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Sound Analysis for Speed Estimation of Induction Motors Under Non-Stationary Conditions

Tomas A. Garcia-Calva, Daniel Morinigo-Sotelo, Konstantinos N. Gyftakis

arXiv:2608.29214v1eess.SP

TL;DR

The paper addresses noninvasive induction-motor speed estimation when conventional sensors are intrusive and acoustic signals are noisy and non-stationary. It combines acoustic blade-passing harmonics with multirate processing and ST-MUSIC, and experimentally tracks dynamic speed changes with close reference agreement and low errors.

  • Problem

    Conventional speed sensors are intrusive, while acoustic speed estimation is challenged by noise, multiple harmonics, and non-stationary operation.

  • Method

    The method extracts rotor-speed-dependent blade-passing harmonics from microphone recordings using multirate processing and ST-MUSIC time-frequency analysis.

  • Results

    The estimator accurately tracks load-induced dynamic speed changes, with RMSE 0.030898 r.p.s., MAE 0.018881 r.p.s., and MAPE 0.0776%.

  • Takeaways & Limitations

    The acoustic approach provides a reliable, non-contact, low-cost option for instantaneous induction-motor speed monitoring under steady and dynamically varying loads.

Abstract

from arXiv · show

This paper presents a novel methodology for the estimation of the rotational speed of induction motors operating under non stationary conditions, using acoustic signals acquired by a low cost microphone. The proposed approach integrates multi rate digital signal processing with advanced time frequency analysis to extract speed dependent harmonic components from motor acoustic emissions, while effectively suppressing electrical interference and electromagnetic noise. Numerical simulations and experimental validations are conducted under both steady state and transient operating conditions, considering a wide variety of speed profiles, including slow ramps and abrupt speed variations. The experimental results demonstrate that the proposed method is capable of accurately tracking rapid and dynamic speed changes caused by load disturbances and mechanical irregularities. The estimated instantaneous speed exhibits a high degree of agreement with reference measurements obtained from a conventional speed sensor. The results confirm that the proposed acoustic based technique provides a reliable, noninvasive, and cost effective solution suitable for speed monitoring of induction motors.

I. INTRODUCTION

Induction motors require accurate monitoring, but conventional speed sensors are intrusive and vulnerable to harsh environments. The paper proposes acoustic speed estimation using multirate processing and ST-MUSIC for non-stationary operation.

  • Induction motors are widely deployed, making accurate condition monitoring important for productivity, safety, and system reliability.
  • Conventional resolvers, tachometers, and encoders provide precise measurements but require intrusive installation, maintenance, and mechanical modifications.
  • Sensorless methods infer rotor speed from measurable motor signals, including electrical variables, vibration, and electromagnetic torque.
  • Acoustic monitoring avoids physical contact and uses commercially widespread microphones, but reliable extraction is difficult under noise and changing operating conditions.
  • The proposed method combines blade-passing harmonics, multirate processing, and ST-MUSIC, with numerical and experimental validation against a tachometric sensor.

II. MATHEMATICAL FOUNDATIONS

The induction motor’s rotating magnetic field establishes synchronous speed, while rotor speed remains lower because electromagnetic torque requires slip. Load changes therefore produce speed transients before a new steady state.

  • A balanced stator supply creates a rotating air-gap magnetic field whose synchronous speed depends on supply frequency and pole-pair count.
  • Electromagnetic torque makes the rotor rotate with the magnetic field, but rotor speed never reaches synchronous speed; their difference is slip.
  • The rotor’s mechanical speed is expressed in revolutions per second.
  • Increasing load torque moves rotor speed farther from synchronous speed and increases slip.
  • Sudden load-torque changes produce transient rotor-speed responses whose duration depends primarily on the equivalent motor-load inertia.

B. Short-Time Analysis Using Subspace Decomposition

The method uses ST-MUSIC to resolve sound-spectrum components while preserving their temporal evolution. It separates signal and noise subspaces to produce sharp frequency peaks for high-resolution time-frequency analysis.

