Improving the modelling efficiency of Hammerstein system using Kalman filter and its parameters optimised using social mimic algorithm: Application to heating and cascade water tanks

Abstract

Identification of Hammerstein systems finds extensive applications in solving the stability and design issues of non-linear dynamic systems. Hence, in this paper, a first attempt is made to solve the parameter estimation problem of Hammerstein non-linear systems by using the evolutionary optimisation algorithm (EOA) coupled Kalman filter (KF). The standard KF produces the best possible optimal states for the particular state estimation problem based on its properly tuned parameters θ^0−, P0−, φ, Q and R termed as initial state, initial error covariance, state transition, process noise covariance and measurement noise covariance, respectively. These parameters must be concurrently tuned to achieve a stable filtering operation. The manual and existing adaptive tuning methods do not guarantee optimality, convergence and also require a large amount of data. Moreover, the adaptive methods tune only a few statistics (Q and R) simultaneously. To defeat these foreknown problems, in the proposed method, initially, a recently established EOA named social mimic optimisation (SMO) algorithm is employed to get the global optimised KF parameters along with an efficient cost function that has been derived based on the model output for the concurrent achievement of all the KF parameters. Finally, the standard KF technique identifies the estimated parameters of the Hammerstein model with those optimised KF parameters. Various numerical and experimental test results demonstrate that the proposed SMO-based KF approach offers high accuracy in estimating the parameters along with the good convergence speed compared to the standard KF, other presented EOA-based KF approaches and recently reported techniques.