A lightweight intelligent landslide displacement prediction method

Abstract

This invention provides a lightweight intelligent landslide displacement prediction method, belonging to the field of geological disaster monitoring and prediction. Its contents include: acquiring historical monitoring displacement time-series data from landslide monitoring points; dynamically normalizing the displacement time-series data; constructing a lightweight prediction model including a gated enhanced ordinary differential equation network and a dynamic residual correction module; synchronously optimizing the basic prediction and residual correction networks through a joint training module, employing a composite loss function including dynamic threshold Huber loss and L2 regularization; and automatically updating the sliding window and calculating the prediction result based on a rolling prediction mechanism when new monitoring data arrives. This invention, through the synergistic optimization of the gated enhanced ordinary differential equation network and dynamic residual correction, ensures a lightweight model while improving prediction accuracy, providing real-time and reliable technical support for early warning and disaster prevention and mitigation decisions for landslide disasters.

Description

Technical Field

[0001] This invention relates to the field of public safety prediction, and more specifically, to a lightweight intelligent landslide displacement prediction method. Background Technology

[0002] Geological disasters that occur every year cause significant casualties and property losses. As one of the most common types of geological disasters, landslides require displacement monitoring and prediction as one of the most important bases for prevention and control. This has very important practical significance for reducing casualties and economic losses caused by landslides.

[0003] However, traditional machine learning models such as linear regression and random forests cannot capture the temporal dynamics of displacement. While models such as Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Transformer models improve temporal modeling capabilities, they have large parameter counts, high model complexity, and static normalization makes them unsuitable for adapting to the time-varying statistical characteristics of landslide displacement. This leads to difficulties such as decreased prediction accuracy, delayed prediction response, and difficulty in deployment on edge devices at monitoring stations. Therefore, establishing an intelligent landslide displacement prediction method that can guarantee prediction accuracy while being lightweight is of great practical significance for improving prediction accuracy and response speed, and increasing emergency response time after early warning. Summary of the Invention

[0004] This invention proposes a lightweight intelligent landslide displacement prediction method. First, it dynamically calculates the mean μ and standard deviation σ through a sliding window and performs real-time normalization to solve the distribution offset problem of traditional static normalization. Second, it constructs a prediction model consisting of a gated augmentation (Ordinary Differential Equation, ODE) network and a dynamic residual correction method. The gated augmentation ODE network generates the initial state through a GRU encoder, and achieves basic prediction through feature-state fusion, gated activation, layer normalization, and ODE solving. The dynamic residual correction module learns the prediction error through a three-layer fully connected network. Finally, it employs a composite loss function including dynamic Huber loss and adaptive regularization to jointly optimize the model parameters. This method, through a sliding window rolling prediction mechanism, improves prediction accuracy, reduces the number of model parameters, and meets the real-time requirements of geological disaster monitoring.

[0005] This invention is implemented as follows:

[0006] The technical solution for achieving the objective of this invention is: a lightweight intelligent landslide displacement prediction method, comprising the following steps:

[0007] Step 1: Obtain historical monitoring displacement time-series data of landslide monitoring points;

[0008] Step 2: The historical monitoring displacement sequence is standardized using a dynamic normalization method to obtain a standardized displacement sequence;

[0009] Step 3: Obtain the basic predicted values ​​by gating and enhancing the ordinary differential equation network;

[0010] Step 4: Obtain the prediction results for loss calculation using the dynamic residual correction method;

[0011] Step 5: Using the dynamic composite loss function as the optimization objective, and based on the prediction results used for loss calculation, the trainable parameters in the gated augmented ordinary differential equation network and the residual correction method are jointly optimized through the backpropagation algorithm.

[0012] The trainable parameters include:

[0013] (1) Weight matrix and bias terms in the core of gated enhanced ordinary differential equation network;

[0014] (2) Weights and bias terms of the fully connected layer in the dynamic residual correction module;

[0015] Step 6: Repeat the calculation process from Step 2 to Step 5 until the preset number of iterations is reached, and finally obtain the prediction model containing the gated enhanced ordinary differential equation network and dynamic residual correction.

