PSI - Issue 24

M. Barsanti et al. / Procedia Structural Integrity 24 (2019) 988–996 M. Barsanti / Structural Integrity Procedia 00 (2019) 000–000

994

7

15

2

400

1.24

1.9

10

300

1.22

1.8

5

200

1.2

1.7

1.18

0

100

1.6

1.16

-5

0

1.14

1.5

-10

-100

1.12

1.4

-100

0.9

1.02

80

0.85

-150

1

60

0.8

0.98

40

0.75

-200

0.96

0.7

20

0.94

-250

0.65

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

Fig. 6. Damping coe ffi cients as a function of the relative excitation frequency for two di ff erent shaft rotational speeds. The dashed bar indicates systematic error (interval of deviation from the reference value for 95% of the calibration procedures). Note that the scales are di ff erent in each panel to highlight the amplitudes of the systematic error bars with respect to the di ff erent ranges of variation of the damping coe ffi cients.

6

2

4

1

1.5

4

1

2

0.5

2

0.5

0

0

0

0

-0.5

-2

-0.5

-2

-1

-4

-1.5

-1

10 -4

-6

10

6

10

4

5

5

5

2

0

0

0

0

-2

-5

-5

-5

-4

-10

-6

-10

-10

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

0.2 0.4 0.6 0.8 1 1.2

Fig. 7. Comparison of systematic errors (dashed lines) with random error for sti ff ness coe ffi cients as a function of the relative excitation frequency for two di ff erent shaft rotational speeds. Full lines: random uncertainty computed using sample standard deviation. Dotted lines: random uncertainty computed using bootstrap technique, as described by Barsanti et al. (2019).

in figure 7, for damping coe ffi cients in Figure 8. For completeness, random errors computed using both methods are reported. As it can be seen, the full and dotted lines are practically overlapping. Sometimes a slight asymmetry of the bootstrap confidence intervals is observable with respect to the Gaussian ones which are, by definition, symmetrical. This could indicate that the use of the Central Limit Theorem is not entirely justified for this dataset. A large variety of confidence intervals width is evident for random errors when the excitation frequency is varied. On the contrary, for systematic error the width of confidence intervals does not vary too much when the excitation frequency is changed. Variations of the setup conditions (shaft speed and static load) seem to influence the value of systematic uncertainty, even if its order of magnitude remains the same. The variation of systematic error when setup conditions are changed is lower than the variation of the random uncertainty as a function of the excitation frequency which, in some conditions, can even be of an order of magnitude.