Machine learning based water quality fluid diffusion feature extraction method

Abstract

This invention discloses a machine learning-based method for extracting water quality fluid diffusion features. To address the challenges of reconstructing spatial diffusion patterns and extracting stable diffusion features due to sparse monitoring points and missing measurements, this invention acquires information such as station location, observation time, water quality parameter values, missing measurement mask, hydraulic distance, flow direction, and sensor status. It constructs operator input data including station confidence and spatial coverage channels, uses a neural operator network to predict the concentration field, and samples and calculates observation residuals at each station. Based on station confidence, it adaptively constructs a measurement noise covariance matrix and inputs the observation residuals, hydraulic distance, and flow direction into a Kalman gain network to assimilate and update the predicted concentration field. Furthermore, it obtains two types of diffusion features through a diffusion feature extraction network and rule calculation, and performs consistent fusion to obtain the final diffusion feature set. Simultaneously, it performs online incremental updates based on a sliding time window. This achieves high-precision reconstruction of the concentration field under sparse observation conditions, enhanced physical consistency of assimilation updates, and improved robustness of diffusion feature extraction.

Description

Technical Field

[0001] This invention relates to the field of water pollution diffusion analysis, and in particular to a method for extracting water fluid diffusion features based on machine learning. Background Technology

[0002] The diffusion process of pollutants in water bodies exhibits significant spatiotemporal dynamics. Reconstructing diffusion morphology and extracting features such as diffusion boundaries, diffusion front locations, and arrival times are crucial foundations for early warning of sudden pollution events, emission regulation, and refined water environment management. With the development of online water quality sensors, IoT communication, and automated data acquisition technologies, water quality monitoring has gradually evolved from manual sampling to continuous observation at multiple sites, providing water quality parameter data with higher temporal resolution. Existing technologies for analyzing diffusion processes mainly include numerical simulation and inversion methods based on hydrodynamic and water quality mechanism models, interpolation reconstruction methods based on spatial statistics, and spatiotemporal prediction methods based on machine learning. Simultaneously, to improve estimation accuracy under limited observation conditions, data assimilation techniques such as Kalman filtering and ensemble Kalman filtering have been developed, and neural operator methods for learning field mapping relationships and neural network assimilation methods for learning Kalman gain have emerged.

[0003] However, existing technologies still have the following shortcomings in engineering applications:

[0004] 1. Monitoring stations are usually sparse due to cost and deployment limitations, and there are situations such as missing data, outliers and sensor drift during actual data collection. Traditional interpolation methods or some data-driven models are difficult to reconstruct the diffusion pattern stably under sparse observation conditions, and are more sensitive to missing data and outliers.

[0005] 2. Traditional assimilation methods often require pre-setting statistical quantities such as measurement noise, which makes it difficult to reflect the differences in sensor reliability at different sites; at the same time, if the assimilation update does not effectively combine hydraulic connectivity, flow direction constraints and propagation delay constraints, it is easy to have backflow propagation or non-physical updates across tributaries.

[0006] 3. Diffusion features rely heavily on thresholds and rules for calculation, and are greatly affected by reconstruction errors and noise. Moreover, existing models mostly use offline training methods, which makes it difficult to adapt and update online over time in continuous monitoring scenarios, resulting in insufficient generalization and stability.

[0007] Therefore, a method for extracting water quality fluid diffusion characteristics that can overcome the shortcomings of the existing technology is a problem that needs to be solved by those skilled in the art. Summary of the Invention

[0008] One objective of this invention is to propose a machine learning-based method for extracting water quality fluid diffusion features. Addressing the problems of existing technologies, such as difficulty in reconstructing spatial diffusion patterns under conditions of sparse monitoring stations, missing observations, and varying sensor reliability; the tendency for assimilation updates to generate non-physical propagation; and insufficient robustness and difficulty in online adaptive diffusion feature extraction, the following technical solution is proposed: Acquire information on station location, observation time, water quality parameter values, missing measurement masks, hydraulic distance, flow direction, and sensor status; calculate station confidence and generate spatial coverage channels as input data for the operator; output a predicted concentration field on a preset grid using a neural operator network; sample and calculate observation residuals at the stations; adaptively construct a measurement noise covariance matrix based on station confidence; input the observation residuals, hydraulic distance, and flow direction into a Kalman gain network to assimilate and update the predicted concentration field; extract diffusion features from the assimilated concentration field using both the network and rules, and perform consistent fusion; incrementally update each network parameter using a sliding time window. This invention achieves the technical effects of improving the accuracy of concentration field reconstruction under sparse observations, enhancing the physical consistency of assimilation updates, improving the stability of diffusion feature extraction, and supporting continuous online updates.

[0009] This invention provides a machine learning-based method for extracting water quality fluid diffusion features, comprising:

[0010] S1. Obtain the site locations, observation times, water quality parameter values, and missing measurement masks for multiple monitoring stations. Obtain hydraulic distance and flow direction information between monitoring stations, and obtain sensor status information corresponding to each monitoring station. S2. Determine the site confidence level for each monitoring station based on the missing measurement masks and sensor status information. Encode the site location, observation time, water quality parameter values, missing measurement masks, and site confidence level as site features. Generate a coverage channel representing the spatial coverage of the monitoring stations on a preset spatial computing grid based on the site location. Combine the site features and coverage channels to form operator input data. S3. Input the operator input data into a neural operator network and output the predicted concentration field on the preset spatial computing grid. S4. Sample the predicted concentration field at the site location to obtain the predicted site value. Calculate the observation residual by combining the predicted site value with the corresponding water quality parameter value. Construct the measurement noise covariance matrix based on the site confidence level. Combine the observation residual and hydraulic distance... S5. The assimilated concentration field is updated by inputting the distance information, flow direction information, and measurement noise covariance matrix into the Kalman gain network to obtain the Kalman gain matrix; S6. The assimilated concentration field is input into the diffusion feature extraction network to obtain the first diffusion feature set. The second diffusion feature set is calculated based on the assimilated concentration field according to the preset feature calculation rules. The consistency index is calculated based on the first diffusion feature set and the second diffusion feature set. The first diffusion feature set and the second diffusion feature set are then fused according to the consistency index to obtain the final diffusion feature set; S7. The operator input data, the assimilated concentration field, and the final diffusion feature set are stored in the sliding time window. When the data of the next observation time is obtained, the parameters of the neural operator network, the Kalman gain network, and the diffusion feature extraction network are incrementally updated based on the sliding time window to reduce the error between the predicted station value and the water quality parameter value at the monitoring station and to reduce the consistency index between the first diffusion feature set and the second diffusion feature set.

