Considering the landing gear's R/E hydraulic system is nonlinear in nature, identifying and isolating its defects is not straightforward. Using the power bond graph (BG), analytical redundancy relations (ARRs) are derived based on the fundamental principle of energy conservation. Boolean logic variables are then introduced to describe the operating state of the system, and finally, global analytic redundancy relations (GARRs) are produced. It is given the corresponding residuals from the GARRs and mapped to the fault signature matrix (FSM) for the purpose of assessing its detectability and isolation. Different progressive types of deficiencies have been studied, including filter blockage, actuator leaks, and landing gear selector valve reversing stuck. The residuals against threshold range results for the injected faults calculated in MATLAB/Simulink showed that this method can considerably detect the faults. In complex nonlinear systems, such as landing gear R/E hydraulic systems, the research methodology can be used to detect faults and monitoring of statuses.