Water quality data prediction method and system based on topological structure evolution dynamic graph

Abstract

The invention discloses a water quality data prediction method and system based on a topological structure evolution dynamic graph. Relates to the technical field of water quality data prediction. Comprising the following steps: step 1, acquiring historical monitoring data of a water quality sensor in the water supply network and a topological structure of the water supply network to obtain dynamic graph topological data; step 2, performing node-level and feature-level mask processing on the dynamic graph topological data; 3, training a static graph topological structure encoder according to the topological data subjected to mask processing; 4, introducing a comparative learning strategy to further improve the learning ability of the graph; and 5, generating a node embedding matrix at each moment by using the graph structure learner, and inputting the node embedding matrix into a time sequence decoder model to predict the water quality attribute at the next moment. According to the method, the node attributes of different topological structures at the next moment can be predicted by using the topological structure and the node attributes at the previous moment, and even reliable prediction can be provided for newly added positions or positions without sensors.

Description

Technical Field

[0001] The present invention relates to the technical field of water quality data prediction, and more particularly to a water quality data prediction method and system based on a topological structure evolution dynamic graph. Background Art

[0002] Graph-like data structures with sensors as the perception layer are often encountered in fields such as environmental protection, water supply and drainage, and hydrology. Examples include water supply and drainage networks, and river networks. However, existing modeling methods based on static graph deep learning techniques often rely on a fixed adjacency matrix, meaning that the topology does not change over time. This modeling approach requires that the sensor layout remain constant over the entire modeling span, significantly limiting its applicability in the water environment industry. In reality, sensor damage, replacement, addition, and removal, along with changes in network topology, are common occurrences. Existing static graph neural network techniques can only retrain the model or ensure consistency in node vectors, discarding previous data and resulting in a waste of resources. Therefore, it is necessary to develop flexible models that can adapt to these situations, using the topology and node attributes of the previous moment to predict the node attributes of a different topology at the next moment. This can even provide reliable predictions for newly added locations or those without sensors.

[0003] Therefore, designing a water quality data prediction method and system based on a topological structure evolution dynamic graph is an urgent problem that needs to be solved by those skilled in the art. Summary of the Invention

[0004] In view of this, the present invention provides a water quality data prediction method and system based on a topology evolution dynamic graph, which can use the topology structure and node attributes of the previous moment to predict the node attributes of a different topology structure at the next moment, and can even provide reliable predictions for newly added locations or locations without sensors.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a water quality data prediction method based on a topological structure evolution dynamic graph, comprising:

[0006] Step 1: Obtain historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data;

[0007] Step 2: Preprocessing the dynamic graph topology data;

[0008] Step 3: Construct a water quality prediction model for the water supply network based on the preprocessed topological data;

[0009] Step 4: Optimize the discriminative ability of the water quality prediction model;

[0010] Step 5: Use the optimized water quality prediction model to predict the water quality attributes at the next moment.

[0011] Preferably, the preprocessing in step 2 includes: processing the dynamic graph topology data into a series of graphs at the same time interval, setting timestamps, converting them into static graph topology data, and normalizing the obtained adjacency matrix, node feature matrix and edge feature matrix of the timestamps.

[0012] Preferably, the step 3 of constructing a water quality prediction model for the water supply network includes: a static encoder and a time series decoder;

[0013] The static encoder selects a static coding graph topology model and constructs corresponding learning tasks and loss functions; after training, the nodes at each moment are embedded into an adjacency matrix and a node feature matrix according to the static coding graph topology model output.

[0014] Preferably, step 4 includes: introducing a self-supervised learning paradigm to train a static encoder, specifically including: introducing node-level masks and feature-level masks, performing mask processing on the node feature matrix, defining a Mask matrix, masking a node or a certain attribute of a node with a ratio p, using a static encoder to convert the input static graph topology data into an implicit representation of nodes and edges, and calculating the node reconstruction loss based on the implicit representation.

[0015] Preferably, step 4 further includes introducing a contrastive learning strategy to perform self-supervised training to enhance the static encoder's ability to discriminate node structure representations, including:

[0016] Positive and negative sample pairs are constructed. For each original image, two views are generated using data augmentation. The two views are respectively input into a static encoder with shared parameters to obtain the corresponding node embeddings. A contrastive loss function is defined and the mask loss is jointly optimized to obtain a jointly optimized static encoder. After training, the node hidden layer matrix generated by the static encoder at each moment is used as the temporal input of the temporal decoder, and the hidden layer matrix of each node is normalized.

