Wavelet decomposition-based sub-item prediction fusion method
By combining SG filtering and wavelet decomposition methods with multinomial and ConvLSTM models, the prediction of ground settlement displacement is performed in parts and the results are fused. This solves the problems of noise interference, nonlinearity and nonstationarity in ground settlement displacement prediction, and improves the accuracy and stability of the prediction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHENGDU UNIVERSITY OF TECHNOLOGY
- Filing Date
- 2026-04-02
- Publication Date
- 2026-06-16
AI Technical Summary
Existing technologies for predicting ground settlement and displacement suffer from problems such as strong noise interference, significant nonlinearity and non-stationarity, mixing of different variable components, and difficulty in using a single prediction model to simultaneously capture both long-term trend fitting and short-term fluctuations.
SG filtering is used for data preprocessing, and continuous wavelet transform and discrete wavelet transform are combined for signal decomposition. Multinomial model and ConvLSTM model are used to predict trend and periodic terms respectively, and random terms are discarded when reconstructing the results, so as to realize the fusion of sub-modeling and prediction results.
It improves the accuracy and robustness of ground settlement displacement prediction, reduces noise interference and model fitting difficulty, enhances the ability to express long-term trends and short-term fluctuations, and obtains more stable and accurate prediction results.
Smart Images
Figure CN122220705A_ABST
Abstract
Description
Technical Field
[0001] This invention provides a component prediction and fusion method based on wavelet decomposition, belonging to the field of land settlement displacement prediction technology. Background Technology
[0002] Current predictions of land subsidence displacement are based on single time-series signal results, without in-depth analysis of the signal's inherent characteristics. Land subsidence refers to the continuous sinking of the Earth's surface due to the compression and deformation of the underground medium or changes in support conditions under the influence of natural processes or human activities. Accurate land subsidence prediction is a crucial link in improving urban risk early warning capabilities, ensuring the orderly operation of cities, and achieving sustainable development. Currently, scholars have conducted extensive research on land subsidence disaster prediction. Related methods have generally evolved from statistical analysis, empirical judgment, and regression model prediction to grey prediction, time series analysis, and methods such as BP neural networks and SVM, and further to a prediction stage that integrates multi-source monitoring data such as InSAR and GNSS with deep learning models such as CNN and LSTM. However, early methods are heavily reliant on linear relationships; grey prediction and time series analysis have high requirements for data stationarity and continuity; BP neural networks and SVM still have shortcomings in spatiotemporal correlation expression and parameter stability; and while current deep learning methods have significantly improved prediction capabilities, they still face problems such as insufficient interpretability, high training costs, and limited generalization ability. While the continuous updates and iterations of settlement prediction methods and models have improved the accuracy of settlement prediction, an important fact has been overlooked: settlement displacement is not a single signal, but consists of long-term settlement displacement trends and periodic fluctuations as well as signal noise, and different displacements have different characteristics.
[0003] Patent CN114692963A discloses a landslide displacement prediction method based on a long short-term memory neural network. It uses wavelet transform to decompose the collected cumulative landslide displacement into trend displacement and periodic displacement according to the time series. A univariate long short-term memory neural network is used to predict the trend displacement, and a multivariate long short-term memory neural network based on an attention mechanism is used to predict the periodic displacement, obtaining the predicted value of the periodic displacement. The predicted values of the trend displacement and the periodic displacement are then superimposed to obtain the predicted value of the cumulative landslide displacement. However, this method has the following technical problems: (1) the time-series signal has high noise, and no noise reduction processing is performed; (2) the model does not consider spatial features and only uses LSTM to capture time-series features.
[0004] Patent CN118031899A discloses a multi-factor roadbed settlement prediction method based on deep learning, which establishes a roadbed settlement observation system; collects data and preprocesses the data; establishes a multi-factor AM-BI-LSTM model using a deep learning machine; defines the input dataset according to the multi-factor AM-BI-LSTM model, and divides the training dataset and test dataset; data segmentation: sets the window segmentation length Lc; model parameter tuning; rolling prediction; selects evaluation indicators to determine the degree of deviation between the predicted value and the measured value. However, this method has the following technical problems: (1) lacks temporal decomposition and data preprocessing, making it difficult to deal with non-stationary settlement sequences; (2) the model only focuses on temporal features and does not explore spatial correlation. Summary of the Invention
[0005] This invention provides a component prediction and fusion method based on wavelet decomposition, aiming to solve the following technical problems:
[0006] 1. To address the issue of strong noise interference in the original settlement displacement sequence, a data preprocessing method combining SG filtering is proposed to improve the smoothness and reliability of the input data;
[0007] 2. To address the issues of significant nonlinearity and nonstationarity in settlement displacement sequences, and the mixing of different variation components, a decomposition method combining continuous wavelet transform and discrete wavelet transform is proposed to achieve effective separation of trend and periodic terms.
