Landslide displacement prediction method based on ARIMA-LSTM

Abstract

The invention discloses a landslide displacement prediction method based on ARIMA-LSTM, and the method comprises the steps: obtaining the original data of landslide displacement, and decomposing the original data of landslide displacement into a trend term and a periodic term through a cumulative moving average method; performing fitting prediction on the trend term by adopting a polynomial function to obtain a trend term prediction result; carrying out residual error compensation prediction on the periodic term by adopting ARIMA model and LSTM network fusion to obtain a periodic term prediction result; and superposing the trend term prediction result and the period term prediction result to generate a total displacement prediction value, constructing a T-t curve based on the total displacement prediction value, calculating a tangent angle, and carrying out landslide grading early warning according to a tangent angle threshold value. According to the invention, the prediction precision of landslide displacement is improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of landslide displacement prediction, and particularly relates to a landslide displacement prediction method based on ARIMA-LSTM. BACKGROUND

[0002] Landslide displacement prediction is the core link of the geological disaster early warning system, and its accuracy directly affects the timeliness and reliability of disaster prevention decision-making. The current technology has the following key bottlenecks: Multi-source interference factor coupling modeling dilemma: landslide displacement evolution is affected by the nonlinear coupling of geological structure, reservoir water level fluctuation and rainfall infiltration and other factors. Periodic scheduling of reservoir water level (such as the Three Gorges Reservoir 145m-175m rise and fall) causes the permeation pressure of the slope body to change dramatically, inducing the shear strength of the soil to decay. Experimental data show that for every 1 meter drop in reservoir water level, the displacement rate can reach 2.3 times the baseline value. At the same time, the sudden increase in pore water pressure caused by heavy rainfall infiltration causes the displacement to present a "step" mutation. Existing models are difficult to quantify the synergistic effect of reservoir water level drop and rainfall, resulting in a deviation of up to 32.3% between the predicted value and the actual displacement.

[0003] Displacement signal decomposition method defects: traditional decomposition techniques have significant limitations: ensemble empirical mode decomposition (EEMD) is prone to modal aliasing and has low noise tolerance, and parameter selection depends on empirical adjustment; in the moving average method, simple moving average (SMA) ignores the timeliness of data, and weighted moving average (WMA) cannot capture sudden fluctuations. Especially when there is high-frequency oscillation in the displacement sequence, the residual rate of existing methods is as high as 18.7%.

[0004] Limitations of prediction model and early warning mechanism: single model prediction bottleneck: the classic ARIMA model can only handle linear relationships and cannot represent the lag effect of reservoir water level; LSTM alone tends to ignore the causal relationship between environmental factors; early warning threshold lacks universality: the S-t curve is dimensionless in displacement and time, resulting in invalidity of the tangent angle criterion. Criteria such as acceleration and rainfall require complex empirical calibration, and the grading standard is difficult to quantify. SUMMARY

[0005] To solve the above technical problems, the application provides a landslide displacement prediction method based on ARIMA-LSTM, which improves the prediction accuracy of landslide displacement.

[0006] To achieve the above purpose, the application provides a landslide displacement prediction method based on ARIMA-LSTM, which comprises: Obtaining landslide displacement original data, and decomposing the landslide displacement original data into a trend item and a periodic item by cumulative moving average method; Fitting and predicting the trend item using a polynomial function to obtain a trend item prediction result; The periodic term is compensated and predicted by using an ARIMA model and an LSTM network in combination, to obtain a periodic term prediction result; The trend term prediction result and the periodic term prediction result are superimposed to generate a total displacement prediction value, a T-t curve is constructed based on the total displacement prediction value, a tangent angle is calculated, and landslide grading early warning is performed according to a tangent angle threshold.

[0007] Optionally, the landslide displacement original data is decomposed into a trend term and a periodic term by using a cumulative moving average method, including: A displacement component at time t is calculated, n displacement monitoring values before time t and the displacement value at time t are accumulated, the accumulated value is divided by n+1 to obtain the trend term, and the periodic term is obtained by subtracting the trend term from the actual displacement.

[0008] Optionally, the trend term is fitted and predicted by using a polynomial function to obtain a trend term prediction result, including: ; wherein, is a predicted value of the trend term displacement, , , , , are polynomial coefficients, and is a constant.

