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 IndicesIMF

OI ij 0.1982 0.0412 0.0336 0.0534 0.2453 0.0557 0.1723

OI total -0.4986

EIMFOI 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.