Daily runoff prediction method based on adaptive graph structure and signal decomposition

Abstract

The invention discloses a daily runoff prediction method based on an adaptive graph structure and signal decomposition, and belongs to the field of daily runoff prediction, and the method comprises the following steps: carrying out the logarithmic transformation of a runoff, rainfall and temperature time sequence of a target drainage basin, and obtaining a transformed time sequence; performing step-by-step complete ensemble empirical mode decomposition on the transformed time sequence to decompose the transformed time sequence into a plurality of intrinsic mode functions and residual terms; constructing an adaptive gating convolutional network based on the adaptive graph structure and a spatial perception gating circulation unit; respectively inputting the intrinsic mode functions and the residual terms obtained after decomposition into the adaptive gated convolutional network to obtain prediction results of the components; and superposing the prediction results of the components, and reconstructing a future runoff prediction value of the target drainage basin.

Description

Technical Field

[0001] This invention belongs to the field of daily runoff prediction technology, and particularly relates to a daily runoff prediction method based on adaptive graph structure and signal decomposition. Background Technology

[0002] Traditional runoff forecasting methods primarily rely on empirical formulas, statistical models, or physical process models. While empirical formulas and statistical models can capture the relationship between runoff and related factors to some extent, they often struggle to effectively handle complex non-stationary and nonlinear characteristics, resulting in limited forecast accuracy. Although physical process models can simulate the runoff formation process from a mechanistic perspective, they require a large number of parameters and detailed watershed characteristic data, and their high model complexity significantly limits their applicability to watersheds with scarce or insufficient data.

[0003] With the development of deep learning technology, data-driven runoff prediction methods have gradually attracted attention. In particular, graph neural networks (GNNs) can model the spatial dependencies between hydrological stations through graph structures, demonstrating certain advantages in multi-station prediction. However, existing GNN models, when applied to runoff prediction, mostly rely on predefined topological spatial relationships, such as river network connectivity or geographical proximity, to construct the graph structure. This static graph construction method limits the model's generalization ability to some extent, especially in watersheds with unclear spatial relationships or sparse monitoring stations, where prediction performance tends to degrade.

[0004] Furthermore, hydrological time series data generally exhibit non-stationary characteristics, including seasonal fluctuations, long-term trends, and extreme events. Directly modeling the original series can easily lead to the model learning incorrect patterns, affecting the accuracy of predictions. Some studies have attempted to mitigate non-stationarity using signal decomposition methods, but how to avoid introducing future information (i.e., data leakage) during the decomposition process and effectively integrate it with deep learning models remains a pressing issue. In addition, hydrological data often suffers from distribution skewness and extreme values; without appropriate data transformation, the model training process may experience numerical instability.

[0005] In summary, existing runoff forecasting technologies still fall short in handling the complexity, non-stationarity, and nonlinearity of hydrological systems, making it difficult to meet the demands for high-precision runoff forecasting. Therefore, a new technical solution is urgently needed that can more effectively capture the spatial dependencies between hydrological stations and combine data transformation and signal decomposition methods to improve the accuracy and generalization ability of runoff forecasting while ensuring data leakage is avoided. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a daily runoff prediction method based on adaptive graph structure and signal decomposition, thereby resolving the issues present in the prior art.

[0007] To achieve the above objectives, this invention provides a daily runoff prediction method based on adaptive graph structure and signal decomposition, comprising:

[0008] Logarithmic transformations were performed on the time series of runoff, precipitation, and temperature in the target watershed to obtain the transformed time series.

[0009] The transformed time series is subjected to stepwise complete set empirical mode decomposition, which decomposes it into several intrinsic mode functions and residual terms;

[0010] An adaptive gated convolutional network is constructed based on an adaptive graph structure and a spatially aware gated recurrent unit.

[0011] The intrinsic mode functions and residual terms obtained from the decomposition are input into the adaptive gated convolutional network to obtain the prediction results of each component;

[0012] The prediction results of each component are superimposed to reconstruct the future runoff prediction value of the target watershed.

[0013] Optionally, the process of performing a logarithmic transformation on the time series of runoff, precipitation, and temperature in the target watershed includes:

[0014] The natural logarithmic transformation was used to process the runoff and precipitation sequences to obtain the processed runoff and precipitation sequences;

[0015] By adding a translation constant to the temperature time series with negative values ​​and then performing a natural logarithmic transformation, the processed temperature series is obtained.

[0016] The transformed time series is obtained based on the processed runoff and precipitation sequences and temperature sequences.

