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Switching detection and active mode recognition in Hybrid Dynamical Systems (HDS) with nonlinear continuous dynamics are considered in this paper. The nonlinear modes are represented by Takagi-Sugeno models. Two methods based on projection techniques are proposed to generate a bank of residuals which are mode indicators: the first one is the well-known parity space method which uses the TS model parameters, the second one is a data-based projection method that does not need the parameter values of the TS model. Robustness of the two methods against parameter uncertainties is discussed. An illustrative example is provided to show the effectiveness of the proposed methods.