Application of EEMD and demodulation principle of symmetric differential energy operator in planetary gearbox

1.EEMD principle

In order to solve the mode aliasing phenomenon of IMF in the process of empirical mode decomposition (EMD), Flandrin et al. Proposed an Improved EMD method based on noise aided analysis. The white noise with uniform spectrum distribution was added to the analysis signal, so that the signals of different time scales would be automatically separated to the corresponding reference scale, namely ensemble empirical mode (EEMD) method.

The core of ensemble empirical mode decomposition is empirical mode decomposition (EMD). On the basis of adding Gaussian white noise, the signal is decomposed into high-order to low-order IMF components. The Gaussian white noise will change the extremum characteristics in the signal, and the IMF component will jointly offset the previous influence, so as to reduce the influence of mode aliasing.

2.Demodulation method of symmetric differential energy operator

Because the traditional energy operator demodulation method still has great error in frequency accuracy, and the instantaneous amplitude and frequency will be very unstable at the end point, so symmetric differential energy operator demodulation method is used.

Firstly, the difference column of discrete signal x (n) is defined

Where the difference sequence is smoothing the original signal x (n), then the difference sequence of Y (n) is:

So we can get the improved energy operator

The approximate value of the new amplitude and frequency of the signal x (n) can be obtained by calculation. As follows:

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