Estimating Impulsive Loads in Duffing's Equation Using Two Methods

This work determines the time-varying impulsive loads, called inputs, in a nonlinear system using two novel input estimation inverse algorithms. Both algorithms use the extended Kalman filter with two different recursive estimators to determine impulsive loads. The extended Kalman filter generates the residual innovation sequences. The estimators use the residual innovation sequences to evaluate the magnitudes and, therefore, the onset time histories of the impulsive loads. Based on the two regression equations, a recursive least-squares estimator with a tunable fading factor is called a conventional input estimation with an adaptive weighting fading factor called an adaptive weighting input estimation. Both are used to estimate on-line inputs involving measurement noise and modeling errors. Numerical simulations of a nonlinear system, Duffing’s equation, demonstrate the accuracy of the proposed methods. Simulation results show that the proposed methods accurately estimate impulsive loads, and the AWIE approach has superior robust estimation capability than the CIE method in the nonlinear system.