Sand content prediction method and system fused with parallel space-time attention

Abstract

The invention discloses a sand content prediction method and system fused with parallel space-time attention, and relates to the technical field of river sand content prediction.The method comprises the steps that the sand content and flow data of a river basin in a monitoring area are collected and preprocessed; constructing a PSTA-LSTM model, and inputting the preprocessed sand content and flow data into the PSTA-LSTM model to obtain sand content prediction results at a plurality of moments in the future; wherein the PSTA-LSTM model adopts a hybrid network architecture fusing a space attention mechanism, a time attention mechanism and an LSTM, and is used for identifying a spatial feature and time dependency relationship in the sand content and flow data. A deep learning method for predicting the sand content of a key section is adopted, an LSTM model is taken as a core, a parallel space-time attention mechanism is combined, an activation function is improved, and the capability of predicting a high sand content sequence and an extreme event is improved.

Description

Technical Field

[0001] This invention relates to the field of river sediment concentration prediction technology, and more specifically to a sediment concentration prediction method and system that integrates parallel spatiotemporal attention. Background Technology

[0002] In sediment-laden river basins, sediment concentration at key cross-sections not only reflects the dynamic process of sediment transport but also serves as a crucial indicator for revealing the coupling relationship between water and sediment and the propagation characteristics of sediment transport waves. It is a key parameter in flood control scheduling, sediment management, and ecological regulation. However, sediment concentration sequences are influenced by multiple factors, including inflow and sediment conditions, tributary inflows, and riverbed scouring. These factors result in complex patterns that are difficult to characterize with simple relationships, and sediment concentrations often exhibit sudden and rapid fluctuations within a short period. Particularly during flood season or flood events, sediment concentrations tend to rise rapidly, approaching or even exceeding historical highs. While existing prediction methods possess a certain degree of accuracy, under extreme high sediment concentration conditions, limitations in hydrological forecasting and computational efficiency often prevent timely responses to these rapid evolutionary characteristics, leading to delays or biases in regulatory schemes.

[0003] Currently, scholars both domestically and internationally have conducted extensive research on sediment concentration prediction, employing methods including physical process-based prediction, traditional empirical regression, and machine learning. Physical process-based prediction methods, such as one-dimensional and two-dimensional hydrodynamic models, combine mathematical equations of river sediment concentration evolution with computer simulation techniques. However, these methods rely heavily on high-quality boundary conditions and numerous real-time adjustments to physical parameters (such as roughness and sediment transport rate formula parameters). This makes it difficult to guarantee the accuracy and real-time performance of predictions under conditions of rapid changes in inflow sediment concentration, such as sudden flood peaks or strong sediment discharge during the flood season. Traditional empirical regression methods do not characterize the specific physical processes of sediment evolution but instead establish empirical correlations between sediment concentration and key influencing factors through mathematical statistics. This method is highly dependent on data representativeness and variable correlation, making it difficult to handle nonlinear changes in sediment concentration sequences and short-term sudden peaks, thus limiting the accuracy and reliability of predictions in complex watersheds and under extreme hydrodynamic and sediment conditions.

[0004] The introduction of machine learning methods has brought a new perspective to the task of sediment concentration prediction. Since machine learning models learn complex relationships from historical data without relying on prior engineering physical models, they help overcome problems caused by imperfect or inaccurate engineering models. Guo Xiuji et al. used multiple machine learning algorithms to predict the sediment concentration at the Sanmenxia Reservoir, reducing reliance on prior physical models and effectively improving the ability to capture sediment concentration trends under conventional hydrological conditions. Chen Xue et al. selected four machine learning models—gradient boosting regression, support vector regression, extreme gradient boosting, and random forest—to predict sediment concentration for the next three hours at the Yanchuan and Zichang hydrological stations, exploring the mapping relationships and multi-factor coupling features in hydrological and sediment data to improve short-term prediction accuracy. Although machine learning methods and their improved algorithms have achieved certain results in the field of sediment concentration prediction, they perform well in a single dimension but are insufficient in capturing coupling effects in scenarios such as cross-section spatial correlations, sudden high-sediment-concentration floods during the flood season, or short-duration sediment discharge peak events, limiting their comprehensive application in water and sediment prediction in complex watersheds.

