A probabilistic approach to model updating and damage identification

A method is presented to improve the robustness of current damage detection methodologies. Measured statistical changes in natural frequencies and mode shapes along with a correlated analytical stochastic finite element model are used to assess the integrity of a structure. The approach accounts for variations in the natural frequencies and mode shapes (due to experimental errors). A perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix. This stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix. The determination of damaged stiffness statistics permits the comparison of probability density functions between the healthy and estimated damaged stiffnesses. A set of probability damage quotients are then found that indicate a confidence level on the existence of damage. The effectiveness of the proposed technique is illustrated using simulated data on a three degree-of-freedom spring-mass system and on an Euler-Bernoulli cantilever beam. The case when mass is considered deterministic is also shown using simulated data. A noise sensitivity analysis was also performed by polluting analytical mode shapes with varying amounts of noise. It was found that for mode shape noise less than 0.1%, the formulation worked fairly well. The method is also applicable to probabilistically solve the model update/refinement problem and is illustrated using simulated data. Finally, probabilistic model update/refinement and damage detection methodologies are verified using experimental data taken on a cantilever aluminum beam. The method was able to probabilistically update an initial best-guess finite element model using experimentally measured statistical changes in the modal parameters. For the identification of damage, it was also able to detect the damage, locate (to a limited extent) the damage, but unable to quantify the level of damage due to the sensitivity of the procedure to the estimation of the damaged mode shapes.