A two-stage off-grid estimation for BTT data

Blade Tip Timing (BTT) enables non-contact measurements of rotating blades by placing probes strategically. Due to the uneven probe layout, BTT signals exhibit periodic irregularities. While recovering parameters like frequency from such signals is possible, achieving high-precision vibration parameters remains challenging. This paper proposed a novel two-stage off-grid estimation method. It leverages a unique array layout (coprime array) to obtain a regular augmented covariance matrix. Subsequently, parameters in the matrix are recovered using the sparse iterative covariance-based estimation method based on covariance fitting criteria. Finally, high-precision estimates of imprecise parameters are obtained using unconditional maximum likelihood estimation, effectively eliminating the effects of basis mismatch. Through substantial numerical and experimental validation, the proposed method demonstrates significantly higher accuracy compared to classical BTT parameter estimation methods, approaching the lower bound of unbiased estimation variance. Furthermore, due to its immunity to frequency gridding, it can track minor frequency deviations, making it more suitable for indicating blade condition.