<p>&nbsp; &nbsp; &nbsp; Blade tip timing (BTT) data is usually an under-sampled signal and is vulnerable to noise and sensor failures. In this paper, based on an arbitrary-angle compressed sensing algorithm and equiangular tight-frame theory, combined with a niching micro-genetic algorithm, a BTT sensor-placement determination method is proposed to ensure higher reconstruction accuracy and reliability. When the dimensions of the sensing matrix are moderate, the index range of arrangements with excellent performance in multi-frequency signal reconstruction is determined by enumerating all the uniform-distribution extraction placements. A two-parameter search method is then proposed. Reconstruction of a mixed signal is carried out to verify the asynchronous signal-reconstruction performance. On this basis, considering the purposes of a larger frequency- <i>multiplication recognition range and probe-installation flexibility, a method for optimizing BTT sensor placement is proposed. Finally, a finite-element simulation of the signal from an aeroengine fan blade is used to verify the reconstruction ability of the proposed method. The results show that the placement determined by the optimization algorithm can achieve similar or even better performance than the optimal placement under uniform-distribution extraction. The proposed sensor-placement optimization method ensures a higher reconstruction success rate and greater robustness of the BTT system, which has significant engineering application value.</i></p>

Optimization of Non-Uniform Sensor Placement for Blade Tip Timing Based on Equiangular Tight Frame Theory

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2021/volume/84898

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