Fault estimation based on ensemble unscented Kalman filter for a class of nonlinear systems with multiplicative fault

ABSTRACT

In this paper, a method for fault estimation with a multiplicative model in a nonlinear system by the unscented Kalman filter is introduced. The faults appear in the form of component, sensor, and actuator in the system equations. By using the augmented method, a fault signal will be as state variable of the system, the system dynamic equations are rewritten to represent a fault as a state variable. The existence of nonlinear equations in the presence of system noises results in an identical non-Gaussian noise, which leads to the difficulty in solving the problem of fault estimation with the unscented Kalman filter. Therefore, a filter combining a Gaussian mixture model (GMM) and the augmented ensemble unscented Kalman filter (AEnUKF) is designed to estimate the fault in this class of nonlinear systems. Suitable conditions and assumptions are appointed to guarantee the convergence of the estimation error. Next, the performance of the proposed method is evaluated by simulating a bioreactor system. The results of the simulation for the multiplicative fault estimation demonstrated performance by the AEnUKF-GMM algorithm better than the AUKF in the presence of non-Gaussian noise.

KEYWORDS:

• Fault estimation
• multiplicative fault
• non-Gaussian noise
• unscented Kalman filter
• augment
• Gaussian mixture model

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

Ali Asghar Sheydaeian Arani

Ali Asghar Sheydaeian Arani received the B.S. degree in Electrical Engineering from K. N. Toosi University of Technology in 2012 and M.Sc. degree in Control Engineering from the Malek Ashtar University of Technology, Tehran, Iran in 2015. In Sep 2015, He joined as a PhD student to Control and System of Science and Research Branch of Azad University of Tehran. His research interests include Fault Detection and Estimation, Nonlinear Control, Automation Control, Robotics.

Mahdi Aliyari Shoorehdeli

Mahdi Aliyari Shoorehdeli received his B.Sc. degree in Electronics Engineering, his M. Sc. degree and Ph.D. degree in Control Engineering from K. N. Toosi University of Technology, in 2001, 2003 and 2008, respectively. He is currently an Assistant Professor with the Department of Mechatronics Engineering, K. N. Toosi University of Technology, Tehran. He is the author of more than 150 papers in international journals and conference proceedings. His research interests include Fault Detection and Diagnosis, Intelligent Control of Mechatronic Systems, and Multi-Objective Optimization.

Ali Moarefianpour

Ali Moarefianpour is an assistant professor of the Electrical Engineering Department, Science and Research Branch, Islamic Azad University, Tehran, Iran. His research interests are Convex Optimization, Industrial Control, and Artificial Intelligence.

Mohammad Teshnehlab

Mohammad Teshnehlab is a professor at the Faculty of Electrical Engineering, K.N.Toosi University of Technology, Tehran, Iran. His research interests include Linear Control, Linear Control, Neural Networks Controller, Knowledge, and Expert Systems, Fuzzy Systems and Control, Evolutionary Optimization, Soft Computing (Neural-Fuzzy Networks, Genetic Algorithms), Advanced Artificial Intelligence.