[0009] Optionally, the ARIMA model is constructed, including: ARIMA parameters are determined by using autocorrelation functions and partial autocorrelation functions, d-order difference processing is performed on the periodic term displacement data, and autoregressive coefficients and moving average coefficients are solved by using a maximum likelihood estimation method.

[0010] Optionally, the LSTM network includes an output of a forgetting gate , an output of an input gate , and an output of an output gate , wherein: The forgetting gate includes: ; The input gate includes: ; The output gate includes: ; wherein, is a Sigmoid function, is a weight matrix of the forgetting gate, is a previous output of a memory block, is a current input, is a bias term of the forgetting gate, is an output of the forgetting gate, is a weight matrix of the input gate, is a bias term of the input gate. It is the output of the input gate. It is the weight matrix of the output gate. It is the bias term of the output gate. It is the output of the output gate.

[0011] Optionally, obtaining the prediction results for the periodic term includes: The initial predicted value of the periodic term is obtained based on the ARIMA model. The residual between the actual value of the periodic term and the initial predicted value of the periodic term is calculated. The residual and the initial predicted value of the periodic term are input into the LSTM network for training to obtain the prediction result of the periodic term.

[0012] Optionally, calculating the tangent angle includes: A continuous function is obtained by performing cubic spline interpolation on the Tt curve. The instantaneous tangent slope is obtained by taking the first derivative of the continuous function. The instantaneous tangent slope is then converted into a tangent angle using the arctangent function.

[0013] Optionally, the threshold for tiered early warning can be set as follows: Tangent angle A blue warning is issued at any time, indicating a tangent angle. A yellow warning is issued at any time, indicating the tangent angle. An orange alert is issued at any time, tangent angle A red alert will be issued at any time.

[0014] Technical effects of the invention: (1) Significantly improved prediction accuracy: The CMA decomposition combined with the ARIMA-LSTM fusion model effectively solves the nonlinear coupling problem in the displacement sequence. Verified by measured data from the Baishuihe landslide, compared with the traditional ARIMA model, the root mean square error (RMSE) decreased from 38.401 mm to 7.024 mm, a reduction of 81.7%; the goodness of fit... The value was increased to 0.996, accurately capturing sudden displacement changes during the decline of reservoir water level and step deformation caused by heavy rainfall.

[0015] (2) Advantages of multi-factor collaborative modeling: In the periodic term prediction, environmental parameters such as reservoir water level and rainfall are integrated simultaneously, breaking through the limitations of single models in representing complex external factors. The model successfully quantifies the correlation between a 1-meter drop in reservoir water level and a 2.3-fold increase in displacement rate, solving the deficiency of traditional methods in modeling lag effects.

[0016] (3) Scientific Quantification of Early Warning Mechanism: The hierarchical early warning based on the tangent angle of the Tt curve eliminates the problem of inconsistent dimensions of the St curve, and achieves: the tangent angle α=45°, 80°, 85° as thresholds to accurately divide the deformation stages of constant speed / weak acceleration / medium acceleration / strong acceleration; the early warning level strictly matches the statutory standard of the "Emergency Response Law", and the false alarm rate is reduced by 40%.

[0017] (4) Enhanced engineering applicability: The model has been validated in the scenario of landslides caused by reservoir water level drop. In particular, the prediction error of displacement fluctuation during the reservoir water level scheduling period of 145m-175m is controlled within 6.3%, providing reliable decision support for major projects such as the Three Gorges Reservoir area. Attached Figure Description

[0018] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart illustrating the landslide displacement prediction method based on ARIMA-LSTM according to an embodiment of the present invention. Figure 2 This is a schematic diagram comparing the extracted trend values ​​in an embodiment of the present invention; Figure 3 This is a schematic diagram comparing the extracted values ​​of periodic items in an embodiment of the present invention; Figure 4 This is a schematic diagram of the trend prediction results in an embodiment of the present invention; Figure 5 This is a flowchart of the ARIMA model according to an embodiment of the present invention; Figure 6 This is a schematic diagram of the LSTM network structure according to an embodiment of the present invention; Figure 7 This is a schematic diagram illustrating the construction of the ARIMA-LSTM model according to an embodiment of the present invention; Figure 8 This is a schematic diagram of the prediction results for the periodic term in an embodiment of the present invention; Figure 9 This is a schematic diagram of the total displacement prediction results in an embodiment of the present invention; Figure 10 This is a schematic diagram comparing the predicted displacements in an embodiment of the present invention; Figure 11 This is a warning diagram for the tangent angle criterion of the Tt curve in an embodiment of the present invention. Detailed Implementation

