A novel sparse reconstruction method for under-sampled blade tip timing signals: Integrating vibration displacement and velocity

In modern aviation engines and turbomachinery, the vibration characteristics of blades are crucial for the safety and performance of machines. Blade tip timing (BTT) technology serves as a key method for monitoring and analyzing blade vibrations, enabling engineers to promptly identify potential faults and anomalies. However, traditional BTT methods often face challenges such as under-sampled data acquisition and improper sensor layout, which compromise the precision and robustness of frequency identification. To address these limitations, a novel displacement and velocity-based blade tip timing (D-V-BTT) method is proposed. Initially, a full pulse waveform-based method is applied to capture the vibration displacement and velocity of the blade as it passes each sensor. Subsequently, a new under-sampled sparse reconstruction method integrating displacement and velocity information is established. A non-convex regularization algorithm is used for reconstructing under-sampled vibration signals at a constant speed, enabling accurate frequency identification of blade tip vibration without prior conditions. Numerical simulations and experimental validations demonstrate the accuracy and validity of the proposed D-V-BTT method. It is demonstrated that the quantity of sensors can be reduced by the D-V-BTT method without decreasing the frequency discrimination accuracy after integrating the displacement and velocity information. Additionally, the D-V-BTT method can reduce the sensitivity to sensor layout.