End Spreading
Sifting might spread signal into
quiescent region
Earthquake : Elcentro
Earthquake Elcentro IMF:
CE(100,3)
Earthquake Elcentro EIMF (3,0.1,50)
Orthogonality Indices
OI ij
0.1982
0.0412
0.0336
0.0534
0.2453
0.0557
0.1723
IMF
OI total
-0.4986
EIMF
OI ij
0.0395
0.0862
0.0570
0.0423
0.0819
0.1682
0.1522
0.0246
0.2225
OI total
0.0606
End spreading
• This is an annoying problem, for to have
some thing before the sensors were
turned on is nonsensical.
• But EMD has the tendency to spread the
signal through the sifting processes.
• End spreading causes deterioration in the
resulting IMF components.
• EEMD solved the problem to a large
extend.
Noised Aided Data Analysis II
Although EEMD alleviates the end
spreading considerably, there are still
cases that signal spreading needs to
be contained.
Noise Aided Data Analysis II
• In EEMD, the finite magnitude noise is
added once in each of the ensemble. The
true solution is obtained as the limit of
having the number in the ensemble
approaching infinite.
• In NADAII, the infinitesimal magnitude
noises is added repeatedly for each IMF
extraction.
Delta Function
Noised Aided Data Analysis II
Delta Function : Data
The Procedure
• Perform EEMD and select the first EIMF component as
the 1st component in the RIMF (Recombined IMF)
• Take the residue and adding noise with amplitude 1/1000
as the data for the first round re-processing to produce
EIMF1.
• Take the 1st EIMF component from EIMF1 as the
second component in the RIMF.
• Take the residue and adding noise with amplitude 1/1000
as the data for the second round re-processing EIMF2.
• (repeat the processes) …….
Delta Function : EIMF(3,0.1,10)
Spreading of the signal
• The widths of the IMF signals become
increasingly wide.
• The spreading increasingly wide into the
quiescent region as shown in th eprevious
figure.
Delta Function :
IMF1(3,0.1,10)
Delta Function :
IMF2(3,0.1,10)
Delta Function :
IMF3(3,0.1,10)
The Re-combined IMF
So far a manual operation.
Delta Function : RIMF
Delta Function : RIMF(1) = EIMF(1)
Delta Function : RIMF(2) = EIMF1(1)
Delta Function : RIMF(3) = EIMF2(1)
Delta Function : RIMF(4) = residue
Delta Function : RIMF(4) = residue
RIMF
• RIMF is a combination of all the individual
EIMFi, for i=1,2,3,…
• The spread of each of the component is
limited by the added noise.
• As a result, the spread is controlled; the
result is more local.