[0019] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0020] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0021] like Figure 1As shown, this embodiment provides a landslide displacement prediction method based on ARIMA-LSTM, including: acquiring raw landslide displacement data, and decomposing the raw landslide displacement data into trend terms and periodic terms using the cumulative moving average method; The trend term is fitted and predicted using a polynomial function to obtain the trend term prediction result; The periodic term is predicted by residual compensation using a fusion of the ARIMA model and the LSTM network to obtain the prediction result of the periodic term. The trend prediction result and the period prediction result are superimposed to generate the total displacement prediction value. Based on the total displacement prediction value, a Tt curve is constructed and the tangent angle is calculated. Landslide classification and early warning are carried out according to the tangent angle threshold.

[0022] Furthermore, the original landslide displacement data is decomposed into trend and periodic terms using the cumulative moving average method, including: Calculate the displacement component at time t, and accumulate the n displacement monitoring values ​​before time t and the displacement value at time t; divide the accumulated value by n+1 to obtain the trend term; subtract the trend term from the actual displacement to obtain the period term.

[0023] Specifically, the implementation process in this embodiment includes: Decomposing landslide displacement into different components provides more refined data, thus aiding in the prediction of displacement trends. Actual displacement changes reveal both trend and periodic variations. Therefore, it's considered to decompose actual displacement into trend displacement and periodic displacement for separate prediction. After comprehensive analysis of data characteristics, cumulative moving averages are used for displacement decomposition. A comparison of the extracted trend and periodic values ​​with the actual displacement is shown below. Figure 2 and Figure 3 As shown. Cumulative Moving Average (CMA): CMA averages all previous data at each time point. Unlike previous methods, it does not require specifying a fixed window size. In general, for the Nth data point, the cumulative moving average is the sum of the previous N data points divided by N. Thus, the cumulative moving average at each time point is the average of the cumulative sums of all data points. Because it considers the influence of all historical data, unlike the simple moving average which only considers the most recent data, it can observe the long-term trend of time series data and clearly reflect the cumulative nature of the data.

[0024] Furthermore, the trend term is fitted and predicted using a polynomial function to obtain the trend term prediction results, including: from Figure 2The extracted trend term approximates a smooth curve, exhibiting a certain trend and regularity. It can be predicted using polynomial fitting, a mathematical method that approximates data points infinitely by fitting a polynomial function. It is effective in both data analysis and prediction, simplifying complex models. By selecting an appropriate polynomial degree, the complexity of the model and the degree of data fit can be balanced. Its inherent flexibility makes polynomial fitting a popular method in various fields. A fourth-order polynomial fitting is performed on the data of each stage of the trend term displacement. The fitting calculation formula is: ; in, It is the predicted value of the trend term displacement. , , , , All are polynomial coefficients. It is a constant. The calculated fourth-order polynomial fitting formula is: ; The predicted results of the trend term displacement are as follows: Figure 4 As shown, the goodness of fit The value is 0.97, indicating that the trend term displacement prediction effect is relatively good.

[0025] Furthermore, constructing an ARIMA model includes: The ARIMA parameters are determined by the autocorrelation function and the partial autocorrelation function. The periodic displacement data are subjected to d-order differencing. The autoregressive coefficients and moving average coefficients are solved by the maximum likelihood estimation method.

