A second order damage detection method is developed by expanding the original eigenparameters using their sensitivity terms with the variations in the structural variants. This vibration-based polynomial method is generated from eigenvalue re-analysis in conjunction with the polynomial algorithm. By incorporating basic forms of the Lagrange factor functions, numerical eigenparameter functions are generalized to multi-variate polynomial interpolated forms. Second order sensitivity terms are computed by differentiating these multi-variate eigenparameter functions with respect to the structural variants. Convergence of different order algorithms are compared using finite element model of a four element cantilever beam structure under various damaged percentage cases. Moreover, finite element model of a four bay modular space truss is established. Damage detections from small to large percentages are carried out through numerical simulations on the space truss. Most of these cases converge efficiently toward the ultimate solutions within 1% termination level. Therefore the BFGS algorithm works well with the nonlinear multi-variate system equations. The algorithm operates robustly with limited number of d.o.f.s in the reduced order model and limited number of vibration modes in the full model.

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