An algorithm for diagnosing structural systems for damage from static response is developed based on a system identification method with an adaptive parameter grouping scheme. The developed algorithm can be used as a diagnostic technique to aid in decisions of repair and rehabilitation of existing structures. Damage is characterized by a reduction in a constitutive property of a parameterized finite element model between two time separated inferences. A data perturbation scheme is proposed both for the baseline structure to establish the damage threshold above which damage can be confidently discerned from noise and for the damaged structure to compute the damage indices. To examine and illustrate the developed algorithm, a numerical simulation study on a planar truss structure is performed.