[0026] Specifically, the implementation process in this embodiment includes: The ARIMA model is a classic model used for time series analysis and forecasting. It is widely applicable across various fields, including economic forecasting, sales forecasting, traffic flow forecasting, weather forecasting, energy demand forecasting, signal processing, and environmental monitoring. Its full name is Autoregressive Moving Average (AR), and it consists of three parts: AR, I, and MA. The AR model, or Autoregressive model, is a simple model for analyzing time series data. It primarily predicts future values ​​based on past values ​​of variables and relies on two classic assumptions: (1) Time-series dependence: In the model, it is assumed that there is a strong correlation between values ​​at different points in time, which means that past values ​​will have a significant impact on future values. In other words, past values ​​are crucial to predicting the future.

[0027] (2) Temporal decay: In the model, it is assumed that the larger the interval between two time points, the weaker the correlation between the two time points.

[0028] Based on the two classic assumptions above, the AR model can be expressed as follows: the value at a future point in time can be a linear combination of all values ​​within a certain past period. This linear combination can be understood as the sum of the weights of each value within the past period reflecting its impact on the current point in time. The formula is as follows: ; In the formula is the time series value at time t, and c is the constant term of the model. These terms represent the impact of time series values ​​from the past 10 time points on the current time point. It is the coefficient of the lagged term. The error term at time point t can also be called the white noise term.

[0029] I This is the differencing process, a common data transformation method that can eliminate seasonality and trends in time series data, making the data more stationary. It calculates the difference between adjacent observations, i.e., the current observation minus the previous observation. The expression for the differencing process of a time series is as follows: ; ; ; In the formula It is the initial time series. For lag operators, t is a time point. It is a stationary sequence obtained after differencing.

[0030] MA stands for Moving Average, which describes the relationship between data and noise at a current point in time. The basic ideas and core principles of the MA model differ from those of the AR model. The MA model assumes that the data sequence is relatively stable over most of the time period. Based on this, the value at each time point will fluctuate due to unpredictable or random events in the past. The white noise is the random component that the model cannot explain; it represents information that the model has not captured. In other words, the MA model uses past "errors" or "shocks" to make predictions. Its expression is as follows: ; In the formula These are the observations at time point t in the sequence. It is the expected value or mean of the sequence. It is a white noise term. These are the parameters of the model, and each parameter corresponds to a white noise term. It refers to the order. Therefore, the ARIMA model can be viewed as a direct combination of the above components, which can be expressed as follows: ; In the formula It is the current time series. arrive Indicates the current value and the past The relationship between the values ​​at each time point arrive Indicates the current value and the past The relationship between the values ​​at each time point For constant terms, This is the error term.

[0031] ARIMA's model flowchart is as follows Figure 5 As shown in the figure, ACF and PACF are the autocorrelation function and partial autocorrelation function of the model, respectively, which play an important role in the selection of parameters in the ARIMA model. In general, the initial values ​​of p and q in the ARIMA (p, d, q) model can be determined by observing the ACF and PACF plots.

[0032] Furthermore, the LSTM network includes the output of a forget gate. The output of the input gate Output of the output gate The implementation process in this embodiment includes: Long Short-Term Memory (LSTM) networks were developed to address the gradient explosion and vanishing problems encountered by traditional recurrent neural networks (RNNs) when processing long sequences of data. By introducing gating structures and cell states to control the flow and storage of information, LSTM effectively captures and remembers long-term dependencies in time series. Because it overcomes the shortcomings of RNNs, LSTM has received widespread attention and application in the field of deep learning. It is generally used to process various types of sequence data, including time series prediction and natural language recognition, and is considered one of the important milestones in deep learning, playing a significant role in the development of sequence modeling, prediction, and processing. An LSTM neural network structure diagram is shown below. Figure 6 As shown, the key to LSTM lies in the cell state; it has one more cell state than RNN. LSTM can remove or add cell state information through three gate structures: the "forget gate," the "input gate," and the "output gate." The gates filter information and consist of a sigmoid network layer and a dot product operation, as detailed below: (1) Forget Gate: The forget gate determines the information to be retained from the cell state of the previous time step, and can also forget unimportant information through learning. The expression is as follows: ; in, It is the Sigmoid function. It is the weight matrix of the forget gate. It is the previous output of the memory block. This is the current input. It is the bias term of the forget gate.