[0005] Furthermore, sudden fluctuations and extreme high-value events in sediment concentration sequences are often difficult to describe using simple linear mappings, which is closely related to the abrupt changes in flood erosion, tributary sediment accumulation, and sediment transport processes. Activation functions, as key components of deep neural networks, can introduce nonlinear transformations into the model, enabling it to better fit complex water-sediment response relationships during feature extraction and pattern recognition. ReLU, due to its high computational efficiency and sparse activation properties, is widely used in various deep neural networks; however, truncation of negative values ​​may lead to the loss of crucial information. Smoothing activation functions such as softplus alleviate the hard truncation problem of ReLU in the negative interval, improving the continuity of gradient propagation; however, compression of negative values ​​may weaken anomalous signals and reduce the ability to respond to extreme high-sediment-concentration events.

[0006] Therefore, in view of the shortcomings of the existing technology, how to provide a method and system for predicting sediment content by integrating parallel spatiotemporal attention, and how to integrate an improved activation function with smoothness characteristics and high response capability to achieve prediction of high sediment content sequences and extreme events are problems that urgently need to be solved by those skilled in the art. Summary of the Invention

[0007] In view of this, the present invention provides a method and system for predicting sediment content by integrating parallel spatiotemporal attention. It adopts a deep learning method for predicting sediment content in key sections. The method takes the LSTM model as the core, combines it with a parallel spatiotemporal attention mechanism, and improves the activation function to achieve prediction of high sediment content sequences and extreme events.

[0008] To achieve the above objectives, the present invention adopts the following technical solution: a method for predicting sand content by fusing parallel spatiotemporal attention, comprising: Collect sediment concentration and flow data of the river basin in the monitoring area, and preprocess the sediment concentration and flow data; A PSTA-LSTM model is constructed, and the preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future time points. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

[0009] Preferably, the PSTA-LSTM model adopts a hybrid network architecture that integrates spatial attention mechanism, temporal attention mechanism and LSTM, including: Spatial and temporal branches operating in parallel; Spatial attention mechanism is used as spatial feature extractor, and temporal attention mechanism is used as temporal feature extractor. The LSTM is used as feature carrier and sequence modeling unit to capture the dynamic dependencies of the input sequence.

[0010] Preferably, in the spatial branch, the input features are weighted and calculated in the spatial dimension using a spatial attention mechanism to form a spatial context representation, which is then processed by LSTM to obtain a global representation of the spatial path; in the temporal branch, the input sequence is fed into LSTM to extract the hidden state, and then the temporal attention weights are calculated based on the hidden state and weighted and aggregated to form a temporal context representation. The features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping.

[0011] Preferably, in the time attention mechanism, the length is set to... The hidden states of the LSTM for the input sequence are: ; in, Indicates the first The hidden state vector at each time step; Calculate the relevance score for each time step: ; in, It is the weight matrix for time attention; For bias terms; For the first The relevance score at each time step; pass right Normalization is performed to generate attention weights for each feature. It is used to generate a time context vector for weighted hidden states.

[0012] Preferably, in the spatial attention mechanism, the multi-station input vector at each time step is set as follows: ; in, Indicates the first The first time step The characteristic values ​​of each station Number of stations; Calculate the correlation score for each station: ; in, It is the weight matrix for spatial attention; For bias terms; For the first The relevance score at each time step; pass right Normalization, generating spatial attention weights And used to weight the input vector to generate a spatial context vector, as shown below: ; ; in, For spatially enhanced input, highlight key station information; This represents element-wise product.

[0013] Preferably, the sequence Inputting the data into an LSTM yields a sequence of hidden states. , For the hidden layer dimension of the LSTM, the hidden state is... A global representation of the spatial path is obtained using pooling operations: ; in, This is a pooling operation used to synthesize the spatial features of each time step. This is the result of spatial attention.

[0014] Preferably, the features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping, including: Joint representation is achieved using vector concatenation operations: ; in, This is a global representation of the spatial path. This is a contextual representation of the time path; After splicing, a nonlinear mapping layer is introduced to obtain ; in, As weight, For bias terms, Used to enhance feature interaction and nonlinear representation capabilities. The feature dimensions after fusion.

