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This paper presents a fault diagnosis method for process faults and sensor faults in a class of nonlinear uncertain systems. The fault detection and isolation architecture consists of a fault detection estimator and a bank of adaptive isolation estimators, each corresponding to a particular fault type. Adaptive thresholds for fault detection and isolation are presented. Fault detectability conditions characterizing the class of process faults and sensor faults that are detectable by the presented method are derived. A simulation example of robotic arm is used to illustrate the effectiveness of the fault diagnosis method.