Landslide instability time prediction method and product based on dynamic selection of landslide early warning model

Abstract

The embodiment of the invention provides a landslide instability time prediction method and product based on landslide early warning model dynamic selection, and relates to the technical field of landslide monitoring and early warning. In the embodiment of the invention, the uncertainty of the candidate model is quantified by adopting the Bayesian method, and the most suitable model with the maximum occurrence probability is objectively selected, so that reliable instability time probability prediction is provided. For a continuous monitoring scene, sequential Bayesian updating and parallel computing are further incorporated into the method, and efficient dynamic updating is allowed to be carried out on instability time prediction when new monitoring data are available. According to the prediction method based on integrated model selection, reasonable balance can be obtained between prediction uncertainty and prediction precision, and the average absolute prediction error of the most probable instability time of prediction is obviously lower than that of a prediction method based on a single model. In a word, the invention provides a practical and probabilistic framework to predict the landslide instability time, and aims to support active landslide risk management.

Description

Technical Field

[0001] The embodiments of the present invention relate to the technical field of landslide monitoring and early warning, and in particular, to a landslide instability time prediction method and product based on dynamic selection of a landslide early warning model. Background Art

[0002] Landslides are one of the most serious geological disasters in the world, causing significant economic losses and casualties every year. Facing huge landslide risks, it is often not feasible to transfer and resettle threatened assets in most cases, and short-term evacuation through a landslide early warning system (EWS) is usually the most effective option. Although an EWS consists of various interacting components, accurately predicting the landslide instability time is a key link in its effective operation and is of great significance for disaster prevention and mitigation work.

[0003] Slopes often exhibit accelerated creep behavior before failure, which is characterized by "the strain rate rapidly increasing with time, eventually leading to unstable failure". This accelerated creep is a key precursor feature of impending failure, and several instability time prediction models have been proposed based on this. Related technologies have found through triaxial tests that the logarithm of the instability time is proportional to the logarithm of the strain rate. Later, this relationship was extended to the accelerated creep stage, and an empirical model for predicting the instability time (i.e., the Satio model) was proposed. It was also found in related technologies that the Satio model may not be applicable to some landslides, and it was modified (called the YAM model) to obtain more accurate predictions. In addition, related technologies have also found through slope model tests that the logarithm of the deformation rate before slope failure is proportional to the logarithm of the acceleration, and the inverse velocity (INV) model was proposed. For simplicity, the simplified inverse velocity (SINV) model with a linear trend is more widely used in practice. The slope (SLO) model was developed on the basis of previous related research, which claims to provide a safer prediction than INV. Although these models provide useful tools for professionals to interpret the instability time from monitoring data, their reliable application in actual engineering still faces some challenges.

[0004] Although these prediction models have been extensively reviewed in the context of post - hoc analysis, the practical requirements they face in forward prediction have received little attention. The most direct challenge is how engineers can select the most suitable prediction model for a specific landslide scenario from multiple competing candidate models. Unfortunately, previous studies have rarely focused on this issue. Due to simplicity or similar prediction accuracy, simple models are usually more popular in practical applications. However, each landslide exhibits a unique deformation pattern, and the evolution of its deformation may vary due to environmental conditions and geological factors. Therefore, simple prediction models may not always be applicable. In other words, no single model can accurately predict the instability time of all landslides. Another option in practice is to integrate multiple models to provide an instability time prediction. However, integrating predictions from multiple models, which may have significant differences among them, may introduce greater errors and uncertainties, making it difficult to evaluate the reliability of the results. Therefore, how to dynamically select the most suitable prediction model based on the available monitoring data is crucial for reliably predicting the failure time. Summary of the Invention

[0005] Embodiments of the present invention provide a method and product for predicting the instability time of a landslide based on dynamic selection of a landslide warning model to at least partially solve the above problems.

[0006] In a first aspect of an embodiment of the present invention, a method for predicting the instability time of a landslide based on dynamic selection of a landslide warning model is provided. The method includes:

[0007] Obtain landslide deformation monitoring data;

[0008] Determine the starting point of landslide accelerated deformation according to the landslide deformation monitoring data, where the starting point of landslide accelerated deformation characterizes that the landslide enters the accelerated deformation stage;

[0009] When it is determined that the landslide enters the accelerated deformation stage, obtain the landslide deformation speed corresponding to each moment in the accelerated deformation stage as observation data, and obtain multiple candidate models and prior information of random variables of each candidate model;

[0010] Based on the observation data and the prior information of random variables of each candidate model, select the most suitable candidate model based on the Bayesian method and quantify the uncertainty of its instability time prediction;

[0011] Perform probabilistic instability time prediction based on the most suitable candidate model to obtain the landslide instability time.

[0012] Optionally, based on the observation data and the prior information of random variables of each candidate model, selecting the most suitable candidate model based on the Bayesian method and quantifying the uncertainty of its instability time prediction includes:

[0013] Let M j represent the j-th candidate model (j = 1, 2,..., N c ), where N c is the number of candidate models; after the landslide OOA point, n sets of observed data d i obtained at time t i (i = 1, 2,..., n) are denoted as D obs = [(t 1 , d 1 ), (t 2 , d 2 ),..., (t n , d n )];

[0014] According to the Bayesian method, under the condition of the observed data in the given landslide acceleration stage, the credibility of the candidate model is defined as the occurrence probability P(M obs |D j ), which is expressed as: obs where

[0015]

[0016] is a normalization constant; P(M ) represents the prior information of model M j . Assuming it follows a uniform distribution in the absence of prior knowledge, then P(M j ) = 1 / N j ; P(D c |M obs ) represents the conditional probability of D j under the condition of the given candidate model M j , that is, the model evidence; P(M obs |D j ) is proportional to P(D obs |M obs ). The most suitable candidate model M j under the given current observed data is selected by comparing the model evidence; *

[0017] The model evidence P(D obs |M j ) is expressed by the total probability theorem:

[0018] P(D obs |M j ) = ∫ θ P(D obs |θ, M j )P(θ|M j )dθ;

[0019] where θ is a vector of random variables; P(θ|M j ) represents the prior probability of model M j ; P(D obs |θ,M j ) represents the likelihood function reflecting the goodness of fit between the candidate model and the observed data. Considering the numerical differences in the observed data between different models, the residuals between the model prediction value D mod (M j ,b) and the observed value D obs are standardized to ensure the objectivity of model comparison; assuming that the standardized residual ε follows a normal random variable with a mean of zero and a standard deviation of σ ε , and assuming statistical independence, the likelihood function P(D obs |θ,M j ) is expressed as:

[0020]

[0021] where σ ε is updated as a random variable, so the random variable vector θ = [b,σ ε ; for a given model M j , the uncertainty associated with the random variable θ is quantified by P(θ|D obs ,M j );

[0022] Using the Bayesian method, the posterior distribution P(θ|D j ,M obs ) of the random variable θ in model M j is expressed as:

[0023] P(θ|D obs ,M j ) = k -1 P(D obs |θ,M j )P(θ|M j )

[0024] where k is a normalization constant and is equal to the model evidence P(D obs |M j );

[0025] Based on the above method, select the candidate model that best fits the current observed data and quantify the uncertainty of its instability time prediction.

[0026] Optionally, the method includes:

[0027] When a new observed value of the landslide deformation speed is obtained, add the new observed value of the landslide deformation speed to the sequence of observed values to obtain a new sequence of observed values. Based on the new observed data and the prior information of the random variables of each candidate model, select the candidate model that best suits the current observed data based on the Bayesian method, and quantify the uncertainty of the prediction of the instability time.

[0028] Optionally, determining the starting point of the landslide accelerating deformation according to the landslide deformation monitoring data includes:

[0029] Determine the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data;

[0030] Determine the speed confidence interval according to the landslide deformation speed corresponding to each moment, and the speed confidence interval represents the speed fluctuation range in the steady-state creep stage of the landslide;

[0031] When the landslide deformation speed at the target moment is greater than the speed confidence interval, determine that the target moment is the starting point of the landslide accelerating deformation.

