An Improved Hilbert Transform for Nonlinear Vibration Signal Analysis

Abstract

The Hilbert transform (HT), as a powerful signal processing method, has been widely applied in analyzing nonlinear and nonstationary signals. Currently, the implementation of HT is realized by the discrete Fourier transform (FT), which, however, is based on the assumption that the signal to be analyzed is periodic in nature and of infinite length. Therefore, the conventional HT of nonlinear signals inherits the leakage and distortion problems introduced by the discrete FT. Although the local maxima interpolation (LMI) based approach demonstrated a significant improvement to the conventional FT based approach, it still underestimates the Hilbert amplitude. In this paper, we propose an improved LMI approach to address the underestimation issue. The HT obtained by the improved approach is proven to be a very close approximation to the analytic HT. Benchmark simulations as well as practical example will show that the new approach can further improve the HT accuracy and consequently identify the dynamic characteristics of a baseline blade successfully.