Dynamic prediction and analysis method and system for node pressure of water supply network

Abstract

The invention discloses a water supply network node pressure dynamic prediction and analysis method and system, and relates to the technical field of water supply network intelligent monitoring, and the method comprises the steps: obtaining topological structure data, historical pressure and flow time sequence data of a water supply network, and generating a pressure flow characteristic matrix through multi-dimensional analysis; performing time sequence dimension reduction on the feature matrix, and extracting time dimension features to construct an optimized feature vector; inputting the optimized feature vector into a variable structure deep neural network for training to obtain a pressure prediction model; analyzing the feature matrix to identify peak periods, and dividing peak interval feature vectors; constructing a pressure propagation space topological graph based on the peak interval feature vector, and calculating a pressure propagation time delay correlation degree to generate a correction coefficient; and inputting the feature vector into a prediction model to obtain an initial prediction value, and generating a dynamic pressure prediction result in combination with the correction coefficient and the topological structure data. The pressure prediction accuracy of the water supply network is improved.

Description

Technical Field

[0001] This invention relates to the field of intelligent monitoring technology for water supply networks, specifically to a method and system for dynamic prediction and analysis of pressure at nodes in water supply networks. Background Technology

[0002] Water supply network pressure prediction methods primarily rely on historical data statistics and simple mathematical models, which cannot accurately reflect the dynamic changes in pressure within the network. Traditional methods often treat each node in the water supply network as an independent entity for prediction, neglecting the pressure propagation correlation between nodes, leading to significant deviations between prediction results and actual operating conditions. Pressure fluctuations are substantial during peak water usage periods, and existing prediction methods fail to specifically model the characteristics of these peak periods, further reducing prediction accuracy.

[0003] Most commonly used pressure prediction models employ fixed-structure neural networks, which struggle to adapt to the complex and variable pressure propagation characteristics of water supply networks. Existing methods do not adequately consider data redundancy when processing time-series data, resulting in inefficient model training and a tendency to overfit. Summary of the Invention

[0004] The purpose of this invention is to provide a method and system for dynamic prediction and analysis of pressure at nodes in water supply networks, aiming to solve at least one of the technical problems existing in the prior art.

[0005] The technical solution of this invention is: a method for dynamic prediction and analysis of pressure at nodes in a water supply network, comprising the following steps: Obtain topology data, historical pressure time-series data, and flow time-series data of the water supply network; Multi-dimensional analysis is performed on historical pressure time-series data and flow time-series data to calculate pressure and flow variation characteristics and generate a pressure and flow feature matrix. Time-series dimensionality reduction is performed based on the pressure-flow feature matrix, and time-dimensional features are extracted through singular value decomposition to construct an optimized feature vector; The optimized feature vector is input into a pre-constructed variable structure deep neural network. The network parameters are adjusted based on the loss function calculation results to train the model and generate a stress prediction model. Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers. Based on the feature vectors of the peak interval, a pressure propagation spatial topology map is constructed, the correlation degree of pressure propagation delay between nodes is calculated, and a correction coefficient for the peak period is generated. The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the correction coefficient of the peak period. Finally, the dynamic pressure prediction results of each node of the water supply network are generated by combining the topology data.

[0006] Multi-dimensional analysis of historical pressure and flow time-series data is performed to calculate pressure-flow variation characteristics and generate a pressure-flow feature matrix, including: Historical pressure and flow time series data are divided into multiple time windows according to the water supply network topology. Segmented sampling is performed within each time window to generate pressure and flow sampling sequences. The rate of change and frequency domain transformation of the pressure and flow sampling sequences are calculated to construct a feature representation space. The pressure change feature vector and flow change feature vector are extracted through adaptive mapping. Based on the water supply network topology, a node spatial location matrix is ​​constructed, and the pressure change feature vector and flow change feature vector are projected onto the node spatial location matrix to generate a feature mapping matrix between nodes. By performing multi-dimensional tensor operations on the feature mapping matrix between nodes, the pressure change feature vector, and the flow change feature vector, a combination of node pressure and flow features is constructed, and the pressure and flow feature matrix is ​​output.

[0007] Time-series dimensionality reduction is performed based on the pressure-flow feature matrix. Singular value decomposition is used to extract time-dimensional features, and an optimized feature vector is constructed, including: The pressure-flow characteristic matrix is ​​segmented and slid along the time dimension to calculate the pressure-flow variation characteristics in each time segment and generate a time-series characteristic component matrix. Singular value decomposition is performed on the temporal feature component matrix to generate a sequence of eigenvalues ​​and eigenvalue decomposition vectors. The contribution rate of the eigenvalue sequence is calculated. A screening threshold is set according to the contribution rate to screen the eigenvalue decomposition vectors. The screened eigenvalue decomposition vectors are then used to construct a low-dimensional temporal feature space. The time-series feature component matrix is ​​projected onto a low-dimensional time feature space, the feature projection weights are calculated, and a pressure-flow mapping matrix is ​​generated. Based on the topological data of the water supply network, the pressure-flow mapping matrix is ​​spatially reconstructed and combined with the low-dimensional time feature space to construct an optimized feature vector.

[0008] The optimized feature vectors are input into a pre-constructed variable-structure deep neural network. The network parameters are adjusted based on the loss function calculation results for training, generating a stress prediction model including: A basic network layer is constructed based on the topology of the water supply network. The basic network layer includes an input layer, an intermediate layer, and an output layer. Dynamic variable connection units are set between each layer. The dynamic variable connection units include network parameters, forming a variable structure deep neural network. The optimized feature vector is mapped hierarchically according to the water supply network topology. The network parameter adjustment amount is calculated based on the pressure spatiotemporal distribution characteristics in the optimized feature vector. The network parameters in the dynamic variable connection unit are updated based on the network parameter adjustment amount. The optimized feature vectors are divided into batches to obtain training batches, and the training batches are subjected to feature normalization processing to obtain normalized feature vectors. The normalized feature vector is input into a variable structure deep neural network for forward propagation calculation to obtain the predicted pressure value; Construct a loss function, calculate the loss value between the predicted pressure value and the historical pressure value, and adjust the network parameters in the dynamic variable connection unit according to the loss value; Repeat the iteration until the loss value is less than the preset convergence threshold, and then determine the converged variable structure deep neural network as the stress prediction model.

[0009] Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers, including: Flow data at adjacent time points are obtained from the pressure-flow characteristic matrix, and the change in flow rate at adjacent time points is calculated through differential operation; A flow rate change sequence is constructed based on the flow rate change, and the flow rate change trend is obtained by calculating the ratio of the positive change rate to the negative change rate in the flow rate change sequence. A time-series mapping is performed on the flow rate change trend to generate a flow rate change trend time distribution curve. The change amplitude in the flow rate change trend time distribution curve is calculated, and the point of maximum change is determined as the peak water consumption point based on the change amplitude. The peak water usage density value is obtained by statistically analyzing the distribution density of peak water usage points on the time axis. The time range in which the peak water usage density value is greater than a preset density threshold is determined as the peak water usage period. Generate peak water usage period identifiers, and mark the locations of peak water usage periods as peak identifiers and the locations of non-peak water usage periods as non-peak identifiers in the peak water usage period identifiers; Based on the peak water usage period identifier, extract the peak period data corresponding to the peak period identifier from the optimized feature vector to form the peak interval feature vector.

[0010] Based on the feature vectors of peak periods, a spatial topology graph of pressure propagation is constructed. The correlation degree of pressure propagation delay between nodes is calculated, and correction coefficients for peak periods are generated, including: Extract node pressure propagation data and node physical connection relationships from the feature vector of the peak interval, and calculate the pressure propagation direction and pressure propagation intensity between nodes; A pressure propagation connection matrix is ​​constructed based on the pressure propagation direction and pressure propagation intensity between nodes, and a pressure propagation spatial topology map is generated based on the pressure propagation connection matrix. In the pressure propagation spatial topology map, the pressure propagation change between nodes is identified, the main pressure propagation path is determined based on the pressure propagation change between nodes, and the pressure propagation delay is obtained by calculating the pressure propagation response time of adjacent nodes along the main pressure propagation path. The pressure propagation delay is arranged according to the time series to generate a pressure propagation response sequence. The pressure fluctuation transmission law in the pressure propagation response sequence is calculated, and the pressure propagation delay correlation degree is obtained based on the pressure fluctuation transmission law. The cumulative impact of node pressure is calculated based on the correlation of pressure propagation delay, and a peak period correction coefficient is generated based on the cumulative impact of node pressure.

