PSI - Issue 64

764 Sayandip Ganguly et al. / Procedia Structural Integrity 64 (2024) 757–765 Ganguly and Roy/ Structural Integrity Procedia 00 (2023) 000 – 000 8 curve pattern of ( ) observed for lower story damage in Case-II may be due to the incorporation of mode shape differences of non-identical DoFs in the numerator and denominator of the Eq. (3). Uncertainties in the measured data of different stories non-proportionally affect the ratio in Eq. (3) and hence, a nonlinear trend is developed. From Fig. 9, plotted for 10% stiffness degradation, it can be interpreted that higher COV results in the large dispersion and asymmetry in the shape of estimated damage quantity distribution. 5. Conclusion In the present study, a numerical model of 10-story shear building is extensively analyzed to evaluate the effect of material and measurement uncertainties on the estimated damage severity. It is observed from the results that the reliability of damage quantification is influenced by factors such as severity and location of damage in presence of both the uncertainties. The investigation also highlights that the formulation proposed by Roy (2022) to quantify damage, demonstrates a consistent reliability across an extensive range of severities. In presence of material uncertainty, the reliability is sufficiently high even below 5% deviation when damage is present adjacent to a higher story. On the other hand, the expression by Chaudhary et al. (2021) shows comparatively lower reliability in determining percentage of stiffness degradation beyond 30%, even at higher deviation levels. However, it performs better in case of medium severity damage at lower stories. At the same time, it is observed that the impact of measurement uncertainty on the reliability of estimated damage differs from that when material uncertainty exists. In presence of measurement noise, damage at upper story is quantified with relatively reduced confidence level. Reliability of damage quantity derived from Chaudhary et al.'s (2021) formulation exhibits an inconsistent variation, particularly, in case of lower story damage. Incorporation of damaged state modal response of one additional DoF in the denominator of Chaudhary et al.'s expression results in this irregular variation. The confidence interval of the two well-established formulations determined in this work facilitates in choosing appropriate closed-form expression for practical applications. It also ensures higher reliability of estimated damage within an intended deviation limit, depending on the damage severity and its location. Furthermore, a reliability analysis obviates the need of extensive case studies to establish these methods. Though both the methods are observed to have considerably higher reliability beyond a certain allowable deviation, the expressions need to be modified for greater reliability below 5% allowable deviation irrespective of damage severity and its location. In future, the impact of other statistical distribution model of uncertainty on the damage quantification also need to be explored in order to examine potential changes in the trend of reliability assessment. Acknowledgements The authors would like to thank 'Hindustan Steelworks Construction Limited' a subsidiary of NBCC (India) Ltd. under the Ministry of Housing & Urban Affairs for funding this work. References Lopez, I., Klijn, S., 2010. A review of uncertainty in flight vehicle structural damage monitoring, diagnosis and control: Challenges and opportunities. Progress in Aerospace Sciences 46, 247-273. Leonel, E., Chateauneuf, A., Venturini, W., 2012. Probabilistic crack growth analyses using a boundary element model: Application in linear elastic fracture and fatigue problems. Engineering Analysis with Boundary Elements 36, 944-959. Reynders, E., Pintelon, R., Roeck, G., 2008. Uncertainty bounds on modal parameters obtained from stochastic subspace identification. Mechanical Systems and Signal Processing 22, 948-969. Chandrasekhar, M., Ganguli, R., 2016. Damage assessment of composite plate structures with material and measurement uncertainty. Mechanical Systems and Signal Processing 75, 75-93. Mendler, A., Dӧhler, M., Ventura, C., 2021. A reliability -based approach to determine minimum detectable damage for statistical damage detection. Mechanical Systems and Signal Processing 154, 107561. Seventekidis, P., Giagopoulos, D., 2023. Model error effects in supervised damage identification of structures with numerically trained classifiers. Mechanical Systems and Signal Processing 184, 109741. Jiang, C., Zheng, J., Han, X., 2017. Probability-interval hybrid uncertainty analysis for structures with both aleatory and epistemic uncertainties: A review. Structural and Multidisciplinary Optimization 57, 2485-2502.