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Adversarial Attacks on Deep Learning-Based False Data Injection Detection in Differential Relays

T0 review · 6 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Adversarial remote-measurement tweaks fool grid relay AI up to 99.7%

desk verdict Useful first demonstration of adversarial attacks on DL-based FDIA detection in differential relays, but the reported dual-success rates are not actually measured by the paper's metric. read the letter →

arxiv 2506.19302 v1 pith:QWEQ6MUA submitted 2025-06-24 cs.LG

Ahmad Mohammad Saber , Aditi Maheshwari , Amr Youssef , Deepa Kundur This is my paper · ORCID
classification cs.LG
keywords adversarialattacksfalsedatainjectionlinecurrentdifferentialrelaydeeplearningdetectionFastGradientSignMethodtrainingsmartgridsecurity
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Deep-learning-based false data injection detectors in line current differential relays can be defeated by adversarial attacks that modify only the remote current measurements. Using an iterative Fast Gradient Sign Method, the paper crafts samples that the detector misclassifies as legitimate faults while the relay's own trip logic is simultaneously satisfied, causing a false trip. On a simulated medium-voltage microgrid, all four tested models (MLP, CNN, LSTM, ResNet) were vulnerable, with the MLP fooled in more than 99% of adversarial cases and the ResNet the least affected. The paper further shows that adversarial training, in which the attack generator is run on the training set and the successful samples are added as labeled FDIAs, substantially restores detection accuracy without degrading fault detection. The point is that ML-based FDIA detection in differential relays is not robust under an attacker who controls remote measurements, and that a specific defense can measurably improve it.

What carries the argument

The load-bearing object is an iterative FGSM attack specialized to the LCDR setting. Its perturbation is $\delta_x = \epsilon \cdot \mathrm{sign}(\nabla_x J(\theta, x', y)) \cdot a$, where $a$ is the maximum absolute value of the input sample, only features originating from remote measurements are perturbed, and the updated sample is clipped so that no element leaves the original sample's minimum-maximum range. The iteration accepts an adversarial sample only if the DL model outputs the fault class and the manipulated remote currents satisfy the relay's operating criterion $i_d \ge i_{op}$, so a successful attack satisfies two independent checks. The defense is adversarial training: the same attack generator is run on the training set, successful adversarial samples are relabeled as FDIAs and added to the training data, and the model is retrained for ten epochs, producing a detector that classifies the adversarial perturbations as attacks.

What would settle it

A concrete test is to replay the reported attacks on a hardware-in-the-loop differential relay using real sampled-value packets (IEC 61850 SV) with communication latency and measurement noise typical of field deployments, and measure the fooling rate under the same $\epsilon=0.5$ and five-iteration budget. If the fooling rates fall substantially below the reported figures—especially the 99.74% MLP figure—the claimed vulnerability is an artifact of the simulated waveforms rather than a property of operational LCDRs.

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Extended reading notes

Core claim

The paper's central claim is that an attacker who fully controls the communication link carrying remote current measurements can craft adversarial false-data-injection attacks that evade deep-learning FDIA detection in line current differential relays and cause a false trip. The attack generates perturbations with the Fast Gradient Sign Method, scaling the sign-gradient step by the sample's amplitude, applying it only to remote-measurement features, clipping to the original value range, and iterating until the sample is misclassified as a legitimate fault while the relay's trip condition holds. On a simulated inverter-based microgrid, the fooling rate reaches 99.74% for the MLP detector proposed in prior LCDR work, whereas the ResNet blocks about 90% of the adversarial samples. The paper therefore concludes that the proposed DLS architectures are not robust under this threat model and that adversarial training materially recovers performance.

Load-bearing premise

The whole evaluation depends on the electromagnetic transient simulation of the benchmark medium-voltage microgrid, with its specific relay settings, measurement noise, sampling rate, and four-cycle observation window, being representative enough of real line current differential relays that the measured attack success rates and the adversarial-training gains transfer to field conditions.