[0016] Step 7: Input the latest sliding window data into the trained prediction model, calculate the final displacement prediction value, and perform inverse normalization on the prediction result;

[0017] Step 8: When new monitoring data arrives, remove the oldest data point and add the new data. Perform dynamic normalization processing on the latest monitoring displacement sequence within the window as in Step 2, and then re-execute Step 7.

[0018] Furthermore, the gated augmented ordinary differential equation (ODE) network is implemented through the following steps:

[0019] Step S31: Dimensionality reduction temporal coding: The standardized displacement sequence is processed by a gated recurrent unit, wherein the hidden layer dimension of the gated recurrent unit is configured as D / 2, and after extracting the D / 2-dimensional hidden state of the final time step, the state is expanded to D dimensions by zero padding as the initial hidden state h0, where D is the reference hidden layer dimension.

[0020] Step S32: Perform pooling downsampling on the normalized displacement sequence with kernel size k and step size 1 to obtain a downsampled sequence of length L / k, where L is the length of the normalized displacement sequence and k is an integer greater than 1;

[0021] Step S33: Combine the downsampled sequence with the initial hidden state h0 and obtain the basic predicted value through a dynamic gating state evolution process.

[0022] Furthermore, the dynamic gating state evolution process is achieved by sequentially executing the following steps:

[0023] S34: Feature-state fusion, the method is: along the feature dimension, the downsampled displacement sequence is concatenated with the initial hidden state of the gated cyclic encoder, and mapped to a high-dimensional space through linear transformation to obtain the feature-state fusion output;

[0024] S35: Gated activation, the method is as follows: First, the feature-state fusion output is equally split into two sub-vectors along the last feature dimension; second, a sigmoid function with an output range of (0,1) is applied to the first sub-vector; third, the sigmoid activation result is multiplied element-wise with the second sub-vector to obtain the gated activation output;

[0025] S36: Layer Normalization: Normalize the gated activation output to obtain the layer normalized output;

[0026] S37: Calculate the hidden state residual: Add the layer normalized output to λ times the initial hidden state of the gated cyclic unit encoder to obtain the residual output, where λ∈[0.05,0.2].

[0027] S38: Solve Ordinary Differential Equations (ODEs): Numerically integrate the derivatives given by the residual output to obtain the ordinary differential equation output;

[0028] S39: Linear Decoding: Maps the output of the ordinary differential equation to the base prediction value through a linear transformation.

[0029] Furthermore, in step four, the dynamic residual correction method comprises the following steps:

[0030] Step S41: Flatten the standardized displacement sequence into one dimension and concatenate it with the basic prediction values ​​of the gated enhanced ordinary differential equation network to form the corrected network input;

[0031] Step S42: Subtract the basic predicted value of the gated enhanced ordinary differential equation network from the actual displacement value at the time to be predicted, and generate residual labels as the output of the corrected network.

[0032] Step S43: Pass the corrected network input through three fully connected layers in sequence: input layer, hidden layer, and output layer. The number of units in the input layer is one-quarter of the dimension of the base hidden layer, and the number of units in the hidden layer is one-eighth of the dimension of the base hidden layer. The input layer and hidden layer use the SiLU activation function, and the output layer is a linear layer. Finally, the error estimate is output.

[0033] Step S44: Add the base prediction value to the error estimate to obtain the prediction result used for loss calculation.

[0034] Furthermore, in step five, the dynamic composite loss function is defined as L total :

[0035] L total =L Huber +β×L regu

[0036] Where β is the dynamic regularization coefficient, which is dynamically set according to the sliding window standard deviation σ according to the following rules:

[0037] When σ≥1.5, β=0.001

[0038] When 0.5<σ<1.5, β= 0.007-0.004σ

[0039] When σ ≤ 0.5, β = 0.005

[0040] L regu The sum of squared L2 norms for all trainable parameters; L Huber The dynamically adjusted Huber loss function is defined as: when |y- When |≤δ, L Huber =0.5×(y- )² When |y- When |>δ, L Huber =δ×(|y- |-0.5×δ)

[0041] Where y represents the actual displacement monitoring value. This represents the prediction result used for loss calculation, where δ is the threshold value, which is 1.5 times the standard deviation σ of the sliding window.

