Motivated by the physical exchange of energy and its dissipation in electro-mechanical systems, we propose a new fault detection method based on data-driven dissipativity analysis. We first identify a dissipativity inequality using one or multiple shots of data obtained from a linear time-invariant system. This dissipativity inequality's storage and supply rate functions assume generic quadratic difference forms encompassing all LTI systems. By analysing the norm of the identified dissipative inequality as the residual function, we can detect the occurrence of faults in real-time without the need to model each fault the system is subjected to. Through academic examples, we demonstrate how we can identify supply rate and storage functions from persistently exciting data shots. We present a practical example of detecting faults on a two-degree-of-freedom planar manipulator with zero missed fault detection rate, which is compared to a standard PCA-based fault detection algorithm.