Fault Classification (FC) Techniques

• Fault Classification (FC) is the supervised assignment of observations to fault classes, addressing both multiclass and multi-label challenges across various domains.
• It leverages a range of inference methods—from MLPs and SVMs to neuro-fuzzy systems—to extract features from raw signals, texts, and modal descriptors.
• Robustness, real-time constraints, and explainability are critical factors, driving research towards multitask, open-set, and proof-based approaches.

Fault classification (FC) denotes the assignment of an observed measurement, signal segment, text record, or execution trace to one fault class or fault label set. In the cited literature, FC is instantiated as multiclass protection in power systems, structural and rotating-machine diagnosis, online monitoring in HPC and IIoT systems, multi-label recognition in power-service texts and compound mechanical faults, and classification of failing automotive software tests by proof-based equivalence (Oelhaf et al., 17 Dec 2025, Netti et al., 2018, Xiaona et al., 2022, Becker et al., 2022, Miraliakbar et al., 2 Apr 2025). The topic is therefore not a single algorithmic problem but a family of supervised and semi-structured inference problems whose formulation depends on the sensing modality, label semantics, operating constraints, and admissible uncertainty.

1. Task structure and label semantics

In several power-system studies, FC is posed as a closed-set multiclass problem with an explicit “no-fault” class. One protection formulation uses $y_i \in \{1,\dots,C\}$ with $C=11$ classes, comprising 10 fault types plus “no-fault,” while a related benchmark evaluates the same 11-class taxonomy over EMT-derived voltage and current windows from eight relays (Oelhaf et al., 17 Dec 2025, Oelhaf et al., 1 Oct 2025). A DFIG/TCSC transmission-line study expands this pattern to 12 classes: AG, BG, CG, AB, BC, CA, ABG, BCG, CAG, ABC, ABCG, and no-fault (Singh et al., 2023). In HPC monitoring, the label set is $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$, and in IIoT monitoring the classification task is likewise 12-way, with eleven injected fault types and a no-fault class (Netti et al., 2018, Alam, 2023).

Other FC settings are explicitly multi-label. In power ICT customer-service text classification, the label set has $m=22$ fault-type categories, and each instance may carry between 1 and 9 labels, with Binary Relevance converting the problem into $m$ independent binary tasks (Xiaona et al., 2022). In rotating electrical machines, each instance is assigned a binary label vector $y=(y_1,y_2)\in\{0,1\}^2$ indicating the presence or absence of unbalance and misalignment; the key difficulty is concurrent-fault diagnosis under disturbing noises and overlapping features (Dineva et al., 2019). This distinction matters because exact-match accuracy, Hamming loss, and macro-averaged $F_1$ quantify different failure modes than ordinary multiclass accuracy.

A distinct formulation appears in automotive software. There, FC is not direct sensor-based pattern recognition but the grouping of failing tests after fault localization and fault explanation. The classification objects are reduced explanations extracted from Hoare-style proofs, and the final classes are equivalence classes under a relation $\simeq$ defined by event sequences and satisfiability of atomic clock constraints (Becker et al., 2022). This suggests that FC, in the broader literature, includes both signal classification and root-cause grouping.

2. Observation models and feature representations

The surveyed work spans raw waveform inputs, engineered spectral or modal descriptors, geometric embeddings, and text embeddings. In centralized power-system protection, each event yields a multivariate time series $X^{(n)} \in \mathbb{R}^{48\times T}$ with $T=6400$ samples, corresponding to 48 channels from three-phase current and voltage measurements at eight relays. After cropping $C=11$0 ms around fault inception and using sliding windows of $C=11$1 ms, each window is flattened to $C=11$2 (Oelhaf et al., 17 Dec 2025). A related benchmark also uses cropped raw voltage/current samples from eight relays, window lengths from 10 ms to 50 ms, 5 ms steps, zero-mean unit-variance standardization, and no handcrafted features (Oelhaf et al., 1 Oct 2025).

