Optimal Zonotopic Kalman Filter-based State Estimation and Fault-diagnosis Algorithm for Linear Discrete-time System with Time Delay

To manage the state estimation and fault-diagnosis problem of linear discrete uncertain systems with time delay, a state estimation and fault-diagnosis algorithm based on an improved zonotopic Kalman filter is proposed under the assumption that the process interference and measurement noise of the systems are unknown but bounded. First, zonotopes are used to contain the nonzero initial conditions of the system with time delay, and an optimal zonotopic Kalman filter is designed by using an iterative replacement method to determine the relationship between the current time and the delayed time. Subsequently, the optimal observer gain of the optimal zonotopic Kalman filter is designed by minimizing the size of the zonotopic sets to estimate the state sets. Next, the fault occurrence is detected by determining whether the true output value of the system is within the upper and lower bounds of the estimated output value, and the fault identification process is completed by the matching probability of the fault type. Finally, the fault-diagnosis of a numerical system, and the pitch system of a wind turbine are used as examples to demonstrate the effectiveness and feasibility of the proposed method for systems with time delay by analyzing the fault diagnosis results. A comparison with a normal fault-matching method indicates that the proposed fault-diagnosis algorithm is more rapid in fault identification.