Burst type landslide grading early warning method

Abstract

The invention provides a sudden landslide grading early warning method, and belongs to the technical field of landslide early warning, and the method comprises the steps: calculating the speed and acceleration through a central difference method; setting a fixed-time sliding window, and dividing data of a current window and historical windows; an expected trend direction is determined through displacement changes, and multi-dimensional statistical testing including abnormal value testing, variance testing and distribution offset testing is carried out on speed and acceleration data in sequence; determining a low-level early warning level based on the significance level of each test; and further introducing a basic window comparison mechanism, and dynamically comparing the current window with the basic window to judge a high-level early warning level so as to construct a burst type landslide grading early warning model. According to the method, the accelerated deformation stage of the landslide can be accurately identified, the timeliness and accuracy of early warning are remarkably improved, the process is clear, calculation is efficient, and core technical support can be provided for intelligent and refined early warning decision making of a geological disaster monitoring and early warning system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of landslide early warning, and particularly relates to a sudden landslide grading early warning method. BACKGROUND

[0002] Landslide disasters seriously threaten people's life and property safety and the safe operation of major projects. Its accurate early warning has always been a core problem in the field of geological disaster prevention. Traditional monitoring and early warning methods mostly rely on the threshold setting of single indicators such as displacement and speed, which is difficult to effectively capture the nonlinear and non-stationary characteristics in the evolution process of landslides. Moreover, the fixed early warning threshold is easily disturbed by geological conditions and external environment, leading to false positives or false negatives. With the progress of monitoring technology, high-frequency and continuous displacement sequences provide a data basis for in-depth analysis of landslide dynamic process. However, how to extract effective and precursor statistical features from these data and build an early warning model that can adapt to data changes and scientifically reflect the accelerating evolution trend of landslides has become the key to current research.

[0003] In recent years, although patent technology innovation has tried to break through the above bottleneck, there are still key limitations: such as a landslide prediction method and system based on multi-source data fusion (CN202510877489.9), which improves the prediction ability by fusing multi-source data and constructing high-order statistics, but the preset danger threshold still lacks dynamic adaptability; a landslide early warning method combined with slope radar visual perception technology (CN202510277477.2), which uses deep learning to enhance feature recognition capability, but there is a monitoring blind area in bad weather, and the real-time early warning capability of landslides still faces challenges; a landslide early warning method based on the kinetic energy change rate of creep-type landslides (CN202111606875.2), which improves the accuracy of kinetic energy change rate prediction through multi-source data fusion and optimization algorithm, but its early warning capability is highly dependent on the integrity of historical data.

[0004] Therefore, it is urgent to build an early warning model that combines multi-dimensional statistical testing, dynamic identification of non-stationary mutation characteristics of displacement sequence, and accurate grading. SUMMARY

[0005] In view of the deficiencies of the prior art, the present application provides a sudden landslide grading early warning method.

[0006] The present application provides a sudden landslide grading early warning method, which comprises:

[0007] Step S1: collecting displacement data of the slope monitoring equipment as the original input data of the sudden landslide grading early warning model;

[0008] Step S2: according to the sampling frequency of the original input data, the central difference method is used to solve the speed and acceleration of the slope;

[0009] Step S3: setting the window size of the speed and the window size of the acceleration, and solving the sample capacity of the window of the speed and the window of the acceleration according to the window size of the speed, the window size of the acceleration and the sampling interval of the original input data;

[0010] Step S4: obtaining the current displacement data and the initial displacement data from the original input data, calculating the difference between the current displacement data and the initial displacement data, the positive difference corresponding to the expected positive trend and the negative difference corresponding to the expected negative trend, and the preset expected trend being the expected positive trend or the expected negative trend;

[0011] Step S5: performing the first multidimensional statistical test between each current window of the speed and the historical window of the speed, and between each current window of the acceleration and the historical window of the acceleration according to the sample capacity of the window of the speed and the window of the acceleration and the preset expected trend, to obtain the first speed outlier test p-value, the first speed variance test p-value, the first speed distribution deviation test p-value, the first acceleration outlier test p-value, the first acceleration variance test p-value and the first acceleration distribution deviation test p-value, and the first multidimensional statistical test including the outlier test, the variance test and the distribution deviation test;

[0012] Step S6: constructing the third-level graded early warning model of the sudden landslide and the fourth-level graded early warning model of the sudden landslide according to the statistical results of the first multidimensional statistical test, and the third-level graded early warning model of the sudden landslide including that the first acceleration outlier test p-value, the first acceleration variance test p-value and the first acceleration distribution deviation test p-value are all less than the preset threshold, and the third-level early warning information is output, and the fourth-level graded early warning model of the sudden landslide including that the first acceleration outlier test p-value is less than the preset threshold and the first acceleration variance test p-value is less than the preset threshold, or the first acceleration outlier test p-value is less than the preset threshold and the first acceleration distribution deviation test p-value is less than the preset threshold, or the first acceleration variance test p-value is less than the preset threshold and the first acceleration distribution deviation test p-value is less than the preset threshold, and the fourth-level early warning information is output;

[0013] Step S7: when the third-level early warning information or the fourth-level early warning information is output, taking the window index of the moment corresponding to the first output early warning information as the end point, selecting all historical speeds and historical accelerations before the early warning information as a candidate window set, selecting the candidate window with the smallest variance as a basic window, and performing the second multidimensional statistical test between each current window and the basic window to obtain the second speed outlier test p-value, the second speed variance test p-value, the second speed distribution deviation test p-value, the second acceleration outlier test p-value, the second acceleration variance test p-value and the second acceleration distribution deviation test p-value;

[0014] Step S8: Based on the statistical results of the first and second multidimensional statistical tests, construct a first-level and second-level graded early warning model for sudden landslides. The first-level graded early warning model includes: a first acceleration outlier test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than a preset threshold. Furthermore, if the second acceleration outlier test p-value, the second acceleration variance test p-value, the second acceleration distribution shift test p-value, the second velocity outlier test p-value, the second velocity variance test p-value, and the second velocity distribution shift test p-value are all less than preset thresholds, then output the first-level early warning information. The second-level graded early warning model includes: a first acceleration outlier test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than preset thresholds. Furthermore, the second acceleration outlier test p-value, the second acceleration variance test p-value, and the second acceleration distribution shift test p-value are all less than preset thresholds.

[0015] The outlier detection includes:

[0016] Step S5.1.1: Based on the velocity window and the acceleration window, calculate the median of the current velocity window, the median of the historical velocity window, the median of the current acceleration window, and the median of the historical acceleration window, and calculate the difference between the medians of the current velocity window and the historical velocity window, and the difference between the medians of the current acceleration window and the historical acceleration window.

[0017] Step S5.1.2: If the median difference between the current window of velocity and the historical window of velocity, and the median difference between the current window of acceleration and the historical window of acceleration are consistent with the sign of the preset expected trend, then continue to execute step S5.1.3; otherwise, do not continue to execute the subsequent steps.

[0018] Step S5.1.3: Sort the current window of velocity and the historical window of velocity in ascending order of velocity to obtain the current sorted velocity sequence and the historical sorted velocity sequence. Sort the current window of acceleration and the historical window of acceleration in ascending order of velocity to obtain the current sorted acceleration sequence and the historical sorted acceleration sequence.

[0019] Step S5.1.4: Based on the current sorted velocity sequence, the historical sorted velocity sequence, the current sorted acceleration sequence, and the historical sorted acceleration sequence, calculate the first observed statistics of velocity and acceleration, using the following formulas:

[0020] ;

[0021] ;

[0022] in, The first observed statistic of velocity, This is the current sorted velocity sequence. The velocity sequence after historical sorting. The median of the historical window of speed. Here, is the median of the current window of velocity, and quantile() is the quantile calculation function. The first observed statistic of acceleration, This is the current sorted acceleration sequence. The acceleration sequence is sorted according to history. The median of the historical window of acceleration. The median of the current window's acceleration;

[0023] Step S5.1.5: Based on the first observed statistic of velocity and the first calculated observed statistic of acceleration, the significance of the calculated statistic is determined by the permutation test, and the p-values ​​of the first velocity outlier test and the first acceleration outlier test are obtained.

[0024] The step of calculating the significance of the statistics based on the first observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​for the first velocity outlier test and the first acceleration outlier test includes:

[0025] Step S5.1.4.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0026] Step S5.1.4.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset;

[0027] Step S5.1.4.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0028] Step S5.1.4.4: Based on the data length of the current velocity window and the historical velocity window, split the rearranged velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, split the rearranged acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation;

[0029] Step S5.1.4.5: Calculate the median of the current window of the velocity after displacement based on the current window of the velocity after displacement; calculate the median of the historical window of the velocity after displacement based on the historical window of the velocity after displacement; calculate the median of the current window of the acceleration after displacement based on the current window of the acceleration after displacement; calculate the median of the historical window of the acceleration after displacement based on the historical window of the acceleration after displacement.