[0017] Preferably, the temporal decoder adopts an RNN model, takes the node hidden layer matrix as input, and the calculation formula is:

[0018] O t =FC(RNN(S t-1 ,Z t )),

[0019] Among them, S t-1 is the hidden state of the previous time step, Z t is the input vector of the current time step, FC is the fully connected layer, O t is the output vector of the current time step, predicting the node attribute value of the current time step;

[0020] The calculation formula of RNN is:

[0021] s t =tanh(Ws t-1 +Ux t )

[0022] o t =Vs t

[0023] Among them, x t is the input vector of the current time step, s t is the hidden state of the current time step, o t is the output vector of the encoder node embedding at the current time step, W is the weight transfer matrix between hidden states, U is the weight matrix from input to hidden state, and V is the weight matrix from hidden state to output.

[0024] Preferably, a water quality data prediction system based on a topological structure evolution dynamic graph comprises:

[0025] Data acquisition module: obtains historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data;

[0026] Preprocessing module: preprocessing the dynamic graph topology data;

[0027] Prediction model building module: Constructs a water quality prediction model for the water supply network based on preprocessed topological data;

[0028] Optimization module: optimizes the discrimination ability of water quality prediction model;

[0029] Prediction module: Use the optimized water quality prediction model to predict the water quality properties at the next moment.

[0030] It can be seen from the above technical solution that compared with the existing technology, the present invention discloses a water quality data prediction method and system based on a topological structure evolution dynamic graph, which can use the topological structure and node attributes of the previous moment to predict the node attributes of a different topological structure at the next moment, and can even provide reliable predictions for newly added locations or locations without sensors. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are merely embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying any creative work.

[0032] Figure 1Flowchart provided for the present invention;

[0033] Figure 2 A topological structure evolution diagram provided by the present invention;

[0034] Figure 3 This is the timing decoder training diagram provided by the present invention. DETAILED DESCRIPTION

[0035] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0036] like Figure 1 As shown, the embodiment of the present invention discloses a water quality data prediction method based on a topological structure evolution dynamic graph, comprising:

[0037] Step 1: Obtain historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data;

[0038] Step 2: Preprocessing the dynamic graph topology data;

[0039] Step 3: Construct a water quality prediction model for the water supply network based on the preprocessed topological data;

[0040] Step 4: Optimize the discriminative ability of the water quality prediction model;

[0041] Step 5: Use the optimized water quality prediction model to predict the water quality attributes at the next moment.

[0042] In another specific embodiment of the present invention, a GCN with self-supervision as the learning goal is selected as the graph structure encoder, and an RNN is selected as the decoder of the node embedding sequence. This embodiment takes the water supply network of a water company in Huizhou City as an example. The historical monitoring data of the water quality sensors in the water supply network and the topological structure of the water supply network are obtained from the database, with the intersection as the node and the network as the edge. The historical monitoring data includes timestamp, pH value, turbidity residual chlorine concentration, dissolved oxygen, chemical oxygen demand, conductivity and temperature, etc., which are used as node attribute features. The edge attribute features include pipe diameter, burial depth, pipe material, etc., and a conventional model is used for this.

[0043] Specifically, the preprocessing in step 2 includes: processing the dynamic graph topology data into a series of graphs at the same time interval, setting timestamps, converting them into static graph topology data, and sorting out the adjacency matrix, node feature matrix and edge feature matrix of the timestamps and then normalizing them.

[0044] In another specific embodiment of the present invention, monitoring data with daily time units from January 1, 2022 to December 31, 2024 are obtained. The interpolation function in the pandas package is used to process missing values, and outliers are identified by calculating the interquartile range. Pay attention to the different time nodes where the sensors are deployed, and sort out the topological map of the most complete sensor moments in the entire time window, a total of 36 nodes. Then, by assigning the node attribute feature to a 0 vector at different times to reflect the existence of the node at the current time, the topological structure relationship at different times is represented, such as Figure 2 As shown. Based on this principle, a series of directed graphs are constructed, with a total of 1096 graphs constructed; the water quality parameters and pipe network parameter types collected by the sensors are shown in Table 1

[0045] Table 1 Water quality parameters and pipe network parameter types collected by sensors

[0046] Timestamp (20221107000000) pH Turbidity (NTU) Residual chlorine (mg / L) Dissolved oxygen (mg / L) COD (mg / L) Temperature (℃) Conductivity (μS / cm) Suspended solids (mg / L) Pressure (Mpa) Outer diameter (mm) Inner diameter(mm) pipes Management age (year) Pipe length (m) Buried depth (m)

[0047] To facilitate subsequent logical presentation, the above content will be abstracted into mathematical descriptions, defining is in the time window T t = directed graph G appearing in {1, 2, ..., T} i =(v k i ,ε k i ) sequence, and its corresponding adjacency matrix is ​​A i ∈R |v|×|v| , define x i k ∈R d For a node v at a certain moment i k ∈V, then the node feature matrix is ​​X i ∈R |v|×d , similarly, the edge feature matrix E can be defined i ∈R |ε|×m After normalizing all the data, we can use the pyGeometric package to construct the graph data with a training, validation, and test ratio of 8:1:1.