[0017] Optionally, the process of performing stepwise complete ensemble empirical mode decomposition on the transformed time series includes:

[0018] The transformed time series is subjected to stepwise complete set empirical mode decomposition in the logarithmic domain;

[0019] At each prediction time, only historical samples prior to the current time are used for decomposition to generate several intrinsic mode functions and residual terms corresponding to the current time.

[0020] Optionally, the adaptive gated convolutional network includes a process for dynamically generating an adjacency matrix and a process for performing spatiotemporal feature extraction.

[0021] Optionally, the process of dynamically generating the adjacency matrix includes:

[0022] Construct two trainable node embedding matrices, and calculate the association weights between each node pair based on the interactions between the node embeddings;

[0023] A nonlinear activation function is applied to the association weights, and a normalization operation is performed in the row direction to generate a directed and dynamically updated adjacency matrix.

[0024] Optionally, the spatiotemporal feature extraction process includes:

[0025] Graph convolution is performed using dynamically generated adjacency matrices and component feature matrices to model spatial dependencies;

[0026] Based on the aforementioned spatial dependency, a gated loop unit is used to characterize the temporal dynamics, thereby enabling the extraction of spatiotemporal features of different components.

[0027] Optionally, the process of inputting the decomposed intrinsic mode functions and residual terms into the adaptive gated convolutional network includes:

[0028] The intrinsic mode functions and residual terms of runoff, precipitation and temperature time series at the same order are combined to form the corresponding component feature matrices;

[0029] Each component feature matrix is ​​assigned an independent adaptive gated convolutional network to form several sub-models;

[0030] In each sub-model, the parameters of the sub-model are set differently according to the scale characteristics of the corresponding component, and optimized by hyperparameter search methods such as cross-validation to obtain the optimal parameter combination that adapts to the characteristics of the current component.

[0031] Optionally, the step of superimposing the prediction results of the components includes:

[0032] The prediction results output by each sub-model are weighted and fused to obtain the runoff prediction results in the logarithmic domain;

[0033] The prediction results in the logarithmic domain are subjected to an antilogarithmic transformation to obtain the future runoff prediction values ​​for the target watershed.

[0034] Compared with the prior art, the present invention has the following advantages and technical effects:

[0035] This invention effectively addresses the problems of non-stationarity, difficulty in accurately depicting complex spatial dependencies, and unstable prediction results in hydrological time series modeling. By introducing an adaptive graph structure, the constructed Adaptive Gated Convolutional Network (ADGGCN) can dynamically capture the potential spatial dependencies between hydrological stations without relying on predefined river network connectivity or geographical proximity. Simultaneously, this invention introduces logarithmic transformation and stepwise CEEMDAN decomposition as preprocessing steps before modeling, effectively mitigating the non-stationarity and extreme value effects of time series data, and improving the stability and accuracy of the decomposition process. Therefore, the Log-CEEMDAN-ADGGCN model proposed in this invention significantly improves the accuracy and robustness of runoff prediction, maintaining high applicability and reliability under different watershed conditions. Attached Figure Description

[0036] 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:

[0037] Figure 1 This is a flowchart of the daily runoff prediction method based on adaptive graph structure and signal decomposition according to an embodiment of the present invention;

[0038] Figure 2 This is a diagram of the adaptive gated convolutional network structure according to an embodiment of the present invention;

[0039] Figure 3 This is a comparison chart of the results of an embodiment of the present invention. Detailed Implementation

[0040] 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.

[0041] 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.

[0042] Example 1.

[0043] like Figure 1As shown, this embodiment provides a daily runoff prediction method based on adaptive graph structure and signal decomposition (Log-CEEMDAN-ADGGCN model), including the following steps: performing logarithmic transformation on the runoff, precipitation, and temperature time series of the target watershed to obtain the transformed time series; in the logarithmic domain, using complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), decomposing the transformed time series into several intrinsic mode functions (IMFs) and residual terms (R); constructing an adaptive gated convolutional network based on the adaptive graph structure and spatially aware gated recurrent units, such as... Figure 2 As shown, the decomposed components of each order are input into the corresponding adaptive gated convolutional network sub-models to obtain the prediction results of each component. In each sub-model, the parameters can be set differently according to the scale characteristics of the components and optimized by methods such as cross-validation. The prediction results output by each sub-model are weighted and fused, and after anti-logarithmic transformation, the future runoff prediction value of the target watershed is obtained.

[0044] This method effectively mitigates the strong nonstationarity and extreme value effects in hydrological time series through logarithmic transformation and stepwise CEEMDAN decomposition, ensuring the stability of the decomposition process and the separability of the components.

