Landslide stability early warning method based on deformation rate probability standardization conversion

Abstract

This invention provides a landslide stability early warning method based on probability normalization transformation of deformation rate, comprising the following steps: data preprocessing, normality test, probability density function fitting, and landslide deformation rate V( m) The process involves cumulative probability density function, standard normalization transformation, warning level classification, and output. First, landslide deformation monitoring is conducted, and cumulative displacement time-series data at key locations on the landslide slope are collected. Then, the cumulative displacement difference and time difference between two consecutive monitoring data points are calculated to obtain the landslide deformation velocity time series. Next, it is verified whether the current landslide deformation velocity frequency distribution conforms to a normal distribution. If it does, the landslide is considered safe, and no warning is issued. Otherwise, the obtained landslide deformation velocity values ​​are set to zero, and the landslide deformation velocity frequency distribution is recalculated. A probability distribution of displacement velocities greater than zero is fitted to obtain its probability density function. The relationship between landslide deformation velocity and the deformation index DI is determined. Finally, the warning level is output.

Description

Technical Field

[0001] This invention relates to the technical field of geological disaster early warning, and in particular to a landslide stability early warning method based on deformation rate probability standardization conversion. Background Technology

[0002] my country is a mountainous country prone to geological disasters, with landslides being particularly severe. These disasters are widespread and extremely dangerous, causing substantial economic losses annually, a fact that cannot be ignored by society. Developing accurate and scientific methods for early warning of landslide stability, enabling the identification and early warning of landslide deformation states, is a crucial means of preventing and controlling landslide geological disasters.

[0003] Commonly used landslide stability early warning methods include stability coefficients and reliability probability criteria, macroscopic prediction criteria, creep curve tangent angle criteria, and deformation rate and acceleration criteria. These methods all have certain applicability, but their limitations cannot be ignored. For example, stability coefficients and reliability probabilities ignore the creep characteristics of the landslide body and the time effect of landslide stability, thus limiting their application to long-term landslide prediction. Macroscopic prediction criteria are easy to obtain, but require verification by professional technicians; otherwise, misjudgments are likely. Creep curve tangent angle criteria are limited by dimensional differences and threshold effects, lacking universality. Landslide deformation is generally considered to involve three stages: initial deformation, isochronous deformation, and accelerated deformation. Evaluation methods based on deformation rate and acceleration rely on typical landslide cumulative displacement-time curve characteristics, which are relatively intuitive. However, due to differences in engineering geological conditions and influencing factors across different slopes, the threshold for landslides is difficult to standardize, limiting their practical application.

[0004] Therefore, proposing a widely applicable and easy-to-use landslide stability early warning method is of great practical significance. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a landslide stability early warning method based on deformation rate probability normalization transformation, aiming to solve the problems of the large limitations and limited use of existing landslide stability early warning methods.

[0006] Embodiments of the present invention provide a landslide stability early warning method based on deformation rate probability normalization transformation, comprising the following steps:

[0007] S1, Data Preprocessing: Landslide deformation monitoring and collection of cumulative displacement time series data at key locations on the landslide surface: S (m) ={s1,s2,…s m};

[0008] S2, Normality Test: Calculate the cumulative displacement difference and time difference between two consecutive monitoring data points to obtain the landslide deformation velocity time series as V. (m) ={v1,v2,…vm After calculating the frequency distribution of landslide deformation velocity, the Liffiefors test is used to preliminarily verify whether the current frequency distribution of landslide deformation velocity satisfies a normal distribution. If it does, the landslide is in a safe state and no warning is issued; otherwise, proceed to the next step.

[0009] S3, Probability density function fitting: After obtaining the value of the landslide deformation velocity as zero, recalculate the frequency distribution of the landslide deformation velocity, and obtain its probability density function by fitting the probability distribution of displacement velocity greater than zero through the Gamma function.

[0010] S4, landslide deformation rate V (m) Cumulative probability density function: Calculate the cumulative probability density function of landslide deformation velocity for the two cases where the velocity is 0 and greater than 0, respectively;

[0011] S5, Standard Normalization Transformation: By transforming the cumulative probability function into an equal probability form, the transformation relationship between the Gamma distribution and the standard normal distribution is established, and the relationship between the landslide deformation rate and the deformation index DI is determined.

