Faraday Predictive partnered with mathematicians from five leading UK universities to investigate the fundamental physics that makes motor current signature analysis work. Here is what they found, and why it matters for industrial condition monitoring.
Background: Why We Commissioned This Research
Faraday Predictive’s MBVI technology analyses the relationship between motor voltage and current to detect faults in rotating machinery, without sensors, without shutdowns, and without accessing the equipment itself. The approach works. Engineers across oil and gas, power generation, water utilities and manufacturing use it every day to catch bearing failures, rotor faults, and mechanical problems before they become costly breakdowns.
But not all of the physics underlying the technique was fully understood at a mathematical level. In particular, the precise reasons why certain fault signatures appear where they do in the current spectrum, and why sidebands sometimes appear asymmetrically, had not been rigorously explained from first principles.
To answer these questions, Faraday Predictive presented the problem to the 162nd European Study Group with Industry (ESGI), hosted by the School of Mathematics at the University of Leeds. The study group brought together mathematicians and engineers from:
- University of Oxford
- University of Leeds
- University of Huddersfield
- University of Bristol
- University of Bath
The resulting report, authored primarily by Mathew Shirley of the University of Oxford with contributions from seventeen researchers, provides the most rigorous mathematical treatment of motor current signature analysis that Faraday Predictive has been party to.
The Problem We Put to the Mathematicians
Motor current signature analysis works by examining the spectrum of a motor’s residual current, the portion of the current waveform that cannot be explained by the applied voltage, for sidebands around the main supply frequency. These sidebands correspond to physical events inside the motor and driven machinery.
We asked the research group to address two specific questions.
- Question 1: What causes the fundamental signal? From the basic equations for voltage and current in a three-phase induction motor, can you derive from first principles the effect on stator current of a change in load torque, or a change in eccentricity of the rotor? How do these compare in magnitude to signals from rotor magnetic asymmetry, such as cracked rotor bars?
- Question 2: What determines where signals appear in the spectrum? Why do fault signals appear as sidebands on a carrier frequency? What causes multiple sidebands? What causes sidebands to appear more strongly on one side of the carrier than the other? What determines which harmonics a signal appears on?
These are not academic questions for their own sake. The answers directly affect how confidently fault signatures can be interpreted in practice, and how reliably different fault types can be distinguished from each other in noisy industrial environments.
What the Research Found
The study group developed and analysed two distinct mathematical models of an induction motor.
Model 1: The Steinmetz Equivalent Circuit
The first model used the Steinmetz equivalent circuit, the standard IEEE-recommended representation of an induction motor. The researchers used both numerical and asymptotic techniques to show how periodic perturbations to the motor’s slip, caused by load variations or mechanical faults, produce sidebands in the stator current spectrum at predictable frequencies either side of the supply frequency.
The key finding was a rigorous mathematical proof that sinusoidal perturbations at a frequency ψ produce sidebands at Ω ± ψ, where Ω is the supply frequency. This confirms and mathematically justifies what experienced MCSA practitioners observe in practice. The Steinmetz model has the advantage of being well-established and straightforward to parameterise from motor nameplate data.
Its limitation is that rotor dynamics only enter the model indirectly through the slip parameter, which means it can only produce symmetric sidebands from sinusoidal perturbations. Real motor spectrums often show asymmetric sidebands, which this model cannot fully explain.
Model 2: A Physics-Based First-Principles Model
The second model was derived from first principles using Faraday’s law of induction, Ohm’s law, and conservation of angular momentum. Rather than treating the rotor as an abstract circuit element, this model explicitly represents the rotor as a set of conducting loops rotating inside the stator’s magnetic field.
This approach allows rotor dynamics to appear directly in the equations, which means a wider range of defects can be modelled explicitly. The researchers demonstrated how the model predicts the residual current spectrum for several specific fault types:
- A single damaged rotor bar, modelled as a change in magnetic flux through one rotor loop, producing asymmetric sidebands whose frequency separation equals twice the slip frequency.
- Rotor precession, where the rotor spins with a wobble at a distinct precession frequency, producing sidebands at the precession frequency as well as additional peaks around the supply frequency.
- Time-varying load, including periodic load fluctuations that produce sidebands at the load modulation frequency. Critically, non-sinusoidal loads (such as square wave or cubic perturbations) produce multiple harmonics, explaining why some fault signatures appear at several sideband locations simultaneously.
- Combined defects, where multiple fault types interact to produce complex, overlapping spectra.
The physical model was also extended to describe the effect of driven machinery on the motor’s current signature, covering both a directly coupled disc and a flexible rotor shaft on rigid supports. This is particularly relevant for detecting faults in driven equipment, such as pump impellers and fan blades, which create load-side signals that propagate back through the motor’s current waveform.
Why Asymmetric Sidebands Occur
One of the most practically useful findings concerns asymmetric sidebands, where a fault produces a stronger signal on one side of the carrier frequency than the other. The Steinmetz model cannot predict this. The physics-based model shows that asymmetry arises from combined load and magnetic flux perturbations, and that the excited frequencies in this case include terms at Ω ± ψ₁, Ω ± ψ₂, and additional cross-terms at Ω − 2θ̇₀ ± ψ₁ and 3Ω − 2θ̇₀ ± ψ₁.
In plain language: when both a mechanical fault and a magnetic asymmetry are present simultaneously, the interaction between them produces sidebands that are not symmetric around the supply frequency. This is a mathematical confirmation of something that condition monitoring engineers had observed empirically but had not been able to explain rigorously.
What This Means in Practice
This research does not change how Faraday Predictive’s systems work. The MBVI technology was already detecting these fault signatures reliably before the mathematics was written down. What the research provides is a deeper understanding of why the signals appear as they do, which has three practical implications.
- More confident fault interpretation. When a spectrum shows asymmetric sidebands, engineers can now point to a mathematical basis for understanding what that asymmetry indicates about the combination of faults present. This reduces uncertainty in diagnosis, particularly for complex or overlapping fault conditions.
- Better differentiation between fault types. The research establishes, from first principles, that different fault types produce distinguishable spectral signatures. A cracked rotor bar, a precessing rotor, and a load-side imbalance each create sidebands at different frequencies and with different symmetry properties. This underpins the diagnostic specificity that MBVI delivers.
- A foundation for future development. The study group identified several directions for further work, including extending the models to permanent magnet motors, refining the treatment of the continuum limit as rotor loop density increases, and developing practical inverse problem methods to extract fault parameters directly from measured spectra. This research represents a foundation that Faraday Predictive will continue to build on.
Download the Full Research Report
The complete ESGI report, including full mathematical derivations, numerical results, spectral plots, and Python code for reproducing the simulations, is available to download.
✔️ Download: Understanding the Fundamentals of Motor Current Signature Analysis (PDF)
The report was produced by the following contributors: Mathew Shirley (lead author, University of Oxford), Alan Champneys, Joaquim Correia, Yahya Farah, Gopal, Mat Hunt, Andrew Lacey, Nico Marrin, Karin Mora, Matthew Moore, Hilary Ockendon, John Ockendon, Dhanesh Patel, Bernard Piette, James Roscoe, Alexander Shaw, and Geo Walker (Faraday Predictive).
Understand the Technology Behind the Results
This research underpins the MBVI analysis at the heart of Faraday Predictive’s condition monitoring systems. To see how that technology is applied in practice:
- What is MBVI? Model-Based Voltage and Current Condition Monitoring Explained
- Electrical Signature Analysis (ESA): How It Works and What It Detects
- Book a free 10-minute demo to see the system applied to your equipment