Damage identification through regularization method. I: Theory

This paper presents a solution procedure for damage identification through measured structural response. The cost functional employed is based on the regulation method for inverse problems. An optimization procedure using the Euler-Lagrange equation is developed to reduce the minimization problem to a two-point boundary value problem (TPBVP) with jump discontinuities. Compared to existing techniques in solving the minimization problem, this approach does not resolve to more advanced mathematical tools and is thus more easily accepted in the engineering application field. Numerical studies of 2-DOF and 10-DOF shear beam-type structures and experimental correlation with a three-story model structure demonstrate the feasibility and accuracy of the proposed approach and are reported in a companion paper.