[0015] Preferably, a sand content prediction system integrating parallel spatiotemporal attention includes: The data acquisition and preprocessing module is used to acquire sediment concentration and flow data of the river basin in the monitoring area, and to preprocess the sediment concentration and flow data. The model building and result output module is used to build a PSTA-LSTM model. The preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future times. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

[0016] As can be seen from the above technical solutions, compared with the prior art, the present invention discloses a method and system for predicting sediment content by integrating parallel spatiotemporal attention, a deep learning method for predicting sediment content in key sections, with an LSTM model as the core, combined with a parallel spatiotemporal attention mechanism, and improved activation function, to achieve the ability to predict high sediment content sequences and extreme events. Attached Figure Description

[0017] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of the research area provided for an embodiment of the present invention.

[0019] Figure 2 This is a schematic diagram of the LSTM memory cell structure provided in an embodiment of the present invention.

[0020] Figure 3 This is a schematic diagram of the PSTA-LSTM sediment concentration prediction model provided in an embodiment of the present invention.

[0021] Figure 4 This is a schematic diagram of the heatmap of the correlation coefficient of the forecasting factors provided in an embodiment of the present invention.

[0022] Figure 5 This is a schematic diagram comparing predictions using different model structures provided in an embodiment of the present invention.

[0023] Figure 6 This is a schematic diagram illustrating the prediction results of different activation functions provided in embodiments of the present invention.

[0024] Figure 7 This is a schematic diagram illustrating different activation function evaluation metrics provided in embodiments of the present invention. Detailed Implementation

[0025] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0026] This invention discloses a method for predicting sand content by fusing parallel spatiotemporal attention, comprising: Collect sediment concentration and flow data of the river basin in the monitoring area, and preprocess the sediment concentration and flow data; A PSTA-LSTM model is constructed, and the preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future time points. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

[0027] The PSTA-LSTM model can simultaneously identify key spatial features and temporal dependencies in the input data, dynamically measure the contribution of each station and historical moment to the target section, and improve the ability to characterize peak events.

[0028] In one specific embodiment of the present invention, the section of the Yellow River from Huaxian to Tongguan in the middle reaches (approximately 109.5°–111.2°E, 34.5°–36.5°N) is selected, such as... Figure 1 As shown, the area is approximately 18,648.34 km². This section is an important sediment transport channel for the Yellow River main stream, encompassing major tributaries such as the Wei River, Fen River, and Luo River. Hydrological stations are located within the area, including Huaxian, Zhuangtou, Longmen, Hejin, and Tongguan. The Tongguan hydrological station is situated at the confluence of the Wei River, the Beiluo River, and the Yellow River main stream, controlling a drainage area of ​​approximately 68.22 × 10⁻⁶ km². Tongguan, at a distance of km², is the final control section of the Yellow River entering the Sanmenxia and Xiaolangdi Reservoirs in its middle reaches. The average annual sediment load at Tongguan accounts for over 70% of the Yellow River's total sediment load. Its sediment primarily originates from the Wei River, the Beiluo River, and the coarse sediment region of the upper Yellow River. The concentration of both fine and coarse sediment at Tongguan makes it a crucial node for sediment transport and evolution in the middle reaches of the Yellow River. The sediment inflow process at Tongguan directly determines the sediment concentration entering the Sanmenxia and Xiaolangdi Reservoirs, playing a decisive role in reservoir sedimentation and the effectiveness of water and sediment regulation.

[0029] This simulation and prediction study is based on measured sediment concentration data from the Tongguan Hydrological Station (2000–2024) and sediment concentration and flow data from major upstream control stations (Longmen, Huaxian, and Zhuangtou). The measured sediment concentration and flow data are from the Yellow River Conservancy Commission Hydrological Bureau and have been linearly interpolated to two-hourly data. To eliminate the influence of dimensional differences and accelerate model training convergence, the normalization formula is as follows: ; in, The normalized value of the data; The minimum value of the data; This represents the maximum value of the data.

[0030] Specifically, the PSTA-LSTM model adopts a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM, such as... Figure 3 As shown, it includes: Spatial and temporal branches operating in parallel; Spatial attention mechanism is used as spatial feature extractor, and temporal attention mechanism is used as temporal feature extractor. The LSTM is used as feature carrier and sequence modeling unit to capture the dynamic dependencies of the input sequence.

