A multi-domain physical constraint differentiable embedding graph bias network anomaly detection method and system

Abstract

The application discloses a kind of multi-domain physical constraint differentiable embedding graph deviation network anomaly detection method and system, specifically relates to abnormal detection technical field, including S1, data acquisition and graph construction, S2, graph attention feature extraction, S3, adaptive adjacency selection, S4, prediction and deviation calculation, S5, obtain priori physical constraint set, S6, calculate the violation of each physical constraint, S7, three complementary embedding strategies, S8, joint optimization target and adaptive weight mechanism, S9, gradient descent end-to-end training, S10, anomaly detection and physical violation degree report.The application physical constraint guided model learns the feature representation consistent with physics, effectively filters the false alarm of "physical impossibility", greatly reduces the false alarm rate, and has wider applicability, thereby solving the problem that PINN of physical information neural network can embed physical laws, but is not applicable to the graph structure scene of algebraic relationship between discrete sensors of valve cooling system, such as pressure balance and thermal balance.

Description

Technical Field

[0001] This invention relates to the field of anomaly detection technology, and more specifically, to a method and system for anomaly detection in multi-domain physically constrained differentiable embedded graph deviation networks. Background Technology

[0002] The UHVDC converter station is the core hub of the power grid. The converter valve cooling system dissipates heat from the converter valve through circulating cooling water. If an abnormality occurs, it will directly lead to the converter valve overheating and shutdown, or even cause a large-scale power outage. The existing valve cooling system monitoring mainly relies on fixed threshold alarms, which have the following problems: (1) Threshold rigidity: It cannot adapt to seasonal temperature differences and site environment differences, resulting in a high false alarm rate in winter and a high risk of missed alarms in summer; (2) Post-event alarm: It only alarms after the parameters exceed the limit, and cannot predict progressive abnormalities (such as pump performance degradation, slight pipeline blockage); (3) No root cause analysis: It is impossible to locate the root cause of the fault after the alarm (such as whether the high inlet valve temperature is a pump problem or a cooling tower / air cooler problem); (4) No cross-parameter correlation: Each sensor is monitored independently, ignoring physical constraint relationships (such as flow rate and pressure difference satisfying the square law relationship, inlet and outlet valve temperature difference and flow rate satisfying the thermal balance relationship), and cannot detect hidden abnormalities such as "all parameters are normal but the physical relationship is destroyed".

[0003] In the prior art, patent publication number CN121807647A discloses a log anomaly detection method based on pattern awareness and synthetic attention mechanism. This method designs a bidirectional guided synthetic attention mechanism to achieve pattern-to-sequence focusing guidance and sequence-to-pattern anomaly backtracking, generating a synthetic anomaly representation that integrates contextual summaries and pattern biases. Finally, an anomaly score and interpretability alert information are output via an MLP classifier. Through this technical solution, the invention can achieve collaborative modeling of macroscopic patterns and microscopic details in log data, significantly improving the accuracy, robustness, and interpretability of anomaly detection in complex scenarios. However, this solution still has the following shortcomings.

[0004] Existing Graph Deviation Networks (GDNs) applied to anomaly detection in valve cooling systems suffer from several drawbacks. These include spurious associations easily learned through pure data-driven approaches, misjudgments due to violations of conservation laws caused by a lack of physical constraints, and insufficient generalization ability across operating conditions. While Physical Information Neural Networks (PINNs) can embed physical laws, their partial differential equation constraints are geared towards continuous spatial fields, making them unsuitable for graph-structured scenarios involving discrete algebraic relationships between sensors in valve cooling systems, such as pressure and thermal balance. Currently, there is no systematic solution combining multi-domain physical constraints with GDNs. Summary of the Invention

[0005] To overcome the aforementioned deficiencies of the prior art, this invention provides a method and system for anomaly detection in multi-domain physically constrained differentiable embedded graph deviation networks, comprising the following specific steps: S1. Data Acquisition and Graph Construction: Collect time-series data of the 38-dimensional sensor of the valve cooling system at each time step, initialize the node and edge set according to the physical and functional relationship of the sensor, complete the construction of the basic graph structure of the sensor, and provide data and structural support for subsequent graph network operations. S2. Graph Attention Feature Extraction: Input time-series data into the two-layer graph attention network of GDN, calculate node attention coefficients and weights through a 4-head multi-head attention mechanism, aggregate node neighborhood features, and mine hidden correlation features between sensor nodes. S3, Adaptive Adjacency Selection: Based on the attention weight of each node, the top 5 best neighbors of each node are selected to construct an adaptive adjacency matrix. At the same time, two types of physically coupled bidirectional edges are injected to make the physical association of the system explicitly integrated into the graph structure. S4. Prediction and Deviation Calculation: The sensor prediction value is output by the decoder MLP, and combined with the actual value, sensor standard deviation and adaptive attention weight, the initial deviation of a single sensor and the overall system anomaly score are calculated to quantify the degree of data anomaly. S5. Obtain the set of prior physical constraints: Construct 6 types of physical constraints specific to the valve cooling system, uniformly adopt differentiable Soft-Clamp function modeling, clarify the residual calculation formula, threshold and temperature parameters of each type of constraint, and form a complete physical constraint system; S6. Calculate the violation amount of each physical constraint: Substitute the model prediction value and node features into the formula of the 6 types of physical constraints to calculate the constraint violation amount with values ​​from 0 to 1. The closer the value is to 1, the more serious the violation of the corresponding physical rule. S7. Three complementary embedding strategies: Through node feature enhancement, edge attention bias, and physical regularization loss, all physical constraints are fused and embedded into the graph bias network from the dimensions of features, graph structure, and loss function, respectively. S8. Joint Optimization Objective and Adaptive Weight Mechanism: The overall optimization objective of the model is constructed by integrating multiple types of losses. An adaptive weight mechanism is designed to dynamically and iteratively adjust the weights of six types of physical constraints. The constraint weights are limited to a fixed range to adapt to the system's operating state. S9. Gradient Descent End-to-End Training: A two-stage gradient descent strategy is used to train the model. In the early stage, only the basic network is trained. In the later stage, multiple types of constraint losses are introduced. Different learning rates and total number of iterations are set. After training is completed, the anomaly classification threshold is determined. S10, Anomaly Detection and Physical Violation Report: Utilizes the trained model to process real-time data, calculates anomaly scores by combining reconstruction errors and physical constraint contributions, triggers tiered alarms when thresholds are exceeded, and synchronously outputs detailed violation detection reports for each physical constraint.

[0006] In a preferred embodiment, the data acquisition and graph construction in step S1 are obtained from the valve cooling system. Each sensor node in Time series data at each time step Constructing sensor maps ,in For a set of sensor nodes, ; This is a set of edges, with the initial edges set based on the physical connections or functional relationships between the sensors. =38 represents the sensor dimension. The time step is determined by the system sampling frequency and the acquisition duration.