[0012] S6, Warning Level Classification and Output: Based on the deformation index value of the last monitoring point and its dangerous zone, the warning level is output.

[0013] Further, in step S3, the probability density function f (v) for:

[0014]

[0015] Where α and β are the shape and scale parameters, respectively, which are estimated using the maximum likelihood method:

[0016]

[0017]

[0018]

[0019] Where m is the number of observation data. This is the average value of all current deformation velocities.

[0020] Furthermore, in step S4, when the landslide deformation rate is greater than 0, the cumulative probability function F is obtained by integrating the probability density function of equation (1). (v) for:

[0021]

[0022] When the landslide deformation rate is equal to 0, its cumulative probability is estimated by the following formula:

[0023]

[0024] Where n is the number of monitoring data points with a velocity of 0;

[0025] At this moment, the landslide deformation velocity V (m) The cumulative probability function G (v) for:

[0026] G(v)=P+(1-P)F(v) (7).

[0027] Further, in step S5, the standard normalization is converted into the landslide deformation velocity v for any data sample point. i After obtaining its cumulative probability value, the x-value corresponding to the cumulative probability value of the standard normal distribution cumulative probability function is the deformation velocity v. i The deformation index DI value.

[0028] Furthermore, the landslide deformation rate V (m) The cumulative probability function G (v) The standard normalization transformation formula is:

[0029]

[0030] After solving, we can obtain:

[0031]

[0032]

[0033] Where c0, c1, c2, d1, d2, and d3 are conversion factors, which are 2.515517, 0.802853, 0.010328, 1.432788, 0.189269, and 0.001308, respectively.

[0034] Furthermore, in step S6, the dangerous interval division of the deformation index is based on the probability distribution characteristics of the standard normal function.

[0035] Furthermore, in step S6, the warning levels are divided as follows: -2 to -1 is strong safety; -1 to 0 is weak safety; 0 to 1 is weak danger; 1 to 2 is strong danger; and 2 and above is extremely dangerous.

[0036] Furthermore, in step S1, the landslide deformation monitoring is conducted at equal time intervals.

[0037] Furthermore, in step S2, the landslide deformation rate is in a uniform unit.

[0038] The beneficial effects of the technical solutions provided by the embodiments of the present invention are as follows:

[0039] 1. The main data basis of the method of the present invention is cumulative displacement data, which is the most readily available and most accurate landslide deformation characteristic parameter and has strong practicality.

[0040] 2. The method of this invention defines a deformation index and a hazard level division interval based on velocity standardization conversion. After the displacement velocity is converted in probability space, the corresponding warning level is obtained to realize the warning. The calculation process of this method is simple, the mathematical principle is accurate, and it has a certain degree of reliability.

[0041] 3. This method is based on the analysis of cumulative displacement curves with significant increasing deformation trends. The analysis process is based on the probabilistic processing of cumulative displacement data according to the deformation law of landslides. It is not limited to specific types of landslides or landslide materials and has a certain degree of universality. Attached Figure Description

[0042] Figure 1 This is a flowchart of an embodiment of the landslide stability early warning method based on deformation rate probability normalization conversion provided by the present invention;

[0043] Figure 2 This is a schematic diagram illustrating the calculation process and early warning zoning principle of the method of the present invention;

[0044] Figure 3 This is a schematic diagram illustrating the application of the method of the present invention to the displacement curve of a convergent landslide.

[0045] Figure 4 This is a schematic diagram illustrating the application of the method of the present invention to the displacement curve of a stable landslide;

[0046] Figure 5 This is a schematic diagram illustrating the application of the method of the present invention to the displacement curve of an exponential landslide;

[0047] Figure 6 This is a schematic diagram illustrating the application of the method of the present invention to the displacement curve of a stepped landslide. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0049] Please refer to Figures 1-2 As shown, Figure 1 This is a flowchart illustrating the computational principle of the method of the present invention. Figure 2 This is a schematic diagram illustrating the calculation process and early warning zoning principle of the method of the present invention. (Refer to...) Figure 1 and 2 This invention introduces a landslide stability early warning method based on deformation rate probability normalization transformation, comprising the following steps:

