Fault diagnosis of a certain class of hybrid systems referred to as structurally reconfigurable (SR) systems is complicated. This is because SR systems tend to switch their configuration, which may or may not be faulty. It is important to identify the mode of the SR system along with the corresponding fault if any, in order to facilitate a fault tolerant action. This paper combines discrete fault diagnosis with mode identification for SR systems to achieve two main objectives: Sensor selection for fault detection, isolation and mode identification, and residual selection for mode identification. The framework is built using a structural analysis-based approach to meet these objectives. This framework is demonstrated for a 10-speed Automatic Transmission, which is an illustrative example of SR systems.