Sparse reconstruction for blade tip timing signal using generalized minimax-concave penalty

Abstract

Rotor blade health monitoring based on the non-contact blade tip timing (BTT) technique has already been proved to be an alternative method to the classical contact strain measurement method. However, the signal sampled by the BTT system is usually undersampled due to the limited BTT sensors. Sparse regularization in the framework of ℓ1-norm has been introduced to identify the blade vibration parameter from the undersampled BTT data. However, the standard sparse regularization based onℓ1-norm penalty generally generates an underestimated solution. Compared with ℓ1-norm penalty, generalized minimax-concave (GMC) penalty as a non-convex penalty has the promising property of amplitude improvement. In this paper, a non-convex optimization model based on GMC penalty is developed for reconstructing the undersampled BTT signal to obtain the accurate blade-tip displacement and blade natural frequency. The optimization model based on GMC penalty is presented to find the global optimal solution for the sparse representation of the BTT signal even if GMC penalty turns out to be a non-convex regularizer. Additionally, the strategy of regularization parameter selection is provided through the blade tip timing simulator. The relationship between the noise level and the regularization parameter is established to provide the strategy of regularization parameter selection in experiment. Finally, the blade spin testing is carried out for measuring the blade vibration by BTT and strain gauge systems. Amplitudes and frequencies of reconstructed BTT signals are compared with the measurements of the strain gauge, which are transferred from the strain at the blade root to the displacement at the blade tip by using the conversion coefficient obtained from the finite element model. Both simulation and experiment demonstrate that compared with the ℓ1-norm penalty, GMC penalty can reconstruct the blade-tip displacement and blade natural frequency with high accuracy.