Table 1
The selected hyperparameter (HP), the expected impact of changing the HP on the ICS2 and the GES2N, and the corresponding motivation are provided.
| # | HP | Expectation ICS2 | Expectation GES2N | Motivation |
|---|---|---|---|---|
| 1 | D: Filter length | Increasing D is expected to generally improve the final objective. | Same as ICS2. | The filter length dictates the flexibility of the filter’s frequency response, and, therefore, the objective is expected to improve as the filter’s length (and flexibility) is increased. However, longer filter lengths are expected to increase the computational time and make convergence more challenging. |
| 2 | CORF: Cyclic Order Resolution Factor | Decreasing the CORF, decreases Δα, which is expected to improve the objective since only its numerator depends on the SES. | Both signal and noise indicators depend on the CORF and are dataset-dependent. | Figure 2a shows two SES; SES (B) has a better cyclic order resolution than SES (P). Improving the CORF is expected to generally increase the amplitudes (circumventing the picket-fence effect). For the GES2N, both the signal and noise indicators are expected to increase when the CORF decreases. Therefore, its overall impact on the objective depends on the sensitivity of the signal and noise indicators. |
| 3 | Δαb: Targeted bands’ width | For a fixed h, increasing Δαb, is expected to improve the objective. The impact of Δαb, on the final objective depends on the dataset. | Same as the ICS2 | Figures 2b and 2c show two examples of Δαb. Increasing Δαb, will increase the size of the signal indicator’s amplitude set (ICS2, GES2N) and since the maximum of each band is used in Equation (4), the signal indicator is expected to remain the same or increase. The opposite is expected for the GES2N’s noise indicator. Figure 2b’s Δαb, is too large and the extraneous component contributes to the signal indicator. If Δαb, is too small, it can be sensitive to small errors in αt, but also some of the fault information could be contained in the GES2N’s noise indicator. Therefore, the overall impact depends on the dataset (e.g., prominent components, length of the signal). |
| 4 | TEP: Targeted Error Percentage | Dataset dependent. An increase in the TEP is expected to decrease the performance generally, but it could enhance other erroneous components, increasing the objective. | Same as the ICS2. | Figure 2d shows that increasing TEP results in the actual cyclic orders of interest to be missed (i.e., the filter’s performance to enhance αc decreases). Still, a large extraneous component contributes to the signal indicator and could result in an overall increase in the objective. |
| 5 | Nh : Number of targeted harmonics | Increasing Nh is expected to increase the objective and the overall performance of the filter, except if some harmonics coincide with an extraneous component | Same as the ICS2 for the signal indicator. More harmonics could also result in a better noise indicator estimate if equation (7) is used. | More harmonics will drive the optimiser to enhance the underlying source and an improved performance is expected. However, higher harmonics of different components often overlap or could have low signal-to-noise ratios for weak damage, which can impede the overall performance of the objective. |
| 6 | ws : Cyclic order band’s weight | N/A | Increasing the weight of a harmonic is expected to generally increase the harmonic’s amplitude. | Increasing the weight of a harmonic incentivises the optimiser to update the design variables to increase the amplitude of the component. Whereas, a harmonic with a weight of 0, will not contribute to the objective. Since the harmonics are related to the same source, a harmonic could still be enhanced even if its weight is zero. It depends on the behaviour of the filter. |
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