Most of the fault identification problems in the discrete event systems literature assume knowledge of the structure of the net system, including the nature (and behavior) of the possible faults. In this paper we deal with this problem within the framework of Petri nets by removing the requirement that the nature (and behavior) of the fault is known. In particular, we devise a way to identify the structure of the faulty transitions of the system given its language. Then, we generalize this procedure to unobservable faults, in which case the structure of the faulty system needs to be recognized from the knowledge of the structure of the fault-free system, and the projection of the faulty system language on the set of non-faulty events, that are assumed to be observable.