A GMC-Based Accelerated Algorithm for Identifying the Frequency and Amplitude of Multimode BTT Signals

The precise identification of vibration parameters from undersampled blade tip timing (BTT) signals is essential for the effective monitoring of rotating blade vibrations. However, the traditional BTT parameter identification method heavily depends on the prior information. Furthermore, in the existing sparse regularization methods, the amplitude of the reconstructed signal is underestimated and the computational efficiency is low, which poses significant challenges to the identification of parameters in practice, especially under multimode vibration. In this study, an accelerated algorithm based on generalized minimax-concave (GMC) sparse regularization is proposed for the accurate and efficient identification of amplitude and frequency parameters from undersampled BTT signals. To overcome the issue of amplitude underestimation, a non-convex GMC penalty is introduced, which improves the sparsity of the estimation and preserves the convexity of the cost function. Moreover, Nesterov's accelerated iterative computation strategy is adopted to rapidly improve the convergence performance obtaining the global optimum. Both simulation and experiment results demonstrate that the proposed algorithm, named accelerated algorithm for GMC (AGMC), significantly improves the computational rate with the inherited merits of accuracy by reconstructing the BTT signal.