[0045] First, an Adaptive Gated Convolutional Network (ADGGCN) is proposed for the modeling stage. Unlike existing graph neural network (GNN) models that rely on static topology, this network dynamically generates an adjacency matrix through node embedding, thereby automatically capturing the spatial dependencies between hydrological stations without relying on predefined river network connectivity or geographical distance. The learned adaptive graph structure can reflect the real hydrological relationships between watersheds, enhancing the physical interpretability and cross-watershed generalization ability of the model, making this method applicable to watersheds lacking clear topological structures or with uncertain spatial relationships.

[0046] As a specific implementation method of this embodiment, it specifically includes: logarithmic transformation:

[0047] For time series without negative values ​​(such as runoff and precipitation), the natural logarithmic transformation is used, defined as follows:

[0048] ;

[0049] in, Represents the original time series. This represents the sequence after logarithmic transformation.

[0050] For time series that may contain negative or near-zero values ​​(such as temperature), first apply a translation constant greater than zero to the entire series. Then perform the natural logarithmic transformation, defined as follows:

[0051] ;

[0052] Logarithmic transformation can stabilize the variance of a time series, reduce the impact of extreme values, and at the same time ensure the rationality of the calculation and numerical stability.

[0053] Stepwise CEEMDAN: at each prediction time... Only historical samples prior to that moment are used. Decompose the data to obtain a set of values ​​related to time. The corresponding intrinsic mode functions (IMFs) and residual terms. This stepwise decomposition method avoids future information from entering the decomposition process, thus effectively eliminating the risk of data leakage.

[0054] Its formal representation is as follows:

[0055] ;

[0056] in, Indicates the time of prediction The historical sequence used; This indicates the first [number] obtained based on this historical sequence. One intrinsic mode function; This represents the residual term.

[0057] CEEMDAN effectively avoids model mixing and achieves lower reconstruction errors. This feature allows this invention to decompose hydrological time series data into multiple IMFs using CEEMDAN, each of which can be modeled independently. The predicted components are then summed to reconstruct the final runoff signal, thereby achieving finer temporal dynamic resolution and improving overall prediction accuracy.

[0058] Adaptive adjacency learning: One of the core challenges of applying graph neural networks to hydrological prediction lies in how to accurately and flexibly define the spatial dependencies between hydrological stations. Existing methods mostly employ static graph structures, whose watershed-specific and time-invariant characteristics limit the model's ability to generalize across regions or cope with dynamically evolving hydrological processes.

[0059] This invention incorporates a data-driven adaptive adjacency learning mechanism into its model. This mechanism dynamically infers graph structure from data through trainable node embedding vectors, enabling the model to automatically capture potential dependencies, dynamic evolutionary features, and asymmetric inter-site connections that are difficult to reveal under static configurations, significantly enhancing the model's adaptability and physical interpretability.

[0060] As a specific implementation of this embodiment, the present invention introduces two learnable node embedding matrices. The adjacency matrix is ​​calculated through their interactions. The formula for calculating the adaptive adjacency matrix is:

[0061] ;

[0062] in, For the number of hydrological stations, For the embedding dimension, ReLU activation ensures non-negative weights, while row-normalized softmax operation ensures that the outgoing edge weights of each node satisfy the probability distribution form, thereby generating a directed and dynamically updatable adjacency matrix to characterize the potential spatial dependencies between hydrological stations.

[0063] Adaptive Gated Convolutional Network (ADGGCN): As the core modeling network of this invention, ADGGCN combines adaptive graph structure with graph convolution (GCN) and gated recurrent units (GRU) for joint modeling of spatial dependencies and temporal dynamics of time series. Its basic idea is to introduce an adaptive adjacency matrix into the gating mechanism of the GRU. The graph convolution operation allows the update of the hidden state to not only rely on historical sequence information, but also dynamically aggregate feature information from adjacent hydrological stations. The specific formula execution process is as follows:

[0064] At time step Input feature vector Hidden state from the previous moment Graph convolution and adaptive adjacency matrix Merge to obtain the reset gate and the update gate :

[0065] ;

[0066] in, This is the Sigmoid activation function.

[0067] Input Historical state after resetting the door adjustment The candidate hidden states are obtained by processing the data through a second graph convolutional layer. :

[0068] ;

[0069] in, This represents element-wise multiplication. It is the hyperbolic tangent activation function.

[0070] Using the update gate The new hidden state is obtained by weighted fusion of the previous hidden state and the candidate hidden state. :

[0071] ;

[0072] After obtaining the final hidden state Subsequently, this invention employs a linear regressor as the output layer to map the hidden representation to the target runoff value. Its calculation form is as follows:

[0073] ;

[0074] in, and These are the trainable weight matrix and the bias term, respectively. Indicates at time step For the first The predicted value of each intrinsic mode function (IMF) or residual term.

