Uncertainty-aware order tracking using interval-valued spectral estimators

Sulieman Ibrahim Mohammad; Yogeesh N.; Mustafa  Abdullah; Rosemary  Varghese; Asokan  Vasudevan; Ashalatha  K.S.

doi:10.59400/sv4071

Uncertainty-aware order tracking using interval-valued spectral estimators

Sulieman Ibrahim Mohammad
Research Fellow, INTI International University, Nilai 71800, Malaysia
Yogeesh N.
Research Fellow, INTI International University, Nilai 71800, Malaysia; Department of Mathematics, Government First Grade College, Tumkur 572101, India
Mustafa Abdullah
Electric Vehicles Engineering Department, Faculty of Engineering, Hourani Center for Applied Scientific Research, Al-Ahliyya Amman University, Amman 19328, Jordan
Rosemary Varghese
Department of Mathematics, Presidency University, Bengaluru 560064, India
Asokan Vasudevan
Faculty of Business and Communications, INTI International University, Nilai 71800, Malaysia
Ashalatha K.S.
Department of Mathematics, Vedavathi Government First Grade College, Hiriyur 577598, India

Article ID: 4071

Keywords: bounded uncertainty, interval analysis, interval-valued spectral estimation, tacholess speed estimation, set-membership uncertainty propagation, angle-domain resampling, order power spectral density (PSD), Welch estimator

Abstract

Order tracking is central to diagnosing rotating machinery under variable speed; however, both tachometer-based and tacholess pipelines typically return point estimates of the order spectrum and therefore under-represent uncertainty due to speed estimation error, phase integration drift, resampling jitter, and finite-record spectral variance. This study develops an uncertainty-aware order tracking framework in which the diagnostic output is an interval-valued order power spectral density (PSD) envelope. The angular speed is modeled as an unknown-but-bounded process , which induces bounds on angular position . These bounds are propagated through angle-domain resampling and a Welch-type spectral estimator to obtain order-wise PSD bounds , together with interval band metrics formed by order-band integration and log-level reporting. A numerical run-up case study with physically plausible harmonic content and broadband noise shows that low-order components can remain stable in peak location, whereas higher orders exhibit measurable peak-shift intervals consistent with phase-warp amplification under bounded mapping uncertainty. The results also quantify a practical coverage-width trade-off: fast endpoint envelopes can lose inclusion under larger uncertainty, indicating when multi-map sampling or tighter set membership bounding should be applied. Overall, the proposed interval-valued spectral estimators enable decision-relevant reporting of uncertainty for order-based health indicators and reduce the risk of overconfident fault declarations in variable-speed condition monitoring.

Published

2026-04-17

How to Cite

Ibrahim Mohammad, S., Yogeesh N., Abdullah, M., Varghese, R., Vasudevan, A., & K.S., A. (2026). Uncertainty-aware order tracking using interval-valued spectral estimators. Sound & Vibration, 60(2). https://doi.org/10.59400/sv4071

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Vol. 60 No. 2 (2026): in progress

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This work is licensed under a Creative Commons Attribution 4.0 International License.

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Uncertainty-aware order tracking using interval-valued spectral estimators

Abstract

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