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

Euler–Bernoulli straight beams in the presence of a single concentrated damage are considered in this paper. The aim of the study is the identification of the damage position and the intensity on the basis of the knowledge of the 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. The 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 onto the exact displacement measurements, with probabilistic quantities of the identified damage parameters being evaluated in closed form. Conditions regarding the position of the measurement instruments to minimize the influence of the instrumental noise are recognized.