[0007] In a preferred embodiment, the graph attention feature extraction in step S2 involves inputting time-series data into the graph attention network layer of the Graph Bias Network (GDN), and calculating the attention coefficients and attention logs between nodes through a multi-head attention mechanism. Attention weight ,in , For nodes , Embedding features, The weight matrix is ​​a learnable matrix. For attention parameter vectors, This represents vector concatenation; the aggregated features are obtained by averaging the outputs of K = gat_heads heads, using two stacked BatchedGATLayer layers, with gat_heads = 4 attention heads.

[0008] In a preferred embodiment, the adaptive adjacency selection in step S3 is based on attention weights, selecting for each node. Construct an adaptive adjacency matrix from the most relevant neighbor nodes. , ,in For nodes Attention weight vector, This indicates taking the highest attention weight. A set of neighbor node indices; during graph construction, additionally inject coupled node pairs C4 (liquid level-temperature-pressure) and C5 (flow rate-pressure difference) as bidirectional edges, so that physical associations are explicitly expressed in the graph structure.

[0009] In a preferred embodiment, in step S4, the prediction and bias calculation involves inputting node features and the adaptive adjacency matrix into the Decoder layer of the multilayer perceptron (MLP) to calculate the predicted value for each sensor. The predicted value Compared with the true value The deviation between the two values ​​is input into the anomaly scoring function to calculate the initial anomaly score. Comprehensive abnormality score ,in For the true value, For sensors Standard deviation training set statistics The sensor weights are adaptively determined by the attention weights.

[0010] In a preferred embodiment, step S5 involves obtaining a set of prior physical constraints for the valve cooling system, wherein each physical constraint is represented in the form of a differentiable Soft-Clamp function. , To constrain the threshold, For temperature parameters, To constrain the residuals, each constraint... The definitions are given in the specific constraint formulas. The physical constraints include the following six types of domain-specific constraints: (1) C1 — Three-way synergistic constraints for pressure stability in nitrogen stabilization system Bypass balance pressure difference: System voltage drop deviation: Voltage regulation capability deviation: Overall constraint value: In the above formula: For expansion tank pressure, For valve pressure, For inlet valve pressure, For the pressure change rate of the expansion tank, For the allowable deviation of bypass balance, Normal system voltage drop Pressure drop tolerance Maximum allowable pressure change rate The default temperature parameter for Soft-Clamp is 0.01. LogSumExp is the smooth maximum value function; (2) C2 — Thermal balance energy conservation constraint of converter valve inlet and outlet valves Temperature difference between inlet and outlet valves: Actual heat dissipation power: Expected heat dissipation power: Thermal balance deviation: In the above formula: For valve outlet temperature, For valve inlet temperature, For cooling water flow rate, For valve group real-time power, For the specific heat capacity of pure water, For the density of pure water, For rated power, For rated heat exchange, Allowable deviation threshold is configurable. The default temperature parameter for Soft-Clamp is 0.02. (3) C3 — Multidimensional constraints on the heat exchange efficiency of cooling towers / air coolers; Actual cooling performance: Fan load and spray pump operation ratio: , Number of NTU heat transfer units: Theoretical cooling efficiency: Soft-Clamp bias : In the above formula: For valve outlet temperature, For valve inlet temperature, For ambient wet-bulb temperature, For cooling water flow rate, For fan speed, For the status of the spray pump, Calibration parameters for rated NTU constants Rated circulating water flow rate Fan rated speed, Spray gain coefficient calibration parameters Allowable deviation threshold The default temperature parameter for Soft-Clamp is 0.05. (4) C4 — Expansion tank level-temperature-pressure coupling constraint; Temperature deviation and pressure deviation: , Expected liquid level: Soft-Clamp bias: In the above formula: To calibrate the reference inlet valve temperature (calibration parameter, selected based on historical data statistics during the system's steady-state operation, with a typical value of 25-30℃), To calibrate the parameters of the reference expansion tank pressure, - The coefficients of the second-order polynomial (model parameters, identified through least squares regression): The percentage of the reference liquid level deviation Temperature sensitivity % / ℃ Pressure sensitivity % / kPa Temperature nonlinearity coefficient % / ℃ 2 , Pressure nonlinearity coefficient % / kPa 2 , Temperature-pressure cross-coupling coefficient % / ℃·kPa For the actual liquid level in the expansion tank, The default temperature parameter for Soft-Clamp is 1.0. (5) C5 — Steady-state flow rate and pressure difference square law constraint of pipeline system Actual pressure difference vs. expected pressure difference: Soft-Clamp bidirectional bias: In the above formula: For inlet valve pressure, For valve pressure, For cooling water flow rate, Configurable parameters for pipeline resistance coefficient, identified using least squares based on historical steady-state data. For steady-state pressure difference threshold, The default temperature parameter for Soft-Clamp is 0.02. It was determined to be a suspected blockage at that time. It was initially determined to be a suspected leak. Parameters for calibrating the fault direction discrimination threshold; (6) C6 — Single-point violation of the three-layer coupling constraint on the conductivity of the cooling medium: Differential coupling detection: , Temperature compensation and value verification: , Overall constraint value: In the above formula: Main circuit cooling water conductivity, For the conductivity of deionized water, For valve inlet temperature, Upper limit of main circuit conductivity The upper limit of the conductivity of deionized water Upper limit constraint for conductivity difference Temperature compensation coefficient, - The default temperature parameter for Soft-Clamp is 0.01.

[0011] In a preferred embodiment, the predicted value is calculated in step S6 based on the violation amount of each physical constraint. Alternatively, the node-level feature representation can be substituted into the physical constraint set to calculate the violation amount of each physical constraint. ,in This indicates that the constraints are fully satisfied. This indicates a serious violation of the constraint.

[0012] In a preferred embodiment, in step S7, the three complementary embedding strategies concatenate constraint violation scores to the corresponding sensor node feature vectors through node feature enhancement NFA, increasing the original input dimension from 1 to 1+C=7, where C=6 is the number of constraints, applicable to all constraints C1-C6; and adjusts the edge weights in the graph attention encoder using physical coupling relationships through edge attention bias EAB. ,in =0.1 is the bias strength coefficient, applicable to coupled constraints C4 level-temperature-pressure and C5 flow-pressure difference; the degree of constraint violation is expressed as a differentiable loss function through the physical regularization loss PRL. The total loss is applied to all constraints C1-C6, and the three strategies are combined to embed the physical constraints into the graph bias network.