[0032] Optionally, determining the starting point of the landslide accelerating deformation according to the landslide deformation monitoring data includes:

[0033] Determine the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data;

[0034] Determine the speed confidence interval according to the landslide deformation speed corresponding to each moment, and the speed confidence interval represents the speed fluctuation range in the steady-state creep stage of the landslide;

[0035] When the landslide deformation speed at the first moment is within the speed confidence interval, determine that the landslide is in the steady-state creep stage at the first moment;

[0036] When the landslide deformation speed at the second moment first exceeds the speed confidence interval, and the landslide deformation speed at the third moment exceeds the speed confidence interval, and the landslide deformation speed at the third moment is greater than the landslide deformation speed at the second moment, determine that the landslide enters the accelerating deformation stage, and the third moment is the next moment of the second moment;

[0037] When the landslide deformation speeds at the second moment, the third moment, and the fourth moment all exceed the speed confidence interval, and the linear fitting slope is greater than 0, determine that the landslide enters the accelerated deformation stage and is in the uniform acceleration stage; the fourth moment is the next moment of the third moment;

[0038] Determine the second moment as the starting point of the landslide accelerating deformation.

[0039] Optionally, determining the speed confidence interval according to the landslide deformation speed corresponding to each moment includes:

[0040] Arrange the landslide deformation speeds corresponding to each moment in ascending order, and use the following formula to determine the lower limit v α / 2 and the upper limit v 1-α / 2 of the confidence interval corresponding to the significance level α:

[0041]

[0042]

[0043] where N is the number of Bootstrap subsamples randomly sampled from the original sample ; represents the time series of landslide deformation speed represents the i-th Bootstrap subsample; Percentile(·) represents the calculation process using the percentile method.

[0044] Optionally, determining the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data includes:

[0045] Obtain time series monitoring data from the landslide deformation monitoring data;

[0046] Obtain the landslide speed at each moment according to the time series monitoring data;

[0047] Perform filtering processing on the landslide speed at each moment to obtain the landslide deformation speed corresponding to each moment.

[0048] A second aspect of the embodiments of the present invention provides a landslide instability time prediction device based on dynamic selection of a landslide warning model. The landslide instability time prediction device based on dynamic selection of a landslide warning model includes:

[0049] A first acquisition module, configured to acquire landslide deformation monitoring data;

[0050] A first determination module, configured to determine a landslide accelerated deformation starting point according to the landslide deformation monitoring data, where the landslide accelerated deformation starting point represents that the landslide enters the accelerated deformation stage;

[0051] A second acquisition module, configured to, when it is determined that the landslide enters the accelerated deformation stage, acquire the landslide deformation speed corresponding to each moment in the accelerated deformation stage as observation data, and acquire a plurality of candidate models and prior information of random variables of each candidate model;

[0052] A selection module, configured to select the most suitable candidate model based on the Bayesian method according to the observation data and the prior information of random variables of each candidate model, and quantify the uncertainty of its instability time prediction;

[0053] A prediction module, configured to predict the probability of instability time based on the most suitable candidate model, so as to obtain the landslide instability time.

[0054] A third aspect of the embodiments of the present invention provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes, it implements the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in the first aspect of the present invention.

[0055] A fourth aspect of the embodiments of the present invention provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in the first aspect of the present invention.

[0056] A fifth aspect of the embodiments of the present invention provides a computer program product, including a computer program / instructions. When the computer program / instructions are implemented by a processor, it implements the steps in the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in the first aspect of the present invention.

[0057] In the embodiments of the present invention, the Bayesian method is used to quantify the uncertainty of candidate models, objectively select the most suitable model with the highest occurrence probability, so as to provide a reliable probability prediction of the instability time. For continuous monitoring scenarios, sequential Bayesian updating and parallel computing are further incorporated into the above method, allowing for efficient dynamic updating of the instability time prediction when new monitoring data becomes available. The proposed prediction method integrating model selection can achieve a reasonable balance between prediction uncertainty and prediction accuracy, and the mean absolute prediction error of predicting the most likely instability time is significantly lower than that of the single-model based prediction method. In summary, the present invention proposes a practical and probabilistic framework for predicting landslide instability time, aiming to support proactive landslide risk management. Compared with the single-model prediction method, the method proposed by the present invention achieves a surprisingly reasonable balance between prediction accuracy and uncertainty, and the mean absolute prediction error of predicting the most likely instability time is only 0.62d. In summary, the present invention proposes a practical and probabilistic framework for predicting landslide instability time, aiming to support proactive landslide risk management. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following will briefly introduce the drawings required for the description of the embodiments of the present invention. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0059] Figure 1It is the flowchart of the steps of the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0060] Figure 2 It is the schematic diagram of the OOA point identification result of a case in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0061] Figure 3 It is the model selection and instability time prediction result based on the original data and filtered data in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0062] Figure 4 It is the deformation monitoring data and OOA point identification results of Cases 1 to 8 in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0063] Figure 5 It is the deformation monitoring data and OOA point identification results of Cases 9 to 15 in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0064] Figure 6 It is the final prediction comparison result of 15 landslide cases in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0065] Figure 7 It is the schematic diagram of the prediction result of a case in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0066] Figure 8 It is the schematic diagram of the prediction result of a case in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0067] Figure 9 It is the schematic diagram of the prediction result of a case in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention;

[0068] Figure 10 It is the schematic diagram of the prediction result of a case in the landslide instability time prediction method dynamically selected based on the landslide warning model provided by the embodiments of the present invention. Detailed implementation manners

[0069] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific implementation manners.

[0070] In an embodiment of the present invention, a step flowchart of a landslide instability time prediction method based on dynamic selection of a landslide warning model is provided, as Figure 1 shown. Specifically, the landslide instability time prediction method based on dynamic selection of a landslide warning model includes the following steps:

[0071] S101, obtaining landslide deformation monitoring data.

[0072] S102, determining the starting point of landslide accelerated deformation according to the landslide deformation monitoring data.

[0073] Among them, the starting point of landslide accelerated deformation represents that the landslide enters the accelerated deformation stage.

[0074] S103, in the case of determining that the landslide enters the accelerated deformation stage, obtaining the landslide deformation speed corresponding to each moment in the accelerated deformation stage as observation data, and obtaining a plurality of candidate models and prior information of random variables of each candidate model;

[0075] S104, based on the observation data and the prior information of random variables of each candidate model, selecting the most suitable candidate model based on the Bayesian method, and quantifying the uncertainty of its instability time prediction;

[0076] S105, performing probabilistic instability time prediction based on the most suitable candidate model to obtain the landslide instability time.

[0077] In an embodiment of the present invention, various monitoring methods can be used to record landslide deformation monitoring data, including tape measures, total stations, crack meters, slope synthetic aperture radar (S-SAR), and satellite-based interferometric SAR (InSAR). Different monitoring tools result in a wide range of monitoring frequencies, which can be divided into high-frequency data sets (≤0.1 d), medium-frequency data sets (0.1 - 1 d), low-frequency data sets (1 - 6 d), and very low-frequency data sets (≥6 d). The classification boundaries of the data sets reflect the typical frequencies of the monitoring tools used; for example, the minimum revisit period of the representative Sentinel-1 satellite is 6 days. The landslide instability time prediction method based on dynamic selection of a landslide warning model provided in the embodiment of the present invention can be applied to data sets of any frequency.

[0078] In an embodiment of the present invention, considering that the scattering in landslide monitoring data blurs the velocity information, filtering can enhance the reliability of landslide instability time prediction. The effectiveness of ordinary filters has been evaluated, and it has been pointed out that the Savitzky-Golay (SG) filter has better performance. The SG filter uses a weighted average method and uses the least squares equation to define the weights of polynomial fitting.

[0079] In the embodiments of the present invention, any mature technical means in the related art can be used to determine the starting point of the landslide's accelerated deformation.

[0080] In an alternative embodiment, step S102 includes the following sub-steps:

[0081] S1021. Determine the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data.

[0082] S1022. Determine the starting point of the landslide's accelerated deformation according to the landslide deformation speed corresponding to each moment.

[0083] In an alternative embodiment, step S1021 includes the following sub-steps:

[0084] S10211. Obtain time series monitoring data according to the landslide deformation monitoring data;

[0085] S10212. Obtain the landslide speed corresponding to each moment according to the time series monitoring data;

[0086] S10213. Perform filtering processing on the landslide speed corresponding to each moment to obtain the landslide deformation speed corresponding to each moment after filtering.

