Methods, systems, and equipment for estimating slope deformation in extreme environments based on interpolation.

Abstract

The present disclosure relates to an extreme environment slope deformation estimation method, system and device based on interpolation method, the method comprises the following steps: determining interval I according to target time node x t ; defining several time nodes in interval I as interpolation time nodes x i ; obtaining the monitoring value corresponding to each interpolation time node, denoted as y i ; defining a function y=f(x) located in interval I; according to interpolation time nodes x i and corresponding monitoring values y i , an interpolation function g(x) of the function y=f(x) is obtained through interpolation method, and the estimation value y t of the displacement amount of the target time node x t is obtained through the interpolation function g(x). The system and device are used to execute the above method. The present disclosure can estimate the slope deformation, and the estimation result is accurate, which is beneficial to the continuous monitoring of the slope deformation.

Description

Technical Field

[0001] This disclosure relates to the field of slope monitoring technology, specifically to a method, system, and equipment for estimating slope deformation in extreme environments based on interpolation. Background Technology

[0002] In extreme environments such as high-altitude and frigid regions, railway lines typically feature numerous steep slope engineering projects. The dynamic effects of earthquakes, freeze-thaw cycles, and rainfall are prominent, making them highly susceptible to severe engineering disasters. Therefore, conducting long-term automated monitoring of slope stability is of great significance for ensuring the safety of on-site construction and railway operation.

[0003] The power consumption of monitoring systems of different types and frequencies varies greatly. Due to the difficulty of laying lines in extreme environments such as high altitude and cold regions, the "solar energy + lead-acid battery" solution is generally adopted. This solution mainly uses solar panels to convert solar energy into electrical energy, which is used to power the load and charge the battery pack. When there is no sunlight, the battery pack powers the load.

[0004] In practical applications, extreme environments are often accompanied by extreme weather conditions. When there are several consecutive days without sunlight, the monitoring system may experience power outages. This can lead to situations where no monitoring data is uploaded for a certain day or several consecutive days during slope monitoring, resulting in blanks in slope deformation monitoring data. This is very detrimental to the continuous monitoring of slope deformation.

[0005] Definitions:

[0006] Runge's phenomenon: Runge's phenomenon refers to the phenomenon that, for certain functions, when constructing high-order polynomial interpolations using uniform nodes, the error at the edges of the interpolation interval can be large. It was discovered by Runge while studying errors in polynomial interpolation. This discovery is important because it shows that a higher order of the interpolating polynomial does not necessarily lead to better results. Summary of the Invention

[0007] To address the problems existing in the prior art, the present disclosure aims to provide a method, system, and device for estimating slope deformation in extreme environments based on interpolation. This disclosure can estimate the horizontal displacement of slope deformation at a target time point based on known monitoring data, and the estimation results are accurate. It can fill gaps in slope deformation monitoring data and facilitate continuous monitoring of slope deformation.

[0008] The extreme environment slope deformation estimation method based on interpolation method disclosed herein includes the following steps:

[0009] S01, Based on the target time node x of the required estimation target. t Determine if the target time node x is included. tThe interval I, where I = [a, b];

[0010] S02. Define the time nodes of several known monitoring values ​​of horizontal displacement of slope deformation within the interval I as interpolation time nodes x. i Let i = 0, 1...n. Obtain the monitoring value of the horizontal displacement of the slope deformation corresponding to each interpolation time node, denoted as y. i Let i = 0, 1, ..., n, and define a function y = f(x) located in the interval I, where x is equal to x0, x1, ..., xn respectively. n When y is equal to y0, y1...y respectively n ;

[0011] S03, Based on the interpolation time node x i and the corresponding monitoring value y i The interpolation function g(x) of the function y = f(x) is obtained by interpolation, and the interpolation function g(x) satisfies:

[0012] g(x i )=y i , i = 0, 1...n;

[0013] S04, Set the target time node x t As input to the interpolation function g(x), obtain g(x) t ) as the target time node x t The estimated value of the horizontal displacement of the slope deformation y t .

[0014] Preferably, in step S03, the interpolation method is Lagrange interpolation and / or cubic spline interpolation.

[0015] Preferably, the Lagrange interpolation method includes the following steps:

[0016] Define the interpolation function g(x) as the Lagrange interpolation function P(x), and find the Lagrange polynomial L of the Lagrange interpolation function P(x). n (x j ):

[0017]

[0018] Among them, l k (x) represents the linear interpolation basis function.