[0013] In a preferred embodiment, in step S8, the joint optimization objective and adaptive weighting mechanism, based on the violation amount, embed the physical constraints as soft constraints into the loss function of the graph deviation network to construct the joint optimization objective. ,in For mean square error loss, For traditional constraint losses, For physical residual loss, To penalize the complexity of the adjacency matrix, a physical sensitivity adaptive weighting mechanism is used to dynamically adjust the weights of each constraint: Where η = 0.01 is the sensitivity adjustment rate. This represents the batch average violation rate of constraint k in this epoch. =0.001 is the lower limit of the weight. = 2.0 is the upper limit of the weight. Initial weights: C1=1.0, C2=1.5, C3=1.0, C4=0.8, C5=1.0, C6=0.5. In step S9, gradient descent is used for end-to-end training of the joint optimization objective until convergence. A two-stage training strategy is employed: in the first stage, if epoch ≤ 5, only... Training the base GDN, lr=0.001; the second stage introduces epoch>5. , and With lr=0.0001 and total epochs=10, after training, the threshold q95 quantile and the severity threshold q99 quantile are calculated on the validation set. In step S10, anomaly detection and physical violation reporting are performed. The trained model is used to detect anomalies in real-time data. The anomaly score is calculated by combining the reconstruction error and the contribution of physical constraints. When the anomaly score exceeds the threshold, a graded alarm is triggered, and a physical constraint violation report is output.

[0014] A multi-domain physical constraint differentiable embedded graph deviation network anomaly detection system implements the above-mentioned multi-domain physical constraint differentiable embedded graph deviation network anomaly detection method, including a data acquisition and preprocessing module, a graph network modeling module, a multi-domain physical constraint calculation module, a joint loss optimization training module, an adaptive weight update module, a real-time inference scoring module, a hierarchical alarm and root cause reporting module, an incremental learning module, and a center-edge collaborative deployment module; The data acquisition and preprocessing module is used to acquire time series data of industrial equipment sensors, complete missing value filling, noise filtering, time series smoothing, normalization and time series sliding window construction, output standardized time series samples and construct sensor topology map; The graph network modeling module has a built-in two-layer multi-head graph attention network GAT and decoder MLP, which are used to complete node feature aggregation, adaptive adjacency matrix filtering, sensor measurement prediction, and output the reconstructed prediction values ​​of each sensor and the attention weight matrix. The multi-domain physical constraint calculation module has built-in 6 types of Soft-Clamp differentiable physical constraint calculation logic. It calculates the constraint violation C1 to C6 in batches based on the actual sensor measurement values ​​and the model's inverse normalization prediction values, providing constraint numerical inputs for feature enhancement, attention bias, and physical regularization loss. The joint loss optimization training module is used to construct a joint total loss function that includes mean squared error loss, traditional constraint loss, physical residual loss, and adjacency matrix complexity penalty, perform two-stage gradient descent end-to-end training, complete the joint optimization of basic GDN pre-training and physical constraints, and obtain the early warning threshold and severe alarm threshold based on the anomaly score statistics of the validation set after training. The adaptive weight update module is used to dynamically update the weight parameters of various physical constraints based on the average constraint violation amount in a single iteration after each training round, limit the weight values ​​to a preset maximum and minimum value range, save the initial weight configuration of each constraint, and provide parameter support for the model training and inference process. The real-time inference scoring module loads the trained network weights, normalized parameters, and alarm thresholds, performs forward inference on the real-time sliding window data, and calculates a global comprehensive anomaly score by integrating the normalized reconstruction error and the contribution of physical constraint violation. The graded alarm and root cause reporting module is used to compare the comprehensive anomaly score with the preset threshold to realize a four-level graded alarm. When an alarm is triggered, the module outputs the Top Suspicious Sensors and the corresponding Physical Constraint Violation Report according to the scores of each sensor node and the amount of each constraint violation, thus completing the fault root cause location. The incremental learning module integrates the ER-GNN experience replay buffer and the TWP topology weight protection regularization term for incremental training of new working conditions and new site data. After training, it verifies the average violation of physical constraints and automatically rolls back the parameter snapshot before training when the model fails, thus suppressing the forgetting of historical working condition identification. The central-edge collaborative deployment module is divided into a central terminal unit and an edge terminal unit. The central terminal unit is used to aggregate historical data from multiple sites to pre-train baseline models and export standardized model packages. The edge terminal unit is used to import model packages to verify their integrity, perform lightweight fine-tuning of models based on local historical data, and complete the activation of production models. It also includes an inference degradation scheduling module, which is used to monitor the online status of sensors and the loading status of models in real time, and to grade and decay anomaly scores according to the number of missing sensors. When a large number of core sensors are missing or the model fails, it automatically switches to a pure physical constraint calculation mode, relying solely on the violation of 6 types of physical constraints to output alarms, ensuring uninterrupted monitoring of the equipment.

[0015] The technical effects and advantages of this invention are as follows: 1. This invention improves detection performance and reliability. Physical constraints guide the model to learn feature representations that conform to physical consistency, significantly increasing the anomaly detection rate. Simultaneously, it effectively filters false alarms of "physically impossible" scenarios, greatly reducing the false alarm rate and making the detection results both accurate and reliable.

[0016] 2. This invention enhances interpretability and generalization ability. Six domain-specific physical constraints directly correspond to the actual equipment of the valve cooling system, realizing the leap from "black box alarm" to "white box diagnosis". It can also distinguish the direction of blockage and leakage. Physical knowledge serves as a stable constraint guide, significantly improving the generalization performance in distributed scenarios.

[0017] 3. The invention has engineering adaptability and knowledge reuse value. The physical constraint coding framework is universal and can be adapted to different valve cooling systems. It supports the structured accumulation and cross-site reuse of system knowledge, and provides an scalable technical foundation for the intelligent operation and maintenance of UHVDC transmission projects. Attached Figure Description

[0018] Figure 1This is a diagram illustrating the overall architecture of the multi-domain physical constraint differentiable embedded graph deviation network anomaly detection method of the present invention.

[0019] Figure 2 This is a schematic diagram of the data acquisition and preprocessing process of the present invention.

[0020] Figure 3 This is a schematic diagram of the mapping relationship between six types of physical constraints and sensors in this invention.

[0021] Figure 4 This is a schematic diagram of the overall architecture of the PC-GDN of the present invention.

[0022] Figure 5 This is a schematic diagram of the physical constraint encoding and embedding process of the present invention.

[0023] Figure 6 This is a schematic diagram of the center-edge collaborative deployment architecture of the present invention. Detailed Implementation

[0024] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the described embodiments are only some aspects of the present invention and do not represent all aspects. Any other solutions based on the embodiments of the present invention, which can be obtained without creative effort, fall within the protection scope of the present invention.

[0025] As attached Figure 1 - Appendix Figure 6 This paper presents a method and system for detecting anomalies in multi-domain physically constrained differentiable embedded graph deviation networks.

[0026] This first embodiment describes the overall architecture of a multi-domain physical constraint differentiable embedded graph deviation network anomaly detection system for ultra-high voltage converter valve cooling systems. For example... Figure 1 As shown, the system adopts a front-end and back-end separated Web architecture, which includes a front-end presentation layer, a back-end service layer, an algorithm core layer and a data persistence layer from top to bottom. The layers communicate with each other through standardized interfaces and the components within each layer are loosely coupled.