[0050] S1, Data Preprocessing: Landslide deformation monitoring and collection of cumulative displacement time series data at key locations on the landslide surface: S (m) ={s1,s2,…s m};

[0051] Specifically, landslide deformation monitoring here can be conducted using in-situ GNSS or other monitoring methods. After collecting data from key locations on the landslide surface, interpolation methods are used to supplement missing monitoring data caused by various factors. Since landslide deformation is the result of a series of uncertain factors, such as inducing factors and observation errors, landslide displacement monitoring data can be considered as random variables, and the landslide deformation rate based on this can also be considered as random variables.

[0052] It is worth noting that the landslide deformation monitoring is conducted at equal time intervals, such as daily or monthly monitoring.

[0053] S2, Normality Test: Calculate the cumulative displacement difference and time difference between two consecutive monitoring data points to obtain the landslide deformation velocity time series as V. (m) ={v1,v2,…v m After calculating the frequency distribution of landslide deformation velocity, the Liffiefors test is used to preliminarily verify whether the current frequency distribution of landslide deformation velocity satisfies a normal distribution. If it does, the landslide is in a safe state and no warning is issued; otherwise, proceed to the next step.

[0054] It is worth noting that the landslide deformation rate mentioned in this step should be in a uniform unit, such as millimeters per day or millimeters per month.

[0055] S3, Probability density function fitting: After obtaining the value of the landslide deformation velocity as zero, recalculate the frequency distribution of the landslide deformation velocity, and obtain its probability density function by fitting the probability distribution of displacement velocity greater than zero through the Gamma function.

[0056] Here, we first assume that the frequency distribution of landslide deformation velocity follows the Gamma distribution. Since the Gamma distribution only applies to non-negative values, we assign 0 to the negative landslide deformation velocity values ​​and then recalculate the frequency distribution of landslide deformation velocity.

[0057] S4, landslide deformation rate V () Cumulative probability density function: Calculate the cumulative probability density function of landslide deformation velocity for the two cases where the velocity is 0 and greater than 0, respectively;

[0058] Here, since the Gamma function only applies to the case where the velocity is greater than 0, and the modified landslide deformation velocity can be 0, the cumulative probability density function of the landslide deformation velocity is calculated for both cases where the velocity is 0 and greater than 0.

[0059] S5, Standard Normalization Transformation: By transforming the cumulative probability function into an equal probability form, the transformation relationship between the Gamma distribution and the standard normal distribution is established, and the relationship between the landslide deformation rate and the deformation index DI is determined.

[0060] In this embodiment, the standard normalization is converted into the landslide deformation velocity v for any data sample point. i After obtaining its cumulative probability value, the x-value corresponding to the cumulative probability value of the standard normal distribution cumulative probability function is the deformation velocity v. i The deformation index DI value.

[0061] S6, Warning Level Classification and Output: Based on the deformation index value of the last monitoring point and its dangerous zone, the warning level is output.

[0062] Here, the dangerous range of the deformation index is divided based on the probability distribution characteristics of the standard normal function. The warning levels are divided as follows: -2 to -1 is very safe; -1 to 0 is weakly safe; 0 to 1 is weakly dangerous; 1 to 2 is very dangerous; and above 2 is extremely dangerous.

[0063] Specifically, in step S3, the probability density function f (v) for:

[0064]

[0065] Where α and β are the shape and scale parameters, respectively, which are estimated using the maximum likelihood method:

[0066]

[0067]

[0068]

[0069] Where m is the number of observation data. This is the average value of all current deformation velocities.

[0070] Specifically, in step S4, when the landslide deformation rate is greater than 0, the cumulative probability function F is obtained by integrating the probability density function of equation (1). (v) for:

[0071]

[0072] When the landslide deformation rate is equal to 0, its cumulative probability is estimated by the following formula:

[0073]

[0074] Where n is the number of monitoring data points with a velocity of 0;

[0075] At this moment, the landslide deformation velocity V (m) The cumulative probability function G (v) for:

[0076] G(v)=P+(1-P)F(v) (7).