[0048] Specifically, the step 3 of constructing a water quality prediction model for the water supply network includes: a static encoder and a time series decoder;

[0049] The static encoder selects a static coding graph topology model and constructs corresponding learning tasks and loss functions; after training, the nodes at each moment are embedded into an adjacency matrix and a node feature matrix according to the static coding graph topology model output.

[0050] Specifically, step 4 includes: introducing a self-supervised learning paradigm to train a static encoder, specifically including: introducing node-level masks and feature-level masks, masking the node feature matrix, defining a Mask matrix, masking a node or a node attribute with a ratio p, using a static encoder to convert the input static graph topology data into an implicit representation of nodes and edges, and calculating the node reconstruction loss based on the implicit representation.

[0051] In another embodiment of the present invention, the node-level mask is to mask the entire feature vector x with probability p for each node i. i Set to -1 vector, the specific expression is as follows:

[0052]

[0053] The feature-level mask is the feature vector x of node i i =[x i1 ,x i2 ,...,x in ], for each dimension j, set it to -1 with probability p. The specific expression is as follows:

[0054]

[0055] Define the Mask matrix M∈{0,1} |v|×d , the overall matrix form can be written as in Indicates element-by-element multiplication. In this embodiment, a certain ratio p = 10% is used to cover a node or a certain attribute of the node, and the GCN is allowed to predict the covered attribute based on other uncovered attributes. The structure and initialization parameters of the GCN model are shown in Table 2. The specific code implementation process is to obtain the node matrix X of the i-th topology graph i , according to X i The shape uses the torch.rand function to generate a random matrix, setting values ​​less than 0.1 to true and all others to false. This approach randomly masks nodes and node attributes with a 10% probability. Since graph data cannot normally have negative values, the masked attribute values ​​are replaced with -1.

[0056] Table 2 Construction parameters of GCN model

[0057]

[0058] Next, GCN is used to encode the input graph into implicit representations of nodes and edges:

[0059] Nodes are represented as:

[0060] is the node feature matrix after node-level masking and feature-level masking; A is the adjacency matrix, and E is the edge feature matrix;

[0061] The calculation logic of the GCN layer is

[0062] Among them, H l represents the node representation of the lth layer, is the adjacency matrix with self-loops added, and D is The degree matrix, σ is the Relu activation function, W l is the learnable weight matrix of layer l.

[0063] The node reconstruction loss is calculated as:

[0064]

[0065] in, is the MSE loss function, L recons is the node reconstruction loss

[0066] x ij is the jth original eigenvalue of the i-th node, is the jth original eigenvalue of the i-th node reconstructed by the model, ∑ i,j M ij is the total number of masked features, used as a normalization factor. Specifically, step 4 also includes introducing a contrastive learning strategy for self-supervised training to enhance the static encoder's ability to discriminate node structure representations, thereby further improving the learning ability of static graphs, including:

[0067] Positive and negative sample pairs are constructed. For each original image, two views are generated using data augmentation. The two views are respectively input into a static encoder with shared parameters to obtain the corresponding node embeddings. A contrastive loss function is defined and the mask loss is jointly optimized to obtain a jointly optimized static encoder. After training, the node hidden layer matrix generated by the static encoder at each moment is used as the temporal input of the temporal decoder, and the hidden layer matrix of each node is normalized.

[0068] Specifically, a data enhancement method of edge perturbation is adopted, and the edge perturbation includes edge deletion and edge addition. Edge deletion is to randomly delete a part of the edges from the dynamic graph topology data and replace the corresponding edge features with minus 1; edge addition is to add several edges that did not originally exist to the dynamic graph topology data and assign forged edge features to them.

[0069] In another specific embodiment of the present invention, to further enhance the GCN encoder's ability to discriminate node structure representations, a contrastive learning strategy is introduced for self-supervised training. This strategy reduces the distance between the representations of positive pairs and increases the distance between the representations of negative pairs. Positive samples perturb the same graph differently, resulting in two views.

