This paper deals with the problem of fault identification in a system. The system is originally modeled by a Petri net, called a nominal (fault-free) net, and faults are considered as unobservable transitions not contained in the nominal net. It is assumed that partial places of the nominal net are observable and the output of the system is defined as an observed evolution, i.e., a sequence involving transitions and markings of the observable places. When faults occur, the observed evolution cannot be generated by the nominal net. We provide an approach that identifies unobservable transitions by constructing and solving an Integer Linear Programming problem according to the observed evolution and the nominal net. A faulty net is obtained by adding the identified unobservable transitions to the nominal one such that it coincides with the observed evolution. In addition, two methods to ensure acyclicity of the identified subnet, i.e., a net that includes unobservable transitions only, are reported. (C) 2018 Elsevier Ltd. All rights reserved.