Abstract
Power grid anomaly detection requires modeling both network topology and device dependencies. Graph neural networks (GNNs) are suitable for this task. However, few prior works have considered the stealthy camouflage behavior of grid anomalies, where faulty devices or malicious attackers intentionally mask their abnormal signals to resemble normal operational patterns. Such camouflages—specifically feature camouflage (manipulating local measurement data) and relation camouflage (establishing deceptive connections with healthy clusters)—significantly degrade the performance of existing GNN-based detectors. This paper proposes a camouflage-resistant graph neural network framework for power grid anomaly detection, termed CR-PGNN. Specifically, the framework first devises a physics-aware similarity measure to quantify the consistency between neighboring equipment based on electrical laws. It then leverages reinforcement learning (RL) to adaptively select the most informative neighbors and relations, effectively filtering out “camouflaged” connections that might dilute anomaly signals. A relation-aware aggregator fuses information across multiple grid relations. Extensive experiments on IEEE benchmark power systems with simulated PMU measurements and synthetically injected stealthy anomalies demonstrate that CR-PGNN outperforms state-of-the-art GNN-based detectors in terms of both detection performance and robustness against camouflage attacks. Code and data are publicly available at https://github.com/123gaoyi/CR-PGNN
Introduction
Smart grid technologies enhance power system efficiency and reliability through sensors, communications, and controls. As the backbone of modern society, grid security is critically important (Boyaci et al. 2021a, b). Anomaly detection for grid equipment is essential to prevent cascading failures and economic losses (Yin et al. 2022).
Graph Neural Networks (GNNs) have become a leading approach for anomaly detection in areas such as fraud detection and infrastructure monitoring (Constante-Flores et al. 2022; Luo et al. 2025). By modeling the grid as a multi-relational graph–nodes as equipment, edges as physical, geographic, or logical links–GNNs capture complex spatial and structural patterns (Yang and Wang 2025). These models assume anomalies deviate from healthy patterns and aggregate neighbor information to detect them Feng et al. (2025); Yu et al. (2024); Chin et al. (2017). However, existing GNN-based detectors face serious challenges due to stealthy camouflage behaviors of modern anomalies (Qiu et al. 2025; Li et al. 2024; Wang et al. 2019). Unlike simple hardware faults, sophisticated attacks or failures deliberately hide their presence to evade monitoring (Asefi et al. 2023). Inspired by empirical studies in fraud detection (Dou et al. 2020; Liu et al. 2021), we identify two types of camouflage in power grids:
Feature Camouflage: Faulty devices manipulate local measurements (e.g., current, voltage, temperature) to stay within normal ranges during early failure stages, appearing statistically similar to healthy nodes. In practice, such camouflage often arises from coordinated cyber-physical attacks. Attackers manipulate PMU data–voltage magnitudes, phase angles, or power injections–to shift anomalies toward normal ranges while maintaining a benign surface. Although these manipulated measurements may look statistically normal, they often introduce subtle inconsistencies with physical laws. Relation Camouflage: Anomalous nodes may be “shielded” by many healthy neighbors through strong physical or logical couplings. In standard GNN aggregation, abnormal signals are diluted by overwhelming normal information.
As shown in Fig. 1, traditional GNNs suffer significant performance drops due to these two camouflage effects. In the left panel, the anomaly signal from a faulty node is overwhelmed by numerous healthy neighbors during blind aggregation, causing signal dilution. In contrast, the right panel presents our proposed CR-PGNN, which uses a physics-aware consistency mechanism to expose feature camouflage, and an RL-based neighbor selector to prune deceptive links related to relation camouflage. By selectively blocking noisy interactions (red dashed lines) while preserving informative relations (green arrows), CR-PGNN purifies anomaly signals and maintains high detection sensitivity in complex grid environments. The main contributions of this paper are summarized as follows:
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This paper proposes a Multi-head Physics Consistency (MPC) module that integrates electrical laws to unmask anomalous nodes attempting feature camouflage, effectively exposing digital mimicry through physical constraints.
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This paper presents a reinforcement learning (RL) neighbor selector to combat relation camouflage, which dynamically optimizes filtering thresholds to prune deceptive connections and prevent anomaly signals from being diluted by healthy clusters.
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This paper conducts extensive experiments on multiple benchmark power system datasets. The results demonstrate that CR-PGNN significantly outperforms state-of-the-art GNN-based methods, especially in scenarios with high levels of camouflage.
The above contributions are guided by three research questions corresponding to the key components of CR-PGNN. The first question examines whether the multi-head physics consistency module effectively unmasks feature-camouflaged anomalies by checking AC power flow residuals. The second question investigates whether the reinforcement learning-based neighbor selector adaptively prunes relation-camouflaged connections to prevent signal dilution. The third question assesses how the relation-aware gated aggregation fuses information across multiple grid relations to improve detection robustness in complex topologies. These questions are systematically examined through experiments on IEEE 14-, 57-, and 118-bus systems.
Problem definition
In this section, this paper formally defines the components of the power grid graph and the objective of camouflage-resistant anomaly detection.