[0008] 3. To address the problem that a single prediction model cannot simultaneously capture both long-term trend fitting and short-term fluctuation characterization, a method of sub-modeling and prediction result fusion is proposed. In this method, a multinomial model is used to predict the trend term, and a ConvLSTM model is used to predict the periodic term, thereby improving the accuracy and robustness of settlement displacement prediction.
[0009] This invention, based on the unique characteristics of settlement displacement, constructs a wavelet decomposition-based component prediction and fusion method. The algorithm involves three components: SG filtering, wavelet decomposition, and component displacement prediction. SG filtering is a smoothing and denoising method based on local polynomial fitting. By fitting the original displacement sequence within a sliding window, it weakens random noise interference while preserving the overall trend and local features of the sequence. In this invention, SG filtering is mainly used to improve the reliability of the original monitoring data and reduce noise, providing high-quality input for subsequent decomposition and prediction. Wavelet decomposition is a multi-scale analysis method suitable for non-stationary time series. In this invention, firstly, continuous wavelet transform (CWT) is used to perform preliminary analysis of the displacement sequence to identify the variation characteristics of the sequence at different time scales; then, discrete wavelet transform (DWT) is used to further decompose the sequence, dividing the original displacement into trend, periodic, and random components, thereby reducing the complexity and non-stationarity of the sequence and providing a foundation for component modeling. Component displacement prediction refers to establishing prediction models for different displacement components obtained from wavelet decomposition. The trend component is predicted using a polynomial model, the periodic component using a ConvLSTM model, and the random component is treated as a residual. Finally, the prediction results of each component are fused and reconstructed to obtain the final displacement prediction value. This method can fully leverage the advantages of different models in trend fitting and fluctuation characterization, thereby improving prediction accuracy.
[0010] The specific technical solution is as follows:
[0011] The wavelet decomposition-based component prediction fusion method includes the following steps:
[0012] Step 1: Obtain time-series InSAR ground subsidence monitoring results;
[0013] Step 2: Pre-processing before ground settlement prediction; specifically including the following sub-steps:
[0014] Step 2.1: Completion of Missing Values in Experimental Data: For areas with localized incoherence in InSAR, the IDW interpolation method is used to interpolate the time-series InSAR monitoring data to obtain spatially complete time-series ground subsidence monitoring data. The calculation formula is:
[0015] For a certain interpolation point with missing values Its estimated value The calculation formula is: ;
[0016] Among them, weight The calculation formula is: ;
[0017] Variable explanation: : The number of points surrounding the interpolation point Measured displacement values of known sample points. The total number of known sample points involved in the interpolation calculation. : Known sample points Interpolation point The spatial distance between them. Weighting index: used to control the degree of influence of distance on weight.
[0018] Step 2.2: Data Normalization: Normalize the time-series InSAR monitoring results data. The calculation formula is as follows: ; Normalized data values typically range from 100 to 1000. or between. : Original time-series InSAR settlement displacement data. : The minimum displacement value in this dataset. : The maximum displacement value in this dataset.
[0019] Step 3: For the acquired time-series monitoring results, causal SG filtering is used to preserve the overall trend and local characteristics of the original settlement displacement while removing signal noise. The calculation formula is:
[0020] Let the time series be Smoothed value after causal SG filtering for: ;
[0021] Variable explanation: :time Filtered sedimentation value. :time And its previous historical subsidence observations. Size of the filter window. : Filtering coefficients obtained by local polynomial least squares fitting.
[0022] Step 4: Continuous wavelet transform is used to identify the variation characteristics of the sequence at different time scales. Subsequently, discrete wavelet transform is used to separate the signal features into trend, periodic, and random components. The decomposition formula for settlement displacement characteristics is as follows: ; : The ground settlement time series signal after preprocessing and filtering. The low-frequency approximation component obtained from wavelet decomposition represents the trend term of settlement. The periodic fluctuation component in the high-frequency detail components obtained by wavelet decomposition represents the periodic term. High-frequency noise and irregular fluctuations in the high-frequency detail components represent random terms.