[0070] First, construct a positive sample pair. For each original image, use data augmentation and perturbation to generate two views:

[0071]

[0072] are the other two views generated after the t-th original image is enhanced. are the two node feature matrices of the enhanced graph, A (1) t A (2) t are the two adjacency matrices of the enhanced graph, E (1) t E (2) t are the two edge features of the enhanced graph.

[0073] Input the two GCN encoders with shared parameters separately to get the corresponding node embeddings:

[0074]

[0075] Z t (1) Z t (2) It is the node representation of the two views;

[0076] Let z i (1) ∈Z t (1) ,z i (2) ∈Z t (2) Represents the embedding vector of node i in the two views

[0077] Define the contrast loss function as NT-Xent loss:

[0078]

[0079] in, is the cosine similarity, and τ is the temperature coefficient 0.5.

[0080] The specific method of edge perturbation is to define the average sampling of perturbation rate ε∈(0,1) and construct the perturbation graph as

[0081]

[0082] The specific operation form of edge deletion is to randomly delete a part of the edges from the original edge set. Let the original edge set be ε t ={(i,j)|A t,ij =1}, sampling Make The adjacency matrix after perturbation is:

[0083]

[0084] The edge feature matrix is:

[0085]

[0086] ε t is the set of all existing edges in the t-th graph, that is, A t,ij =1, The subset of edges that need to be deleted is sampled from the original edge set. Denotes random deletion of edges in proportion ∈.

[0087] After deleting an edge, the corresponding edge feature is replaced by -1.

[0088] The specific operation of adding edges is to add several edges that do not exist in the original graph and assign them fake edge features.

[0089] The set of non-connected pairs is sampling Make The adjacency matrix after perturbation is

[0090]

[0091] The edge feature matrix is

[0092]

[0093] where φ edge is the eigenvector of the virtual edge, filled with the average value instead

[0094]

[0095] Then the joint optimization objective of mask loss and contrast loss becomes

[0096] L total =L recons +λ·L contrast , where λ is the weight parameter

[0097] Among them, L total is the total loss, L reconsFor the node reconstruction loss mentioned above, L contrast is the contrast loss.

[0098] Specifically, the temporal decoder adopts an RNN model and takes the node hidden layer matrix as input. The calculation formula is:

[0099] O t =FC(RNN(S t-1 ,Z t )),

[0100] Among them, S t-1 is the hidden state of the previous time step, Z t is the input vector of the current time step, FC is the fully connected layer, O t is the output vector of the current time step, predicting the node attribute value of the current time step;

[0101] The calculation formula of RNN is:

[0102] s t =tanh(Ws t-1 +Ux t )

[0103] o t =Vs t

[0104] Among them, x t is the input vector of the current time step, s t is the hidden state of the current time step, o t is the output vector of the encoder node embedding at the current time step, W is the weight transfer matrix between hidden states, U is the weight matrix from input to hidden state, and V is the weight matrix from hidden state to output.

[0105] In another specific embodiment of the present invention, the hyperparameter optimization framework selects the optuna package, defines the learning rate, hidden layer features, and batch as hyperparameters, and the optimization goal is to obtain the minimum MSE value, that is, Where θ represents the hyperparameter combination, H represents the set hyperparameter search space, LMSE represents the mean square error loss on the validation set, and in this example, the search space for the feature dimension size of the hidden layer node in GCN is defined as hidden_dim∈{32,64,128}, and the search space for the learning rate is lr∈{10 -3 ,10 -4 ,2×10 -5}, the batch search space is bs∈{4,8,16}, the search space of weight parameter λ is λ∈{0.2,0.4,0.6,0.8}, and the framework will output the hyperparameter combination that minimizes MSE as 32, 1e-4, 16, 0.4

[0106] After training, the node hidden layer matrix Z generated by the model at each moment is used i ∈R |v|×d As the time series input of the next model. Note that the order of Z needs to be arranged in sequence according to the timestamp and cannot be disrupted. The hidden layer matrix of each node is normalized: in

[0107] Among them, z t,i μ is the embedding vector of the i-th node at time t, with dimension d. i is the mean of the embedding vector of the i-th node, averaged over the dimensions. i is the standard deviation of the embedding vector of the i-th node.

[0108] The structural parameters and training parameters of RNN are as follows Figure 3 As shown in Table 3, after hyperparameter optimization, 80% of the data was used as the training set, and the remaining 20% ​​was used as the validation set and the test set.