[0019] Preferably, the cubic spline interpolation method includes the following steps:

[0020] Define the interpolation function g(x) as a cubic spline interpolation function S(x), where S(x) ∈ C. 2[a,b], and in each segment interval [x] j ,x j+1 The expression above is a cubic polynomial, where a = x0. <x1<...x n =b is the interpolation time node, and at node x j Given the function value y j =f(x) j (j=0,1,2,...,n), and the following holds true:

[0021] S(x j )=y j j = 0, 1, 2, ..., n;

[0022] When the first derivatives at the two endpoints of the interval [a, b] can be calculated, then at the two endpoints a = x0 and b = x0 respectively... n By applying the first boundary condition, the endpoint equations are obtained; the first boundary condition is:

[0023] S'(x0)=f'0,S'(x n )=f' n ;

[0024] When the second derivatives at the two endpoints of the interval [a, b] can be calculated, then at the two endpoints a = x0 and b = x0 respectively, the second derivatives at the two endpoints of the interval [a, b] are: n By applying the second boundary condition, the endpoint equations are obtained; the second boundary condition is:

[0025] S(x0) = f"0, S(x) n )=f” n .

[0026] Preferably, in step S02, at the target time node x t Several interpolation time nodes with equal time intervals are selected before and after.

[0027] Preferably, in step S03, the Lagrange interpolation function P(x) and the cubic spline interpolation function S(x) of the function y=f(x) are obtained by Lagrange interpolation and cubic spline interpolation, respectively.

[0028] In step S04, the target time node x t Using these as inputs to the Lagrange interpolation function P(x) and the cubic spline interpolation function S(x), respectively, the values ​​at the target time node x are obtained. t Lagrange estimates of the horizontal displacement of slope deformation y t1 And cubic spline estimated value y t2 ;

[0029] When the Lagrange interpolation function P(x) exhibits a significant Runge phenomenon, the estimated value y t Calculate using the following formula:

[0030] y t =y t2 ;

[0031] When the endpoint equation is associated with the first boundary condition, the estimated value y t Calculate using the following formula:

[0032] y t =0.5*y t1 +0.5*y t2 ;

[0033] When the endpoint equation is associated with the second boundary condition, the estimated value y t Calculate using the following formula:

[0034] y t =0.2*y t1 +0.8*y t2 .

[0035] This disclosure discloses an extreme environment slope deformation estimation system based on interpolation, comprising:

[0036] The interval definition module is used to define the target time node x based on the estimated target. t Determine if the target time node x is included. t The interval I, where I = [a, b];

[0037] The function definition module is used to define the time nodes of the monitoring values ​​of several known horizontal displacements of slope deformation within the interval I as the interpolation time nodes x. i Let i = 0, 1...n. Obtain the monitoring value of the horizontal displacement of the slope deformation corresponding to each interpolation time node, denoted as y. i Let i = 0, 1, ..., n, and define a function y = f(x) located in the interval I, where x is equal to x0, x1, ..., xn respectively. n When y is equal to y0, y1...y respectively n ;

[0038] The interpolation function acquisition module is used to obtain the interpolation function based on the interpolation time node x. i and the corresponding monitoring value y i The interpolation function g(x) of the function y = f(x) is obtained by interpolation, and the interpolation function g(x) satisfies:

[0039] g(x i )=y i , i = 0, 1...n;

[0040] The estimation module is used to obtain the target time node x. t As input to the interpolation function g(x), the value at the target time node x is obtained. t The estimated value of the horizontal displacement of the slope deformation y t .

[0041] Preferably, the extreme environment slope deformation estimation system based on interpolation further includes:

[0042] The on-site monitoring module is used to acquire monitoring values ​​of the horizontal displacement of slope deformation in the monitoring area.

[0043] A solar power supply module, which is electrically connected to the field monitoring module, is used to supply power.

[0044] This disclosure discloses a computer device including a processor and a memory connected by a signal, wherein the memory stores at least one instruction or at least one program, and the at least one instruction or the at least one program executes the extreme environment slope deformation estimation method based on interpolation method as described above when loaded by the processor.

[0045] The present disclosure discloses a computer-readable storage medium having stored thereon at least one instruction or at least one program, which, when loaded by a processor, executes the extreme environment slope deformation estimation method based on interpolation as described above.