[0011] The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the peak period correction coefficient. Combined with the topology data, the dynamic pressure prediction results of each node of the water supply network are generated, including: The peak interval feature vector is divided into data according to the time window to obtain the prediction sequence. The prediction sequence is normalized to obtain the prediction data. The prediction data is input into the pressure prediction model to obtain the initial pressure prediction value. The node pressure correction amount is calculated based on the peak period correction coefficient, and the node pressure correction amount is superimposed with the initial pressure prediction value to obtain the corrected prediction value. Extract the spatial location and connection relationship of nodes from the topology data, construct the pressure propagation influence coefficient matrix between nodes, and calculate the pressure propagation attenuation based on the pressure propagation influence coefficient matrix. The corrected predicted value is combined with the pressure propagation attenuation to calculate the dynamic pressure prediction results for each node of the water supply network.

[0012] This invention provides a system for dynamic prediction and analysis of water supply network node pressure, the system comprising: The data acquisition module is used to acquire topology data, historical pressure time series data, and flow time series data of the water supply network. The feature analysis module is used to perform multi-dimensional analysis on historical pressure time series data and flow time series data, calculate the pressure and flow change characteristics, and generate a pressure and flow feature matrix. The dimensionality reduction module is used to perform time-series dimensionality reduction based on the pressure-flow feature matrix. It extracts time-dimensional features through singular value decomposition and constructs an optimized feature vector. The model training module is used to input optimized feature vectors into a pre-built variable structure deep neural network, adjust the network parameters through the loss function calculation results, and generate a stress prediction model. Peak identification module is used to analyze the flow change trend in the pressure and flow feature matrix, identify the peak water use period identifier, and divide the optimized feature vector into peak interval feature vector according to the peak period identifier. The correction coefficient generation module is used to construct a pressure propagation spatial topology map based on the feature vector of the peak interval, calculate the correlation degree of pressure propagation delay between nodes, and generate the correction coefficient for the peak period. The pressure prediction module is used to input the peak interval feature vector into the pressure prediction model to obtain the initial pressure prediction value, correct the initial pressure prediction value according to the peak period correction coefficient, and generate the dynamic pressure prediction results of each node of the water supply network by combining the topology data.

[0013] One technical solution provided in this embodiment of the invention is an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in any of the aforementioned methods.

[0014] One technical solution provided in this embodiment of the invention is a computer-readable storage medium storing computer program instructions, which, when executed by a processor, implement the steps in any of the aforementioned methods.

[0015] This invention effectively extracts key features from pressure and flow data through multi-dimensional analysis and time-series dimensionality reduction, reducing data redundancy and improving computational efficiency. The use of a variable-structure deep neural network adaptively adjusts the network structure, enhancing the model's ability to fit complex pressure changes. By identifying peak periods and constructing a pressure propagation spatial topology map, the pressure propagation characteristics between nodes are accurately characterized, improving prediction accuracy during peak periods. The prediction results are further optimized by combining correction coefficients generated from time-delay correlation, further improving accuracy. This method fully considers the pressure propagation relationships between nodes in the water supply network, achieving accurate prediction of dynamic changes in network pressure and providing reliable technical support for the intelligent operation and management of water supply networks. Attached Figure Description

[0016] Figure 1 A flowchart of a method for dynamic prediction and analysis of water supply network node pressure provided in an embodiment of the present invention; Figure 2 This is a flowchart illustrating the generation process of peak-period correction coefficients based on node pressure propagation in an embodiment of the present invention. Detailed Implementation

[0017] like Figure 1 As shown, Figure 1 This is a flowchart of a method for dynamic prediction and analysis of water supply network node pressure provided in an embodiment of the present invention. The method includes the following steps: Obtain topology data, historical pressure time-series data, and flow time-series data of the water supply network; Multi-dimensional analysis is performed on historical pressure time-series data and flow time-series data to calculate pressure and flow variation characteristics and generate a pressure and flow feature matrix. Time-series dimensionality reduction is performed based on the pressure-flow feature matrix, and time-dimensional features are extracted through singular value decomposition to construct an optimized feature vector; The optimized feature vector is input into a pre-constructed variable structure deep neural network. The network parameters are adjusted based on the loss function calculation results to train the model and generate a stress prediction model. Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers. Based on the feature vectors of the peak interval, a pressure propagation spatial topology map is constructed, the correlation degree of pressure propagation delay between nodes is calculated, and a correction coefficient for the peak period is generated. The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the correction coefficient of the peak period. Finally, the dynamic pressure prediction results of each node of the water supply network are generated by combining the topology data.

[0018] Multi-dimensional analysis of historical pressure and flow time-series data is performed to calculate pressure-flow variation characteristics and generate a pressure-flow feature matrix, including: Historical pressure and flow time series data are divided into multiple time windows according to the water supply network topology. Segmented sampling is performed within each time window to generate pressure and flow sampling sequences. The rate of change and frequency domain transformation of the pressure and flow sampling sequences are calculated to construct a feature representation space. The pressure change feature vector and flow change feature vector are extracted through adaptive mapping. Based on the water supply network topology, a node spatial location matrix is ​​constructed, and the pressure change feature vector and flow change feature vector are projected onto the node spatial location matrix to generate a feature mapping matrix between nodes. By performing multi-dimensional tensor operations on the feature mapping matrix between nodes, the pressure change feature vector, and the flow change feature vector, a combination of node pressure and flow features is constructed, and the pressure and flow feature matrix is ​​output.

[0019] First, historical monitoring data from the water supply network is preprocessed to ensure data quality. Preprocessing includes outlier detection and correction; data points exceeding the normal range are identified using statistical indicators, and missing data are filled using nearest-nearest-value interpolation. For abrupt outliers, a moving median filter is used for smoothing while preserving the data's trend characteristics.

[0020] After data preprocessing, historical pressure and flow time-series data are divided into multiple time windows based on the water supply network topology. The division of time windows considers the periodicity of flow changes in the water supply network, generally selecting a 24-hour period as the basic cycle, and further subdividing it according to actual water usage patterns. A day can be divided into multiple time windows, such as the early morning low-water period, the morning peak water usage period, the daytime stable period, and the evening peak period. For example, historical data from a certain area's water supply network shows that peak water usage is concentrated between 7:00 and 9:00 AM and between 6:00 and 8:00 PM. Based on this, corresponding time windows can be set to accurately capture the pressure and flow variation characteristics at different times.

[0021] Within each time window, pressure and flow data are sampled in segments to generate pressure and flow sampling sequences. The sampling frequency is dynamically adjusted based on the rate of data change, increasing the sampling frequency in areas of rapid change and appropriately decreasing it in areas of stable change. An adaptive sampling algorithm is applied during the sampling process; when the rate of change in pressure or flow is detected to exceed a preset threshold, the number of sampling points in that segment is automatically increased. For a certain water supply network node, if the pressure drop rate is detected to be more than 1.5 times the normal value between 7:00 and 7:30 AM, the sampling interval for that period is shortened from the standard 5 minutes to 2 minutes to capture the characteristics of sudden pressure changes.

[0022] The generated pressure and flow sampling sequences are subjected to rate of change calculation and frequency domain transformation to construct a feature representation space. The rate of change calculation employs the time-difference method, calculating the ratio of pressure and flow changes between adjacent sampling points to the time interval to obtain the instantaneous rate of change. For long-term sequences, a multi-scale sliding window difference method is introduced to calculate short-term, medium-term, and long-term rates of change, forming a multi-level description of variation features. The frequency domain transformation uses the Fast Fourier Transform technique to convert the time-domain signal into a frequency-domain representation, extracting the periodic features of pressure and flow fluctuations.