  • Acoustic load disturbances appear as time-varying harmonics, requiring joint resolution of spectral content and temporal evolution.
  • ST-MUSIC tracks non-stationary harmonics through high-resolution time-frequency analysis.
  • The sound autocorrelation matrix is modeled as the sum of signal and noise autocorrelation matrices.
  • The resulting spectrum displays sharp peaks at sound-oscillation frequencies, supporting high-resolution time-frequency analysis.

III. BLADE PASSING FREQUENCIES

Blade-passing frequencies arise from periodic aerodynamic interactions and form a harmonic family linked to fan rotation. Prime-order components are typically stronger because blade-arrangement symmetry selectively reinforces or cancels harmonics.

  • A fan with Nb blades produces a base blade-passing frequency from the rotational frequency, and periodic blade passages generate harmonic spectral lines.
  • The periodic acoustic pressure signal can be modeled as repeated single-blade pressure signatures, with TB defined as the passage period.
  • The complete BPF family contains harmonics at integer multiples of the base frequency.
  • When driven by an induction motor, BPF harmonics become directly linked to rotor speed and can therefore support speed estimation.
  • Prime-order BPF components typically have higher amplitudes because aerodynamic symmetry causes selective reinforcement or cancellation across harmonics.

IV. PROPOSED METHODOLOGY

The methodology estimates induction-motor speed from acoustic measurements through a five-stage signal-processing chain, beginning with microphone acquisition and anti-aliasing before digitization.

  • IV. PROPOSED METHODOLOGY: The processing chain comprises signal acquisition, sampling-rate conversion, filtering, short-time analysis, and frequency-to-speed conversion.The complete chain is illustrated in Fig. 1.
  • IV. PROPOSED METHODOLOGY: A microphone converts sound-pressure variations into a voltage signal, which is analog low-pass filtered at 30 kHz before digitization.
  • IV. PROPOSED METHODOLOGY: The block diagram summarizes the proposed motor speed estimation method.

B. Sampling Rate Conversion

Sampling-rate conversion narrows the acoustic signal to the relevant band, after which short-time spectral analysis supports high-resolution estimation of the speed-related harmonic.

  • B. Sampling Rate Conversion: A digital low-pass filter and factor-20 down-sampling isolate components below 2 kHz and reduce the sampling rate from 80 kHz to 4 kHz.The pass-band and stop-band transitions are designed to avoid amplitude distortion in the preserved band.
  • B. Sampling Rate Conversion: After conversion, the signal has a 250 µs sampling period and bandwidth [0, 2) kHz.
  • B. Sampling Rate Conversion: Overlapping 256-sample rectangular-window segments are independently transformed for time-localized spectral analysis.The subspace-based estimator is selected for its superior frequency resolution over classical methods.

E. Frequency-to-Speed Conversion

The method converts estimated harmonic frequency into rotational speed by tracking the 11th blade-passing-frequency harmonic in each short-time segment.

  • E. Frequency-to-Speed Conversion: The frequency axis is mapped to revolutions per second using the 11th blade-passing-frequency harmonic as the instantaneous speed feature.The harmonic frequency is estimated at each short-time segment before conversion.
  • E. Frequency-to-Speed Conversion: The multi-rate and filtering stages concentrate signal content in the relevant harmonic band, while high-resolution estimation distinguishes harmonics from noise in low-SNR measurements.

V. NUMERICAL RESULTS

Numerical simulations model dynamic induction-motor operation and its fan-acoustic harmonic structure under abrupt load-torque changes, with the 11th harmonic selected for speed estimation.