[0031] Specifically, in the spatial branch, the spatial attention mechanism is used to weight the input features in the spatial dimension to form a spatial context representation, which is then processed by LSTM to obtain the global representation of the spatial path; in the temporal branch, the input sequence is fed into LSTM to extract the hidden state, and then the temporal attention weights are calculated based on the hidden state and weighted and aggregated to form a temporal context representation. The features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping.

[0032] Specifically, Temporal Attention (TA) is used to highlight key time steps in the sequence that contribute significantly to the prediction target. In Temporal Attention, let the length be... The hidden states of the LSTM for the input sequence are: ; in, Indicates the first The hidden state vector at each time step; Calculate the relevance score for each time step: ; in, It is the weight matrix for time attention; For bias terms; For the first The relevance score at each time step; pass right Normalization is performed to generate attention weights for each feature. This is used to generate a weighted hidden state temporal context vector, as shown in the following equation: ; .

[0033] Specifically, the spatial attention mechanism (SA) is used to identify the degree of influence of different input stations on the sediment content of the target station; In the spatial attention mechanism, let the multi-station input vector at each time step be: ; in, Indicates the first The first time step The characteristic values ​​of each station Number of stations; Calculate the correlation score for each station: ; in, It is the weight matrix for spatial attention; For bias terms; For the first The relevance score at each time step; pass right Normalization, generating spatial attention weights And used to weight the input vector to generate a spatial context vector, as shown below: ; ; in, For spatially enhanced input, highlight key station information; This represents element-wise product.

[0034] Specifically, the sequence Inputting the data into an LSTM yields a sequence of hidden states. , For the hidden layer dimension of the LSTM, the hidden state is... A global representation of the spatial path is obtained using pooling operations: ; in, This is a pooling operation used to synthesize the spatial features of each time step. This is the result of spatial attention.

[0035] Specifically, Long Short-Term Memory (LSTM) neural networks are a special type of Recurrent Neural Network (RNN) that replaces RNN neurons in the hidden layers with LSTM neurons, forgetting invalid information and updating valid information. The memory unit structure is as follows: Figure 2 As shown.

[0036] LSTM achieves its function of updating neuronal information through three constructed "gate" structures. The forget gate controls whether the memory unit state from the previous time step is retained at the current time step, as shown in the following equation: ; The input gate, while selectively forgetting the previous state, introduces important information from the current moment, thus dynamically updating the memory, as shown in the following formula: ; The first two stages combine the long-term memory of the LSTM with the current memory to update the cell state. Finally, there's the output gate, which uses a function... The cell state is processed, and the resulting value is multiplied by the output of the activation function to obtain the information that will be output, as shown in the following formula: .

[0037] Specifically, the features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping, including: Joint representation is achieved using vector concatenation operations: ; in, This is a global representation of the spatial path. This is a contextual representation of the time path; Considering the scale difference between the two types of features, a nonlinear mapping layer is introduced after concatenation, resulting in: ; in, As weight, For bias terms, Used to enhance feature interaction and nonlinear representation capabilities. The feature dimensions after fusion.

[0038] Specifically, the "hard truncation" characteristic of the ReLU function in the low-value region leads to gradient discontinuity, affecting the stability of model training; the softplus function ensures gradient continuity in the low-value region, but its growth is too slow in the high-value region. Therefore, a smooth non-negative activation function, Smooth-ReLU (SReLU), is designed to combine the advantages of ReLU and softplus. Softplus is used to handle the low-value region of ReLU, ensuring gradient smoothness and non-negativity. A linear enhancement segment is used in the high-value region, similar to ReLU's fast response to positive values, capturing the continuity of function values ​​and first derivatives at the turning points of sand concentration peak changes. This achieves a fusion of softplus and ReLU, balancing training stability and high-value response capability.

[0039] ; in, The sediment content threshold, corresponding to the key value in the model data that requires enhanced response, is set to 42. During reservoir operation, taking the Xiaolangdi Reservoir as an example, values ​​exceeding 40 kg / m³... 3 The power generation tunnel will be shut down, and at this time the sand content at the Tongguan section is 42 kg / m³-44 kg / m³. 3 . The slope of the linear segment in the high-value region, used to enhance the sensitivity to peak sediment concentration, was determined to be 1.2 through cross-validation of the training set. That is: .