Multi-relational grid graph
This paper represents the power grid as a multi-relational graph \(\mathcal {G} = (\mathcal {V}, \mathcal {E}, \mathcal {K}, \textbf{X})\), where \(\mathcal {V} = \{u_1, u_2, \dots , u_n\}\) denotes the set of n grid entities (e.g., buses, transformers). \(\mathcal {K} = \{\kappa _1, \kappa _2, \dots , \kappa _m\}\) represents m types of distinct relations between entities, such as physical transmission lines, geographic proximity, or communication links. For each relation \(\kappa \in \mathcal {K}\), the edge set is defined as \(\mathcal {E}_\kappa = \{(u_i, u_j) \mid u_i, u_j \in \mathcal {V}\}\), where each edge characterizes a specific interaction under relation \(\kappa\). The attribute matrix \(\textbf{X} \in \mathbb {R}^{n \times d}\) contains d-dimensional measurement vectors (e.g., active power, voltage magnitude, phase angle) for each node. Physical relations are derived from transmission line connectivity. Geographic proximity is defined as a k-nearest neighbor graph based on bus coordinates with \(k=5\). Logical control dependencies are constructed from SCADA hierarchical control mappings. Among these relations, physical connections are most critical for anomaly detection as they are constrained by electrical laws; non-physical relations serve as auxiliary information and receive lower attention weights in the later gated aggregation mechanism.
Stealthy anomaly detection
Given the multi-relational graph \(\mathcal {G}\), the task is to learn a binary mapping function \(f: \mathcal {V} \rightarrow \{0, 1\}\). For any node \(u_i \in \mathcal {V}\), \(y_i = 1\) indicates an anomalous state (e.g., a hidden fault or a compromised sensor), while \(y_i = 0\) represents a normal operating state. Unlike vanilla graph-based detection, stealthy anomaly detection focuses on scenarios where \(u_i\) is an anomalous node (\(y_i=1\)) but attempts to evade detection through: Statistical Mimicry (Feature Camouflage): \(u_i\) manipulates its features \(\textbf{x}_i\) such that the distance \(\Vert \textbf{x}_i - \textbf{x}_j\Vert\) is minimized for \(j \in \mathcal {N}(u_i)\) where \(y_j=0\). Topological Concealment (Relation Camouflage): \(u_i\) is embedded in a dense neighborhood \(\mathcal {N}(u_i)\) where the majority of neighbors are healthy, i.e., \(|\{u_j \in \mathcal {N}(u_i) \mid y_j=0\}| \gg |\{u_j \in \mathcal {N}(u_i) \mid y_j=1\}|\). To evaluate camouflage resistance quantitatively, we define the camouflage strength \(\gamma\) for a node with feature manipulation as \(\gamma = \Vert \textbf{x}_i^{cam} - \bar{\textbf{x}}_{\mathcal {N}}\Vert / \Vert \textbf{x}_i^{orig} - \bar{\textbf{x}}_{\mathcal {N}}\Vert\), where \(\bar{\textbf{x}}_{\mathcal {N}}\) is the mean feature vector of its healthy neighbors. A lower \(\gamma\) indicates stronger camouflage, with \(\gamma =0\) representing complete statistical mimicry. In this paper, a detector is considered camouflage-resistant if it maintains an F1-score above 0.85 when \(\gamma \ge 0.3\).
GNN-based detection framework
The core of identifying these nodes lies in the aggregation of neighborhood information across multiple relations. For a node \(u_i\) under relation \(\kappa\), the l-th layer embedding \(\textbf{h}_i^{(l, \kappa )}\) is typically updated as:
where \(\mathcal {N}_i^\kappa\) is the set of neighbors of \(u_i\) under relation \(\kappa\). Our goal is to optimize this aggregation process to be resilient against the aforementioned mimicry and concealment strategies. While effective under normal conditions, the aggregation mechanism in Eq. (1) becomes vulnerable in the presence of camouflage behaviors. Feature camouflage reduces the distinguishability between anomalous and normal nodes in the feature space, whereas relation camouflage causes anomaly information to be diluted by dominant benign neighbors during message passing. Consequently, conventional neighborhood aggregation may inadvertently reinforce misleading signals and hinder anomaly detection.
Methodology
In this section, we elaborate on the architectural intricacies of CR-PGNN (Fig. 2), an adaptive framework specifically engineered to fulfill the objective of stealthy anomaly detection as formally defined in Section Problem definition. The system is structured into a logical pipeline that progressively transforms raw, potentially manipulated grid measurements into purified, high-level representations through a physics-informed selective aggregation mechanism.
Multi-dimensional feature alignment and embedding
As defined in our problem formulation, the input to our model is the attribute matrix \(\textbf{X} \in \mathbb {R}^{n \times d}\), where each measurement vector \(\textbf{x}_i\) contains critical electrical parameters. However, raw data from PMU sources often exhibit heterogeneous scales and temporal noise. To project these features into a high-dimensional latent manifold, we utilize a hierarchical embedding initialization:
The inclusion of Batch Normalization ensures that the gradient flow remains stable during the early stages of training, particularly when dealing with the extreme value fluctuations common in grid fault transients. This initial representation \(\textbf{h}_i^{(0)}\) encapsulates the local state of entity \(u_i\) before any relational information is propagated. By mapping the d-dimensional input to a larger \(d_{hid}\) space, this paper provides sufficient capacity for the subsequent layers to distinguish between normal operational variations and intentional Statistical Mimicry.