Editorial extensions

If this is right

  • The MLP-based FDIA detector proposed in prior LCDR literature should not be deployed against an adversary who can modify remote measurements; its fooling rate under the stated threat model exceeds 99%.
  • ResNet is the most robust of the four architectures tested, but even it is not immune: 9.78% of adversarial samples evade it, so architecture choice alone does not solve the problem.
  • Adversarial training recovers most of the detection capability against FGSM-crafted adversarial FDIAs while preserving high fault-detection accuracy, according to the paper's confusion-matrix results.
  • Attack success increases with perturbation magnitude $\epsilon$, so an operator that bounds admissible perturbation amplitudes can reduce, but not eliminate, the risk.
  • The added inference delay (0.755 to 1.37 ms, under 2 ms in real-time simulation) is small next to the relay's 1.5-to-2-cycle operating time, so the defense does not obviously slow protection.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because the paper evaluates white-box attacks where the adversary knows the model, a natural next test is whether the same fooling rates survive black-box transfer attacks or smaller perturbation budgets; the paper's own sensitivity results suggest the risk is reduced but not eliminated at lower $\epsilon$.
  • Editorial inference: since a successful sample must also satisfy the relay's trip condition, defense-in-depth that independently validates the physical plausibility of the trip could break the attack even when the classifier is fooled.
  • Editorial inference: the paper's fixed observation window, noise range, and single benchmark microgrid imply that retraining on different noise levels, window lengths, or line configurations would test whether adversarial training generalizes beyond the exact dataset used here.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

6 major / 6 minor

Summary. The paper studies adversarial false-data injection attacks against deep-learning-based FDIA detectors embedded in line current differential relays. It formulates an FGSM-based attack that perturbs only remote measurements, with a stated dual success criterion of both misclassifying the manipulated sample as a fault and triggering the LCDR trip condition. The authors evaluate four DLS architectures (MLP, CNN, LSTM, ResNet) on a PSCAD-simulated CIGRE microgrid, report high fooling rates, propose adversarial training as a defense, and validate detection latency on a real-time HIL testbed. The central claim is that all evaluated DL-based FDIA detectors are vulnerable to the proposed adversarial FDIAs, with MLP the most vulnerable and ResNet the least.

Significance. If the reported results are reproduced, the paper identifies a practically important vulnerability class: small perturbations to remote current measurements can make DL-based FDIA detectors classify an attack as a fault while the protected line trips. The comparison of four architectures, the public dataset, and the real-time HIL latency validation are concrete strengths. The adversarial-training results are useful as a first robustness check, though their current evaluation is limited to FGSM. The paper's contribution is significant for smart-grid cybersecurity because LCDRs are safety-critical protection devices, and the authors correctly emphasize the dual physical-and-learning success condition that is often missing in adversarial-attack studies on power systems.