[0011] Optionally, S1 includes:

[0012] Obtain the location of multiple monitoring stations, where the location is the spatial coordinate of each monitoring station in a unified coordinate system;

[0013] Obtain the observation time corresponding to the multiple monitoring stations and the water quality parameter values ​​at the observation time;

[0014] For each monitoring station at each observation time, a missing measurement mask is determined based on whether there is a valid water quality parameter value at the monitoring station. When there is a valid water quality parameter value, the missing measurement mask takes a first preset value. When there is no valid water quality parameter value, the missing measurement mask takes a second preset value. The first preset value and the second preset value are different.

[0015] Obtain hydraulic distance information between the multiple monitoring stations, wherein the hydraulic distance information is the distance along the water body connection path;

[0016] Obtain flow direction information among the multiple monitoring stations, wherein the flow direction information is used to characterize the upstream and downstream relationships among the multiple monitoring stations;

[0017] Obtain sensor status information corresponding to each monitoring station. The sensor status information includes self-test results or fault identifiers used to characterize the sensor's working status.

[0018] Optionally, S2 includes:

[0019] The sensor reliability score of each monitoring station is determined based on the sensor status information, and the validity of the water quality parameter values ​​of each monitoring station at each observation time is determined by combining the missing measurement mask. Based on the validity determination, the station confidence level of each monitoring station is obtained.

[0020] The station location, observation time, water quality parameter value, missing measurement mask and the station confidence level are numerically processed and spliced ​​in a preset order to obtain the station feature vector corresponding to each monitoring station.

[0021] The site feature vector is mapped to the corresponding grid point in the preset spatial computing grid according to the site location to generate a site feature channel, wherein the site feature channel of the grid point not mapped to the monitoring site takes a preset fill value;

[0022] A coverage channel is generated on the preset spatial computing grid, wherein the coverage channel includes a distance channel and an observation density channel. The distance channel is the distance from each grid point to the nearest monitoring station, and the observation density channel is the ratio of the number of monitoring stations with valid water quality parameter values ​​in the preset neighborhood to the area of ​​the preset neighborhood.

[0023] The site feature channel and the coverage channel are superimposed along the channel dimension to obtain the operator input data.

[0024] Optionally, S3 includes:

[0025] Arrange the operator input data into an input tensor according to the grid point order of the preset spatial calculation grid;

[0026] The input tensor is fed into the up-dimensional mapping layer of the neural operator network to obtain the hidden representation;

[0027] Perform at least one spectral domain convolution operation on the latent representation to obtain an updated latent representation, wherein the spectral domain convolution operation includes performing a fast Fourier transform on the latent representation to obtain a spectral domain representation, multiplying the spectral domain representation with trainable weight parameters to obtain an updated spectral domain representation, and performing an inverse fast Fourier transform on the updated spectral domain representation to obtain the updated latent representation.

[0028] The updated hidden representation is input into the projection layer of the neural operator network, and the predicted concentration values ​​of each grid point of the preset spatial computing grid are output to obtain the predicted concentration field.

[0029] Optionally, S4 includes:

[0030] Based on the location of the monitoring station, a sampling mapping relationship is established from the preset spatial computing grid to the location of the monitoring station, and the predicted concentration field is sampled at the location of the monitoring station according to the sampling mapping relationship to obtain the predicted station value.

[0031] The observation residual is obtained by subtracting the predicted station values ​​from the water quality parameter values ​​at the corresponding observation times.

[0032] A measurement noise covariance matrix is ​​constructed based on the site confidence level, wherein the measurement noise covariance matrix is ​​a diagonal matrix and the diagonal elements are negatively correlated with the site confidence level of the corresponding monitoring site;

[0033] The observation residual, hydraulic distance information, flow direction information, and measurement noise covariance matrix are input into a Kalman gain network to obtain a Kalman gain matrix. The Kalman gain network constrains the propagation weight of the observation residual based on the hydraulic distance information and the flow direction information, so that the propagation weight along the flow direction is greater than the propagation weight against the flow direction.

[0034] The observation residuals are weighted based on the Kalman gain matrix to obtain the grid update amount, and the grid update amount is superimposed with the predicted concentration field to obtain the assimilation concentration field.

[0035] Optionally, S5 includes:

[0036] The assimilation concentration field is input into the diffusion feature extraction network, which outputs the first diffusion feature set, which includes the diffusion boundary, diffusion center line, diffusion front position and arrival time.

[0037] The second diffusion feature set is calculated based on the assimilation concentration field according to the preset feature calculation rules. The preset feature calculation rules include using a first preset concentration threshold to determine the diffusion boundary, where the diffusion boundary is a boundary curve or boundary set in the assimilation concentration field where the concentration value satisfies the first preset concentration threshold; using the geometric center trajectory of the high-concentration connected region along the flow direction to determine the diffusion center line; using the grid point that satisfies the first preset concentration threshold along the flow direction and is the farthest away to determine the diffusion front position; and using the assimilation concentration field within the sliding time window to determine the moment when the concentration value at each preset position first reaches the first preset concentration threshold as the arrival time.

[0038] The consistency index is obtained by calculating the difference between the same-named diffusion features in the first diffusion feature set and the second diffusion feature set.

[0039] A fusion weight is generated based on the consistency index, and the first diffusion feature set and the second diffusion feature set are weighted and fused using the fusion weight to obtain the final diffusion feature set.

[0040] Optionally, S6 includes:

[0041] After completing steps S2 to S5 at each observation time, the operator input data, assimilation concentration field and final diffusion feature set corresponding to the observation time are stored in the sliding time window in chronological order. When the number of items stored in the sliding time window reaches the preset upper limit, the operator input data, assimilation concentration field and final diffusion feature set corresponding to the earliest observation time are deleted.

[0042] After obtaining the station location, observation time, water quality parameter value, missing measurement mask, hydraulic distance information, flow direction information, and sensor status information as described in step S1 for the next observation time, step S3 is re-executed based on the operator input data stored in the sliding time window to obtain the predicted concentration field. The prediction error between the predicted station value at the monitoring station and the water quality parameter value stored in the sliding time window is calculated based on the predicted concentration field and the water quality parameter value stored in the sliding time window.

[0043] The first diffusion feature set is obtained by inputting the assimilation concentration field stored within the sliding time window into the diffusion feature extraction network, and the second diffusion feature set is calculated based on the assimilation concentration field according to the preset feature calculation rules. Then, the consistency index between the first diffusion feature set and the second diffusion feature set is calculated.

[0044] The prediction error and the consistency index are weighted and summed according to preset weights to obtain the update objective function. Based on the update objective function, the parameters of the neural operator network, the Kalman gain network, and the diffusion feature extraction network are incrementally updated to obtain the updated neural operator network, the updated Kalman gain network, and the updated diffusion feature extraction network.