[0087] Let S i represent the landslide deformation monitoring data at time t i (i = 1, 2,..., n), then the time series monitoring data can be expressed as S = [(t 1 , S 1 ), (t 2 , S 2 ),...,(t n , S n )], and the landslide speed v i at time t i can be obtained using the following formula:

[0088]

[0089] In the embodiments of the present invention, step S1023 includes:

[0090] Perform filtering processing on the landslide speed at each moment using the following formula to obtain the landslide deformation speed corresponding to each moment:

[0091]

[0092] where C 1j is the weight matrix C = (J T J) -1 J TFor the first row, T is the transpose operator of the matrix, and J is a Vandermonde matrix with m rows and k + 1 columns (m is the length of the filtering window, and k is the polynomial order); is the landslide deformation velocity corresponding to the i-th moment obtained by filtering, v j is the j-th original velocity within the corresponding filtering window.

[0093] For SG filtering of non-uniformly spaced monitoring data, it can be converted to uniformly spaced data through interpolation techniques.

[0094] The polynomial degree and the filtering window length are key parameters affecting the filtering performance. Considering the computational cost and the filtering performance, cubic polynomials are usually used. The selection of the filtering window length is affected by many factors. Usually, the potential window length is between 5 and 15 points, and it should be determined by evaluating the filtering effect of each research case in practical applications. If the noise effect is significant, the window length can be increased.

[0095] Before a landslide occurs, the slope deformation usually exhibits the classic three-stage creep evolution characteristics. According to the classic interpretation, the velocity in the steady-state creep stage of the landslide is constant under ideal conditions. However, due to various noise effects, the actual velocity often fluctuates around this constant value. When the landslide enters the acceleration stage, the velocity continuously increases and deviates from the normal fluctuation range (NFR). Therefore, the key to real-time identification of the OOA point is to determine whether the current landslide velocity deviates from the NFR.

[0096] The NFR of the velocity of each landslide in the steady-state creep stage is different and lacks a unified definition. Based on the statistical characteristics of the filtered velocity data of a specific landslide the velocity NFR in the steady-state creep stage can be defined by the velocity confidence interval (CI). Since the landslide velocity may exhibit non-normal statistical characteristics, in the embodiments of the present invention, the generalized percentile method is used to calculate its CI.

[0097] Specifically, the step S1022 includes the following sub-steps:

[0098] S10221, determining the velocity confidence interval according to the landslide deformation velocity corresponding to each moment, where the velocity confidence interval characterizes the velocity fluctuation range in the steady-state creep stage of the landslide;

[0099] S10222, when the landslide deformation velocity at the target moment is greater than the velocity confidence interval, determining the target moment as the starting point of the landslide accelerated deformation.

[0100] Specifically, in an alternative embodiment, for the large sample landslide monitoring data obtained by high-frequency monitoring means (such as Global Navigation Satellite System, crack meter, ground-based synthetic aperture radar, etc.), step S10221 includes: arranging the landslide deformation speeds corresponding to each moment in ascending order, and determining the lower limit v of the speed confidence interval corresponding to the significance level α using the following formula α / 2 and the upper limit v 1-α / 2 :

[0101]

[0102] where Percentile(·) represents the calculation process using the percentile method, represents the landslide deformation speed time series

[0103] Although this method performs well with a large sample size (n > 50), it may not provide reliable estimates with a small sample size (n ≤ 50).

[0104] In practice, small sample monitoring data is often encountered, such as deformation monitoring information from satellite-based InSAR, total station, and 3D laser scanning technology. In this case, for the small sample landslide monitoring data obtained by low-frequency monitoring means (such as total station, manual measurement, satellite synthetic aperture radar, etc.), step S10221 includes:

[0105] Arranging the landslide deformation speeds corresponding to each moment in ascending order, and determining the lower limit v of the speed confidence interval corresponding to the significance level α using the Bootstrap method based on the following formula α / 2 and the upper limit v 1-α / 2 :

[0106]

[0107]

[0108] where N is the number of Bootstrap subsamples randomly sampled and constructed from the original sample ; represents the landslide deformation speed time series represents the i-th Bootstrap subsample; Percentile(·) represents the calculation process using the percentile method.

[0109] The Bootstrap method, also known as the resampling method, is a very commonly used technique in the field of statistics. Its core idea is very simple: by repeatedly randomly sampling from the existing data (allowing the same data to be sampled repeatedly), a new sample set is simulated to estimate the statistical quantities of interest (such as the mean, median, or standard deviation, etc.).

[0110] Specifically, the steps to calculate the confidence interval using the percentile method can specifically include:

[0111] Step 1: Generate Bootstrap subsamples: Randomly and with replacement, draw a sample of the same size as the original sample from the original sample. Repeat this process multiple times (for example, 1000 times or more) to form multiple Bootstrap samples.

[0112] Step 2: Calculate the statistic for each Bootstrap subsample: Calculate the statistic of interest (such as the mean, median, variance, etc.) for each Bootstrap sample.

[0113] Step 3: Sort the statistics: Sort the statistics calculated from all Bootstrap subsamples in ascending order.

[0114] Step 4: Determine the percentiles: Determine the percentiles of the confidence interval. For example, for a 95% confidence interval, the statistic values at the 2.5th percentile and the 97.5th percentile need to be found.

[0115] Step 5: Calculate the confidence interval: Find the values corresponding to the 2.5th percentile and the 97.5th percentile among the sorted statistics; the range between these two values is the 95% confidence interval.

[0116] Based on the accurate estimation of the velocity CI in the steady-state creep stage, the OOA point can be identified in real time by determining whether the current velocity vi is within the calculated CI range. In particular, in the embodiments of the present invention, α = 0.05 is adopted, that is, 95% CI.

[0117] In order to improve the reliability of the technical solution proposed in the embodiments of the present invention for engineering practitioners in practical scenarios, the following four criteria are set in the embodiments of the present invention to evaluate the current deformation state of the landslide identified by OOA:

[0118] Criterion 0: The current v i is within the CI range, that is, the landslide is in the steady-state creep stage;

[0119] Criterion 1: The current v i exceeds the CI for the first time, which may be a potential precursor to the acceleration stage or may also be spike noise;

[0120] Criterion 2: At least two consecutive velocities vi , v i+1 exceeds CI and v i < v i+1 , indicating that the landslide is very likely to enter the acceleration stage;

[0121] Criterion 3: At least three consecutive velocities v i , v i+1 , v i+2 exceed CI, and the slope of their linear fit is greater than 0, indicating that the landslide has entered the acceleration stage;

[0122] When it is determined that the landslide is in the acceleration stage (i.e., reaches Criterion 3), the point where Criterion 1 is finally reached is regarded as the starting point of the accelerated deformation of the landslide.

[0123] In the embodiments of the present invention, according to the common landslide instability time prediction model based on velocity. After converting the observed values (i.e., velocity v, or inverse velocity 1 / v) to the left side of the equation, candidate models are obtained. In step S103, the multiple candidate models can be as shown in the following examples:

[0124] Table 1. Examples of candidate models

[0125] Number Name Expression Observed Value Unknown Parameter Model 1 SINV <![CDATA[1 / v = A(t c - t)]]> 1 / v, t <![CDATA[A,t c > Model 2 INV <![CDATA[1 / v = A(t c - t)]]> 1 / v, t <![CDATA[A,t c ,α]]> Model 3 Satio <![CDATA[v = a / (t c - t)]]> v, t <![CDATA[a,t c > Model 4 YAM <![CDATA[v=[a / (t c -t)] 1 / β > v, t <![CDATA[a,t c ,β]]>

[0126] The Bayesian method can quantify uncertainty and select the most suitable model, while allowing continuous updating of the prediction to match the landslide dynamic monitoring task. These advantages make the Bayesian method an attractive approach to address the model selection challenge.

