Parameter identification of spring-mass-damper model for bouncing people

Abstract

Bouncing, which refers to the up-and-down movement of the human body with both feet remaining on the ground, is one of the most common human-induced dynamic loads for civil structures such as sports stadiums and concert halls. Although researchers have focused on the modeling of bouncing-induced loads, studies on the excitation source (the bouncing person) have not gained much attention. The spring-mass-damper model with a pair of internal biomechanical forces is the simplest model to represent a bouncing person. The model parameters, such as stiffness and damping, though very important for application and for HSI (Human Structure Interaction) analysis, have been rarely reported. This study utilized the particle filter (a step-by-step system identification method) to identify human SMD (Spring-Mass-Damper) model parameters from measured bouncing forces obtained by a wireless insole system. A total of 173 continuous bouncing force signals were recorded and divided into 6800 bouncing cycles, from which the SMD model parameters were identified. The results indicated that human natural frequency and high-order biomechanical load factors have a linear trend against the bouncing frequency, while the damping ratio and first-order BLF (Biomechanical Load Factor) share a parabolic relation. For each model parameter, a skew normal distribution was fitted, and the fitting parameters were found to be dependent on the bouncing frequency range. The influence of HSI on the model parameters was also experimentally investigated, indicating that a vibrating surface leads to a lower human natural frequency and a higher damping ratio value.