[0042] The beneficial effects of this invention are as follows: This invention provides a lightweight intelligent landslide displacement prediction method. The constructed dynamic normalization processing mechanism, by calculating the mean μ and standard deviation σ of the sliding window in real time, can retain the local statistical characteristics of recent data, effectively solving the distribution shift problem caused by traditional static normalization. The improved liquid neural ODE basic prediction module adopts a gated enhancement design and a fixed step-size solver, significantly improving the prediction accuracy of long sequences while reducing the number of parameters. The dynamic residual correction module reduces prediction errors through multilayer sensing units and gradient truncation techniques. The joint training module and composite loss function achieve progressive collaborative optimization of basic prediction and error correction. The organic combination of the above technologies provides reliable technical support for reducing the number of model parameters and realizing real-time monitoring and early warning of landslide displacement. Attached Figure Description

[0043] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0044] Figure 1 This is a flowchart of a lightweight intelligent landslide displacement prediction method provided by an embodiment of the present invention;

[0045] Figure 2 This is a flowchart of a gated enhanced ordinary differential equation network provided in an embodiment of the present invention;

[0046] Figure 3 This is a comparison chart of the predicted results and measured values ​​of the method of the present invention provided in the embodiments of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the implementation examples and accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] The method of this invention will be illustrated below using a specific case of real-time landslide displacement prediction.

[0049] like Figure 1 A lightweight intelligent landslide displacement prediction method includes the following steps:

[0050] Step 1: Obtain historical monitoring displacement time-series data of landslide monitoring points;

[0051] Step 2: The historical monitoring displacement sequence is standardized using a dynamic normalization method to obtain a standardized displacement sequence;

[0052] Step 3: Obtain the basic predicted values ​​by gating and enhancing the ordinary differential equation network;

[0053] Step 4: Obtain the prediction results for loss calculation using the dynamic residual correction method;

[0054] Step 5: Using the dynamic composite loss function as the optimization objective, and based on the prediction results used for loss calculation, the trainable parameters in the gated augmented ordinary differential equation network and the residual correction method are jointly optimized through the backpropagation algorithm.

[0055] The trainable parameters include:

[0056] (1) Weight matrix and bias terms in the core of gated enhanced ordinary differential equation network;

[0057] (2) Weights and bias terms of the fully connected layer of the dynamic residual correction module.

[0058] Step 6: Repeat the calculation process from Step 2 to Step 5 until the preset number of iterations is reached, and finally obtain the prediction model containing the gated enhanced ordinary differential equation network and dynamic residual correction.

[0059] Step 7: Input the latest sliding window data into the trained prediction model, calculate the final displacement prediction value, and perform inverse normalization on the prediction result;

[0060] Step 8: When new monitoring data arrives, remove the oldest data point and add the new data. Perform dynamic normalization processing on the latest monitoring displacement sequence within the window as in Step 2, and then re-execute Step 7.

[0061] Furthermore, the gated augmented ordinary differential equation (ODE) network is implemented through the following steps:

[0062] Step S31: Dimensionality reduction temporal coding: The standardized displacement sequence is processed by a gated recurrent unit, wherein the hidden layer dimension of the gated recurrent unit is configured as D / 2, and after extracting the D / 2-dimensional hidden state of the final time step, the state is expanded to D dimensions by zero padding as the initial hidden state h0, where D is the reference hidden layer dimension.

[0063] By directly setting the hidden layer dimension of GRU to D / 2, the number of parameters is significantly reduced, achieving lightweight temporal coding, and the lower-dimensional GRU output can prevent overfitting of the initial state.

[0064] Step S32: Perform pooling downsampling on the normalized displacement sequence with kernel size k and step size 1 to obtain a downsampled sequence of length L / k, where L is the length of the normalized displacement sequence and k is an integer greater than 1;

[0065] Step S33: Combine the downsampled sequence with the initial hidden state h0 and obtain the basic predicted value through a dynamic gating state evolution process.

