Data missing reservoir water volume prediction method based on multi-source data time sequence fusion and interpretability

Abstract

The invention discloses a multi-source data time sequence fusion and interpretability-based data missing reservoir water volume prediction method, which comprises the following steps of: 1, through reverse derivation of reservoir output flow and evaporation capacity of a reservoir, obtaining reduced water volume which only considers reservoir input flow and ignores loss water volume such as reservoir output flow, and taking the reduced water volume as an equivalent substitution variable of reservoir input runoff volume; 2, collecting meteorological data, and forming a data set with the reduced water volume; 3, building a time sequence fusion converter model, and meanwhile, designing an automatic parameter optimization module, so that the time investment of a parameter adjustment link is reduced, and the subjectivity and limitation of manual parameter adjustment are avoided; and 4, water volume prediction and variable importance analysis. According to the method, the index of the reduced water volume is used for replacing the reservoir flow, meanwhile, the weather forecast which is known data in the future is fully used for construction and prediction of the prediction model, the problem that part of reservoirs lack the reservoir flow is solved, high prediction precision is guaranteed, and meanwhile the defect of'black box 'of a traditional model is overcome.

Description

A Reservoir Water Quantity Prediction Method Based on Multi-Source Data Time Series Fusion and Interpretability Technical Field

[0001] This invention relates to the field of water conservancy engineering prediction, specifically a method for predicting water volume in reservoirs with missing data based on a multi-source data temporal fusion transformer (TFT) model. Background Technology

[0002] Reservoir inflow is a core foundational data point for optimized reservoir operation, flood control and disaster reduction, and rational allocation of water resources. Accurate inflow forecasting directly impacts the safety and economic efficiency of reservoir operation. Accurate inflow forecasting provides a scientific basis for flood control operations during the flood season and water supply security during the dry season, effectively reducing water waste and disaster risks, and is a key support for the intelligent operation of water conservancy projects.

[0003] Traditional hydrological forecasting methods can be broadly categorized into two types: hydraulic mechanism models based on hydrological principles and data-driven models based on big data. Mechanism models focus on hydrophysical processes, constructing a predictive framework by quantifying intrinsic mechanisms and simulating processes such as evapotranspiration, runoff generation, and confluence to predict runoff. However, the complexity of hydrological systems leads to unavoidable uncertainties, and model performance is highly dependent on parameter calibration and requires high data integrity, thus limiting the applicability of these mechanistic models. Data-driven models, on the other hand, do not require explicit understanding of hydrophysical mechanisms; instead, they rely on massive amounts of historical data to mine the correlation between features and target variables.

[0004] However, many reservoirs built in the early stages or located in remote areas share the common problem of missing or incomplete inflow monitoring data. Traditional hydrological forecasting methods rely heavily on complete historical runoff sequences. When data is missing, mechanistic models cannot be calibrated, and data-driven models are difficult to construct due to the lack of predictive targets. Furthermore, they generally suffer from two major limitations: the inability to utilize known future meteorological information and the "black box" nature of the models.

[0005] Existing studies mostly obtain inflow data indirectly through methods such as hydrological model inversion and analogy with similar watersheds. However, these methods often rely on the calibration of complex hydrophysical process parameters or are limited by differences in the underlying surface of the watershed. Their practicality and accuracy are difficult to meet the daily scheduling needs of reservoirs. Summary of the Invention

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a reservoir water volume prediction method applicable to scenarios where inflow runoff data is missing. It aims to integrate future meteorological data under the condition of missing inflow runoff data to achieve high-precision and interpretable reservoir water volume prediction.

[0007] To achieve the aforementioned objectives, this invention employs the following technical solution: The method for predicting water volume in a reservoir with missing data based on multi-source data time-series fusion is characterized by the following steps: Step 1: Collecting operational monitoring data for T consecutive historical time steps of the reservoir and calculating the restored water volume for those T consecutive historical time steps; Step 2: Obtaining the reservoir's basin meteorological data and upstream water replenishment data, marking them with time features, and then constructing an input feature set together with the restored water volume. ,in, h represents historical data for T consecutive historical time steps. t The historical data of the reservoir at the t-th historical time step includes: basin meteorological data, restored water volume, upstream water replenishment data, and temporal characteristics; For the future data of the reservoir over J consecutive future time steps, f j For the future data of the reservoir at the j-th future time step, including: watershed meteorological data and temporal characteristics; Step 3: Build a time-series fusion transformer model, including: variable selection network, LSTM encoder, LSTM decoder, gated residual network, multi-head self-attention layer, and output layer, and The data were processed to obtain the predicted reduction water volume at J time steps. Step 4: Based on the predicted value of reduced water volume The MAE loss function is constructed using the restored water volume at historical time steps and used to train the time-series fusion transformer model, thereby obtaining a trained time-series fusion transformer model to predict future restored water volume. Simultaneously, the weight coefficient sequence of historical data generated by the network is selected as the dependent variable. and the weighted coefficient sequence of future data and the context vector generated by the gated residual network Analysis of historical water volume, watershed meteorological data, and temporal characteristics The contribution of water volume, watershed meteorological data and temporal characteristics are used to generate importance distribution maps.

