Landslide deformation prediction method based on GA-GM (1,1) power model

Abstract

The present invention discloses a landslide deformation prediction method based on the GA-GM (1,1) power model, which solves the GM (1,1) power model power exponent α and sequence length m through the GA algorithm, and then obtains the GM (1,1) power model related parameters, such as the initial condition s (1) The invention can ensure that the relevant parameters are optimized, thereby ensuring that the final predicted landslide occurrence time is close to the actual landslide occurrence time, thereby improving the accuracy of geological disaster prediction.

Description

Technical Field

[0001] The invention belongs to the technical field of landslide prediction and forecasting, and relates to a landslide deformation prediction and forecasting method, in particular to a GA-GM (1,1) power model method for landslide deformation prediction and forecasting. Background Art

[0002] Due to the complexity of landslide evolution and the limitations of our understanding of geotechnical structures, landslides can be viewed as complex gray systems with some known and some unknown information. The GM(1,1) power model, based on gray system theory, can then be used to predict and forecast landslides. However, directly using the GM(1,1) power model for landslide prediction is not ideal. This is because the results of the GM(1,1) power model are affected by factors such as initial conditions, sequence length, and power exponent. For example, a power exponent of 0 represents the GM(1,1) model, 2 represents the Verhulst model, and 3 represents the collaborative prediction model. These models have been used in landslide prediction and forecasting, but they can produce different prediction results for the same landslide. Because there are no clear standards for the values ​​of initial conditions, sequence length, and power exponent, practical applications are often based on empirical determination. Therefore, different values ​​of initial conditions, sequence length, and power exponent can lead to widely varying prediction results. Summary of the Invention

[0003] The technical problem to be solved by the present invention is to provide a landslide deformation prediction method to obtain the optimal power index, optimal sequence length and optimal initial conditions of the GM (1,1) power model, and realize high-precision prediction of landslide deformation.

[0004] To solve the above technical problems, the present invention provides a landslide deformation prediction method based on the GA-GM (1,1) power model, which includes the following steps:

[0005] Step 1) inputting landslide deformation monitoring data, and performing a cumulative addition on the initial deformation monitoring sequence to generate a new deformation monitoring sequence;

[0006] Step 2) Determine the value range of the power value α and the sequence length m;

[0007] Step 3) Setting the values ​​of GA algorithm related parameters, including population size, maximum genetic generations, crossover probability, and mutation probability;

[0008] Step 4) setting the GA algorithm fitness function, which comprehensively considers the influence of the sum of the average relative error E and the grey model accuracy index posterior difference ratio C;

[0009] Step 5) GM(1,1) power model is iteratively solved using GA algorithm. When the fitness function reaches the minimum value or the maximum genetic generation, the optimal power index α, the optimal sequence length m, the development coefficient a and the gray action b are obtained.

[0010] Step 6) Determine the initial condition s based on the optimal sequence m value (1) t0, the power index α, time interval Δt, development coefficient a, gray action b and initial condition s (1) Substitute t0 and t0 into the following formula to obtain the landslide occurrence time t.

[0011]

[0012] Furthermore, the step 1) generates a new deformation monitoring sequence by accumulating the data as follows:

[0013] Assume that the initial deformation monitoring sequence S (0) ={s (0) (1),s (0) (2),...,s (0) (n)}, where n is the length of the deformation monitoring sequence;

[0014] The new deformation monitoring sequence is:

[0015] S (1) ={s (1) (1),s (1) (2),...,s (1) (n)}, where

[0016] Furthermore, the value range of α is 1<α≤10, and the value range of m is 4≤m≤n.

[0017] Furthermore, the fitness function of the GA algorithm is:

[0018]

[0019] Among them: ω1, ω2 are weights, both of which are 1;

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] [a,b] T =[BT B] -1 B T Y N ;

[0026]

[0027] Y N =[s (0) (2),s (0) (3),…,s (0) (n)] T

[0028] Among them, a is the development coefficient, b is the gray action, and t0 is the initial calculation time.