[0040] In one specific embodiment of the present invention, the predictive performance of the model is evaluated using mean absolute error (MAE), root mean square error (RMSE), Nash efficiency coefficient (NSE), peak relative error (PRE), and coefficient of determination (R).

[0041] MAE is used to evaluate the average deviation between model predictions and actual data, reflecting the model's robustness to overall error. ; The RMSE quantifies the variance between the model's predictions and the actual data, reflecting the overall error between the predicted and true values: ; NSE measures the goodness of fit of model predictions to the observed mean, reflecting the model's ability to explain the variability of the observed data. ; PRE measures the accuracy of a model in predicting time series extreme values, and intuitively reflects the model's fitting accuracy to the maximum value: ; R measures the model's ability to interpret data, and its value is [0,1]. The closer R is to 1, the better the model fits the data. ; In the above formula: This is the measured value of the sand content; This is the predicted value for sediment content; This represents the average value of the measured sand content; This is to predict the average value of the sediment content; This represents the measured peak value.

[0042] Results Analysis

[0043] Feature factor selection

[0044] The sediment concentration variation at Tongguan Station is influenced by the combined effects of water and sediment inflows from the Yellow River, Wei River, and the upper reaches of the Beiluo River. Hydrological characteristics from three key stations—Longmen (upper reaches of the Yellow River main stream), Huaxian (upper reaches of a tributary of the Wei River), and Zhuangtou (upper reaches of a tributary of the Beiluo River)—were selected as model inputs: Longmen Station has a large inflow and high sediment concentration, making it the main sediment source for Tongguan; Huaxian Station represents the uncertainty and seasonal variation of sediment input in the Wei River basin; and Zhuangtou Station primarily captures short-term sediment peaks caused by localized torrential rain runoff. Model input factors include: a. Upstream water-sediment boundary factors: flow rates at three monitoring stations With sediment content This reflects the characteristics of water and sediment input and transport in different river systems; b. Water-sediment transport coupling factor: using time series information of upstream flow and sediment concentration to reflect the driving effect of water flow on sediment transport.

[0045] Figure 4 The sediment content of the Tongguan section is given. Heatmap of Pearson correlation coefficients with each input factor. As shown in the graph, The sediment concentration at Tongguan Station showed a significant positive correlation with that at Longmen Station and Huaxian Station, indicating that the main stream of the Yellow River and the tributaries of the Wei River play a dominant role in the sediment concentration at Tongguan Station. The correlation with that at Zhuangtou Station was moderate, reflecting the phased impact of short-term sand peaks caused by local rainstorms on sediment concentration. The correlation with the flow factor was low (the highest being about 0.547), suggesting that the changes in sediment concentration at Tongguan are more controlled by upstream water and sediment input and transport mechanisms, rather than simple changes in water volume.

[0046] Model parameter settings

[0047] Four models, categorized into three types, were selected for comparison. The basic structural parameters of the four models should be consistent: input sequence length of 6, number of hidden layers of 2, number of hidden units of 64, number of iterations of 100, and learning rate of 1×10⁻⁶. -3 The optimizer is Adam.

[0048] The different models differ only in their attention structure and its dimensions. The first type of model selects a single LSTM model; the second type of model uses a single attention mechanism combined with LSTM to construct TA-LSTM and SA-LSTM models; the third type of model uses a sequential attention mechanism, where the input sequence is spatially attended before being fed into the LSTM model, and then subjected to a temporal attention mechanism to achieve prediction.

[0049] a. LSTM model

[0050] It does not include an attention mechanism and is used for comparison with benchmarks.

[0051] b. TA-LSTM model, SA-LSTM model

[0052] The temporal attention dimension of the TA-LSTM model is set to 32; the spatial attention dimension of the SA-LSTM model is set to 64.

[0053] c. SSTA-LSTM model, PSTA-LSTM model

[0054] The SSTA-LSTM spatial attention dimension is set to 64, and the temporal attention dimension is set to 32; the PSTA-LSTM spatial attention dimension is set to 128, and the temporal attention dimension is set to 64.

[0055] Model prediction results and comparison

[0056] Model Structure Comparison Analysis

[0057] In Method 1, the test samples are input into each trained model to obtain the predicted sequences, which are then compared with the measured values ​​(see...). Figure 5 Typical sand peaks were selected for localized magnified analysis. Overall, all models can reproduce the main trends in sediment concentration at Tongguan, but the amplitude and time lag of the peak stage differ.