[0023] After the feature representation space is constructed, pressure change feature vectors and flow rate change feature vectors are extracted through adaptive mapping. The adaptive mapping process uses principal component analysis (PCA) to reduce dimensionality, retaining the feature components that explain the highest proportion of variance. For feature extraction in different time windows, a dynamic weight allocation mechanism is adopted, adjusting the feature weights based on the historical probability of anomalies during that period. Pressure fluctuations at a certain pipeline node during the morning peak better reflect system stability; therefore, higher weights are assigned to the pressure change features during this period.

[0024] A node spatial location matrix is ​​constructed based on the water supply network topology. This matrix describes the spatial relationships and connectivity characteristics between nodes in the network. The construction of the node spatial location matrix considers factors such as the physical distance between nodes, pipe connections, pipe diameter, and material properties. For complex networks, a method combining adjacency matrices and weight matrices from graph theory is introduced to accurately represent the topological relationships and hydraulic connectivity between nodes.

[0025] The extracted pressure and flow rate feature vectors are projected onto the node spatial location matrix to generate a feature mapping matrix between nodes. The projection process employs a spatially weighted mapping algorithm, considering the hydraulic correlation and spatial distance attenuation effects between nodes. The feature mapping strength between adjacent nodes is inversely proportional to their spatial distance and hydraulic connectivity. For two adjacent nodes in a pipe network, if the pipe length between them is 200 meters and the pipe diameter is 300 millimeters, the feature mapping strength between them will be higher than that between nodes with smaller pipe diameters or greater distances.

[0026] Multi-dimensional tensor operations are performed on the inter-node feature mapping matrix, pressure change feature vector, and flow rate change feature vector to construct a pressure-flow rate feature combination for each node, outputting a pressure-flow rate feature matrix. The tensor operations combine high-order matrix multiplication and convolution to capture the high-order nonlinear characteristics of pressure-flow rate changes. A self-correction mechanism is introduced during the computation process to dynamically adjust the feature combination weights based on historical prediction accuracy, thereby improving the model's generalization ability.

[0027] This technical solution enables accurate dynamic prediction and comprehensive analysis of pressure at nodes in water supply networks. This method significantly improves the accuracy and real-time performance of water supply network pressure prediction, effectively identifying abnormal pressure fluctuations and potential leakage areas within the network. Through multi-dimensional feature extraction and tensor calculation, the predictive model's adaptability to complex scenarios is enhanced. This method not only improves the intelligent operation and maintenance level of water supply networks but also provides data support for network optimization design and energy consumption reduction, achieving safer, more stable, and more efficient operation of the water supply system.

[0028] Time-series dimensionality reduction is performed based on the pressure-flow feature matrix. Singular value decomposition is used to extract time-dimensional features, and an optimized feature vector is constructed, including: The pressure-flow characteristic matrix is ​​segmented and slid along the time dimension to calculate the pressure-flow variation characteristics in each time segment and generate a time-series characteristic component matrix. Singular value decomposition is performed on the temporal feature component matrix to generate a sequence of eigenvalues ​​and eigenvalue decomposition vectors. The contribution rate of the eigenvalue sequence is calculated. A screening threshold is set according to the contribution rate to screen the eigenvalue decomposition vectors. The screened eigenvalue decomposition vectors are then used to construct a low-dimensional temporal feature space. The time-series feature component matrix is ​​projected onto a low-dimensional time feature space, the feature projection weights are calculated, and a pressure-flow mapping matrix is ​​generated. Based on the topological data of the water supply network, the pressure-flow mapping matrix is ​​spatially reconstructed and combined with the low-dimensional time feature space to construct an optimized feature vector.

[0029] The pressure-flow feature matrix is ​​segmented and slid-processed along the time dimension. The pressure-flow variation characteristics within each time segment are calculated, generating a time-series feature component matrix. The window size for segmented sliding is dynamically adjusted based on the characteristics of the water supply network, typically using a 6-hour window as the baseline. The sliding step is set to 30 minutes to ensure sufficient overlap between time windows and guarantee the continuity of feature extraction. For historical data of a certain water supply network, starting from 00:00, 6 hours of data are taken as the first window, and the pressure-flow variation characteristics of each node within this window are calculated. The window then slides forward 30 minutes, taking data from 0:30 to 6:30 as the second window, and so on, until the entire time range is covered.

[0030] Within each sliding window, characteristic parameters of pressure and flow rate variation are calculated, including average value, variance, slope of the trend, and fluctuation frequency. The slope of the trend is obtained through linear fitting, reflecting the overall direction of pressure or flow rate change within that time period; the fluctuation frequency is characterized by the number of peaks and troughs in the data. For the morning peak water usage period, the pressure data at a certain node shows a significant downward trend between 6:00 and 8:00, with a negative slope and a high fluctuation frequency, indicating high and drastic water demand during this period. Conversely, during the nighttime trough period, the pressure slope at the same node is close to zero, and the fluctuation frequency is low, indicating stable water demand during this period. By calculating the characteristic parameters for all sliding windows, a time-series characteristic component matrix is ​​formed, which contains the complete variation characteristics of pressure and flow rate over time.

[0031] Singular Value Decomposition (SVD) is a powerful matrix factorization technique that decomposes an original matrix into a product of three matrices. The diagonal elements of the diagonal matrix are the singular values, representing the importance of each principal component. After performing SVD on the time-series characteristic component matrix of a water supply network, a series of singular values ​​are obtained, ordered from largest to smallest. The eigenvectors corresponding to the largest singular values ​​represent the most significant patterns of change in the data, such as the main periodic variations in daily water usage patterns; while the eigenvectors corresponding to smaller singular values ​​may represent noise or secondary patterns of change.

[0032] The contribution rate of the eigenvalue sequence is calculated based on the ratio of each eigenvalue to the sum of all eigenvalues. A screening threshold is then set based on the contribution rate to select the eigenvalue decomposition vectors. The contribution rate represents the proportion of the principal component corresponding to that eigenvalue in the original data variation. Typically, eigenvalues ​​with a cumulative contribution rate of 85% to 95% and their corresponding eigenvectors are selected. For a water supply network, the cumulative contribution rate of the top 10 eigenvalues ​​obtained from the decomposition reaches 92%, indicating that these 10 principal components already contain most of the information in the original data. Therefore, the screening threshold can be set to 92%, retaining the top 10 eigenvalue decomposition vectors. The selected eigenvalue decomposition vectors are then used to construct a low-dimensional time feature space. This space has a dimension much lower than that of the original data, but retains the main features of the data.

[0033] The time-series feature component matrix is ​​projected onto a low-dimensional time feature space, and the feature projection weights are calculated to generate a pressure-flow mapping matrix. The projection process essentially finds the optimal representation of the original high-dimensional data in the low-dimensional feature space, with the projection weights reflecting the importance of each original feature in the low-dimensional space. For the pressure data of a certain water supply network, the variation characteristics during the morning and evening peak periods receive higher projection weights in the low-dimensional space, indicating that the data from these periods contribute significantly to the overall features. The resulting pressure-flow mapping matrix is ​​a compact representation of the original data in the low-dimensional feature space, significantly reducing dimensionality while retaining key information.

[0034] Based on the topological data of the water supply network, the pressure-flow mapping matrix is ​​spatially reconstructed and combined with a low-dimensional temporal feature space to construct an optimized feature vector. The spatial reconstruction process considers the topological relationships between nodes in the water supply network, using graph theory algorithms to calculate the connection strength and hydraulic transmission characteristics between nodes. Pressure-flow changes between adjacent nodes are strongly correlated, while those between distant nodes are less correlated. According to the topology of a certain water supply network, the changes in nodes on the main pipe have a greater impact on the entire network, thus assigning them higher spatial weights; while the characteristics of the terminal nodes of branch pipes are mainly affected by local users, resulting in lower spatial weights. Combining the spatially reconstructed pressure-flow mapping matrix with the low-dimensional temporal feature space forms the final optimized feature vector. This vector includes both temporal variation features and considers the influence of the spatial topology, providing high-quality feature input for subsequent pressure prediction.

