In recent years, robust fault diagnosis of nonlinear systems has received much more attention due to the universal existence of nonlinearities and model uncertainties in practice. By introducing a new adaptive law and sliding mode observers with boundary layer control into Polycarpou's online approximator, we propose a fast and robust fault diagnosis strategy for a class of nonlinear systems in this article. The robustness and stability are proved theoretically by the Lyapunov method and the detectability conditions as well as the upper bound of detection time are given, which demonstrate that the detection time of our strategy is much shorter than that of Polycarpou's approach. Simulation results on the three-tank system "DTS200" show the effectiveness and fastness of the proposed strategy.