.1 to 10.0. For the standard deviation of the noise, four different values ​​are set: 0.1, 0.01, 0.001, and 0.0001. These values ​​correspond to different assumptions about the noise in the model. Smaller values ​​make the model more sensitive to noise, while larger values ​​make the model more robust. Finally, the best performance hyperparameter combination is obtained by the average performance score of each cross-validation.

[0105] The core of the GPR model is to define a suitable kernel function. The kernel function calculates the similarity between input points, determines the correlation between input points, and the smoothness and complexity of the function. In order to compare the differences of the GPR model under different kernel functions, four different kernel functions, RBF, Matérn (v = 3 / 2, 5 / 2) and quadratic rational kernel function (RQard), were used to model the data set, and the performance of the model was evaluated by evaluation indicators to select a more effective kernel function. The performance evaluation indicators of the GPR prediction model for the maximum flushing distance of debris flow under different kernel functions are shown in Table 7:

[0106] Table 7

[0107]

[0108] Note: 3 / 2 represents the smoothness parameter v in the Matérn kernel function

[0109] Taking the GPR model under the Matérn_3 / 2 kernel function as an example, the posterior distribution of each test sample is as follows: Figure 3 As shown in the figure, the prediction result of each test sample is different from the single-point numerical prediction of the conventional model, but is a normal distribution in the form of probability. When the maximum discharge distance of the debris flow is larger or smaller, its normal distribution curve tends to be more "short and fat"; when the maximum discharge distance tends to the middle value, its normal distribution image tends to be "tall and thin", and the prediction probability tends to be closer to the mean. This is because the proportion of the maximum discharge distance of debris flow in the middle value in the training data set is relatively large. As the number of training samples in this area increases, the uncertainty of the prediction becomes smaller, and the image appears to be "tall and thin".

[0110] The prediction results of the GPR model for the maximum outflow distance of debris flow in the test set under the Matérn_3 / 2 kernel function are as follows: Figure 4 As shown. When the maximum outflow distance of the debris flow is large or small, its absolute error value tends to increase; when the maximum outflow distance tends to the middle value, its absolute error tends to decrease. This trend is due to the fact that the proportion of debris flow maximum outflow distance values ​​in the middle value is relatively large in the training data set. As the number of training samples in this area increases, the accuracy of the prediction results is better, that is, the absolute error is smaller, which is mutually complementary to the law of the posterior distribution in the previous article. In the GPR prediction model, most of the errors between the predicted values ​​of the GPR model based on the Matérn kernel function and the measured values ​​are distributed between 15% and 20%, which shows that the predicted values ​​of the GPR model are close to the measured values.

[0111] In summary, when the GPR model is used to predict the maximum discharge distance of debris flow, the GPR model based on the Matérn (v=3 / 2) kernel function has the best prediction ability, and while ensuring that the error is relatively minimal, the posterior distribution curve of the prediction result tends to be "tall and thin", indicating that the uncertainty of its prediction result is smaller and the prediction accuracy is greater. Therefore, the Matérn (v=3 / 2) kernel function is used to construct the GPR model of the maximum discharge distance of debris flow.

[0112] 4) Model Evaluation

[0113] In this model, several evaluation indicators are selected to evaluate the model performance, including root mean square error (RMSE), determination coefficient (R 2 ), mean square error (MAE) and other indicators to evaluate the model performance, and further analyze the model prediction ability by comparing it with other conventional machine learning algorithms.

[0114] In order to intuitively demonstrate the effectiveness of the maximum outflow distance prediction method of debris flow based on the Gaussian process regression (GPR) model in this embodiment, several common machine learning methods are used for comparative analysis, including K-nearest neighbor (KNN), support vector machine (SVM) and decision tree (DT). Since each algorithm contains one or more important hyperparameters, in order to find the best hyperparameter combination of the maximum outflow distance prediction model of debris flow and avoid errors and overfitting caused by data partitioning, the grid search and 5-fold cross validation method are used for hyperparameter optimization. The three evaluation indicators R of the five models on the test set are used as the evaluation index. 2 , RMSE and MAE are used as model optimization indicators, and a set of hyperparameter combinations with the best prediction effect is selected, and this hyperparameter combination is considered to be the optimal hyperparameter of the model. The hyperparameter search space and its optimal hyperparameters are shown in Table 8.

[0115] Table 8

[0116]

[0117] After determining the optimal hyperparameter combination, the maximum length prediction model of debris flow was established on the data set according to the optimal hyperparameters. 2 , RMSE, and MAE values ​​were used to evaluate the predictive ability of the selected model through quantitative analysis, as shown in Table 9.