[0030] Step S5.1.4.6: Calculate the first permutation statistic for velocity based on the median of the current window of the permuted velocity and the median of the historical windows of the permuted velocity; calculate the first permutation statistic for acceleration based on the median of the current window of the permuted acceleration and the median of the historical windows of the permuted acceleration, using the following formula:

[0031] ;

[0032] ;

[0033] in, The first permutation statistic for velocity, Let be the first permutation statistic of acceleration, and quantile() be the quantile calculation function. The median of the velocity in the current window after the permutation. The median of the historical velocity window after the replacement; The median of the acceleration in the current window after the permutation. The median of the historical window of acceleration after the replacement. For the current window of the velocity after the displacement, For the historical window of the velocity after the replacement, For the current window of the displacement acceleration, This is the historical window of acceleration after the displacement;

[0034] Step S5.1.4.7: Repeat steps S5.1.4.3 to S5.1.4.6 to calculate the first permutation statistic of the Nth velocity and the first permutation statistic of the Nth acceleration;

[0035] Step S5.1.4.8: Based on the first permutation statistic of N velocities, the first permutation statistic of N accelerations, the first observation statistic of velocity, and the first observation statistic of acceleration, calculate the significance level and obtain the p-value for the outlier test of the first velocity and the p-value for the outlier test of the first acceleration.

[0036] The variance test includes:

[0037] Step S5.2.1: Calculate the range of velocity data in the current window based on the current velocity window; calculate the range of velocity data in the historical window based on the historical velocity window; calculate the range of acceleration data in the current window based on the current acceleration window; calculate the range of acceleration data in the historical acceleration window based on the historical acceleration window.

[0038] Step S5.2.1: Calculate the second observed statistic of velocity based on the range of the current window velocity data and the range of the historical window velocity data; calculate the second observed statistic of acceleration based on the range of the current window acceleration data and the range of the historical window acceleration data, using the following formula:

[0039] ; ;

[0040] in, This is the second observed statistic of velocity. The second observed statistic of acceleration, This represents the range of the current window speed data. The range of historical window speed data, The range of the current window's acceleration data. The range of historical acceleration data;

[0041] Step S5.2.3: Based on the second observed statistics of velocity and acceleration, the significance of the statistics is calculated using the permutation test to obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

[0042] The step of calculating the significance of the statistics based on the second observed statistics of velocity and the second observed statistics of acceleration using a permutation test to obtain the p-values ​​of the first velocity variance test and the first acceleration variance test includes:

[0043] Step S5.2.3.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0044] Step S5.2.3.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset;

[0045] Step S5.2.3.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0046] Step S5.2.3.4: Based on the data length of the current velocity window and the historical velocity window, rearrange the velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, rearrange the acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation.

[0047] Step S5.2.3.5: Based on the current window of the velocity after displacement, calculate the difference between the maximum and minimum values ​​of the current window of the velocity after displacement; based on the historical window of the velocity after displacement, calculate the difference between the maximum and minimum values ​​of the historical window of the velocity after displacement; based on the current window of the acceleration after displacement, calculate the difference between the maximum and minimum values ​​of the current window of the acceleration after displacement; based on the historical window of the acceleration after displacement, calculate the difference between the maximum and minimum values ​​of the historical window of the acceleration after displacement.

[0048] Step S5.2.3.6: Calculate the second permutation statistic for velocity based on the difference between the maximum and minimum values ​​of the current window of the permuted velocity and the difference between the maximum and minimum values ​​of the historical window of the permuted velocity; calculate the second permutation statistic for acceleration based on the difference between the maximum and minimum values ​​of the current window of the permuted acceleration and the difference between the maximum and minimum values ​​of the historical window of the permuted acceleration, using the following formula:

[0049] ;

[0050] ;

[0051] in, The second permutation statistic for velocity, The second permutation statistic for acceleration, The difference between the maximum and minimum values ​​of the velocity in the current window after the replacement. The difference between the maximum and minimum values ​​of the historical velocity after the replacement. This is the difference between the maximum and minimum values ​​of the current window's acceleration after the displacement. This is the difference between the maximum and minimum values ​​of the historical acceleration after the displacement.

[0052] Step S5.2.3.7: Repeat steps S5.2.3.1 to S5.2.3.6 to calculate the second permutation statistic of the Nth velocity and the second permutation statistic of the Nth acceleration;

[0053] Step S5.2.3.8: Based on the second permutation statistic of N velocities, the second permutation statistic of N accelerations, the second observation statistic of velocity, and the second observation statistic of acceleration, calculate the significance level and obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

[0054] The distribution shift test includes:

[0055] Step S5.3.1: Calculate the median velocity of the current window based on the current velocity window; calculate the median velocity of the historical windows based on the historical velocity windows; calculate the median acceleration of the current window based on the current acceleration window; calculate the median acceleration of the historical windows based on the historical acceleration windows.

[0056] Step S5.3.2: Calculate the difference between the median of the current window velocity and the median of the historical window velocity; calculate the difference between the median of the current window acceleration and the median of the historical window acceleration.

[0057] Step S5.3.3: If the median difference between the current velocity and the historical window velocity, and the median difference between the current acceleration and the historical window velocity are both consistent with the pre-set expected trend, proceed to step S5.3.4 to continue the anomaly determination of the distribution offset test; otherwise, directly determine "no anomaly" and do not proceed to the next step.

[0058] Step S5.3.4: Calculate the observation statistics based on the current window of velocity, the historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration.

[0059] Step S5.3.5: Based on the third observation statistic of velocity and the third observation statistic of acceleration, use the permutation test to calculate the significance of the statistics, and obtain the p-value of the first velocity distribution shift test and the p-value of the first acceleration distribution shift test.

[0060] The observation statistics are calculated based on the current window of velocity, the historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration. The calculation formula is as follows:

[0061] ; ;

[0062] ; ;

[0063] ; ;

[0064] ; ;

[0065] ; ;

[0066] ; ;

[0067] in, The third observational statistic for velocity, The third observational statistic for acceleration, This represents the extreme value of the speed within the historical window. This represents the extreme value of acceleration within the historical window. The velocity sequences of the historical windows are sorted in ascending order to form a new sequence. The acceleration sequences of the historical window are sorted in ascending order to form a new sequence. This is the median of historical window speeds. The median of the current window speed. The median of historical window acceleration. The median of the current window acceleration. The five data points closest to the end of the current window are the current window speed. The acceleration of the current window is represented by the 5 data points closest to the end of the window, and mean() is the average value function. The latest velocity is the data point at the very end of the current window. The latest acceleration is the data point at the very end of the current window's acceleration. The current window speed is the k-th data point closest to the end of the window. The acceleration of the current window is the k-th data point closest to the end of the window. For the most recent data points at the end that are greater than or less than the historical extreme threshold, For acceleration data points in the most recent data that are greater than or less than the historical extreme threshold, quantile() is the quantile calculation function. , where is the average offset of the current window's velocity outliers. The standard deviation of the historical window speed data. This represents the average offset of the current window's acceleration outliers. The standard deviation of historical acceleration data. For the j-th speed data point within the historical window, This is the average of historical window speed data. For the j-th acceleration data point within the historical window, is the average value of historical acceleration data within the window, and n is the number of data points within the window.

[0068] The step of calculating the significance of the statistics based on the third observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​of the first velocity distribution shift test and the first acceleration distribution shift test includes:

[0069] Step S5.3.5.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0070] Step S5.3.5.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset;

[0071] Step S5.3.5.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0072] Step S5.3.5.4: Based on the data length of the current velocity window and the historical velocity window, rearrange the velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, rearrange the acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation.

[0073] Step S5.3.5.4: Sort the values ​​in the current window of the replaced velocity from smallest to largest to obtain the sorted current velocity sequence; sort the values ​​in the historical window of the replaced velocity from smallest to largest to obtain the sorted historical velocity sequence; sort the values ​​in the current window of the replaced acceleration from smallest to largest to obtain the sorted current acceleration sequence; sort the values ​​in the historical window of the replaced acceleration from smallest to largest to obtain the sorted historical acceleration sequence.

[0074] Step S5.3.5.5: Calculate the median of the sorted current velocity sequence based on the sorted current velocity sequence; obtain the median of the sorted historical velocity sequence based on the sorted historical velocity sequence; calculate the median of the sorted current acceleration sequence based on the sorted current acceleration sequence; calculate the median of the sorted historical acceleration sequence based on the sorted historical acceleration sequence.

[0075] Step S5.3.5.6: Calculate the extreme values ​​of velocity in the historical window after replacement based on the historical velocity window after replacement; calculate the extreme values ​​of acceleration in the historical window after replacement based on the historical acceleration window after replacement.

[0076] Step S5.3.5.6: Based on the current window of the replaced velocity, select the last 5 consecutive velocity data points of the current window of the replaced velocity; based on the current window of the replaced acceleration, select the last 5 consecutive acceleration data points of the current window of the replaced acceleration.

[0077] Step S5.3.5.7: Based on the extreme values ​​of velocity and acceleration in the historical window after permutation, the five consecutive velocity data points at the end, and the five consecutive acceleration data points at the end, calculate the third permutation statistic of velocity and the third permutation statistic of acceleration.

[0078] Step S5.3.5.8: Based on the third permutation statistic of velocity, the third permutation statistic of acceleration, the third observation statistic of velocity, and the third observation statistic of acceleration, the significance of the statistics is calculated using the permutation test, and the p-values ​​of the first acceleration distribution shift test and the first velocity distribution shift test are obtained.

