Evaluation of aging infrastructure has been a world-wide concern for decades due to its economic, ecological and societal importance. Existing structures usually have large amounts of unknown reserve capacity that may be evaluated though structural identification in order to avoid unnecessary expenses related to the repair, retrofit and replacement. However, current structural identification techniques that take advantage of measurement data to infer unknown properties of physics-based models fail to provide robust strategies to accommodate systematic errors that are induced by model simplifications and omissions. In addition, behavior diagnosis is an ill-defined task that requires iterative acquisition of knowledge necessary for exploring possible model classes of behaviors. This aspect is also lacking in current structural identification frameworks. This paper proposes a new iterative framework for structural identification of complex aging structures based on model falsification and knowledge-based reasoning. This approach is suitable for ill-defined tasks such as structural identification where information is obtained gradually through data interpretation and in-situ inspection. The study of a full-scale existing bridge in Wayne, New Jersey (USA) confirms that this framework is able to support structural identification through combining engineering judgment with on-site measurements and is robust with respect to effects of systematic uncertainties. In addition, it is shown that the iterative structural-identification framework is able to explore the compatibility of several model classes by model-class falsification, thereby helping to provide robust diagnosis and prognosis.