PSI - Issue 64

Sayandip Ganguly et al. / Procedia Structural Integrity 64 (2024) 757–765 Ganguly and Roy/ Structural Integrity Procedia 00 (2023) 000 – 000

762

6

reliability for Case-I. In contrast to this, Chaudhary et al.’s (2021) expression shows varied degree of reliability depending on damage severity, location, and COV of material uncertainty. In the numerator of Eq. (3), the difference between healthy and damaged states’ modal responses neutralizes the effect of uncertainty variation to a greater extent. However, additional uncertainties originated from the denominator due to modal response ̂ −2 in Eq. (3), results the scattered variation in Case-II. As stiffness values are assigned randomly at different stories with respect to the mean, for some damage locations the denominator may be less or greater than actual value. This uncertainty along with the effect of damage extent on ( ̂ −1 − ̂ −2 ) determines the impact on the estimated value with respect to the actual one. Depending on this, at different damage severity and location, reliability trend also varies irregularly.

Fig. 6. ( ) at 1% 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) 3 rd story, (e) 5 th story, and (f) 7 th story damage at different damage severities. The PDF of damage quantity derived from both the equations for 10% damage at 3rd, 5th, and 7th stories is shown in Fig. 5. The impact of damage location is visible in this figure, particularly for damage at 7th story, when material uncertainty attains 10% COV. However, the mean value remains consistent across both scenarios at 1% and 5% COV. Notably, there is a significant discrepancy in the shift of mean damage quantities at 10% COV, in comparison to other two, when estimated using Roy’s (2022) expression than that obtained from Eq. (3).

Fig. 7. ( ) at 5% 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. 4.2 Reliability analysis with measurement uncertainty The reliability analysis of estimated damage in presence of measurement uncertainty ensures a comprehensive evaluation of underlying methodology. As two closed-form equations considered in this work are dependent only on the modal displacements of damaged story and its adjacent upper or lower stories (Fig. 1(a)), the Gaussian distribution