[0035] This technical solution enables effective dimensionality reduction and feature extraction of water supply network pressure and flow data, significantly improving the accuracy and efficiency of dynamic pressure prediction at water supply network nodes. By capturing the main changing patterns in the time dimension through singular value decomposition and combining this with spatial reconstruction of the network topology, a highly expressive optimized feature vector is constructed. This accurately captures the main changing patterns of water supply network pressure and flow, effectively filters out noise interference, reduces data redundancy, and improves computational efficiency.

[0036] The optimized feature vectors are input into a pre-constructed variable-structure deep neural network. The network parameters are adjusted based on the loss function calculation results for training, generating a stress prediction model including: A basic network layer is constructed based on the topology of the water supply network. The basic network layer includes an input layer, an intermediate layer, and an output layer. Dynamic variable connection units are set between each layer. The dynamic variable connection units include network parameters, forming a variable structure deep neural network. The optimized feature vector is mapped hierarchically according to the water supply network topology. The network parameter adjustment amount is calculated based on the pressure spatiotemporal distribution characteristics in the optimized feature vector. The network parameters in the dynamic variable connection unit are updated based on the network parameter adjustment amount. The optimized feature vectors are divided into batches to obtain training batches, and the training batches are subjected to feature normalization processing to obtain normalized feature vectors. The normalized feature vector is input into a variable structure deep neural network for forward propagation calculation to obtain the predicted pressure value; Construct a loss function, calculate the loss value between the predicted pressure value and the historical pressure value, and adjust the network parameters in the dynamic variable connection unit according to the loss value; Repeat the iteration until the loss value is less than the preset convergence threshold, and then determine the converged variable structure deep neural network as the stress prediction model.

[0037] A basic network layer is constructed based on the water supply network topology. This basic network layer includes an input layer, an intermediate layer, and an output layer, with dynamically variable connection units between each layer, forming a variable-structure deep neural network. The number of nodes in the input layer corresponds to the dimension of the optimized feature vector. For a water supply network with 100 nodes, the dimension of its optimized feature vector is 200, so the input layer has 200 neurons. The intermediate layer adopts a multi-layer design. Considering the complex topology of the water supply network, four intermediate layers are designed, with the number of neurons in each layer decreasing from 160 to 64, facilitating layer-by-layer feature abstraction. The number of neurons in the output layer corresponds to the prediction target. When predicting the pressure values ​​of each node in the water supply network for the next 24 hours, the number of neurons in the output layer is 100. Unlike the fixed connection structure of traditional neural networks, each dynamically variable connection unit includes weight parameters, bias parameters, and connection state parameters. The connection state parameters determine whether the connection is activated, enabling dynamic adjustment of the network structure. Initially, all connections are active. The weight parameters are randomly initialized using a normal distribution with a mean of 0 and a standard deviation of 0.1, and the initial value of the bias parameter is set to 0.01.

[0038] The optimized feature vectors are hierarchically mapped according to the water supply network topology. Network parameter adjustments are calculated based on the spatiotemporal pressure distribution characteristics of the optimized feature vectors, and the network parameters in the dynamically variable connection units are updated based on these adjustments. The hierarchical mapping process considers the physical connections of the water supply network, mapping the feature information of adjacent nodes to nearby neurons in the network, maintaining topological consistency. For the main pipelines in the water supply network, their node features are mapped to connection paths with higher weights in the network; branch pipe node features are mapped to connection paths with lower weights. The spatiotemporal pressure distribution characteristics are obtained by calculating the correlation matrix of each dimension of the optimized feature vectors. For highly correlated feature dimensions, the connection weights between them are strengthened; for feature dimensions with low correlation, the connection weights are reduced or the connection state is set to inactive. Taking a water supply network node as an example, if its pressure change is strongly correlated with upstream nodes, the connection weights between the corresponding neurons are strengthened; if it has low correlation with distant nodes, the corresponding connection is weakened or disconnected. The calculation of network parameter adjustments uses an adaptive method: for critical connections with significant impact on the network, the adjustment range is small to ensure stability; for redundant connections, the adjustment range is larger to promote network structure optimization.

[0039] The optimized feature vectors are batched to obtain training batches, and the training batches are then normalized to obtain normalized feature vectors. Batch partitioning considers temporal continuity and spatial correlation, assigning feature vectors of adjacent nodes within consecutive time periods to the same batch, enhancing the model's ability to learn local features. For historical data from the water supply network, the data is divided into 6-hour units, with each batch containing 32 samples. Feature normalization employs the maximum-minimum normalization method, unifying features of different dimensions to the 0-1 range, eliminating the influence of dimensions and improving training efficiency. For pressure features, typically ranging from 0.2 MPa to 0.6 MPa, normalization converts them into dimensionless values ​​of 0-1; flow characteristics undergo similar processing. Normalization parameters are determined based on the statistical characteristics of the training set and applied to subsequent validation and test sets to ensure consistency.

[0040] Normalized feature vectors are input into a variable-structure deep neural network for forward propagation to obtain predicted pressure values. The forward propagation process follows the network hierarchy, calculating layer by layer from the input layer to the output layer. In each layer, activated connections are determined based on the connection state parameters of the dynamically variable connection units. These activated connections are then weighted and summed, and the activation function is applied to obtain the layer's output. The intermediate layers use modified linear unit activation functions, which are computationally simple and effectively alleviate the gradient vanishing problem; the output layer uses a linear activation function, suitable for regression prediction tasks. During forward propagation, to address the nonlinear hydraulic characteristics in the water supply network, skip connections are added to the intermediate layers to directly transmit features from lower layers to higher layers, enhancing the model's expressive power. For pressure surges in the network, an attention mechanism unit is designed to adaptively adjust the weights of different features, improving the ability to identify anomalies.

[0041] A loss function is constructed to calculate the loss between predicted and historical pressure values. The network parameters in the dynamically variable connected units are adjusted based on this loss. The loss function uses a combination of mean squared error and regularization terms. The mean squared error term measures the difference between the predicted and actual values, while the regularization term controls model complexity and prevents overfitting. Considering the specific characteristics of water supply network pressure prediction, a time continuity penalty term is added to the loss function to penalize abrupt changes in the predicted value's time series, ensuring the smoothness and reasonableness of the prediction results. An improved backpropagation algorithm is used to adjust network parameters. The gradient of the loss function with respect to each parameter is calculated, and an optimizer with an adaptive learning rate is used to update the parameters. The initial learning rate is set to 0.001 and gradually decreased during training to ensure algorithm convergence. For updating the connection state parameters, sparsity constraints are introduced to encourage the network to form a sparse connection structure, improving computational efficiency.

[0042] The training process iterates until the loss value falls below a preset convergence threshold, at which point the converged variable-structure deep neural network is identified as the pressure prediction model. During iteration, the validation set is evaluated and the validation loss is calculated every 100 training batches. An early stopping mechanism is triggered when the validation loss fails to decrease after five consecutive evaluations to prevent overfitting. The convergence threshold is dynamically set based on the size and complexity of the water supply network, typically ranging from 1% to 5% of the initial training loss value. For example, in a medium-sized water supply network with an initial loss value of 0.15 and a convergence threshold of 0.006, the loss value drops below the threshold after approximately 5000 training batches, ending the training process. The final pressure prediction model retains the optimal parameter combination from the training process—the model parameters that perform best on the validation set—ensuring the model's generalization ability.

[0043] The proposed variable-structure deep neural network pressure prediction method significantly improves the accuracy and reliability of pressure prediction at water supply network nodes. By using dynamically variable connection units, the network structure is adaptively adjusted, effectively capturing the complex pressure variation patterns in water supply networks. It can more accurately simulate the nonlinear hydraulic characteristics of the network. This method not only reduces prediction errors but also possesses strong robustness and generalization ability, adapting to water supply networks of varying sizes and complexities, providing reliable technical support for intelligent operation and maintenance and pressure optimization control of water supply networks.