[0079] The third permutation statistic for velocity and the third permutation statistic for acceleration are calculated based on the extreme values ​​of velocity and acceleration in the historical window after permutation, the last five consecutive velocity data points, and the last five consecutive acceleration data points. The calculation formulas are as follows:

[0080] ; ;

[0081] ; ;

[0082] ; ;

[0083] ;

[0084] ;

[0085] in, This is the third permutation statistic for velocity. The third permutation statistic for acceleration, The extreme values ​​of the historical window speed after the replacement. The extreme values ​​of historical window acceleration after replacement. Five consecutive velocity data points at the end. For the last 5 consecutive acceleration data points, This represents the kth consecutive velocity data point at the end of the current window after the replacement. This represents the kth consecutive acceleration data point at the end of the current window after the replacement. These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. This represents the average offset of the current window velocity outliers after the replacement. The standard deviation of the historical window speed data after replacement. This represents the average offset of the current window's acceleration outliers after the replacement. The standard deviation of the historical window acceleration data after permutation. For the j-th velocity data within the replaced historical window, The average value of the historical window speed data after replacement. For the j-th acceleration data point within the replaced historical window, This represents the average value of the historical window acceleration data after the replacement.

[0086] Beneficial effects:

[0087] This application proposes a graded early warning method for sudden landslides. It calculates velocity and acceleration using the central difference method; sets a fixed-duration sliding window to divide the data into current and historical windows; determines the expected trend direction through displacement changes; and sequentially performs multidimensional statistical tests on the velocity and acceleration data, including outlier tests, variance tests, and distribution shift tests. Based on the significance level of each test, it determines the low-level early warning level (Level 4 graded early warning model, Level 3 graded early warning model); further, it introduces a basic window comparison mechanism, dynamically comparing the current window with the basic window to determine the high-level early warning level (Level 2 graded early warning model, Level 1 graded early warning model), thereby constructing a graded early warning model for sudden landslides. This method can accurately identify the accelerated deformation stage of landslides, significantly improving the timeliness and accuracy of early warnings. Furthermore, it has a clear process and high computational efficiency, providing core technical support for intelligent and refined early warning decision-making in geological disaster monitoring and early warning systems. Attached Figure Description

[0088] Figure 1 Flowchart of a sudden landslide classification and early warning method according to an embodiment of the present invention;

[0089] Figure 2 A schematic diagram of a sudden landslide classification and early warning method according to an embodiment of the present invention;

[0090] Figure 3 A diagram showing the graded early warning results of an embodiment of the present invention. Detailed Implementation

[0091] The specific implementation methods of this application will be further described in detail below with reference to the accompanying drawings and embodiments.

[0092] In existing technologies, multi-source data are typically fused and higher-order statistics are constructed to improve predictive capabilities, but their preset danger thresholds still lack dynamic adaptability; some methods have monitoring blind spots under severe weather conditions or are highly dependent on the completeness of historical data. This application proposes a sudden landslide classification and early warning method that can dynamically and accurately identify the accelerated deformation stage of landslides, significantly improving the timeliness and accuracy of early warnings, and does not rely on the completeness of historical data, thus eliminating monitoring blind spots under severe weather conditions.

[0093] This application proposes a method for graded early warning of sudden landslides, integrating outlier testing, variance testing, and distribution shift testing. When these three methods are used independently, they often struggle to handle the complex signals in landslide early warning systems. For example, outlier testing may miss some abrupt changes, variance testing only captures increased data fluctuations, and distribution shift testing focuses on changes in statistical distribution. Using these three methods alone is insufficient to comprehensively determine whether a true catastrophic abrupt change has occurred. This application effectively integrates these three methods: outlier testing acts as a "trigger," rapidly scanning data to identify prominent outliers and providing an initial warning for subsequent diagnosis; variance testing and distribution shift testing act as "discriminators," helping to analyze more deeply whether the anomaly is systematic, i.e., whether it is a sudden event or merely localized random fluctuations; and a "confirmation" mechanism based on a baseline window comparison confirms whether the anomaly pattern truly reflects a systematic change and further determines its threatening nature. Each test leverages its strengths, complementing and working together.

[0094] Existing landslide early warning methods typically rely on simple threshold settings or complex machine learning models for rapid response to abrupt change signals. These methods often fail to respond to abrupt change signals in real time and effectively, especially when data fluctuates significantly, and are prone to false alarms or missed alarms. The method in this application, however, rapidly detects abrupt change signals through outlier detection, providing early warnings.

[0095] The method presented in this application can effectively distinguish between "harmless fluctuations" and "harmful mutations": unlike traditional simple threshold methods, this method combines variance tests and distribution shift tests, which can effectively identify systematic changes in data and determine whether a true state transition has occurred. This hierarchical response mechanism allows early warning to go beyond simply detecting mutation signals; it can further assess the severity of mutation signals and make more scientific and evidence-based judgments by comparing the results of the current window with historical and baseline window data.

[0096] Traditional landslide early warning methods typically involve noise reduction of the data and function fitting to capture trend changes, often ignoring potential signals within the noise. This application, however, performs data analysis directly without noise removal, employing statistical testing methods, fundamentally breaking through the limitations of traditional thinking. The method in this application does not rely on any form of fitting; instead, it extracts key information directly from the original data by calculating statistical significance.

[0097] Compared with traditional mutation signal identification methods: Traditional mutation signal identification methods usually rely on simple threshold settings or single outlier detection, which are prone to producing a high false alarm rate.

[0098] Example 1:

[0099] This embodiment provides a method for graded early warning of sudden landslides, such as... Figure 1 , Figure 2 The following are included:

[0100] Step S1: Collect displacement data from slope monitoring equipment as the raw input data for the sudden landslide classification and early warning model;

[0101] In this embodiment, displacement data is collected from the slope monitoring equipment as the raw input data, which is a portion of the raw input data.

[0102] Step S2: Based on the sampling frequency of the original input data, use the central difference method to solve for the velocity and acceleration of the slope;

[0103] In this embodiment, the slope velocity is calculated using the following formula: ;

[0104] Among them, v i For the i-th velocity, d i Let $i$ be the i-th displacement data, $i = 1, 2, 3, ..., m$, where $m$ is the total number of displacement data and $∆t$ is the displacement data time interval, i.e., the sampling interval of the original input data.

[0105] The acceleration of the slope is calculated using the following formula: ;

[0106] Among them, a i Let m be the i-th acceleration, i = 1, 2, 3, ..., m.

[0107] Step S3: Set the window size for velocity and the window size for acceleration. Based on the window size for velocity, the window size for acceleration, and the sampling interval of the original input data, calculate the sample capacity of the velocity window and the acceleration window.

[0108] In this embodiment, the window size for both velocity and acceleration is set to 24h. Based on the sampling interval ∆t of the original input data, the sample capacity n for solving the velocity and acceleration windows is: ;

[0109] The velocity and acceleration data windows are as follows:

[0110] ;

[0111] ;

[0112] Where i ≥ 2n, For the current window dataset of the i-th velocity, This is the current window dataset for the i-th acceleration data. For the historical window dataset of the i-th speed, Let be the historical window dataset for the i-th acceleration data.

[0113] Step S4: Obtain the current displacement data and initial displacement data from the original input data, calculate the difference between the current displacement data and the initial displacement data. If the difference is positive, it corresponds to the expected positive trend; if the difference is negative, it corresponds to the expected negative trend. The preset expected trend is either the expected positive trend or the expected negative trend.

[0114] In this embodiment, the displacement data d is calculated. i The difference between the initial displacement d0 and the expected trend direction is determined. A positive difference corresponds to a positive expected trend, while a negative difference corresponds to a negative expected trend.

[0115] At this point, the expected trend needs to be preset as either a positive or negative trend.

[0116] Step S5: Based on the sample size of the velocity window and the acceleration window, and the preset expected trend, perform the first multidimensional statistical test between the current window of each velocity and the historical window of velocity, and between the current window of each acceleration and the historical window of acceleration, to obtain the p-values ​​for the first velocity outlier test, the first velocity variance test, the first velocity distribution shift test, the first acceleration outlier test, the first acceleration variance test, and the first acceleration distribution shift test. The first multidimensional statistical test includes: outlier test, variance test, and distribution shift test.

[0117] Step S6: Based on the statistical results of the first multidimensional statistical test, construct a third-level and a fourth-level early warning model for sudden landslides. The third-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test, the first acceleration variance test, and the first acceleration distribution shift test are all less than preset thresholds, then output third-level early warning information. The fourth-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test and the first acceleration variance test are both less than preset thresholds, or if the p-values ​​of the first acceleration anomaly test and the first acceleration distribution shift test are both less than preset thresholds, or if the p-values ​​of the first acceleration variance test and the first acceleration distribution shift test are both less than preset thresholds, then output fourth-level early warning information.

[0118] Step S7: After outputting the third-level or fourth-level warning information, take the window index corresponding to the first output warning information as the endpoint, select all historical velocities and historical accelerations before the warning information occurred as a candidate window set, select the candidate window with the smallest variance as the base window, and perform a second multidimensional statistical test between each current window and the base window to obtain the p-values ​​for the second velocity outlier test, the second velocity variance test, the second velocity distribution offset test, the second acceleration outlier test, the second acceleration variance test, and the second acceleration distribution offset test.