Multi-head physics consistency module
To address the challenge of feature camouflage, where \(\Vert \textbf{x}_i - \textbf{x}_j\Vert\) is minimized by an adversary, CR-PGNN employs a MPC module. The core intuition is that while an anomalous node \(u_i\) can manipulate its digital features to mimic a healthy neighbor \(u_j\), it cannot easily deceive the fundamental physical laws governing the grid topology.
For each relation type \(\kappa \in \mathcal {K}\), this work projects the embeddings into M independent consistency subspaces. For the m-th head, the projection is:
The similarity score \(\mathcal {S}(u_i, u_j)^{(l, \kappa )}\) is then calculated by coupling the latent distance with the physical consistency residual \(\Gamma _{i,j}\). In our framework, \(\Gamma _{i,j}\) is mathematically derived from the AC power flow mismatch:
where \(V, \theta\) are voltage magnitudes and angles, and \(X_{ij}\) is the line reactance. Equation (4) uses a lossless line approximation for efficiency. While real grids have line losses and reactive constraints, this simplified model captures the first-order physical inconsistencies introduced by feature camouflage. For typical high-voltage transmission lines, the series resistance is significantly smaller than the reactance (\(R \ll X\)), which justifies this approximation and limits active power estimation error to within \(5\%\) (Kundur 2007). The final similarity \(\mathcal {S}\) is an ensemble of M heads:
This multi-head approach allows the model to simultaneously monitor different physical properties, such as active power balance and reactive power compensation. If a connection exhibits high \(\Gamma _{i,j}\), the similarity score is heavily penalized, effectively unmasking nodes that “look" normal but “act" in violation of grid physics. While \(\Gamma _{i,j}\) characterizes the physical inconsistency at the edge level, CR-PGNN further aggregates these residuals to quantify node-level physical violations. Specifically, for each node \(u_i\), this work defines a physics consistency loss as:
This loss measures the average AC power flow mismatch between node \(u_i\) and its neighbors, serving as a compact indicator of whether the reported measurements of \(u_i\) are physically plausible under the grid topology. Although averaging across neighbors may cancel opposing violations, the MPC module mitigates this issue by using multi-head attention. The head-specific weights \(\omega _m\) in Eq. (5) learn to emphasize edges where \(\Gamma _{i,j}\) is large, effectively performing a weighted aggregation rather than a simple average. During training, this work tracks the temporal variation of the physics consistency loss to guide adaptive neighborhood pruning. The change in physical inconsistency is defined as:
A positive \(\Delta \mathcal {L}_{\text {phys}}\) indicates increasing physical violations caused by deceptive neighbors, whereas a negative value suggests improved physical consistency after pruning. In practical deployments, PMU measurements inevitably contain sensor noise and operational fluctuations. Since such variations generally preserve the physical consistency of neighboring equipment, they typically result in relatively small residual values. In contrast, persistent deviations caused by camouflage behaviors tend to produce significantly larger consistency violations, enabling the proposed MPC module to distinguish abnormal manipulations from normal measurement uncertainty.
RL-based adaptive neighbor pruning
To combat relation camouflage, CR-PGNN autonomously optimizes threshold \(p_\kappa ^{(l)}\) to prune deceptive edges. Without adaptive pruning, GNN aggregation is dominated by benign signals, causing high false negatives.
This selection is modeled as a sequential decision process, where an RL agent maintains policy \(\pi _\phi\) for each relation \(\kappa\). The RL policy is a two-layer MLP (hidden dim 32, ReLU). Its state input comprises similarity distribution statistics and historical physical consistency. It outputs three actions \(\{+\delta , -\delta , 0\}\) via softmax to adjust the filtering threshold. Reward F1 is computed on a validation set to prevent overfitting, and the policy is updated every 5 epochs using REINFORCE. During training, the filtering thresholds \(p_{\kappa }^{(l)}\) are initialized to 0.5 for all relations and layers, and are constrained within the interval [0, 1] through clipping operations to prevent overly aggressive pruning or excessive neighborhood preservation. At each epoch t, the agent perceives a state \(\textbf{s}_t^{(\kappa )}\) that encapsulates the current distribution of similarity scores:
The skewness term further characterizes the asymmetry of the similarity distribution. A highly skewed distribution often indicates the coexistence of a dominant cluster of consistent neighbors and a small subset of structurally divergent nodes, providing additional cues for adaptive neighbor filtering. The state representation uses global statistics for computational efficiency, as adding node-level features would increase state dimensionality from 5 to \(O(|\mathcal {V}|)\) and make RL training infeasible. The skewness term captures distribution asymmetry, which indirectly encodes local structural information. The agent selects an action \(a_t \in \{+\delta , -\delta , 0\}\) to update \(p_\kappa ^{(l)}\). The filtered neighbor set \(\widehat{\mathcal {N}}_i^\kappa\) is then dynamically reconstructed:
The reward function \(\mathcal {R}_t\) is designed to jointly encourage detection performance and physical plausibility. In addition to maximizing the F1-score, this paper incorporates a lightweight physics-aware regularization based on the temporal change of the physics consistency loss:
where \(\Delta \mathcal {L}_{\text {phys}}^{(t)} = \mathcal {L}_{\text {phys}}^{(t)} - \mathcal {L}_{\text {phys}}^{(t-1)}\) measures the variation of physical inconsistency after neighbor pruning, and \(|\widehat{\mathcal {N}}^\kappa |\) denotes the size of the retained neighborhood to prevent excessive sparsification. The coefficients \(\lambda\) and \(\eta\) are small constants that balance detection accuracy, physical consistency, and structural preservation. Based on experimental validation, the optimal balance among detection accuracy, physical consistency, and structural preservation is achieved when \(\lambda = 0.1\) and \(\eta = 0.01\). To improve optimization stability, the policy network is updated at a lower frequency than the graph encoder. This design reduces the interaction between rapidly changing node representations and policy optimization, thereby alleviating training oscillation and promoting stable convergence.