[0045] Optionally, the neural operator network in step S3 is a graph neural operator network, which constructs graph structure data based on the preset spatial computing grid, wherein the edge weights of the graph are determined by hydraulic distance information and flow direction information, and the graph neural operator network outputs the predicted concentration field on the preset spatial computing grid.

[0046] Optionally, the Kalman gain network introduces a propagation delay constraint based on hydraulic distance information when calculating the propagation weight. The propagation delay constraint is used to limit the contribution of the observation residual to the update of grid points that exceed the preset delay range, thereby reducing non-physical updates across cross sections or tributaries.

[0047] Optionally, the diffusion feature extraction network outputs the feature uncertainty corresponding to each diffusion feature while outputting the first diffusion feature set. The consistency index is calculated jointly based on the first diffusion feature set, the second diffusion feature set, and the feature uncertainty, and the fusion weight is negatively correlated with the feature uncertainty.

[0048] The beneficial effects of this invention are:

[0049] 1. By introducing missing measurement masks, site confidence and spatial coverage channels to encode sparse observations, and combining them with neural operator networks to realize the mapping from sparse points to continuous concentration fields, the accuracy and robustness of concentration field reconstruction under the conditions of sparse monitoring points and missing measurements are improved.

[0050] 2. Based on the site confidence, an adaptive measurement noise covariance matrix is ​​constructed, and hydraulic distance, flow direction and propagation delay constraints are introduced into the Kalman gain network to make the assimilation update more consistent with the laws of water body connectivity and downstream propagation, reduce non-physical errors such as upstream propagation and cross-tributary updates, and improve the reliability of the assimilation results.

[0051] 3. The diffusion feature extraction of the assimilation concentration field is divided into two paths: network prediction features and rule calculation features. The final features are obtained through a fusion strategy guided by consistency index and uncertainty. At the same time, online incremental updates are combined with sliding time windows to make diffusion features such as diffusion boundary, front position and arrival time more stable, interpretable and adaptable to environmental changes in long-term operation. Attached Figure Description

[0052] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0053] Figure 1 This is a flowchart of a water quality fluid diffusion feature extraction method based on machine learning proposed in this invention. Detailed Implementation

[0054] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0055] refer to Figure 1 A machine learning-based method for extracting water quality fluid diffusion features, comprising:

[0056] S1. Obtain the site locations, observation times, water quality parameter values, and missing measurement masks for multiple monitoring stations. Obtain hydraulic distance and flow direction information between monitoring stations, and obtain sensor status information corresponding to each monitoring station. S2. Determine the site confidence level for each monitoring station based on the missing measurement masks and sensor status information. Encode the site location, observation time, water quality parameter values, missing measurement masks, and site confidence level as site features. Generate a coverage channel representing the spatial coverage of the monitoring stations on a preset spatial computing grid based on the site location. Combine the site features and coverage channels to form operator input data. S3. Input the operator input data into a neural operator network and output the predicted concentration field on the preset spatial computing grid. S4. Sample the predicted concentration field at the site location to obtain the predicted site value. Calculate the observation residual by combining the predicted site value with the corresponding water quality parameter value. Construct the measurement noise covariance matrix based on the site confidence level. Combine the observation residual and hydraulic distance... S5. The assimilated concentration field is updated by inputting the distance information, flow direction information, and measurement noise covariance matrix into the Kalman gain network to obtain the Kalman gain matrix; S6. The assimilated concentration field is input into the diffusion feature extraction network to obtain the first diffusion feature set. The second diffusion feature set is calculated based on the assimilated concentration field according to the preset feature calculation rules. The consistency index is calculated based on the first diffusion feature set and the second diffusion feature set. The first diffusion feature set and the second diffusion feature set are then fused according to the consistency index to obtain the final diffusion feature set; S7. The operator input data, the assimilated concentration field, and the final diffusion feature set are stored in the sliding time window. When the data of the next observation time is obtained, the parameters of the neural operator network, the Kalman gain network, and the diffusion feature extraction network are incrementally updated based on the sliding time window to reduce the error between the predicted station value and the water quality parameter value at the monitoring station and to reduce the consistency index between the first diffusion feature set and the second diffusion feature set.

[0057] In this specific embodiment, S1 includes:

[0058] Multi-source information acquisition and structured processing are completed by jointly acquiring data from the monitoring data access terminal and the hydrodynamic topology data terminal.

[0059] The monitoring data access terminal pre-maintains a list of monitoring stations, extracts the location of each monitoring station according to its unique identifier, and uniformly converts it to the CGCS2000 Cartesian coordinate system. The station location is denoted as […]. ,in Indicates the index of monitoring sites. Indicates the first The location of each monitoring station. Indicates the first The eastward coordinates of each monitoring station in the CGCS2000 coordinate system, in meters. Indicates the first The northward coordinates of each monitoring station in the CGCS2000 coordinate system, in meters;

[0060] The monitoring data access terminal synchronizes the timestamps collected from all sites using the Network Time Protocol (NTP) and follows a fixed step size. Generate observation time series ,in This represents the time interval between adjacent observations, expressed in seconds. Indicates the first A standardized timestamp for each observation moment. Indicates the index of the observation time;

[0061] At each observation time The monitoring data access terminal parses the water quality parameter values ​​from the messages uploaded by the stations. And convert them to a unified standard. ,in Indicates the first Each monitoring station at the observation time The water quality parameter values ​​are defined in this embodiment as the concentration values ​​of the same pollution index with dimensions of _____. ;

[0062] For each monitoring station, the missing data mask at each observation time is determined using a binary method and stored synchronously with the water quality parameter values. The missing data mask is denoted as... And it satisfies the formula:

[0063] ;

[0064] in Indicates the first Each monitoring station at the observation time The missing measurement mask below indicates that 1 represents a first preset value and is used to characterize the existence of a valid water quality parameter value, while 0 represents a second preset value and is used to characterize the absence of a valid water quality parameter value. The valid value refers to the numerical result successfully parsed from the monitoring message that passes the range check and falls within the sensor's measurement range. Inside;

[0065] The hydrodynamic topology data terminal pre-stores river system topology data, including river centerlines, connectivity relationships, and natural flow direction attributes, and constructs the river system topology data into a directed weighted graph model. ,in Represents a topological model of a water system. This represents a set of nodes, including monitoring station nodes and river confluence / branching nodes. This represents a set of directed edges, where each directed edge follows the natural flow direction and is weighted with the length of the corresponding river segment's centerline in meters.