[0127] Let M j represent the j-th candidate model (j = 1, 2,..., N c ), where N c is the number of candidate models. Assume that after the OOA point of the landslide, n sets of observed data d i are obtained at times t i (i = 1, 2,..., n), denoted as D obs = [(t 1 , d 1 ), (t 2 , d 2 ),..., (t n , d n )]. According to the Bayesian model selection method, under the condition of the observed data of the landslide acceleration stage, the credibility of the candidate model can be defined as the occurrence probability P(M obs | D j ), which can be expressed as: obs

[0128] ​

[0129] wherein, is a normalization constant; P(M j ) represents the prior information of model M j . In the absence of prior knowledge, it is usually assumed to follow a uniform distribution, that is, P(M j ) = 1 / N c ; P(D obs |M j ) represents the conditional probability of D j under the condition of the given candidate model M obs , that is, the model evidence. Obviously, P(M j |D obs ) is proportional to P(D obs |M j ). Therefore, the most suitable prediction model M * under the given observed data can be selected by comparing the model evidences. Mathematically, the model evidence P(D obs |M j ) can be expressed by the total probability theorem:

[0130] P(D obs |M j ) = ∫ θ P(D obs |θ, M j )P(θ|M j ) dθ (8)

[0131] wherein, θ is a vector of random variables; P(θ|M j ) represents the prior probability of model M j ; P(D obs |θ, M j ) represents the likelihood function reflecting the goodness of fit between the candidate model and the observed data. Considering the numerical differences of the observed data between different models, the residuals between the model predicted value D mod (M j , b) and the observed value D obs are standardized to ensure the objectivity of model comparison. Assume that the standardized residual ε follows a normal random variable with a mean of zero and a standard deviation of σ ε , and assume statistical independence. Then the likelihood function P(D obs |θ, M j ) can be expressed as:

[0132]

[0133] wherein, σ ε can be updated as a random variable. Therefore, the random variable vector θ = [b, σ ε . In addition, for the given model M j, the uncertainty associated with the random variable θ can be quantified by P(θ|D obs ,M j ). Using Bayesian inference, the posterior distribution P(θ|D j of the random variable θ in the model M obs ,M j ) can be expressed as:

[0134] P(θ|D obs ,M j ) = k -1 P(D obs |θ,M j )P(θ|M j ) (10)

[0135] where k is a normalization constant and is equal to the model evidence P(D obs |M j ). Therefore, using the above method, the candidate model most suitable for the current observed data can be selected, and the uncertainty of its instability time prediction can be quantified, and the instability time of the landslide can be predicted probabilistically.

[0136] Based on the posterior distribution of the instability time P(θ|D obs ,M j ), the instability time window t c at the corresponding significance level can be calculated. The embodiment of the present invention uses a 95% high density interval (HDI) as the instability time window. HDI refers to the value range interval that contains the highest density in the posterior probability distribution at a given confidence level (i.e., 95%).

[0137] The difficulty in using the Bayesian method lies in calculating the posterior distribution, which largely depends on the computational techniques for sampling from the posterior distribution. Sequential Monte Carlo (SMC), as a mature sampling technique, can effectively sample the posterior PDF P(θ|D obs ,M j ), and at the same time estimate the model evidence P(D obs |M j ) as a byproduct. The embodiment of the present invention uses the SMC sampler in the Python library PyMC3.

[0138] Thus, in the embodiment of the present invention, according to the observed data and the prior information of the random variables of each candidate model, the most suitable candidate prediction model can be selected based on the above formulas (7)-(10) based on the Bayesian method, and the uncertainty of its instability time prediction can be quantified.

[0139] In practice, the landslide deformation monitoring data is continuously updated. Whenever new monitoring data becomes available, it is necessary to quickly update the prediction results of the landslide instability time. Therefore, in the embodiments of the present invention, the method may further include the following steps: when an observed value of a new landslide deformation velocity is obtained, use the posterior information of the random variables of each candidate model in the previous update as the new prior information. Based on the new observed data and the prior information of the random variables of each candidate model, select the most suitable candidate prediction model based on the sequential Bayesian method, and quantify the uncertainty of its instability time prediction.

[0140] Specifically, based on the above method, the embodiments of the present invention propose a real-time dynamic probability prediction method for landslide instability time by combining sequential Bayesian update and parallel computing. The specific description is as follows:

[0141] (1) Prepare the input data, including the prior information of each candidate model and its random variables and the landslide deformation monitoring data in the landslide acceleration deformation stage. Among them, SINV and Satio require at least 3 velocity data in the first prediction, while INV and YAM require at least 4 velocity data.

[0142] (2) For each candidate model, use formula (7) to select the most suitable prediction model for the given observed value. Since this involves multiple independent analysis processes, use the Joblib library to parallelize the calculation on multiple CPU cores to reduce the calculation time. Then use formula (10) for Bayesian update, update the prior distribution of the random variable θ in the most suitable model, obtain the posterior probability density function (PDF) of the failure time, and use its 95% high density interval (HDI) as the predicted instability time window.

[0143] (3) When there is new landslide deformation in the acceleration stage, use the posterior information updated last time as the prior information. Under the framework of sequential Bayesian theory, combined with parallel processing, use formula (7) and formula (10) to dynamically select the most suitable model according to the latest observed value, and obtain the latest probability prediction result of the instability time in real time.

[0144] (4) Whenever new observed values are available, repeat step 3 to obtain the latest probability instability time prediction based on the most suitable model.

[0145] For the Bayesian model selection and update of each candidate model in Table 3, it is necessary to determine the prior information of the random variable θ, including the unknown parameter b of each model and the standard deviation σ of the error. ε. Generally, when the prior knowledge of random variables is limited, non-informative (e.g., uniform distribution) prior distributions are widely used. In addition, a sufficiently large prior distribution range can prevent the updated results from being significantly affected by prior boundaries. Moreover, when there are many observations, the influence of the initial prior information on the updated results can be ignored, and the sequential Bayesian updating method helps to further reduce this influence. Therefore, in the embodiments of the present invention, it is assumed that the prior information of all random variables follows a uniform distribution, and its range is determined by historical data and expert judgment. Table 4 summarizes the prior distribution ranges of all random variables. Considering the differences in monitoring frequencies in various situations, for convenience, the unit of the prior distribution of the instability time (usually hours and days) is consistent with its monitoring frequency. To ensure a sufficiently large prior range while avoiding invalid predictions, the time of the last observation is taken as t c The lower bound of the prior distribution, i.e., (t last ,t last +500].

[0146] Table 2. Prior PDFs of the candidate model random variables

[0147]

[0148] In the embodiments of the present invention, to illustrate the implementation and performance of the proposed method, an example of an artificial synthetic monitoring data set for real-time identification of OOA points is given. The advantage of synthetic data is that the true values of the monitoring data can be known, thus better verifying the performance of the method. The speed monitoring data is generated using a piecewise function based on the YAM model, expressed as follows:

[0149]

[0150] where v represents the speed data at time t, where t ∈ [0, 99]. The parameters a and β of the YAM model are set to 2500 and 2 respectively. The OOA point time t OOA is defined as 75; the instability time t c is set to 100. The generated monitoring data consists of discrete points that follow the continuous mathematical equation provided by Equation (7) and are spaced one time unit apart. In addition, random values following a standard normal distribution (i.e., mean of 0 and standard deviation of 1) are added to simulate the noise in the monitoring data.

[0151] Figure 2Shows the synthetic data and the filtered monitoring data in the embodiments of the present invention, as well as the OOA points determined using the method proposed in the embodiments of the present invention. Among them, part (a) is the synthetic data, (b) is the OOA point recognition result based on the synthetic data, and part (c) is the OOA point recognition result based on the filtered data. Among them, in part (a), the orange points represent the original velocity data, the green points represent the filtered velocity data, the blue line represents the ideal velocity curve, the red dashed line corresponds to the landslide instability time, and the purple dashed line corresponds to the true OOA point. In part (b), the green points correspond to criterion 0, the yellow points correspond to criterion 1, the orange points correspond to criterion 2, the red points correspond to criterion 3, the blue dashed line corresponds to the ideal velocity curve, the red dashed line corresponds to the instability time, and the orange dashed line corresponds to the OOA point determined using the method proposed in the embodiments of the present invention. In part (c), the green points correspond to criterion 0, the yellow points correspond to criterion 1, the orange points correspond to criterion 2, the red points correspond to criterion 3, the blue dashed line corresponds to the ideal velocity curve, the red dashed line corresponds to the instability time, and the orange dashed line corresponds to the OOA point determined using the method proposed in the embodiments of the present invention.