[0118] Table 9

[0119]

[0120] In the maximum outflow distance prediction model of debris flow, the R 2The value is 0.6676, which is the highest among all models, indicating that the model can explain 67.76% of the variation proportion of the output variable and fit the data well. In contrast, the R 2 It is only 0.4575, indicating that SVM has a lower ability to explain the variation ratio of the output variable; the RMSE of PCA-GPR (Matérn_3 / 2) and KNN are 0.1049 and 0.1031 respectively, which are very close and the lowest among all models, indicating that both PCA-GPR (Matérn_3 / 2) and KNN have higher prediction accuracy, and the deviation between their predicted values ​​and actual values ​​is smaller; the MAE of PCA-GPR (Matérn_3 / 2) is 0.0949, which is at a low level among all models, but the MAE of KNN is even lower, only 0.0767, indicating that KNN has a smaller deviation in the absolute error between the predicted value and the actual value than PCA-GPR (Matérn_3 / 2), and may be more stable on some data points.

[0121] By comprehensively comparing the values ​​of the three indicators, it can be seen that PCA-GPR (Matérn_3 / 2) is better than KNN in explaining the changes in the output variables, while the two are similar in overall prediction performance. The difference is that the prediction results of the GPR model are different from the single numerical prediction of the conventional prediction model, but a probability distribution form that can simultaneously provide the prediction results and quantify the uncertainty of the prediction results. For the problem of predicting the maximum run-out distance of debris flow, which is affected by multiple factors and has strong uncertainty, the GPR prediction model can better explain the uncertainty in the prediction results of the maximum run-out distance of debris flow than the conventional machine learning model.

[0122] This embodiment further provides a storage medium, the storage medium includes a stored program, wherein the prediction method is executed when the program is run.

[0123] This embodiment further provides a processor, which is used to run a program, wherein the prediction method is executed when the program is running.

[0124] The embodiments described above are only descriptions of the preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the design spirit of the present invention, various modifications and improvements made to the technical solutions of the present invention by ordinary technicians in this field should all fall within the protection scope determined by the claims of the present invention.

Claims

1. A method for predicting the maximum discharge distance of debris flow based on PCA-GPR, characterized in that: include: Obtain the influencing factors of the maximum outflow distance of debris flow in the target area; The influencing factors are input into a debris flow maximum rushing out distance prediction model to obtain a probability distribution prediction result of the debris flow maximum rushing out distance, wherein the debris flow maximum rushing out distance prediction model is constructed based on a Gaussian process regression model GPR and is obtained through training with a training set, wherein the training set is a data set including factors affecting the maximum rushing out length of the debris flow and the corresponding maximum rushing out distance, and before training, the factors affecting the maximum rushing out length of the debris flow are subjected to dimensionality reduction processing.

2. The method for predicting the maximum discharge distance of debris flow based on PCA-GPR according to claim 1, characterized in that: The influencing factors include basin area, basin elevation difference, material source reserves, and average longitudinal slope.

3. The method for predicting the maximum flushing distance of debris flow based on PCA-GPR according to claim 1, characterized in that: Before the dimension reduction processing is performed on the factors that affect the maximum flushing length of the debris flow, the method also includes: cleaning the factors that affect the maximum flushing length of the debris flow, processing missing values ​​and abnormal values, and obtaining pre-processed data.

4. The method for predicting the maximum flushing distance of debris flow based on PCA-GPR according to claim 3, characterized in that: The dimension reduction processing of the factors affecting the maximum flushing length of the debris flow includes: performing principal component analysis PCA on the pre-processed data to obtain the feature data set after dimension reduction.

5. The method for predicting the maximum discharge distance of debris flow based on PCA-GPR according to claim 4, characterized in that: Performing principal component analysis (PCA) on the preprocessed data includes: Performing standardization on the preprocessed data to obtain standardized data; Calculating a covariance matrix according to the standardized data, and performing eigenvalue decomposition according to the covariance matrix to obtain eigenvalues; The first several principal components are selected according to the eigenvalues ​​and contribution rates, and the preprocessed data are projected into the principal component space to obtain a feature data set after dimensionality reduction.

6. The method for predicting the maximum discharge distance of debris flow based on PCA-GPR according to claim 1, characterized in that: The training set process of the debris flow maximum flushing distance prediction model includes: obtaining the best hyperparameter combination through grid search combined with cross validation.

7. The method for predicting the maximum flushing distance of debris flow based on PCA-GPR according to claim 1, characterized in that: The kernel function used in the Gaussian process regression model is the Matérn_3 / 2 kernel function.

8. A storage medium, characterized in that: The storage medium includes a stored program, wherein the program executes the method according to any one of claims 1 to 7 when executed.

9. A processor, characterized in that: The processor is used to run a program, wherein the program executes the method according to any one of claims 1 to 7 when running.

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