Bayesian damage identification of simply supported beams from elastostatic data

This paper considers a statistical method for damage identification of simply-supported elastic beams from static data. The problem is cast as an inverse problem and analyzed in Bayesian inversion framework. The main goal is to obtain a probabilistic model for the spatial distribution of the damage across a beam given limited and noisy data on the static beam response. A principal distinction of the proposed method is its ability to identify not only an estimate of the damage occurred to the beam but also the uncertainty (error) associated with such an estimate. Moreover, the proposed method uses simple static data instead of dynamic or spectral data, unlike the majority of research work published in the literature. This is a challenge as static data is a rather limited source of information about the underlying physical system compared to dynamic data. Finally, the proposed method does not involves any computationally expensive high-dimensional integration algorithms unlike the existing methods. According to the numerical analysis conducted in this paper, the result obtained by using the proposed damage identification method lies within one standard deviation interval.