Study on application of optimizing resonance-demodulation technology in mechanical fault diagnosis

We make use of the signal from x( )t and ˆ( )x to get that:

z x jx r t j( )t ( )t ( )t ( ) [ ( )t ]= + θ (5)

and θ ( ) are used to estimate the signal amplitude envelope and instantaneous frequency. In this case, Hilbert Transform Separation Algorithm (HTSA) can be stated as:

r x x a( )t ( )t ( )t ( )t= + ≈2 2 (6)

ωθ ( ) ( ) ( )

( )d dt

x x i

⎡ ⎣⎢

⎤ ⎦⎥

⎧⎨⎩ ⎫⎬⎭

(7)

At the end of the envelope signal spectrum analysis, envelope spectrum of the signal can be obtained.