Sparse reconstruction of blade tip-timing signals for multi-mode blade vibration monitoring

Severe blade vibrations may reduce the useful life of the high-speed blade. Nowadays, non-contact measurement using blade tip-timing (BTT) technology is becoming promising in blade vibration monitoring. However, blade tip-timing signals are typically under-sampled. How to extract characteristic features of unknown multi-mode blade vibrations by analyzing these under-sampled signals becomes a big challenge. In this paper, a novel BTT analysis method for reconstructing unknown multi-mode blade vibration signals is proposed. The method consists of two key steps. First, a sparse representation (SR) mathematical model for sparse blade tip-timing signals is built. Second, a multi-mode blade vibration reconstruction algorithm is proposed to solve this SR problem. Experiments are carried out to validate the feasibility of the proposed method. The main advantage of this method is its ability to reconstruct unknown multi-mode blade vibration signals with high accuracy. The minimal requirements of probe number are also presented to provide guidelines for BTT system design.