[0027] The front-end presentation layer supports functions such as real-time monitoring dashboard, model management, data access, alarm management, constraint configuration, and system management.

[0028] The backend service layer is divided into four layers based on their responsibilities: API routing layer, business service layer, algorithm core layer, and data access layer. The algorithm core layer encapsulates GDN training and inference, physical constraint calculation, and incremental learning algorithms.

[0029] The data persistence layer adopts a dual database strategy: a relational database stores business metadata, and a time-series database stores sensor sampling data and anomaly scoring time-series data.

[0030] The system supports both containerized production deployment and local development deployment. Production deployment uses container orchestration tools, including relational database service containers, time-series database service containers, backend service containers, and frontend static resource service containers. Local development deployment allows direct integration testing of the backend development server and the frontend development server.

[0031] Example 2: Data Acquisition and Preprocessing In this example, the system is configured with an N=39-dimensional core sensor, covering six physical quantities of the valve cooling system: pressure, temperature, flow rate, power, liquid level, and conductivity. It supports three industrial communication protocols for data acquisition: Kafka, MQTT, and Modbus TCP. For example... Figure 2 As shown, data cleaning includes the following three steps.

[0032] Step 1: Forward Imputation of Missing Values. A forward imputation strategy is used, imputing a maximum of 5 consecutive time steps. The criteria are: a system sampling frequency of 1Hz, and a maximum tolerable missing value duration of 5 seconds corresponding to the typical recovery time of a brief sensor communication interruption. Step 2: Rolling Z-Score Outlier Replacement. The Z-Score of each sensor is calculated within a rolling window. Outliers satisfying |z| > 4 are replaced using the window's median value (based on the probability of |z| > 4 under a normal distribution of approximately 0.0063%, effectively distinguishing between real physical anomalies and sensor noise spikes). Step 3: Moving Average Smoothing. A 3-point moving average is used to smooth the data. The criteria are: 3-point smoothing can effectively suppress high-frequency sensor noise while preserving signal trends.

[0033] The cleaned data was normalized using the Z-Score method: x_norm = (x - mean) / scale, where the mean and standard deviation were statistically obtained from the training set and persisted during the training phase, and loaded and used during the inference phase. A sliding window method was used to construct the time series samples: window size W = 30, determined based on the fact that a 30-second window can cover the typical response time constant of 20-40 seconds for the thermodynamic process of a valve-cooled system, with a step size of 1. The output window matrix shape is B, W, N, where B is the number of samples. The validation set partition ratio was 0.2, and the partitioning method was forward partitioning of the time series to avoid data leakage.

[0034] Example 3: Physical constraint modeling, such as Figure 3 As shown, the six types of physical constraints (C1-C6) define the coupling relationships between various physical quantities in the valve cooling system. Each constraint uses a uniform Soft-Clamp differentiable function: Where r is the constraint residual (normalized deviation between actual physical value and expected value), r=0 indicates that the constraint is fully satisfied, and r>0 indicates that the constraint is violated; θ is the constraint threshold (upper limit of tolerable deviation); τ is the temperature parameter (controlling the smoothness of the Soft-Clamp transition).

[0035] 3.1 C1 — Three Cooperative Constraints for Pressure Stabilization in the Nitrogen Pressure Stabilization System: The C1 constraint is associated with the expansion tank pressure. (P001) Inlet valve pressure (P002) Outlet valve pressure (P003) Three sensors. The physical topology of the system is a closed loop: the water outlet pipe at the bottom of the expansion tank and the return pipe of the outlet valve merge before the inlet of the main circulation pump. After being pressurized by the main circulation pump, the cooling water is distributed to the inlet valve side, flows through the converter valve tower to dissipate heat, and then flows back to the merging point. The nitrogen gas cushion at the top of the expansion tank achieves pressure stabilization.

[0036] Bypass balancer constraints: System voltage drop constraint: Pressure change rate sub-constraint: Overall constraint value: In the above formula: For expansion tank pressure, For valve pressure, For inlet valve pressure, For the pressure change rate of the expansion tank, The allowable deviation for bypass balancing (calibration parameter, based on historical steady-state data statistics, typical value 0.02MPa). Normal system pressure drop (calibrated parameter, mean steady-state data, typical value 0.15-0.25MPa) Permissible pressure drop deviation (calibration parameter, taken as 5%–10%) Maximum permissible pressure change rate (calibration parameter, calculated from historical data, representing the 99th percentile of the expansion tank pressure change rate during normal operation; typical value: 0.001 MPa / s). This is the Soft-Clamp temperature parameter (default 0.01), where This is the LogSumExp function for smoothing maximum values.

[0037] 3.2 C2 — Thermal balance energy conservation constraint for converter valve inlet and outlet: The C2 constraint is based on the first law of thermodynamics and is related to the outlet valve temperature. Inlet valve temperature Cooling water flow rate Real-time power of valve group Four sensors. Physical principle: Power devices such as thyristors generate heat due to conduction and switching losses, which is absorbed by the circulating coolant (pure water) and carried out of the valve body. The temperature difference between the inlet and outlet valves, the flow rate, and the heat exchange satisfy the energy conservation relationship.

[0038] Calculation steps: Temperature difference Actual heat dissipation power ; Expected heat dissipation power ,in For valve outlet temperature, For valve inlet temperature, For cooling water flow rate, For valve group real-time power, For the specific heat capacity of pure water, For the density of pure water, Rated power (configurable parameter, taken from the converter valve design manual). Rated heat exchange capacity (configurable parameter, taken from the valve cooling system design manual). This is the temperature parameter for Soft-Clamp (default 0.02). Constraint values: ,in The allowable deviation threshold (configurable parameter, default 5%).

[0039] 3.3 C3 — Effectiveness-NTU Method for Multidimensional Constraints on Heat Exchange Efficiency of Cooling Towers / Air Coolers: The C3 constraint is based on the Effectiveness-NTU heat exchange theory and is related to the outlet valve temperature. Inlet valve temperature Ambient wet-bulb temperature Cooling water flow rate Fan speed Spray pump status (Switching signal) Six types of sensor data. Core physical principle: Cooling efficiency ε is the ratio of actual temperature drop to theoretical maximum temperature drop, NTU is the number of heat transfer units, and the two satisfy... Calculation steps: Actual cooling performance: Fan load and spray pump operation ratio: , NTU heat transfer unit count: Theoretical cooling efficiency: Soft-Clamp bias : In the above formula: For valve outlet temperature, For valve inlet temperature, For ambient wet-bulb temperature, For cooling water flow rate, For fan speed, For the status of the spray pump, This is the rated NTU constant (calibration parameter, calculated from rated operating conditions). Rated circulating water flow rate Fan rated speed, The spray gain coefficient calibration parameters were determined through comparative tests under wet / dry conditions, with typical values ​​ranging from 1.1 to 1.3. Allowable deviation threshold This is the temperature parameter for Soft-Clamp (default 0.05).

