This paper proposes a left invertible cascade nonlinear system structure with a dynamic inversion based input reconstruction laws, forming a novel model-based actuator fault detection and isolation (FDI) algorithm. Actuator is viewed as subsystem connected with the process subsystem in series, thus identifying actuator faults with advancing FDI algorithm in the subsystem whose outputs are assumed unmeasured. The left invertibility of individual subsystem is required for ensuring faults occurred in actuator subsystem can be transmitted to the process subsystem uniquely, and for reconstructing process inputs, also actuator outputs, from measured process outputs. Effectiveness of the proposed approach is demonstrated on an intensified HEX reactor developed by the Laboratoire de Génie Chimique (LGC -Toulouse, France).