[0044] Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers, including: Flow data at adjacent time points are obtained from the pressure-flow characteristic matrix, and the change in flow rate at adjacent time points is calculated through differential operation; A flow rate change sequence is constructed based on the flow rate change, and the flow rate change trend is obtained by calculating the ratio of the positive change rate to the negative change rate in the flow rate change sequence. A time-series mapping is performed on the flow rate change trend to generate a flow rate change trend time distribution curve. The change amplitude in the flow rate change trend time distribution curve is calculated, and the point of maximum change is determined as the peak water consumption point based on the change amplitude. The peak water usage density value is obtained by statistically analyzing the distribution density of peak water usage points on the time axis. The time range in which the peak water usage density value is greater than a preset density threshold is determined as the peak water usage period. Generate peak water usage period identifiers, and mark the locations of peak water usage periods as peak identifiers and the locations of non-peak water usage periods as non-peak identifiers in the peak water usage period identifiers; Based on the peak water usage period identifier, extract the peak period data corresponding to the peak period identifier from the optimized feature vector to form the peak interval feature vector.

[0045] The pressure-flow characteristic matrix stores pressure and flow data for each node in the water supply network at different times, arranged in chronological order. The flow data portion is extracted, and time-series difference operations are performed on each node to obtain a sequence of flow changes. Flow values ​​at adjacent times are obtained, and the difference between the flow values ​​at subsequent times and those at previous times is calculated. The sampling interval is typically set to 15 or 30 minutes to balance data granularity and computational complexity. For a node on the main pipeline of a certain water supply network, its flow data changes from 200 m³ / h in the early morning within a 24-hour period. 3 / h gradually rose to 600m at 8:00 AM 3 / h, then the fluctuation decreased to 300m at 16:00. 3 / h, rising again to 550m in the evening. 3The flow rate is measured in cubic meters per hour, eventually reaching its lowest point at night. By using differential calculations, the sequence of flow rate changes at each time point can be obtained; for example, the flow rate change between 3 AM and 4 AM is 20 m³ / h. 3 / h, while the flow rate changes by 80m between 7 am and 8 am. 3 / h reflects the differences in water demand at different times.

[0046] The rate of change of flow is defined as the amount of change in flow per unit time, characterizing how quickly the flow changes. Dividing the flow change at adjacent moments by the time interval yields the rate of change at that corresponding moment. The rate of change is categorized as positive or negative, with positive indicating an increase in flow and negative indicating a decrease. Within each fixed time window, the absolute values ​​of the cumulative positive and negative rates of change are calculated, and their ratio forms a flow trend indicator. An indicator greater than 1 indicates an overall upward trend in flow within that time window, less than 1 indicates an overall downward trend, and close to 1 indicates frequent fluctuations but relatively small overall changes. The time window is typically set to 1 hour, with a sliding step of 15 minutes. For the aforementioned node, within the time window from 6:00 AM to 8:00 AM, the cumulative positive rate of change is 160 m³ / s. 3 / h, the cumulative absolute value of the negative rate of change is 40m 3 The ratio of 4 / h indicates that water demand is growing rapidly during this period; while in the time window from 10 am to 12 pm, the ratio is close to 0.5, indicating that water demand is beginning to decline.

[0047] A time-series mapping process is performed to generate a time distribution curve of the flow rate change trend. The amplitude of the change in the time distribution curve is calculated, and the point of maximum change is determined as the peak water consumption point. The time-series mapping process maps the flow rate change trend index onto a 24-hour time axis, forming a continuous time distribution curve. This curve is smoothed using a moving average method to eliminate the impact of short-term fluctuations, with a window size typically of three time points. The amplitude of the smoothed curve at each time point is calculated, i.e., the absolute value of the curve's slope, representing the severity of the flow rate change. The amplitudes are sorted, and the top 20% are selected as the candidate set for the point of maximum change. From the candidate set, local maxima are selected, i.e., the points with the largest amplitude within a range of three time points before and after the peak water consumption point, which are then determined as the peak water consumption point. For typical residential water supply networks, the points of maximum change usually occur at 6:30 AM, 7:15 AM, 6:00 PM, and 6:45 PM, corresponding to concentrated water consumption activities by residents, resulting in rapid flow rate changes.

[0048] Peak water usage density values ​​are obtained by statistically analyzing the distribution density of peak water usage points along the time axis. The time range where the peak water usage density value exceeds a preset density threshold is defined as the peak water usage period. The kernel density estimation method is used to calculate the distribution density of peak water usage points along the time axis. A Gaussian kernel function is selected, and the bandwidth parameter is adaptively adjusted according to the data distribution, typically ranging from 0.5 hours to 1 hour. For each time point, the weighted cumulative contribution of surrounding peak points is calculated to obtain the peak water usage density value for that time point. The preset density threshold is determined based on the actual characteristics of the water supply network, usually set at 50% of the maximum density value. The time period continuously exceeding the density threshold is defined as the peak water usage period. For the aforementioned network, statistical calculations show two main peak water usage periods: 6:00 AM to 9:00 AM and 5:30 PM to 8:30 PM, which closely match residents' daily routines. In some commercial areas, a peak water usage period may also occur from 11:30 AM to 1:30 PM, indicating that different functional areas have different water usage patterns.

[0049] Peak water usage period identifiers are generated, marking peak water usage periods as peak indicators and non-peak water usage periods as non-peak indicators. These peak water usage period identifiers are represented as binary sequences, corresponding to each time point on the time axis. For a given peak water usage period, it is marked with "1" to indicate a peak indicator; other periods are marked with "0" to indicate a non-peak indicator. To enhance the stability of the identifiers, morphological processing is performed on the identifier sequence, including filling isolated non-peak points and removing isolated peak points. When three or more consecutive time points are marked as peak indicators, with one non-peak indicator in between, that point is also changed to a peak indicator; when a single point is marked as a peak indicator, and the two points before and after it are non-peak indicators, that point is changed to a non-peak indicator. This processing ensures the continuity and integrity of peak periods. For the actual water supply network, the peak indicator sequence exhibits a clear two-peak characteristic within a 24-hour cycle, corresponding to morning and evening peaks respectively.

[0050] The optimized feature vector contains complete information on the pressure and flow characteristics of water supply network nodes over time. Based on the generated peak water usage period identifiers, feature data corresponding to the time points marked as peak periods are selected and combined chronologically to form a peak interval feature vector. This peak interval feature vector retains all feature information from peak water usage periods and is a key input for peak-period pressure prediction. If the original optimized feature vector contains feature data from 96 time points, after peak period filtering, the peak interval feature vector may only contain data from 28 time points, significantly reducing the data volume while retaining the feature information of key periods. For the optimized feature vector of the aforementioned network, feature data from two time periods—6:00 AM to 9:00 AM and 5:30 PM to 8:30 PM—are extracted to form the peak interval feature vector, which specifically describes the pressure and flow characteristics during peak water usage periods.

[0051] This invention accurately captures flow rate variation patterns through differential operations and rate of change analysis; it scientifically defines peak water usage periods using kernel density estimation; and it optimizes peak period identifiers based on morphological processing to ensure the rationality of peak period division. It not only accurately identifies peak water usage characteristics in different functional areas but also adapts to seasonal changes and differences in water usage patterns on special dates. The resulting peak period feature vector focuses on data from key time periods, avoiding interference from off-peak data, improving the specificity of feature expression, and laying the foundation for accurate peak-period pressure prediction.

[0052] like Figure 2 As shown, a spatial topology map of pressure propagation is constructed based on the feature vectors of peak intervals. The correlation degree of pressure propagation delay between nodes is calculated, and correction coefficients for peak periods are generated, including: Extract node pressure propagation data and node physical connection relationships from the feature vector of the peak interval, and calculate the pressure propagation direction and pressure propagation intensity between nodes; A pressure propagation connection matrix is ​​constructed based on the pressure propagation direction and pressure propagation intensity between nodes, and a pressure propagation spatial topology map is generated based on the pressure propagation connection matrix. In the pressure propagation spatial topology map, the pressure propagation change between nodes is identified, the main pressure propagation path is determined based on the pressure propagation change between nodes, and the pressure propagation delay is obtained by calculating the pressure propagation response time of adjacent nodes along the main pressure propagation path. The pressure propagation delay is arranged according to the time series to generate a pressure propagation response sequence. The pressure fluctuation transmission law in the pressure propagation response sequence is calculated, and the pressure propagation delay correlation degree is obtained based on the pressure fluctuation transmission law. The cumulative impact of node pressure is calculated based on the correlation of pressure propagation delay, and a peak period correction coefficient is generated based on the cumulative impact of node pressure.