[0046] The method, system, and equipment for estimating slope deformation in extreme environments based on interpolation described in this disclosure have the advantage of using the monitoring values ​​of slope horizontal displacement at several interpolation time points as known data. A function y = f(x) is established based on the correspondence between the interpolation time points and the monitoring values. The interpolation function g(x) of function f(x) is further obtained using interpolation. The target time point is used as the input to the interpolation function g(x) to obtain the estimated value y of the slope horizontal displacement at that target time point. t This disclosure can estimate the horizontal displacement of slope deformation at a target time node based on known monitoring data, and the estimation results are accurate. It can fill the gaps in slope deformation monitoring data and is beneficial to the continuous monitoring of slope deformation. Attached Figure Description

[0047] Figure 1 This is a flowchart of the steps of the extreme environment slope deformation estimation method based on interpolation described in this embodiment;

[0048] Figure 2 This is a schematic diagram of the structure of the computer device described in this embodiment;

[0049] Figure 3This is a Lagrange interpolation curve of the monitoring data from sensor No. 1 in this embodiment;

[0050] Figure 4 This is a Lagrange interpolation curve of the monitoring data from sensor No. 2 in this embodiment;

[0051] Figure 5 This is a Lagrange interpolation curve of the monitoring data from sensor No. 3 in this embodiment;

[0052] Figure 6 This is a Lagrange interpolation curve of the monitoring data from sensor No. 4 in this embodiment;

[0053] Figure 7 This is a Lagrange interpolation curve of the monitoring data from sensor No. 5 in this embodiment;

[0054] Figure 8 This is a cubic spline function curve of the monitoring data from sensor No. 1 in this embodiment;

[0055] Figure 9 This is a cubic spline function curve of the monitoring data from sensor No. 2 in this embodiment;

[0056] Figure 10 This is a cubic spline function curve of the monitoring data from sensor No. 3 in this embodiment;

[0057] Figure 11 This is a cubic spline function curve of the monitoring data from sensor No. 4 in this embodiment;

[0058] Figure 12 This is a cubic spline function curve of the monitoring data from sensor No. 5 in this embodiment.

[0059] Figure labeling: 101 - Processor, 102 - Memory. Detailed Implementation

[0060] like Figure 1 As shown, the extreme environment slope deformation estimation method based on interpolation described in this disclosure includes the following steps:

[0061] S01, Based on the estimated target time node x t Determine if the target time node x is included t The interval I, where I = [a, b]; specifically, in actual monitoring, the field monitoring terminal typically reports monitoring data to the back-end system on a daily basis, i.e., estimating the target time node x of the target. t Typically, it refers to a specific day or several days within a continuous monitoring process, thus including the target time node x. tThe interval I is the number of days before and after the target time node. For example, if a data gap occurs on the 8th day of continuous monitoring and the data on the 8th day needs to be estimated, then the interval I can be selected as [1, 14].

[0062] S02, Define several consecutive time nodes within interval I as interpolation time nodes x. i Let i = 0, 1, ..., n. Obtain the monitoring value of the horizontal displacement of the slope deformation corresponding to each interpolation time node, denoted as y. i Let i = 0, 1...n. Typically, integer days within the interval I are used as interpolation time nodes. For example, the first day of the continuous monitoring process is used as the interpolation time node x0, the second day as the interpolation time node x1, and so on. Correspondingly, the monitoring data reported on the first day is used as the monitoring value of the interpolation time node x0 and recorded as y0, and the monitoring data reported on the second day is used as the monitoring value of the interpolation time node x1 and recorded as y1.

[0063] Define a function y = f(x) located in the interval I, such that the function y = f(x) satisfies the condition that when x equals x0, x1, ..., xn, ... n When y is equal to y0, y1...y respectively n That is, the function f(x) is used to characterize the interpolation time node x. i Compared with the monitored value y i The correspondence.

[0064] S03, Based on the interpolation time node x i and the corresponding monitoring value y i The interpolation function g(x) for the function y = f(x) is obtained by interpolation. The interpolation function g(x) satisfies the following in the interval [a, b]:

[0065] g(x i )=y i , i = 0, 1...n;

[0066] That is, the interpolation function satisfies g(x) i )=f(x i ), i = 0, 1...n.

[0067] Typically, the interpolation function g(x) is represented as a straight line or curve on the coordinate axes, and the interpolation function g(x) passes successively through the sample points (x0, y0), (x1, y1)...(x...). n y n ).

[0068] S04, Set the target node x t As input to the interpolation function g(x), obtain the interpolation function g(x) at the target node x. t The function value at that point, i.e., g(x)t ) as the target time node x t The estimated value of the horizontal displacement of the slope deformation y t .