[0023] For a given time series signal Its continuous wavelet transform The calculation formula is: ;
[0024] Variable explanation: The wavelet coefficients obtained after continuous wavelet transform reflect the characteristics of the signal at a specific scale and location. : The input raw ground settlement time series signal. Scale parameters The scaling of the wavelet function is controlled by the frequency of the signal. : Translation parameter, controls the translation of the wavelet function on the time axis, corresponding to the time position of the signal. Mother wavelet function. : Complex conjugate of the mother wavelet function. Energy normalization factor ensures that wavelet transforms at different scales have the same energy.
[0025] DWT is used for efficient multi-resolution reconstruction and signal decoupling. The calculation formula is: ; : Representing a moment The original time series signal refers to the time series InSAR ground subsidence monitoring values after preprocessing and SG filtering for noise reduction. : Represents the maximum number of decomposition levels in the discrete wavelet transform. : Represents the first The approximate component of the layer is extracted as a trend term displacement and input into the subsequent polynomial model for cell-by-cell modeling. : Represents the first The detail components of the layer, among which Corresponding patent logic: With The changes in detail components capture the local fluctuation characteristics of the signal at different high-frequency scales. : Represents all arrive The sum of the layer detail components.
[0026] Step 5: The obtained trend term displacement sequence is modeled using a multinomial model on a pixel-by-pixel basis. The periodic term displacement sequence is learned using ConvLSTM to study the periodic fluctuations of settlement displacement, while the random term is treated as a residual and discarded. Trend term multinomial model formula: ;
[0027] Variable explanation: For the predicted value of the trend term, For time steps, Let be the order of the polynomial. The parameters are fitted to the model. ConvLSTM replaces matrix multiplication in ordinary LSTM with convolution operations to capture spatiotemporal features. Its state update formula is: ; ; ; ; ;
[0028] Variable explanation: :time Input data. : The current and previous hidden states. : The current and previous cell states. These are the input gate, forget gate, and output gate, respectively. and : These are the convolutional kernel weights and bias terms learned during model training, respectively. : Represents a two-dimensional convolution operation. : Represents the Hadama product. : Sigmoid activation function.
[0029] Step 6: Evaluate the accuracy of the model component prediction results; the evaluation metrics include mean absolute error (MAE) and root mean square error (RMSE). , ;
[0030] In the formula, S is the predicted value. t These are measured values.
[0031] Step 7: Overlay the results of the sub-displacement predictions to obtain the cumulative displacement prediction value of ground settlement.
[0032] The beneficial effects of this invention are as follows: By systematically optimizing the data preprocessing, signal decomposition, component modeling, and result reconstruction in the ground subsidence prediction process, the accuracy, stability, and reliability of the prediction results are effectively improved. Specifically, addressing the data loss problem caused by local decoherence in InSAR monitoring, this invention uses the IDW spatial interpolation method to fill in missing values, constructing a spatially complete temporal data matrix. It also combines causal SG filtering to denoise the temporal data, preserving the original overall subsidence trend and local features while strictly adhering to temporal causality, avoiding the data crossing problem that may occur in traditional bidirectional filtering in prediction tasks, thereby improving the integrity of spatiotemporal data and the reliability of the prediction benchmark. Furthermore, by combining the feature recognition capability of Continuous Wavelet Transform (CWT) and the multi-resolution analysis capability of Discrete Wavelet Transform (DWT), the complex non-stationary subsidence signal is decomposed into trend, periodic, and random components, achieving effective separation of different signal components and reducing feature interference caused by mixed modeling of multiple driving factors, thus reducing the difficulty of model fitting. Simultaneously, for the feature differences of different components, multinomial models and ConvLSTM are used respectively. The model performs component-by-component predictions, which not only ensures the stability and computational efficiency of the trend term prediction, but also enhances the ability to express the complex spatiotemporal dynamic characteristics of the periodic term, thus balancing prediction accuracy and efficiency. In addition, in the result reconstruction stage, high-frequency random terms are treated as residuals and discarded, which effectively reduces the interference of observation errors and environmental noise on the prediction results, reduces the risk of model overfitting, and makes the final cumulative settlement displacement prediction results more stable, accurate, and more in line with the actual evolution law of ground settlement. Attached Figure Description
[0033] Figure 1 This is a flowchart of the present invention;
[0034] Figure 2 This is a schematic diagram of the ground settlement location in the embodiment;
[0035] Figure 3 This is one of the schematic diagrams of SG filtering and displacement decomposition in the embodiment;
[0036] Figure 4 This is one of the schematic diagrams of SG filtering and displacement decomposition in the embodiment;
[0037] Figure 5 This is one of the schematic diagrams of SG filtering and displacement decomposition in the embodiment;
[0038] Figure 6 This is one of the schematic diagrams of SG filtering and displacement decomposition in the embodiment;
[0039] Figure 7 A schematic diagram of the ConvLSTM model structure for an embodiment.