[0040] 3.4 C4 — Expansion tank level-temperature-pressure coupling constraint: The C4 constraint describes the second-order polynomial coupling relationship between the expansion tank liquid level and the inlet valve temperature and expansion tank pressure, and is associated with the actual expansion tank liquid level. Inlet valve temperature and expansion tank pressure Physical Principle: The expansion tank liquid level is simultaneously affected by multiple factors, including changes in cooling medium temperature, system pressure fluctuations, nitrogen pressure changes, and cooling medium leakage or replenishment. This constraint establishes a second-order polynomial nonlinear temperature-pressure-liquid level coupling model with the liquid level percentage as the state variable. Calculation Steps: Temperature deviation and pressure deviation: , Expected liquid level: Soft-Clamp bias: In the above formula: To calibrate the reference inlet valve temperature (calibration parameter, selected based on historical data statistics during the steady-state operation of the system, typical value 25-30℃), To calibrate the reference expansion tank pressure (calibration parameter) - The coefficients of the second-order polynomial (model parameters, identified through least squares regression): The percentage of the reference liquid level deviation Temperature sensitivity % / ℃ Pressure sensitivity % / kPa Temperature nonlinearity coefficient % / ℃ 2 , Pressure nonlinearity coefficient % / kPa 2, (Temperature-pressure cross-coupling coefficient % / (°C·kPa)) For the actual liquid level in the expansion tank, This is the temperature parameter for Soft-Clamp (default 1.0).

[0041] 3.5 C5 — Steady-state flow rate and pressure difference square law constraint for pipeline systems: The C5 constraint is based on pipeline fluid mechanics theory and is related to the inlet valve pressure. Outlet valve pressure And the cooling water flow rate Q. Physical principle: When cooling water undergoes fully developed turbulent flow in a pipe, the pressure loss is proportional to the square of the flow rate (Δp = KQ). 2 This equation describes the inherent resistance characteristics of a piping system. When a blockage occurs in the pipe, the resistance increases (the actual pressure difference is higher than the expected value); when a leak occurs, the effective flow cross-section increases (the actual pressure difference is lower than the expected value). Calculation steps: Actual pressure difference vs. expected pressure difference: Soft-Clamp bidirectional bias: In the above formula: For inlet valve pressure, For valve pressure, For cooling water flow rate, The pipeline resistance coefficient (configurable parameter, identified by least squares based on historical steady-state data) This is the steady-state differential pressure threshold (calibration parameter, residual threshold after temperature compensation, typical value 5%). For the Soft-Clamp temperature parameter (default 0.02), when It was determined to be a suspected blockage at that time. It was initially determined to be a suspected leak. The threshold for determining the direction of the fault (calibration parameter, default 5%).

[0042] 3.6 C6 — Three-layer coupling constraint of cooling medium conductivity The C6 constraint detects abnormalities in the conductivity of the cooling medium from three levels, and correlates them with the conductivity of the main circuit cooling water. Deionized water conductivity and inlet valve temperature Physical principle: The conductivity σ is directly proportional to the ion concentration in water, and conductivity is a highly temperature-sensitive physical quantity (the conductivity increases by about 2% for every 1°C increase in temperature). Temperature compensation is a necessary condition for the sum value constraint.

[0043] First layer (hard boundary) single-point upper limit detection: . The upper limit of the main circuit conductivity (configurable parameter, μS / cm, taken from the setting table of the valve cooling system design manual, typical value 0.5-1.0μS / cm). The upper limit of the conductivity of deionized water (configurable parameter, taken from the design manual, typical value 0.1-0.2 μS / cm).

[0044] Second-layer (relative index) difference coupling detection: , . The upper limit of the conductivity difference constraint (configurable parameter, μS / cm, calibration).

[0045] Third layer (absolute index) temperature compensation and value detection: temperature compensation factor (dimensionless), where κ is the conductivity temperature compensation coefficient (configurable parameter, calibrated, typical value 0.02·℃). -1 Conductivity after temperature compensation . Upper limit of sum constraint (configurable parameter, μS / cm, calibration).

[0046] Overall constraint value: The three-layer constraint forms a progressive protection system from "water quality of each loop - ion exchanger efficiency - global ion load".

[0047] Example 4: Construction of GDN Graph Deviation Network Model, as follows Figure 4 As shown, the GDN is an encoder-decoder structure. The encoder consists of two stacked graph attention networks (GAT), and the decoder is a linear projection layer. The input dimension feature_dim is determined according to the NFA policy: feature_dim=1 when NFA is off, and feature_dim=7 when NFA is on.

[0048] The graph attention layer employs a concatenated attention mechanism, with an attention logarithm. Attention weight Neighbor aggregation ,in , For learnable parameters, , For nodes , The embedding features. When EAB is enabled, a bias is applied to the coupled edges of C4 / C5. .

[0049] The graph structure is constructed based on attention weights. Construction: After excluding self-loops for each node, select nodes in descending order of attention weight. Each neighbor is added to the self-loop edge (i,i). When EAB is enabled, the coupled node pair of C4 and C5 is additionally injected as a bidirectional edge.

[0050] The GDN forward propagation outputs three results: reconstruction output Attention weight matrix Node-level deviation score.

[0051] During the inference phase, the anomaly scoring fusion module calculates the comprehensive anomaly score by combining the reconstruction error and the contribution of physical constraints: in For the normalized reconstruction error of sensor i, To reconstruct the scale parameters (obtained from the validation set during the training phase). For adaptive physical weights (EMA mechanism update). Weighted violation contribution of physical constraints to sensor i (obtained through the external constraint engine).

[0052] Example 5: PC-GDN physical constraint enhancement mechanism, such as Figure 4 and Figure 5 As shown, the PC-GDN embeds physical constraints into the GDN through three complementary strategies, corresponding to the injection of physical information at the feature level, graph structure level, and loss level, respectively. These three strategies can be enabled independently.

[0053] Node Feature Enhancement: In each training / inference step, the violation contribution of each constraint to the node is concatenated to the node's original features. When enabled, the model input dimension is expanded from 1 to 1+K=7, and each node adds 6 constraint contribution channels on top of the sensor measurement channels.

[0054] Side attention configuration: For the physically coupled nodes C4 (level-temperature-pressure) and C5 (flow-pressure difference), apply a bias on the logarithm of the attention. ,in The bias intensity coefficient, This represents the batch average violation rate of the associated constraints. When → When the bias is 0, it approaches + Enhance information transmission on this side; when → When the bias is 1, it approaches 0, suppressing the transmission of information along that edge. After the bias is applied, it is renormalized using softmax.

[0055] Physical regularization loss: Reconstructs the output of GDN during the training phase. Inverse normalization to physical space yields After calculating the amount of constraint violation, the loss is calculated. By incorporating the total loss, an end-to-end differentiable physical consistency constraint is achieved. The inverse normalization method is as follows: ,in The standard deviation of each sensor, The values ​​are the average values ​​of each sensor, which are obtained and persisted from the training set during the training phase.