[0152] It can be clearly seen from Figure 2 that the original data with noise obscures the velocity trend and may interfere with the judgment of practitioners. According to the original monitoring data, the identified OOA point is 87, which is 12 unit times later than the true OOA point (75) due to the influence of noise (as shown in part b of Figure 2 ). In contrast, data filtering significantly reduces the noise and clarifies the deformation trend. The OOA point identified using the filtered data is 78, which only differs from the true value (75) by 3 unit times (as shown in part c of Figure 2 ). This small difference is acceptable because during the transition stage between the steady state and the accelerating state, the increase in the filtered velocity is negligible, confusing the boundary between these two stages. In this case, it is challenging to accurately determine the OOA by any method (including methods based on expert experience). In summary, the comprehensive example test shows that data filtering can significantly improve the data quality, and the OOA point recognition method proposed in the embodiments of the present invention has good performance.

[0153] Before determining the OOA point, the landslide velocity monitoring data needs to be preprocessed using the SG filtering method of formula (2). It can be seen from the results that the SG filter effectively reduces the noise in the monitoring data and clearly reveals the deformation trend of the landslide. This provides a good basis for subsequent determination of the OOA point.

[0154] In the embodiments of the present invention, further based on all the acceleration data identified from the original data set and the filtered data set, the predicted last (i.e., t = 99) instability time using the method proposed in the embodiments of the present invention is as shown in Figure 3As shown in Table 3. From the perspective of model selection, both datasets strongly favor the YAM model, with a probability of occurrence higher than 0.99. This is consistent with the previous hypothesis and confirms the performance of the proposed method in identifying the most suitable model. Regarding the prediction of the instability time, the mean instability times of the original and filtered datasets predicted by the most suitable model are 100.12 and 100.01 respectively, which are very close to the true value (100). In addition, the 95% HDI of the instability time prediction contains the true instability time, demonstrating the effectiveness of the prediction method. It is worth noting that the standard deviation of the instability time based on the filtered data (0.16) is smaller than that based on the original data (0.57), indicating that filtering reduces the uncertainty of the prediction and enhances the confidence of the prediction.

[0155] Table 3 Results of instability time prediction based on synthetic data

[0156]

[0157] In the embodiments of the present invention, landslide deformation monitoring data can be obtained from any instrument source to calculate the corresponding landslide speed, and it is filtered using the SG filter described in the above embodiments.

[0158] In the embodiments of the present invention, the OOA point identification method given in the above embodiments can be used to evaluate the deformation stage in real time. If the landslide enters the accelerated deformation stage, the next step is taken; otherwise, continuous monitoring is continued.

[0159] In the embodiments of the present invention, after determining that the landslide enters the accelerated deformation stage, the Bayesian method described in the above embodiments can be used to select the most suitable prediction model under the current observation data and quantify the uncertainty of its instability time prediction, realizing the probability prediction of the landslide instability time.

[0160] Finally, it should be emphasized that in the embodiments of the present invention, the landslide instability time can be predicted dynamically and in real time, and the latest instability time prediction can be obtained when new monitoring data is obtained.

[0161] In the embodiments of the present invention, a historical landslide dataset is established, which includes 15 historical landslide cases and has complete monitoring data reported in the literature. The cases in the dataset use a variety of different monitoring methods (total station, spaceborne InSAR, crack meter, etc.), cover a variety of slope types (natural, artificial fill, and mining slopes), and vary in volume, material, instability mechanism, and triggering factors. The monitoring data of most cases is obtained by digitizing scientific literature using WebPlotDigitizer software. The monitoring period of each case is long enough to include the transition between the stable creep stage and the accelerated creep stage.

[0162] In the embodiments of the present invention, the landslide deformation monitoring data corresponding to 15 historical landslide cases were classified according to the data monitoring frequency, aiming to capture the differences in different monitoring frequencies to verify the general applicability of the method proposed in the embodiments of the present invention. Table 4 summarizes the detailed information of the landslide cases.

[0163] Table 4. Information of the landslide case dataset

[0164]

[0165]

[0166] In the embodiments of the present invention, when evaluating the landslide deformation state, only the monitoring data available before the current moment is used to simulate the actual application scenario. The OOA identification results of the 15 landslide cases considered in the embodiments of the present invention are as Figure 4 and Figure 5 shown, Figure 4 showing the deformation monitoring data and OOA point identification results of Cases 1 to 8, Figure 5 showing the deformation monitoring data and OOA point identification results of Cases 9 to 15. It can be seen that in the 15 cases, the OOA points related to the final landslide instability were detected early enough (an average of 36.20 days) to enable timely prediction of the instability time. Among them, the OOA point of the Cadia tailings dam landslide monitored by satellite InSAR was determined 95.78 days before the instability, while the latest acceleration trend leading to the collapse of the No. 1 open-pit mine landslide monitored by GB-SAR was detected 0.92 days before the instability. The results show that for the 15 landslide cases with different monitoring instruments and monitoring frequencies, the proposed method can successfully identify the OOA points in a real-time scenario.

[0167] In addition, it is also necessary to timely identify the latest landslide deformation trend. The method proposed in the embodiments of the present invention detected repeated acceleration stages in multiple landslide cases, such as the Iron Mine landslide, the Letlhakane landslide, the No. 1 open-pit mine landslide, and the Preonoz landslide. These findings are consistent with the actual deformation trend, verifying the excellent performance of the proposed method. Landslides are affected by rainfall, human activities, and stability degradation, resulting in accelerated deformation. However, when the influence of external factors is mitigated or weakened by the self-organization effect, it may lead to the landslide reaching a new steady state. The method proposed in the embodiments of the present invention can use the latest deformation monitoring data to update the current deformation state in real time. When the landslide deformation continues to accelerate under the positive feedback mechanism and leads to instability, the method can also successfully identify the final OOA point.

[0168] Finally, on the same workstation ( Core TMUnder the condition of an i5-14600KF CPU @ 3.5 GHz and 32 GB of RAM, the computational efficiency of the proposed method was evaluated by simulating a real landslide monitoring scenario (i.e., dynamically and real-time identifying OOA points as new monitoring data is obtained). In the scenario of small-sample monitoring data, each OOA point detection can be completed within 0.2 seconds; in the case of large-sample monitoring data, each OOA point detection can be completed within 0.1 seconds, and this process can be considered to be completed in real time. Taking the Vajont landslide (small-sample monitoring data set, 21 data points) and the Preonoz landslide (large-sample monitoring data set, 649 data points) as examples, the total time for OOA point identification was 3.50 seconds and 9.44 seconds, respectively. This method has a low computational cost and excellent performance, and can provide strong support for the real-time interpretation of landslide monitoring data in practical applications.

[0169] In summary, the OOA point identification method proposed in the embodiments of the present invention is general and can achieve real-time automatic identification, and performs well among different monitoring methods for 15 landslide cases considered. This provides the key and necessary conditions for the successful implementation of landslide warning.

[0170] Based on the identified OOA points, the landslide instability time prediction method dynamically selected based on the landslide warning model proposed in the embodiments of the present invention was further applied to all landslide cases with monitoring data in the acceleration stage. In the same computing environment ( Core TM i5-14600KF CPU @ 3.5 GHz, 32 GB of RAM), the dynamic prediction of the instability time of 15 landslides was carried out by simulating a real landslide warning scenario. Whenever new landslide monitoring data in the acceleration stage is obtained, the prediction of the instability time of each landslide can be completed within 160 seconds, with the shortest calculation time being approximately 40 seconds and the median being approximately 85 seconds. Compared with high-frequency monitoring (e.g., 30-minute sampling interval), this process can be considered to be carried out in real time. In the embodiments of the present invention, the most probable value (t m ), mean (μ t ), standard deviation (σ t ), and 95% HDI were obtained from the posterior probability distribution of the instability time to characterize the instability time prediction results. The most probable value and 95% HDI provide direct information for key warning decisions, while the mean and standard deviation reflect the central tendency and prediction uncertainty.