[0069] Furthermore, the interpolation method in step S03 is Lagrange interpolation and / or cubic spline interpolation.

[0070] Specifically, the Lagrange interpolation method includes the following steps:

[0071] Given that the function y = f(x) is defined on the interval I = [a, b], and that a ≤ x ≤ 0 <x1...<x n The values ​​of ≤b are y0, y1...y n Then the Lagrange interpolation function P(x) satisfies:

[0072] P(x i )=y i , i = 0, 1...n;

[0073] If P(x) is an algebraic polynomial of degree no more than n, then:

[0074] P(x) = a0 + a1x + ... + a1x n ;

[0075] Among them, a i Let P(x) be a real number and P(x) be an interpolation polynomial.

[0076] By discussing the simple cases of n=1 and n=2 respectively, we can see that if the nth degree polynomial l j (x)(j=0,1,2,...,n) has n+1 nodes x0 <x1...<x n The above conditions are met:

[0077]

[0078] These n+1 nth degree polynomials are called l0(x), l1(x), ..., l n (x) represents the nodes x0, x1, ..., x2. n nth-order interpolation basis functions on.

[0079] From the simple cases of n=1 and n=2, the expression for the nth-order interpolation basis function can be obtained by analogy:

[0080]

[0081] Then L satisfies n (x j )=y i The interpolation polynomial L for (j = 0, 1, ..., n) n(x) can be represented as:

[0082]

[0083] By l k From the definition of (x), we know that:

[0084]

[0085] Interpolation polynomials of the form above L n (x) is called the Lagrange interpolation polynomial.

[0086] If we introduce notation:

[0087] ω n+1 (x)=(x-x0)(x-x1)…(xx n );

[0088] Then we can obtain:

[0089]

[0090] In practical applications, the Lagrange polynomial can be directly called in MATLAB software. The interpolation time nodes of the known data can be used as independent variables, and the corresponding monitoring values ​​at each interpolation time node can be used as the dependent variable input as sample data. This allows the construction of a polynomial in the form of... Figures 3-7 The Lagrange interpolation curve can then be used to estimate the target time node x of the target. t Output the x-coordinate of the Lagrange interpolation curve. t The corresponding y t The value, x, is estimated using Lagrange interpolation based on the data from each sample point. t The monitoring value of the horizontal displacement of the slope deformation at the corresponding time.

[0091] Another interpolation method is cubic spline interpolation, which can be used to estimate blank data. The cubic spline interpolation method specifically includes the following steps:

[0092] Define the interpolation function g(x) as a cubic spline interpolation function S(x), then the cubic spline interpolation function S(x) ∈ C 2 [a,b], and in each segment interval [x] j ,x j+1 The expression above is a cubic polynomial, where a = x0. <x1<...x n =b is the interpolation time node, and at node x j Given the function value y j =f(x) j (j=0,1,2,...,n), and the following holds true:

[0093] S(xj )=y j j = 0, 1, 2, ..., n.

[0094] Cubic spline interpolation functions typically require the endpoints of the interval [a,b] to be a = x0 and b = x0. n Associative boundary conditions are usually given according to the requirements of the actual problem, and there are three common types:

[0095] Given the values ​​of the first derivatives at both ends, we have:

[0096] S'(x0)=f'0,S'(x n )=f' n ;

[0097] Given function values ​​f(x0) and f(x1) at two nodes x0 and x1, the two-point formula with remainder is:

[0098]

[0099]

[0100] ξ0, ξ1∈(x0,x1);

[0101] The three-point formula is:

[0102]

[0103]

[0104]

[0105] ξ0, ξ1, ξ2∈(x0,x2);

[0106] Given the values ​​of the second derivatives at both ends, we have:

[0107] S(x0) = f"0, S(x) n )=f” n ;

[0108] The five-point numerical differential formula for the second derivative:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114] When f(x) is x n When ~x0 is a periodic function, then S(x) is also required to be a periodic function. In this case, the boundary conditions should satisfy:

[0115]

[0116] This type of boundary condition requires the function to satisfy a periodic function, which does not exist in actual engineering. Therefore, it will not be discussed further in this embodiment.

[0117] For the first type of boundary condition, two equations can be derived:

[0118]

[0119]

[0120] For the second type of boundary condition, the endpoint equations can be obtained directly:

[0121] M0 = f0”, M n =f n ".