[0109] The optimization goal is to minimize the mean square error (MSE) loss function on the validation set:

[0110] Among them, y i Represents the attribute value of the i-th node predicted by the RNN model, Represents the true attribute value of the i-th node in the RNN model

[0111] Convergence judgment condition: If the verification loss does not decrease significantly within 10 rounds, it is set to terminate early.

[0112] Table 3 Optimized parameters of the GCN model

[0113]

[0114]

[0115] Specifically, a water quality data prediction system based on a topological structure evolution dynamic graph includes:

[0116] Data acquisition module: obtains historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data;

[0117] Preprocessing module: preprocessing the dynamic graph topology data;

[0118] Prediction model building module: Constructs a water quality prediction model for the water supply network based on preprocessed topological data;

[0119] Optimization module: optimizes the discrimination ability of water quality prediction model;

[0120] Prediction module: Use the optimized water quality prediction model to predict the water quality properties at the next moment.

[0121] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. Reference can be made to the common and similar parts between the various embodiments. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the method description.

[0122] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not limited to the embodiments shown herein but is intended to conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A water quality data prediction method based on a topological structure evolution dynamic graph, characterized in that: include: Step 1: Obtain historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data; Step 2: Preprocessing the dynamic graph topology data; Step 3: Construct a water quality prediction model for the water supply network based on the preprocessed topological data; Step 4: Optimize the discriminative ability of the water quality prediction model; Step 5: Use the optimized water quality prediction model to predict the water quality attributes at the next moment.

2. The water quality data prediction method based on topological structure evolution dynamic graph according to claim 1 is characterized in that: The preprocessing in step 2 includes: processing the dynamic graph topology data into a series of graphs at the same time interval, setting a timestamp, converting it into static graph topology data, and sorting out the adjacency matrix, node feature matrix and edge feature matrix of the timestamp and then normalizing them.

3. The water quality data prediction method based on topological structure evolution dynamic graph according to claim 2 is characterized in that: The step 3 of constructing a water quality prediction model for the water supply network includes: a static encoder and a time series decoder; The static encoder selects a static coding graph topology model and constructs corresponding learning tasks and loss functions; after training, the nodes at each moment are embedded into an adjacency matrix and a node feature matrix according to the static coding graph topology model output.

4. The water quality data prediction method based on topological structure evolution dynamic graph according to claim 3 is characterized in that: The step 4 includes: introducing a self-supervised learning paradigm to train a static encoder, specifically including: introducing node-level masks and feature-level masks, masking the node feature matrix, defining a mask matrix, masking a node or a node attribute with a ratio p, using a static encoder to convert the input static graph topology data into an implicit representation of nodes and edges, and calculating the node reconstruction loss based on the implicit representation.

5. The water quality data prediction method based on topological structure evolution dynamic graph according to claim 3 is characterized in that: The step 4 also includes introducing a contrastive learning strategy to perform self-supervised training to enhance the static encoder's ability to discriminate node structure representations, including: Positive and negative sample pairs are constructed. For each original image, two views are generated using data augmentation. The two views are respectively input into a static encoder with shared parameters to obtain the corresponding node embeddings. A contrastive loss function is defined and the mask loss is jointly optimized to obtain a jointly optimized static encoder. After training, the node hidden layer matrix generated by the static encoder at each moment is used as the temporal input of the temporal decoder, and the hidden layer matrix of each node is normalized.

6. The water quality data prediction method based on topological structure evolution dynamic graph according to claim 5 is characterized in that: The temporal decoder adopts the RNN model and takes the node hidden layer matrix as input. The calculation formula is: About t =FC(RNN(S t-1 ,Z t )), Among them, S t-1 is the hidden state of the previous time step, Z t is the input vector of the current time step, FC is the fully connected layer, O t is the output vector of the current time step, predicting the node attribute value of the current time step; The calculation formula of RNN is: S t =tanh(Ws t-1 +Ux t ) about t =Sun t Among them, x t is the input vector of the current time step, s t is the hidden state of the current time step, o t is the output vector of the encoder node embedding at the current time step, W is the weight transfer matrix between hidden states, U is the weight matrix from input to hidden state, and V is the weight matrix from hidden state to output.

7. A water quality data prediction system based on a topological structure evolution dynamic graph, characterized in that: include: Data acquisition module: obtains historical monitoring data of water quality sensors in the water supply network and the topological structure of the water supply network to obtain dynamic graph topology data; Preprocessing module: preprocessing the dynamic graph topology data; Prediction model building module: Constructs a water quality prediction model for the water supply network based on preprocessed topological data; Optimization module: optimizes the discrimination ability of water quality prediction model; Prediction module: Use the optimized water quality prediction model to predict the water quality properties at the next moment.

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