By contrast, classical vibration-based FC often relies on physically motivated feature extraction. For cylindrical shells, pseudomodal energies are obtained by integrating the real and imaginary parts of the inertance FRF over narrow frequency bands around resonances. From 19 measurement locations and 17 natural frequencies, this yields 646 PMEs per test, later reduced to 10 features by SOF ranking or PCA before classification (0705.2236). A related cylinder study extracts 17 natural frequencies and 17 mode shapes over 19 positions, producing 340 raw modal features per measurement and then reducing them to 10 PCA scores (0705.0197).

Several studies compress temporal signals into low-dimensional summaries. In the DFIG/TCSC setting, a one-level db4 DWT is applied to phase and ground currents, and only the maxima of the level-1 detail coefficients are retained, giving the four-dimensional feature vector $C=11$3 (Singh et al., 2023). In a series-compensated transmission line, the LS-SVM scheme uses only the first one-fourth of the post-fault cycle, namely 5 current samples per phase, with no DFT or wavelet preprocessing (Dubey et al., 2016).

More recent FC work uses non-Euclidean or learned representations. The Grassmann-manifold approach fits an ARMA model to bus measurements, constructs a finite observability matrix, and represents each record by an orthonormal basis $C=11$4 for its observability subspace, i.e. as a point on $C=11$5 (K. et al., 2024). Cross-talk multitask learning for physically coupled machine systems uses STFT spectrograms as inputs to a 2D-CNN with Frequency Layer Normalization (Yi et al., 5 Feb 2026). In multi-label power-text FC, Chinese word segmentation, stop-word removal, 400-dimensional GloVe embeddings averaged over words, and TF–IDF-based label mining define the representation pipeline (Xiaona et al., 2022). The representation layer is therefore highly domain dependent, but the unifying pattern is dimensionality reduction toward class-discriminative structure.

3. Model families and inference mechanisms

A compact MLP is a recurring baseline in power-system FC. One formulation implements $C=11$6 with two fully connected layers, ReLU activations, and a final softmax:

$C=11$7

trained by cross-entropy over sliding windows (Oelhaf et al., 17 Dec 2025). In benchmarking, a scikit-learn MLP with hidden_layer_sizes=(100,), activation='relu', and solver='adam' is compared against logistic regression, ridge, SGD, KNN, SVC, tree ensembles, and boosting methods (Oelhaf et al., 1 Oct 2025).

FC has also long been implemented with SVMs, GMMs, neuro-fuzzy systems, and modular binary decompositions. The Takagi–Sugeno neuro-fuzzy model uses 10 normalized PME inputs, $C=11$8 first-order Sugeno rules, Gaussian membership functions, affine consequents, least-squares updates for consequent parameters, and gradient descent for antecedent parameters (0705.2236). For cylinder faults, GMM, SVM, and MLP are all trained on the same 10-dimensional PCA representation; GMM uses $C=11$9 diagonal-covariance components per class and EM learning, while SVM uses an exponential RBF kernel (0705.0197). In the LS-SVM transmission-line scheme, the multiclass problem is decomposed into four binary modules indicating whether phases R, Y, B, and ground are involved; logic on the four outputs maps to SLG, LL, DLG, and three-phase fault types (Dubey et al., 2016).

Beyond conventional classifiers, FC increasingly appears in multitask and cascaded designs. SMTCNN combines change-point segmentation by an LSTM autoencoder, binary anomaly refinement by a two-layer LSTM, and final 12-class fault classification by another two-layer LSTM (Alam, 2023). RNDR introduces cross-talk layers between task-specific branches so that fault labels are learned jointly with physically coupled auxiliary variables such as drone type, maneuvering direction, or compound-fault components (Yi et al., 5 Feb 2026). In power ICT text FC, BR-GBDT applies Gradient Boosting Decision Trees independently to each label under the Binary Relevance decomposition (Xiaona et al., 2022). The model space is therefore heterogeneous: generative, discriminative, kernel, fuzzy, ensemble, neural, multitask, and even proof-theoretic approaches all occur in the literature.

