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Uncertainty-aware order tracking using interval-valued spectral estimators
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DOI：10.59400/sv4071.png)
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Abstract
En 中文
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 omega(t) E [omega-(t),omega+(t)], which induces bounds on angular position 0(t) E [0-(t), 0+(t)]. These bounds are propagated through angle-domain resampling and a Welch-type spectral estimator to obtain order-wise PSD bounds S(m) E [S-(m), S+(m)], 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.
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
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1
Papers:
21
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