Identification of a cantilever beam’s spatially uncertain stiffness

This study identifies non-homogeneous stiffnesses in a non-destructive manner from simulated noisy measurements of a structural response. The finite element method serves as a discretization for the respective cantilever beam example problems: static loading and modal analysis. Karhunen–Loève expansions represent the stiffness random fields. We solve the inverse problems using Bayesian inference on the Karhunen–Loève coefficients, hereby introducing a novel resonance frequency method. The flexible descriptions of both the structural stiffness uncertainty and the measurement noise characteristics allow for straightforward adoption to measurement setups and a range of non-homogeneous materials. Evaluating the inversion performance for varying stiffness covariance functions shows that the static analysis procedure outperforms the modal analysis procedure in a mean sense. However, the solution quality depends on the position within the beam for the static analysis approach, while the confidence interval height remains constant along the beam for the modal analysis. An investigation of the effect of the signal-to-noise ratio reveals that the static loading procedure yields lower errors than the dynamic procedure for the chosen configuration with ideal boundary conditions.