[0058] The basic LSTM model can capture overall fluctuations, but it exhibits lag at high values, with low peak amplitude and an overly smooth curve. The results indicate that without an attention mechanism, the model struggles to identify the time-lag characteristics of upstream sediment surges and their downstream transport, resulting in insufficient peak response, typically manifested as "peak passivation."

[0059] The SA-LSTM model with spatial attention improved the peak fitting, but the fluctuation of continuous high value segments still showed bias, indicating that the extraction of spatial features alone enhanced the identification of tributary sedimentation processes, but had limited response to sudden changes in sediment load caused by local rainstorms and resuspension.

[0060] The TA-LSTM model enhances sequence dependence through time attention, resulting in peak fitting that more closely approximates measured values, reflecting the model's ability to capture time-cumulative effects and lag responses. However, fluctuations between peaks still do not fully reflect the spatial superposition effect of sediment from multiple sources, and relying solely on time weights is insufficient to reveal the spatial coupling characteristics of tributary sediment collection.

[0061] The SSTA-LSTM model employs serial spatial-temporal attention, which improves prediction accuracy in both peak and fluctuation segments. However, due to the unidirectional propagation of information along the sequence, the role of spatial features in subsequent time step updates is limited, resulting in a response delay, reflecting the "spatial-temporal dependence asymmetry" characteristic in sediment transport.

[0062] The PSTA-LSTM model, through its parallel spatiotemporal attention structure, outperforms other models in both peak amplitude and timing prediction. This structure can simultaneously identify "upstream multi-source sediment inflow" and "downstream time-delay response," strengthening the spatial coupling of tributary sediment distribution and reflecting the propagation inertia of sediment over time, thus accurately reproducing the peak and decay patterns of sediment concentration at the Tongguan section.

[0063] Table 1 lists the performance metrics of the five models. As the structure evolves from the basic LSTM to PSTA-LSTM, the RMSE shows a decreasing trend, while the NSE continues to rise, and the correlation coefficient R reaches 0.891, reflecting the advantages of the parallel spatiotemporal attention structure in information fusion and the representation of sediment transport patterns.

[0064] Table 1 Evaluation Indicators for Different Model Structures

[0065] Comparison of different activation functions

[0066] This paper compares the performance of ReLU, SReLU, and softplus activation functions in the PSTA-LSTM model using Method 1, focusing on their effectiveness in predicting extreme sediment concentration fluctuations and sudden peaks. Figure 6 and Figure 7 As can be seen, the prediction accuracy of each activation function varies significantly under different data fluctuation characteristics.

[0067] During periods of stable sediment concentration fluctuations, the ReLU activation function fits the data well. However, its prediction error increases significantly when facing extreme fluctuations, failing to accurately capture sudden peaks. The predicted curve exhibits a lag characteristic and cannot reflect rapid changes in actual data in a timely manner. The softplus activation function, due to its smoothing properties, demonstrates high stability during stable fluctuations, but it lags behind during sudden peak periods, with peak amplitudes lower than actual values, making it difficult to accurately describe sediment variation patterns under extreme fluctuations. In contrast, the SReLU activation function enhances the model's adaptability to sudden peaks through a nonlinear adjustment mechanism, enabling it to respond quickly to drastic changes in sediment concentration. Its predicted curve during high sediment peak periods is closer to the measured values, accurately capturing the characteristics of extreme fluctuations.

[0068] Further from Figure 7 It is evident that SReLU outperforms ReLU and softplus in all evaluation metrics, demonstrating that SReLU can more accurately reflect actual sediment variation patterns, and exhibits significant robustness and adaptability, especially in handling extreme events.

[0069] The embodiments of the present invention have the following beneficial technical effects: (1) A parallel spatiotemporal attention structure is proposed, which simultaneously extracts time series features and spatial cross-sectional features independently, fully preserves spatiotemporal complementary information, and improves the model's response capability to extreme floods and high sediment peak events; (2) Design a smooth non-negative activation function Smooth-ReLU (SReLU), which combines the advantages of ReLU and softplus, and improves the model’s sensitivity to high sand content processes and fitting accuracy while ensuring gradient continuity and training stability. (3) Taking the Tongguan Station, a key section in the middle and lower reaches of the Yellow River, as the research object, we carried out prediction verification by combining historical hydrological and sediment data, and systematically evaluated the applicability of the model.