Relation-aware gated aggregation
The final stage involves fusing information across the set of filtered neighborhoods \(\widehat{\mathcal {N}}_i^\kappa\) for all \(|\mathcal {K}|\) relations. Recognizing that different relations provide varying degrees of evidence, we utilize a gated fusion mechanism:
The global embedding \(\textbf{h}_i^{(l)}\) is updated via a relation-level attention bottleneck:
where \(\beta _{i,\kappa } = \textrm{softmax}_{\kappa }(p_{\kappa }^{(l)} \cdot \tanh (\textbf{W}_{att}[\textbf{h}_i^{(t-1)}; \textbf{m}_i^{(t,\kappa )}]))\) is the attention coefficient. The residual connection \(\textbf{h}_i^{(t-1)}\) preserves information from previous layers, which helps mitigate over-smoothing when multiple GNN layers are stacked. The entire CR-PGNN framework is optimized using a dual-objective loss. For the node classification task, this work employs a Weighted Cross-Entropy Loss to handle the extreme class imbalance (\(y_i=1 \ll y_i=0\)):
Simultaneously, the RL policy \(\pi _\phi\) is updated via Policy Gradient to maximize the cumulative reward \(\mathbb {E}[\sum \mathcal {R}_t]\). By alternating between GNN parameter updates and RL threshold adjustments, CR-PGNN converges to a state where the graph topology is purified and the anomaly detector is robust against camouflage strategies. This joint optimization ensures that the model remains sensitive to subtle faults while being resilient to topological noise. The main computational steps of CR-PGNN are summarized in Algorithm 1.
Experiments
In this section, this paper conducts extensive experiments to evaluate the performance of CR-PGNN. We aim to answer the following research questions: (1) Does CR-PGNN outperform state-of-the-art GNNs in detecting stealthy anomalies? (2) How effective is the RL-based pruning in mitigating relation camouflage? (3) Does the physics-aware similarity measure effectively identify feature mimicry?
Experimental setup
This paper evaluates the performance of CR-PGNN using three standard power system benchmarks: the IEEE 14-bus,Footnote 1 57-bus,Footnote 2 and 118-bus Footnote 3 systems. To simulate modern wide-area monitoring scenarios, we utilize synchronized PMU (Phasor Measurement Unit) data generated through AC power flow simulation under different operating conditions as the primary observation source. For each bus (node) \(u_i \in \mathcal {V}\), the feature vector \(\textbf{x}_i \in \mathbb {R}^d\) is composed of simulated synchronized measurements, specifically voltage magnitude \(V_i\), phase angle \(\theta _i\), and active/reactive power injections, generated under controlled operating conditions via AC power flow simulations. These datasets are transformed into multi-relational graphs \(\mathcal {G}\) that incorporate physical transmission topology, geographical distance, and logical control dependencies to capture the complex spatial correlations of the grid.
To rigorously evaluate the robustness of CR-PGNN against stealthy attacks, this work synthetically injects anomalous samples into the benchmark systems following controlled camouflage strategies. Specifically, 10%−20% of the nodes in each system are randomly selected as anomalous nodes, while ensuring that the selected nodes are spatially distributed across different grid regions to avoid excessive locality bias. For each experimental run, anomaly injection is repeated five times with different random seeds, and the averaged results are reported.
For feature camouflage generation, the original PMU measurements of anomalous nodes are perturbed toward the statistical center of their neighboring normal nodes. Specifically, for an anomalous node \(u_i\), its manipulated feature vector is generated as:
where \(\alpha \in [0.6,0.8]\) controls the camouflage strength and \(\epsilon \sim \mathcal {N}(0,\sigma ^2)\) denotes small Gaussian perturbations constrained within the normal operational fluctuation range. This process ensures that anomalous measurements remain statistically similar to healthy operational states while still violating underlying physical consistency.
For relation camouflage generation, each anomalous node is additionally connected to several healthy nodes under different graph relations. Specifically, 30% additional edges are injected into the physical or logical relation graphs by preferentially linking anomalous nodes to high-degree normal nodes. This operation intentionally embeds anomalies into dense healthy neighborhoods, thereby amplifying the message dilution effect during neighborhood aggregation.
