Compressed sensing based on dictionary learning for reconstructing blade tip timing signals

Blade tip timing (BTT) is a promising technique for the blade vibration measurement. Since under-sampling is an inherent drawback of BTT measurement, compressed sensing theory which enables the recovery of sparse signals provides a novel method to the reconstruction of BTT signals. Considering the variability of the excitation method and the material of blades under actual working condition, the instantaneous displacement of each blade could not be merely modeled as multiple component sine waves. Therefore, proper dictionary is needed for the representation of sparse blade tip vibration signals. We proposed a method for reconstructing irregular blade tip deflection signals in this paper which consists of four key steps. First, based on the optical probe placements, measurement matrix for compressed sensing is determined. Secondly, a mathematical model of BTT signals is proposed based on sparse representation. Third, combining the K-SVD dictionary learning method, training dictionary is realized through experimental results of measured blade displacements under nonlinear case. Finally, blade tip-timing signals are recovered by Basis Pursuit Algorithm. Numerical simulation examples of strain gage signals from vibration experiments are performed to prove the validation of mentioned methods. The main advantage of this method is the well adapting to feature identification of blades vibrations in strong nonlinear case.