[0056] Example 6: Model training process, as follows Figure 1 As shown, a two-stage training strategy is adopted. In the first stage (epoch≤5), only L_MSE is used to train the base GDN with a learning rate lr=0.001, allowing the GDN to learn a stable sensor reconstruction representation first. In the second stage (epoch>5), physical constraints are introduced, and the learning rate is reduced to lr=0.0001.

[0057] Total loss .in Always enabled to reconstruct mean squared error; For traditional constraint loss, the constraint violation amount is calculated based on the input physical value; The constraint violation amount is calculated for the inverse normalized predicted value as the physical residual loss. As a penalty for adjacency matrix complexity, , This is the GAT attention weight matrix.

[0058] Adjust the constraint weights after each training round: Where η = 0.01 is the sensitivity adjustment rate. Let $k$ be the batch average violation of constraint $k$ for this epoch. .

[0059] Initial weights: .

[0060] An early stopping mechanism is used to monitor the validation set loss, with a patience of 5 rounds. After training, the q95th quantile of the overall score is calculated on the validation set as the warning threshold (default 0.50), and the q99th quantile is calculated as the severity threshold (default 0.90). At the same time, the reconstruction scale parameter σ_scale of each sensor is calculated.

[0061] Example 7: Reasoning and anomaly scoring. The system triggers reasoning at regular intervals. The steps are as follows: (1) Load the current production model weights and the normalization parameters (mean, scale) and thresholds saved during the training phase; (2) Construct the sensor input vector at the current moment; (3) Fill in missing values ​​forward and normalize Z-Score to construct a window matrix; (4) Calculate the reconstructed output x̂ and attention weights using GDN forward propagation; (5) Calculate the comprehensive anomaly score using the anomaly scoring fusion module, calculate the C1-C6 constraint violation amount using the external constraint engine, and output the anomaly level, a list of suspicious sensors, and the root cause text.

[0062] Anomaly scoring: Anomaly scores are calculated by combining the reconstruction error and the contribution of physical constraints. Normalized reconstruction error. ,in Reconstruction scale parameters for each sensor calculated during the training phase. Node scores. ,in For adaptive physical weights (EMA update). Weighted violation contribution of physical constraints for sensor i. Comprehensive anomaly score. Alarm classification: based on The comparison with the threshold triggers a graded alarm: L0 - Normal (score<0.50), L1 - Warning (0.50≤score<0.75), L2 - Alarm (0.75≤score<0.90), L3 - Severe (score≥0.90).

[0063] Root cause localization: When the anomaly level reaches L1 or above, select the Top-K (default K=3) suspicious sensors, combine them with constraint contribution to identify the most serious violation of physical constraints, and generate root cause text.

[0064] Inference degradation strategy: L0: Core sensors are complete, normal inference. L1: A small number of non-core sensors are missing (≤2), continue inference. L2: A large number of non-core sensors are missing or 1 core sensor is missing. Multiply by a 0.8 attenuation factor. Level L3: When ≥2 core sensors are missing or no usable model is available, switch to pure rule engine mode and determine anomalies solely by calculating constraint violations through the external constraint engine.

[0065] Example 8: Incremental Learning This embodiment employs an incremental learning mechanism of Experience Replay and Topology Weight Protection (ER-GNN+TWP). The experience replay buffer uses a fixed capacity to store historical samples, ensuring the diversity of historical patterns. Topology weight protection is based on Fisher information. Calculate parameter importance and add a regularization term to the incremental training loss. ,in For the current parameter, This is a snapshot of the parameters before incremental training. The physical anchor validator verifies the average constraint violation after incremental training; if it exceeds a threshold, it automatically rolls back to the previous level. .

[0066] During incremental training: (1) the new data is cleaned and normalized, and merged with the old windows in the replay buffer; (2) all new windows are added to the training. Extract old windows from the replay buffer and merge them into the training set; (3) Physical anchor point verification, if it fails, roll back to the parameter snapshot before training.

[0067] Forgetting estimation: forgetting index ,in and These represent the mean squared errors on the old validation set before and after incremental training, respectively. It indicates that nothing has been forgotten.

[0068] Example 9: Central-Edge Collaborative Deployment like Figure 6 As shown. In this embodiment, historical data from multiple converter stations are aggregated at the central end to train a shared baseline model. The aggregation strategy is weighted sampling based on the system data volume. After training, a model package is exported, containing model weight files, metadata files (including graph structure, normalization parameters, thresholds, and hyperparameters), and integrity verification values.

[0069] Edge-end import and fine-tuning: After importing the model package at the edge, an integrity check is performed. After the check passes, light-weight fine-tuning is performed on-site: incremental training of ER-GNN+TWP is conducted based on local data from the past 30 days. This allows the model to adapt to the specific equipment characteristics and operating conditions at the edge.

[0070] Model Deployment: After fine-tuning, the model is deployed as a production version and bound to the current system's production model, completing the entire process from pre-training at the central end to deployment and activation at the edge.

[0071] The model version lifecycle includes four states: draft, published, withdrawn, and archived. Tags include central pre-training, edge import, and in-situ fine-tuning. Version information includes graph structure, constraint weights, inference threshold, training hyperparameters, and evaluation metrics.

[0072] Experimental verification shows that, in the test set, data from a certain UHV converter station from April 2025 to April 2026 (one year total), with a sampling frequency of 1Hz and aggregation via a 10-second sliding window, including 5000 manually annotated anomalies, the performance comparison of PC-GDN, the original GDN, and various baseline methods is as follows: PC-GDN significantly outperformed the original GDN and baseline methods in all performance metrics. In particular, the physical violation rate decreased from 23.7% to 0.8%, the F1 score increased from 84.3% to 95.5%, and the anomaly detection rate improved by 11.2 percentage points.

[0073] Cross-site transfer validation: The model trained at station A (±800kV converter station, equipment from a certain manufacturer, temperate climate zone) was directly applied to station B (±800kV converter station, equipment from a different manufacturer, subtropical climate zone). The data from station B was not used for any training samples. Experimental results: GDN (direct application from station A training) AUC-ROC was 0.812 (a relative decrease of 12.2%), while PC-GDN (direct application from station A training) was 0.923 (a decrease of only 5.5%). Conclusion: The introduction of physical constraints provides the model with stable prior knowledge across stations. Even without fine-tuning, PC-GDN significantly outperforms GDN at station B.

