The influence of instrumental errors on the static identification of damage parameters for elastic beams

Euler-Bernoulli straight beams in presence of a single concentrated damage are considered in this paper. Aim of the study is the identification of damage position and intensity on the basis of the knowledge of displacement measurements by static tests on the damaged beam. Explicit solutions of the inverse damage identification problem are presented for the case of simply supported beams. Sensitivity of the identified damage parameters to instrumental noise is explored by making use of the presented explicit solutions. The instrumental noise is modelled as a random variable superimposed to exact displacement measurements, and probabilistic quantities of the identified damage parameters are evaluated in closed form. Conditions regarding the position of the measurement instruments to minimize the influence of the instrumental noise are recognized.