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arxiv: 2606.10437 · v1 · pith:WRDKJ3N2new · submitted 2026-06-09 · ⚛️ physics.app-ph · physics.data-an

Virtual-Array Operational Modal Analysis of Rolling Tires Using a Single Tire Cavity Accelerometer

Pradosh Pritam Dash , Ricardo Burdisso , Pablo A Tarazaga This is my paper

Pith reviewed 2026-06-27 11:08 UTC · model grok-4.3

classification ⚛️ physics.app-ph physics.data-an
keywords operational modal analysisrolling tiretire cavity accelerometervirtual arraycircumferential modesstochastic subspace identificationfrequency domain decomposition
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The pith

A single tire cavity accelerometer creates a virtual array to identify rolling tire vibration modes using the non-integer drum diameter ratio.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a method for operational modal analysis of rolling tires that relies on only one wireless accelerometer inside the tire cavity plus two optical sensors. Signals recorded over multiple revolutions are clustered by the sensor's exact circumferential position at each impact, using the mismatch between tire and drum diameters to produce dense non-repeating sampling. This clustering effectively builds a virtual circumferential array from a single physical sensor. Standard modal identification tools are then applied after order tracking removes periodic contact effects, and the covariance-based stochastic subspace method extracts eleven circumferential modes up to 240 Hz. The technique is positioned as simpler and cheaper than laser vibrometer setups and usable on treaded tires.

Core claim

Responses from a single tire cavity accelerometer can be clustered into a virtual circumferential array by leveraging the non-integer ratio of tire to drum diameters together with optical timing of impacts and sensor position; after conditioning by order tracking, frequency domain decomposition and covariance-based stochastic subspace identification are applied, with the latter successfully identifying eleven circumferential modes up to 240 Hz.

What carries the argument

The virtual sensor array synthesized by clustering single TCA responses according to circumferential position at each cleat impact, enabled by the non-integer tire-drum diameter ratio.

If this is right

  • Enables modal characterization of rolling tire dynamics under realistic operating conditions without multiple sensors.
  • Provides a lower-cost and simpler alternative to laser Doppler vibrometer methods that also works on treaded tires.
  • The covariance-based stochastic subspace identification approach yields more robust results than frequency domain decomposition for this data.
  • The method is adaptable to on-road testing of tires in actual vehicle operation.
  • Supports better understanding of low-frequency tire vibrations that contribute to structure-borne vehicle noise.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The virtual-array idea from diameter mismatch could be tested on other rotating components such as wheels or rotors where adding sensors is difficult.
  • If the sampling remains uniform at higher speeds, the frequency range might extend beyond 240 Hz without hardware changes.
  • An on-vehicle version could support continuous monitoring of tire structural health during normal driving.
  • Similar clustering from repeated passes might reduce sensor count in other vibration studies of cyclic systems.

Load-bearing premise

The non-integer ratio between tire and drum diameters produces sufficiently dense, uniform, and non-repeating circumferential sampling across revolutions so that clustered responses synthesize a true virtual array without spatial aliasing.

What would settle it

A side-by-side test in which mode frequencies or shapes extracted from the single-sensor virtual array diverge from those measured simultaneously with a physical array of multiple accelerometers mounted around the same rolling tire.

Figures

Figures reproduced from arXiv: 2606.10437 by Pablo A Tarazaga, Pradosh Pritam Dash, Ricardo Burdisso.

