Detecting eccentricity levels in induction motors via persistent homology

Kristian Gochi; Ahtziri González; Juan Anzurez; Kristian Gochi; Ahtziri González; Juan Anzurez

doi:10.3934/electreng.2026025

AIMS Electronics and Electrical Engineering

2026, Volume 10, Issue 4: 605-626. doi: 10.3934/electreng.2026025

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Research article Topical Sections

Detecting eccentricity levels in induction motors via persistent homology

1.
División de Estudios de Posgrado, Facultad de Ingeniería Eléctrica, Universidad Michoacana de San Nicolás de Hidalgo, Avenida Francisco J. Mújica S/N, 58030, Morelia, Michoacán, México
2.
Instituto de Matemáticas, Universidad Nacional Autónoma de México, Boulevard Juriquilla 3001, Querétaro 76230, México

Received: 22 March 2026 Revised: 04 August 2026 Accepted: 17 August 2026 Published: 09 September 2026

We propose a persistent homology procedure to estimate the severity of mixed eccentricity in three-phase induction motors from line-current measurements. Currents are generated in ANSYS RMxprt/Maxwell under no-load operation for both star and delta connections across six eccentricity levels. Each steady-state frame is embedded as a point cloud in $ \mathbb{R}^3 $ and approximated with alpha complexes to compute persistence diagrams and Betti curves. We define descriptors based on the topological properties and behaviors of the Betti curves. Under the delta connection, we add a new descriptor associated with noise in 2-homology. All descriptors exhibit monotonic trends with increasing eccentricity and allow quadratic fits that enable interpolation of intermediate eccentricity levels. We also show that alpha complexes implemented in GUDHI provide substantial computational advantages over Vietoris-Rips complexes implemented in Ripser.
- fault diagnosis,
- three-phase induction motors,
- eccentricity,
- topological data analysis,
- persistent homology,
- Betti curves
Citation: Kristian Gochi, Ahtziri González, Juan Anzurez. Detecting eccentricity levels in induction motors via persistent homology[J]. AIMS Electronics and Electrical Engineering, 2026, 10(4): 605-626. doi: 10.3934/electreng.2026025

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Abstract

We propose a persistent homology procedure to estimate the severity of mixed eccentricity in three-phase induction motors from line-current measurements. Currents are generated in ANSYS RMxprt/Maxwell under no-load operation for both star and delta connections across six eccentricity levels. Each steady-state frame is embedded as a point cloud in $ \mathbb{R}^3 $ and approximated with alpha complexes to compute persistence diagrams and Betti curves. We define descriptors based on the topological properties and behaviors of the Betti curves. Under the delta connection, we add a new descriptor associated with noise in 2-homology. All descriptors exhibit monotonic trends with increasing eccentricity and allow quadratic fits that enable interpolation of intermediate eccentricity levels. We also show that alpha complexes implemented in GUDHI provide substantial computational advantages over Vietoris-Rips complexes implemented in Ripser.

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