In this paper, for the fault detection of a single-input single-output (SISO) system, we use chaotic oscillator to generate the excitation of the system under test (SUT), and use non-uniform method to reconstruct the phase space of the output time series. Directional Lyapunov exponent is defined around the equilibrium point in the phase space, and it is used to analyze the eigen-structure of the output phase space around its equilibrium point, thus the fault detection of the SISO system is realized. The simulation results show that parameter changes of the SUT will affect the phase space structure around its equilibrium point, and the directional Lyapunov exponent is sensitive to these changes.