Second order perturbation with BFGS optimization for damage detection of fixed-fixed beam

A generic method is formulated to estimate damage location and extent from the explicit perturbation terms of eigenparameters. Specific permutation numbers and generalized Kronecker delta functions are composed. Stiffness parameters are estimated from these equations, inversely, using BFGS optimization. The algorithm is iterative, and it terminates under certain criteria. A fixed-fixed beam with even elements is used as test structure to investigate the applicability of the developed approach. In six elements beam, second order algorithm converges faster to 1% d-norm for small percentage damage. Meanwhile, first order algorithm converges faster for medium percentage damage. Both first and second order algorithms are nearly the same for large percentage damage. In all percentage damages, second order algorithm converges faster to the minimum percentage error vectors. For eight elements large percentage damage and ten elements small percentage damage, second order algorithm converges faster to their termination criteria.