Spectrum forming and its high-performance implementations for the blade tip timing signal processing

Blade Tip Timing (BTT) is a critical non-contact technique for monitoring rotating blade vibrations, yet its effectiveness is hindered by under-sampled signals that violate the Nyquist criterion. Traditional methods for BTT signal processing often rely on prior information or specific operational conditions, limiting their applicability. This paper introduces Spectrum Forming (SF), a novel framework tailored for BTT signal analysis, to address spectral aliasing and enhance vibration feature extraction. SF redefines “beamforming” concepts in BTT contexts, interpreting “beam” as vibrational energy at specific frequencies and “forming” as phase synchronization across probes. Building on SF, advanced methods—including non-negative least squares (De-NNLS), non-convex optimization with generalized mini–max concave penalty (De-GMCP), CLEAN based on frequency coherence (CLEAN-FC), and functional spectrum forming (FSF)—are developed to suppress aliasing and improve resolution. Numerical simulations and experimental studies on rotating blade disks and compressor rotors validate the efficacy of these methods. Results demonstrate that CLEAN-FC achieves superior aliasing suppression and target frequency detection at low signal-to-noise ratios (SNRs), while De-GMCP excels in amplitude accuracy. The proposed SF framework and its extensions offer robust, high-performance solutions for under-sampled BTT signal processing. The Python code to implement part of the numerical simulation can be downloaded from https://github.com/zhang19980521/sf_mssp.git.