[0066] In the directed weighted graph model The above method calculates the hydraulic distance between any two monitoring stations along the water body connection path using the shortest path search. The hydraulic distance is denoted as . And in matrix form Storage, in Indicates from monitoring station Reach the monitoring station along the directed edge direction The shortest connected path length, in meters. This represents the hydraulic distance matrix formed by pairwise combinations of all monitoring stations;

[0067] While calculating hydraulic distance, flow direction information is generated based on directed reachability and presented as a binary relation matrix. Storage, in Represents the flow direction information matrix. Indicates the upstream-downstream relationship if and only if in the directed weighted graph model There are monitoring stations to monitoring station When a directed reachable path And characterize the monitoring sites For monitoring sites upstream stations, otherwise And it indicates that there is no reachability relationship from upstream to downstream;

[0068] Sensor status information is obtained from the self-test results and fault identification fields synchronously uploaded by the monitoring station and standardized and coded as follows: ,in Indicates the first Each monitoring station at the observation time The sensor status information and the set of values ​​are as follows 1 indicates that the self-test passed and there is no fault indicator; 2 indicates that the self-test failed; 3 indicates that a fault indicator exists.

[0069] The output of step S1 is the observation time. To create structured data records for batches And write it to the same data cache.

[0070] In this specific embodiment, S2 includes:

[0071] At the observation time For site location Water quality parameter values Missing test mask and sensor status information Perform confidence calculations and gridded encoding to form operator input data;

[0072] Firstly based on and Complete the validity determination and sensor reliability score calculation. and In range However, the difference between two consecutive valid reports exceeds the fixed mutation threshold. If so, the report will be deemed invalid and Set to 0, where This represents the threshold for abrupt changes in water quality parameters, and the unit is 1. ;

[0073] After completing the validity determination, the site confidence level is calculated. and will Limited to Within the interval, the confidence level of the station Determine using the following formula:

[0074] ;

[0075] in Indicates the first Each monitoring station at the observation time The site confidence level Indicates the first Each monitoring station at the observation time The missing test mask below and This indicates the existence of valid water quality parameter values. This indicates that no valid water quality parameter values ​​exist. Indicates the first Each monitoring station at the observation time The sensor status information below and Indicates that the self-test has passed. This indicates that the self-test failed. This indicates the presence of a fault indicator. The coefficient 0.5 represents a fixed reduction in confidence level when the self-test fails but still has limited reference value.

[0076] Then the site location Observation time Water quality parameter values Missing test mask and site confidence The data is quantified and then concatenated in a fixed order to generate site feature vectors. The fixed order is as follows: normalized eastward coordinates, normalized northward coordinates, normalized time, normalized water quality parameter values, missing measurement mask, and station confidence level.

[0077] The normalized eastward coordinates are derived from Subtract the minimum eastward boundary of the preset spatial computation grid Then divide by the eastward span of the grid. The normalized north coordinates are obtained from Subtract the minimum northbound boundary of the preset spatial computation grid Then divide by the grid's northward span. The normalized time is obtained from the observation time. relative to the preset start time The second-level offset divided by a fixed time scale The normalized water quality parameter values ​​are obtained from... Divide by the upper limit of the range We obtain the above normalization results, and all of them are restricted to a truncation method within a certain range. To ensure numerical stability within the range;

[0078] Then based on the site location site feature vectors Mapping to a preset spatial computing grid to generate site feature channels, the preset spatial computing grid being at a fixed resolution The grid is a two-dimensional regular grid divided by m, and the grid boundary is expanded outward from the smallest bounding rectangle of all monitoring station locations with a fixed boundary margin. The mapping rule is determined by dividing the difference between the station location and the coordinates of the grid origin by... and The data is rounded to the nearest grid index to obtain a unique grid point corresponding to that site. When multiple sites are mapped to the same grid point, the site confidence level is used as the basis for the mapping. Select the site feature vector with the highest confidence level from largest to smallest. Write to this grid point;

[0079] For grid points not mapped to monitoring stations, the station feature channel is filled with a preset value of 0 to indicate that there is no station observation input for that grid point;

[0080] A coverage channel is further generated on the preset spatial computing grid and combined with the site feature channel. The coverage channel consists of a distance channel and an observation density channel. The distance channel calculates the Euclidean distance from each grid point to the nearest monitoring site and applies it according to a fixed distance scale. Normalized and truncated to The observation density channel has a fixed neighborhood radius at each grid point. Statistical neighborhood satisfies The number of monitoring stations divided by the adjacent area After obtaining the density value, it is then processed according to a fixed density scale. Normalized and truncated to This allows the coverage channel to simultaneously characterize both site sparsity and effective observation density.

[0081] Finally, the site feature channel and the coverage channel are superimposed along the channel dimension to form the operator input data. ,in A multichannel tensor with the same size as the preset spatial computation grid.

[0082] In this specific embodiment, S3 includes:

[0083] Input data into the operator The predicted concentration field on the preset spatial computational grid is used as the input and output of the neural operator network. ;

[0084] in Indicates the index of the observation time. Indicates the observation time The corresponding multi-channel input tensor has the same spatial dimensions as the preset spatial computation grid and includes site feature channels and coverage channels. The preset spatial computation grid consists of... Each grid row and It consists of grid columns and the total number of grids is . Predicting concentration field This represents the predicted concentration value for each grid point on the grid, in units of 1. ;

[0085] To simultaneously satisfy the spectral domain modeling capability of spatially regular grids and the connectivity constraints of water bodies, this step employs a graph neural operator network as the neural operator network, arranging its inputs in the order of grid points to form an input tensor. Simultaneously, graph structure data is constructed based on a pre-defined spatial computational grid to provide connectivity propagation priors. Specifically, each grid point is considered a graph node, and the set of grid nodes is denoted as... and The directed weighted graph model of the water system topology Use it as a base map and project each grid point onto it. The location of the nearest river segment's centerline is used as a virtual hydrodynamic node, and based on the virtual hydrodynamic node... The shortest directed path length is calculated by the hydraulic distance between any two grid nodes and denoted as . ,in and This represents the grid node index, with values ​​ranging from 1 to... Indicates from grid node Along the water body connectivity path to the grid node The hydraulic distance is in meters;

[0086] Simultaneously based on The directed reachability determines the flow direction information and is denoted as ,in Represents grid nodes For grid nodes The upstream node has a directed reachable path along the flow direction. This indicates that there is no directed reachable path along the flow direction;

[0087] Only retain the condition that satisfies the condition during graph edge construction. Adjacency relationships are formed into a set of directed edges. ,in This represents a hydraulic distance cutoff threshold to limit graph sparsity and reduce long-distance non-physical coupling across tributaries;

[0088] For each directed edge Calculate edge weights And write it into the adjacency weight matrix ,in By hydraulic distance Distance decay is achieved using an exponential decay function, and the distance scale parameter is taken as... and from the flow of information Applying a directional reduction factor multiplies the countercurrent direction weight by a fixed reduction coefficient. This results in the propagation contribution along the flow direction being greater than the propagation contribution against the flow direction;