Figure 1
Figure 1. Figure 1: Geometry Visualization of Tire Size 195/65R15 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Rolling Resistance Rig at the Center for Tire Research (CenTiRe), Virginia Tech [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: (a) Axes Reference System for Cleat Test Setup, (b) SAE J670 Tire Axis System [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Design Schematic of Cleat Assembly 2.1.4 Tire Cavity Accelerometer (TCA) The TCA is a remote-controlled, radio-linked tread vibration measurement system. A schematic of the system is shown in [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematic of the TCA-based Tread Vibration Measurement System [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Tread Vibration Measuring System: (a) TCA modules on wheel, (b) TCA transmitter [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) Schematic of TCA mounting procedure, (b) TCA mounted on the actual tire [PITH_FULL_IMAGE:figures/full_fig_p006_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Illustration and (b) Working Principle of the Photoelectric Sensor (SM312LVMHS) [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Optical Sensors and Fixtures 2.1.6 Operating Conditions and Data Acquisition The results presented here focus on a drum speed of 30 km h−1 and a spindle load of 1334 N (300 lbf). The tire temperature was allowed to stabilize at 26 ◦C to 27 ◦C prior to each test iteration to ensure consistency in measurement. Data was acquired simultaneously across six channels at 4096 Hz for 300 s. 2.2 Synthesis of the Vir… view at source ↗
Figure 10
Figure 10. Figure 10: (a) Test-Setup (b)OPR signals for the drum and the tire, (c) Estimated frequency of [PITH_FULL_IMAGE:figures/full_fig_p009_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Schematic of Cleat Test Setup illustrating the diameter ratio (spindle load [PITH_FULL_IMAGE:figures/full_fig_p010_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a) Convention used for estimating TCA position during cleat impact, (b) Estimated [PITH_FULL_IMAGE:figures/full_fig_p010_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Distribution of TCA Positions During Cleat Impacts (30 kph / 1334 N) [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Flowchart for TCA Signal Conditioning 2.3.1 Step 1: Order Tracking (OT) Analysis The vibration due to running deflection is periodic with the tire revolution. An OT analysis, synchronized with the Tire OPR signal, was performed to estimate and subtract this periodic com￾ponent ( [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Demonstration of Order Tracking Analysis to separate the periodic tread vibration [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: (a) TCA signals in cluster No. 19, (b) Roller schematic showing the TCA positions [PITH_FULL_IMAGE:figures/full_fig_p013_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: TCA Signal after Resampling/Averaging and Exponential Weighting [PITH_FULL_IMAGE:figures/full_fig_p013_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Power Spectrum of TCA Vibration showing the three characteristic frequency regions [PITH_FULL_IMAGE:figures/full_fig_p015_18.png] view at source ↗
Figure 19
Figure 19. Figure 19: Complex Mode Indicator Function (CMIF) comprising the first five singular values [PITH_FULL_IMAGE:figures/full_fig_p016_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Mode Shapes Corresponding to the Identified Circumferential Modes from FDD [PITH_FULL_IMAGE:figures/full_fig_p017_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Stabilization Diagram using SSI-Cov The mode shapes exhibit the expected increase in nodal lines with frequency. The presence of multiple modes around the first circumferential resonance (R1) suggests mode splitting due to the loading condition and rotational effects, consistent with the observations of Kindt et al. [10] for stationary loaded tires. 3.3 Discussion Comparison of OMA Methods: A direct compa… view at source ↗
Figure 22
Figure 22. Figure 22: Mode Shapes of Circumferential Rolling Modes [PITH_FULL_IMAGE:figures/full_fig_p019_22.png] view at source ↗
Figure 23
Figure 23. Figure 23: Cross-MAC between Mode Shapes from FDD and SSI-Cov [PITH_FULL_IMAGE:figures/full_fig_p020_23.png] view at source ↗
Figure 24
Figure 24. Figure 24: (a) Mode shape animation and (b) Complexity (Nyquist) plot of the mode at 215.72 Hz [PITH_FULL_IMAGE:figures/full_fig_p021_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Mode Shape at 215.72 Hz showing displacement at the Contact Patch [PITH_FULL_IMAGE:figures/full_fig_p022_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Cleat Test Schematic showing motion of the TCA during measurement [PITH_FULL_IMAGE:figures/full_fig_p022_26.png] view at source ↗
read the original abstract

The dynamics of rolling tires significantly influence the low-frequency (0-500 Hz) structure-borne noise within vehicles. Accurately characterizing these dynamics under realistic operating conditions remains challenging. Current state-of-the-art methods, primarily relying on Laser Doppler Vibrometers (LDV), are complex to implement, time-intensive, and generally limited to smooth tires in laboratory environments due to issues with speckle formation on treaded surfaces. This study introduces an innovative strategy for Operational Modal Analysis (OMA) of a rolling tire using a single wireless Tire Cavity Accelerometer (TCA) together with two optical sensors. The methodology leverages the non-integer ratio between the tire and drum diameters in a test rig to create a virtual sensor array. By utilizing optical sensors to time-stamp the cleat impact (on the drum) precisely and the TCA position (on the tire), the vibration responses from multiple revolutions are clustered according to the TCA's circumferential position at the moment of impact. This effectively synthesizes responses from an array of virtual sensors distributed around the tire circumference using data from a single test run. The clustered signals are conditioned using order tracking to remove periodic components arising from contact patch deformation. Both Frequency Domain Decomposition (FDD) and Covariance-based Stochastic Subspace Identification (SSI-Cov) were employed for modal identification. The SSI-Cov method proved more robust, successfully identifying 11 circumferential modes up to 240 Hz. The proposed approach offers a significantly more efficient, cost-effective method for characterizing rolling tire dynamics, which is readily applicable to treaded tires and adaptable for on-road testing.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces an experimental method for operational modal analysis (OMA) of rolling tires that uses a single wireless tire cavity accelerometer (TCA) together with two optical sensors. By exploiting the non-integer ratio between tire and drum diameters in a test rig, vibration responses from multiple revolutions are clustered by TCA circumferential position at cleat-impact instants to synthesize a virtual sensor array; order tracking removes periodic contact-patch effects, after which both frequency-domain decomposition (FDD) and covariance-driven stochastic subspace identification (SSI-Cov) are applied. The authors report that SSI-Cov robustly identifies 11 circumferential modes up to 240 Hz and claim the approach is more efficient and applicable to treaded tires than laser-Doppler-vibrometer methods.

