Robust layout optimization for blade tip timing measurement

Rotating blades are fundamental but fragile components in turbomachinery, and damage to rotating blades severely endanger the operational safety. Thus, it is vital to monitor the blade condition. Blade tip timing (BTT) is a potential vibration measurement technique for blade condition monitoring owing to its noncontact property and long service life. However, due to the limited number of probes allowed to be installed, BTT data is severely undersampled and the amount of information it carries is closely related to the layout. Consequently, layout optimization is drawing considerable attention in the field of BTT. Layout optimization is drawing considerable attention in the field of BTT. In this paper, we propose an efficient layout optimization strategy based on compressed sensing (CS), which originates from two key findings: 1) we find the relationship between the minimal circumferential angle (MCA) in layout and failure risk in CS model. Based on this finding, we derive the recommended MCA to avoid model errors in sparse representation and unacceptable computational complexity in layout optimization. 2) We find the equivalence of the complete and minimal sensing matrices in coherence-based layout optimization. This finding prompts us to replace the complete sensing matrix with the minimal one to simplify calculations. Finally, both numerical simulations and BTT experiments validate the effectiveness of the proposed layout optimization strategy.