[0053] The peak-period feature vector contains pressure and flow data for each node during peak water usage periods, as well as physical connection information between nodes. The pressure propagation direction is determined by analyzing the sequence of pressure changes at consecutive time points between adjacent nodes. When the pressure change at the upstream node precedes that at the downstream node, the pressure propagation direction is determined to be from upstream to downstream. For two adjacent nodes A and B in a water supply network, if a pressure change at node A at time t causes a corresponding pressure change at node B at time t+1, the pressure propagation direction is determined to be from A to B. The pressure propagation intensity is quantified by calculating the correlation between pressure changes between adjacent nodes, reflecting the degree of influence of pressure fluctuations transmitted from one node to another. Pressure time-series data of nodes during peak periods are selected, and the correlation coefficient of pressure changes between nodes is calculated using the sliding time window method. The window size is generally set to 30 minutes, and the sliding step size is 5 minutes. For a main pipeline node and a branch pipeline node in a certain network, the calculated pressure propagation intensity value is 0.85, indicating that pressure changes in the main pipeline have a strong impact on the branch pipeline node.

[0054] A pressure propagation connection matrix is ​​constructed based on the pressure propagation direction and intensity between nodes, and a pressure propagation spatial topology map is generated based on this matrix. The pressure propagation connection matrix is ​​a two-dimensional matrix, where row and column indices correspond to node numbers in the water supply network, and matrix elements represent the pressure propagation relationship between corresponding node pairs. Matrix element values ​​are determined by both the pressure propagation direction and intensity; positive values ​​indicate pressure propagation from the row-indexed node to the column-indexed node, negative values ​​indicate the opposite direction, and the magnitude of the value represents the propagation intensity. For node pairs without a direct pressure propagation relationship, matrix elements are set to zero. During the construction process, connections with pressure propagation intensities below a threshold are considered noise and set to zero; the threshold is typically set to 0.2. Based on the constructed pressure propagation connection matrix, a pressure propagation spatial topology map is generated using graphical visualization techniques. Nodes represent physical nodes in the water supply network, edges represent pressure propagation paths between nodes, the direction of the edges corresponds to the pressure propagation direction, and the thickness or color intensity of the edges represents the pressure propagation intensity.

[0055] The pressure propagation spatial topology map identifies pressure propagation changes between nodes, determines the main pressure propagation path based on these changes, and calculates the pressure propagation response time of adjacent nodes along the main path to obtain the pressure propagation delay. The pressure propagation change is defined as the magnitude of pressure transmission change between adjacent nodes per unit time, obtained by calculating the rate of change of pressure difference between node pairs within a continuous time window. For pressure fluctuations during peak periods, a pressure change detection threshold is set; when a pressure change exceeds the threshold, it is recorded as a valid pressure propagation event. For a typical water supply network, the pressure change detection threshold is set to 0.05 MPa. The edges in the pressure propagation spatial topology map are sorted according to the magnitude of the pressure propagation change, and the top 30% of edges with the largest propagation changes form the main pressure propagation path network. Along the main pressure propagation path, the propagation time of pressure fluctuations between adjacent nodes is calculated; that is, the time required from a significant pressure change at an upstream node to the downstream node detecting the corresponding change, defined as the pressure propagation delay. For a specific main path in a water supply network, the starting node experiences a pressure drop at 6:30 AM during the morning peak, the intermediate node detects the corresponding change at 6:32 AM, and the terminal node detects the change at 6:35 AM. Based on this, the pressure propagation delays between adjacent nodes are calculated to be 2 minutes and 3 minutes, respectively.

[0056] Pressure propagation delays are arranged in a time series to generate pressure propagation response sequences. The pressure fluctuation transmission pattern within these sequences is calculated, and the pressure propagation delay correlation is derived based on this pattern. The pressure propagation response sequence is formed by arranging the nodes along the main pressure propagation path in chronological order of pressure fluctuation propagation. For each significant pressure fluctuation event, the cumulative time required for the fluctuation to propagate from the source point to each node is recorded, forming a pressure propagation response sequence. Statistical analysis is performed on these sequences to calculate the mean, variance, and distribution characteristics of the response time at each node, extracting the pressure fluctuation transmission pattern. This pattern includes three aspects: fluctuation propagation speed, attenuation characteristics, and path dependence. Based on the extracted pressure fluctuation transmission pattern, the pressure propagation delay correlation between nodes is calculated, representing the strength of the temporal correlation between pressure changes between nodes. The correlation calculation considers the stability and consistency of the propagation delay, and normalization maps the correlation value to between 0 and 1; a larger value indicates a stronger correlation. For two adjacent nodes on a main pipeline in a water supply network, the pressure propagation delay correlation is 0.92, indicating a high correlation and stable time delay between the pressure changes of the two nodes.

[0057] The cumulative impact of node pressure is calculated based on the correlation of pressure propagation delay, and a peak-period correction coefficient is generated based on this impact. The cumulative impact of node pressure is defined as the cumulative effect of pressure changes on a node from all other nodes in the network, considering the importance of the influencing source, propagation path, and time delay. During calculation, for each node, all its upstream nodes are traced back along the main pressure propagation path. The influence contribution of each upstream node is calculated based on the correlation of pressure propagation delay and path length, and the total impact is obtained by summing these contributions. A distance attenuation factor is introduced into the impact calculation to reduce the influence of distant nodes as the propagation distance increases. For terminal nodes in the water supply network, the cumulative impact of pressure is relatively high, indicating that their pressure status is easily affected by the combined influence of multiple upstream nodes. Based on the cumulative impact of node pressure, a peak-period correction coefficient is generated to adjust the prediction weights of different nodes during peak periods in the pressure prediction model. The correction coefficient calculation incorporates a time-period characteristic factor to consider the differences in characteristics between different peak periods. The correction coefficients for morning and evening peak periods differ, reflecting the differences in water usage behavior and pressure propagation characteristics at different times. For a critical node in a certain pipeline network, the morning peak correction factor is 1.25 and the evening peak correction factor is 1.15, indicating that the node is more significantly affected by network pressure fluctuations during the morning peak period.

[0058] This invention proposes a peak-period correction method based on pressure propagation spatial topology analysis, enabling in-depth analysis and precise characterization of the dynamic changes in pressure at water supply network nodes. By constructing a pressure propagation spatial topology map, the propagation paths and intensity relationships of pressure fluctuations between nodes are visually displayed. By identifying the main pressure propagation path and calculating the propagation delay, the propagation speed and spatiotemporal distribution characteristics of pressure fluctuations in the network are revealed. By generating peak-period correction coefficients, the sensitivity and adaptability of the prediction model during peak periods are effectively adjusted. By introducing the concept of cumulative influence, a comprehensive quantification of factors affecting node pressure is achieved, improving the accuracy and reliability of the prediction model under complex operating conditions, and providing strong support for intelligent scheduling and anomaly identification of water supply networks.

[0059] The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the peak period correction coefficient. Combined with the topology data, the dynamic pressure prediction results of each node of the water supply network are generated, including: The peak interval feature vector is divided into data according to the time window to obtain the prediction sequence. The prediction sequence is normalized to obtain the prediction data. The prediction data is input into the pressure prediction model to obtain the initial pressure prediction value. The node pressure correction amount is calculated based on the peak period correction coefficient, and the node pressure correction amount is superimposed with the initial pressure prediction value to obtain the corrected prediction value. Extract the spatial location and connection relationship of nodes from the topology data, construct the pressure propagation influence coefficient matrix between nodes, and calculate the pressure propagation attenuation based on the pressure propagation influence coefficient matrix. The corrected predicted value is combined with the pressure propagation attenuation to calculate the dynamic pressure prediction results for each node of the water supply network.