Significance. If the virtual-array construction is shown to be free of spatial aliasing and the modal identifications are corroborated by spectra, mode shapes, and reference comparisons, the work would supply a low-cost, laboratory-to-road extensible technique for characterizing rolling-tire dynamics in the 0–500 Hz band that is directly relevant to structure-borne noise prediction.

major comments (2)
  1. [Abstract and §3] Abstract and §3 (virtual-array synthesis): the central claim that the non-integer tire–drum diameter ratio produces a sufficiently dense, uniform, and non-repeating circumferential sampling (spacing ≪ half-wavelength at 240 Hz) without spatial aliasing is asserted but unsupported by any reported diameter ratio, computed position sequence, or explicit aliasing check; this assumption is load-bearing for the validity of all subsequent modal results.
  2. [Abstract and results section] Abstract and results section: the headline result of 11 identified circumferential modes is stated without accompanying spectra, mode-shape plots, coherence values, stabilization diagrams, or quantitative comparison to any LDV reference data or error metrics, preventing independent assessment of identification quality.
minor comments (1)
  1. [Abstract] The abstract would benefit from a brief parenthetical mention of the measured diameter ratio or the number of virtual sensors synthesized.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and agree that additional details and visualizations are needed to strengthen the presentation of the virtual-array method and modal results.

read point-by-point responses

  1. Referee: [Abstract and §3] Abstract and §3 (virtual-array synthesis): the central claim that the non-integer tire–drum diameter ratio produces a sufficiently dense, uniform, and non-repeating circumferential sampling (spacing ≪ half-wavelength at 240 Hz) without spatial aliasing is asserted but unsupported by any reported diameter ratio, computed position sequence, or explicit aliasing check; this assumption is load-bearing for the validity of all subsequent modal results.

    Authors: We agree that the specific diameter ratio, position sequence, and aliasing verification are essential and were not sufficiently detailed. In the revised manuscript we will report the exact tire and drum diameters, tabulate or plot the computed circumferential positions at successive cleat impacts, and add an explicit spatial-sampling analysis confirming that the effective spacing remains well below the half-wavelength at 240 Hz, thereby satisfying the Nyquist criterion for the identified modes. revision: yes

  2. Referee: [Abstract and results section] Abstract and results section: the headline result of 11 identified circumferential modes is stated without accompanying spectra, mode-shape plots, coherence values, stabilization diagrams, or quantitative comparison to any LDV reference data or error metrics, preventing independent assessment of identification quality.

    Authors: We acknowledge that the results section requires supporting visualizations. The revision will add representative auto-spectra from the virtual array, the identified circumferential mode shapes, SSI-Cov stabilization diagrams, and coherence or singular-value plots. Direct quantitative LDV comparisons are outside the scope of the present treaded-tire experiments, but we will include a qualitative discussion of consistency with prior LDV literature on smooth tires and any available error metrics from the OMA procedures. revision: yes

Circularity Check

0 steps flagged

No circularity: purely experimental data collection and standard modal identification

full rationale

The paper presents an experimental technique that clusters single-sensor responses into a virtual array using the physical non-integer tire-drum diameter ratio, then applies off-the-shelf FDD and SSI-Cov algorithms. No equations, fitted parameters, or predictions are defined in terms of the target modal results. The sampling-density assumption is an unverified physical premise rather than a self-referential derivation. No self-citations are load-bearing for the central claim, and the work contains no mathematical reduction of outputs to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The method rests on the domain assumption of non-integer diameter ratio enabling virtual sampling and on standard OMA assumptions of linearity and stationarity within each clustered bin; no free parameters or invented entities are introduced.

axioms (1)
  • domain assumption Non-integer tire-to-drum diameter ratio produces dense, uniform circumferential sampling across revolutions
    Stated in the methodology paragraph describing virtual array creation.

pith-pipeline@v0.9.1-grok · 5828 in / 1057 out tokens · 25473 ms · 2026-06-27T11:08:00.727577+00:00 · methodology

discussion (0)

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Reference graph

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