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In this paper, an extension to rules-based fault detection is demonstrated utilizing properties of the Koopman operator. The Koopman operator is aninfinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics. The definition of the Koopman operator enables algorithms thatcan evaluate the magnitude and coincidence of time-series data. Using spectral properties of this operator, diagnostic rule signals generated from buildingmanagement system (BMS) trend data can be decomposed into components that allow the capture of device behavior at varying time-scales and to agranular level. As it relates to the implementation of fault detection (FDD), this approach creates additional spatial and temporal characterizations ofrule signals providing additional data structure and increasing effectiveness with which classification techniques can be applied to the analysis process. Theapproach permits a knowledge base to be applied in a similar manner to that of a rules-based approach, but the introduced extensions also facilitate thedefinition of new kinds of diagnostics and overall provide increased analysis potential.