Limited Sensor-Based Probabilistic Damage Detection Using Combined Normal–Lognormal Distributions

Abstract

A methodology for probabilistic damage detection in Bayesian framework without any requirement of mode matching is presented with detailed formulations on finite element model updating using incomplete modal data measured using limited number of sensors. Multiple modal measurement/data sets from multiple different sensor set-ups can be used in the proposed methodology with further scope for using repeated measurements from any single sensor set-up. Combined normal–lognormal multivariate distribution is considered in the Bayesian framework. Strictly positive random parameters are assigned with lognormal distribution, while the remaining random parameters are assigned with normal distribution. In this work, the normal distribution is incorporated for the likelihood function, which consists of the eigen-system equation error and the error between the system mode shapes and experimental mode shapes. On the other hand, mass and stiffness parameters are assigned with the lognormal distribution. Detailed formulations for probabilistic identification of changes/damages are also developed. The proposed approach is validated using a three-dimensional building structure considering multiple simulated damage cases. Performance in updating and damage detection is evaluated based on multi-set-up and multi-dataset considerations. Besides, the proposed technique is compared with the similar Bayesian updating solely based on normal distribution and the Gibbs sampling.