*4.1. Simulated signal*

If a center spring wear fault has occurred, this will cause serious hydraulic shock in the hydraulic pump, which can be reflected as impulsive feature in morphology of the fault signal. Thus, *x*1(*t*) (an impulsive signal with periodic exponential attenuation) is used to simulate the fault signal. There are also some background noises in the fault pump; thus, *x*2(*t*) of Gauss white noise with standard deviation of 0.5 is adopted to simulate the background noises.

The purpose of the simulation experiment is used to validate the effectiveness of Autogram to extract *x*1(*t*) of the simulated impulsive fault in theory.

The simulated signal is expressed in Equation(6):

$$\mathbf{x}'(t) = \mathbf{x}\_1(t) + \mathbf{x}\_2(t) \tag{6}$$

frequency (Hz)

where *x*1(*t*) is used to simulate an impulsive fault, and it is an exponential attenuation signal with periodic frequency of 30 Hz. It is 3*e*-400*<sup>t</sup>* sin(300π*t*) in a period. *x*2(*t*) is Gauss white noise with a standard deviation of 0.5, and it is used to simulate a background noise. The sampling frequency is 2048 Hz.

The simulated signal in frequency domain is shown in Figure 2.

**Figure 2.** Spectrum of the simulated signal.
