PSI - Issue 60

11

Akshay Kumar/ Structural Integrity Procedia 00 (2023) 000 – 000

A. Kumar et al. / Procedia Structural Integrity 60 (2024) 541–552

551

Table 2: Results of uncertainty analysis

Wilks

Monte Carlo

Contact time (s) 95/95 value

Contact temperature (K)

Contact time (s)

Contact temperature (K)

95/95 value

Mean 182.7 193.7

s.d.

95% 201 296

Mean 955.4 953.0

s.d 4.6

95% 963 990

Case 1 Case 2

215 385

965 992

10.9 62.1

22.5

The contact time and the contact temperature obtained from the Wilks method is greater than the 95 percentile value obtained from Monte Carlo simulation. This however may not be the case always. The Wilks ’ method gives a value which is greater than 95 percentile with a confidence of 95%. Thus, there is always a 5% chance that the value obtained from Wilks’ method can be less than the 95 percentile value. The relative frequency histograms of contact time and contact temperature for the Case 2 with 5% cov on stress exponent and activation energy is shown in Fig. 9 and 10 respectively. The lognormal distribution fitted the contact time data for both the cases. The comparison of the probability distribution function for the two cases is shown in Fig. 11.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Relative Frequency

70-110 110-150 150-190 190-230 230-270 270-310 310-350 350-390

Contact Time (s)

Fig. 9: Relative frequency histogram for contact time in Case 2

Fig. 10: Relative frequency histogram of contact temperature for Case 2 The scatter in the Case 2 is significantly higher than that in Case 1. The cov for contact time in Case 1 is 6% and that in Case 2 is 32%. Monte Carlo simulation aids this kind of data analysis in order to make informed decisions regarding the system. The number of simulations considered in this study were only 60. This number is good to fit in a probability density function and to estimate the parameters. However, when the statistic of the data like mean, standard deviation, percentile values etc. are evaluated, it is not be possible to evaluate the confidence levels. As the associated confidence intervals for the output of interest are needed, significantly more number of Monte Carlo simulations are required. 0 0.1 0.2 0.3 0.4 900-914 914-928 928-942 942-956 956-970 970-984 984-998 Relative Frequency Contact Temperature (K)