[0119] Step S8: Based on the statistical results of the first and second multidimensional statistical tests, construct a first-level and second-level graded early warning model for sudden landslides. The first-level graded early warning model includes: a first acceleration outlier test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than a preset threshold. Furthermore, if the second acceleration outlier test p-value, the second acceleration variance test p-value, the second acceleration distribution shift test p-value, the second velocity outlier test p-value, the second velocity variance test p-value, and the second velocity distribution shift test p-value are all less than preset thresholds, then output the first-level early warning information. The second-level graded early warning model includes: a first acceleration outlier test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than preset thresholds. Furthermore, the second acceleration outlier test p-value, the second acceleration variance test p-value, and the second acceleration distribution shift test p-value are all less than preset thresholds.

[0120] The outlier detection evaluates the speed of the current window compared to historical windows. , ), Current window vs. history window acceleration ( , Are there any outliers, including:

[0121] Step S5.1.1: Based on the velocity window and the acceleration window, calculate the median of the current velocity window, the median of the historical velocity window, the median of the current acceleration window, and the median of the historical acceleration window, and calculate the difference between the medians of the current velocity window and the historical velocity window, and the difference between the medians of the current acceleration window and the historical acceleration window.

[0122] In this embodiment, the median of the current and historical windows of velocity and acceleration data is calculated:

[0123] ; ;

[0124] ; ;

[0125] ;

[0126] ; ;

[0127] in, The median of the speed in the current window. The median of the historical window of speed. The median of the current window's acceleration. B is the median of the historical acceleration window, and median() is the median function; m To find the sequence; b k To find the sequence B m The k-th value after sorting in ascending order; m is the number of samples in the sequence; β v β is the median difference between the current window of velocity and the historical windows of velocity; a This is the median difference between the current window of acceleration and the historical windows of acceleration.

[0128] Step S5.1.2: If the median difference between the current window of velocity and the historical window of velocity, and the median difference between the current window of acceleration and the historical window of acceleration are consistent with the sign of the preset expected trend, then continue to execute step S5.1.3; otherwise, do not continue to execute the subsequent steps.

[0129] In this embodiment, the median difference β between the current window of speed and the historical window of speed is... v The median difference β between the current window of acceleration and the historical window of acceleration. aIf the direction of the expected trend preset in step S4 is the same, the subsequent steps for judging outliers are executed; otherwise, it is directly judged as "no outlier" and the subsequent steps are not executed.

[0130] Step S5.1.3: Sort the current window of velocity and the historical window of velocity in ascending order of velocity to obtain the current sorted velocity sequence and the historical sorted velocity sequence. Sort the current window of acceleration and the historical window of acceleration in ascending order of velocity to obtain the current sorted acceleration sequence and the historical sorted acceleration sequence.

[0131] In this embodiment, the speed sequences of the current window and the history window ( , Sort them in ascending order to form a new sequence. , ; The acceleration sequence of the current window and the history windows ( , Sort them in ascending order to form a new sequence. , .

[0132] Step S5.1.4: Based on the current sorted velocity sequence, the historical sorted velocity sequence, the current sorted acceleration sequence, and the historical sorted acceleration sequence, calculate the first observed statistics of velocity and acceleration, using the following formulas:

[0133] ;

[0134] ;

[0135] ;

[0136] ; ; ; ;

[0137] in, The first observed statistic of velocity, This is the current sorted velocity sequence. The velocity sequence after historical sorting. The median of the historical window of speed. Here, is the median of the current window of velocity, and quantile() is the quantile calculation function. The first observed statistic of acceleration, This is the current sorted acceleration sequence. The acceleration sequence is sorted according to history. The median of the historical window of acceleration. Let X be the median of the current window of acceleration, quantile() be the quantile calculation function, X be the sequence formed by sorting the sequence to be calculated in ascending order, b be the quantile probability, and [ ] be the rounding down function. For the f-th data in the sorted sequence, Let be the number of data points in the sorted dataset, e be the quantile index, and f be the integer part of e. It is the decimal part of e.

[0138] Step S5.1.5: Based on the first observed statistic of velocity and the first calculated observed statistic of acceleration, the significance of the calculated statistic is determined by the permutation test, and the p-values ​​of the first velocity outlier test and the first acceleration outlier test are obtained.

[0139] The step of calculating the significance of the statistics based on the first observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​for the first velocity outlier test and the first acceleration outlier test includes:

[0140] Step S5.1.4.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0141] Step S5.1.4.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset. The calculation formula is as follows: ; ;

[0142] in, For the merged velocity dataset; D a This is a dataset of post-acceleration data.

[0143] Step S5.1.4.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0144] In this embodiment, random permutation is required to merge the dataset. D a The values ​​in the dataset are randomly rearranged to obtain the rearranged velocity dataset. Rearranged acceleration dataset .

[0145] Step S5.1.4.4: Based on the data length of the current velocity window and the historical velocity window, split the rearranged velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, split the rearranged acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation;

[0146] Step S5.1.4.5: Calculate the median of the current window of the velocity after displacement based on the current window of the velocity after displacement; calculate the median of the historical window of the velocity after displacement based on the historical window of the velocity after displacement; calculate the median of the current window of the acceleration after displacement based on the current window of the acceleration after displacement; calculate the median of the historical window of the acceleration after displacement based on the historical window of the acceleration after displacement.

[0147] In this embodiment, the median of the current and historical windows of the velocity and acceleration data after the displacement is calculated:

[0148] ; ;

[0149] ; ;

[0150] in, The median of the velocity in the current window after the permutation. The median of the historical window of velocity after the replacement. The median of the acceleration in the current window after the permutation. The median is the median of the historical window of acceleration after the permutation, and median() is the median function. For the current window of the velocity after the displacement, For the historical window of the velocity after the replacement, For the current window of the displacement acceleration, This represents the historical window of acceleration after the displacement.

[0151] Step S5.1.4.6: Calculate the first permutation statistic for velocity based on the median of the current window of the permuted velocity and the median of the historical windows of the permuted velocity; calculate the first permutation statistic for acceleration based on the median of the current window of the permuted acceleration and the median of the historical windows of the permuted acceleration, using the following formula:

[0152] ;

[0153] ;

[0154] in, The first permutation statistic for velocity, Let be the first permutation statistic of acceleration, and quantile() be the quantile calculation function. The median of the velocity in the current window after the permutation. The median of the historical window of velocity after the replacement. The median of the acceleration in the current window after the permutation. The median of the historical window of acceleration after the replacement. For the current window of the velocity after the displacement, For the historical window of the velocity after the replacement, For the current window of the displacement acceleration, This is the historical window of acceleration after the displacement;

[0155] Step S5.1.4.7: Repeat steps S5.1.4.3 to S5.1.4.6 to calculate the first permutation statistic of the Nth velocity and the first permutation statistic of the Nth acceleration;

[0156] Step S5.1.4.8: Based on the first permutation statistic of N velocities, the first permutation statistic of N accelerations, the first observation statistic of velocity, and the first observation statistic of acceleration, calculate the significance level and obtain the p-value for the outlier test of the first velocity and the p-value for the outlier test of the first acceleration.

[0157] In this embodiment, after repeated random permutations and calculation of the permutation statistic 1000 times, the significance level (p-value) is calculated. The p-value is the probability of obtaining a test statistic that is the same as or more extreme than the observed data, given a statistical model and the null hypothesis H0 being true. Here, the null hypothesis H0 states that the velocity or acceleration in the current window does not show outliers compared to historical windows. If the p-value is small, it means that the probability of observing such data (or more extreme data) is small when the null hypothesis is true, therefore the null hypothesis is rejected, and it is considered that the velocity or acceleration in the current window shows significant outliers compared to historical windows. If the p-value is large, there is insufficient evidence to reject the null hypothesis, that is, the data does not show significant outliers in the velocity or acceleration of the current window compared to historical windows. ; ;

[0158] in, The significance level of outliers in the current window's speed compared to historical windows, i.e., the p-value for the first speed outlier test. The significance level of outliers in acceleration when comparing the current window with historical windows, i.e., the p-value for the first acceleration outlier test, E v The permutation statistic for velocity data is greater than the observation statistic. > The number of times E aThe permutation statistic for acceleration data is greater than the observation statistic. > The number of permutations is N, where N = 1000.

[0159] The variance tests evaluate the speed of the current window compared to the historical window. , ), Current window vs. history window acceleration ( , Does the volatility (dispersion) of the sample increase, including:

[0160] Step S5.2.1: Calculate the range of velocity data in the current window based on the current velocity window; calculate the range of velocity data in the historical window based on the historical velocity window; calculate the range of acceleration data in the current acceleration window based on the current acceleration window; calculate the range of acceleration data in the historical acceleration window based on the historical acceleration window. The calculation formulas are as follows:

[0161] ; ;

[0162] ; ;

[0163] in, This represents the range of the current window speed data. Here, represents the range of historical window velocity data, and represents the range of current window acceleration data. represents the range of the current window speed data, max() is the maximum value function, and min() is the minimum value function.

[0164] Step S5.2.1: Calculate the second observed statistic of velocity based on the range of the current window velocity data and the range of the historical window velocity data; calculate the second observed statistic of acceleration based on the range of the current window acceleration data and the range of the historical window acceleration data, using the following formula:

[0165] ; ;

[0166] in, This is the second observed statistic of velocity. The second observed statistic of acceleration, This represents the range of the current window speed data. The range of historical window speed data, The range of the current window's acceleration data. The range of historical acceleration data;

[0167] Step S5.2.3: Based on the second observed statistics of velocity and acceleration, the significance of the statistics is calculated using the permutation test to obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

[0168] The step of calculating the significance of the statistics based on the second observed statistics of velocity and the second observed statistics of acceleration using a permutation test to obtain the p-values ​​of the first velocity variance test and the first acceleration variance test includes:

[0169] Step S5.2.3.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0170] Step S5.2.3.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset. The calculation formula is as follows: ; ;

[0171] in, For the merged velocity dataset, D a This is the merged acceleration dataset.