[0008] The method for predicting water volume in a reservoir with missing data based on multi-source data time-series fusion, as described in this invention, is characterized by the following steps in step 1: Step 1.1: Based on the water level data of the reservoir over T consecutive historical time steps and its corresponding water surface area data, the functional relationship between the water level and the water surface area of ​​the reservoir is fitted using equation (1): (1) In equation (1): A t Z represents the water surface area of ​​the reservoir at the t-th historical time step. t Let be the water level of the reservoir at the t-th historical time step; a and b are two coefficients of the functional relationship between the reservoir water level and the water surface area, and c is the constant term of the functional relationship between the reservoir water level and the water surface area; Step 1.2: Use equation (2) to obtain the evaporation E of the reservoir at the t-th historical time step.t : (2) In equation (2): K is the evaporation coefficient of the area where the reservoir is located; e t Let be the evaporation amount of the reservoir at the t-th historical time step; Step 1.3: Based on the water level data of the reservoir for T consecutive historical time steps and the corresponding reservoir capacity data, use equation (3) to fit the functional relationship between the water level and the reservoir capacity: (3) In equation (3): V t Let be the reservoir capacity at the t-th historical time step; d, e, and f are the three coefficients of the functional relationship between the reservoir water level and the reservoir capacity, and g is the constant term of the functional relationship between the reservoir water level and the reservoir capacity; Step 1.4: Based on the principle of water balance, the outflow and evaporation of the reservoir over the T consecutive historical time steps are restored, and the restored water volume V at the t-th historical time step of the reservoir is obtained by using equation (4) considering only the inflow and ignoring the outflow. R,t : (4) In equation (4): V r,t Let t be the outflow of water from the reservoir at the t-th historical time step.

[0009] Furthermore, step 3 includes the following steps: Step 3.1: to and Input variables separately and process them in the network to generate a weighted coefficient sequence of historical data. and the weighted coefficient sequence of future data ,in, Let be the weight coefficient for the t-th historical time step; The weight coefficients for the j-th future time step are used; the feature vector of the historical data for the t-th historical time step is generated using equation (5). The feature vector of the future data at the j-th future time step Thus, the time-varying feature matrix of historical data is obtained. and the time-varying feature matrix of future data Where T represents transpose; In equation (5): For weighted mapping operators; Step 3.2: The LSTM encoder for... Processing is performed to generate the hidden state matrix of historical data. ,in, Let be the hidden state vector at the t-th historical time step; Step 3.3: [The rest of the text appears to be a series of steps and incomplete sentences, possibly due to OCR errors. A more coherent translation would require the full context.] and The input is processed in the LSTM decoder to generate the hidden state matrix of future data. ,in, Let be the hidden state vector for the j-th future time step; Step 3.4: The gated residual network includes two layers of gated residual networks, and ... and The fused temporal feature enhancement matrix is ​​processed. Step 3.5: The multi-head self-attention layer utilizes an attention mechanism to... Processing is performed to generate an attention matrix. Step 3.6: The output layer uses equation (7) to obtain the prediction feature matrix Z, and then uses equation (8) to obtain the predicted value of the reduced water volume at J time steps. ; In equation (7) and (8): is the nonlinear activation function; W1 is the weight of the linear transformation and the nonlinear activation layer; b1 is the bias vector of the linear transformation and the nonlinear activation layer; (8) In equation (8): W2 is the weight of the linear transformation output layer; b2 is the bias vector of the linear transformation output layer.

[0010] Furthermore, step 3.4 includes the following steps: Step 3.4.1: Using equation (6) to... The data is processed to obtain a summary vector of historical data. : (6) Step 3.4.2: The input is fed into the first-layer gated residual network and then subjected to nonlinear transformation by the gated linear unit (GLU). Repeat the extraction J times to generate context vectors for J historical observation data. Step 3.4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and The inputs are fed into a second-layer gated residual network for processing to generate a temporal feature enhancement matrix. ,in, This is the temporal feature enhancement vector for the j-th future time step.