The CR-PGNN is implemented using PyTorch and DGL. The model consists of a two-layer GNN with a hidden dimension \(d_{hid} = 64\). The MPC module uses \(M=4\) heads to monitor different physical properties simultaneously. The RL agent, responsible for adaptive pruning, is trained via Policy Gradient with a learning rate of 0.001 to optimize the filtering thresholds \(p_{\kappa }^{(l)}\). The total number of trainable parameters is approximately 0.34M, with the RL policy network contributing 1,632 parameters (two-layer MLP with hidden dimension 32). All experiments are conducted on an NVIDIA RTX 4090 GPU with a consistent train/test split of 70/30. This configuration is chosen because the RTX 4090 provides inference latency (8.4 ms per sample) comparable to mid-range GPUs typically deployed in utility control centers (e.g., Tesla T4), both satisfying real-time monitoring requirements. The 70/30 split reflects operational scenarios where historical data is abundant but online adaptation is limited.
Overall performance comparison
To verify the effectiveness of CR-PGNN, we compare its performance against 16 state-of-the-art baselines. These include general GNN models (GCN, GAT, and GraphSAGE), which perform neighborhood aggregation without explicit anomaly-aware mechanisms; fraud-specific detectors (GraphConsis, CARE-GNN, PC-GNN, and BWGNN), which are designed to mitigate deceptive or camouflaged neighborhood information; advanced robust graph neural networks (SimP-GNN, MSDG, GAD-NR, RGCN, H2-GCN, FAGCN, and MAFI), which enhance resilience against structural perturbations, graph noise, and heterophily; and two physics-based methods (WLS and Interval Analysis), which serve as purely physical baselines that detect anomalies via state estimation residuals and interval power flow, respectively. As demonstrated in Table 1, CR-PGNN consistently achieves superior performance across all IEEE bus systems. Based on the experimental results, we have the following key observations:
Effectiveness against Stealthy Camouflage: CR-PGNN significantly outperforms specialized fraud detectors such as CARE-GNN and PC-GNN, with a substantial F1-score improvement in the IEEE 118-bus system. While these baselines primarily address statistical distribution shifts, they struggle to distinguish subtle feature camouflage designed to mimic normal operational bounds because statistical features alone cannot reveal physically inconsistent but statistically similar patterns. By incorporating the MPC module, CR-PGNN validates the physical legitimacy of node measurements using AC power flow residuals \(\Gamma _{i,j}\), effectively unmasking anomalies that are statistically deceptive but physically inconsistent.
Robustness via Adaptive Pruning: Compared to advanced robust models like MSDG and MAFI, CR-PGNN maintains a higher Recall in the 118-bus system. This advantage stems from the RL-based adaptive neighbor pruning module. While attention-based models (e.g., GAT, FAGCN) can be easily misled by relation camouflage where anomalous nodes are shielded by dense healthy clusters, these models lack a mechanism to actively exclude deceptive neighbors. The RL agent adaptively optimizes the filtering threshold \(p_{\kappa }^{(l)}\) to exclude such connections, preventing the dilution of abnormal signals by overwhelming benign neighborhood information.
Performance in Complex Topologies: As the grid complexity increases from the 14-bus to the 118-bus system, the performance gap between CR-PGNN and the baselines widens. Traditional GNNs suffer from over-smoothing or signal dilution in large-scale multi-relational graphs because they aggregate all neighbors indiscriminately. CR-PGNN’s relation-aware gated aggregation ensures that only the most physically consistent and informative relations contribute to the final state representation \(\textbf{h}_i^{(l)}\), ensuring high detection stability in diverse operational scenarios. In contrast, purely physics-based methods such as WLS and Interval Analysis lack the capacity to learn adaptive patterns from data and rely solely on fixed residual thresholds, making them vulnerable to stealthy anomalies and resulting in F1-scores below 0.74 across all test systems.
Visualization analysis
To further visually demonstrate CR-PGNN’s comprehensive performance advantages, this work selects five representative baseline models spanning diverse graph learning paradigms, including general-purpose GNNs (GraphSAGE and RGCN), frequency-domain graph models (FAGCN), and anomaly detection-oriented GNNs (BWGNN and GAD-NR). The comparative results are illustrated using radar charts in Fig. 3. To enhance discrimination in high-performance regions, the radial axis is scaled with 10% intervals ranging from 50% to 100%. Several key observations can be drawn:
(1) Overall Detection Superiority: CR-PGNN (highlighted by the bold red profile) consistently encloses the largest area across all IEEE bus systems, indicating superior performance under multiple evaluation metrics. In particular, CR-PGNN demonstrates a clear advantage over the strongest baselines in terms of F1-score and AUC-ROC, reflecting its enhanced ability to distinguish camouflaged anomalies from normal operational states.
(2) Robustness to Increasing System Scale: As the grid size increases from the 14-bus to the 118-bus system, conventional GNNs such as GraphSAGE and RGCN experience noticeable performance degradation, which can be attributed to over-smoothing and signal dilution in large-scale relational graphs. In contrast, CR-PGNN maintains consistently strong F1-scores across all system scales, highlighting the effectiveness of the physics-consistency constraint in suppressing spurious perturbations while preserving informative anomaly signals.