[0060] The peak-hour feature vector refers to a dataset composed of node pressure, flow rate data, and network topology information collected during peak water usage periods in a water supply network. Dividing the data into time windows is to capture short-term pressure variation characteristics within peak periods. A sliding window technique is typically used, with a window size of 30 minutes and a sliding step of 5 minutes. For a given water supply network's peak-hour feature vector, which includes node pressure and flow rate data for two peak periods—6:00-8:00 AM and 6:00-8:00 PM—multiple prediction sequences are obtained through a 30-minute sliding window. These prediction sequences are then normalized to eliminate the influence of different units and improve the generalization ability of the prediction model. The normalization process uses a maximum-minimum normalization method, mapping each feature value to a range between 0 and 1. For the pressure data of a node in the water supply network during the morning peak period, the original value range is 0.3 MPa to 0.45 MPa, which is mapped to a value between 0 and 1 after normalization. Normalized forecast data is input into a pressure prediction model, which is built on a recurrent neural network and includes an input layer, multiple hidden layers, and an output layer. This model is capable of capturing long-term and short-term dependencies in time-series data. The model input consists of normalized historical pressure and flow data of nodes, along with time characteristics. The output is the predicted pressure value of the node for future periods. For a key node in a water supply network, given its pressure and flow data from the previous 30 minutes, the model predicts the pressure change trend of that node over the next 15 minutes, yielding an initial pressure prediction value of 0.38 MPa.

[0061] The peak-hour correction factor is derived from pressure propagation spatial topology analysis, reflecting the degree to which different nodes are affected by network pressure fluctuations during peak hours. The node pressure correction is calculated by multiplying the peak-hour correction factor by a baseline correction value, taking into account specific water usage patterns and pressure fluctuation characteristics during peak hours. The baseline correction value is determined based on historical data statistical analysis, reflecting the pressure difference between peak and normal periods. For areas in the water supply network with high morning peak usage, the node correction factor is higher. For example, the morning peak correction factor for a certain residential area node is 1.25, the baseline correction value is 0.05 MPa, and the calculated node pressure correction is 0.0625 MPa. The calculated node pressure correction is then superimposed on the initial pressure prediction value to obtain the corrected prediction value. For the aforementioned residential area node, the initial pressure prediction value is 0.38 MPa; after superimposing the pressure correction of 0.0625 MPa, the corrected prediction value is 0.3175 MPa, more accurately reflecting the actual pressure status of the node during peak hours.

[0062] The topology data includes the spatial coordinates, connection relationships, and pipe parameter information of each node in the water supply network. Node spatial locations are represented by three-dimensional coordinates, node connection relationships record the direct connection status between nodes, and pipe parameters include pipe diameter, length, and roughness. For a specific water supply network, spatial location data for 100 nodes and 150 connection relationships between nodes were extracted. Based on the extracted node spatial locations and connection relationships, a pressure propagation influence coefficient matrix between nodes was constructed. This matrix is ​​a symmetric matrix, with row and column indices corresponding to node numbers, and matrix elements representing the degree of pressure propagation influence between corresponding node pairs. The influence coefficient calculation considers the physical distance between nodes, pipe characteristics, and network structure features; the closer the node pair, the larger the pipe diameter, and the more direct the connection, the greater its influence coefficient. The constructed influence coefficient matrix reflects the pressure propagation characteristics of the entire water supply network, providing a basis for subsequent calculations of pressure propagation attenuation. Pressure propagation attenuation represents the loss of pressure during the propagation from one node to another, and its calculation considers the influence coefficient, propagation distance, and network load status. For two nodes that are far apart in a water supply network, the pressure propagation attenuation is relatively large, such as 0.1 MPa between the main pipe and the terminal pipe; while for adjacent nodes, the attenuation is usually small, possibly only 0.01-0.02 MPa.

[0063] The dynamic pressure prediction results for each node in the water supply network are generated by combining the corrected predicted value with the pressure propagation attenuation. This combined calculation uses the corrected predicted value as a basis and adjusts it according to the pressure propagation attenuation to obtain a more realistic dynamic pressure prediction result. The calculation process considers the node's location in the network, the pressure status of upstream nodes, and their influence on the current node. For each node in the water supply network, the set of upstream influencing nodes is determined, the pressure attenuation from each upstream node to the current node is calculated, and combined with the corrected predicted value of the current node, the final dynamic pressure prediction result is obtained. For a terminal node in a residential area, its corrected predicted value is 0.3175 MPa. After considering the pressure propagation attenuation of 0.02 MPa from the upstream main pipe node, the final dynamic pressure prediction result is 0.2975 MPa. The generated dynamic pressure prediction results not only reflect the pressure variation characteristics unique to peak hours but also consider the influence of network topology on pressure propagation, making the prediction results more accurate and reliable.

[0064] This invention achieves accurate prediction of pressure at nodes in water supply networks by introducing peak-hour correction coefficients and pressure propagation influence coefficient matrices. This method fully considers water usage characteristics and pressure propagation patterns during peak hours, making targeted optimizations and adjustments to traditional prediction models, significantly improving prediction accuracy. By comprehensively considering pressure correction and propagation attenuation, it effectively captures the dynamic pressure change characteristics in water supply networks, solving the problem of large prediction deviations during peak hours in traditional methods.

[0065] The water supply network node pressure dynamic prediction and analysis system provided in this embodiment of the invention includes: The data acquisition module is used to acquire topology data, historical pressure time series data, and flow time series data of the water supply network. The feature analysis module is used to perform multi-dimensional analysis on historical pressure time series data and flow time series data, calculate the pressure and flow change characteristics, and generate a pressure and flow feature matrix. The dimensionality reduction module is used to perform time-series dimensionality reduction based on the pressure-flow feature matrix. It extracts time-dimensional features through singular value decomposition and constructs an optimized feature vector. The model training module is used to input optimized feature vectors into a pre-built variable structure deep neural network, adjust the network parameters through the loss function calculation results, and generate a stress prediction model. Peak identification module is used to analyze the flow change trend in the pressure and flow feature matrix, identify the peak water use period identifier, and divide the optimized feature vector into peak interval feature vector according to the peak period identifier. The correction coefficient generation module is used to construct a pressure propagation spatial topology map based on the feature vector of the peak interval, calculate the correlation degree of pressure propagation delay between nodes, and generate the correction coefficient for the peak period. The pressure prediction module is used to input the peak interval feature vector into the pressure prediction model to obtain the initial pressure prediction value, correct the initial pressure prediction value according to the peak period correction coefficient, and generate the dynamic pressure prediction results of each node of the water supply network by combining the topology data.

[0066] One technical solution provided in this embodiment of the invention is an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps in any of the aforementioned methods.

[0067] One technical solution provided in this embodiment of the invention is a computer-readable storage medium storing a computer program, wherein the processor executes the computer program to implement the steps in any of the aforementioned methods.

[0068] The specific embodiments described above are preferred embodiments of the present invention and are not intended to limit the specific scope of the present invention. The scope of the present invention includes, but is not limited to, these specific embodiments. All equivalent changes made in accordance with the shape and structure of the present invention are within the protection scope of the present invention.

Claims

1. A method for dynamic prediction and analysis of pressure at nodes in a water supply network, characterized in that, Includes the following steps: Obtain topology data, historical pressure time-series data, and flow time-series data of the water supply network; Multi-dimensional analysis is performed on historical pressure time-series data and flow time-series data to calculate pressure and flow variation characteristics and generate a pressure and flow feature matrix. Time-series dimensionality reduction is performed based on the pressure-flow feature matrix, and time-dimensional features are extracted through singular value decomposition to construct an optimized feature vector; The optimized feature vector is input into a pre-constructed variable structure deep neural network. The network parameters are adjusted based on the loss function calculation results to train the model and generate a stress prediction model. Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers. Based on the feature vectors of the peak interval, a pressure propagation spatial topology map is constructed, the correlation degree of pressure propagation delay between nodes is calculated, and a correction coefficient for the peak period is generated. The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the correction coefficient of the peak period. Finally, the dynamic pressure prediction results of each node of the water supply network are generated by combining the topology data.