[0011] The present invention provides an electronic device, comprising a memory and a processor, wherein the memory is used to store a program that supports the processor in executing the data-missing reservoir water volume prediction method, and the processor is configured to execute the program stored in the memory.

[0012] The present invention discloses a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs the steps of the data-missing reservoir water volume prediction method.

[0013] Compared with existing technologies, the beneficial effects of this invention are as follows: 1. It solves the problem of model construction under conditions of missing data: This invention breaks through the inherent paradigm and constructs a physically meaningful "restored water volume" index through the principle of water balance, using it as an equivalent substitute target for inflow runoff. This approach avoids the bottleneck of missing data and provides a direct and reliable technical path for reservoirs lacking inflow data.

[0014] 2. This invention achieves forward-looking predictions by integrating future information, significantly improving prediction accuracy: Existing mainstream data-driven models can only rely on historical data for extrapolation and cannot utilize weather forecast information that can be obtained in advance. The TFT model used in this invention, through its unique structure, explicitly incorporates the multi-day weather forecast sequence as a deterministic input into the prediction process. This enables the model to respond to changes in key driving factors such as future rainfall and temperature, thereby achieving more accurate predictions.

[0015] 3. Provides inherent model interpretability, breaking the "black box" limitation: This invention does not approximate the understanding of the model through ex post facto interpretation methods, but utilizes the inherent interpretability mechanism of the TFT model. Its variable selection network can automatically quantify the contribution of historical water volume, various meteorological factors, and temporal characteristics to each prediction result. This makes the prediction logic transparent and traceable, greatly enhancing the credibility and acceptability of the prediction results in scheduling decisions, and effectively solving the concerns in the water conservancy field regarding the "black box" nature of deep learning models. Attached Figure Description

[0016] Figure 1 is a flowchart of the overall steps of the method of the present invention; Figure 2 is a flowchart of the TFT model; Figure 3 is the distribution of the importance of input features in the Encoder stage of Dongpu Reservoir; Figure 4 is the distribution of the importance of input features in the Decoder stage of Dongpu Reservoir. Detailed Implementation

[0017] In this embodiment, a method for predicting reservoir water volume missing based on multi-source data time-series fusion is proposed, which uses "restored water volume" as an equivalent substitute prediction target for inflow. A Temporal Fusion Transformer (TFT) model is introduced to construct a prediction framework that can fuse future meteorological data and possesses inherent interpretability. Specifically, as shown in Figure 1, the method includes: Step 1: Setting the time scale to daily, collecting operational monitoring data for T consecutive historical time steps of the reservoir, and calculating the restored water volume for T consecutive historical time steps, using the restored water volume to replace the inflow as the prediction target; Step 1.1: Based on the water level data and corresponding water surface area data for T consecutive historical time steps of the reservoir, using equation (1) to fit the functional relationship between the water level and water surface area of ​​the reservoir: (1) In equation (1): A tZ represents the water surface area of ​​the reservoir at the t-th historical time step. t Let t be the water level of the reservoir at the t-th historical time step; a and b are two coefficients of the functional relationship between the reservoir water level and the water surface area, and c is the constant term of the functional relationship between the reservoir water level and the water surface area.

[0018] Step 1.2: Use equation (2) to obtain the evaporation E of the reservoir at the t-th historical time step. t : (2) In equation (2): K is the evaporation coefficient of the area where the reservoir is located, and its value is determined according to the specific geographical location of the reservoir; e t Let be the evaporation rate of the reservoir at the t-th historical time step.

[0019] Step 1.3: Based on the water level data of the reservoir for T consecutive historical time steps and the corresponding reservoir capacity data, fit the functional relationship between the water level and the reservoir capacity using equation (3): (3) In equation (3): V t Let be the reservoir capacity at the t-th historical time step; d, e, and f are the three coefficients of the functional relationship between the reservoir water level and the reservoir capacity, and g is the constant term of the functional relationship between the reservoir water level and the reservoir capacity; Step 1.4: Based on the principle of water balance, the outflow and evaporation of the reservoir over the T consecutive historical time steps are restored, and the restored water volume V at the t-th historical time step of the reservoir is obtained by using equation (4) considering only the inflow and ignoring the outflow. R,t : (4) In equation (4): V r,t Let t be the outflow of water from the reservoir at the t-th historical time step.