[0029] The beneficial effect of the present invention is that the power index α and sequence length m of the GM (1,1) power model are solved by the GA algorithm, and then the relevant parameters of the GM (1,1) power model, such as the initial condition s (1) The entire solution process requires no human intervention, preventing the algorithm from falling into local optima. This robustness ensures that the relevant parameters obtained are optimal, ensuring that the final predicted landslide occurrence time is close to the actual landslide occurrence time, thereby improving the accuracy of geological disaster prediction. Furthermore, compared to the Verhulst model and the collaborative prediction model, this method achieves higher prediction accuracy and has significant application value in geological disaster prevention and mitigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 A schematic flow chart of a landslide deformation prediction method according to a specific embodiment of the present invention is shown;

[0031] Figure 2 shows the fitness evolution curve provided by the application embodiment of the present invention;

[0032] Figure 3 The curve of the evolution of the power index α and the sequence length m provided by the application embodiment of the present invention is shown;

[0033] in, Figure 3 (a) is the evolution curve of power exponent α; Figure 3 (b) in the figure is the evolution curve of sequence length m. DETAILED DESCRIPTION

[0034] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0035] like Figure 1 As shown, in an embodiment of the present invention, a landslide deformation prediction method based on the GA-GM (1,1) power model includes the following steps:

[0036] Step 1) Input the landslide deformation monitoring data and perform data preprocessing to remove the gross errors in the data to form the initial deformation monitoring sequence S (0) ={s (0) (1),s (0) (2),...,s (0) (n)}, where n is the length of the deformation monitoring sequence.

[0037] Step 2) Generate a new deformation monitoring sequence by accumulating the initial deformation monitoring sequence

[0038] S (1) ={s (1) (1),s (1) (2),...,s (1) (n)}, where

[0039] Step 3) Determine the value range of the power value α and the sequence length m.

[0040] Step 4) Set the values ​​of GA algorithm related parameters, including population size, maximum genetic generations, crossover probability, and mutation probability.

[0041] Step 5) Set the GA algorithm fitness function, which comprehensively considers the influence of the sum of the average relative error E and the posterior difference ratio C of the grey model accuracy index.

[0042] Step 6) Use the GA algorithm to iteratively solve the GM(1,1) power model, perform selection, crossover and mutation operations of the GA algorithm, and obtain the optimal power index α, optimal sequence length m, development coefficient a and gray action b when the fitness function reaches the minimum value or the maximum genetic generation.

[0043] Step 7) Determine the initial condition s based on the optimal sequence m value (1) t0, the power index α, time interval Δt, development coefficient a, gray action b and initial condition s (1) Substitute t0 and t0 into the following formula to obtain the landslide occurrence time t.

[0044]

[0045] According to Saito creep theory, the landslide displacement-time curve is an S-shaped growth curve. In some embodiments of the present invention, the value range of α is 1<α≤10, and the value range of m is 4≤m≤n.

[0046] In some embodiments of the present invention, the GA algorithm fitness function is:

[0047]

[0048] Among them: ω1, ω2 are weights, both of which are 1;

[0049]

[0050]

[0051]

[0052]

[0053]

[0054] [a,b] T =[B T B] -1 B T Y N ;

[0055]

[0056] Y N =[s (0) (2),s (0) (3),…,s (0) (n)] T

[0057] Among them, a is the development coefficient, b is the gray action, and t0 is the initial calculation time.

[0058] In order to verify the prediction and forecasting effect of the GA-GM (1,1) power model of the present invention, the present invention is further described below in conjunction with specific application examples.

[0059] (1) Landslide deformation monitoring data input and pre-processing Example Taking the data obtained from the new landslide deformation monitoring of Wolong Temple in Table 1 as an example, the data were input into the calculation program.

[0060] Table 1 Original landslide deformation monitoring data

[0061]

[0062] (2) The actual time of the Wolong Temple landslide was May 5, 1971. In order to verify the prediction effect of the GA-GM (1,1) power model, a model was established based on 30 monitoring data between April 1, 1971 and April 30, 1971 to predict the occurrence time of the landslide.

[0063] (3) According to the grey system theory, the original deformation monitoring sequence is accumulated and generated to obtain a new deformation monitoring sequence. The results are shown in the following table.

[0064] Table 2 Deformation monitoring data after one-time accumulation

[0065] date Deformation value (mm) date Deformation value (mm) date Deformation value (mm) 1971-4-1 9.2 1971-4-11 116.8 1971-4-21 283 1971-4-2 18.6 1971-4-12 130.3 1971-4-22 303 1971-4-3 28.6 1971-4-13 144.3 1971-4-23 326 1971-4-4 38.7 1971-4-14 159.3 1971-4-24 350 1971-4-5 49 1971-4-15 175.4 1971-4-25 375.2 1971-4-6 59.4 1971-4-16 191.8 1971-4-26 401.2 1971-4-7 69.9 1971-4-17 209 1971-4-27 428.2 1971-4-8 80.7 1971-4-18 226.6 1971-4-28 456.4 1971-4-9 91.8 1971-4-19 244.8 1971-4-29 486.4 1971-4-10 103.8 1971-4-20 263.8 1971-4-30 517.4

[0066] (4) Set the values ​​of the relevant parameters of the GA algorithm. The GA algorithm parameters are set as follows: population size 30, maximum genetic generations 300, crossover probability 0.7, and mutation probability 0.01.