(3) Balanced Precision–Recall Trade-off: Compared with frequency-based and wavelet-based baselines (e.g., FAGCN and BWGNN), which tend to favor either Precision or Recall, CR-PGNN achieves a more balanced trade-off between the two. This balanced profile indicates that the proposed physics-guided reinforcement learning selector can accurately localize stealthy attacks without inducing excessive false alarms under normal operating fluctuations.
Effectiveness of physics-guided consistency module
To further investigate how the proposed CR-PGNN distinguishes stealthy cyber-attacks from normal operations, this paper conducts a statistical analysis of the physics consistency residuals (\(\mathcal {L}_{phys}\)). In our framework, this residual serves as a crucial metric for quantifying the degree of deviation from physically consistent power flow behavior at each node. As illustrated in Fig. 4, a clear and significant separation can be observed between the residual distributions of benign and malicious samples:
Normal States Analysis: For normal operational samples (\(N=1600\)), the residuals are strictly concentrated in a near-zero interval ([0, 0.08]). As shown in the zoomed-in inset, minor fluctuations exist due to measurement noise, but the overall magnitude remains extremely low, confirming that benign states strictly adhere to physical constraints.
Anomalous Attacks Analysis: In contrast, anomalous samples (\(N=400\)) exhibit widespread residuals ranging from 0.22 to 0.98. Even for camouflaged attacks that mimic normal patterns, intrinsic physical inconsistencies result in a substantial increase in \(\mathcal {L}_{phys}\). The multi-modal distribution reflects the diversity of attack intensities and affected locations.
Detection Robustness: The decision boundary (\(\tau = 0.2\)) effectively separates the two distributions with no observable overlap. This explains why CR-PGNN outperforms purely data-driven baselines: the physics-guided module projects stealthy attacks into a high-residual space well separated from normal states. The zoomed-in inset further highlights the scale difference, spanning nearly two orders of magnitude, demonstrating the robustness of physical consistency regularization.
Camouflage Strength Distribution. Fig. 5 presents the histogram of \(\gamma\) values across all injected anomalies. The distribution covers a wide range from strong (\(\gamma \approx 0\)) to weak (\(\gamma \approx 1\)) camouflage, with approximately \(46.8\%\) of samples having \(\gamma \ge 0.3\), providing sufficient test cases to verify the success criterion (\(\textrm{F1}>0.85\) when \(\gamma \ge 0.3\)). Combined with the F1-score of 0.875 on the IEEE 118-bus system reported in Table 1, these results confirm that CR-PGNN maintains reliable detection performance under the defined camouflage conditions. This broad coverage demonstrates that our experimental design captures both strong and weak camouflage scenarios, substantiating the reliability and generalizability of the reported performance.
Interpretability of RL-based relation selection
The proposed CR-PGNN utilizes a RL agent to adaptively select graph relations. To demonstrate its interpretability, this paper visualizes the selection probability matrix in Fig. 6.
The heatmap reveals a sparse yet structured selection pattern. The RL agent assigns high probabilities (above 0.9) to stable physical neighbors (the diagonal-dominant regions), ensuring the robustness of message passing. Notably, for certain camouflaged edges that propagate adversarial perturbations, the agent successfully assigns near-zero selection weights, thereby isolating the influence of attacks from the rest of the network.
This behavior is closely related to the proposed physics-guided consistency mechanism. Specifically, edges associated with larger physical consistency residuals \(\Gamma _{i,j}\) exhibit lower relation similarity scores during adaptive neighbor evaluation, making them more likely to be suppressed by the RL-based pruning policy. Consequently, physically inconsistent relations contribute less to subsequent message aggregation, thereby reducing the propagation of camouflage-induced perturbations across the graph.
Ablation study
To investigate the contribution of each component, variants are constructed by adding components incrementally to a base model. The base model is a standard two-layer GCN with mean aggregation, which serves as a common baseline in graph anomaly detection. Variants are built upon this base as follows: +HEI adds the hierarchical embedding initialization module, +RAG further adds the relation-aware gated aggregation, +RL replaces static neighborhood aggregation with RL-based adaptive neighbor pruning, and +MPC (full CR-PGNN) further incorporates the multi-head physics consistency module. This additive design measures the marginal gain of each component.
Table 2 presents the quantitative results of different variants. Overall, each addition leads to a noticeable improvement in performance, demonstrating that every module contributes to the effectiveness of CR-PGNN. Among all variants, +RL and +MPC exhibit the largest gains. The addition of MPC consistently improves Precision and F1-score, highlighting the importance of physical consistency modeling in identifying camouflaged anomalies. Specifically, on the IEEE 118-bus system, adding MPC increases Precision from 0.812 to 0.892 and F1-score from 0.803 to 0.875. The largest improvement in Recall is observed when RL is added, particularly on the IEEE 118-bus system (from 0.682 to 0.794), indicating that adaptive neighbor pruning plays a critical role in preserving anomaly information under relation camouflage. Furthermore, similar performance trends are observed across all benchmark systems, demonstrating the robustness and scalability of the proposed framework.
Sensitivity and robustness analysis
This section evaluates the robustness of CR-PGNN by investigating its sensitivity to six key hyperparameters and environmental factors on the IEEE 118-bus system.