major comments (6)
  1. [Section II-B / Algorithm 3] The class-label mapping is stated inconsistently: Section II-B says ŷ=0 and ŷ=1 denote a legitimate fault and a malicious FDIA, respectively, while the same paragraph says y=0 and y=1 denote an FDIA and a fault, respectively. Algorithm 3's condition 'if (ŷ(x)=1) and (y=1)' is therefore either vacuous or, under the intended label convention, selects fault samples rather than FDIA samples for adversarial-sample generation. This makes the defense procedure ambiguous and must be corrected before the adversarial-training results can be reproduced.
  2. [Section III-B / Eq. (13)] Equation (13) defines the fooling rate using only model misclassification to the target class; it contains no term checking ||i_d|| ≥ i_op from Eq. (4), despite Section III-B's constraint 3 requiring the dual success criterion and the abstract's claim that the attack also triggers the LCDR to trip. Because an FGSM perturbation can move an initially tripping sample out of the trip region, the reported success rates, including the >99.7% figure, may count samples that would not actually trip the relay. The metric should be revised, or the authors should provide a post-hoc verification that every counted sample satisfies Eq. (4).
  3. [Section III-B / Algorithm 2] Algorithm 2's pseudocode cannot execute as written: the while loop returns in both branches of the inner if on the first iteration, so the loop over N_itr never iterates, and the 'Ensure problem constraints' step is left unspecified without referencing Eq. (4). This makes the attack-generation procedure and the adversarial-training augmentation in Algorithm 3 non-reproducible. The pseudocode should be corrected to iterate properly and to explicitly check the LCDR trip condition.
  4. [Section III-A3 / Section III-B] The threat model is internally inconsistent. Section III-A3 states that the adversary applies FGSM 'in a black-box manner, i.e., without accessing the exact model parameters,' but Eq. (10) requires the loss gradient ∇_x J(θ,x,y) with respect to the model parameters, and Algorithm 2 takes f_θ as input. The authors should clarify whether the attack is white-box or black-box; if black-box, they should describe the surrogate model and report transferability results.
  5. [Section VI / Algorithm 3] The adversarial-training evaluation is non-adaptive: the defense is trained and tested using only FGSM-generated samples with the same ε values, and no results are reported against PGD, C&W, or adaptive attacks. The paper's conclusion that adversarial training makes models 'robust to adversarial FDIAs' is therefore stronger than the evidence supports; the claim should be scoped to robustness against FGSM-style attacks.
  6. [Section IV-E2 / Table II / Fig. 10] The attack-success numbers are not reconciled with each other. Section IV-E2 reports an MLP attack success rate of 99.74%, Table II reports 97.24% poisoned samples for MLP, and Fig. 10 reports FR reaching 97.44% at ε≥0.5 for MLP. These may reflect different definitions, but the paper does not explain the relationship, and all values are single-point estimates with no confidence intervals or multiple-seed variation, which is insufficient for a security claim of this strength.
minor comments (6)
  1. [Eq. (13)] The equation contains a long ellipsis placeholder ('..............') that should be removed in the final typeset version.
  2. [References] Reference [49] displays 'M ˛ adry' and should be corrected to 'Madry'.
  3. [Table II] The term 'Poisoned Samples' is ambiguous because it normally refers to training-data poisoning; here it appears to mean the fraction of FDIA samples successfully turned into adversarial samples, and this should be stated explicitly.
  4. [Section II-B] The list of investigated models begins at item '2) CNNs', so item 1) for the MLP appears to be missing.
  5. [Section IV-E2] For ResNet, 'successfully detecting 90.2% of adversarial FDIA samples' and Table II's 9.78% poisoned samples are complements, but the text does not state this relation, which initially reads as a contradiction.
  6. [Section VI-B] The authors note that protocol-specific latency, packet loss, and synchronization errors were not modeled; this limitation should also appear in the conclusion or abstract, since it bounds the real-world applicability of the latency claim.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the attack-success and adversarial-training results are empirical measurements, not derivations that reduce to their own inputs.

full rationale

The claimed derivation chain is: generate PSCAD-simulated FDIA and fault data satisfying the LCDR trip condition (1)-(4); train MLP/CNN/LSTM/ResNet classifiers on that data; craft FGSM perturbations on remote measurements; measure fooling rate on the resulting test set; then apply adversarial training and re-measure. None of these steps defines the target quantity in terms of itself. The fooling rate in Eq. (13) is a measured statistic over test samples, not a fitted parameter being renamed as a prediction. The use of the authors' prior MLP scheme [10] as an attacked baseline is a legitimate experimental input: the model is retrained in this paper and the vulnerability claim is assessed against its actual behavior, so the self-citation is not load-bearing. The adversarial-training evaluation is non-adaptive in the sense that the same FGSM attack is used both to generate training augmentations and to build the adversarial test set, which limits the strength of the robustness claim, but this is an evaluation limitation rather than circular reasoning. One genuine correctness concern is that the abstract claims attacks succeed 'while also triggering the LCDR to trip,' yet Eq. (13) defines FR using only the misclassification conditions I(y_i != yhat(x') and yhat(x') = y_target), with no term checking ||i_d|| >= i_op from Eq. (4); Algorithm 2's constraint check is also unspecified. That is a measurement/validation gap, not a circular reduction, so it does not raise the circularity score. Overall, the paper's central vulnerability result is self-contained empirical work, and no step reduces by construction to its inputs.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central experimental results rest on simulation and threat-model assumptions rather than fitted free parameters. The key free parameters are attack hyperparameters chosen by the authors; the LCDR settings are taken from prior protection literature. No new physical entities are introduced.

