T ( n H 4 id a in c m S A w m p ( tr d d f c F The slow-flow (NSI). To show numerical post Hilbert spectral 40], nonlinear dentifying the and nonstationa ntrinsic mode characteristic ti multi-scale dec Some recent EM As a result of E where ( ) ( ) k mc t 1 2 measured time physically mea (and physically ransform (WT dominant harm dynamics in the for each subsy component at F Fig. 2 Reconst model (4) pro w this we firs -processing tec l analysis was dynamics [41characteristic ary processes. e functions (IM ime scale, wh composition of MD developme EMD analysis, is the m-th N. By this c series; howev aningful with t y meaningful) ) spectra of the monics of the w e time series. O stem, namely 2 ) for the LO ig. 1 Response truction of the ovides an imp st review the chnique for an introduced in -44] and dama time scales in In particular, MFs); these a ose linear sup f a measured t ents can be fou we write the a ( ) 1 ( ) ( ) k kx t c t dominant IM onstruction pro ver, due to th the rest being ) IMFs can be e original time wavelet spectra. On the right of (1) 1 ( ) c t (LF LO O, and two dom es of NES (left e LO and NES ortant theoreti basic element nalyzing nonsta Huang et al. [ age detection [ measured time EMD yields a are oscillatory erposition reco time series in t und in referenc d hoc numeric ( ) ( ) k mc t MF of the resp ocess the super he ad hoc natu of spurious na e identified b series: the ins . This process f Fig. 2 we rec O component a minant IMFs c t) and LO dur S displacemen ical foundation ts of empirica ationary and no [27,35-37], num [45,46] have a e series, is ada a complete and y modes emb onstructs the m terms of embe es [37,47-50]. al decompositi ( ) ( ), k Nc t k ponse ( ) kx t , rposition of th ure of the sifti ature. As discu y comparing tantaneous freq also identifies construct the re at 1 - it turns (2) 1 ( ) c t (LF NE ring (right) 1:3 nts: CX-A (left n for performin al mode decom onlinear time merous applica appeared. This aptive, highly e d nearly (but no edded in the measured time edded oscillato ion of the dyna 1, , k n associated wi e N leading IM ting algorithm ussed in previo their instantan quencies of the s the dominant esponses of sys s out that this ES component) 3 TRC t) and EMD (r ng nonlinear s mposition (EM series. Since E ations to system s decompositio efficient, and s ot completely) time series, e series. In oth ory modes at d amics of the ge ith the fast f MFs reconstru only a subset ous work [41,4 neous frequen e dominant IM time scales (o stem (5) using is negligible) and (2) 2 ( ) c t (H right) system identifi MD), conceived EMD combine m identificatio on method, bas suitable for non ) orthogonal ba each with its her words EMD different time s eneral system ( frequency m uct approximate t of these IMF 42,44], the dom ncies to the w MFs coincide w or frequencies) two dominant and (1) 2 ( ) c t (H HF NES comp ication d as a d with on [38sed on nlinear asis of s own D is a scales. (1) as (8) , with ely the Fs are minant wavelet with the of the t IMFs HF LO onent) 516
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