Physical constraints fused equiangular tight frame method for Blade Tip Timing sensor arrangement

Blade Tip Timing (BTT) method is increasingly implemented for rotating blade health monitoring for its non-contact property. However, the BTT data is usually highly undersampled as only a few sensors could be installed on the case. Due to the limited number of sensors installed, the arrangement can have a significant impact on BTT data quality. Different from the exhaustive method used in previous researches, in this paper, a mathematical model guided by optimizing objective is proposed for sensor configuration. Considering the dimensional characteristics of the sampling matrix, this paper no longer uses a single matrix coherence value as the optimization target, but adopts the Equiangular tight frame matrix as the goal of the whole sampling matrix. Moreover, this paper first considers the physical constraints of the actual installation and modal prior on the sensor arrangement. The physical constraints fused equiangular tight frame method is then solved by an alternating minimization approach. In addition, considering the disadvantages of the previous vibration parameter identification algorithms in terms of amplitude recovery and noise filtering, an iterative reweighted L1-norm based parameter identification method is applied to obtain the vibration parameters from the highly undersampled BTT data with better amplitude reconstruction accuracy. Both the simulation and experiment results are given to verify the effectiveness of the developed methods.