[0077] Specifically, the landslide deformation velocity V (m) The cumulative probability function G (v) The standard normalization transformation formula is:

[0078]

[0079] After solving, we can obtain:

[0080]

[0081]

[0082] Where c0, c1, c2, d1, d2, and d3 are conversion factors, which are 2.515517, 0.802853, 0.010328, 1.432788, 0.189269, and 0.001308, respectively.

[0083] It is worth noting that the principle of this method is to compare the current deformation rate with the historical deformation rate in the probability space, which relies on historical monitoring data. Therefore, it needs to be based on long-term monitoring, and the longer the monitoring time, the more accurate it is.

[0084] The beneficial effects of the technical solutions provided by the embodiments of the present invention are as follows:

[0085] 1. The main data basis of the method of the present invention is cumulative displacement data, which is the most readily available and most accurate landslide deformation characteristic parameter and has strong practicality.

[0086] 2. The method of this invention defines a deformation index and a hazard level division interval based on velocity standardization conversion. After the displacement velocity is converted in probability space, the corresponding warning level is obtained to realize the warning. The calculation process of this method is simple, the mathematical principle is accurate, and it has a certain degree of reliability.

[0087] 3. This method is based on the analysis of cumulative displacement curves with significant increasing deformation trends. The analysis process is based on the probabilistic processing of cumulative displacement data according to the deformation law of landslides. It is not limited to specific types of landslides or landslide materials and has a certain degree of universality.

[0088] In actual monitoring, landslide cumulative displacement curves with obvious growth trends can be divided into four categories: convergent, stable, exponential, and step-type. Figure 3-6This document describes the application effect of the method of the present invention in the above-mentioned four types of linear landslide deformation early warning embodiments.

[0089] Figure 3 This diagram illustrates the application of the method of the present invention to the displacement curve of a convergent landslide. This embodiment uses the Muping landslide, located on the left bank of the Qingjiang River, with a loose, mixed soil and rock structure. The values ​​were calculated based on deformation monitoring curves from 1993 to 1994. The results show that in the initial stage with a high deformation rate, the deformation index is located in the strong warning zone. As the landslide gradually stabilizes, the deformation index value continuously decreases until it reaches the weakly stable zone, which is consistent with the deformation state of the landslide, indicating that the landslide is currently in a stable state. The deformation index in the method of the present invention will not produce false alarms in the early warning of convergent landslides.

[0090] Figure 4 This diagram illustrates the application of the method of the present invention to the displacement curve of a stable landslide. This embodiment uses the La Clapiere landslide in France as an example, and the deformation index is calculated from 12 years of deformation monitoring data from 1983 to 1995. The results show that although the landslide maintains a slow creeping state year-round, the deformation index does not consistently remain high. In the early deformation stage of the landslide, the deformation index initially provides a weak warning, while in its accelerated deformation stage (within 1987), it presents a strong or even extremely strong warning, consistent with the accelerated crisis that occurred in 1987. Subsequently, the warning index maintains a weak warning and stable prediction for many years, indicating that although the current landslide remains in a creeping state, it is not yet severe compared to the historical maximum deformation rate, and therefore will not become unstable. The deformation index in the method of the present invention will not produce false alarms in the early warning of stable landslides.

[0091] Figure 5 This diagram illustrates the application of the method of the present invention to the displacement curve of an exponential landslide. This example illustrates the Huangci landslide, located in China, which failed in February 1995. The deformation index results were calculated from deformation monitoring data from July 15, 1994 to January 26, 1995. The results show that during the initial creep stage of the landslide, the deformation index occasionally fell within the weak warning range but remained in the stable range most of the time. Later in the monitoring period, after the landslide deformation accelerated, the deformation index began to shift from a weak warning to a strong warning, until an extremely strong warning appeared just before the landslide's failure. This is consistent with the landslide's deformation evolution. The deformation index in the method of the present invention provides a good early warning of the potential failure of an exponential landslide.