[0070] In one specific embodiment of the present invention, a sand content prediction system integrating parallel spatiotemporal attention includes: The data acquisition and preprocessing module is used to acquire sediment concentration and flow data of the river basin in the monitoring area, and to preprocess the sediment concentration and flow data. The model building and result output module is used to build a PSTA-LSTM model. The preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future times. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

[0071] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0072] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for predicting sand content by integrating parallel spatiotemporal attention, characterized in that, include: Collect sediment concentration and flow data of the river basin in the monitoring area, and preprocess the sediment concentration and flow data; A PSTA-LSTM model is constructed, and the preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future time points. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

2. The method for predicting sand content by fusing parallel spatiotemporal attention as described in claim 1, characterized in that, The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM mechanisms, including: Spatial and temporal branches operating in parallel; Spatial attention mechanism is used as spatial feature extractor, and temporal attention mechanism is used as temporal feature extractor. The LSTM is used as feature carrier and sequence modeling unit to capture the dynamic dependencies of the input sequence.

3. The method for predicting sand content by fusing parallel spatiotemporal attention according to claim 2, characterized in that, In the spatial branch, the spatial attention mechanism is used to weight the input features in the spatial dimension to form a spatial context representation, which is then processed by LSTM to obtain the global representation of the spatial path. In the temporal branch, the input sequence is fed into LSTM to extract the hidden state, and then the temporal attention weights are calculated based on the hidden state and weighted and aggregated to form a temporal context representation. The features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping.

4. The method for predicting sand content by fusing parallel spatiotemporal attention according to claim 3, characterized in that, In the time-attention mechanism, let the length be... The hidden states of the LSTM for the input sequence are: ； in, Indicates the first The hidden state vector at each time step; Calculate the relevance score for each time step: ； in, It is the weight matrix for time attention; For bias terms; For the first The relevance score at each time step; pass right Normalization is performed to generate attention weights for each feature. It is used to generate a time context vector for weighted hidden states.

5. The method for predicting sand content by fusing parallel spatiotemporal attention according to claim 3, characterized in that, In the spatial attention mechanism, let the multi-station input vector at each time step be: ； in, Indicates the first The first time step The characteristic values ​​of each station Number of stations; Calculate the correlation score for each station: ； in, It is the weight matrix for spatial attention; For bias terms; For the first The relevance score at each time step; pass right Normalization to generate spatial attention weights And used to weight the input vector to generate a spatial context vector, as shown below: ； ； in, For spatially enhanced input, highlight key station information; This represents element-wise product.

6. The method for predicting sand content by fusing parallel spatiotemporal attention according to claim 5, characterized in that, will sequence Inputting the data into an LSTM yields a sequence of hidden states. , For the hidden layer dimension of the LSTM, the hidden state is... A global representation of the spatial path is obtained using pooling operations: ； in, This is a pooling operation used to synthesize the spatial features of each time step. This is the result of spatial attention.

7. The method for predicting sand content by fusing parallel spatiotemporal attention according to claim 3, characterized in that, The features output from the temporal and spatial branches are concatenated in the fusion layer, and feature interaction and scale unification are achieved through nonlinear mapping, including: Joint representation is achieved using vector concatenation operations: ； in, This is a global representation of the spatial path. This is a contextual representation of the time path; After splicing, a nonlinear mapping layer is introduced, resulting in: ； in, As weight, For bias terms, Used to enhance feature interaction and nonlinear representation capabilities. The feature dimensions after fusion.

8. A sediment concentration prediction system integrating parallel spatiotemporal attention, employing the sediment concentration prediction method integrating parallel spatiotemporal attention as described in any one of claims 1-7, characterized in that, include: The data acquisition and preprocessing module is used to acquire sediment concentration and flow data of the river basin in the monitoring area, and to preprocess the sediment concentration and flow data. The model building and result output module is used to build a PSTA-LSTM model. The preprocessed sediment concentration and flow data are input into the PSTA-LSTM model to obtain the sediment concentration prediction results for several future times. The PSTA-LSTM model employs a hybrid network architecture that integrates spatial attention, temporal attention, and LSTM to identify spatial features and temporal dependencies in sediment content and flow data.

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