Title: Modelling the nonlinear oscillations due to vertical bouncing using a multi-scale restoring force system identification method

Authors: Yuzhu Guo; Lingzhong Guo; Vitomir Racic; Shu Wang; S.A. Billings

Addresses: Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK; School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100191 China; INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Sheffield, S1 3JD, UK ' Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK; INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Sheffield, S1 3JD, UK ' INSIGNEO Institute for in Silico Medicine, The University of Sheffield, Sheffield, S1 3JD, UK; Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, S1 3JD, UK; Department of Civil and Environmental Engineering, Politecnico di Milanok, Milan, Italy ' Department of Civil and Structural Engineering, The University of Sheffield, Sheffield, S1 3JD, UK ' Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK; INSIGNEO Institute for in Silico Medicine The University of Sheffield, Sheffield, S1 3JD, UK

Abstract: 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.

Keywords: iOFR; iterative orthogonal forward regression; RFS; restoring force surface method; multi-scale; radial basis function; hybrid model.

DOI: 10.1504/IJSISE.2018.090607

International Journal of Signal and Imaging Systems Engineering, 2018 Vol.11 No.1, pp.52 - 64

Received: 09 Mar 2017
Accepted: 11 Oct 2017
Published online: 23 Mar 2018 *