  • V. NUMERICAL RESULTS: The simulations use an 18.45 kVA, 400 V AC, 50 Hz, two-pole-pair squirrel-cage induction motor with total inertia J = 1.0 kg m2.The model includes electrical and mechanical dynamics for transient and steady-state behavior.
  • V. NUMERICAL RESULTS: The acoustic model targets the fan’s BPF harmonic spectrum rather than absolute sound-pressure levels or the turbulent flow field.Rotating-force and thickness-source representations are used for the kinematically determined BPF structure.
  • V. NUMERICAL RESULTS: Time-dependent step load torque changes alter slip and motor speed, producing corresponding changes in the simulated BPF time-frequency representation.
  • V. NUMERICAL RESULTS: Load increases shift BPF components downward and load decreases shift them upward; higher-order harmonics show greater sensitivity to speed variations.The 11th harmonic illustrates time-varying acoustic spectral changes caused by loading and rotational-speed changes.
  • V. NUMERICAL RESULTS: The 11th BPF harmonic balances detectable amplitude with speed sensitivity and lies within the effective response of the low-cost acoustic sensor.

VI. TEST BENCH

The laboratory test bench combines an induction motor, controllable braking, acoustic acquisition, filtering, and data recording for acoustic-based speed estimation.

  • Test bench: The bench uses a three-phase Siemens induction motor coupled to a controllable Lucas-Nülle magnetic brake.The brake provides manual or voltage-controlled torque settings, along with tachometer and torque sensing.
  • Acoustic acquisition: A low-cost unidirectional microphone captures the target motor’s sound while attenuating noise from surrounding machinery.The microphone is a Shenggu SG-108 model, and its directional characteristic emphasizes the acoustic signal of interest.
  • Signal acquisition: The acoustic signal is filtered and acquired through an LTC 1564 filter and an NI cDAQ-9174 chassis with an NI-9215 module.The setup is illustrated in Fig. 4.

VII. EXPERIMENTAL RESULTS

Experiments evaluate acoustic speed estimation across steady-state, load-step, non-constant-load, and oscillating-load conditions. The method tracks transient speed changes closely and achieves low error against tachometer reference measurements.

  • Signal processing: Processed acoustic signals constrain spectral content and improve robustness to environmental noise before speed-related component localization.Sample-rate conversion removes spectral density beyond 2 kHz, filtering removes [0, 1.7) kHz components, and subspace decomposition isolates dominant components.
  • Steady-state operation: 24.75 r.p.s. average speed was estimated under no-load operation, close to the 25 r.p.s. synchronous speed.The no-load experiment used a 5-second acoustic decomposition and revealed minor low-frequency fluctuations and slight speed ripples.
  • Load-step tests: 23.88 r.p.s. was reached after a positive load step, followed by convergence to 24.07 r.p.s.The estimated speed initially remained at 24.81 r.p.s.; the load torque was applied at 1.9 seconds and the minimum occurred at 2.09 seconds.
  • Load-step tests: 24.04 to 24.81 r.p.s. acceleration was tracked after abrupt load removal, with a fast response across both steady-state regimes.The load was removed at t = 2.1 s, and the estimate settled around the new steady-state value.
  • Non-stationary load tests: 24.25–24.6 r.p.s. variations were accurately captured under gradual and rapid non-constant-load changes.The experiment emulated realistic torque profiles containing both gradual and rapid variations.
  • Non-stationary load tests: 24.12–24.5 r.p.s. variations, including approximately 0.25 r.p.s. steps, were tracked during oscillating-load tests.The method captured sudden decreases and abrupt increases in response to ascending and descending torque steps.
  • Reference validation: RMSE was 0.030898 r.p.s., MAE was 0.018881 r.p.s., and MAPE was 0.0776% against tachometer measurements.Steady-state intervals, load transitions, and transient step events were evaluated after time alignment and resampling.

VIII. CONCLUSION

The study validates acoustic, subspace-based instantaneous speed estimation for a three-phase induction motor under steady and dynamically varying loads. It tracks transient speed changes and mechanical irregularities, while remaining promising for non-invasive condition monitoring, though startup and shutdown regimes require further study.

  • Experimental results validate reliable instantaneous-speed estimation under steady-state and dynamically varying load conditions.
  • The method tracks transient variations caused by load changes and inherent mechanical irregularities by isolating speed-dependent harmonics from noise.
  • A slight delay relative to direct sensor measurements does not significantly compromise feasibility for real-time monitoring on dedicated hardware.
  • Additional investigation is required for challenging regimes such as startup and shutdown transients.
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