[0020] Step 2: Similarly, set the time scale to daily, acquire the reservoir's basin meteorological data and upstream water replenishment data, and label the data with time features to generate seasonal and monthly labels. The reservoir's basin meteorological data includes daily rainfall, daily average temperature, and daily average wind speed. Rainfall data comes from rain gauges within the reservoir's basin, while other meteorological data comes from the National Oceanic and Atmospheric Administration (NOAA). Seasonal features are divided and labeled according to natural quarters: March-May, June-August, September-November, and December-February are labeled as spring, summer, autumn, and winter, respectively, using categorical variables. Months are labeled according to the Gregorian calendar months of January to December, using numerical variables.

[0021] The above data, together with the amount of reduced water, constitute the input feature set. ,in, h represents historical data for T consecutive historical time steps. t The data for the reservoir at the t-th historical time step includes basin meteorological data, reduced water volume, upstream water replenishment data, seasonal labels, and monthly labels. For the future data of the reservoir over J consecutive future time steps, f j The future data for the j-th future time step of the reservoir includes: basin meteorological data, seasonal labels, and monthly labels.

[0022] Step 3: Traditional machine learning and deep learning models can only rely on historical data for feature learning, unable to distinguish between known and predicted variables, making it difficult to optimize prediction logic using future data. Their prediction accuracy is limited in complex scenarios such as sudden rainfall changes, and they also suffer from a "black box" problem, lacking interpretability. To address these issues, a Temporal Fusion Transformer (TFT) model is built, as shown in Figure 2, including: a variable selection network, an LSTM encoder, an LSTM decoder, a gated residual network, a multi-head self-attention layer, and an output layer. The data were processed to obtain the predicted reduction water volume at J time steps. Distribution of variable importance.

[0023] Step 3.1: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require and Input variables separately and process them in the network to generate a weighted coefficient sequence of historical data. and the weighted coefficient sequence of future data ,in, Let be the weight coefficient for the t-th historical time step; Let be the weight coefficient for the j-th future time step.

[0024] The feature vector of historical data at the t-th historical time step is generated using equation (5). The feature vector of the future data at the j-th future time step Thus, the time-varying feature matrix of historical data is obtained. and the time-varying feature matrix of future data , where T represents transpose.

[0025] In equation (5): This is a weighted mapping operator.

[0026] Step 3.2: LSTM encoder pair Processing is performed to generate the hidden state matrix of historical data. ,in, Let be the hidden state vector at the t-th historical time step; Step 3.3: [The rest of the text appears to be a series of steps and incomplete sentences, possibly due to OCR errors. A more coherent translation would require the full context.] and The input is processed in the LSTM decoder to generate the hidden state matrix of future data. ,in, Let be the hidden state vector at the j-th future time step.

[0027] Step 3.4: Gated residual network, including two layers of gated residual network, and for and The fused temporal feature enhancement matrix is ​​processed. Step 3.4.1: Use equation (6) to... The data is processed to obtain a summary vector of historical data. : (6) Step 3.4.2: The input is fed into the first-layer gated residual network and then subjected to nonlinear transformation by the gated linear unit (GLU). Repeat the extraction J times to generate context vectors for J historical observation data. .

[0028] Step 3.4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation and The inputs are fed into a second-layer gated residual network for processing to generate a temporal feature enhancement matrix. Where T represents transpose. This is the temporal feature enhancement vector for the j-th future time step; Step 3.4.2: The future hidden state matrix generated by the LSTM decoder... With historical context vectors The inputs are fed into the second-layer gated residual network to generate the temporal feature enhancement matrix. Where T represents transpose. This is the enhancement vector for the j-th time series feature.

[0029] Step 3.5: Construct a multi-head self-attention layer; Step 3.5.1: Use equation (7) to generate the Query matrix, Key matrix, and Value matrix for each time step: In equation (7): Q j K j V j Let be the Query matrix, Key matrix, and Value matrix for the j-th future time step, respectively. , , This is the linear mapping weight matrix corresponding to the matrix.

[0030] Step 3.5.2: Calculate the attention at each prediction time step using equation (8): In equation (8): T represents transpose; For the attention at the j-th future time step; d kThe feature dimension of the Key matrix; Step 3.6.3: Perform the above projection and calculation J times in parallel, and finally concatenate the attention from each prediction time step to generate the attention matrix. , where T represents transpose.

