In this work, a novel approach for the automated fault detection and diagnostics (AFDD) of building HVAC operation is introduced utilizing properties of the Koopman operator to extend the capabilities of rules-based FDD approaches. The Koopman operator is an infinite-dimensional, linear operator that captures nonlinear, finite dimensional dynamics. These mathematical aspects translate into algorithms which can effectively evaluate the magnitude and coincidence of data. Using properties of the operator, building management system (BMS) trend data can be decomposed into components which allow the capture of device-to-device interactions as well as device behavior at varying time-scales.