[0092] Figure 6This is a schematic diagram illustrating the application of the method of the present invention to the displacement curve of a stepped landslide. This example illustrates the Xintan landslide, located in China, which failed in June 1985. The deformation index results were calculated from deformation monitoring data from December 1977 to May 1985. The results show that during the initial creep stage of the landslide, the deformation index occasionally fell within the weak warning range but remained in the stable range most of the time. At locations corresponding to significant shifts in landslide deformation during the mid-term monitoring, the landslide deformation index output strong and extremely strong warning signals. Several months before the landslide became unstable, the landslide deformation index rose from a weak warning to a strong warning and even an extremely strong warning range, reaching a maximum of 4.14. The deformation index in the method of the present invention provides a good early warning of the failure of stepped landslides.

[0093] In this document, the directional terms such as front, back, top, and bottom are defined based on the location of the components in the accompanying drawings and their relative positions to each other, solely for the purpose of clarity and convenience in expressing the technical solution. It should be understood that the use of these directional terms should not limit the scope of protection claimed in this application.

[0094] Where there is no conflict, the above embodiments and features described herein can be combined with each other.

[0095] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A landslide stability early warning method based on deformation rate probability normalization transformation, characterized in that, Includes the following steps: S1, Data Preprocessing: Monitoring landslide deformation and collecting cumulative displacement time series data at key locations on the landslide surface: ; S2, Normality Test: The landslide deformation velocity time series is obtained by calculating the cumulative displacement difference and time difference between two consecutive monitoring data. After calculating the frequency distribution of landslide deformation velocity, the Liffiefors test is used to preliminarily verify whether the current frequency distribution of landslide deformation velocity satisfies a normal distribution. If it does, the landslide is in a safe state and no warning is issued; otherwise, proceed to the next step. S3, Probability density function fitting: After obtaining the value of the landslide deformation velocity as zero, recalculate the frequency distribution of the landslide deformation velocity, and obtain its probability density function by fitting the probability distribution of displacement velocity greater than zero through the Gamma function. The probability density function for: ， (1) in, and The shape and scale parameters are obtained by estimating them using the maximum likelihood method. （2） （3） （4） Where m is the number of observation data. This is the average of all current deformation velocities; S4, landslide deformation rate Cumulative probability density function: Calculate the cumulative probability density function of landslide deformation velocity for the two cases where the velocity is 0 and greater than 0, respectively; When the landslide deformation velocity is greater than 0, the cumulative probability function is obtained by integrating the probability density function of equation (1). for: ， （5）； When the landslide deformation rate is equal to 0, its cumulative probability is estimated by the following formula: ， （6） ； Where n is the number of monitoring data points with a velocity of 0; At this point, the landslide deformation rate cumulative probability function for: （7）； S5, Standard Normalization Transformation: By transforming the cumulative probability function into an equal probability form, the transformation relationship between the Gamma distribution and the standard normal distribution is established, and the relationship between the landslide deformation rate and the deformation index DI is determined. The standard normalization is converted to the landslide deformation velocity for any data sample point. After obtaining its cumulative probability value, the x-value corresponding to the cumulative probability value of the standard normal distribution cumulative probability function is the deformation rate. The deformation index DI value; landslide deformation rate cumulative probability function The standard normalization transformation formula is: （8）； After solving, we can obtain: （9）； （10）； in, , , , , , These are all conversion factors, namely 2.515517, 0.802853, 0.010328, 1.432788, 0.189269, and 0.001308; S6, Warning Level Classification and Output: Based on the deformation index value of the last monitoring point and its dangerous zone, the warning level is output.

2. The landslide stability early warning method based on deformation rate probability normalization transformation as described in claim 1, characterized in that, In step S6, the dangerous interval of the deformation index is divided based on the probability distribution characteristics of the standard normal function.

3. The landslide stability early warning method based on deformation rate probability normalization transformation as described in claim 2, characterized in that, In step S6, the warning levels are divided as follows: -2 to -1 is strong safety; -1 to 0 is weak safety; 0 to 1 is weak danger; 1 to 2 is strong danger; and 2 and above is extremely dangerous.

4. The landslide stability early warning method based on deformation rate probability normalization transformation as described in claim 1, characterized in that, In step S1, the landslide deformation monitoring is conducted at equal time intervals.

5. The landslide stability early warning method based on deformation rate probability normalization transformation as described in claim 1, characterized in that, In step S2, the landslide deformation rate is in a uniform unit.

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