[0040] Figure 8 This is one of the schematic diagrams illustrating the selection of points for the prediction results in the embodiment.
[0041] Figure 9 This is the second schematic diagram of the prediction results selection in the example.
[0042] Figure 10 The third schematic diagram of the prediction results selection in the example;
[0043] Figure 11 The fourth illustration shows the selection of points for the prediction results in the example.
[0044] Figure 12 The fifth illustration shows the selection of points for the prediction results in the example.
[0045] Figure 13 This is the sixth schematic diagram of the prediction results selection in the example.
[0046] Figure 14 This is one of the schematic diagrams illustrating the model prediction accuracy verification results in the embodiment.
[0047] Figure 15 This is the second schematic diagram illustrating the verification results of the model prediction accuracy in the embodiment.
[0048] Figure 16 This is one of the schematic diagrams of the model prediction results in the example embodiment;
[0049] Figure 17 This is the second schematic diagram of the model prediction results in the example embodiment;
[0050] Figure 18 The third illustration shows the model prediction results of the example.
[0051] Figure 19 The fourth illustration shows the model prediction results of the example.
[0052] Figure 20 The fifth illustration shows the model prediction results of the example.
[0053] Figure 21 This is the sixth illustration of the model prediction results in the example.
[0054] Figure 22 The seventh illustration shows the model prediction results of the example.
[0055] Figure 23 This is the eighth schematic diagram of the model prediction results in the example embodiment;
[0056] Figure 24 This is the ninth illustration of the model prediction results in the example.
[0057] Figure 25This is the tenth illustration of the model prediction results in the example.
[0058] Figure 26 This is illustrative diagram of the model prediction results in the example embodiment;
[0059] Figure 27 The 12th illustration shows the model prediction results of the example.
[0060] Figure 28 This is thirteenth of the schematic diagrams illustrating the model prediction results in the example.
[0061] Figure 29 Fourteenth illustration of the model prediction results in the example;
[0062] Figure 30 This is diagram 15 of the model prediction results for an example. Detailed Implementation
[0063] The specific technical solutions of the present invention will be described with reference to the embodiments.
[0064] like Figure 1 As shown, the component prediction fusion method based on wavelet decomposition includes the following steps:
[0065] Step 1: Obtain time-series InSAR ground subsidence monitoring results; in this embodiment, the ground subsidence location is as follows: Figure 2 As shown.
[0066] Step 2: Pre-processing before ground settlement prediction; specifically including the following sub-steps:
[0067] Step 2.1: Completion of Missing Values in Experimental Data: For areas with localized incoherence in InSAR, the IDW interpolation method is used to interpolate the time-series InSAR monitoring data to obtain spatially complete time-series ground subsidence data. The calculation formula is as follows:
[0068] For a certain interpolation point with missing values Its estimated value The calculation formula is: ;
[0069] Among them, weight The calculation formula is: ;
[0070] Variable explanation: : The number of points surrounding the interpolation point Measured displacement values of known sample points. The total number of known sample points involved in the interpolation calculation. : Known sample points Interpolation point The spatial distance between them. The weighting index (usually set to 2) is used to control the degree of influence of distance on the weight.
[0071] Step 2.2: Data Normalization: The time-series InSAR monitoring results need to be normalized to eliminate the influence of different units between data and prevent large data differences from affecting prediction accuracy. The calculation formula is as follows: ; Normalized data values typically range from 100 to 1000. or between. : Original time-series InSAR settlement displacement data. : The minimum displacement value in this dataset. : The maximum displacement value in this dataset.
[0072] Step 3: For the acquired time-series monitoring results, causal SG filtering (local polynomial fitting) is used to retain the overall trend and local characteristics of the original settlement displacement while removing signal noise. The calculation formula is:
[0073] Let the time series be Smoothed value after causal SG filtering for: ;
[0074] Variable explanation: :time Filtered sedimentation value. :time and previous historical subsidence observations (reflecting causality, only taking values from the past). (points). : Size of the filter window (i.e., using past data) (Historical data points). : Filtering coefficients obtained by local polynomial least squares fitting.