Physics-consistency weight \(\alpha\) : As shown in Fig. 7(a), the F1-score peaks at \(\alpha = 0.6\). When \(\alpha\) increases beyond 0.6, the F1-score gradually declines because the model over-relies on physical residuals while underestimating topological patterns that still provide useful information for non-camouflaged nodes.
Anomaly ratio: Fig. 7(b) illustrates that as the anomaly ratio increases from 5% to 25%, CR-PGNN maintains a stable F1-score compared to CARE-GNN. This stability stems from the RL agent dynamically tightening pruning thresholds when anomaly density rises, preserving message purity under high-intensity attacks.
RL reward weight \(\beta\) : \(\beta\) controls the trade-off among detection accuracy, physical consistency, and graph sparsity. A \(\beta\) between 0.4 and 0.5 yields the best trade-off. When \(\beta\) is too low, the agent retains excessive edges and relation camouflage persists; when \(\beta\) is too high, aggressive pruning loses informative neighbors and reduces Recall.
Neighbor filtering threshold p : Performance is optimal when p is in [0.5, 0.7]. A fixed \(p=0.6\) yields F1=0.841, while CR-PGNN’s adaptive thresholds achieve 0.875 by varying p per node based on local neighborhood density.
Hidden dimension d : Performance saturates at \(d=64\). Increasing to 128 or 256 does not improve accuracy but increases model size and slows inference, confirming that power system states can be captured in a compact embedding space.
GNN layers L : Optimal depth is \(L=2\) or 3. At \(L=4\), the F1-score drops due to over-smoothing. The RL module partially mitigates this by pruning edges, which reduces effective propagation depth compared to standard GNNs.
Computational complexity analysis
On the IEEE 118-bus system with an NVIDIA RTX 4090 GPU, CR-PGNN achieves 8.4 ms inference latency per sample and 119 samples/sec throughput at batch size 1, well within real-time requirements. The total model size is 0.34M parameters (0.52 MB in float32). The RL-based pruning reduces average neighborhood size from 14.2 to 6.8 edges, cutting message passing cost by 52%. In deployment with mid-range GPUs (e.g., Tesla T4), estimated latency is 12–15 ms per sample, still satisfying real-time constraints.
Related work
Graph neural networks for anomaly and intrusion detection
GNNs have been extensively explored for anomaly detection due to their capability in modeling relational dependencies. E-GraphSAGE (Lo et al. 2021) applied message passing to network flow graphs for intrusion detection in IoT environments. Caville et al. (2022) proposed Anomal-E, a self-supervised GNN that learns edge embeddings without labeled data. Zoubir and Missaoui (2024) combined scattering transform with GNNs for multi-resolution traffic representation. Sun et al. (2024) designed GNN-IDS to integrate attack graphs with temporal measurements for attack attribution. Other approaches include hybrid GNN-transformer architectures (Govindarajan and Muzamal 2025), continual learning (Qu et al. 2025), and hyperbolic space representations (Zhang et al. 2025). A survey by (Zhong et al. 2024) highlights open challenges such as dynamic graph construction and robustness to adversarial perturbations. Despite these advances, most existing GNN-based intrusion detection models assume that anomalous nodes exhibit distinguishable statistical features or sparse abnormal connections, which may not hold under deliberate camouflage behaviors where attackers manipulate features or hide within benign neighborhoods. In contrast, CR-PGNN does not rely on statistical distinguishability; its MPC module exposes camouflage via physical consistency.
Robust and spectral GNN methods for anomaly detection
To address vanilla GNN vulnerability to noise and perturbations, researchers have developed robust and spectral architectures. Tang et al. (2022) introduced BWGNN, which applies spectral wavelet filters to enhance sensitivity to anomalous frequency components. Zheng et al. (2024) developed a graph adversarial training framework that purifies graph structure against poisoning attacks. (Liu et al. 2023) investigated graph contrastive learning for anomaly detection. Aslan et al. (2025) proposed \(\beta\)-GNN, an ensemble framework that dynamically balances information from a base GNN and an auxiliary network through a learnable parameter \(\beta\), enabling adaptive resistance to graph structure perturbations. Other works have explored hybrid models combining GNNs with autoencoders or attention mechanisms (Chetoui et al. 2025), as well as heterogeneous and dynamic GNNs (Jiang et al. 2025). Surveys (Qiao et al. 2025; Ekle and Eberle 2024) highlight persistent challenges in scalability and interpretability. Several recent studies have applied deep Q-networks to intrusion detection in IIoT and edge-based SIoT environments, including open-set detection (Yu et al. 2023), zero-day attack detection (Shen et al. 2024), stochastic game-based optimization (Yu et al. 2024), and multi-teacher knowledge distillation (Shen et al. 2026). Although these robust variants improve stability under random noise or adversarial perturbations, they largely remain data-driven and lack explicit mechanisms to identify stealthy anomalies that intentionally mimic normal feature distributions or exploit neighborhood aggregation to conceal abnormal signals. The RL-based adaptive neighbor selector in CR-PGNN addresses this gap by actively pruning deceptive connections.