[0075] Sub-model construction and optimization for IMF prediction: After decomposing the logarithmic sequence into several IMF components and residual terms using CEEMDAN, this invention constructs an independent ADGGCN sub-model for each component. Specifically, for the first... The IMF of the order of runoff, precipitation, and temperature is concatenated into an input feature matrix and fed into the corresponding ADGGCN sub-model for spatiotemporal modeling and prediction. To ensure the prediction accuracy of components at different scales, this invention differentiates the hyperparameter configurations of each sub-model and optimizes them through methods such as cross-validation to obtain the optimal parameter combination that adapts to the characteristics of the component.

[0076] Predictive fusion and inverse transformation: The prediction results of all sub-models are weighted and fused according to the variance contribution rate of each IMF, and then added to the residual prediction results to obtain the predicted value in the logarithmic domain.

[0077] ;

[0078] Finally, the target watershed at time step is obtained through anti-logarithmic transformation. Runoff forecast values:

[0079] ;

[0080] The Log-CEEMDAN-ADGGCN model constructed in this embodiment can capture spatiotemporal dependencies by using multi-variable inputs such as precipitation, runoff, and temperature from multiple stations in a single-step runoff prediction process without requiring manual definition of the river network topology. Compared with traditional static graph and single LSTM models, it improves the prediction accuracy of flood peak and baseflow period while maintaining cross-basin transferability.

[0081] As another specific implementation of this embodiment, the following steps are included:

[0082] Step 1: Collect time series data on runoff, precipitation, and temperature from 14 hydrological stations in the Poyang Lake basin, spanning 4383 days. Divide the data into training, validation, and test sets in a 6:2:2 ratio.

[0083] Step 2: Perform a logarithmic transformation on the original time series to stabilize the variance and reduce the impact of extreme values. For runoff and precipitation series without negative values, a natural logarithmic transformation is directly applied:

[0084] ;

[0085] For temperature series containing negative or near-zero values, first add a positive translation constant of 4 (the lowest temperature is -3 degrees Celsius), then perform a logarithmic transformation:

[0086] ;

[0087] Step 3: In the logarithmic domain, use CEEMDAN to decompose the time series of each variable to obtain... One IMF and one residual term:

[0088] ;

[0089] in, Indicates the time of prediction The historical sequence used; This indicates the first [number] obtained based on this historical sequence. One intrinsic mode function; This represents the residual term.

[0090] Step 4: Concatenate the obtained runoff IMF, precipitation IMF, and temperature IMF of the same order along the feature dimensions to form the first... The input feature matrix of the first-order components is then used to generate training samples using a sliding window approach: each sample uses a feature sequence of 12 consecutive days as input to predict the runoff value for the next day.

[0091] Step 5, based on node embedding vectors Dynamically calculate the adjacency matrix:

[0092] ;

[0093] in, For the number of hydrological stations, For the embedding dimension. ReLU activation ensures non-negative weights.

[0094] Step 6: In each IMF sub-model, ADGGCN is used to perform spatiotemporal modeling of the stitched features. The core update formula is as follows:

[0095] At time step Input feature vector Hidden state from the previous moment Graph convolution and adaptive adjacency matrix Merge to obtain the reset gate and the update gate :

[0096] ;

[0097] in, This is the Sigmoid activation function.

[0098] Input Historical state after resetting the door adjustment The candidate hidden states are obtained by processing the data through a second graph convolutional layer. :

[0099] ;

[0100] in, This represents element-wise multiplication. It is the hyperbolic tangent activation function.

[0101] Using the update gate The new hidden state is obtained by weighted fusion of the previous hidden state and the candidate hidden state. :

[0102] ;

[0103] After obtaining the final hidden state Then, a linear regressor is used as the output layer to map the hidden representation to the target runoff value. Its calculation form is as follows:

[0104] ;

[0105] in, and These are the trainable weight matrix and the bias term, respectively. Indicates at time step For the first The predicted value of each intrinsic mode function (IMF) or residual term.

[0106] Step 7: For each IMF sub-model, set different hyperparameters such as learning rate and hidden layer dimension according to the component scale characteristics, and use 5-fold cross-validation for tuning. Each model is trained independently 10 times, and the average value of the test set metrics is taken as the final performance result to reduce the uncertainty caused by random initialization.