[0172] Step S5.2.3.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0173] Step S5.2.3.4: Based on the data length of the current velocity window and the historical velocity window, rearrange the velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, rearrange the acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation.

[0174] In this embodiment, random permutation is required to merge the dataset. D a The values ​​in the dataset are randomly rearranged to obtain the rearranged velocity dataset. Rearranged acceleration dataset .

[0175] Step S5.2.3.5: Based on the current window of the replaced velocity, calculate the difference between the maximum and minimum values ​​of the current window of the replaced velocity; based on the historical window of the replaced velocity, calculate the difference between the maximum and minimum values ​​of the historical window of the replaced velocity; based on the current window of the replaced acceleration, calculate the difference between the maximum and minimum values ​​of the current window of the replaced acceleration; based on the historical window of the replaced acceleration, calculate the difference between the maximum and minimum values ​​of the historical window of the replaced acceleration. The calculation formulas are as follows:

[0176] ; ;

[0177] ; ;

[0178] in, For the current window of the velocity after the displacement, For the historical window of the velocity after the replacement, For the current window of the displacement acceleration, For the historical window of acceleration after displacement, max() is the maximum value function, and min() is the minimum value function. The difference between the maximum and minimum values ​​of the velocity in the current window after the replacement. The difference between the maximum and minimum values ​​of the historical velocity after the replacement. This is the difference between the maximum and minimum values ​​of the current window's acceleration after the displacement. This is the difference between the maximum and minimum values ​​of the historical acceleration after the displacement.

[0179] Step S5.2.3.6: Calculate the second permutation statistic for velocity based on the difference between the maximum and minimum values ​​of the current window of the permuted velocity and the difference between the maximum and minimum values ​​of the historical window of the permuted velocity; calculate the second permutation statistic for acceleration based on the difference between the maximum and minimum values ​​of the current window of the permuted acceleration and the difference between the maximum and minimum values ​​of the historical window of the permuted acceleration, using the following formula:

[0180] ;

[0181] ;

[0182] in, The second permutation statistic for velocity, The second permutation statistic for acceleration, The difference between the maximum and minimum values ​​of the velocity in the current window after the replacement. The difference between the maximum and minimum values ​​of the historical velocity after the replacement. This is the difference between the maximum and minimum values ​​of the current window's acceleration after the displacement. This is the difference between the maximum and minimum values ​​of the historical acceleration after the displacement.

[0183] Step S5.2.3.7: Repeat steps S5.2.3.1 to S5.2.3.6 to calculate the second permutation statistic of the Nth velocity and the second permutation statistic of the Nth acceleration;

[0184] Step S5.2.3.8: Based on the second permutation statistic of N velocities, the second permutation statistic of N accelerations, the second observation statistic of velocity, and the second observation statistic of acceleration, calculate the significance level and obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

[0185] In this embodiment, after repeating the random permutation and calculating the permutation statistic 1000 times, the p-value is calculated. The p-value is the probability of obtaining a test statistic that is the same as or more extreme than the observed data, given a statistical model and the null hypothesis H0 being true. Here, the null hypothesis H0 states that the fluctuation of the velocity or acceleration of the current window is not significantly increased compared to the historical window. If the p-value is small, it means that the probability of observing such data (or more extreme data) is small when the null hypothesis is true, so the null hypothesis is rejected, and it is considered that the fluctuation of the velocity or acceleration of the current window is significantly increased compared to the historical window. If the p-value is large, there is insufficient evidence to reject the null hypothesis, that is, the data does not show that the fluctuation of the velocity or acceleration of the current window is significantly increased compared to the historical window. ; ;

[0186] in, The significance level of the increase in velocity fluctuation between the current window and historical windows is defined as the p-value of the first velocity variance test. The significance level of the increase in acceleration fluctuation between the current window and the historical window, i.e., the p-value of the first acceleration variance test, E v The permutation statistic for velocity data is greater than the observation statistic. > The number of times E a The permutation statistic for acceleration data is greater than the observation statistic. > The number of permutations is N, where N = 1000.

[0187] The distribution offset test evaluates the speed of the current window compared to the historical window. , ), Current window vs. history window acceleration ( , Whether the distribution pattern of ) suddenly shifts, including:

[0188] Step S5.3.1: Calculate the median velocity of the current window based on the current velocity window; calculate the median velocity of the historical windows based on the current velocity window; calculate the median acceleration of the current window based on the current acceleration window; calculate the median acceleration of the historical windows based on the historical acceleration window.

[0189] In this embodiment, the median of the current and historical windows of velocity and acceleration data is calculated:

[0190] ; ; ; ;

[0191] ; ;

[0192] in, The median of the current window speed. This is the median of historical window speeds. The median of the current window acceleration. The median is the historical window acceleration, and median() is the median function.

[0193] Step S5.3.2: Calculate the difference between the median current window velocity and the median historical window velocity; calculate the difference between the median current window acceleration and the median historical window acceleration, using the following formula: ; ;

[0194] Where, β v β is the median difference between the current and historical window speeds. a This represents the median difference between the current and historical window accelerations.

[0195] Step S5.3.3: If the median difference between the current velocity and the historical window velocity, and the median difference between the current acceleration and the historical window velocity are both consistent with the pre-set expected trend, proceed to step S5.3.4 to continue the outlier determination for distribution offset test; otherwise, directly determine "no outlier" and do not proceed to the next step.

[0196] In this embodiment, the median difference β between the current and historical window velocities and accelerations is... v β a If the trend direction is the same as the expected trend direction set in step S4, the subsequent outlier determination is performed; otherwise, it is directly determined as "no outlier".

[0197] Step S5.3.4: Calculate the observation statistics based on the current window of velocity, the current historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration.

[0198] In this embodiment, the velocity and acceleration sequence of the historical window ( , Sort them in ascending order to form a new sequence. , ;

[0199] The observation statistics are calculated based on the current window of velocity, the current historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration. The calculation formula is as follows:

[0200] ; ;

[0201] ; ;

[0202] ; ;

[0203] ; ;

[0204] ; ;

[0205] ; ;

[0206] in, The third observational statistic for velocity, The third observational statistic for acceleration, This represents the extreme value of the speed within the historical window. This represents the extreme value of acceleration within the historical window. The velocity sequences of the historical windows are sorted in ascending order to form a new sequence. The acceleration sequences of the historical window are sorted in ascending order to form a new sequence. This is the median of historical window speeds. The median of the current window speed. The median of historical window acceleration. The median of the current window acceleration. The five data points closest to the end of the current window are the current window speed. The acceleration of the current window is represented by the 5 data points closest to the end of the window, and mean() is the average value function. The latest velocity is the data point at the very end of the current window. The latest acceleration is the data point at the very end of the current window's acceleration. The current window speed is the k-th data point closest to the end of the window. The acceleration of the current window is the k-th data point closest to the end of the window. For the most recent data points at the end that are greater than or less than the historical extreme threshold, For acceleration data points in the most recent data that are greater than or less than the historical extreme threshold, quantile() is the quantile calculation function. This represents the average offset of the current window's velocity outliers. The standard deviation of the historical window speed data. This represents the average offset of the current window's acceleration outliers. The standard deviation of historical acceleration data. For the j-th speed data point within the historical window, This is the average of historical window speed data. For the j-th acceleration data point within the historical window, is the average value of historical acceleration data within the window, and n is the number of data points within the window.

[0207] In this embodiment, when > 0, If the result is >0, continue with the subsequent calculations; otherwise, it will be directly judged as "no abnormality".

[0208] Step S5.3.5: Based on the third observation statistic of velocity and the third observation statistic of acceleration, the significance of the statistics is calculated using the permutation test, and the p-values ​​of the first acceleration distribution shift test and the first velocity distribution shift test are obtained.

[0209] The step of calculating the significance of the statistics based on the third observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​of the first acceleration distribution shift test and the first velocity distribution shift test includes:

[0210] Step S5.3.5.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset;

[0211] Step S5.3.5.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset. The calculation formula is as follows: ; ;

[0212] in, For the merged velocity dataset; D a This is the merged acceleration data.

[0213] Step S5.3.5.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset;

[0214] In this embodiment, random permutation is required to merge the dataset. D a The values ​​in the dataset are randomly rearranged to obtain the rearranged velocity dataset. Rearranged acceleration dataset .

[0215] Step S5.3.5.4: Based on the data length of the current velocity window and the historical velocity window, split the rearranged velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, split the rearranged acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation;

[0216] Step S5.3.5.4: Sort the values ​​in the current window of the replaced velocity from smallest to largest to obtain the sorted current velocity sequence; sort the values ​​in the historical window of the replaced velocity from smallest to largest to obtain the sorted historical velocity sequence; sort the values ​​in the current window of the replaced acceleration from smallest to largest to obtain the sorted current acceleration sequence; sort the values ​​in the historical window of the replaced acceleration from smallest to largest to obtain the sorted historical acceleration sequence.