[0122] In practical applications, cubic spline interpolation functions can be directly called in MATLAB software. The interpolation time nodes of the known data can be used as independent variables, and the corresponding monitoring values ​​at each interpolation time node can be used as the dependent variable input as the sample data. This allows the construction of a spline interpolation function in the form of... Figures 8-12 The cubic spline function curve can then be used to estimate the target time node x of the target. t Output the x-coordinate of the cubic spline function curve. t The corresponding y t The value, x, is estimated using cubic spline interpolation based on data from each sample point. t The monitoring value of the horizontal displacement of the slope deformation at the corresponding time.

[0123] Furthermore, in step S02, several interpolation time nodes with equal time intervals are selected before and after the target time node. For example, in this embodiment, when the target time node of the target to be estimated is the 8th day, the monitoring data from the 1st to the 7th day and the 9th to the 14th day can be obtained as sample data to make the sample data relatively evenly distributed at both ends of the estimation point.

[0124] Furthermore, in the aforementioned embodiments, blank data of the monitored values ​​can be estimated using Lagrange interpolation and cubic spline interpolation, respectively, and one method can be selected for implementation. In a preferred embodiment, blank data can be estimated using both methods to allow the two sets of estimated values ​​to corroborate each other. More preferably, based on the characteristics of the data, the two sets of estimated values ​​can be combined to perform reasonable calculations to obtain the final estimated value, making the estimated value closer to the actual value and improving the estimation accuracy, as detailed below:

[0125] In step S04, the target time node x t Using these as inputs to the Lagrange interpolation function P(x) and the cubic spline interpolation function S(x), respectively, the values ​​at the target time node x are obtained. t Lagrange estimates of the horizontal displacement of slope deformation y t1 And cubic spline estimated value y t2 ;

[0126] When the Lagrange interpolation function P(x) exhibits a significant Runge phenomenon, the estimated value y t Calculate using the following formula:

[0127] y t =y t2 ;

[0128] When the endpoint equation is associated with the first boundary condition, the estimated value y t Calculate using the following formula:

[0129] y t =0.5*y t1 +0.5*y t2 ;

[0130] When the endpoint equation is associated with the second boundary condition, the estimated value y t Calculate using the following formula:

[0131] y t =0.2*y t1 +0.8*y t2 .

[0132] Because Lagrange interpolation has a high polynomial degree when there are many interpolation points, it may exhibit Runge's phenomenon, leading to numerical instability. Whether the Lagrange interpolation function P(x) exhibits Runge's phenomenon can be determined by observing the error between the value on the fitted curve of the Lagrange interpolation function P(x) and the corresponding known value.

[0133] After practical verification, the above-mentioned method combining Lagrange's estimated value y was designed. t1 And cubic spline estimated value y t2 Calculate the final estimated value yt The formula, when the Lagrange interpolation function P(x) exhibits Runge's phenomenon, will change the Lagrange estimate y. t1 The weights are configured to be 0, and the cubic spline estimate y is designed based on the boundary conditions associated with the cubic spline interpolation function S(x). t2 By configuring appropriate weights, this embodiment combines the characteristics of Lagrange interpolation and cubic spline interpolation to rationally design the final estimated value y. t The calculation formula can make the estimated value y t It is closer to the actual value, reducing estimation error.

[0134] The following will use actual monitoring data to verify the accuracy of the interpolation-based slope deformation estimation method described in this embodiment. The monitoring values ​​of the horizontal displacement of the slope obtained by 15 sensors for 14 consecutive days in a high-altitude and cold environment are shown in the table below:

[0135] Table 1. Horizontal displacement (mm) obtained from 15 sensors over the first 7 days.

[0136]

[0137] Table 2 shows the horizontal displacement (mm) obtained from the 15 sensors over the next 7 days.

[0138]

[0139] First, we analyze the accuracy of the Lagrange interpolation method. Assuming that on day 8, the on-site monitoring terminal failed to upload monitoring data due to a power outage, and the monitoring data for days 1-7 and 9-14 are known, we estimate the monitoring data for day 8 using the extreme environment slope deformation estimation method described in this embodiment. Following the steps above, we use days 1-7 and 9-14 as interpolation time nodes (independent variables), and the corresponding monitoring values ​​as dependent variables input as sample data. This allows us to construct a... Figures 3-7 The Lagrange interpolation curve, Figures 3-7 The Lagrange interpolation curves of sensors numbered 1-5 were extracted and observed. Figure 3 When the horizontal axis is 8, the corresponding vertical axis value is 0.42mm, while the actual monitored value is 0.449mm, with an error of approximately 0.03mm. Figure 4When the horizontal axis is 8, the corresponding vertical axis value is 1.17mm, while the actual measured value is 1.158mm, with an error of 0.012mm. A detailed comparison of the actual detection data and estimated values ​​of the sensors in the first five sections shows that the errors of both are less than 0.1mm. This error is acceptable in the field of slope deformation monitoring, meaning that the Lagrange interpolation method can be applied to the slope deformation monitoring process. Its estimated value is close to the actual measured value, and in the actual monitoring process, the proportion of days when data cannot be obtained is usually very small. Therefore, the Lagrange interpolation method has high practicality for data estimation in the actual slope deformation monitoring process.

