Boundary Extension Technique for HHT Based on Response Surface Method

HHT is widely used to analyze nonlinear and non-stationary signals. But how to extend boundaries of signals in decomposition processes is a key problem of HHT. A new technique based on response surface method (RSM), which establishes the recursive relations between sample points of signals, is presented to deal with this difficult problem. Besides, the boundary extension problem arising from HHT can be described by mathematical least squares problem but traditional gradient algorithms may diverge when the Hessian matrix of the object function of the least squares problem is non-positive. It has been proved that the generalized inverse of the linear equations (derived from the linear least squares problem) by singular value decomposition is the solution of original linear least squares problems. Thereby the divergence problem is also solved. Analysis results with respect to simulation signals and measured signals show that the method with new boundary extension technique performs successfully for HHT.