[0089] The structure of the graph neural operator network consists of an up-dimensional mapping layer, The layer consists of operator blocks and projection layers in sequence. The up-dimensional mapping layer linearly maps the input channel vector at each grid point to the hidden representation dimension. The operator block performs a fusion computation of "global update of spectral domain convolution + local update of graph propagation" on the hidden representation and uses residual connections to stabilize training. The spectral domain convolution is implemented on a regular grid through fast Fourier transform and only low-frequency modes are retained. and To represent large-scale diffusion patterns, the specific spectral domain convolution operation is as follows:

[0090] ;

[0091] in Indicates the operator block index and its value ranges from 0 to... Indicates the first The input implicit representation tensor of each operator block has a space size of . And in the channel dimension The spectral domain representation is obtained by performing a two-dimensional fast Fourier transform on the spatial dimension. This represents the two-dimensional inverse fast Fourier transform to return to the spatial domain. This represents the element-wise complex multiplication operation in the spectral field. Indicates the first Trainable spectral domain weight parameters of each operator block, and only for the retained... A non-zero value is assigned to each low-frequency mode to achieve mode truncation. This represents the updated implicit representation generated by spectral domain convolution;

[0092] Graph propagation local updates using the adjacency weight matrix For each grid node, the implicit representation of its hydraulically connected neighbors is aggregated and obtained through linear transformation. ,in The updated implicit representation generated by graph propagation is represented, and the linear transformation parameters of graph propagation are shared across all grid nodes to ensure consistency of operator form;

[0093] Each operator block will and The results are obtained by summing the channels and sequentially applying GELU nonlinear activation and layer normalization. The projection layer will ultimately represent the hidden layer. The predicted concentration field of a single channel is output through linear mapping. And crop its values ​​to L is to meet the range constraints of water quality parameters.

[0094] In this specific embodiment, S4 includes:

[0095] At the observation time Based on predicted concentration field Site confidence To achieve assimilation updates oriented towards hydraulic connectivity constraints to obtain the assimilation concentration field ;

[0096] Firstly, based on the location of the monitoring stations The origin coordinates of the preset spatial calculation grid and resolution Establish a sampling mapping relationship from grid to site. The sampling mapping relationship The grid is composed of the four vertex grid point indices of the grid cell where the site falls and their bilinear interpolation weights, and is calculated once during system initialization and then stored permanently.

[0097] At each observation time Read And according to the sampling mapping relationship The predicted station value is obtained by performing bilinear interpolation sampling at the station location. ,in Indicates the first Each monitoring station at the observation time The following are predicted values ​​obtained from sampling the predicted concentration field, and the units are... ;

[0098] Predict site values Water quality parameter values The observed residuals are obtained by subtraction. and only for those that satisfy the missing test mask Sites participate in assimilation to form an effective site set. ,in Indicates the observation time The following is a set of indexes of monitoring stations with valid water quality parameter values, and its elements are... ,make This represents the number of valid sites and assembles the observation residuals into an observation residual vector in ascending order of site index. ;

[0099] Subsequently, based on site confidence... Construct the measurement noise covariance matrix The measurement noise covariance matrix It is a diagonal matrix with diagonal elements negatively correlated with the confidence scores of the corresponding stations, and is determined by the following formula:

[0100] ;

[0101] in Indicates the observation time The measurement noise covariance matrix is ​​as follows. This represents an operator that generates a diagonal matrix using the input sequence as its diagonal elements. Indicates the first At the observation time, the effective stations The measurement noise variance is given in units of Indicates that valid sites are in the set The sequential index in the array has a value range of 1 to 1. Indicates the relationship with the first The site confidence scores for each valid site, with a value range of [value missing]. This represents the minimum standard deviation of measurement noise at a confidence level of 1. This represents the maximum standard deviation of measurement noise at a confidence level of 0.

[0102] Then observe the residual vector Hydraulic distance from effective stations to grid points Flow direction information from effective stations to grid points and the measurement noise covariance matrix Input Kalman gain network to output Kalman gain matrix ,in This represents the grid point index, with values ​​ranging from 1 to... Indicates from a valid site Along the water body connectivity path to the grid point The hydraulic distance, in meters, is calculated using the shortest directed path from a directed weighted graph model of the water system topology. Indicates the flow direction constraint identifier and when the grid point Located at a valid site When the downstream reachable range otherwise This represents the gain mapping that propagates the observation residuals from the site space to the grid space;

[0103] The Kalman gain network adopts a deterministic structure of "pairwise feature encoding + attention aggregation" and fixes the parameter values ​​with two fully connected perceptron layers and Softmax normalization. The first fully connected layer inputs pairwise feature vectors. Mapped to a hidden dimension of 32 and activated using ReLU, the second fully connected layer outputs each pair. Unnormalized propagation score and The propagation weights are obtained by performing Softmax on the dimension, thus ensuring that the sum of the propagation weights of each grid point to all valid sites is 1. This represents the log-stable term, and in the calculation of the propagation score, it is achieved by satisfying... The back-current propagation score multiplied by a fixed reduction factor The weight of propagation along the flow is greater than the weight of propagation against the flow.

[0104] Simultaneously, a propagation delay constraint is introduced to limit non-physical updates across sections or tributaries. Specifically, the propagation delay is defined as... And set a fixed reference flow rate With fixed delay limit ,when When the corresponding propagation score is set to an unselectable state, its Softmax weight is 0, so that the observation residual does not contribute to the update of grid points that exceed the preset time delay range;

[0105] Based on Kalman gain matrix For the observation residual vector The grid update amount is obtained by weighted calculation. and update the grid amount After rearranging the grid points into an updated field of the same size as the predicted concentration field, and comparing it with the predicted concentration field... The assimilation concentration field is obtained by adding the points one by one. Furthermore, the assimilation concentration field values ​​are clipped to... To meet the range constraints of water quality parameters.

[0106] In this specific embodiment, S5 includes:

[0107] At the observation time With assimilation concentration field The system extracts and fuses diffusion features using a single field as input, and outputs the final diffusion feature set. ;

[0108] in Represents the assimilation concentration field with spatial size of And it corresponds one-to-one with the preset spatial computing grid and the unit is Indicates the index of the observation time. Indicates the observation time The final diffusion feature set includes four types of diffusion features: diffusion boundary, diffusion centerline, diffusion front position, and arrival time.

[0109] First of all Input diffusion feature extraction network Obtain the first diffusion feature set and the corresponding set of characteristic uncertainties ,in This represents a diffusion feature extraction network. This represents the set of trainable parameters for the diffusion feature extraction network. This represents the first diffusion feature set of the network output. This represents the set of feature uncertainties that correspond one-to-one with the diffusion features of the same name in the first diffusion feature set, and the uncertainty values ​​are non-negative real numbers.

