The accurate monitoring of blade vibration under operating conditions is essential in turbo-machinery testing. Blade tip timing (BTT) is a promising non-contact technique for the measurement of blade vibrations. However, the BTT sampling data are inherently under-sampled and contaminated with several measurement uncertainties. How to recover frequency spectra of blade vibrations though processing these under-sampled biased signals is a bottleneck problem. A novel method of BTT signal processing for alleviating measurement uncertainties in recovery of multi-mode blade vibration frequency spectrum is proposed in this paper. The method can be divided into four phases. First, a single measurement vector model is built by exploiting that the blade vibration signals are sparse in frequency spectra. Secondly, the uniqueness of the nonnegative sparse solution is studied to achieve the vibration frequency spectrum. Thirdly, typical sources of BTT measurement uncertainties are quantitatively analyzed. Finally, an improved vibration frequency spectra recovery method is proposed to get a guaranteed level of sparse solution when measurement results are biased. Simulations and experiments are performed to prove the feasibility of the proposed method. The most outstanding advantage is that this method can prevent the recovered multi-mode vibration spectra from being affected by BTT measurement uncertainties without increasing the probe number.
Keywords: blade tip timing; measurement uncertainty; multi-mode vibration; sparse representation; vibration frequency spectrum recovery.