[0217] In this embodiment, the historical window of the velocity after replacement is obtained by splitting the original length. The current window of velocity after displacement Historical window of acceleration after replacement The current window of acceleration after displacement Then, sort the values ​​in the window from smallest to largest to obtain the sorted historical speed sequence. The current velocity sequence after sorting Sorted historical acceleration sequence The current acceleration sequence after sorting Calculate the statistic after the permutation.

[0218] Step S5.3.5.5: Calculate the median of the sorted current velocity sequence based on the sorted current velocity sequence; obtain the median of the sorted historical velocity sequence based on the sorted historical velocity sequence; calculate the median of the sorted current acceleration sequence based on the sorted current acceleration sequence; calculate the median of the sorted historical acceleration sequence based on the sorted historical acceleration sequence.

[0219] In this embodiment, the median of the current and historical windows of the velocity and acceleration data after the displacement is calculated:

[0220] ; ;

[0221] ; ;

[0222] in, This is the median of the current velocity sequence after sorting. The median of the sorted historical velocity sequence. This is the median of the current acceleration sequence after sorting. is the median of the sequential historical acceleration sequence; median() is the median function.

[0223] Step S5.3.5.6: Calculate the extreme values ​​of velocity in the historical window after replacement based on the historical velocity window after replacement; calculate the extreme values ​​of acceleration in the historical window after replacement based on the historical acceleration window after replacement.

[0224] In this embodiment, the extreme values ​​of the historical window after the permutation are calculated:

[0225] ;

[0226] ;

[0227] in, The extreme values ​​of the historical window speed after the replacement. This represents the extreme value of historical window acceleration after the replacement.

[0228] Step S5.3.5.6: Based on the current window of the replaced velocity, select multiple consecutive velocity data points at the end of the current window of the replaced velocity; based on the current window of the replaced acceleration, select multiple consecutive acceleration data points at the end of the current window of the replaced acceleration.

[0229] In this embodiment, five consecutive data points at the end of the current window after the permutation are selected:

[0230] ;

[0231] ;

[0232] in, The last five consecutive velocity data points of the current window after the displacement; R perm a The last five consecutive acceleration data points of the current window after the displacement are used. The i-th consecutive velocity data point at the end of the current window after the velocity replacement. The i-th consecutive acceleration data point at the end of the current window after the displacement.

[0233] Step S5.3.5.7: Based on the extreme values ​​of velocity and acceleration in the historical window after permutation, and multiple consecutive velocity and acceleration data points at the end, calculate the third permutation statistic for velocity and the third permutation statistic for acceleration. The calculation formulas are as follows:

[0234] ; ;

[0235] ; ;

[0236] ; ;

[0237] ;

[0238] ;

[0239] in, This is the third permutation statistic for velocity. The third permutation statistic for acceleration, The extreme values ​​of the historical window speed after the replacement. The extreme values ​​of historical window acceleration after replacement. Five consecutive velocity data points at the end. For the last 5 consecutive acceleration data points, For the kth consecutive velocity data point at the end, For the kth consecutive acceleration data point at the end, These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. This represents the average offset of the current window velocity outliers after the replacement. The standard deviation of the historical window speed data after replacement. This represents the average offset of the current window's acceleration outliers after the replacement. The standard deviation of the historical window acceleration data after permutation. This represents the j-th velocity data point within the replaced historical window; The average value of the historical window speed data after replacement. For the j-th acceleration data point within the replaced historical window, This represents the average value of the historical window acceleration data after the replacement.

[0240] Step S5.3.5.8: Based on the third permutation statistic of velocity, the third permutation statistic of acceleration, the third observation statistic of velocity, and the third observation statistic of acceleration, the significance of the statistics is calculated using the permutation test, and the p-values ​​of the first acceleration distribution shift test and the first velocity distribution shift test are obtained.

[0241] In this embodiment, after repeating the random permutation and calculating the permutation statistic 1000 times, the p-value is calculated. The p-value is the probability of obtaining a test statistic that is the same as or more extreme than the observed data, given a statistical model and the null hypothesis H0 being true. Here, the null hypothesis H0 states that the distribution of the velocity or acceleration in the current window is the same as that in the historical window. If the p-value is small, it means that the probability of observing such data (or more extreme data) is small when the null hypothesis is true. Therefore, the null hypothesis is rejected, and it is considered that the distribution of the velocity or acceleration in the current window has significantly shifted compared to the historical window. If the p-value is large, there is insufficient evidence to reject the null hypothesis, that is, the data does not show a significant shift in the distribution of the velocity or acceleration in the current window compared to the historical window. ; ;

[0242] in, The significance level of the velocity distribution morphology shift between the current window and historical windows, i.e., the p-value of the first velocity distribution shift test, is used. The significance level of the acceleration distribution morphology shift between the current window and historical windows, i.e., the p-value of the first acceleration distribution shift test, E v The permutation statistic for velocity data is greater than the observation statistic. > The number of times E a The permutation statistic for acceleration data is greater than the observation statistic. > The number of permutations is N, where N = 1000.

[0243] Step S6: Based on the statistical results of the first multidimensional statistical test, construct a third-level and a fourth-level early warning model for sudden landslides. The third-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test, the first acceleration variance test, and the first acceleration distribution shift test are all less than preset thresholds, then output third-level early warning information. The fourth-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test and the first acceleration variance test are both less than preset thresholds, or if the p-values ​​of the first acceleration anomaly test and the first acceleration distribution shift test are both less than preset thresholds, or if the p-values ​​of the first acceleration variance test and the first acceleration distribution shift test are both less than preset thresholds, then output fourth-level early warning information.

[0244] In this embodiment, the initial early warning judgment condition is as follows: Based on the results of multidimensional statistical tests, a graded early warning model for low-level (level 3 and level 4) sudden landslides is constructed:

[0245] Level 3 Warning: < 0.05 & < 0.05 & < 0.05 (meaning that compared with historical windows, the p-value for acceleration outlier test is <0.05, the p-value for acceleration variance test is <0.05, and the p-value for acceleration distribution offset test is <0.05).

[0246] Level 4 Warning: ( < 0.05 & < 0.05 ) / ( < 0.05 & < 0.05 ) / ( < 0.05 & < 0.05 ) (Compared to historical windows, the current window has an acceleration outlier test p-value < 0.05 and an acceleration variance test p-value < 0.05, or an acceleration outlier test p-value < 0.05 and an acceleration distribution offset test p-value < 0.05, or an acceleration variance test p-value < 0.05 and an acceleration distribution offset test p-value < 0.05).

[0247] Step S7: After outputting the third-level or fourth-level warning information, take the window index corresponding to the first output warning information as the endpoint, select all historical velocities and historical accelerations before the warning information occurred as a candidate window set, select the candidate window with the smallest variance as the base window, and perform a second multidimensional statistical test between each current window and the base window to obtain the p-values ​​for the second velocity outlier test, the second velocity variance test, the second velocity distribution offset test, the second acceleration outlier test, the second acceleration variance test, and the second acceleration distribution offset test.

[0248] In this embodiment, a base window needs to be selected, and a second multidimensional statistical test is performed between each current window and the base window.

[0249] First, construct a set of candidate windows:

[0250] Candidate window range: Starting from the window index corresponding to the first warning time, all historical velocity and acceleration data before the warning occurred are selected as the candidate window set. Each candidate window contains n data points; all velocity data {v1, v2, ..., v...} before the first warning occurs are collected. u} (u >= n) are determined as candidate objects for the baseline window, where the m-th candidate window W m = {v m+n-1 ,v m+n ,…,v m+2n-2} (m + 2n-2 <= u), the sample size of each candidate window is n.

[0251] Candidate window variance calculation: Calculate the variance σ of the velocity for each candidate window. m 2 The calculation formula is as follows:

[0252] ; ;

[0253] Where, σ m 2 The variance of the velocity for each candidate window, v mk This represents the k-th velocity data point in the m-th candidate window.

[0254] Secondly, the base window is selected: the candidate window with the smallest variance is chosen as the base window W. base ;

[0255] Step S8: Based on the statistical results of the second multidimensional statistical test, construct a first-level graded early warning model and a second-level graded early warning model for sudden landslides. The first-level graded early warning model includes: a first acceleration anomaly test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than a preset threshold. Furthermore, the second acceleration anomaly test p-value, the second acceleration variance test p-value, the second acceleration distribution shift test p-value, the second velocity anomaly test p-value, the second velocity variance test p-value, and the second velocity distribution shift test p-value are all less than preset thresholds. Then, output the first-level early warning information. The second-level graded early warning model includes: a first acceleration anomaly test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than preset thresholds. Furthermore, the second acceleration anomaly test p-value, the second acceleration variance test p-value, and the second acceleration distribution shift test p-value are all less than preset thresholds.

[0256] In this embodiment, the basic window comparison analysis is performed as follows: For each sliding window after the first warning, the current window data and the basic window data are compared using statistical tests in steps S1 to S5 to obtain six statistical test parameters: the second speed outlier test p-value. Second acceleration outlier test p-value Second velocity variance test p-value Second acceleration variance test p-value Second velocity distribution offset test p-value Second acceleration distribution offset test p-value , respectively, represent the significance levels of outliers in the current window's velocity and acceleration compared to the base window, the significance levels of increased fluctuations, and the significance levels of distribution pattern shifts.

[0257] Advanced warning level determination: The Level 1 and Level 2 warning levels are determined based on the comparison results of the baseline window.