[0031] Step 3.6: The feedforward output layer uses equation (9) to obtain the prediction feature matrix Z, and then uses equation (10) to obtain the predicted value of the reduced water volume at J time steps. ; In equation (9): is the nonlinear activation function; W1 is the weight of the linear transformation and the nonlinear activation layer; b1 is the bias vector of the linear transformation and the nonlinear activation layer; In equation (10): W2 is the weight of the linear transformation output layer; b2 is the bias vector of the linear transformation output layer.

[0032] Step 4: Based on the predicted value of reduced water volume The MAE loss function is constructed using the restored water volume at historical time steps and used to train the time-series fusion transformer model, thereby obtaining a trained time-series fusion transformer model to predict future restored water volume. Simultaneously, the weight coefficient sequence of historical data generated by the network is selected as the dependent variable. and the weighted coefficient sequence of future data and the context vector generated by the gated residual network Analysis of historical water volume and watershed meteorological data, including temporal characteristics. The contribution of each variable is used to generate a distribution map of the importance of each variable.

[0033] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0034] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

[0035] The experiment used operational monitoring data from Dongpu Reservoir and Dafangying Reservoir in Hefei City, Anhui Province, as well as meteorological data monitored by meteorological stations within the two reservoir basins. Based on the same data, three traditional prediction models—LSTM, GRU, and LightGBM—were selected as benchmark models, and their prediction accuracy was compared with that of the TFT model. The coefficient of determination (R²) was also selected. 2 The root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE) are used as indicators to evaluate the accuracy of predictions.

[0036] In this specific implementation, the Optuna parameter automatic optimization method is used to update the parameters in the temporal fusion transformer model, replacing the traditional time-consuming and experience-dependent manual parameter tuning. This optimization method intelligently explores and locks the optimal hyperparameter combination of the TFT model within a defined search space. This design gives the method strong adaptability, enabling it to automatically adjust the model configuration for different reservoirs and climate zones, thus achieving excellent prediction performance quickly in diverse application scenarios. This not only significantly lowers the barrier to entry for the method but also significantly improves the overall robustness and engineering promotion efficiency of the technical solution. Parameter search range: gradient pruning threshold (0.01-1.0), number of attention heads (1-15), hidden layer dimension (8-128), continuous variable hidden layer dimension (8-128), learning rate (0.001-0.1), Dropout random deactivation ratio (0-0.3). The optimal hyperparameter values ​​determined through iterative optimization using the Optuna method on the Dongpu Reservoir and Dafangying Reservoir datasets are shown in Table 1.

[0037] Table 1 Table 2 compares the prediction accuracy of each model on the Dongpu Reservoir and Dafangying Reservoir datasets. It can be seen that the TFT model has higher prediction accuracy.

[0038] Table 2 Figures 3 and 4 show the distribution of variable importance when the TFT model learns from historical data and the distribution of variable importance during the prediction process, respectively. By quantifying the proportion of importance of input features, the logic of model prediction is clearly demonstrated, breaking the "black box" problem of traditional machine learning and deep learning.

Claims

1. A method for predicting water volume in reservoirs with missing data based on multi-source data time-series fusion, characterized in that, The process includes the following steps: Step 1: Collect the operation monitoring data of the reservoir for T consecutive historical time steps, and calculate the amount of water restored in the reservoir for T consecutive historical time steps; Step 2: After acquiring the watershed meteorological data and upstream water replenishment data of the reservoir and marking them with time features, construct the input feature set together with the restored water volume. ,in, h represents historical data for T consecutive historical time steps. t The historical data of the reservoir at the t-th historical time step includes: basin meteorological data, reduced water volume, upstream water replenishment data, and temporal characteristics; For the future data of the reservoir over J consecutive future time steps, f j For the future data of the reservoir at the j-th future time step, including: watershed meteorological data and temporal characteristics; Step 3: Build a time-series fusion transformer model, including: variable selection network, LSTM encoder, LSTM decoder, gated residual network, multi-head self-attention layer, and output layer, and The data were processed to obtain the predicted reduction water volume at J time steps. Step 4: Based on the predicted value of reduced water volume The MAE loss function is constructed using the restored water volume at historical time steps and used to train the time-series fusion transformer model, thereby obtaining a trained time-series fusion transformer model to predict future restored water volume. Simultaneously, the weight coefficient sequence of historical data generated by the network is selected as the dependent variable. and the weighted coefficient sequence of future data and the context vector generated by the gated residual network Analysis of historical water volume, watershed meteorological data, and temporal characteristics The contribution of water volume, watershed meteorological data and temporal characteristics are used to generate importance distribution maps.