[0140] The accuracy of the cubic spline interpolation method is analyzed below. Assuming that on day 8, the on-site monitoring terminal failed to upload monitoring data due to a power outage, the monitoring data for days 1 to 7 and 9 to 14 are known. Using the extreme environment slope deformation estimation method described in this embodiment, the monitoring data for day 8 is estimated. Following the steps above, days 1 to 7 and 9 to 14 are taken as interpolation time nodes, i.e., independent variables, and the corresponding monitoring values ​​are taken as dependent variables and input as sample data. Thus, a method can be constructed as follows... Figures 8-12 The cubic spline interpolation function curve, Figures 8-12 The cubic spline interpolation function curves of sensors numbered 1-5 were extracted and observed. Figure 8 When the horizontal axis is 8, the corresponding vertical axis value is 0.43mm, while the actual monitored value is 0.449mm, with an error of approximately 0.02mm. Figure 9 When the horizontal axis is 8, the corresponding vertical axis value is 1.17 mm, while the actual measured value is 1.158 mm, with an error of 0.012 mm. A detailed comparison of the actual detection data and estimated values ​​of the sensors in the first five sections shows that the errors of both are less than 0.1 mm. This error is acceptable in the field of slope deformation monitoring, meaning that the cubic spline interpolation method can be applied to the slope deformation monitoring process. Its estimated value is close to the actual measured value, and in the actual monitoring process, the proportion of days when data cannot be obtained is usually very small. Therefore, the cubic spline interpolation method has high practicality for data estimation in the actual slope deformation monitoring process.

[0141] The above application examples have verified the extreme environment slope deformation estimation method based on interpolation in this embodiment through actual measurement data. When using Lagrange interpolation and cubic spline interpolation, the monitoring values ​​at the target time nodes can be accurately estimated. The estimation is accurate and has small error, making it suitable for actual monitoring processes.

[0142] This embodiment also provides a slope deformation estimation system for extreme environments based on interpolation, including:

[0143] The interval definition module is used to define the target time node x based on the estimated target. tDetermine if the target time node x is included. t The interval I, where I = [a, b];

[0144] The function definition module is used to define the time nodes of the monitoring values ​​of several known horizontal displacements of slope deformation within the interval I as the interpolation time nodes x. i Let i = 0, 1...n. Obtain the monitoring value of the horizontal displacement of the slope deformation corresponding to each interpolation time node, denoted as y. i Let i = 0, 1, ..., n, and define a function y = f(x) located in the interval I, where x is equal to x0, x1, ..., xn respectively. n When y is equal to y0, y1...y respectively n ;

[0145] The interpolation function acquisition module is used to obtain the interpolation function based on the interpolation time node x. i and the corresponding monitoring value y i The interpolation function g(x) of the function y = f(x) is obtained by interpolation, and the interpolation function g(x) satisfies:

[0146] g(x i )=y i , i = 0, 1...n;

[0147] The estimation module is used to obtain the target time node x. t As input to the interpolation function g(x), the value at the target time node x is obtained. t The estimated value of the horizontal displacement of the slope deformation y t .

[0148] The extreme environment slope deformation estimation system based on interpolation in this embodiment is based on the same inventive concept as the method embodiment described above. It can be understood with reference to the description of the method embodiment above, and will not be repeated here.

[0149] Furthermore, the extreme environment slope deformation estimation system includes:

[0150] The field monitoring module is used to acquire the monitoring value of the horizontal displacement of the slope deformation in the monitoring area. The field monitoring module usually includes multiple horizontal displacement sensors, which are buried at a certain depth in the slope soil to monitor the horizontal displacement of the slope soil and thus reflect the amount of slope deformation. The field monitoring module usually also includes a signal processing module to process the monitoring signals from the sensors and a communication module to communicate with the back-end system to report the monitoring data.