[0107] Step 8, Prediction Fusion and Inverse Transformation: The prediction results of all sub-models are weighted and fused according to the variance contribution rate of each IMF, and then added to the residual prediction results to obtain the predicted value in the logarithmic domain.

[0108] ;

[0109] Finally, the target watershed at time step is obtained through anti-logarithmic transformation. Runoff forecast values:

[0110] ;

[0111] Step 9: To verify the effectiveness of the Log-CEEMDAN-ADGGCN method, the following comparative models were constructed under the same dataset and training conditions: Long Short-Term Memory Network (LSTM); Adaptive Graph Gated Convolutional Network (ADGGCN, without CEEMDAN decomposition); CEEMDAN-ADGGRU (decomposition only, without logarithmic transformation).

[0112] Step 10: Using Nash efficiency coefficient (NSE) and root mean square error (RMSE) as the main evaluation indicators, the performance of the proposed Log-CEEMDAN-ADGGCN method is compared with three comparative models (LSTM, ADGGCN, and CEEMDAN-ADGGCN). The comparison results are as follows: Figure 3 As shown, the Log-CEEMDAN-ADGGCN model achieves the highest average value and minimum fluctuation in the NSE metric, while also achieving the lowest error in the RMSE metric, significantly outperforming other models. This demonstrates the necessity and superiority of the combined use of logarithmic transformation and CEEMDAN decomposition, as well as adaptive graph modeling.

[0113] 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 method for daily runoff prediction based on adaptive graph structure and signal decomposition, characterized in that, The method comprises the following steps: logarithmic transformation is performed on runoff, precipitation and temperature time series of a target basin to obtain transformed time series; the transformed time series is decomposed into a plurality of intrinsic mode functions and residual terms by stepwise complete ensemble empirical mode decomposition; an adaptive gated convolutional network is constructed based on an adaptive graph structure and a spatial perception gated recurrent unit; the decomposed intrinsic mode functions and residual terms are respectively input into the adaptive gated convolutional network to obtain prediction results of each component; the prediction results of each component are superimposed to reconstruct a future runoff prediction value of the target basin.

2. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 1, characterized in that, The process of logarithmic transformation on runoff, precipitation and temperature time series of a target basin comprises: natural logarithmic transformation is performed on runoff and precipitation sequences to obtain processed runoff and precipitation sequences; a temperature time series is logarithmically transformed after a constant greater than zero is added to the whole temperature time series to obtain a processed temperature sequence; transformed time series is obtained based on the processed runoff and precipitation sequences and the temperature sequence.

3. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 1, characterized in that, The process of stepwise complete ensemble empirical mode decomposition on the transformed time series comprises: stepwise complete ensemble empirical mode decomposition is performed on the transformed time series in a logarithmic domain; at each prediction time, only historical samples before the current time are used for decomposition to generate a plurality of intrinsic mode functions and residual terms corresponding to the current time.

4. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 1, characterized in that, The adaptive gated convolutional network comprises a process for dynamically generating an adjacency matrix and a process for performing spatiotemporal feature extraction.

5. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 4, characterized in that, The process for dynamically generating an adjacency matrix comprises: two trainable node embedding matrices are constructed, and the correlation weight between each pair of nodes is calculated based on the interaction between the node embeddings; a nonlinear activation function is applied to the correlation weight, and a normalization operation is performed in the row direction to generate a directed and dynamically updated adjacency matrix.

6. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 4, characterized in that, The process for spatiotemporal feature extraction comprises: graph convolution is performed using the dynamically generated adjacency matrix and the component feature matrix to model spatial dependency; based on the spatial dependency, the time dynamics of different components are described through a gated recurrent unit to realize spatiotemporal feature extraction.

7. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 1, characterized in that, The process of inputting the decomposed intrinsic mode functions and residual terms into the adaptive gated convolutional network comprises: the intrinsic mode functions and residual terms of runoff, precipitation and temperature time series at the same order are combined to form corresponding component feature matrices; an independent adaptive gated convolutional network is assigned to each component feature matrix to form a plurality of sub-models; in each sub-model, the parameters of the sub-model are set differently according to the scale characteristics of the corresponding component, and are optimized through hyperparameter search methods such as cross-validation to obtain an optimal parameter combination suitable for the current component characteristics.

8. The adaptive graph structure and signal decomposition based daily runoff prediction method according to claim 1, characterized in that, The step of superimposing the prediction results of each component comprises: the prediction results output by each sub-model are weighted and fused to obtain runoff prediction results in a logarithmic domain; an inverse logarithmic transformation is performed on the prediction results in the logarithmic domain to obtain a future runoff prediction value of the target basin.

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