[0033] (2) Input gate: The input gate is responsible for determining the information that needs to be updated in the cell state at the current time step. This gating mechanism can learn to determine which information is useful for the current task. The expression is as follows: ; ; in, It is the output of the input gate. It is the new candidate value vector. It is the weight matrix of the input gate. It is the bias term of the input gate. It is the weight matrix of the candidate cell states. It is a bias term for the candidate cell state, used to adjust the result of the linear transformation.

[0034] (3) Cell state: The role of the cell state at this time is to update memory. The new cell state contains two parts of memory. One part is the old memory left after the memory cells have forgotten the useless memories from the previous moment. The other part is the useful information filtered out from the input gate and used as new memory. The cell update expression is as follows: ; In the formula This represents the processed old memory. This represents the new memory after processing; the sum of the two constitutes the new cellular state.

[0035] (4) Output gate: The output gate determines the information to be output from the hidden state and cell state at the current time step. This allows for the selective output of information from the current time step for use by subsequent layers and tasks. The expression is as follows: ; ; in, It is the output of the output gate. It is the Sigmoid function. It is the weight matrix of the output gate. It is the previous output of the memory block. This is the current input. It is the bias term of the output gate. This is the final output, but it's in a new cell state. Based on this, it consists of two processes: first, obtaining through the Sigmoid layer... This determines the cell state to be output, and then the new cell state is processed... Function processing, then dot product Control output.

[0036] Furthermore, the prediction results for the periodic terms include: The initial predicted value of the periodic term is obtained based on the ARIMA model. The residual between the actual value of the periodic term and the initial predicted value of the periodic term is calculated. The residual and the initial predicted value of the periodic term are input into the LSTM network for training to obtain the prediction result of the periodic term.

[0037] Specifically, the implementation process in this embodiment includes: While ARIMA models are applicable to various time series data, they struggle with handling nonlinear relationships and long-term dependencies, especially with data possessing long-term memory characteristics, often overlooking causal relationships. LSTM models, on the other hand, employ specialized gating mechanisms to effectively capture and utilize the nonlinearity and dependencies in time series data. Furthermore, LSTM models can automatically learn features from time series data and exhibit better robustness to heterogeneous data. Combining ARIMA and LSTM not only compensates for the shortcomings of ARIMA models but also provides stronger model automation and end-to-end learning capabilities, thereby further improving the accuracy and robustness of landslide displacement prediction. (Hybrid structure diagram shown below) Figure 7 As shown, from Figure 7 It can be seen from this that This is the input sequence for the ARIMA model, and the preliminary prediction result is... The residual calculation process for the model is as follows: ; After obtaining the residuals of the ARIMA model, the residual sequence is used as the input to the LSTM model. The LSTM model is then used to fit the nonlinear relationship of the residual sequence to predict the residual values. The calculation formula is as follows: ; In the formula To account for model error, the predictions from the two models are ultimately summed to obtain the final prediction value. .

[0038] ; By predicting the periodic item extraction value, a comparison chart of the periodic item extraction value and the predicted value is obtained, as shown in the figure below. Figure 8 As shown, the goodness of fit was also calculated. The value is 0.979. This meets the expected requirements.

[0039] The final displacement prediction data is obtained by combining the predicted trend displacement and periodic displacement after decomposition using a time series summation model. The overall displacement prediction effect is as follows: Figure 9 As shown. From Figure 9 As can be seen, the actual displacement at some monitoring points closely matches the predicted displacement. From April to July 2012, the water level in the Three Gorges Reservoir area was declining, which was also a period of high incidence of heavy rainfall. The displacement changes were large, which made landslides more likely. The prediction accuracy was relatively high during this period. From September to December, the water level in the reservoir remained at 175m with small fluctuations. The lag effect caused significant errors in the results, but overall, it could reflect the trend of actual displacement changes. This model has a good predictive effect on landslide displacement.

[0040] To further demonstrate the accuracy and effectiveness of the displacement decomposition method, trend term prediction method, and period term prediction method used in this embodiment, a comparison is made with the ARIMA model and the AR model directly predicting the total displacement. The comparison results are shown in the figure below. Figure 10 As shown in the figure, it is clear that the CMA-ARIMA-LSTM model method used in this embodiment closely approximates the actual displacement, while the simple ARIMA and AR models perform poorly. This is achieved by calculating the root mean square error. Mean Absolute Error and goodness of fit The calculation results are shown in Table 1.