Power system and smart grid applications
In power systems, GNN-based methods have been increasingly adopted to capture topological and physical dependencies. Boyaci et al. (2021a) proposed a GNN framework for joint detection and localization of stealth False Data Injection Attacks (FDIAs). Yin et al. (2024) evaluated GNNs against traditional ML methods for cyber attack detection on IEEE test systems. GraphKAN Wu et al. (2025) integrates GATs and Kolmogorov–Arnold Networks to model physical and logical dependencies. Hybrid GNN and temporal models (Zhang et al. 2025) have been studied to capture evolving operational states. These studies highlight the importance of tailoring GNN architectures to domain-specific challenges such as physical consistency. Among the baselines evaluated in this paper, standard GNNs such as GCN (Kipf 2016), GAT (Petar et al. 2018), and GraphSAGE (Hamilton et al. 2017) perform neighborhood aggregation without anomaly-aware mechanisms, limiting their effectiveness under camouflage. Fraud detectors including GraphConsis (Liu et al. 2020), CARE-GNN (Dou et al. 2020), and PC-GNN (Liu et al. 2021) are designed to mitigate deceptive neighborhood information, yet they rely on statistical similarity measures and remain vulnerable when feature distributions are deliberately matched. Robust GNNs like BWGNN (Tang et al. 2022), GAD-NR (Roy et al. 2024), RGCN (Zhu et al. 2019), H2-GCN (Zhu et al. 2020), FAGCN (Bo et al. 2021), MSDG (Zhao et al. 2024), and MAFI (Jiang et al. 2021) enhance resilience against structural perturbations but lack domain-specific physical constraints and adaptive pruning. Despite significant advances, existing methods often rely on handcrafted graph construction or large amounts of labeled data, making them less adaptable to sophisticated camouflage attacks. Furthermore, the integration of domain-specific physics remains an open challenge. CR-PGNN addresses these challenges by directly integrating AC power flow equations into the detection framework.
Conclusion
This paper presented CR-PGNN, a camouflage-resistant graph neural network for stealthy anomaly detection in smart grids. By integrating physics-aware consistency modeling with reinforcement learning based adaptive neighbor selection, the proposed framework effectively mitigates both feature camouflage and relation camouflage. Extensive experiments on IEEE benchmark systems demonstrated consistent improvements over existing graph-based detectors in terms of detection accuracy and robustness. The results indicate that incorporating domain-specific physical constraints into graph representation learning provides an effective mechanism for exposing statistically deceptive behaviors while preserving critical structural information. Furthermore, adaptive relation filtering helps prevent anomaly signals from being overwhelmed by benign neighborhood information, particularly in complex grid environments. However, the current framework assumes a static grid topology and relies on the availability of accurate physical measurements, which may limit its applicability in real-time dynamic environments. Future work will focus on extending CR-PGNN to dynamic grid scenarios through temporal graph modeling and investigating more sophisticated coordinated attacks involving multiple simultaneously manipulated nodes.
Data Availability
Data will be made available on request.
Notes
https://github.com/MATPOWER/matpower/blob/master/data/case14.m
https://github.com/MATPOWER/matpower/blob/master/data/case57.m
https://github.com/MATPOWER/matpower/blob/master/data/case118.m
Abbreviations
- \(\mathcal {G} = (\mathcal {V}, \mathcal {E}, \mathcal {K}, \textbf{X})\) :
-
Multi-relational power grid graph
- \(u_i \in \mathcal {V}\) :
-
The i-th grid entity (node)
- \(\kappa \in \mathcal {K}\) :
-
A specific relation type (e.g., physical, geographic)
- \(\mathcal {E}_\kappa\) :
-
Set of edges under relation \(\kappa\)
- \(\mathcal {N}_i^\kappa\) :
-
Neighbors of node \(u_i\) under relation \(\kappa\)
- \(\textbf{x}_i \in \mathbb {R}^d\) :
-
Initial measurement feature vector of node \(u_i\)
- \(\textbf{h}_i^{(l)}\) :
-
Hidden state embedding of node \(u_i\) at layer l
- \(y_i \in \{0, 1\}\) :
-
Ground truth label of node \(u_i\) (0: normal, 1: anomaly)
- \(\mathcal {S}(u_i, u_j)\) :
-
Physics-aware similarity score between \(u_i\) and \(u_j\)
- \(p_\kappa ^{(l)}\) :
-
Filtering threshold for relation \(\kappa\) at layer l
- \(\theta\) :
-
Trainable parameters of the GNN layers
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Ya Guo: Conceptualization, Methodology, Validation, Software, Investigation, Data curation, Writing - original draft, Writing - review & editing. Junyi Wang: Funding acquisition, Supervision, Project administration, Writing - review & editing. Boyu Liu: Supervision, Resources, Carrying out additional analyses, Writing - review & editing. Dong Li: Writing - review & editing. Zhaotai Meng: Writing - review & editing. Ying Zhu: Writing - review & editing.
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Guo, Y., Wang, J., Liu, B. et al. Camouflage-resistant graph neural networks for power grid anomaly detection. Cybersecurity 9, 219 (2026). https://doi.org/10.1186/s42400-026-00656-6
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DOI: https://doi.org/10.1186/s42400-026-00656-6