[0151] A solar power module, electrically connected to the field monitoring module, is used to supply power. The solar power module typically includes a solar panel and a battery, used to convert solar energy into electrical energy to power the field monitoring module.

[0152] like Figure 2 As shown, this embodiment also provides a computer device, including a processor 101 and a memory 102 connected via a bus signal. The memory 102 stores at least one instruction or at least one program segment. When the at least one instruction or the at least one program segment is loaded by the processor 101, it executes the extreme environment slope deformation estimation method based on interpolation as described above. The memory 102 can be used to store software programs and modules. The processor 101 executes various functional applications by running the software programs and modules stored in the memory 102. The memory 102 may mainly include a program storage area and a data storage area. The program storage area may store the operating system, application programs required for functions, etc.; the data storage area may store data created according to the use of the device, etc. In addition, the memory 102 may include high-speed random access memory, and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other volatile solid-state storage device. Accordingly, the memory 102 may also include a memory controller to provide the processor 101 with access to the memory 102.

[0153] The methods and embodiments provided in this disclosure can be executed in a computer terminal, server, or similar computing device; that is, the aforementioned computer device may include a computer terminal, server, or similar computing device. The internal structure of the computer device may include, but is not limited to, a processor, a network interface, and memory. The processor, network interface, and memory within the computer device may be connected via a bus or other means.

[0154] The processor 101 (or CPU, Central Processing Unit) is the computing and control core of the computer device. The network interface may optionally include a standard wired interface or a wireless interface (such as Wi-Fi, mobile communication interface, etc.). The memory 102 is the storage device in the computer device used to store programs and data. It is understood that the memory 102 here may be a high-speed RAM storage device, or a non-volatile storage device, such as at least one disk storage device; optionally, it may also be at least one storage device located remotely from the processor 101. The memory 102 provides storage space that stores the operating system of the electronic device, which may include, but is not limited to: Windows (an operating system), Linux (an operating system), Android (a mobile operating system), iOS (a mobile operating system), etc., and this disclosure does not limit this; furthermore, the storage space also stores one or more instructions suitable for loading and execution by the processor 101, which may be one or more computer programs (including program code). In the embodiments of this specification, the processor 101 loads and executes one or more instructions stored in the memory 102 to implement the extreme environment slope deformation estimation method based on interpolation described in the above method embodiments.

[0155] This disclosure also provides a computer-readable storage medium storing at least one instruction or at least one program segment, which, when loaded by processor 101, executes the extreme environment slope deformation estimation method based on interpolation as described above. The aforementioned computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of this disclosure.

[0156] According to embodiments of this disclosure, the computer-readable storage medium can be a non-volatile computer-readable storage medium. Examples include, but are not limited to: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this disclosure, the computer-readable storage medium can be any tangible medium that contains or stores a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0157] In the description of this disclosure, it should be understood that the orientation or positional relationship indicated by directional terms such as "front, back, up, down, left, right", "horizontal, vertical, horizontal" and "top, bottom" is usually based on the orientation or positional relationship shown in the accompanying drawings and is only for the convenience of describing this disclosure and simplifying the description. Unless otherwise stated, these directional terms do not indicate or imply that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on the scope of protection of this disclosure.

[0158] For those skilled in the art, various other corresponding changes and modifications can be made based on the technical solutions and concepts described above, and all such changes and modifications should fall within the protection scope of the claims disclosed herein.

