General-order Perturbation with a Skew-symmetric Approach for Structural Health Monitoring of a Modular Beam

Abstract

A unique health monitoring method is formulated via a skew-symmetric approach in which the damage location and extent are estimated from the perturbation of a specific set of eigenparameters. The perturbed orthonormal equation is generated from the perturbation of the eigenvectors and eigenvalues to obtain the kth skew-symmetric coefficients. Meanwhile the perturbed eigenvalue equation is generated from the perturbation of the eigenparameters and linear expansion of the stiffness matrix to obtain other skew-symmetric coefficients. Throughout this process, specific permutation numbers and generalized Kronecker delta functions are manipulated. Then these skew-symmetric coefficients are simplified to obtain the symmetric coefficients. A finite element model of a modular beam is used as a test structure to investigate the applicability of the developed method. A fixed—fixed boundary condition is imposed on the two ends to approximate the actual operating situation. Different order perturbation algorithms are established based on the perturbation equations. Stiffness parameters are computed from these equations, inversely, using an optimization method. The algorithm is iterative in nature and terminates under certain criteria. Various small to large percentage systematic damaged cases are simulated under different perturbation orders. The results are compared and evaluated using health monitoring curves and estimation error manifolds, and their efficiencies and convergences are discussed.