Issue 66

R. B. P. Nonato, Frattura ed Integrità Strutturale, 65 (2023) 17-37; DOI: 10.3221/IGF-ESIS.66.02

Tabs. 4 and 5 present some statistical parameters referred to UIQs and SRQs treated herein. The values obtained from simulations performed are indicated as estimated in the pertinent columns. The relative errors are calculated between the deterministic and the simulated ones. The magnitudes of the relative errors obtained correspond to a good agreement of the simulations compared to the information initially provided, which is partially explained by the use of LHS as the method of uncertainty propagation. These tables also present the coefficient of variation (COV), in which UIQ 0 a could be observed as having the highest COV. Followed by 0 a , in descending order, t , D , and m close this list of UIQs, i.e. the largest standard dispersion of the UIQs comes from 0 a , and the smallest from m (the most efficient UIQ in recovering the previously given information). In addition, the relative errors shown in Tab. 5 address small magnitudes, highlighting that in what refers to lower and upper bounds, 0 a presents the largest values of relative error. In what concerns mean, t is the largest. In this case, the UIQ with the highest COV ( 0 a ) also has the lowest efficiency to retrieve the previously given information. Therefore, it is important to note that the COV of a simulated UIQ is not always related to its efficiency in recovering the information given.

Parameter

Estimated range

Estimated mean

Estimated standard deviation

m

[2.9925; 3.0149]

3.0001

0.0058

0 a ( mm )

[2.4001; 2.6997]

2.5004

0.0777

  mm t   mm D   cycles N

[12.3001; 12.8999]

12.5022

0.1557

[272.3176; 274.3639]

273.0120

0.5332

[2.2760; 3.0470] x 10 9 0.1460 x 10 9 Table 4: Estimated range, mean, and standard deviation of the five main parameters. 2.6490 x 10 9

Parameter

RE of LB (%)

RE of UB (%)

RE of mean (%)

COV

m

0.0001

0.0001

0.0031

0.0019

0 a ( mm )

0.0012

0.0127

0.0163

0.0311

  mm t   mm D   cycles N

0.0001

0.0010

0.0172

0.0125

0.0002

0.0004

0.0044

0.0020

Not applicable Not applicable 0.0396 Table 5: Relative errors (RE) related to lower bound (LB), upper bound (UB), and mean, besides the coefficient of variation (COV) of the main parameters. In what refers to the convergence of the means of the UIQs related to their deterministic values, a certain degree of stabilization of the means is achieved and the adoption of a criteria of   4 1 10 % is verified only at  3957 r N ,  9787 r N ,  3662 r N , and  3888 r N realizations for UIQs m , 0 a , t , and D , respectively. In the context of these simulations, the generated information leads to the conclusion that 0 a is the most restrictive parameter aiming at reducing the computational effort involved. In view of this, the number of realizations was selected to be 10000. In addition to the bi-level sensitivity analysis (SA) performed, graphical SAs are presented in Figs. 8 and 9. These scatter plots represent a mapping of how the UIQs influence the behavior of the main SRQ N , which may help in decision making processes related to mechanical design and enable studies to reduce the dispersion based on the obtained information. These plots also address the degree of dependence of N related to the involved UIQs, which can be represented herein by the correlation coefficient. Tab. 6 presents the correlation coefficients corresponding to the influence of the UIQs m , 0 a , t , and D on the levels corresponding to their interaction with the SRQs r S , r K , / da dN , and N . From this table, when m goes from the first to the second level, the correlation is incremented significantly by 323.5%. However, the 0.1360

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