*4.2. Analysis of the simulated signal based on standard Autogram*

Standard Autogram is adopted to extract the simulated fault feature information, and the colormap presentation obtained based on the Equation (2) is displayed in Figure 3.

Standard Autogram-Kmax=6.6 @ level 1, Bw=512Hz, fc=256Hz

**Figure 3.** Colormap presentation of the simulated signal based on standard Autogram.

The maximum value *kurtosis* 6.6 is assigned to the node (1, 1), with a center frequency of 256 Hz and a bandwidth of 512 Hz. Thus, the node (1, 1) is used as data source for future investigation, and the no threshold spectrum, upper threshold spectrum, and lower threshold spectrum are shown in Figure 4.

**Figure 4.** Spectrums of the simulated signal data source node (1, 1) based on standard Autogram. (**a**) No threshold spectrum; (**b**) Upper threshold spectrum; (**c**) Lower threshold spectrum.

Among the three figures in Figure 4, simulated fault feature information at fault feature frequency 30 Hz and all of its harmonics are only extracted only in Figure 4a. The amplitude values based on no threshold processing in Figure 4a are the largest, and all of them are larger than those in the simulated signal spectrum in Figure 2. It can be seen that standard Autogram extracts the information effectively, and the extraction ability of Autogram based on no threshold processing is the strongest.

#### *4.3. Analysis of thesimulated signal based on Upper Autogram*

The upper Autogram is applied to extract the simulated fault feature information and the colormap presentation can be obtained based on Equation (3), as shown in Figure 5.

The maximum value *kurtosisu* is 5.3, and it is assigned to the node (3, 4), with center frequency of 448 Hz and a bandwidth of 128 Hz. Thus, the node (3, 4) is used as data source for further investigation, and the no threshold spectrum, upper threshold spectrum, and lower threshold spectrums are illustrated in Figure 6.

It is very clear that there is no simulated fault feature information at fault feature frequency of 30 Hz with its harmonics in Figure 6, and there are many background noises. Thus, the feature information cannot be effectively extracted by upper Autogram based on lower threshold processing.

**Figure 5.** Colormap presentation of the simulated signal based on upper Autogram.

**Figure 6.** Spectrums of the simulated signal data source node (1, 1) based on upper Autogram. (**a**) No threshold spectrum; (**b**) Upper threshold spectrum; (**c**) Lower threshold spectrum.

#### *4.4. Analysis of the simulated signal based on Lower Autogram*

The simulated fault feature information is extracted by lower Autogram, and the colormap presentation based on the Equation (4) is shown in Figure 7.

**Figure 7.** Colormap presentation of the simulated signal based on Lower Autogram.

The maximum value *kurtosisl* is 2.3 and corresponds to node (2, 1), the node has a center frequency of 128 Hz and a bandwidth of 256 Hz. Node (2, 1) is adopted as a data source for further investigation, and the no threshold spectrum, upper threshold spectrum, and lower threshold spectrums are demonstrated in Figure 8.

**Figure 8.** Spectrums of the simulated signal data source node (2, 1) based on lower Autogram. (**a**) No threshold spectrum; (**b**) Upper threshold spectrum; (**c**) Lower threshold spectrum.

It can be seen in Figure 8 that the simulated fault feature information at fault feature frequency 30 Hz with some harmonics can be extracted. The amplitude values obtained based on no threshold processing in Figure 8a are the larger than in Figure 8b,c, and the amplitude values in Figure 8 are all larger than those in Figure 2. Thus, lower Autogram is effective in extracting the information, and its extraction ability based on no threshold processing is the strongest.

Compared with standard Autogram based on no threshold processing in Figure 4, the fault feature information with many harmonics cannot be extracted by lower Autogram, and their amplitude values are small.

From the results of standard Autogram (Figure 4), upper Autogram (Figure 6), and lower Autogram (Figure 8), it can be concluded that standard Autogram has the strongest extraction ability, with background noises more greatly reduced.
