Propagation of material uncertainty in modal parameters and its influence in damage quantification of shear buildings

Abstract

Structural health monitoring (SHM) plays a crucial role in post-disaster mitigation in investigating the serviceability of an existing structure. The physical properties, namely mass density, cross-sectional area, Poisson’s ratio, modulous of elasticity, etc., vary spatially throughout a real system. These uncertainties propagate in the modal parameters involved in SHM techniques. In this study, the elastic modulous has been considered the primary source of uncertainty. A detailed literature survey has been performed to identify the suitable probability distribution recommended for defining material uncertainty. Although the Gaussian distribution cannot replicate realistic material behaviour, its explicit implementation makes it prevalent. However, based on the principle of maximum entropy, the gamma distribution is the most appropriate recommendation among all non-Gaussian continuous distributions ranging [0, ∞). The Karhunen–Loève (KL) expansion has been adopted to discretize the stochastic field to determine the spectral mass and stiffness of a multi-damaged axially vibrating prismatic cantilever bar-type structure. Closed-form orthogonal pairs of eigensolutions of the KL expansion considering (Adhikari and Friswell, 2010) exponential covariance function have been derived. The expressions for spectral mass and stiffness for a multi-damaged cantilever bar considering material uncertainty have been developed. The uncertainty propagation in the modal properties has been estimated. The complete procedure has been followed to identify uncertainty propagation in damage severity of a common class of civil structures like shear buildings. The influence of material uncertainty in determining the damage severity of a structure with numerable degrees of freedom using a non-destructive approach has been explored. Extensive simulations have been performed to evaluate the effectiveness of the present study in a multi-damaged bar as well as shear building. Statistical parameters, namely mean and standard deviation of natural frequencies, modal displacement and damage severity have been determined. The uncertainty propagation has been reflected in the mean value for varying input stochasticity. However, the standard deviation remained consistent for undamaged as well as damaged structure irrespective of material uncertainty type. Considering gamma distribution in material stochasticity, the spread of uncertainty propagation has been more than the Gaussian distribution. However, experimental studies need to be performed further to investigate the stochastic behaviour in modal parameters of a real structure.