[0066] Furthermore, the dynamic gating state evolution process is achieved by sequentially executing the following steps:

[0067] S34: Feature-state fusion, the method is: along the feature dimension, the downsampled displacement sequence is concatenated with the initial hidden state of the gated cyclic encoder, and mapped to a high-dimensional space through linear transformation to obtain the feature-state fusion output;

[0068] S35: Gated activation, the method is as follows: First, the feature-state fusion output is equally split into two sub-vectors along the last feature dimension; second, a sigmoid function with an output range of (0,1) is applied to the first sub-vector; third, the sigmoid activation result is multiplied element-wise with the second sub-vector to obtain the gated activation output;

[0069] S36: Layer Normalization: Normalize the gated activation output to obtain the layer normalized output;

[0070] S37: Calculate the hidden state residual: Add the layer normalized output to λ times the initial hidden state of the gated cyclic unit encoder to obtain the residual output, where λ∈[0.05,0.2].

[0071] S38: Solve Ordinary Differential Equations (ODEs): Numerically integrate the derivatives given by the residual output to obtain the ordinary differential equation output;

[0072] S39: Linear Decoding: Maps the output of the ordinary differential equation to the base prediction value through a linear transformation.

[0073] Furthermore, in step four, the dynamic residual correction method comprises the following steps:

[0074] Step S41: Flatten the standardized displacement sequence into one dimension and concatenate it with the basic prediction values ​​of the gated enhanced ordinary differential equation network to form the corrected network input;

[0075] Step S42: Subtract the basic predicted value of the gated enhanced ordinary differential equation network from the actual displacement value at the time to be predicted, and generate residual labels as the output of the corrected network.

[0076] Step S43: Pass the corrected network input through three fully connected layers in sequence: input layer, hidden layer, and output layer. The number of units in the input layer is one-quarter of the dimension of the base hidden layer, and the number of units in the hidden layer is one-eighth of the dimension of the base hidden layer. The input layer and hidden layer use the SiLU activation function, and the output layer is a linear layer. Finally, the error estimate is output.

[0077] Step S44: Add the base prediction value to the error estimate to obtain the prediction result used for loss calculation.

[0078] Furthermore, in step five, the dynamic composite loss function is defined as L total :

[0079] L total =L Huber +β×L regu；

[0080] Where β is the dynamic regularization coefficient, which is dynamically set according to the sliding window standard deviation σ according to the following rules:

[0081] When σ≥1.5, β=0.001;

[0082] When 0.5<σ<1.5, β= 0.007-0.004σ;

[0083] When σ ≤ 0.5, β = 0.005;

[0084] L regu The sum of squared L2 norms for all trainable parameters; L Huber The dynamically adjusted Huber loss function is defined as follows:

[0085] When |y- When |≤δ, L Huber =0.5×(y- )² When |y- When |>δ, L Huber =δ×(|y- |-0.5×δ)

[0086] Where y represents the actual displacement monitoring value. This represents the prediction result used for loss calculation, where δ is the threshold value, which is 1.5 times the standard deviation σ of the sliding window.

[0087] The experimental data came from the online monitoring data of a tailings dam, and a total of 2,568 sets of monitoring sample data were obtained. The first 2,092 sets of data were used to train the model, and the last 476 sets of data were used for prediction.

[0088] The specific implementation process is as follows:

[0089] like Figure 1 A lightweight intelligent landslide displacement prediction method includes the following steps:

[0090] Step 1: Obtain historical monitoring displacement time-series data of landslide monitoring points;

[0091] Step 2: The historical monitoring displacement sequence is standardized using a dynamic normalization method to obtain a standardized displacement sequence;

[0092] The window length is set to 120, the sliding step is 1, and the normalization method used is:

[0093] X norm =(X-μ) / (σ+10 -6 )

[0094] Where X is the historical monitoring displacement sequence, X norm For standardized displacement sequences;

[0095] Step 3: Obtain the basic predicted values ​​by gating and enhancing the ordinary differential equation network;

[0096] The baseline hidden layer has a dimension of 64, a downsampling kernel size of k=3, λ=0.1, uses mean pooling, and employs the fourth-order Runge-Kutta method for ordinary differential equations.

