Identification of Stiffness, Damping and Biological Force of SMD Model for Human Walking

Abstract

This paper proposes an iterative identification approach to extract the stiffness, damping and coefficients of biological force of a spring-mass-damper (SMD) model for human beings in walking. Gait experiment records from 73 test subjects were used for the identification. The three-dimensional motion capture technology was adopted in the walking tests. Thirty-nine reflective markers were attached to each test subject during the test and the trajectories of each marker were monitored by motion capture system. The displacement, velocity and acceleration of center-of-mass of a subject in each test case were then obtained by the system. Assume that the biological force can be expressed by Fourier series, the parameters, including stiffness and damping of SMD model and coefficients of biological force, are identified by the following two steps. Step 1, initial guesses of damping ratio and natural frequency of SMD are introduced into the equation of motion to identify the coefficients of the first several orders of Fourier series and a new stiffness parameter. Step 2, acceleration resonance assumption is adopted to determine a new damping ratio parameter. Replace the conjectured/identified values in the previous step with the new values and repeat the above two steps until presumed convergence criteria is satisfied. The identified mean value of damping ratio and natural frequency of SMD slightly increase with the increase of walking frequency. The identified damping ratios are found larger than published values for people in standing posture.