Identification of an open crack model in a beam based on force–response measurements

In general, the system identification implies the estimation of system model parameters from the experimental force–response measurements. In the present work, a general identification algorithm has been developed to estimate crack flexibility coefficients and the crack depth based on the force–response information. The general identification algorithm is extended to overcome practical limitations of measuring number of degrees of freedom (dofs). For reducing the number of response measurements, the static reduction scheme is incorporated into the identification algorithm. The Euler–Bernoulli beam element is used in the finite element modeling. The transverse surface crack is considered to remain open. The crack has been modeled by a local compliance matrix of four degrees of freedom. This compliance matrix contains diagonal and off-diagonal terms. A harmonic force of known amplitude and frequency is used to dynamically excite the beam. The present identification algorithms have been illustrated through numerical examples. The identification algorithms are tested against measurement noise and have been found to be reasonably robust against the measurement noise. The technique requires that the force to be known. Hence, in a real system the accuracy of result depends on the obtained force.