[0097] Step 4: Obtain the prediction results for loss calculation using the dynamic residual correction method;

[0098] Step 5: Using the dynamic composite loss function as the optimization objective, and based on the prediction results used for loss calculation, the trainable parameters in the gated augmented ordinary differential equation network and the residual correction method are jointly optimized through the backpropagation algorithm.

[0099] The trainable parameters include:

[0100] (1) Weight matrix and bias terms in the core of gated enhanced ordinary differential equation network;

[0101] (2) Weights and bias terms of the fully connected layer of the dynamic residual correction module.

[0102] The backpropagation algorithm uses the Adam optimizer with a learning rate of 0.001.

[0103] Step 6: Repeat the calculation process from Step 2 to Step 5 until the preset number of iterations is reached, and finally obtain the prediction model containing the gated enhanced ordinary differential equation network and dynamic residual correction.

[0104] The maximum number of iterations is set to 300.

[0105] Step 7: Input the latest sliding window data into the trained prediction model, calculate the final displacement prediction value, and perform inverse normalization on the prediction result;

[0106] Step 8: When new monitoring data arrives, remove the oldest data point and add the new data. Perform dynamic normalization processing on the latest monitoring displacement sequence within the window as in Step 2, and then execute Step 7 to achieve rolling prediction.

[0107] Figure 3The comparison between the predicted results and the actual values ​​of this invention is shown. It can be seen that the consistency between the predicted results and the actual values ​​is very high, and it can predict the landslide displacement trend well.

[0108] To further verify the advantages of the method of the present invention, the LSTM model, GRU model and the method of the present invention were compared respectively. The hidden layer dimension and learning rate of LSTM and GRU were consistent with the baseline hidden layer dimension and learning rate of the method of the present invention.

[0109] To fully compare the performance of each model, mean absolute error (MAE), percentage absolute error (MAPE), root mean square error (RMSE), and goodness-of-fit R-squared were used. 2 Four indicators were used to quantitatively evaluate each model. Each model was calculated ten times, and the average value of each indicator was obtained. Table 1 shows the comparison of the evaluation results of each model.

[0110] Table 1 Comparison of Evaluation Indicators for Each Model

[0111]

[0112] As shown in Table 1, among the three methods, the method of this invention achieved the best performance in all evaluation metrics, demonstrating its high prediction accuracy. Furthermore, the method of this invention has the fewest parameters compared to other models, making it more lightweight and suitable for deployment on edge devices. In summary, this case study proves that the method of this invention not only has high computational accuracy but also a lower parameter count than popular deep learning methods such as LSTM and GRU. It can effectively improve the efficiency of landslide displacement prediction and edge deployment capabilities, providing a basis for landslide safety management and the prevention of major accidents.

