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Fault diagnosis is crucial for ensuring the safe operation of complex engineering systems. Although discrete-event diagnosis methods are used extensively, they do not easily address parametric fault isolation in systems with complex continuous dynamics. This paper presents a novel event-based approach for diagnosis of abrupt parametric faults in continuous systems, based on a qualitative abstraction of measurement deviations from the nominal behavior. From a continuous model of the system, we systematically derive dynamic fault signatures expressed as event-based fault models, which are used, in turn, for designing an event-based diagnoser of the system and determining system diagnosability. The proposed approach is applied to a subset of the Advanced Diagnostics and Prognostics Testbed, which is representative of a spacecraft's electrical power system. We present experimental results from the actual testbed, as well as detailed simulation experiments that examine the performance of our diagnosis algorithms under different fault magnitudes and noise levels.