[0258] Level 1 warning conditions: < 0.05 & < 0.05 & < 0.05 & < 0.05 & <0.05 & < 0.05 & < 0.05 & < 0.05 & < 0.05 & < 0.05 (Compared to historical windows, the current window has p-values ​​for acceleration outlier test, acceleration variance test, acceleration distribution shift test, and velocity variance test all < 0.05; and compared to the baseline window, the current window also has p-values ​​for acceleration outlier test, acceleration variance test, acceleration distribution shift test, velocity outlier test, velocity variance test, and velocity distribution shift test all < 0.05); Level 2 warning conditions: < 0.05 & <0.05 & < 0.05 & < 0.05 & < 0.05 & < 0.05 & < 0.05 (Compared to historical windows, the current window has p-values ​​< 0.05 for acceleration outlier test, p-values ​​< 0.05 for acceleration variance test, p-values ​​< 0.05 for acceleration distribution offset test, and p-values ​​< 0.05 for velocity variance test; and compared to the baseline window, the current window has p-values ​​< 0.05 for acceleration outlier test, p-values ​​< 0.05 for acceleration variance test, and p-values ​​< 0.05 for acceleration distribution offset test); In this embodiment, based on the multi-level warning results determined in output steps S6 to S8, a corresponding graded warning chart is drawn as follows. Figure 3 As shown.

Claims

1. A method for graded early warning of sudden landslides, characterized in that, include: Step S1: Collect displacement data from slope monitoring equipment as the raw input data for the sudden landslide classification and early warning model; Step S2: Based on the sampling frequency of the original input data, use the central difference method to solve for the velocity and acceleration of the slope; Step S3: Set the window size for velocity and the window size for acceleration. Based on the window size for velocity, the window size for acceleration, and the sampling interval of the original input data, calculate the sample capacity of the velocity window and the acceleration window. Step S4: Obtain the current displacement data and initial displacement data from the original input data, calculate the difference between the current displacement data and the initial displacement data. If the difference is positive, it corresponds to the expected positive trend; if the difference is negative, it corresponds to the expected negative trend. The preset expected trend is either the expected positive trend or the expected negative trend. Step S5: Based on the sample size of the velocity window and the acceleration window, and the preset expected trend, perform the first multidimensional statistical test between the current window of each velocity and the historical window of velocity, and between the current window of each acceleration and the historical window of acceleration, to obtain the p-values ​​for the first velocity outlier test, the first velocity variance test, the first velocity distribution shift test, the first acceleration outlier test, the first acceleration variance test, and the first acceleration distribution shift test. The first multidimensional statistical test includes: outlier test, variance test, and distribution shift test. Step S6: Based on the statistical results of the first multidimensional statistical test, construct a third-level and a fourth-level early warning model for sudden landslides. The third-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test, the first acceleration variance test, and the first acceleration distribution shift test are all less than preset thresholds, then output third-level early warning information. The fourth-level early warning model for sudden landslides includes: if the p-values ​​of the first acceleration anomaly test and the first acceleration variance test are both less than preset thresholds, or if the p-values ​​of the first acceleration anomaly test and the first acceleration distribution shift test are both less than preset thresholds, or if the p-values ​​of the first acceleration variance test and the first acceleration distribution shift test are both less than preset thresholds, then output fourth-level early warning information. Step S7: After outputting the third-level or fourth-level warning information, take the window index corresponding to the first output warning information as the endpoint, select all historical velocities and historical accelerations before the warning information occurred as a candidate window set, select the candidate window with the smallest variance as the base window, and perform a second multidimensional statistical test between each current window and the base window to obtain the p-values ​​for the second velocity outlier test, the second velocity variance test, the second velocity distribution offset test, the second acceleration outlier test, the second acceleration variance test, and the second acceleration distribution offset test. Step S8: Based on the statistical results of the first and second multidimensional statistical tests, construct a first-level and second-level graded early warning model for sudden landslides. The first-level graded early warning model includes: a first acceleration anomaly test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than a preset threshold. Furthermore, if the second acceleration anomaly test p-value, the second acceleration variance test p-value, the second acceleration distribution shift test p-value, the second velocity anomaly test p-value, the second velocity variance test p-value, and the second velocity distribution shift test p-value are all less than preset thresholds, then output the first-level early warning information. The second-level graded early warning model includes: a first acceleration anomaly test p-value, a first acceleration variance test p-value, a first acceleration distribution shift test p-value, and a first velocity variance test p-value all less than preset thresholds. Furthermore, the second acceleration anomaly test p-value, the second acceleration variance test p-value, and the second acceleration distribution shift test p-value are all less than preset thresholds.

2. The method for graded early warning of sudden landslides according to claim 1, characterized in that, The outlier detection includes: Step S5.1.1: Based on the velocity window and the acceleration window, calculate the median of the current velocity window, the median of the historical velocity window, the median of the current acceleration window, and the median of the historical acceleration window, and calculate the difference between the medians of the current velocity window and the historical velocity window, and the difference between the medians of the current acceleration window and the historical acceleration window. Step S5.1.2: If the median difference between the current window of velocity and the historical window of velocity, and the median difference between the current window of acceleration and the historical window of acceleration are consistent with the sign of the preset expected trend, then continue to execute step S5.1.3; otherwise, do not continue to execute the subsequent steps. Step S5.1.3: Sort the current window of velocity and the historical window of velocity in ascending order of velocity to obtain the current sorted velocity sequence and the historical sorted velocity sequence. Sort the current window of acceleration and the historical window of acceleration in ascending order of velocity to obtain the current sorted acceleration sequence and the historical sorted acceleration sequence. Step S5.1.4: Based on the current sorted velocity sequence, the historical sorted velocity sequence, the current sorted acceleration sequence, and the historical sorted acceleration sequence, calculate the first observed statistics of velocity and acceleration, using the following formulas: ； ； in, The first observed statistic of velocity, This is the current sorted velocity sequence. The velocity sequence after historical sorting. The median of the historical window of speed. Here, is the median of the current window of velocity, and quantile() is the quantile calculation function. The first observed statistic of acceleration, This is the current sorted acceleration sequence. The acceleration sequence is sorted according to history. The median of the historical window of acceleration. The median of the current window's acceleration; Step S5.1.5: Based on the first observed statistic of velocity and the first calculated observed statistic of acceleration, the significance of the calculated statistic is determined by the permutation test, and the p-values ​​of the first velocity outlier test and the first acceleration outlier test are obtained.

3. The method for graded early warning of sudden landslides according to claim 2, characterized in that, The step of calculating the significance of the statistics based on the first observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​for the first velocity outlier test and the first acceleration outlier test includes: Step S5.1.4.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset; Step S5.1.4.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset; Step S5.1.4.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset; Step S5.1.4.4: Based on the data length of the current velocity window and the historical velocity window, split the rearranged velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, split the rearranged acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation; Step S5.1.4.5: Calculate the median of the current window of the velocity after displacement based on the current window of the velocity after displacement; calculate the median of the historical window of the velocity after displacement based on the historical window of the velocity after displacement; calculate the median of the current window of the acceleration after displacement based on the current window of the acceleration after displacement; calculate the median of the historical window of the acceleration after displacement based on the historical window of the acceleration after displacement. Step S5.1.4.6: Calculate the first permutation statistic for velocity based on the median of the current window of the permuted velocity and the median of the historical windows of the permuted velocity; calculate the first permutation statistic for acceleration based on the median of the current window of the permuted acceleration and the median of the historical windows of the permuted acceleration, using the following formula: ； ； in, The first permutation statistic for velocity, Let be the first permutation statistic of acceleration, and quantile() be the quantile calculation function. The median of the velocity in the current window after the permutation. The median of the historical velocity window after the replacement; The median of the acceleration in the current window after the permutation. The median of the historical window of acceleration after the replacement. For the current window of the velocity after the displacement, For the historical window of the velocity after the replacement, For the current window of the displacement acceleration, This is the historical window of acceleration after the displacement; Step S5.1.4.7: Repeat steps S5.1.4.3 to S5.1.4.6 to calculate the first permutation statistic of the Nth velocity and the first permutation statistic of the Nth acceleration; Step S5.1.4.8: Based on the first permutation statistic of N velocities, the first permutation statistic of N accelerations, the first observation statistic of velocity, and the first observation statistic of acceleration, calculate the significance level and obtain the p-value for the outlier test of the first velocity and the p-value for the outlier test of the first acceleration.