[0110] The diffusion feature extraction network Employing a defined multi-task encoder-decoder structure and using a single channel As input, the encoder contains four levels of downsampled convolutional blocks, with each level consisting of two layers. Convolution and ReLU activation are combined, and downsampling is performed using a convolution with a stride of 2. The number of channels in the four levels is as follows: The decoder contains four levels of upsampled convolutional blocks, with each level consisting of bilinear upsampling and two layers. Convolutional and ReLU activations are combined and concatenated with the corresponding encoder level via skip connections;

[0111] The network output is configured with four task heads that share decoder features, where the diffusion boundary task head outputs the boundary probability map. The diffusion centerline task head outputs a centerline probability map. Spreading forward position mission head output forward heatmap The arrival time task header outputs an arrival time graph. And its value is relative to the preset start time. The second-level offset;

[0112] Set uncertainty output headers for the four task headers mentioned above and output logarithmic variance plots. The variance plot is then transformed using softplus(•) to ensure non-negativity. Subsequently, the variance plot is averaged across the spatial dimension to obtain the uncertainty scalars for the four types of diffusion characteristics. and form ,in A plot showing the uncertainty variance at the diffusion boundary. A plot showing the uncertainty variance of the diffusion centerline. A variance plot representing the uncertainty of the diffusion front's position. A plot showing the variance of the uncertainty in arrival time. The scalar representing the uncertainty at the diffusion boundary. The scalar representing the uncertainty of the diffusion centerline. A scalar representing the uncertainty of the position of the diffusion front. A scalar representing the uncertainty of arrival time;

[0113] Will and Binarization with a fixed threshold of 0.5 yields boundary and centerline masks, which are then processed by connected component filtering and thinning to obtain vector representations of the diffusion boundary and diffusion centerline. The corresponding features in will Take the coordinates of the grid point where the maximum value is located as the position of the diffusion front and... In the preset location set The arrival time is obtained by sampling at the corresponding grid point as... The corresponding features in, where This represents a set of preset locations, and during system initialization, a preset location is set every 1000 m along the river centerline and projected onto the nearest grid point to form a fixed set;

[0114] Secondly, based on the assimilation concentration field The second diffusion feature set is calculated according to the preset feature calculation rules. The preset feature calculation rule uses a first preset concentration threshold. To ensure a unique threshold and consistency with the entire process, the diffusion boundary is determined by constructing a binary mask on the grid. And a moving square algorithm is used to extract The set of boundary curves is obtained from the isovalue boundaries from 1 to 0, and the diffusion centerline passes through... Selecting a directed weighted graph model along the topology of the river system The maximum connected region downstream is divided into slices every 200 m based on the cumulative downstream distance. The geometric center of all grid points within each slice is calculated, and the geometric centers of adjacent slices are connected downstream to obtain a centerline. The diffusion front position is determined by selecting the grid point with the largest cumulative downstream distance within the maximum connected region. The arrival time is determined by reading the nearest [timeframe] within the sliding time window. Frame assimilation concentration field and for each preset position The concentration of the sample first satisfies the condition of not less than The observation time is used as the arrival time, and if the threshold is not reached within the sliding time window, the arrival time is marked as infinity for subsequent fusion determination;

[0115] Then to and The consistency index is calculated based on the diffusion characteristics of the same name, and the characteristic uncertainty is incorporated into the consistency index. Specifically, the consistency index of the diffusion boundary adopts the symmetric Hausdorff distance divided by the distance normalization scale. Then divide by The final consistency index is obtained by taking the average distance from the point on the two centerlines to the curve, normalizing it in the same way, and dividing by . The consistency index of the diffusion front positions is calculated by using the hydraulic distance between the two forward points, normalizing it in the same way, and dividing by . The arrival time consistency index is calculated by dividing the absolute difference between two arrival times by the time normalization scale. Then divide by ,in Indicates the distance normalization scale. Indicates the time normalization scale. This represents the stability constant to avoid division by zero;

[0116] Finally, based on the consistency index, a fusion weight is generated, and the first diffusion feature set and the second diffusion feature set are fused to obtain the final diffusion feature set. The fusion is performed separately for each type of diffusion feature, and the fusion weight is negatively correlated with the feature uncertainty and also negatively correlated with the consistency index. The fusion weight and the fusion result are determined by the following formula:

[0117] ;

[0118] in Indicates the diffusion feature type index and takes the value These correspond to the diffusion boundary, diffusion centerline, diffusion front position, and arrival time, respectively. Indicates the observation time Next The fusion weights of diffusion-like features and their value ranges are as follows: This represents the Sigmoid function. This represents the fixed weighting coefficient of the consistency index item. This represents the fixed weighting coefficient for the uncertainty term. Indicates the observation time Next The consistency index of diffusion-like characteristics is a non-negative real number. Indicates the observation time Next The uncertainty of the diffusion-like characteristic is a scalar and a non-negative real number. Indicates the first diffusion feature set The values ​​of the diffusion-like feature, Indicating the second diffusion feature set The values ​​of the diffusion-like feature, Indicates the first diffusion feature set after fusion. The values ​​of the diffusion-like feature;

[0119] Among them, the diffusion boundary and the diffusion centerline are first... and After uniformly rasterizing into a binary mask, press Point-by-point weighting and re-execution of boundary and centerline extraction are performed to obtain geometrically consistent vector results. The numerical results of the diffusion front position and arrival time are directly correlated. Perform weighted summation to obtain the final value and write it. .

[0120] In this specific embodiment, S6 includes:

[0121] Online incremental updates are achieved using a sliding time window, and the parameters of the neural operator network, Kalman gain network, and diffusion feature extraction network are synchronously corrected.

[0122] At the observation time After completing steps S2 to S5, input the operator data corresponding to the observation time. Assimilation concentration field and the final diffusion feature set Write to the sliding time window in chronological order. ,in It uses a first-in-first-out circular buffer structure with a maximum capacity set to 1. frame, This represents the maximum number of stored frames in the sliding time window and is related to the system sampling step size. The coverage duration was jointly determined to be 14400 s;

[0123] After writing The number of records in the database exceeds At that time, delete the earliest observation time corresponding to and To keep the window length constant;

[0124] When the next observation time is obtained After receiving the data in step S1, proceed with the execution. Before field reconstruction and feature extraction, we first use a sliding time window. Perform an incremental parameter update on the three types of networks, specifically from The operator input data of each frame is read in chronological order. Then repeat step S3 to obtain the corresponding predicted concentration field. ,in This represents the frame index within the sliding time window and corresponds to a specific historical observation time. Subsequently, the sampling mapping relationship that has been fixed and stored in step S4 is used. At the location of each monitoring station Sampling is performed to obtain predicted station values and from The water quality parameter values ​​of the same station at the same time were obtained by parsing the station feature channels. and missing test mask In order to satisfy The prediction error is calculated on the set of sites and the mean squared error is used as the prediction error term. ;

[0125] At the same time from Read the assimilation concentration field of each frame And input the diffusion feature extraction network Obtain the first diffusion feature set and characteristic uncertainty set Then, based on the preset feature calculation rules and fixed thresholds established in step S5... from Calculate the second diffusion feature set For each of the two types of diffusion features, a consistency index is calculated, and the consistency index is averaged over the time dimension and the feature type dimension to obtain the consistency index item. ;

[0126] The updated objective function is obtained by weighting the prediction error term and the consistency index term according to preset weights.