4. Metrics, benchmarks, and reported performance

The dominant evaluation metrics are accuracy, precision, recall, and $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$0, but their aggregation differs with task structure. In power protection, one robustness study defines per-class $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$1, $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$2, and $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$3, with overall $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$4 as the unweighted average across classes, and additionally introduces a relative performance-loss metric $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$5 under degradation scenario $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$6 (Oelhaf et al., 17 Dec 2025). The broader benchmark likewise reports macro-averaged precision, recall, and $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$7 over the 11 classes (Oelhaf et al., 1 Oct 2025). Multi-label studies instead use Hamming loss, micro/macro precision-recall-$$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$8, or subset accuracy (Xiaona et al., 2022, Dineva et al., 2019).

Reported performance is correspondingly diverse. In power-system protection, the best benchmarked FC model is the MLP, reaching $$Y=\{\text{healthy}, \text{leak}, \text{memeater}, \text{ddot}, \text{dial}, \text{cpufreq}, \text{pagefail}, \text{ioerr}, \text{copy}\}$$9 at 50 ms windows and remaining at least $m=22$0 down to 20 ms; gradient boosting is competitive only at longer windows, and most other classical models remain below $m=22$1 (Oelhaf et al., 1 Oct 2025). Under nominal conditions in the robustness study, the same general MLP-based FC setting yields $m=22$2 (Oelhaf et al., 17 Dec 2025). On the Grassmann manifold, the projection-metric SVM achieves aggregate weighted results of accuracy $m=22$3, precision $m=22$4, recall $m=22$5, $m=22$6-score $m=22$7, and MCC $m=22$8 over 10-fold cross-validation (K. et al., 2024).

Outside power systems, cylinder-fault studies report 98% accuracy for GMM, 94% for SVM, and 88% for MLP in one experiment, while the PME-based neuro-fuzzy model reaches 91.62% total classification accuracy with optimized thresholds (0705.0197, 0705.2236). In HPC systems, Random Forest attains overall $m=22$9-score $m$0 under 5-fold cross-validation in timestamp order (Netti et al., 2018). In IIoT, SMTCNN yields Accuracy $m$1, Precision $m$2, Recall $m$3, Specificity $m$4, and $m$5 (Alam, 2023). In power ICT text classification, BR-GBDT achieves $m$6 on the ICT CS dataset, versus $m$7 for BR+LR and $m$8 for ML-KNN (Xiaona et al., 2022). In Tennessee Eastman online monitoring, classification accuracy improves from about 61% for a flat SVM on raw windowed data to about 82% with Riemannian features and to about 84.5% when SPC summary features are added (Miraliakbar et al., 2 Apr 2025).

An objective caveat is that not all studies report directly comparable metrics. The Wavelet–ANN DFIG/TCSC study reports training MSE $m$9 and qualitative robustness under varying conditions, but no explicit accuracy, precision-recall, or confusion-matrix figures are tabulated (Singh et al., 2023).

5. Robustness, generalization, and real-time constraints

Robustness is a central differentiator between laboratory FC and deployable FC. In centralized power protection, FC remains highly stable under missing current, missing voltage, moderate downsampling, transient communication loss, and any single relay or substation outage: missing current gives $y=(y_1,y_2)\in\{0,1\}^2$0, missing voltage gives $y=(y_1,y_2)\in\{0,1\}^2$1, any single relay loss causes at most about $y=(y_1,y_2)\in\{0,1\}^2$2 loss, and temporal dropout up to 20 ms keeps $y=(y_1,y_2)\in\{0,1\}^2$3 within $y=(y_1,y_2)\in\{0,1\}^2$4 (Oelhaf et al., 17 Dec 2025). The same study identifies a specific failure mode: dropping an entire phase causes $y=(y_1,y_2)\in\{0,1\}^2$5 to fall to $y=(y_1,y_2)\in\{0,1\}^2$6, $y=(y_1,y_2)\in\{0,1\}^2$7, or $y=(y_1,y_2)\in\{0,1\}^2$8 for phase A, B, or C loss, corresponding to relative losses of 14%, 12.7%, and 13.1% (Oelhaf et al., 17 Dec 2025). This directly contradicts the common assumption that high nominal $y=(y_1,y_2)\in\{0,1\}^2$9 is sufficient evidence of field readiness.