4. The method for graded early warning of sudden landslides according to claim 1, characterized in that, The variance test includes: Step S5.2.1: Calculate the range of velocity data in the current window based on the current velocity window; calculate the range of velocity data in the historical window based on the historical velocity window; calculate the range of acceleration data in the current window based on the current acceleration window; calculate the range of acceleration data in the historical acceleration window based on the historical acceleration window. Step S5.2.1: Calculate the second observed statistic of velocity based on the range of the current window velocity data and the range of the historical window velocity data; calculate the second observed statistic of acceleration based on the range of the current window acceleration data and the range of the historical window acceleration data, using the following formula: ； ； in, This is the second observed statistic of velocity. The second observed statistic of acceleration, This represents the range of the current window speed data. The range of historical window speed data, The range of the current window's acceleration data. The range of historical acceleration data; Step S5.2.3: Based on the second observed statistics of velocity and acceleration, the significance of the statistics is calculated using the permutation test to obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

5. The method for graded early warning of sudden landslides according to claim 4, characterized in that, The step of calculating the significance of the statistics based on the second observed statistics of velocity and the second observed statistics of acceleration using a permutation test to obtain the p-values ​​of the first velocity variance test and the first acceleration variance test includes: Step S5.2.3.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset; Step S5.2.3.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset; Step S5.2.3.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset; Step S5.2.3.4: Based on the data length of the current velocity window and the historical velocity window, rearrange the velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, rearrange the acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation. Step S5.2.3.5: Based on the current window of the velocity after displacement, calculate the difference between the maximum and minimum values ​​of the current window of the velocity after displacement; based on the historical window of the velocity after displacement, calculate the difference between the maximum and minimum values ​​of the historical window of the velocity after displacement; based on the current window of the acceleration after displacement, calculate the difference between the maximum and minimum values ​​of the current window of the acceleration after displacement; based on the historical window of the acceleration after displacement, calculate the difference between the maximum and minimum values ​​of the historical window of the acceleration after displacement. Step S5.2.3.6: Calculate the second permutation statistic for velocity based on the difference between the maximum and minimum values ​​of the current window of the permuted velocity and the difference between the maximum and minimum values ​​of the historical window of the permuted velocity; calculate the second permutation statistic for acceleration based on the difference between the maximum and minimum values ​​of the current window of the permuted acceleration and the difference between the maximum and minimum values ​​of the historical window of the permuted acceleration, using the following formula: ； ； in, The second permutation statistic for velocity, The second permutation statistic for acceleration, The difference between the maximum and minimum values ​​of the velocity in the current window after the replacement. The difference between the maximum and minimum values ​​of the historical velocity after the replacement. This is the difference between the maximum and minimum values ​​of the current window's acceleration after the displacement. This is the difference between the maximum and minimum values ​​of the historical acceleration after the displacement. Step S5.2.3.7: Repeat steps S5.2.3.1 to S5.2.3.6 to calculate the second permutation statistic of the Nth velocity and the second permutation statistic of the Nth acceleration; Step S5.2.3.8: Based on the second permutation statistic of N velocities, the second permutation statistic of N accelerations, the second observation statistic of velocity, and the second observation statistic of acceleration, calculate the significance level and obtain the p-value of the first velocity variance test and the p-value of the first acceleration variance test.

6. The method for graded early warning of sudden landslides according to claim 1, characterized in that, The distribution shift test includes: Step S5.3.1: Calculate the median velocity of the current window based on the current velocity window; calculate the median velocity of the historical windows based on the historical velocity windows; calculate the median acceleration of the current window based on the current acceleration window; calculate the median acceleration of the historical windows based on the historical acceleration windows. Step S5.3.2: Calculate the difference between the median of the current window velocity and the median of the historical window velocity; calculate the difference between the median of the current window acceleration and the median of the historical window acceleration. Step S5.3.3: If the median difference between the current velocity and the historical window velocity, and the median difference between the current acceleration and the historical window velocity are both consistent with the pre-set expected trend, proceed to step S5.3.4 to continue the anomaly determination of the distribution offset test; otherwise, directly determine "no anomaly" and do not proceed to the next step. Step S5.3.4: Calculate the observation statistics based on the current window of velocity, the historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration. Step S5.3.5: Based on the third observation statistic of velocity and the third observation statistic of acceleration, use the permutation test to calculate the significance of the statistics, and obtain the p-value of the first velocity distribution shift test and the p-value of the first acceleration distribution shift test.

7. The method for graded early warning of sudden landslides according to claim 6, characterized in that, The observation statistics are calculated based on the current window of velocity, the historical window of velocity, the current window of acceleration, and the historical window of acceleration to obtain the third observation statistics of velocity and the third observation statistics of acceleration. The calculation formula is as follows: ； ； ； ； ； ； ； ； ； ； ； ； in, This is the third observed statistic for velocity. The third observational statistic for acceleration, This represents the extreme value of the speed within the historical window. This represents the extreme value of acceleration within the historical window. The velocity sequences of the historical windows are sorted in ascending order to form a new sequence. The acceleration sequences of the historical window are sorted in ascending order to form a new sequence. This is the median of historical window speeds. The median of the current window speed. The median of historical window acceleration. The median of the current window acceleration. The five data points closest to the end of the current window are the current window speed. The acceleration of the current window is represented by the 5 data points closest to the end of the window, and mean() is the average value function. The latest velocity is the data point at the very end of the current window. The latest acceleration is the data point at the very end of the current window's acceleration. The current window speed is the k-th data point closest to the end of the window. The acceleration of the current window is the k-th data point closest to the end of the window. For the most recent data points at the end that are greater than or less than the historical extreme threshold, For acceleration data points in the most recent data that are greater than or less than the historical extreme threshold, quantile() is the quantile calculation function. , where is the average offset of the current window's velocity outliers. The standard deviation of the historical window speed data. This represents the average offset of the current window's acceleration outliers. The standard deviation of historical acceleration data. For the j-th speed data point within the historical window, This is the average of historical window speed data. For the j-th acceleration data point within the historical window, is the average value of historical acceleration data within the window, and n is the number of data points within the window.

8. A method for graded early warning of sudden landslides according to claim 6, characterized in that, The step of calculating the significance of the statistics based on the third observed statistics of velocity and acceleration using a permutation test to obtain the p-values ​​of the first velocity distribution shift test and the first acceleration distribution shift test includes: Step S5.3.5.1: Merge the current window of velocity and the historical window of velocity to obtain the merged velocity dataset; Step S5.3.5.2: Merge the current window of acceleration and the historical window of acceleration to obtain the merged acceleration dataset; Step S5.3.5.3: Randomly rearrange the values ​​in the merged velocity dataset to obtain a rearranged velocity dataset; randomly rearrange the values ​​in the merged acceleration dataset to obtain a rearranged acceleration dataset; Step S5.3.5.4: Based on the data length of the current velocity window and the historical velocity window, rearrange the velocity dataset into: the current velocity window after permutation and the historical velocity window after permutation; based on the data length of the current acceleration window and the historical acceleration window after permutation, rearrange the acceleration dataset into: the current acceleration window after permutation and the historical acceleration window after permutation. Step S5.3.5.4: Sort the values ​​in the current window of the replaced velocity from smallest to largest to obtain the sorted current velocity sequence; sort the values ​​in the historical window of the replaced velocity from smallest to largest to obtain the sorted historical velocity sequence; sort the values ​​in the current window of the replaced acceleration from smallest to largest to obtain the sorted current acceleration sequence; sort the values ​​in the historical window of the replaced acceleration from smallest to largest to obtain the sorted historical acceleration sequence. Step S5.3.5.5: Calculate the median of the sorted current velocity sequence based on the sorted current velocity sequence; obtain the median of the sorted historical velocity sequence based on the sorted historical velocity sequence; calculate the median of the sorted current acceleration sequence based on the sorted current acceleration sequence; calculate the median of the sorted historical acceleration sequence based on the sorted historical acceleration sequence. Step S5.3.5.6: Calculate the extreme values ​​of velocity in the historical window after replacement based on the historical velocity window after replacement; calculate the extreme values ​​of acceleration in the historical window after replacement based on the historical acceleration window after replacement. Step S5.3.5.6: Based on the current window of the replaced velocity, select the last 5 consecutive velocity data points of the current window of the replaced velocity; based on the current window of the replaced acceleration, select the last 5 consecutive acceleration data points of the current window of the replaced acceleration. Step S5.3.5.7: Based on the extreme values ​​of velocity and acceleration in the historical window after permutation, the five consecutive velocity data points at the end, and the five consecutive acceleration data points at the end, calculate the third permutation statistic of velocity and the third permutation statistic of acceleration. Step S5.3.5.8: Based on the third permutation statistic of velocity, the third permutation statistic of acceleration, the third observation statistic of velocity, and the third observation statistic of acceleration, the significance of the statistics is calculated using the permutation test, and the p-values ​​of the first acceleration distribution shift test and the first velocity distribution shift test are obtained.

9. A method for graded early warning of sudden landslides according to claim 6, characterized in that, The third permutation statistic for velocity and the third permutation statistic for acceleration are calculated based on the extreme values ​​of velocity and acceleration in the historical window after permutation, the last five consecutive velocity data points, and the last five consecutive acceleration data points. The calculation formulas are as follows: ； ； ； ； ； ； ； ； in, This is the third permutation statistic for velocity. The third permutation statistic for acceleration, This represents the extreme value of the historical window speed after the replacement. The extreme values ​​of historical window acceleration after the replacement. Five consecutive velocity data points at the end. For the last 5 consecutive acceleration data points, This represents the kth consecutive velocity data point at the end of the current window after the replacement. This represents the kth consecutive acceleration data point at the end of the current window after the replacement. These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. These are the velocity data points in the recent data that are greater than or less than the historical extreme threshold after replacement. This represents the average offset of the current window velocity outliers after the replacement. The standard deviation of the historical window speed data after replacement. This represents the average offset of the current window's acceleration outliers after the replacement. The standard deviation of the historical window acceleration data after permutation. For the j-th velocity data within the replaced historical window, The average value of the historical window speed data after replacement. For the j-th acceleration data point within the replaced historical window, This represents the average value of the historical window acceleration data after the replacement.

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