Modelling the Nonlinear Oscillations Due to Vertical Bouncing Using a Multi-Scale Restoring Force System Identification Method

Human vertical bouncing motion is studied using a system identification method. A multi-scale mathematical model is identified directly from real experimental data to characterise the nonlinear oscillation associated with the vertical bouncing. A new method which combines the restoring force surface (RFS) method and the iterative orthogonal forward regression (iOFR) algorithm is proposed to determine the model structure and estimate the associated parameters. Two types of sub-models are used to study the nonlinear oscillations in different scales. Results show that the model predicted outputs provide excellent predictions of the experimental data and the models are capable of reproducing the nonlinear oscillations in both time and frequency domain.