*4.4. Extensive Materials*

This subsection provides extensive descriptions for how the rules are justified using tabularised quantitative information.

Table 1 digests how the first rule was established in Section 4.1, based on the resampled, resmoothed, and mean–var. transformed data on the X axis (see Section 3.3 and Figures A7a, A8a and A9a), with the setting that wind-speed (WS) = 6 m/s. Table 2 is numerically presented on the Y axis (see Section 3.3 and Figures A7b, A8b and A9b), because rule 1 says that using the information either on the X-axis or on the Y-axis is okay.

**Table 1.** Resampled, resmoothed mean–var. transformed data on the X axis (WS = 6 m/s). (**a**) Min/var. peak/valley Stats for the 3.0-blade turbine. (**b**) Min/var. peak/valley stats for the 2.5-blade turbine. (**c**) Min/var. peak/valley stats for the 2.0-blade turbine.



**Table 2.** Resampled, resmoothed mean–var. transformed data on the Y axis (WS = 6 m/s). (**a**) Min/var. peak/valley stats for the 3.0-blade turbine. (**b**) Min/var. peak/valley stats for the 2.5-blade turbine. (**c**) Min/var. peak/valley stats for the 2.0-blade turbine.

In these tables, ID is the number of the data entry in the resmoothed and resampled dataset in 3.3, based on the retrieval of the initial 1024 signals of each data sequence in 3.2. For example, in Table 2b, the 'Mean' and 'Var.' for 'ID' = 12 means the data entries with clocks [(12 − 1) × 8, (12) × 8 − 1] in the source accelerometer data sequence (which is 0-started) have a mean value of 1.145866 and a variance of 0.154981. 'Peak' = 0 and 'Valley' = 1 means that a valley appears here (as can be seen, in this table, entries that are neither a peak nor a valley in the figure are not shown here), and this valley is having a value delimited by ['Valley Top', 'Valley Bot.'] = [0.990884, 1.300847], while the 'Valley Range' of it is 0.309963. For this identified extreme, 'Peak Top', 'Peak Bot.' and 'Peak Range' do not receive any value because they are not peaks (see also in the corresponding subfigure in Figure A8b).

Rule 1 is obvious from these tables. Along the X or Y axis, either the peak range or the valley range of the 2.5-blade turbine is far greater than the peak range or the valley range of a 3.0-blade turbine or a 2.0-blade turbine. This is more salient when a total summary for all cases and the average is given in Table 3 (e.g., when wind-speed = 6 m/s, on Y axis, 0.072865 (2.5-blade) >> 0.018713 (3.0-blade) > 0.017087 (2.0-blade); 0.187026 (2.5-blade) >> 0.01901 (3.0-blade) > 0.016757 (2.0-blade)). That is, for a 2.5-blade turbine, the variance at the peak or valley along the X or Y axis is at least triple or more than the 3.0-blade or 2.0-blade cases.


Finally, Rule 2 should also be obvious from these tables. See in Table 3. For the 3.0-blade settings, on the Z axis, from the average of all valley values to the average of all peak values (i.e., the fluctuation), the numbers are 2.034987, 3.076206, 3.185465 and 3.424772, respectively, imposing the four wind-speeds. However, for the 2.0-blade settings, on the same axis, these numbers are 1.869613, 2.928724, 3.110773 and 3.074410, respectively. All of these numbers are below those of the 3.0-blade settings (while other settings are identical) by 7% (8.8%, 5%, 2.4% and 11.4%) in average. This quantified rule can be applied, and the reason for this is related to electromechanical conversion: more electricity is produced by the wind turbine when no blade is missing.
