Verifying hyperparameter sensitivities of optimal filter design methods for fault signature enhancement

Recent advances in vibrations, noise, and their use for machine monitoring

Open Access

Table 5

The hyperparameter sensitivity verification analysis for the GES2N is presented. Table 1 is used as the basis, with a check mark (✓) indicating alignment between the results in Figure 5 and Table 1.

#	HP	Measurements			Comment
		1	2	3
1	D	✓	✓	✓	${\tilde{M}}_{g e s 2 n}$ is proportional to D, which makes sense. Meas. 3’s SES, obtained using D = 16, contains prominent fault components (e.g., when compared to D = 256), but also an increased noise floor. The increased noise floor results in a lower ${\tilde{M}}_{g e s 2 n}$ .
2	CORF	✓	✓	✓	The signal and noise components’ amplitudes decreased when the CORF increased. Still, the noise components decreased more (i.e., higher sensitivity), resulting in an overall increase in ${\tilde{M}}_{g e s 2 n}$ when CORF 4. Decreasing the CORF did not affect the results, highlighting that the baseline Δα is already in the saturation region.
3	Δα_b	✓	✓	✓	${\tilde{M}}_{g e s 2 n}$ is proportional to Δα_b. No extraneous components are enhanced when increasing Δα_b. If Δα_b is too small, some fault components manifest in the noise indicator. This is penalised by the optimiser, which results in a smaller ${\tilde{M}}_{g e s 2 n}$ .
4	TEP	✓	✓	✓	Increasing the TEP results in a lower ${\tilde{M}}_{g e s 2 n}$ and a worse SES (for Meas. 2 and 3).
5	N_h	✓	✓	✓	The ${\tilde{M}}_{g e s 2 n}$ is generally proportional to N_h and only unaffected by the perturbations in a few cases.
6	*w_s*	–	✓	✓	Meas. 1 has insufficient information to conclude. Meas. 2 and 3: H₊ results in more prominent higher harmonics. The lower harmonics are more prominent, and the higher harmonics are absent for H_-. For H₁ only the first few harmonics are prominent (fewer than H_-). The first few harmonics are prominent for H_1:5, with the sixth and higher harmonics attenuated.

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