2. The method for predicting water volume in a reservoir with missing data based on multi-source data time-series fusion according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Based on the water level data of the reservoir for T consecutive historical time steps and the corresponding water surface area data, use equation (1) to fit the functional relationship between the water level and the water surface area of ​​the reservoir: (1) In equation (1): A t Z represents the water surface area of ​​the reservoir at the t-th historical time step. t Let be the water level of the reservoir at the t-th historical time step; a and b are two coefficients of the functional relationship between the reservoir water level and the water surface area, and c is the constant term of the functional relationship between the reservoir water level and the water surface area; Step 1.2: Use equation (2) to obtain the evaporation E of the reservoir at the t-th historical time step. t : (2) In equation (2): K is the evaporation coefficient of the area where the reservoir is located; e t Let be the evaporation amount of the reservoir at the t-th historical time step; Step 1.3: Based on the water level data of the reservoir for T consecutive historical time steps and the corresponding reservoir capacity data, use equation (3) to fit the functional relationship between the water level and the reservoir capacity: (3) In equation (3): V t Let be the reservoir capacity at the t-th historical time step; d, e, and f are the three coefficients of the functional relationship between the reservoir water level and the reservoir capacity, and g is the constant term of the functional relationship between the reservoir water level and the reservoir capacity; Step 1.4: Based on the principle of water balance, the outflow and evaporation of the reservoir over the T consecutive historical time steps are restored, and the restored water volume V at the t-th historical time step of the reservoir is obtained by using equation (4) considering only the inflow and ignoring the outflow. R,t : (4) In equation (4): V r,t Let t be the outflow of water from the reservoir at the t-th historical time step.

3. The method for predicting water volume in a reservoir with missing data based on multi-source data time-series fusion according to claim 2, characterized in that, Step 3 includes the following steps: Step 3.1: To and Input variables separately and process them in the network to generate a weighted coefficient sequence of historical data. and the weighted coefficient sequence of future data ,in, Let be the weight coefficient for the t-th historical time step; The weight coefficients for the j-th future time step are used; the feature vector of the historical data for the t-th historical time step is generated using equation (5). The feature vector of the future data at the j-th future time step Thus, the time-varying feature matrix of historical data is obtained. and the time-varying feature matrix of future data Where T represents transpose; In equation (5): For weighted mapping operators; Step 3.2: The LSTM encoder for... Processing is performed to generate the hidden state matrix of historical data. ,in, Let be the hidden state vector at the t-th historical time step; Step 3.3: [The rest of the text appears to be a series of steps and incomplete sentences, likely due to OCR errors. A more coherent translation would require the full context.] and The input is processed in the LSTM decoder to generate the hidden state matrix of future data. ,in, Let be the hidden state vector for the j-th future time step; Step 3.4: The gated residual network includes two layers of gated residual networks, and ... and The fused temporal feature enhancement matrix is ​​processed. Step 3.5: The multi-head self-attention layer utilizes an attention mechanism to... Processing is performed to generate an attention matrix. Step 3.6: The output layer uses equation (7) to obtain the prediction feature matrix Z, and then uses equation (8) to obtain the predicted value of the reduced water volume at J time steps. ； In equation (7) and (8): is the nonlinear activation function; W1 is the weight of the linear transformation and the nonlinear activation layer; b1 is the bias vector of the linear transformation and the nonlinear activation layer; (8) In equation (8): W2 is the weight of the linear transformation output layer; b2 is the bias vector of the linear transformation output layer.

4. The method for predicting water volume in a reservoir with missing data based on multi-source data time-series fusion according to claim 3, characterized in that, Step 3.4 includes the following steps: Step 3.4.1: Using equation (6) to... The data is processed to obtain a summary vector of historical data. ： (6) Step 3.4.2: The input is fed into the first-layer gated residual network and then subjected to nonlinear transformation by the gated linear unit (GLU). Repeat the extraction J times to generate context vectors for J historical observation data. Step 3.4.3: [The text appears to be incomplete and contains several grammatical errors. A more accurate translation would require the full context.] and The inputs are fed into a second-layer gated residual network for processing to generate a temporal feature enhancement matrix. ,in, This is the temporal feature enhancement vector for the j-th future time step.

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing the data-missing reservoir water volume prediction method according to any one of claims 1-4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, When the computer program is run by the processor, it performs the steps of the method for predicting water volume in a reservoir with missing data as described in any one of claims 1-4.

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