[0067] (5) According to the aforementioned power exponent α and sequence length m, the initial α and m populations are randomly generated and floating point encoded;

[0068] (6) According to the aforementioned fitness function, the GA algorithm performs selection, crossover, and mutation operations until the fitness function reaches a minimum value or the maximum genetic generation number is reached and the operation is stopped.

[0069] (7) By Figure 2 、 Figure 3 It can be seen that after 300 iterations of evolution, the algorithm has converged, and the optimal power index α is finally calculated to be 1.3017, the optimal sequence length m is 20, and then s is obtained. (1) t0=57.4, t0 is April 11, 1971, Δt is 1 day, and the landslide predicted by the final model will occur on May 1, 1971, which is 4 days earlier than the actual landslide occurrence time.

[0070] For comparison, based on the same deformation monitoring sequence, the Verhulst model predicted the landslide to occur on May 12, 1971, and the collaborative prediction model predicted the landslide to occur on May 15, 1971. The prediction results of the two models lagged behind the actual landslide occurrence by 7 and 10 days, respectively, and the time errors were larger than those of the GA-GM(1,1) power model.

[0071] The GA-GM(1,1) power model method for landslide deformation prediction and forecasting can be used to test various combinations of power exponents and sequence lengths. Ultimately, the optimal power exponent and sequence length, and thus the optimal initial conditions, are determined based on the optimal fitness function. The entire calculation process is automatically iterative and highly robust, eliminating the need for researchers to worry about the tedious calculations of power exponents, sequence lengths, and initial conditions; they only need to ensure the rationality of the forecast results. Furthermore, compared to the Verhu l st model and collaborative forecasting model, this method achieves higher forecast accuracy and has significant application value in geological disaster prevention and mitigation.

[0072] Parts of the present invention that are not described in detail belong to common knowledge among those skilled in the art.

Claims

1. A landslide deformation prediction method based on GA-GM (1,1) power model, characterized by: The steps include: Step 1) inputting landslide deformation monitoring data, and performing a cumulative addition on the initial deformation monitoring sequence to generate a new deformation monitoring sequence; Step 2) Determine the value range of the power value α and the sequence length m; Step 3) Setting the values ​​of GA algorithm related parameters, including population size, maximum genetic generations, crossover probability, and mutation probability; Step 4) setting the GA algorithm fitness function, which comprehensively considers the influence of the sum of the average relative error E and the grey model accuracy index posterior difference ratio C; Step 5) GM(1,1) power model is iteratively solved using GA algorithm. When the fitness function reaches the minimum value or the maximum genetic generation, the optimal power index α, the optimal sequence length m, the development coefficient a and the gray action b are obtained. Step 6) Determine the initial condition s based on the optimal sequence m value (1) t0, the power index α, time interval Δt, development coefficient a, gray action b and initial condition s (1) Substitute t0 and t0 into the following formula to obtain the landslide occurrence time t, The step 1) generates a new deformation monitoring sequence by accumulating the data as follows: Assume that the initial deformation monitoring sequence S (0) ={s (0) (1),s (0) (2),...,s (0) (n)}, where n is the length of the deformation monitoring sequence; The new deformation monitoring sequence is: S (1) ={s (1) (1),s (1) (2),...,s (1) (n)}, where 2. The landslide deformation prediction method based on the GA-GM (1,1) power model according to claim 1 is characterized in that: The value range of α is 1<α≤10, and the value range of m is 4≤m≤n.

3. The landslide deformation prediction method based on the GA-GM (1,1) power model according to claim 2 is characterized in that: The GA algorithm fitness function set in step 4) is: Among them: ω1, ω2 are weights, both of which are 1; [a,b] T =[B T B] -1 B T Y N ; Y N =[s (0) (2),s (0) (3),...,s (0) (n)] T Among them, a is the development coefficient, b is the gray action, and t0 is the initial calculation time.

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