1. A fault detection system for detecting a fault in a process system, comprising: a first circuit configured to modify an input of the process system with a periodic modifying signal, wherein the first circuit is part of an extremum seeking controller and wherein the periodic modifying signal applied to the input of the process system comprises a dither signal applied to the input for probing for a performance gradient used by the extremum seeking controller to optimize the process system; and a second circuit configured to receive an output from the process system and to compare a signal component from the output of the process system to a function of the dither signal and to determine whether a fault exists based on at least one of a detected reduction of the signal component and an unexpected transformation of the signal component; wherein the second circuit is configured to provide an output signal indicative of the presence of the fault to at least one of a computerized system, a memory device, a communications device, and an electronic display.