[0171] It is crucial to evaluate the reliability of the final prediction results, as it directly relates to the success of the final early warning. Table 5 lists the probability prediction results of the last instability time for 15 landslide cases. Among the selected models, the SINV model was chosen by the most cases (8 cases), followed by the INV model (4 cases) and the Satio model (3 cases), while the YAM model was not selected. The embodiments of the present invention use three metrics to evaluate the accuracy and uncertainty of the prediction: (a) the deviation between the most likely instability time and the actual instability time, (b) the interval length of the 95% HDI (reflecting the uncertainty of the prediction), (c) whether the HDI includes the actual instability time. For the prediction results, the most likely instability time in all cases was close to the actual instability time, with the minimum, average, and maximum errors being 0.02 h, 0.62 d, and 2.40 d, respectively; the minimum, average, and maximum lengths of the 95% HDI were 1.09 h, 8.21 d, and 68.38 d, respectively; the actual instability times of all cases fell within the predicted instability time intervals, indicating successful prediction. Overall, the proposed method performed well in predicting the instability time in these cases.

[0172] Table 5. Final prediction results of landslide instability time based on the most suitable prediction model

[0173]

[0174]

[0175] To highlight the advantages of the proposed model selection method, the prediction results obtained from the embodiments of the present invention were compared with the prediction results of each candidate model for 15 landslide cases (as Figure 6As shown, in order to emphasize the differences in predictions, linear coordinates are used for the relative errors in the range of -10 to 10, and logarithmic coordinates are used for relative errors beyond this range. In the final predictions of 15 landslide cases, the average errors of the most likely instability times predicted by the SINV, INV, Satio, and YAM models alone are 1.08 d, 8.38 d, 46.58 d, and 40.85 d, respectively; the average lengths of the 95% HDI predictions are 9.56 d, 45.10 d, 61.62 d, and 129.39 d, respectively; and the 95% HDI predictions fail to cover the actual instability times in 3 cases, 1 case, 6 cases, and 7 cases, respectively, indicating prediction failures. In contrast, the proposed model selection method can well balance the accuracy and uncertainty of predictions, thus making reliable predictions. A small number of observations at the beginning of the acceleration stage make it difficult to accurately characterize the landslide deformation trend, resulting in a high degree of uncertainty in model selection and instability time prediction, especially for the more complex INV and YAM models. As monitoring progresses, more observations and sequential update methods help to dynamically select a model suitable for the current deformation evolution characteristics and accurately calibrate the instability time. In the case study, the proposed method tends to provide the best predictions and is in close agreement with the actual instability time, demonstrating the excellent performance of the method proposed in the embodiments of the present invention.

[0176] Finally, based on the models selected in Table 6, the final prediction results of landslide cases at different monitoring frequencies are summarized. The method provided in the embodiments of the present invention provides a more accurate prediction of the instability time for landslide cases with a higher monitoring frequency, and the most likely instability time is closer to the actual instability time. A higher monitoring frequency also improves the credibility of decision-making, reduces the standard deviation, and narrows the 95% HDI of the predicted instability time. This advantage may be due to the fact that the rich observations obtained through a high monitoring frequency can more precisely depict the landslide deformation evolution, providing a basis for accurate and reliable instability time prediction. A lower monitoring frequency often means fewer observed values, thus introducing more significant prediction uncertainties, that is, a larger standard deviation and interval length. Therefore, increasing the landslide monitoring frequency is crucial for reliable instability time prediction.

[0177] Table 6. Prediction results of the instability time of landslide cases at different monitoring frequencies

[0178]

[0179] In summary, the method proposed in the embodiments of the present invention, with integrated model selection, can overwhelmingly outperform traditional single-model prediction methods, making it a practical tool for landslide early warning. At the same time, 15 case studies demonstrate the feasibility of the method proposed in the embodiments of the present invention for predicting the landslide instability time under various monitoring methods, proving its general applicability.

[0180] In the embodiments of the present invention, four representative landslide cases are selected, and different monitoring methods with different frequencies are used to illustrate in detail the performance of the method proposed in the embodiments of the present invention.

[0181] 1. Preonoz Landslide

[0182] In the embodiments of the present invention, the Preonoz landslide is mainly composed of amphibolite and gneiss, and it has experienced several large-scale catastrophic damages in history. According to the landslide deformation data monitored by crack gauges starting from May 1, 2012, this landslide event was reviewed again using the proposed method. Let t = 0 represent the first measurement date, then the landslide instability failure time is 14.06 d. First, the SG filter is used to preprocess the original velocity data (as shown in part (a) of Figure 5 . Then, the embodiments of the present invention evaluate the velocity NFR (i.e., 95% CI) at each monitoring moment in real time (as shown in part (a) of Figure 5 . Combining the OOA point real-time identification criterion proposed by the present invention, two key OOA points are determined (as shown in part (b) of Figure 5 . The first landslide acceleration event finally converges to a new steady state, while the second landslide acceleration event finally leads to landslide instability. These results are consistent with the actual decisions described in this case, and the method proposed in the embodiments of the present invention detects the OOA point earlier and provides more safety margins.

[0183] In practice, the authorities should pay attention when the landslide accelerates for the first time, although this does not immediately lead to damage. Based on all the monitoring data in the first acceleration stage (as shown in part (c) of Figure 7 , the method proposed in the invention embodiments is used to predict the landslide instability time (as shown in part (d) of Figure 7 . The probability of selecting the INV model is 0.91, and the most likely instability time predicted by it is 8.77 d, and the 95% HDI range is [7.33 d, 10.03 d], which is several days later than the last observation time (5.69 d) in the first acceleration stage. The results show that although the landslide has entered the acceleration stage, the possibility of its immediate damage is low, and monitoring should continue to make more reliable decisions.

[0184] Using the data in the second acceleration stage (as shown in part (e) of Figure 7 , the final prediction result (as shown in part (f) of Figure 7(as shown in part (f)). The most likely instability times predicted by the SINV, INV, Satio, and YAM models are 13.87, 14.12, 14.10, and 14.29 d, respectively. Among them, the results predicted by the INV and Satio models are closest to the actual instability time (14.06 d). The 95% HDIs predicted by the two models are [14.00 d, 14.23 d] and [14.08 d, 14.12 d], respectively. Although the Satio model provides a narrower HDI and less uncertainty, it fails to cover the actual instability time and is thus a failed prediction. The method provided in the embodiments of the present invention firmly selects the INV model with a probability of occurrence of 0.99 because it reasonably balances the uncertainty and accuracy of the prediction.

[0185] Among them, Figure 7 shows the results of the Preonoz landslide case analysis. Part (a) shows the filtered velocity and its NFR (95% CI) results; part (b) shows the monitoring data and the OOA point identification results; part (c) shows the monitoring data of the first acceleration stage, part (d) shows the predicted results of the instability time corresponding to the first acceleration stage; part (e) shows the monitoring data of the second acceleration stage, and part (f) shows the predicted results of the instability time corresponding to the second acceleration stage.

[0186] 2. Iron Mine Landslide

[0187] In this case, the prism station measurement technology was used to monitor the deformation of an iron ore slope. The overall angle of the slope is about 75°, and the height is 80 m. Eventually, wedge-shaped sliding instability occurred due to being cut and surrounded by structural planes on both sides. Figure 6 Part (a) in shows the deformation data of the Iron Mine landslide recorded by station No. 65 with a frequency of 1 d. The original data was processed using the SG filtering method, and the further OOA identification results are as Figure 6 shown in part (b). During the entire deformation stage, a total of three landslide acceleration events were detected. The first acceleration event was characterized by a brief and slight increase in velocity, followed by stability, while the second was a brief increase and then a decrease to the normal fluctuation range. The final acceleration event was detected at t = 53 d, and the velocity continued to increase until the landslide failed at t = 70 d. The method successfully identified multiple landslide acceleration events and updated the OOA point identification results in real time according to the latest monitoring data, demonstrating the good performance of the method. According to the monitoring data of the final acceleration stage leading to the failure, the method proposed in the embodiments of the present invention was used to predict the landslide failure time, simulating the real warning process. The SINV model was selected, and the probability of occurrence of the model increased from 0.40 to 0.96, indicating an increasing confidence in selecting this model. Figure 8Part (c) shows the expected lifetime of the landslide obtained from the most likely instability time predicted by the selected model, which is in good agreement with the actual trend, verifying the prediction results. Figure 8 Part (d) shows the 95% HDI of the instability time predicted by the selected model, which well contains the actual instability time. Moreover, as the monitoring data increases, the window of the instability time predicted by the sequential update method narrows and finally converges to the actual instability time.