[0075] Step 4: Continuous wavelet transforms are used to identify the variation characteristics of the sequence at different time scales. Then, discrete wavelets are used to separate the signal features into trend, periodic, and random components. The decomposition formula for the settlement displacement characteristics is: ; : The ground settlement time series signal after preprocessing and filtering. The low-frequency approximation component obtained from wavelet decomposition represents the trend term of settlement. The periodic fluctuation component in the high-frequency detail component obtained by wavelet decomposition represents the periodic term. High-frequency noise and irregular fluctuations in the high-frequency detail components represent random terms (residuals).
[0076] For a given time series signal Its continuous wavelet transform The calculation formula is: ;
[0077] Variable explanation: The wavelet coefficients obtained after continuous wavelet transform reflect the characteristics of the signal at a specific scale and location. : The input raw ground settlement time series signal. Scale parameter. The scaling of the wavelet function corresponds to the frequency of the signal. The larger the value, the lower the frequency characteristic. The smaller the value, the higher the frequency of the feature. Translation parameter: Controls the translation of the wavelet function on the time axis, corresponding to the time position of the signal. Mother wavelet, such as the db family of wavelets. : Complex conjugate of the mother wavelet function. Energy normalization factor ensures that wavelet transforms at different scales have the same energy.
[0078] DWT is used for efficient multi-resolution reconstruction and signal decoupling. The calculation formula is: ; : Representing a moment The original time-series signal. In the present invention, it refers to the time-series InSAR ground subsidence monitoring values after preprocessing and SG filtering for noise reduction. : Represents the maximum number of decomposition levels (scale) of the discrete wavelet transform. This parameter determines the depth to which the signal is stripped away. : Represents the first The layer's approximation component. Corresponding patent logic: It contains the lowest frequency and most gently changing part of the signal, reflecting the long-term evolution of ground subsidence. In the current invention, this term is extracted as a trend displacement and input into the subsequent polynomial model for pixel-by-pixel modeling. : Represents the first The layer's detail component, where Corresponding patent logic: With The changes in detail components capture the local fluctuation characteristics of the signal at different high-frequency scales. : Represents all arrive The sum of the layer detail components.
[0079] SG filtering and displacement decomposition are as follows Figures 3 to 6 As shown.
[0080] Step 5: The obtained trend term displacement sequence is modeled using a multinomial model on a pixel-by-pixel basis, and the periodic term displacement sequence is modeled using... Figure 7 The ConvLSTM shown learns the periodic fluctuations of settlement displacement, while the random term is treated as a discarded residual. The formula for the trend term polynomial model is: ;
[0081] Variable explanation: For the predicted value of the trend term, For time steps, Let be the order of the polynomial. The parameters are fitted to the model. ConvLSTM replaces matrix multiplication in ordinary LSTM with convolution operations to capture spatiotemporal features. Its state update formula is: ; ; ; ; .
[0082] Variable explanation: :time The input data (i.e., the separated periodic displacement space matrix). : The hidden state (spatial feature map) of the current and previous time steps. : The current and previous cell states. These are the input gate, forget gate, and output gate, respectively. and : These are the convolutional kernel weights and bias terms learned during model training, respectively. : Represents a two-dimensional convolution operator. : Represents the Hadamard product (i.e., the product of corresponding matrix elements). : Sigmoid activation function.
[0083] Prediction results selection points as follows Figures 8 to 13 As shown.
[0084] Step 6: Evaluate the accuracy of the model component prediction results; the evaluation metrics include mean absolute error (MAE) and root mean square error (RMSE). , .
[0085] In the formula, S is the predicted value.t These are measured values.
[0086] Step 7: Superimpose the results of the partial displacement predictions to obtain the cumulative predicted value of ground settlement displacement. The model prediction accuracy verification results are as follows: Figure 14 and Figure 15 As shown in the diagram. A schematic diagram of the model prediction results is shown below. Figures 16 to 30 .
Claims
1. A component prediction and fusion method based on wavelet decomposition, characterized in that, Includes the following steps: Step 1: Obtain time-series InSAR ground subsidence monitoring results; Step 2: Pre-treatment before ground settlement prediction; Step 3: For the acquired time-series monitoring results, causal SG filtering is used to retain the overall trend and local characteristics of the original settlement displacement while removing signal noise; Step 4: Use continuous wavelet transform to identify the variation characteristics of the sequence at different time scales, and then use discrete wavelet to separate the signal features into trend, periodic and random terms; Step 5: The obtained trend term displacement sequence is modeled using a multinomial model on a pixel-by-pixel basis, the periodic term displacement sequence is learned using ConvLSTM to learn the periodic fluctuations of settlement displacement, and the random term is treated as a residual and discarded. Step 6: Evaluate the accuracy of the model component prediction results; the evaluation metrics include mean absolute error (MAE) and root mean square error (RMSE). Step 7: Overlay the results of the sub-item displacement predictions to obtain the cumulative displacement prediction value of ground settlement.
