Structural Damage Identification: A Probabilistic Approach

Abstract

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 modal properties of a structure (due to experimental errors in the test procedure). 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 graphical and statistical 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 aluminum beam.