WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 21, 2026
An Electro-Thermal State Matrix Framework for Interpretable PMSM Inverter Fault Diagnosis Using Chromatic Fingerprints
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Abstract: Fault detection in PMSM inverters is usually done through measurement or hand-crafted features of
electrical and thermal parameters. Although such methods can perform with excellent accuracy in classification
tasks, they provide limited insight into the physics of fault development. This paper presents a methodology for
diagnosing faults in inverters through an interpretable fault diagnosis technique using Physical State Vector (PSV),
Electro-Thermal State Matrix (ETSM), and Chromatic Fingerprints.
The suggested approach consists of first converting the raw data measured in PMSM into physical representations
of the electrical, thermal, and electro-thermal features. Then, the data is represented in an ETSM, where
electrical behavior, thermal conditions, and electro-thermal interrelations are distinctly distinguished. The ETSM
is converted to a chromatic fingerprint, which is a graphical representation of the system state. To test the
diagnostic potential of the proposed representation, the statistical color features obtained from the fingerprints
are classified via a Random Forest model.
Validation of the experimental work was carried out by using publicly available data related to the fault diagnosis of
the PMSM inverter, which included 10,892 samples from nine different operating conditions. Because each class is
one continuous 10 Hz recording, a blocked temporal cross-validation is used as the primary protocol, and repeated
stratified cross-validation is reported for comparison. The chromatic fingerprint reached 89.4 ± 6.6% accuracy and
84.9 ± 8.9% Macro-F1 in blocked cross-validation (95.5 ± 0.5% and 93.6% in random folds), against 98.1 ± 3.0%
for the raw sensors. Feature importance, grouped permutation importance, SHAP, and layer-ablation analyses
showed that thermal descriptors were the main source of discriminative information in this dataset (73.9 ± 0.9% of
impurity importance), whereas removing the electro-thermal layer did not reduce accuracy, so no complementary
information was demonstrated for it. Chromatic fingerprint distances correlated with class confusion (Spearman
ρ = −0.83).
The presented results show a trade-off between diagnostic effectiveness and physical interpretability of the
developed representation. In contrast to sensor-based methods, the proposed framework offers an electro-thermal
representation, which is capable of providing both fault diagnosis and visualization of the PMSM fault states,
within the limits of a single dataset.
Keywords:
PMSM fault diagnosis, Electro-Thermal State Matrix, Physical State Vector, Chromatic Fingerprint, Explainable Artificial Intelligence, Condition Monitoring, Random Forest
Pages: 419-435
DOI: 10.37394/23203.2026.21.37