[0188] Among them, Figure 8 shows the results of the iron ore landslide: Part (a) represents the filtered velocity and its NFR (95% CI); Part (b) represents the monitoring data and the OOA point identification results; Part (c) represents the results of the dynamic prediction of the expected lifetime of the landslide; Part (d) represents the results of the dynamic prediction of the instability time.

[0189] 3. Landslide on Mount Beni

[0190] On December 28, 2002 (t = 268.00d in the example of the present invention), on the east side of Mount Beni in Florence, Italy, a landslide with a volume of 500,000 m 3 occurred. The landslide body is jointed basalt and ophiolitic breccia covering limestone. The east slope of Mount Beni experienced quarrying activities from the 1940s to the 1980s, but was closed due to safety issues. The authorities installed portable logging instruments on the main cracks and measured the landslide deformation every few days.

[0191] Similarly, the original data was filtered, and OOA points were identified based on this. The results are shown in Figure 9 Parts (a) and (b). The first OOA point appeared at t = 33.52 days, when the landslide might be in the decelerating creep stage and then entered the steady-state creep stage. The second OOA point appeared at t = 162.44d, and then the velocity increased, but suddenly decelerated at t = 200.68d, disrupting the accelerating trend. In this case, determining the latest OOA point is crucial for reliable prediction. After the deceleration, the analysis was restarted, and the latest OOA point was determined to be t = 209.52d. After that, the velocity continued to increase until the instability failure.

[0192] Based on the data in the latest acceleration stage, the landslide failure time was predicted. The occurrence probability of each candidate model at each update is shown in Figure 9 Part (c). Generally speaking, in most updates, the Satio model has a higher occurrence probability. The exceptions are the 3rd and 4th updates, in which the occurrence probability of the YAM model exceeds that of the Satio model, but then decreases. This fluctuation may be due to the sudden increase in the landslide velocity at the 3rd and 4th updates, which makes the deformation evolution trend difficult to predict, so a more complex model is needed.

[0193] The dynamic prediction results based on the most suitable model are as follows Figure 9 shown in (d). Based on the continuous monitoring data and the sequential Bayesian update method, the predicted most likely instability time converges to the actual instability time. In the final prediction, the most likely instability time is 269.82 d, with a difference of only 1.82 d from the actual instability time (268.00 d). The 95% HDI of the predicted instability time always includes the actual instability time for each update. The more updates are made, the narrower the window of the predicted instability time, and the final predicted instability time window is [266.84 d, 274.87 d]. Therefore, the proposed method can be applied to the dynamic prediction scenario with real-time landslide monitoring.

[0194] Among them, Figure 9 shows the results of the Beni landslide. Part (a) represents the filtered velocity and its NFR (95% CI); part (b) represents the monitoring data and the OOA point identification results; part (c) represents the dynamic model selection, and part (d) represents the corresponding instability time prediction.

[0195] 4. Cadia Tailings Dam Landslide

[0196] In this case, the historical deformation of the Cadia Tailings Dam landslide since 2017 was analyzed using the satellite InSAR method and Sentinel-1 data (revisit time of 12 d), and its velocity record is as shown in part (a). For simplicity, November 16, 2016 was set as t = 0 d, and the landslide instability time is 431.78 d. According to the established procedure, the original velocity data was filtered, and the OOA points were determined using the proposed method. Figure 7 Part (b) shows the OOA point identification results. The first OOA point appears at t = 12 d, and then the landslide velocity drops to the normal fluctuation range, indicating that the landslide enters the steady-state creep stage. Subsequently, the last OOA point is detected at t = 336 d, and the velocity continues to increase until the final failure. This finding is consistent with the object-oriented analysis results in the related technology, proving the effectiveness of the proposed method. Figure 7 Shown in the detailed dynamic instability time prediction based on the data in the acceleration stage in part (c). At the same time,

[0197] Based on Figure 10 the data in the acceleration stage in part (c) for the detailed dynamic instability time prediction. At the same time, Figure 10Part (d) shows the probability distribution of the instability time predicted by the most suitable model. Initially, the method proposed in the present invention selected the INV model in the first three updates and finally selected the SINV model. As the monitored data obtained increased, the average value of the predicted instability time changed from 501.50 d at the first update to 433.86 d at the last update, while the standard deviation decreased from 118.85 d to 10.73 d, indicating a significant reduction in the prediction uncertainty. The most likely predicted instability time changed from 409.55 d (with a difference of 22.23 d from the actual instability time) to 432.00 d (with an error of 0.22 d). The 95% HDI also converged from [372.02 d, 770.33 d] to [420.76 d, 446.65 d]. Therefore, the proposed dynamic model selection method can still be well applied to the real-time landslide failure time prediction under the condition of extremely low monitoring frequency of satellite InSAR.

[0198] Among them, Figure 10 shows the landslide results of the Cadia tailings dam: part (a) represents the filtering velocity and its NFR (95% CI); part (b) shows the monitored data and the OOA point identification results; part (c) shows the monitored data in the acceleration stage; part (d) shows the corresponding probability prediction of the instability time.

[0199] In summary, it can be seen that the method proposed in the embodiment of the present invention performs well in identifying multiple acceleration stages and provides reliable instability time prediction according to the final acceleration stage.

[0200] Based on the same inventive concept, the embodiment of the present invention also provides a landslide instability time prediction device based on dynamic selection of a landslide warning model. The landslide instability time prediction device based on dynamic selection of a landslide warning model includes:

[0201] A first acquisition module for acquiring landslide deformation monitoring data;

[0202] A first determination module for determining the starting point of landslide accelerated deformation according to the landslide deformation monitoring data, and the starting point of landslide accelerated deformation characterizes that the landslide enters the accelerated deformation stage;

[0203] A second acquisition module for, when it is determined that the landslide enters the accelerated deformation stage, acquiring the landslide deformation velocity corresponding to each moment in the accelerated deformation stage as observation data, and acquiring a plurality of candidate models and prior information of random variables of each candidate model;

[0204] A selection module for selecting the most suitable candidate model based on the Bayesian method according to the observation data and the prior information of random variables of each candidate model, and quantifying the uncertainty of its instability time prediction;

[0205] A prediction module, configured to predict the probability of instability time based on the most suitable candidate model, so as to obtain the landslide instability time.

[0206] Based on the same inventive concept, an embodiment of the present invention further provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor. When the processor executes, it implements the steps in the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in any of the above embodiments.

[0207] Based on the same inventive concept, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, it implements the steps in the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in any of the above embodiments.

[0208] Based on the same inventive concept, an embodiment of the present invention provides a computer program product, including a computer program / instructions. When the computer program / instructions are executed by a processor, they implement the steps in the landslide instability time prediction method based on dynamic selection of a landslide warning model as described in any of the above embodiments.

[0209] Each embodiment in this specification is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other.

[0210] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a device, or a computer program product. Therefore, the embodiments of the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the embodiments of the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0211] The embodiments of the present invention are described with reference to the flowcharts and / or block diagrams of the methods, terminal devices (devices), and computer program products according to the embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, and the combination of processes and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable terminal devices to generate a machine, so that the instructions executed by the processor of the computer or other programmable terminal devices generate a device for realizing the functions specified in Figure 1 one process or multiple processes and / or blocks Figure 1 one block or multiple blocks.

[0212] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable terminal device to work in a particular manner, such that the instructions stored in the computer-readable memory produce a manufacture including an instruction device that implements the functions specified in one or more processes and / or blocks Figure 1 of one or more processes and / or blocks Figure 1 specified in the block or blocks.

[0213] These computer program instructions can also be loaded onto a computer or other programmable terminal device, such that a series of operational steps are performed on the computer or other programmable terminal device to produce a computer-implemented process, whereby the instructions executed on the computer or other programmable terminal device provide steps for implementing the functions specified in one or more processes and / or blocks Figure 1 of one or more processes and / or blocks Figure 1 specified in the block or blocks.