Cross-individual generalization is another recurring failure mode. In wave-propagation FC for hydraulic rock drills, raw-series methods collapse when training on one pseudo-individual and testing on five others: 1NN-DTW on raw series gives 35% balanced accuracy, SVM on raw series 35%, and InceptionTime on raw series 34%. Relative features built from differences to a per-individual no-fault reference reduce this degradation, with InceptionTime on the DTW time-shift feature $F_1$0 reaching 62% cross-individual accuracy and about 73% under majority voting over consecutive cycles (Jakobsson et al., 2022). This suggests that reference-relative representations can be more transferable than absolute waveforms when individual variability is large.

Real-time FC also imposes strict latency budgets. In the power benchmark, MLP inference time is $F_1$1 ms per window and is stated to meet typical relay latency requirements below 5 ms (Oelhaf et al., 1 Oct 2025). The LS-SVM relay scheme operates with one-fourth-cycle inputs and total classification delay of about 5–10 ms (Dubey et al., 2016). In HPC systems, feature extraction over a 60 s window every 10 s takes about 340 ms for 16 cores on one thread, while Random Forest prediction adds about 2 ms per core; the resulting worst-case reaction lag is 60 s and the average detection latency about 30 s (Netti et al., 2018). In IIoT, SMTCNN is trained and evaluated on a commodity gateway at one-minute sampling rates, and in chemical-process monitoring the FARM hierarchy lets practitioners tune the false alarm rate through the SPC threshold $F_1$2 while triggering classification only after a detection alarm (Alam, 2023, Miraliakbar et al., 2 Apr 2025).

6. Extended formulations: open-set, explainable, multitask, and proof-based FC

Several recent studies expand FC beyond closed-set label assignment. A KL-divergence framework for time-series diagnosis models each batch by a Gaussian pdf, compares it to class-specific sets of pdfs, and can output “No-Fault,” a set of plausible known-fault hypotheses, or “Unknown Fault” when all known classes are rejected. The same framework is explicitly designed for imbalanced datasets, class overlap, and unknown faults, and includes a fault-size estimator based on convex mixtures of nearest training pdfs (Lundgren et al., 2020). This formulation treats ambiguity as part of the output rather than as an error to be suppressed.

Explainability is treated as a first-class problem in ABIGX. For fault classification, ABIGX defines a classification-SPE on penultimate-layer representations, computes an adversarial fault reconstruction baseline $F_1$3, and then applies integrated gradients from $F_1$4 to the observed sample. The framework introduces “fault-class smearing” as the tendency of multiclass gradients to attribute importance to irrelevant fault classes, proves that ABIGX mitigates this more effectively than ordinary Integrated Gradients, and shows on wafer-map classification that ABIGX reaches Correctness–AUC 0.839 versus 0.571 for saliency, 0.814 for IG, and 0.812 for DeepLIFT (Zhuo et al., 2023).

Multitask FC exploits physically coupled variables rather than ignoring them. In RNDR, drone fault classification is learned jointly with drone type and maneuvering direction, while compound motor-fault classification is decomposed into concurrent tasks for inner-race fault, outer-race fault, misalignment, and unbalance. Macro-$F_1$5 reaches 0.90 on the drone dataset and 0.86 or 0.89 on the motor dataset, depending on whether the input is single-channel or multi-channel (Yi et al., 5 Feb 2026). A plausible implication is that auxiliary labels can regularize FC when the signal structure is entangled with operational context.

Finally, some FC work abandons pattern classification altogether in favor of formal reasoning. In automotive software, fault localization, fault explanation, and proof-template equivalence reduce 100 failing traces to 6 equivalence classes, with 95 of 100 annotated faults found plus 10 previously undetected ones (Becker et al., 2022). In that setting, the “class” is a formally characterized failure reason rather than a learned cluster in feature space.

Taken together, these directions show that FC is no longer adequately described as a static multiclass classifier over fixed features. The literature instead treats it as a broader diagnostic layer that may be closed-set or open-set, single-label or multi-label, raw-input or model-based, nominally accurate or robustness-audited, and increasingly subject to explainability and deployment constraints.