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Adaptive weighting input estimation for nonlinear systems

This work determines the time-varying load, called input, in a nonlinear system using a novel input estimation inverse algorithm. The algorithm employs the linearised Kalman filter (LKF) with a recursive estimator to determine shocks. The LKF generates the residual innovation sequences, and the estimator uses the residual innovation sequences to evaluate the magnitudes and, therefore, the onset time histories of the shocks. Based on this regression equation, a recursive least-squares estimator weighting by an adaptive fading factor is used to estimate on-line the shocks involving measurement noise and modelling errors. Numerical simulations of a nonlinear system, Duffing's equation, demonstrate the accuracy of the proposed method, adaptive weighting input estimation. Simulation results show that the proposed method improves the accuracy, efficiency and robustness of the conventional input estimation approach.