[0127] ;

[0128] in This represents the overall objective function used for online incremental updates. This represents the weighting coefficient of the prediction error term. Indicates the predicted station value at the monitoring station within the sliding time window. Water quality parameter values The mean square error between them This represents the weighting coefficient of the consistency indicator item. Represents the first diffusion feature set within the sliding time window. With the second diffusion feature set The average value of the consistency index between them;

[0129] in accordance with parameters of neural operator networks Kalman gain network parameters and diffusion feature extraction network parameters Perform backpropagation and incremental updates, where This represents the complete set of trainable parameters of a neural operator network. This represents the complete set of trainable parameters for a Kalman gain network. This represents the complete set of trainable parameters for the diffusion feature extraction network.

[0130] Incremental updates use the Adam optimizer and have fixed hyperparameters. The learning rate is set to And execute at each new observation time. Sub-gradient update step, each gradient update step is based on All frames within the batch are used as training data and the gradient vector is applied. Pruning with a norm upper limit of 1 to suppress numerical explosion;

[0131] After completing the above incremental updates, the updated neural operator network, updated Kalman gain network, and updated diffusion feature extraction network are obtained and used for... Perform steps S2 to S5 to achieve online adaptive correction over time.

[0132] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

[0133] This invention couples the continuous field prediction capability of neural operator networks with the observation correction capability of neural assimilation. Under conditions of sparse monitoring points and missing or anomaly detection, the neural operator network first maps the station observations to a predicted concentration field on a preset spatial computing grid. Then, the predicted field is sampled at the station location, and the observation residuals are calculated. The residuals are spatially propagated and weighted through a Kalman gain network to obtain the assimilated concentration field. Based on this, diffusion features such as diffusion boundaries, diffusion centerlines, diffusion front positions, and arrival times are further extracted. Incremental updates through sliding time windows allow the model parameters to be continuously corrected with new observations. This combination enables sparse point information to be transformed into stable spatial diffusion morphology reconstruction results, further improving the usability and reliability of diffusion features, thereby effectively improving the technical problem of "difficulty in reconstructing and extracting diffusion features under sparse point conditions".

[0134] To address this technical problem, this invention improves the algorithm structure to meet engineering constraints: First, it encodes the sparse observation set by introducing missing measurement masks, station confidence, and spatial coverage channels, enabling the network to distinguish between missing and valid observations, express station reliability, and perceive the sparsity of spatial observations, thus improving reconstruction robustness. Second, it explicitly introduces hydraulic distance and flow direction information into the Kalman gain network and applies downstream propagation constraints and propagation delay constraints. Simultaneously, it adaptively constructs a measurement noise covariance matrix based on station confidence, reducing non-physical errors such as upstream propagation and cross-tributary updates. Third, through the consistency index and fusion mechanism of "network feature extraction" and "rule-based feature calculation," it forms a closed-loop constraint between concentration field reconstruction and diffusion feature extraction, further improving the stability and interpretability of diffusion features, and together with online incremental updates, ensuring continuous adaptability in long-term operating scenarios.

Claims

1. A method for extracting water quality fluid diffusion features based on machine learning, characterized in that, include: S1. Obtain the site location, observation time, water quality parameter value, and missing measurement mask of multiple monitoring stations; obtain the hydraulic distance information and flow direction information between monitoring stations; and obtain the sensor status information corresponding to each monitoring station. S2. Determine the site confidence level of each monitoring station based on the missing measurement mask and sensor status information; encode the site location, observation time, water quality parameter value, missing measurement mask, and site confidence level as site features; generate a coverage channel representing the spatial coverage of the monitoring stations on a preset spatial computing grid based on the site location; and combine the site features and coverage channel to form operator input data. S3. Input the operator input data into the neural operator network and output the predicted concentration field on the preset spatial computing grid. S4. Sample the predicted concentration field at the site location to obtain the predicted site value, and calculate the observation residual by comparing the predicted site value with the corresponding water quality parameter value. Construct the measurement noise covariance matrix based on the site confidence. Input the observation residual, hydraulic distance information, flow direction information, and measurement noise covariance matrix into the Kalman gain network to obtain the Kalman gain matrix, update the predicted concentration field, and obtain the assimilated concentration field; S5. Input the assimilated concentration field into the diffusion feature extraction network to obtain the first diffusion feature set. Calculate the second diffusion feature set based on the assimilated concentration field according to the preset feature calculation rules. The consistency index is calculated between the first diffusion feature set and the second diffusion feature set, and the first diffusion feature set and the second diffusion feature set are fused according to the consistency index to obtain the final diffusion feature set; S6, the operator input data, assimilation concentration field and the final diffusion feature set are stored in the sliding time window. When the data of the next observation time is obtained, the parameters of the neural operator network, Kalman gain network and diffusion feature extraction network are incrementally updated based on the sliding time window to reduce the error between the predicted station value and the water quality parameter value at the monitoring station, and to reduce the consistency index between the first diffusion feature set and the second diffusion feature set.

2. The method for extracting water quality fluid diffusion features based on machine learning according to claim 1, characterized in that, S1 includes: Obtain the location of multiple monitoring stations, where the location is the spatial coordinate of each monitoring station in a unified coordinate system; Obtain the observation time corresponding to the multiple monitoring stations and the water quality parameter values ​​at the observation time; For each monitoring station at each observation time, a missing measurement mask is determined based on whether there is a valid water quality parameter value at the monitoring station. When there is a valid water quality parameter value, the missing measurement mask takes a first preset value. When there is no valid water quality parameter value, the missing measurement mask takes a second preset value. The first preset value and the second preset value are different. Obtain hydraulic distance information between the multiple monitoring stations, wherein the hydraulic distance information is the distance along the water body connection path; Obtain flow direction information among the multiple monitoring stations, wherein the flow direction information is used to characterize the upstream and downstream relationships among the multiple monitoring stations; Obtain sensor status information corresponding to each monitoring station. The sensor status information includes self-test results or fault identifiers used to characterize the sensor's working status.

