At the era of big data, industrial plants generate significant scale of data which contain plenty information of operation. Data-driven approach is becoming increasingly popular in the research of fault diagnosis. In this paper, a novel data-driven fault detection approach named implicit model approach (IMA) is proposed for typical nonlinear system. This approach is inspired by the subspace relevant method which is widely applied in system identification. Residual estimator, which is the key for fault detection, is generated by subspace relevant method in IMA without any prior knowledge of system. Nonlinear system in this paper is formulated with Takagi-Sugeno (T-S) fuzzy model. Every subsystem of T-S fuzzy model is presented as linear timeinvariant model. IMA is used to obtain sub-residual estimator for each subsystem. The overall residual estimator is constructed with a kind of method named parallel distributed compensation (PDC), based on which the fault detection algorithm for typical nonlinear system is generated. The proposed algorithm is validated on a simulating platform of a compact reactor. The simulated results show that the algorithm based on IMA is effective for fault detection of the typical nonlinear system in nuclear plant.