“…It is difficult to find a rigorous definition of the adaptive decomposition algorithm; however, we think that such a type of method can form a series of sparse representations in the decomposition process, which is different with “rigid” methods, such as the Fourier or wavelets transforms, corresponding to the use of some basis (or frame) designed independently of the processed signal [ 1 , 2 ]. As many kinds of signals in engineering problems are non-linear and non-stationary, such as fault signals of mechanical equipment [ 3 , 4 , 5 , 6 , 7 , 8 ], some modal test signals [ 9 ], acoustic signals of non-destructive testing [ 10 , 11 ] and condition monitoring signals for rail track [ 12 , 13 , 14 ], the adaptive decomposition algorithm has superiority for analyzing these signals, because of decomposition flexibility.…”