[0074] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method and system for anomaly detection in multi-domain physically constrained differentiable embedded graph deviation networks, characterized in that: Including specific steps: S1. Data Acquisition and Graph Construction: Collect time-series data of the 38-dimensional sensor of the valve cooling system at each time step, initialize the node and edge set according to the physical and functional relationship of the sensor, complete the construction of the basic graph structure of the sensor, and provide data and structural support for subsequent graph network operations. S2. Graph Attention Feature Extraction: Input time-series data into the two-layer graph attention network of GDN, calculate node attention coefficients and weights through a 4-head multi-head attention mechanism, aggregate node neighborhood features, and mine hidden correlation features between sensor nodes. S3, Adaptive Adjacency Selection: Based on the attention weight of each node, the top 5 best neighbors of each node are selected to construct an adaptive adjacency matrix. At the same time, two types of physically coupled bidirectional edges are injected to make the physical association of the system explicitly integrated into the graph structure. S4. Prediction and Deviation Calculation: The sensor prediction value is output by the decoder MLP, and combined with the actual value, sensor standard deviation and adaptive attention weight, the initial deviation of a single sensor and the overall system anomaly score are calculated to quantify the degree of data anomaly. S5. Obtain the set of prior physical constraints: Construct 6 types of physical constraints specific to the valve cooling system, uniformly adopt differentiable Soft-Clamp function modeling, clarify the residual calculation formula, threshold and temperature parameters of each type of constraint, and form a complete physical constraint system; S6. Calculate the violation amount of each physical constraint: Substitute the model prediction value and node features into the formula of the 6 types of physical constraints to calculate the constraint violation amount with values ​​from 0 to 1. The closer the value is to 1, the more serious the violation of the corresponding physical rule. S7. Three complementary embedding strategies: Through node feature enhancement, edge attention bias, and physical regularization loss, all physical constraints are fused and embedded into the graph bias network from the dimensions of features, graph structure, and loss function, respectively. S8. Joint Optimization Objective and Adaptive Weight Mechanism: The overall optimization objective of the model is constructed by integrating multiple types of losses. An adaptive weight mechanism is designed to dynamically and iteratively adjust the weights of six types of physical constraints. The constraint weights are limited to a fixed range to adapt to the system's operating state. S9. Gradient Descent End-to-End Training: A two-stage gradient descent strategy is used to train the model. In the early stage, only the basic network is trained. In the later stage, multiple types of constraint losses are introduced. Different learning rates and total number of iterations are set. After training is completed, the anomaly classification threshold is determined. S10, Anomaly Detection and Physical Violation Report: Utilizes the trained model to process real-time data, calculates anomaly scores by combining reconstruction errors and physical constraint contributions, triggers tiered alarms when thresholds are exceeded, and synchronously outputs detailed violation detection reports for each physical constraint.

2. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S1, data acquisition and graph construction are performed in the valve cooling system. Each sensor node in Time series data at each time step Constructing sensor maps ,in For a set of sensor nodes, ; This is a set of edges, with the initial edges set based on the physical connections or functional relationships between the sensors. =38 represents the sensor dimension. The time step is determined by the system sampling frequency and the acquisition duration.

3. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S2, graph attention feature extraction involves inputting time-series data into the graph attention network layer of the Graph Bias Network (GDN), and calculating the attention coefficients and attention logs between nodes using a multi-head attention mechanism. Attention weight ,in , For nodes , Embedding features, The weight matrix is ​​a learnable matrix. For attention parameter vectors, This represents vector concatenation; the aggregated features are obtained by averaging the outputs of K = gat_heads heads, using two stacked BatchedGATLayer layers, with gat_heads = 4 attention heads.

4. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S3, adaptive adjacency selection is based on attention weights, selecting for each node. Construct an adaptive adjacency matrix from the most relevant neighbor nodes. , ,in For nodes Attention weight vector, This indicates taking the highest attention weight. A set of neighbor node indices; during graph construction, additionally inject coupled node pairs C4 (liquid level-temperature-pressure) and C5 (flow rate-pressure difference) as bidirectional edges, so that physical associations are explicitly expressed in the graph structure.

5. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S4, the prediction and bias calculation involves inputting node features and the adaptive adjacency matrix into the Decoder layer of the multilayer perceptron (MLP) to calculate the predicted value for each sensor. The predicted value Compared with the true value The deviation between the two values ​​is input into the anomaly scoring function to calculate the initial anomaly score. Comprehensive abnormality score ,in For the true value, For sensors Standard deviation training set statistics The sensor weights are adaptively determined by the attention weights.

6. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S5, the set of prior physical constraints is obtained. Obtain the set of prior physical constraints for the valve cooling system, where each physical constraint is represented in the form of a differentiable soft-clamp function. , As a constraint threshold, For temperature parameters, To constrain the residuals, each constraint... The definitions are given in the specific constraint formulas. The physical constraints include the following six types of domain-specific constraints: (1) C1 — Three-way synergistic constraints for pressure stability in nitrogen stabilization system Bypass balance pressure difference: System voltage drop deviation: Voltage regulation capability deviation: Overall constraint value: In the above formula: For expansion tank pressure, For valve pressure, For inlet valve pressure, For the pressure change rate of the expansion tank, For the allowable deviation of bypass balance, Normal system voltage drop Pressure drop tolerance Maximum allowable pressure change rate The default temperature parameter for Soft-Clamp is 0.

01. LogSumExp is the smooth maximum value function; (2) C2 — Thermal balance energy conservation constraint of converter valve inlet and outlet valves Temperature difference between inlet and outlet valves: Actual heat dissipation power: Expected heat dissipation power: Thermal balance deviation: In the above formula: For valve outlet temperature, For valve inlet temperature, For cooling water flow rate, For valve group real-time power, For the specific heat capacity of pure water, For the density of pure water, For rated power, For rated heat exchange, Allowable deviation threshold is configurable. The default temperature parameter for Soft-Clamp is 0.

02. (3) C3 — Multidimensional constraints on the heat exchange efficiency of cooling towers / air coolers; Actual cooling performance: Fan load and spray pump operation ratio: , Number of NTU heat transfer units: Theoretical cooling efficiency: Soft-Clamp bias : In the above formula: For valve outlet temperature, For valve inlet temperature, For ambient wet-bulb temperature, For cooling water flow rate, For fan speed, For the status of the spray pump, Calibration parameters for rated NTU constants Rated circulating water flow rate Fan rated speed, Spray gain coefficient calibration parameters Allowable deviation threshold The default temperature parameter for Soft-Clamp is 0.

05. (4) C4 — Expansion tank level-temperature-pressure coupling constraint; Temperature deviation and pressure deviation: , Expected liquid level: Soft-Clamp bias: In the above formula: To calibrate the reference inlet valve temperature (calibration parameter, selected based on historical data statistics during the system's steady-state operation, with a typical value of 25-30℃), To calibrate the parameters of the reference expansion tank pressure, - The coefficients of the second-order polynomial (model parameters, identified through least squares regression): The percentage of the reference liquid level deviation Temperature sensitivity % / ℃ Pressure sensitivity % / kPa Temperature nonlinearity coefficient % / ℃ 2 , Pressure nonlinearity coefficient % / kPa 2 , Temperature-pressure cross-coupling coefficient % / ℃·kPa For the actual liquid level in the expansion tank, The default temperature parameter for Soft-Clamp is 1.