[0214] Although the preferred embodiments of the embodiments of the present invention have been described, those skilled in the art can make additional changes and modifications once they learn the basic creative concepts. Therefore, the appended claims are intended to be construed to include the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present invention.

[0215] Finally, it should also be noted that in this text, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover non-exclusive inclusion, such that a process, method, article or terminal device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or terminal device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or terminal device comprising the element.

[0216] The above has introduced in detail a landslide instability time prediction method based on dynamic selection of a landslide warning model. In this article, specific examples are used to elaborate on the principle and implementation manner of the present invention. The description of the above embodiments is only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manner and application scope. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A landslide instability time prediction method based on dynamic selection of landslide early warning model, characterized in that: The method comprises: Obtain landslide deformation monitoring data; Determine a landslide accelerated deformation starting point according to the landslide deformation monitoring data, wherein the landslide accelerated deformation starting point indicates that the landslide has entered an accelerated deformation stage; When it is determined that the landslide has entered the accelerated deformation stage, the deformation speed of the landslide corresponding to each moment in the accelerated deformation stage is obtained as observation data, and a priori information of multiple candidate models and random variables of each candidate model is obtained; According to the observed data and the prior information of the random variables of each candidate model, the most suitable candidate model is selected based on the Bayesian method, and the uncertainty of its instability time prediction is quantified; The probabilistic instability time is predicted based on the most suitable candidate model to obtain the landslide instability time.

2. The method for predicting landslide instability time based on dynamic selection of landslide early warning model according to claim 1 is characterized in that: According to the observed data and the prior information of the random variables of each candidate model, the most suitable candidate model is selected based on the Bayesian method, and the uncertainty of its instability time prediction is quantified, including: Let M j represents the jth candidate model (j=1,2,...,N c ), where N c is the number of candidate models; after the landslide OOA point, at t i n groups of observation data d obtained at time (i=1,2,...,n) i , denoted as D obs =[(t1,d1),(t2,d2),...,(t n ,d n )]; According to the Bayesian method, under the given observation data of the landslide acceleration stage, the credibility of the candidate model is defined as D obs The probability of occurrence of the model under the condition P(M j |D obs ), expressed as: in, is a normalizing constant; P(M j ) represents the model M j In the absence of prior knowledge, it is assumed that it obeys a uniform distribution, that is, P(M j )=1 / N c ; P(D obs |M j ) represents a given candidate model M j D under the condition obs The conditional probability of model evidence; P(M j |D obs ) and P(D obs |M j ), and selects the most suitable candidate model M given the current observation data by comparing model evidence. * ; Model evidence P(D obs |M j ) can be expressed using the total probability theorem: P(D obs |M j )=∫ θ P(D obs |θ,M j )P(θ|M j )dθ; Where θ is a random variable vector; P(θ|M j ) represents the model M j The prior probability of obs |θ,M j ) represents the likelihood function reflecting the goodness of fit between the candidate model and the observed data. Considering the numerical differences of the observed data between different models, the model prediction value D mod (M j ,b) and the observed value D obs The residuals between are standardized to ensure the objectivity of model comparison; it is assumed that the standardized residual ε has a mean of zero and a standard deviation of σ ε Normal random variables, and assuming statistical independence, the likelihood function P(D obs |θ,M j ) is expressed as: Among them, σ ε As a random variable, the random variable vector θ = [b,σ ε ]; For a given model M j , the uncertainty associated with the random variable θ is expressed by P(θ|D obs ,M j ) to quantify; Using the Bayesian approach, the model M j The posterior distribution of the random variable θ in P(θ|D obs ,M j ) is expressed as: P(θ|D obs ,M j )=k -1 P(D obs |θ,M j )P(θ|M j ) Where k is a normalization constant and is equal to the model evidence P(D obs |M j ); Based on the above steps, the candidate model that best fits the current observation data is selected and the uncertainty of its instability time prediction is quantified.

3. The method for predicting landslide instability time based on dynamic selection of landslide early warning model according to claim 2 is characterized in that: The method comprises: When new observations of landslide deformation velocity are obtained, the new observations of landslide deformation velocity are added to the observation sequence to obtain a new observation sequence. According to the new observation data and the prior information of the random variables of each candidate model, the candidate model that best suits the current observation data is selected based on the Bayesian method, and the uncertainty of its instability time prediction is quantified.

4. The method for predicting landslide instability time based on dynamic selection of landslide early warning model according to claim 1 is characterized in that: Determining the starting point of accelerated landslide deformation according to the landslide deformation monitoring data includes: Determining the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data; Determine a velocity confidence interval according to the landslide deformation velocity corresponding to each moment, wherein the velocity confidence interval represents the velocity fluctuation range of the landslide in the steady-state creep stage; When the landslide deformation velocity at the target time is greater than the velocity confidence interval, the target time is determined as the starting point of the landslide accelerated deformation.

5. The method for predicting landslide instability time based on dynamic selection of landslide early warning model according to claim 1 is characterized in that: Determining the starting point of accelerated landslide deformation according to the landslide deformation monitoring data includes: Determining the landslide deformation speed corresponding to each moment according to the landslide deformation monitoring data; Determine a velocity confidence interval according to the landslide deformation velocity corresponding to each moment, wherein the velocity confidence interval represents the velocity fluctuation range of the landslide in the steady-state creep stage; When the deformation velocity of the landslide at the first moment is within the velocity confidence interval, determining that the landslide is in a steady-state creep stage at the first moment; When the landslide deformation velocity at the second moment exceeds the velocity confidence interval for the first time, and the landslide deformation velocity at the third moment exceeds the velocity confidence interval, and the landslide deformation velocity at the three moments is greater than the landslide deformation velocity at the second moment, it is determined that the landslide enters the accelerated deformation stage, and the third moment is the next moment of the second moment; When the deformation speed of the landslide at the second moment, the third moment and the fourth moment all exceed the speed confidence interval and the linear fitting slope is greater than 0, it is determined that the landslide has entered the accelerated deformation stage and is in the uniform acceleration stage; the fourth moment is the next moment of the third moment; The second moment is determined as the starting point of accelerated deformation of the landslide.

6. The method for predicting landslide instability time based on dynamic selection of landslide early warning model according to claim 4 or 5, characterized in that: The velocity confidence interval is determined according to the landslide deformation velocity corresponding to each moment, including: Arrange the landslide deformation velocities corresponding to each moment in ascending order, and use the following formula to determine the lower limit v of the confidence interval corresponding to the significance level α: α / 2 and upper limit v 1-α / 2 : Among them, N is the number of samples from the original The number of Bootstrap subsamples constructed by random sampling; Represents the time series of landslide deformation velocity represents the i-th Bootstrap subsample; Percentile(·) represents the calculation process using the percentile method.

7. A landslide instability time prediction device based on dynamic selection of landslide early warning model, characterized in that: The landslide instability time prediction device based on dynamic selection of the landslide early warning model comprises: The first acquisition module is used to acquire landslide deformation monitoring data; A first determination module is used to determine a starting point of accelerated deformation of the landslide according to the landslide deformation monitoring data, wherein the starting point of accelerated deformation of the landslide indicates that the landslide has entered an accelerated deformation stage; The second acquisition module is used to obtain the landslide deformation speed corresponding to each moment of the accelerated deformation stage as observation data when it is determined that the landslide has entered the accelerated deformation stage, and to obtain a priori information of multiple candidate models and random variables of each candidate model; A selection module, for selecting the most suitable candidate model based on the Bayesian method according to the observed data and the prior information of the random variables of each candidate model, and quantifying the uncertainty of its instability time prediction; The prediction module is used to predict the probabilistic instability time based on the most suitable candidate model to obtain the landslide instability time.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the method for predicting landslide instability time based on dynamic selection of a landslide early warning model according to any one of claims 1 to 6 is implemented.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for predicting landslide instability time based on dynamic selection of a landslide early warning model as described in any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instruction is executed by a processor, the steps in the method for predicting landslide instability time based on dynamic selection of a landslide early warning model as described in any one of claims 1 to 6 are implemented.

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