CS-Based sensor placement optimization for blade tip timing using estimation-variance lower-bound and mutual-coherence criterion

Blade tip timing (BTT) is widely used for non-contact blade vibration monitoring, but the limited number of casing-mounted sensors leads to strongly non-uniform undersampling, which may reduce identification accuracy. To improve the reconstruction performance of undersampled BTT signals, this paper proposes a compressed-sensing-oriented sensor placement optimization method based on the estimation-variance mutual-coherence (EVMC) criterion. The proposed criterion is constructed from two complementary degradation mechanisms in compressed-sensing-based BTT reconstruction: frequency-support ambiguity during sparse atom selection and coefficient-estimation uncertainty after support determination. The proposed method relates sensor installation angles to BTT sampling instants and the sensing matrix, thereby formulating sensor placement optimization as a sensing-matrix design problem for sparse frequency recovery. Specifically, the target-oriented mutual-coherence (MC) term is used to reduce the correlation among target-related dictionary atoms, thus improving support recovery and suppressing spurious components. Meanwhile, the estimation-variance lower-bound (EVLB) term evaluates the estimation stability of sparse frequency coefficients after the active support is determined. Numerical simulations demonstrate that the EVMC layout achieves better frequency tracking, suppression of rotation-frequency-spaced sideband components, and amplitude estimation than the compared layouts, with the lowest amplitude relative errors in both single-mode and multi-mode cases. Experimental validation further shows good agreement with strain-gauge measurements, yielding average and maximum relative frequency errors of 0.12% and 0.54%, respectively. These results confirm that the proposed method improves the reliability of compressed-sensing-based BTT reconstruction without increasing the number of sensors.