0. (5) C5 — Steady-state flow rate and pressure difference square law constraint of pipeline system Actual pressure difference vs. expected pressure difference: Soft-Clamp Two-way deviation: In the above formula: For inlet valve pressure, For valve pressure, For cooling water flow rate, Configurable parameters for pipeline resistance coefficient, identified using least squares based on historical steady-state data. For steady-state pressure difference threshold, The default temperature parameter for Soft-Clamp is 0.

02. When it is determined to be a suspected blockage, It was initially determined to be a suspected leak. Parameters for calibrating the fault direction discrimination threshold; (6) C6 — Single-point violation of the three-layer coupling constraint on the conductivity of the cooling medium: Differential coupling detection: , Temperature compensation and value detection: , Overall constraint value: In the above formula: Main circuit cooling water conductivity, For the conductivity of deionized water, For valve inlet temperature, Upper limit of main circuit conductivity The upper limit of the conductivity of deionized water Upper limit constraint for conductivity difference Temperature compensation coefficient, - The default temperature parameter for Soft-Clamp is 0.

01.

7. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S6, the violation amount of each physical constraint is calculated and the predicted value is used. Alternatively, the node-level feature representation can be substituted into the physical constraint set to calculate the violation amount of each physical constraint. ,in This indicates that the constraints are fully satisfied. This indicates a serious violation of the constraint.

8. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: In step S7, the three complementary embedding strategies use node feature enhancement NFA to concatenate constraint violation scores to the corresponding sensor node feature vectors, increasing the original input dimension from 1 to 1+C=7, where C=6 is the number of constraints, applicable to all constraints C1-C6; and the edge weights in the graph attention encoder are adjusted using physical coupling relationships through edge attention bias EAB. ,in =0.1 is the bias strength coefficient, applicable to coupled constraints C4 level-temperature-pressure and C5 flow-pressure difference; the degree of constraint violation is expressed as a differentiable loss function through the physical regularization loss PRL. The total loss is applied to all constraints C1-C6, and the three strategies are combined to embed the physical constraints into the graph bias network.

9. The anomaly detection method and system for multi-domain physically constrained differentiable embedded graph deviation networks according to claim 1, characterized in that: The joint optimization objective and adaptive weight mechanism in step S8 Based on the violation amount, the physical constraints are embedded as soft constraints into the loss function of the graph deviation network to construct a joint optimization objective. ,in For mean square error loss, For traditional constraint loss, For physical residual loss, To penalize the complexity of the adjacency matrix, a physical sensitivity adaptive weighting mechanism is used to dynamically adjust the weights of each constraint: Where η = 0.01 is the sensitivity adjustment rate. This represents the batch average violation rate of constraint k in this epoch. =0.001 is the lower limit of the weight. = 2.0 is the upper limit of the weight. Initial weights: C1=1.0, C2=1.5, C3=1.0, C4=0.8, C5=1.0, C6=0.

5. In step S9, gradient descent is used for end-to-end training of the joint optimization objective until convergence. A two-stage training strategy is employed: in the first stage, if epoch ≤ 5, only... Training the base GDN, lr=0.001; the second stage introduces epoch>

5. , and With lr=0.0001 and total epochs=10, after training, the threshold q95 quantile and the severity threshold q99 quantile are calculated on the validation set. In step S10, anomaly detection and physical violation reporting are performed. The trained model is used to detect anomalies in real-time data. The anomaly score is calculated by combining the reconstruction error and the contribution of physical constraints. When the anomaly score exceeds the threshold, a graded alarm is triggered, and a physical constraint violation report is output.

10. An anomaly detection system for a multi-domain physically constrained differentiable embedded graph deviation network, characterized in that: The anomaly detection method for multi-domain physically constrained differentiable embedded graph deviation networks according to any one of claims 1-9 includes a data acquisition and preprocessing module, a graph network modeling module, a multi-domain physical constraint calculation module, a joint loss optimization training module, an adaptive weight update module, a real-time inference scoring module, a hierarchical alarm and root cause reporting module, an incremental learning module, and a center-edge collaborative deployment module. The data acquisition and preprocessing module is used to acquire time series data of industrial equipment sensors, complete missing value filling, noise filtering, time series smoothing, normalization and time series sliding window construction, output standardized time series samples and construct sensor topology map; The graph network modeling module has a built-in two-layer multi-head graph attention network GAT and decoder MLP, which are used to complete node feature aggregation, adaptive adjacency matrix filtering, sensor measurement prediction, and output the reconstructed prediction values ​​of each sensor and the attention weight matrix. The multi-domain physical constraint calculation module has built-in 6 types of Soft-Clamp differentiable physical constraint calculation logic. It calculates the constraint violation C1 to C6 in batches based on the actual sensor measurement values ​​and the model's inverse normalization prediction values, providing constraint numerical inputs for feature enhancement, attention bias, and physical regularization loss. The joint loss optimization training module is used to construct a joint total loss function that includes mean squared error loss, traditional constraint loss, physical residual loss, and adjacency matrix complexity penalty, perform two-stage gradient descent end-to-end training, complete the joint optimization of basic GDN pre-training and physical constraints, and obtain the early warning threshold and severe alarm threshold based on the anomaly score statistics of the validation set after training. The adaptive weight update module is used to dynamically update the weight parameters of various physical constraints based on the average constraint violation amount in a single iteration after each training round, limit the weight values ​​to a preset maximum and minimum value range, save the initial weight configuration of each constraint, and provide parameter support for the model training and inference process. The real-time inference scoring module loads the trained network weights, normalized parameters, and alarm thresholds, performs forward inference on the real-time sliding window data, and calculates a global comprehensive anomaly score by integrating the normalized reconstruction error and the contribution of physical constraint violation. The graded alarm and root cause reporting module is used to compare the comprehensive anomaly score with the preset threshold to realize a four-level graded alarm. When an alarm is triggered, the module outputs the Top Suspicious Sensors and the corresponding Physical Constraint Violation Report according to the scores of each sensor node and the amount of each constraint violation, thus completing the fault root cause location. The incremental learning module integrates the ER-GNN experience replay buffer and the TWP topology weight protection regularization term for incremental training of new working conditions and new site data. After training, it verifies the average violation of physical constraints and automatically rolls back the parameter snapshot before training when the model fails, thus suppressing the forgetting of historical working condition identification. The central-edge collaborative deployment module is divided into a central terminal unit and an edge terminal unit. The central terminal unit is used to aggregate historical data from multiple sites to pre-train baseline models and export standardized model packages. The edge terminal unit is used to import model packages to verify their integrity, perform lightweight fine-tuning of models based on local historical data, and complete the activation of production models. It also includes an inference degradation scheduling module, which is used to monitor the online status of sensors and the loading status of models in real time, and to grade and decay anomaly scores according to the number of missing sensors. When a large number of core sensors are missing or the model fails, it automatically switches to a pure physical constraint calculation mode, relying solely on the violation of 6 types of physical constraints to output alarms, ensuring uninterrupted monitoring of the equipment.

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