3. The water quality fluid diffusion feature extraction method based on machine learning according to claim 1, characterized in that, S2 include: The sensor reliability score of each monitoring station is determined based on the sensor status information, and the validity of the water quality parameter values ​​of each monitoring station at each observation time is determined by combining the missing measurement mask. Based on the validity determination, the station confidence level of each monitoring station is obtained. The station location, observation time, water quality parameter value, missing measurement mask and the station confidence level are numerically processed and spliced ​​in a preset order to obtain the station feature vector corresponding to each monitoring station. The site feature vector is mapped to the corresponding grid point in the preset spatial computing grid according to the site location to generate a site feature channel, wherein the site feature channel of the grid point not mapped to the monitoring site takes a preset fill value; A coverage channel is generated on the preset spatial computing grid, wherein the coverage channel includes a distance channel and an observation density channel. The distance channel is the distance from each grid point to the nearest monitoring station, and the observation density channel is the ratio of the number of monitoring stations with valid water quality parameter values ​​in the preset neighborhood to the area of ​​the preset neighborhood. The site feature channel and the coverage channel are superimposed along the channel dimension to obtain the operator input data.

4. The method for extracting water quality fluid diffusion features based on machine learning according to claim 1, characterized in that, S3 includes: Arrange the operator input data into an input tensor according to the grid point order of the preset spatial calculation grid; The input tensor is fed into the up-dimensional mapping layer of the neural operator network to obtain the hidden representation; Perform at least one spectral domain convolution operation on the latent representation to obtain an updated latent representation, wherein the spectral domain convolution operation includes performing a fast Fourier transform on the latent representation to obtain a spectral domain representation, multiplying the spectral domain representation with trainable weight parameters to obtain an updated spectral domain representation, and performing an inverse fast Fourier transform on the updated spectral domain representation to obtain the updated latent representation. The updated hidden representation is input into the projection layer of the neural operator network, and the predicted concentration values ​​of each grid point of the preset spatial computing grid are output to obtain the predicted concentration field.

5. The method for extracting water quality fluid diffusion features based on machine learning according to claim 1, characterized in that, S4 includes: Based on the location of the monitoring station, a sampling mapping relationship is established from the preset spatial computing grid to the location of the monitoring station, and the predicted concentration field is sampled at the location of the monitoring station according to the sampling mapping relationship to obtain the predicted station value. The observation residual is obtained by subtracting the predicted station values ​​from the water quality parameter values ​​at the corresponding observation times. A measurement noise covariance matrix is ​​constructed based on the site confidence level, wherein the measurement noise covariance matrix is ​​a diagonal matrix and the diagonal elements are negatively correlated with the site confidence level of the corresponding monitoring site; The observation residual, hydraulic distance information, flow direction information, and measurement noise covariance matrix are input into a Kalman gain network to obtain a Kalman gain matrix. The Kalman gain network constrains the propagation weight of the observation residual based on the hydraulic distance information and the flow direction information, so that the propagation weight along the flow direction is greater than the propagation weight against the flow direction. The observation residuals are weighted based on the Kalman gain matrix to obtain the grid update amount, and the grid update amount is superimposed with the predicted concentration field to obtain the assimilation concentration field.

6. The water quality fluid diffusion feature extraction method based on machine learning according to claim 1, characterized in that, S5 include: The assimilation concentration field is input into the diffusion feature extraction network, which outputs the first diffusion feature set, which includes the diffusion boundary, diffusion center line, diffusion front position and arrival time. The second diffusion feature set is calculated based on the assimilation concentration field according to the preset feature calculation rules. The preset feature calculation rules include using a first preset concentration threshold to determine the diffusion boundary, where the diffusion boundary is a boundary curve or boundary set in the assimilation concentration field where the concentration value satisfies the first preset concentration threshold; using the geometric center trajectory of the high-concentration connected region along the flow direction to determine the diffusion center line; using the grid point that satisfies the first preset concentration threshold along the flow direction and is the farthest away to determine the diffusion front position; and using the assimilation concentration field within the sliding time window to determine the moment when the concentration value at each preset position first reaches the first preset concentration threshold as the arrival time. The consistency index is obtained by calculating the difference between the same-named diffusion features in the first diffusion feature set and the second diffusion feature set. A fusion weight is generated based on the consistency index, and the first diffusion feature set and the second diffusion feature set are weighted and fused using the fusion weight to obtain the final diffusion feature set.

7. The water quality fluid diffusion feature extraction method based on machine learning according to claim 1, characterized in that, S6 include: After completing steps S2 to S5 at each observation time, the operator input data, assimilation concentration field and final diffusion feature set corresponding to the observation time are stored in the sliding time window in chronological order. When the number of items stored in the sliding time window reaches the preset upper limit, the operator input data, assimilation concentration field and final diffusion feature set corresponding to the earliest observation time are deleted. After obtaining the station location, observation time, water quality parameter value, missing measurement mask, hydraulic distance information, flow direction information, and sensor status information as described in step S1 for the next observation time, step S3 is re-executed based on the operator input data stored in the sliding time window to obtain the predicted concentration field. The prediction error between the predicted station value at the monitoring station and the water quality parameter value stored in the sliding time window is calculated based on the predicted concentration field and the water quality parameter value stored in the sliding time window. The first diffusion feature set is obtained by inputting the assimilation concentration field stored within the sliding time window into the diffusion feature extraction network, and the second diffusion feature set is calculated based on the assimilation concentration field according to the preset feature calculation rules. Then, the consistency index between the first diffusion feature set and the second diffusion feature set is calculated. The prediction error and the consistency index are weighted and summed according to preset weights to obtain the update objective function. Based on the update objective function, the parameters of the neural operator network, the Kalman gain network, and the diffusion feature extraction network are incrementally updated to obtain the updated neural operator network, the updated Kalman gain network, and the updated diffusion feature extraction network.

8. The method for extracting water quality fluid diffusion features based on machine learning according to claim 1, characterized in that, The neural operator network in step S3 is a graph neural operator network, which constructs graph structure data based on the preset spatial computing grid. The edge weights of the graph are determined by hydraulic distance information and flow direction information. The graph neural operator network outputs the predicted concentration field on the preset spatial computing grid.

9. The method for extracting water quality fluid diffusion features based on machine learning according to claim 5, characterized in that, The Kalman gain network introduces a propagation delay constraint based on hydraulic distance information when calculating propagation weights. This propagation delay constraint is used to limit the contribution of observation residuals to the update of grid points that exceed a preset delay range, thereby reducing non-physical updates across cross sections or tributaries.

10. The method for extracting water quality fluid diffusion features based on machine learning according to claim 6, characterized in that, The diffusion feature extraction network outputs the feature uncertainty corresponding to each diffusion feature while outputting the first diffusion feature set. The consistency index is calculated jointly based on the first diffusion feature set, the second diffusion feature set, and the feature uncertainty, and the fusion weight is negatively correlated with the feature uncertainty.

Images