Mr. Frank Lopez Profile

Frank Lopez

at Univ of Houston

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Proceedings Article | 11 June 2002 Paper

Nonlinear damage detection using a time-domain minimum rank perturbation theory

Frank Lopez, David Zimmerman

Proceedings Volume 4702, (2002) https://doi.org/10.1117/12.469877

KEYWORDS: Matrices, Data modeling, Finite element methods, Vector spaces, Complex systems, Tolerancing, Detection and tracking algorithms, Damage detection, Mechanical engineering, Numerical integration

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Modal Minimum Rank Perturbation Theory (MRPT) computes perturbation matrices approximating structural changes from one linear state to another due to damage. The number of measured flexible modes determines the rank of the computed perturbation and is usually low in comparison with model dimension. This work extends a time-domain MRPT (TD-MRPT) for detection of state-dependent stiffness damage. TD-MRPT computes an instantaneous stiffness perturbation with the force balance residual arising in successive time steps. Recursive rank-1 updating of the current stiffness estimate results in a cumulating stiffness matrix that converges to the unknown stiffness regardless of the rank difference between the nominal and perturbed matrices. As a result, damage is detected at onset and is exactly tracked in the case of a rank-1 nonlinearity. Time variation of higher-rank nonlinearities will be approximated provided the rate of change is slow compared with the algorithmic convergence rate. Numerical integration is used to render dependency solely on acceleration response measurement and a time-dependent elemental subspace recognition procedure was employed for detecting damage location and extent in the case of incomplete spatial measurements. The algorithm is evaluated with a nonlinear three degree-of-freedom oscillator and virtual experimental data from a 96-degree-of-freedom structure corrupted with artificial measurement noise.

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