2. The method according to claim 1, characterized in that, Multi-dimensional analysis of historical pressure and flow time-series data is performed to calculate pressure and flow variation characteristics, generating a pressure and flow feature matrix, including: Historical pressure and flow time series data are divided into multiple time windows according to the water supply network topology. Segmented sampling is performed within each time window to generate pressure and flow sampling sequences. The rate of change and frequency domain transformation of the pressure and flow sampling sequences are calculated to construct a feature representation space. The pressure change feature vector and flow change feature vector are extracted through adaptive mapping. Based on the water supply network topology, a node spatial location matrix is ​​constructed, and the pressure change feature vector and flow change feature vector are projected onto the node spatial location matrix to generate a feature mapping matrix between nodes. By performing multi-dimensional tensor operations on the feature mapping matrix between nodes, the pressure change feature vector, and the flow change feature vector, a combination of node pressure and flow features is constructed, and the pressure and flow feature matrix is ​​output.

3. The method according to claim 1, characterized in that, Time-series dimensionality reduction is performed based on the pressure-flow feature matrix. Singular value decomposition is used to extract time-dimensional features, and an optimized feature vector is constructed, including: The pressure-flow characteristic matrix is ​​segmented and slid along the time dimension to calculate the pressure-flow variation characteristics within each time segment and generate a time-series characteristic component matrix. Singular value decomposition is performed on the temporal feature component matrix to generate a sequence of eigenvalues ​​and eigenvalue decomposition vectors. The contribution rate of the eigenvalue sequence is calculated. A screening threshold is set according to the contribution rate to screen the eigenvalue decomposition vectors. The screened eigenvalue decomposition vectors are then used to construct a low-dimensional temporal feature space. The time-series feature component matrix is ​​projected onto a low-dimensional time feature space, the feature projection weights are calculated, and a pressure-flow mapping matrix is ​​generated. Based on the topological data of the water supply network, the pressure-flow mapping matrix is ​​spatially reconstructed and combined with the low-dimensional time feature space to construct an optimized feature vector.

4. The method according to claim 1, characterized in that, The optimized feature vectors are input into a pre-constructed variable-structure deep neural network. The network parameters are adjusted based on the loss function calculation results for training, generating a stress prediction model including: A basic network layer is constructed based on the topology of the water supply network. The basic network layer includes an input layer, an intermediate layer, and an output layer. Dynamic variable connection units are set between each layer. The dynamic variable connection units include network parameters, forming a variable structure deep neural network. The optimized feature vector is mapped hierarchically according to the water supply network topology. The network parameter adjustment amount is calculated based on the pressure spatiotemporal distribution characteristics in the optimized feature vector. The network parameters in the dynamic variable connection unit are updated based on the network parameter adjustment amount. The optimized feature vectors are divided into batches to obtain training batches, and the training batches are subjected to feature normalization processing to obtain normalized feature vectors. The normalized feature vector is input into a variable structure deep neural network for forward propagation calculation to obtain the predicted pressure value; Construct a loss function, calculate the loss value between the predicted pressure value and the historical pressure value, and adjust the network parameters in the dynamic variable connection unit according to the loss value; Repeat the iteration until the loss value is less than the preset convergence threshold, and then determine the converged variable structure deep neural network as the stress prediction model.

5. The method according to claim 1, characterized in that, Analyze the flow rate change trend in the pressure-flow characteristic matrix, identify peak water usage periods, and divide the optimized feature vector into peak interval feature vectors according to the peak period identifiers, including: Flow data at adjacent time points are obtained from the pressure-flow characteristic matrix, and the change in flow rate at adjacent time points is calculated through differential operation; A flow change rate sequence is constructed based on the flow change amount, and the flow change trend is obtained by calculating the ratio of the positive change rate to the negative change rate in the flow change rate sequence. A time-series mapping is performed on the flow rate change trend to generate a flow rate change trend time distribution curve. The change amplitude in the flow rate change trend time distribution curve is calculated, and the point of maximum change is determined as the peak water consumption point based on the change amplitude. The peak water usage density value is obtained by statistically analyzing the distribution density of peak water usage points on the time axis. The time range in which the peak water usage density value is greater than a preset density threshold is determined as the peak water usage period. Generate peak water usage period identifiers, and mark the locations of peak water usage periods as peak identifiers and the locations of non-peak water usage periods as non-peak identifiers in the peak water usage period identifiers; Based on the peak water usage period identifier, extract the peak period data corresponding to the peak period identifier from the optimized feature vector to form the peak interval feature vector.

6. The method according to claim 1, characterized in that, Based on the feature vectors of peak periods, a spatial topology graph of pressure propagation is constructed. The correlation degree of pressure propagation delay between nodes is calculated, and correction coefficients for peak periods are generated, including: Extract node pressure propagation data and node physical connection relationships from the feature vector of the peak interval, and calculate the pressure propagation direction and pressure propagation intensity between nodes; A pressure propagation connection matrix is ​​constructed based on the pressure propagation direction and pressure propagation intensity between nodes, and a pressure propagation spatial topology map is generated based on the pressure propagation connection matrix. In the pressure propagation spatial topology map, the pressure propagation change between nodes is identified, the main pressure propagation path is determined based on the pressure propagation change between nodes, and the pressure propagation delay is obtained by calculating the pressure propagation response time of adjacent nodes along the main pressure propagation path. The pressure propagation delay is arranged according to the time series to generate a pressure propagation response sequence. The pressure fluctuation transmission law in the pressure propagation response sequence is calculated, and the pressure propagation delay correlation degree is obtained based on the pressure fluctuation transmission law. The cumulative impact of node pressure is calculated based on the correlation of pressure propagation delay, and a peak period correction coefficient is generated based on the cumulative impact of node pressure.

7. The method according to claim 1, characterized in that, The initial pressure prediction value is obtained by inputting the feature vector of the peak period into the pressure prediction model. The initial pressure prediction value is then corrected according to the peak period correction coefficient. Combined with the topology data, the dynamic pressure prediction results of each node of the water supply network are generated, including: The peak interval feature vector is divided into data according to the time window to obtain the prediction sequence. The prediction sequence is normalized to obtain the prediction data. The prediction data is input into the pressure prediction model to obtain the initial pressure prediction value. The node pressure correction amount is calculated based on the peak period correction coefficient, and the node pressure correction amount is superimposed with the initial pressure prediction value to obtain the corrected prediction value. Extract the spatial location and connection relationship of nodes from the topology data, construct the pressure propagation influence coefficient matrix between nodes, and calculate the pressure propagation attenuation based on the pressure propagation influence coefficient matrix. The corrected predicted value is combined with the pressure propagation attenuation to generate dynamic pressure prediction results for each node of the water supply network.

8. A dynamic prediction and analysis system for water supply network node pressure, used to implement the method described in any one of claims 1-7, characterized in that, The system includes: The data acquisition module is used to acquire topology data, historical pressure time series data, and flow time series data of the water supply network. The feature analysis module is used to perform multi-dimensional analysis on historical pressure time series data and flow time series data, calculate the pressure and flow change characteristics, and generate a pressure and flow feature matrix. The dimensionality reduction module is used to perform time-series dimensionality reduction based on the pressure-flow feature matrix. It extracts time-dimensional features through singular value decomposition and constructs an optimized feature vector. The model training module is used to input optimized feature vectors into a pre-built variable structure deep neural network, adjust the network parameters through the loss function calculation results, and generate a stress prediction model. Peak identification module is used to analyze the flow change trend in the pressure and flow feature matrix, identify the peak water use period identifier, and divide the optimized feature vector into peak interval feature vector according to the peak period identifier. The correction coefficient generation module is used to construct a pressure propagation spatial topology map based on the feature vector of the peak interval, calculate the correlation degree of pressure propagation delay between nodes, and generate the correction coefficient for the peak period. The pressure prediction module is used to input the peak interval feature vector into the pressure prediction model to obtain the initial pressure prediction value, correct the initial pressure prediction value according to the peak period correction coefficient, and generate the dynamic pressure prediction results of each node of the water supply network by combining the topology data.

9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer program instructions that, when executed by a processor, implement the steps of the method as described in any one of claims 1 to 7.

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