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One of the most significant systems that can be expressed by partial differential equations (PDEs) is the transmission pipeline system. To avoid the accidents that originated from oil and gas pipeline leakage, the exact location and quantity of leakage are required to be recognized. The designed goal is a leakage diagnosis based on the system model and the use of real data provided by transmission line systems. Nonlinear equations of the system have been extracted employing continuity and momentum equations. In this paper, the extended Kalman filter (EKF) is used to detect and locate the leakage and to attenuate the negative effects of measurement and process noises. Besides, a robust extended Kalman filter (REKF) is applied to compensate for the effect of parameter uncertainty. The quantity and the location of the occurred leakage are estimated along the pipeline. Simulation results show that REKF has better estimations of the leak and its location as compared with that of EKF. This filter is robust against process noise, measurement noise, parameter uncertainties, and guarantees a higher limit for the covariance of state estimation error as well. It is remarkable that simulation results are evaluated by OLGA software.

The purpose of this paper is to provide a robust solution for fault detection in the induction motor. The structure of nonlinear unknown input observer is investigated for observer design in this paper. Recently, rotor defect is considered as the most important non-electric fault in induction motors. One of the challenges in rotor fault detection is the uncertainty in the mechanical load of the motor and the harmonics in the electric power. Accordingly, these cases are considered as disturbances for unknown input observer and their effects on the residual signal are eliminated. The results of the simulation show the performance of the observer to diagnose the induction motor rotor fault in different scenarios.