[0113] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A lightweight intelligent landslide displacement prediction method, characterized in that, Includes the following steps: Step 1: Obtain historical monitoring displacement time-series data of landslide monitoring points; Step 2: The historical monitoring displacement sequence is standardized using a dynamic normalization method to obtain a standardized displacement sequence; Step 3: Obtain the basic predicted values ​​by gating and enhancing the ordinary differential equation network; Step 4: Obtain the prediction results for loss calculation using the dynamic residual correction method; Step 5: Using the dynamic composite loss function as the optimization objective, and based on the prediction results used for loss calculation, the trainable parameters in the gated augmented ordinary differential equation network and the residual correction method are jointly optimized through the backpropagation algorithm. The trainable parameters include: (1) Weight matrix and bias terms in the core of gated enhanced ordinary differential equation network; (2) Weights and bias terms of the fully connected layer in the dynamic residual correction module; Step 6: Repeat the calculation process from Step 2 to Step 5 until the preset number of iterations is reached, and finally obtain the prediction model containing the gated enhanced ordinary differential equation network and dynamic residual correction. Step 7: Input the latest sliding window data into the trained prediction model, calculate the final displacement prediction value, and perform inverse normalization on the prediction result; Step 8: When new monitoring data arrives, remove the oldest data point and add the new data. Perform dynamic normalization processing on the latest monitoring displacement sequence within the window as in Step 2, and then re-execute Step 7. The gated enhanced ordinary differential equation network is implemented through the following steps: Step S31: Dimensionality reduction temporal coding: The standardized displacement sequence is processed by a gated recurrent unit, wherein the hidden layer dimension of the gated recurrent unit is configured as D / 2, and after extracting the D / 2-dimensional hidden state of the final time step, the state is expanded to D dimensions by zero padding as the initial hidden state h0, where D is the reference hidden layer dimension. Step S32: Perform pooling downsampling on the normalized displacement sequence with kernel size k and step size 1 to obtain a downsampled sequence of length L / k, where L is the length of the normalized displacement sequence and k is an integer greater than 1; Step S33: Combine the downsampled sequence with the initial hidden state h0 and obtain the basic predicted value through a dynamic gating state evolution process; The dynamic gating state evolution process is achieved by sequentially executing the following steps: S34: Feature-state fusion, the method is: along the feature dimension, the downsampled displacement sequence is concatenated with the initial hidden state of the gated cyclic encoder, and mapped to a high-dimensional space through linear transformation to obtain the feature-state fusion output; S35: Gated activation, the method is as follows: First, the feature-state fusion output is equally split into two sub-vectors along the last feature dimension; second, a sigmoid function with an output range of (0,1) is applied to the first sub-vector; third, the sigmoid activation result is multiplied element-wise with the second sub-vector to obtain the gated activation output; S36: Layer Normalization: Normalize the gated activation output to obtain the layer normalized output; S37: Calculate the hidden state residual: Add the layer normalized output to λ times the initial hidden state of the gated cyclic unit encoder to obtain the residual output, where λ∈[0.05,0.2]. S38: Solve the ordinary differential equation: Numerically integrate the derivative given by the residual output to obtain the ordinary differential equation output; S39: Linear Decoding: Maps the output of the ordinary differential equation to the base prediction value through a linear transformation.

2. The lightweight intelligent landslide displacement prediction method as described in claim 1, characterized in that, In step two, the dynamic normalization method is implemented through the following steps: Step S21: Set a sliding window of fixed length and calculate the mean μ and standard deviation σ of the monitored displacement sequence within the window in real time; Step S22: Based on the μ and σ parameters of the current window, standardize the monitored displacement sequence within the window to obtain a standardized displacement sequence; The sliding window is updated as new monitoring data arrives, and the normalization calculation only uses historical data within the window.

3. The lightweight intelligent landslide displacement prediction method as described in claim 1, characterized in that, In step four, the dynamic residual correction method comprises the following steps: Step S41: Flatten the standardized displacement sequence into one dimension and concatenate it with the basic prediction values ​​of the gated enhanced ordinary differential equation network to form the corrected network input; Step S42: Subtract the basic predicted value of the gated enhanced ordinary differential equation network from the actual displacement value at the time to be predicted, and generate residual labels as the output of the corrected network. Step S43: Pass the corrected network input through three fully connected layers in sequence: input layer, hidden layer, and output layer. The number of units in the input layer is one-quarter of the dimension of the base hidden layer, and the number of units in the hidden layer is one-eighth of the dimension of the base hidden layer. The input layer and hidden layer use the SiLU activation function, and the output layer is a linear layer. Finally, the error estimate is output. Step S44: Add the base prediction value to the error estimate to obtain the prediction result used for loss calculation.

4. The lightweight intelligent landslide displacement prediction method as described in claim 1, characterized in that, In step five, the dynamic composite loss function is defined as L total : L total =L Huber +β×L regu ; Where β is the dynamic regularization coefficient, which is dynamically set according to the sliding window standard deviation σ according to the following rules: When σ≥1.5, β=0.001; When 0.5<σ<1.5, β=0.007-0.004σ; When σ ≤ 0.5, β = 0.005; L regu The sum of squared L2 norms for all trainable parameters; L Huber The dynamically adjusted Huber loss function is defined as follows: When |y-ŷ|≤δ, L Huber =0.5×(y-ŷ)²; when |y-ŷ|>δ, L Huber =δ×(|y-ŷ|-0.5×δ); where y represents the actual displacement monitoring value, ŷ represents the predicted result used for loss calculation, and δ is the threshold value, which is 1.5 times the standard deviation σ of the sliding window.

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