Non-convex sparse regularization via convex optimization for blade tip timing

Blade Tip Timing (BTT), an emerging technology poised to replace strain gauges, enables contactless measurement of rotor blade vibration. However, the blade vibration signals measured by BTT systems often suffer from significant undersampling. Sparse reconstruction methods are instrumental in addressing the challenge of undersampled signal reconstruction. However, traditional approaches grounded in ℓ₁ regularization tend to underestimate the amplitude of the true solution. This underestimation is particularly pronounced in the resonance state of the rotor blade, hindering effective prediction of the blade's operational state. To overcome this limitation, this paper introduces a novel non-convex regularized BTT model, employing a non-convex penalty term with convex-preserving properties to achieve nearly unbiased reconstruction accuracy. Additionally, we propose a new threshold iteration algorithm designed for the swift solution of this model. The accuracy and robustness of the proposed method in identifying the multimodal vibration parameters of rotor blades are validated through simulations and experiments. Comparatively, the proposed method closely aligns with the Orthogonal Matching Pursuit (OMP) method in recognizing blade multimodal vibration amplitude, showcasing significant improvement over the ℓ₁ regularization method. Furthermore, it demonstrates lower sensitivity to changes in BTT probe layout when compared to the OMP and ℓ₁ regularization methods.