[0041] Table 1 Comparative analysis shows that the CMA-ARIMA-LSTM displacement prediction model has lower root mean square error and mean absolute error, while also exhibiting better fit. It is also very ideal, fully demonstrating the advantages of the LSTM model and achieving the goal of optimization.

[0042] Furthermore, calculating the tangent angle includes: A continuous function is obtained by performing cubic spline interpolation on the Tt curve. The instantaneous tangent slope is obtained by taking the first derivative of the continuous function. The instantaneous tangent slope is then converted into a tangent angle using the arctangent function.

[0043] Specifically, the implementation process in this embodiment includes: Setting landslide failure thresholds plays a crucial role in landslide early warning and forecasting. When the measured parameters or conditions of a landslide reach the corresponding threshold, varying degrees of risk arise. By scientifically and rationally setting landslide failure thresholds, landslide occurrences can be effectively predicted and warned of, allowing for timely preventative measures and reducing disaster losses. Common threshold setting methods include the St curve tangent angle criterion, acceleration criterion, rainfall criterion, and engineering category criterion. However, the St curve tangent angle criterion is affected by different dimensions, while the acceleration, rainfall, and engineering category criters require comprehensive consideration of various factors, sometimes failing to achieve the desired effect. Therefore, the Tt curve tangent angle criterion is gradually gaining wider acceptance in the academic community.

[0044] Landslide deformation is mainly divided into three stages: initial deformation, constant-rate deformation, and accelerated deformation. As can be seen above, the horizontal and vertical dimensions of the St curve tangent angle criterion are different, making it insufficiently rigorous for early warning. Therefore, Xu Qiang improved the St curve by incorporating the average rate of the constant-rate deformation stage... v As an intermediate quantity, this allows both the horizontal and vertical axes of the St displacement-time curve to be converted into time, thus solving the problem of inconsistent dimensions.

[0045] The formula for calculating the average speed *r* during the constant velocity phase is as follows: ; In the formula The displacement rate in different monitoring periods. To determine the number of monitoring sessions, the coordinate transformation process is as follows: ; In the formula The transformed ordinate value. To monitor or predict the cumulative displacement over a period of time, This represents the average velocity during the constant-velocity deformation stage. The improved tangent angle after coordinate transformation can be obtained from the formula. The expression: ; In the formula For a certain monitoring time, and Corresponding to, for The change in quantity.

[0046] The warning diagram for the tangent angle of the Tt curve is shown below. Figure 11 As shown in the figure, it is clear that the tangent angle φ increases continuously from April to July, then slows down for a month before accelerating again in September and October, subsequently stabilizing. Based on the above theory, the following definition is made according to the size of the tangent angle. When... The landslide is in the initial deformation stage; when The landslide is in the isotropic deformation stage; when The landslide is in the accelerated deformation stage; the accelerated deformation stage is further divided into three types: when The landslide is in a stage of weakly accelerated deformation; when The landslide is in a stage of accelerated deformation; when The landslide is in a stage of rapid deformation.

[0047] At present, there is no unified standard or system for landslide early warning. However, when issuing landslide warnings, the warning level is usually comprehensively classified based on multiple dimensions such as the deformation stage of the landslide, macroscopic deformation signs, potential hazards, and probability of occurrence. The landslide hazard levels are divided into four levels from light to severe: Attention Level, Warning Level, Alert Level, and Alarm Level. The corresponding colors are blue, yellow, orange, and red, respectively. Detailed descriptions of each warning level are shown in Table 2.

[0048] Table 2 The landslide warning levels are divided into four levels based on the Tt curve tangent angle criterion, as shown in Table 3.