2. The wavelet decomposition-based component prediction and fusion method according to claim 1, characterized in that, Step 2 includes the following sub-steps: Step 2.1: Completion of missing values in experimental data: For areas with localized incoherence in InSAR, the IDW interpolation method is used to interpolate the time-series InSAR monitoring data to obtain spatially complete time-series ground subsidence monitoring data; the calculation formula is: For a certain interpolation point with missing values Its estimated value The calculation formula is: ； Among them, weight The calculation formula is: ； Variable explanation: : The number of points surrounding the interpolation point Measured displacement values of a known sample point; The total number of known sample points involved in the interpolation calculation; : Known sample points Interpolation point Spatial distance between them; Weighting index: used to control the degree of influence of distance on weight; Step 2.2: Data Normalization: Normalize the time-series InSAR monitoring results data. The calculation formula is as follows: ； Normalized data values typically range from 100 to 1000. or between; Raw time-series InSAR settlement displacement data; The minimum displacement value in this dataset; : The maximum displacement value in this dataset.
3. The wavelet decomposition-based component prediction and fusion method according to claim 1, characterized in that, The calculation formula for step 3 is: Let the time series be Smoothed value after causal SG filtering for: ； Variable explanation: :time Filtered sedimentation value; :time and previous historical settlement observations; Size of the filter window; : Filtering coefficients obtained by local polynomial least squares fitting.
4. The wavelet decomposition-based component prediction and fusion method according to claim 1, characterized in that, The decomposition formula for the settlement displacement characteristics in step 4 is: ； : The ground settlement time series signal after preprocessing and filtering; The low-frequency approximate component obtained by wavelet decomposition represents the trend term of settlement. The periodic fluctuations in the high-frequency detail components obtained from wavelet decomposition represent the periodic terms. High-frequency noise and irregular fluctuations in the high-frequency detail components represent random terms; For a given time series signal Its continuous wavelet transform The calculation formula is: ； Variable explanation: The wavelet coefficients obtained after continuous wavelet transform reflect the characteristics of the signal at a specific scale and location. : The input raw ground settlement time series signal; Scale parameters The scaling of the wavelet function is controlled, corresponding to the frequency of the signal; Translation parameter: controls the translation of the wavelet function on the time axis, corresponding to the time position of the signal; Mother wavelet function; The complex conjugate of the mother wavelet function; Energy normalization factor ensures that wavelet transforms at different scales have the same energy; DWT is used for efficient multi-resolution reconstruction and signal decoupling. The calculation formula is: ； : Representing a moment The original time series signal refers to the time series InSAR ground subsidence monitoring values after preprocessing and SG filtering for noise reduction; : Represents the maximum number of decomposition levels in the discrete wavelet transform; : Represents the first The approximate component of the layer is extracted as the trend term displacement and input into the subsequent polynomial model for cell-by-cell modeling. : Represents the first The detail components of the layer, among which Corresponding patent logic: With The changes in detail components capture the local fluctuation characteristics of the signal at different high-frequency scales; : Represents all arrive The sum of the layer detail components.
5. The wavelet decomposition-based component prediction and fusion method according to claim 1, characterized in that, The formula for the trend term polynomial model in step 5 is: ； Variable explanation: For the predicted value of the trend term, For time steps, Let be the order of the polynomial. The parameters are fitted to the model; ConvLSTM replaces the matrix multiplication of ordinary LSTM with convolution operations to capture spatiotemporal features; Its state update formula is: ； ； ； ； ； Variable explanation: :time Input data; The current and previous hidden states; The current and previous cell states; These are the input gate, forget gate, and output gate, respectively. and These are the convolutional kernel weights and bias terms learned during model training, respectively. : Represents a two-dimensional convolution operation; : Represents the Hadama product; : Sigmoid activation function.
6. The wavelet decomposition-based component prediction and fusion method according to claim 1, characterized in that, The formulas for the mean absolute error (MAE) and root mean square error (RMSE) in step 6 are as follows: ； ； In the formula, S is the predicted value. t These are measured values.