The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis
Citations
188 citations
188 citations
188 citations
Cites methods from "The empirical mode decomposition an..."
...The multifrequency content of the transient response is evident and is quantified in Figure 17(b), where the instantaneous frequency of the time series is computed by applying the numerical Hilbert transform (Huang et al. (1998))....
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...The multifrequency content of the transient response is evident and is quantified in Figure 17(b), where the instantaneous frequency of the time series is computed by applying the numerical Hilbert transform (Huang et al. (1998)). As energy decreases due to damping dissipation, a series of eight resonance capture cascades is observed, i.e., of transient resonances of the NES with a number of nonlinear modes of the system. The complexity of the nonlinear dynamics of the system is evidenced by the fact that of these eight captures only two (labeled IV and VII in Figure 17(b)) involve the linearized in-phase and out-of-phase modes of the linear oscillator, with the remaining involving essentially nonlinear interactions of the NES with different low- and high-frequency nonlinear modes of the system. During each resonance capture the NES passively absorbs energy from the nonlinear mode involved, before escape from resonance capture occurs and the NES transiently resonates with the next mode in the series. In essence, the NES acts as a passive, broadband boundary controller, absorbing, confining, and eliminating vibration energy from the linear oscillator. Similar types of resonance capture cascades were reported in previous works where grounded NESs, weakly coupled to the linear structure, were examined (Vakakis et al. (2003))....
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188 citations
Cites background or methods from "The empirical mode decomposition an..."
...Using an iterative method known as sifting method, IMFs are obtained for a signal (Huang et al., 1998; Pachori et al., 2015; Martis et al., 2012)....
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...The basis of EMD is to decompose a signal x (t) into sets of frequency and amplitude modulated signal components, Intrinsic Mode Functions (IMFs) that has its own characteristic oscillations (Huang et al., 1998)....
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...AC CE PT ED M AN US CR IP T EMD is signal dependent and adaptive approach, which is highly efficient (Huang et al., 1998)....
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...The EMD methodology is described in (Huang et al., 1998)....
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...Finally extract the IMF from a signal by subtracting the average of envelopes (maxima and minima) (Huang et al., 1998)....
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188 citations
References
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...(ii) Lorenz equation The famous Lorenz equation (Lorenz 1963) was proposed initially to study deterministic non-periodic flow....
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...A brief tutorial on the Hilbert transform with the emphasis on its physical interpretation can be found in Bendat & Piersol (1986)....
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"The empirical mode decomposition an..." refers methods in this paper
...In order to obtain meaningful instantaneous frequency, restrictive conditions have to be imposed on the data as discussed by Gabor (1946), Bedrosian (1963) and, more recently, Boashash (1992): for any function to have a meaningful instantaneous frequency, the real part of its Fourier transform has…...
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5,806 citations
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...In general, if more quantitative results are desired, the original skeleton presentation is better; if more qualitative results are desired, the smoothed presentation is better....
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...Therefore, the parameter, ν, defined as N21 −N20 = 1 π2 m4m0 −m22 m2m0 = 1 π2 ν2, (3.7) offers a standard bandwidth measure (see, for example, Rice 1944a, b, 1945a, b; Longuet-Higgins 1957)....
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