An annular pulsed detonation combustor (PDC) basically consists of a number of detonation tubes which are firing in a predetermined sequence into a common downstream annular plenum. Fluctuating initial conditions and fluctuating environmental parameters strongly affect the detonation. Operating such a setup without misfiring is delicate. Misfiring of individual combustion tubes will significantly lower performance or even stop the engine. Hence, an operation of such an engine requires a misfiring detection. Here, a supervised data driven machine learning approach is used for the misfiring detection. The features used as inputs for the classifier are extracted from measurements incorporating physical knowledge about the given setup. To this end, a neural network is trained based on labeled data which is then used for classification purposes, i.e., misfiring detection. A surrogate, nonreacting experimental setup is considered in order to develop and test these methods.