A damage detection technique based upon incompletely measured frequency response function is developed. Structure with damage can be understood as modified system and this fact is closely related to structure dynamic modification theory. Many trials to detect damage applying structure dynamics theory have been introduced, but it is thought that application to practical situation is limited. Actually conventional methods are effective to detect damage locations as long as the initial finite element model is accurate and the responses at all the degrees of freedom can be measured experimentally. But these two conditions are practically impossible to be met, with the exception of geometrically simple structures. This work suggests a damage detection method not utilizing an accurate analytical finite element model but based upon incompletely measured frequency responses, noting that the reduced dynamical system is an inverse of incompletely measured frequency responses. According to the work, it is seemed that the algorithm is very practical since only measured frequency responses are needed while other methods require exact analytic model. On the other hand if applying the work to a real structure, lots of experiment should be sacrificed. To relieve experimental load a method, substructure detection, is proposed. According to the substructure damage detection, as an inspection domain, substructure domains are considered instead of entire domain, thus experimental load can be drastically relieved. In addition, damage severity is treated in this paper since sometimes it is worthy of determine damage severity. To estimate the damage level measured responses
and damage model is utilized and then optimization algorithm is applied. Two test examples, including a structure with joints, are chosen to verify the method. From both numeric and test example, it is found that the proposed method can be an alternative to conventional damage detection methods.
