This paper is concerned with an innovative strategy that maps chronicles, that are timed discrete event models, to a k-dimensional Euclidean space via random projections. The proposed approach is a projection that takes into account both characteristics of events, namely event types, and temporal constraints of chronicles. This will lead to an unbounded convex polytope in the Euclidean space that contains all the possible instances of the corresponding chronicle. It allows to easily and efficiently compare chronicles. Such comparisons are useful in a fault diagnosis purpose to discriminate chronicles representing behaviors of dynamic processes. Examples and preliminary results are provided in this paper to introduce the proposed methodology.