free parameters (3)
  • epsilon (FGSM perturbation magnitude) = 0.5 (swept in Section V-A)
    Attack perturbation magnitude; all headline fooling rates use this value, so results are conditional on it.
  • N_itr (FGSM iterations) = 5 (sensitivity checked at 50)
    Number of FGSM iterations; Algorithm 2's control flow contradicts the iterative description.
  • adversarial training epochs = 10
    Retraining duration for the defense; chosen without justification or sensitivity analysis.
assumptions (5)
  • domain assumption Dolev-Yao attacker controls the communication link carrying remote current measurements and can eavesdrop, modify, and inject packets, while local copper-wire measurements remain unmodifiable.
    Section III-A2. This defines the attack surface; if local measurements are also manipulable or the link cannot be fully controlled, the attack's scope and success rates change.
  • domain assumption The LCDR operating equations (1)-(4) with settings id0=0.05 kA, ib=0.585 kA, m1=0.2, m2=0.4 accurately describe relay tripping.
    Sections II-A and IV-A. Both FDIA sample generation and the trip-success criterion depend on this standard differential-relay model.
  • domain assumption PSCAD/EMTDC simulation of the CIGRE medium-voltage benchmark microgrid with 35-60 dB AWGN produces realistic local and remote current waveforms for faults and FDIAs.
    Sections IV-A and IV-B. All training and testing data come from this simulation; no physical field data is used.
  • ad hoc to paper FGSM gradient-sign perturbations constrained to remote features and clipped to the input range yield physically plausible manipulated currents that still satisfy the relay trip condition.
    Sections III-B and Algorithm 2. The paper does not validate that perturbed samples correspond to feasible injected phasors after clipping and amplitude scaling.
  • ad hoc to paper Adversarial training on samples generated by the same FGSM algorithm is sufficient to assess robustness against adversarial FDIAs.
    Section VI. The defense is tested only against the same attack distribution; no adaptive or stronger attacks are evaluated.

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Cite this review

Pith. "Pith review of Adversarial Attacks on Deep Learning-Based False Data Injection Detection in Differential Relays." pith.science (2026). https://pith.science/paper/QWEQ6MUA

@misc{pith2026250619302,
  author       = {Pith},
  title        = {Pith review of: Adversarial Attacks on Deep Learning-Based False Data Injection Detection in Differential Relays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QWEQ6MUA}},
  note         = {Machine review of arXiv:2506.19302}
}
read the original abstract

The application of Deep Learning-based Schemes (DLSs) for detecting False Data Injection Attacks (FDIAs) in smart grids has attracted significant attention. This paper demonstrates that adversarial attacks, carefully crafted FDIAs, can evade existing DLSs used for FDIA detection in Line Current Differential Relays (LCDRs). We propose a novel adversarial attack framework, utilizing the Fast Gradient Sign Method, which exploits DLS vulnerabilities by introducing small perturbations to LCDR remote measurements, leading to misclassification of the FDIA as a legitimate fault while also triggering the LCDR to trip. We evaluate the robustness of multiple deep learning models, including multi-layer perceptrons, convolutional neural networks, long short-term memory networks, and residual networks, under adversarial conditions. Our experimental results demonstrate that while these models perform well, they exhibit high degrees of vulnerability to adversarial attacks. For some models, the adversarial attack success rate exceeds 99.7%. To address this threat, we introduce adversarial training as a proactive defense mechanism, significantly enhancing the models' ability to withstand adversarial FDIAs without compromising fault detection accuracy. Our results highlight the significant threat posed by adversarial attacks to DLS-based FDIA detection, underscore the necessity for robust cybersecurity measures in smart grids, and demonstrate the effectiveness of adversarial training in enhancing model robustness against adversarial FDIAs.

Figures

Figures reproduced from arXiv: 2506.19302 by the authors.

Figure 1
Figure 1. Adversarial attack process: Adding subtle perturbations [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Operating characteristics of the LCDR [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Illustration of an FDIA to falsely trip LCDR [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Test system. B. Performance Evaluation Scenarios The objective of DL-based modules in this paper is to detect FDIAs, by differentiating them from genuine faults, once the LCDR’s fault detection module is triggered whether by a fault or an FDIA. For this reason, a compr…
Figure 5
Figure 5. Figure 5: Illustration of i2 locus for successful FDIAs against LCDRAC , (a): i2 values that would trip LCDRAC (in kA), (b): phasor α values for multiplicative FDIAs (i2 × α yields a value for the remote current that trips the LCDR) measurements of LCDRAC under normal system ope…
Figure 6
Figure 6. Figure 6: Original performance metrics before adversarial attacks [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: Confusion matrices without adversarial attacks [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: Performance metrics under adversarial attacks [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: Confusion matrices under adversarial attacks [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]
Figure 11
Figure 11. Figure 11: Confusion matrices after adversarial training [PITH_FULL_IMAGE:figures/full_fig_p010_11.png]
Figure 13
Figure 13. Figure 13: Oscilloscope snapshot, FDIA detection time. [PITH_FULL_IMAGE:figures/full_fig_p011_13.png]

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.