PSI - Issue 64

Sayandip Ganguly et al. / Procedia Structural Integrity 64 (2024) 757–765 Ganguly and Roy/ Structural Integrity Procedia 00 (2023) 000 – 000 7 is applied to corresponding modal values. Modal displacements of each DoF is normally distributed about mean modal displacement corresponding to stiffness ̅ with similar number of sample points ( ) as used for material uncertainty analysis. This synthetically generated Gaussian noise infused mode shape values are then explicitly applied on Eq. (3) and Eq. (4) to estimate the reliability of equations. The effect of the propagation of measurement uncertainty with 1% COV is depicted in Fig. 6 for both Case-I and II. It is observed from Fig. 6 that measurement uncertainty slightly affects the trend of reliability in Case-I than Case-II. At a particular level of deviation, there exists a positive correlation between R( ) and damages severity. R( ) estimated in Case-II shows inconsistent variation over the range of damage values considered in this study. Damage severity of 15% and 25% are predicted with greater reliability and within 10% deviation for any COV. Results of 5% and 10% COVs are also plotted in Figs. 7 and 8 respectively. 763

Fig. 8. ( ) at 10% COV of measurement uncertainty estimated in Case-I for (a) 3rd story, (b) 5th story, and (c) 7th story damage and in Case II for (d) 3rd story, (e) 5th story, and (f) 7th story damage at different damage severities.

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Fig. 9. PDF of estimated damage quantity in presence of measurement uncertainty for damage at (a) 3rd, (b) 5th, and (c) 7th stories in Case-I, for damage at (d) 3rd, (e) 5th, and (f) 7th stories in Case-II. It is noticed from these figures that unlike material uncertainty, at a particular allowable deviation, the maximum reliability is less for higher story damage than lower stories in presence of measurement uncertainties. This is due to the influence of the shape of mode. At the 3rd story, the inclination of the first mode shape is generally observed to be less steep in comparison to the 7th story. Consequently, when encountering a comparable deviation in modal displacements between higher and lower stories, the alteration in mode shape slope due to damage is notably more pronounced at upper levels. This phenomenon leads to less reliable predictions of higher story damage at a particular limit state for both Case-I and II. However, the deviation of mean estimated damage quantity from actual damage value is found almost similar to the effect of material uncertainty. The maximum deviation is 2.8% for Case-I, among the considered damage locations and 3.5% for Case-II, averaged over all COVs. In Case-II, the degree of reliability seems to become linear in trend with the shift of damage location to higher stories at 5% and 10% COVs. The initial