Boundary extension for Hilbert–Huang transform inspired by gray prediction model

One of the open problems to which Hilbert–Huang transform (HHT) inevitably confront is end effect, a plague from which many data analysis methods have been suffering from the beginning. Aiming at mitigating end effects of HHT, a boundary extension method is introduced, which is based on the well-known gray prediction model termed as GM(1,1). Using the idea of cubic spline, the calculation of derivative to accumulated generating operation (AGO) series in GM(1,1) model is developed. We further make full use of residual series produced in the GM(1,1) model to achieve better prediction precision. According to numerical experiments on synthetic and real world signals, as well as comparisons of the proposed method with other six generally acknowledged methods, including the original HHT, multiple residual error gray model (MREM), “window frame”, mirror extending (ME), autoregressive (AR) model, and artificial neural network (ANN) based HHT, it is demonstrated that our method significantly reduces end effects and improves decomposition and transformation results of HHT.

► The idea of cubic spline ameliorates the calculation of derivative to AGO.
► Residual series modifies prediction precision of the GM(1,1) model.
► GM-HHT provides comparable results with other widely accepted methods.
► GM-HHT is a feasible choice for analyzing synthetic and real world signals.