Nonlinear system modeling and fault detection method using set membership estimation and T-S fuzzy model

A modeling method is proposed and applied in fault detection for nonlinear dynamical systems with unknown but bounded noises. Since the Takagi-Sugeno (T-S) fuzzy model is a universal approximator, it is used to model the nonlinear dynamical system when the system runs without a fault. After some input and output data of the system are obtained, the input space is partitioned using a fuzzy clustering algorithm. Assuming that the system noise and approximation error are unknown but bounded, the consequence parameters of the T-S fuzzy model of the system are determined by means of a linear-in-parameter set membership estimation algorithm. An interval containing the actual output of the system running without a fault can be easily predicted based on the result of the estimation. If the measured output is out of the predicted interval, it can be determined that a fault has occurred. Simulation results show the effectiveness of the proposed method.