Optimization of Nonuniform Sensor Placement for Blade Tip Timing Based on Equiangular Tight Frame Theory

Abstract

Blade tip timing (BTT) data are usually an under-sampled signal and are vulnerable to noise and sensor failures. In this paper, based on an arbitrary-angle compressed-sensing method and equiangular tight frame theory, combined with a niching microgenetic algorithm, a method for placing BTT sensors is proposed to ensure higher reconstruction accuracy and reliability. If the dimensions of the sensing matrix are moderate, the index range of arrangements with excellent performance in multifrequency 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. Thus, to achieve a larger frequency multiplication recognition range and probe-installation flexibility, a method for optimizing the BTT sensor placement is proposed. Finally, a finite-element simulation of the signal from an aero-engine 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 has a high reconstruction success rate and the BTT system is robust. This approach has significant value for engineering applications.