Claims

1. A method for estimating deformation of a slope in an extreme environment based on an interpolation method, characterized by, The method comprises the following steps: S01、According to the target time node x of the target to be estimated t , determine the interval I containing the target time node x t , interval I = [a, b]; S02, define the time nodes of the monitoring values of the slope deformation horizontal displacement in the interval I as interpolation time nodes x i , i = 0, 1...n, obtain the monitoring value of the slope deformation horizontal displacement corresponding to each interpolation time node, denoted as y i , i = 0, 1...n, define the function y = f(x) located in the interval I, and x is equal to x0, x1...x n , respectively, and y is equal to y0, y1...y n , respectively; S03. According to the interpolation time node x i and the corresponding monitoring value y i , an interpolation function g(x) of the function y = f(x) is obtained by interpolation, which satisfies: g(x i ) = y i , i = 0, 1...n; S04、obtaining the target time node x t As the input of the interpolation function g(x), obtaining g(x t ) as the estimated value y t of the slope deformation horizontal displacement amount of the target time node x t ; In step S03, the interpolation method is Lagrange interpolation and cubic spline interpolation, The cubic spline interpolation comprises the following steps: defining the interpolation function g(x) as a cubic spline interpolation function S(x) ∈ C 2 [a,b] and on each sub-interval [x j j+1 ] is a cubic polynomial, where a = x0< x1<... x n = b are the interpolation time nodes and the function values y j = f(x j ) are given at the nodes x j j, j = 0,1,2,...,n, and holds:​ S(x j ) = y j , j = 0, 1, 2,..., n; When the first derivative of the two endpoints of the interval [a, b] is available, the endpoint equations are obtained at the two endpoints a = x0, b = x n A first boundary condition is associated to obtain the endpoint equation; the first boundary condition is: S'(x0) = f'0, S'(x n ) = f' n ; When the second derivative of the two endpoints of the interval [a, b] is available, the endpoint equations are obtained at the two endpoints a = x0, b = x n A second boundary condition is associated to obtain the endpoint equation; the second boundary condition is: S"(x0) = f"0, S"(x n ) = f" n ; In step S03, a Lagrange interpolation function P(x) and a cubic spline interpolation function S(x) of the function y=f(x) are respectively obtained by Lagrange interpolation and cubic spline interpolation; In the step S04, the target time node x t is obtained as the input of the Lagrange interpolation function P(x) and the cubic spline interpolation function S(x) respectively, and the Lagrange estimation value y t and the cubic spline estimation value y t1 of the horizontal displacement of the slope deformation at the target time node x t2 are obtained respectively. when the Lagrange interpolation function P(x) exhibits a clear Runge phenomenon, the estimate y t is calculated as follows: y t = y t2 ; when the endpoint equation relates the first boundary condition, the estimate value y t is calculated as follows: y t = 0.5 * y t1 + 0.5 * y t2 ; when said endpoint equation relates said second boundary condition, said estimate y t is calculated as follows: y t = 0.2 * y t1 + 0.8 * y t2 .

2. The method of claim 1, wherein the method is characterized by, The Lagrange interpolation comprises the following steps: defining the interpolation function g(x) as a Lagrange interpolation function P(x), finding a Lagrange polynomial L for the Lagrange interpolation function P(x) n (x j ): wherein, l k (x) denotes a linear interpolation basis function.

3. The method of claim 1, wherein the method is characterized by, In step S02, at the target time node x t A plurality of interpolation time nodes with equal time intervals are selected before and after the target time node.

4. An extreme environment slope deformation estimation system based on interpolation method for performing the extreme environment slope deformation estimation method based on interpolation method according to any one of claims 1 to 3, characterized by, It comprises: an interval defining module configured to determine an interval I containing the target time node x t of the estimation target according to the target time node x t of the estimation target, the interval I=[a, b]. a function definition module, which is configured to define time nodes of monitoring values of a plurality of known slope deformation horizontal displacement amounts in the interval I as interpolation time nodes x i , i=0, 1...n, obtain monitoring values of the slope deformation horizontal displacement amounts corresponding to each of the interpolation time nodes, denoted as y i , i=0, 1...n, define a function y=f(x) located in the interval I, and when x is equal to x0, x1...x n , y is equal to y0, y1...y n , respectively. The interpolation function acquisition module is used to obtain the interpolation function based on the interpolation time node x. i and the corresponding monitoring value y i The interpolation function g(x) of the function y = f(x) is obtained by interpolation, and the interpolation function g(x) satisfies: g(x i ) = y i , i = 0, 1...n; an estimation value obtaining module, configured to obtain an estimation value y t of the horizontal displacement of the slope deformation at the target time node x t as an input of the interpolation function g(x) t .

5. The system for estimating deformation of a slope in an extreme environment based on an interpolation method according to claim 4, wherein, It also comprises: A field monitoring module for obtaining a monitoring value of the horizontal displacement of the slope deformation of the monitoring area; A solar power supply module electrically connected with the field monitoring module for power supply.

6. A computer device comprising a processor and a memory connected by a signal, characterized in that, The memory stores at least one instruction or at least one program, and the at least one instruction or the at least one program is loaded by the processor to execute the extreme environment slope deformation estimation method based on the interpolation method according to any one of claims 1-3.

7. A computer-readable storage medium having stored thereon, at least one instruction or at least one piece of program, characterized in that, The at least one instruction or the at least one program is loaded by the processor to execute the extreme environment slope deformation estimation method based on the interpolation method according to any one of claims 1-3.

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