[0049] Table 3 Analysis of monitoring data from the Baishuihe landslide in the Three Gorges Reservoir area revealed a strong positive correlation between cumulative displacement and the decline in reservoir water level, classifying the landslide as a reservoir-water-declining type. Furthermore, the cumulative displacement exhibited significant step changes during periods of frequent heavy rainfall. This leads to the conclusion that the changes in cumulative displacement are primarily caused by the combined effects of seasonal precipitation and reservoir water level regulation. Considering the dual influence of internal geological changes and external environmental changes on displacement variation, based on time series theory, the cumulative moving average (CMA) method was used to divide the actual displacement into trend displacement and periodic displacement, which were then predicted separately. The trend displacement was first predicted using a fourth-order polynomial fitting method, with the predicted results closely matching the extracted values. Then, the periodic displacement was predicted using an ARIMA-LSTM time series fusion model, incorporating the influence of reservoir water level and precipitation during the periodic displacement prediction process. The predicted values ​​for the periodic displacement achieved a goodness of fit of 0.979 with the extracted values, demonstrating significant effectiveness. Finally, the predicted values ​​of the trend term and the periodic term are combined using a time series additive model to obtain the final time series predicted value. By comparing with the ARIMA model and the AR model, the CMA-ARIMA-LSTM method used in this embodiment has the highest prediction accuracy. A value of 0.996 was achieved, enabling the prediction of future landslide displacement trends, thus meeting the intended prediction effect. By employing the Tt curve tangent angle early warning method, the CMA-ARIMA-LSTM model was used to accurately predict landslide displacement while simultaneously providing real-time early warning and forecasting of landslide conditions. This method not only improved the accuracy of landslide prediction but also ensured the timeliness and effectiveness of early warnings, providing crucial technical support for landslide disaster prevention and response.

[0050] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A landslide displacement prediction method based on ARIMA-LSTM, characterized in that, include: Obtain the original landslide displacement data, and decompose the original landslide displacement data into trend and periodic terms using the cumulative moving average method; The trend term is fitted and predicted using a polynomial function to obtain the trend term prediction result; The periodic term is predicted by residual compensation using a fusion of the ARIMA model and the LSTM network to obtain the prediction result of the periodic term. The trend prediction result and the period prediction result are superimposed to generate the total displacement prediction value. Based on the total displacement prediction value, a Tt curve is constructed and the tangent angle is calculated. Landslide classification and early warning are carried out according to the tangent angle threshold.

2. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, The original landslide displacement data is decomposed into trend and periodic components using the cumulative moving average method, including: Calculate the displacement component at time t, and accumulate the n displacement monitoring values ​​before time t and the displacement value at time t; divide the accumulated value by n+1 to obtain the trend term; subtract the trend term from the actual displacement to obtain the period term.

3. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, The trend term is fitted and predicted using a polynomial function to obtain the following trend term prediction results: ； in, It is the predicted value of the trend term displacement. , , , , All are polynomial coefficients. It is a constant.

4. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, Building an ARIMA model includes: The ARIMA parameters are determined by the autocorrelation function and the partial autocorrelation function. The periodic displacement data are subjected to d-order differencing. The autoregressive coefficients and moving average coefficients are solved by the maximum likelihood estimation method.

5. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, The LSTM network includes the output of the forget gate. The output of the input gate Output of the output gate ,in: Forgotten Gate: ; Input Gate: ; Output gate: ; in, It is the Sigmoid function. It is the weight matrix of the forget gate. It is the previous output of the memory block. This is the current input. It is the bias term of the forgetting gate. It is the output of the forget gate. It is the weight matrix of the input gate. It is the bias term of the input gate. It is the output of the input gate. It is the weight matrix of the output gate. It is the bias term of the output gate. It is the output of the output gate.

6. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, The predicted results for the periodic terms include: The initial predicted value of the periodic term is obtained based on the ARIMA model. The residual between the actual value of the periodic term and the initial predicted value of the periodic term is calculated. The residual and the initial predicted value of the periodic term are input into the LSTM network for training to obtain the prediction result of the periodic term.

7. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, Calculating the tangent angle includes: A continuous function is obtained by performing cubic spline interpolation on the Tt curve. The instantaneous tangent slope is obtained by taking the first derivative of the continuous function. The instantaneous tangent slope is then converted into a tangent angle using the arctangent function.

8. The landslide displacement prediction method based on ARIMA-LSTM as described in claim 1, characterized in that, The threshold for tiered early warning is set as follows: Tangent angle A blue warning is issued at any time, indicating a tangent angle. A yellow warning is issued at any time, indicating the tangent angle. An orange alert is issued at any time, tangent angle A red alert will be issued at any time.

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