A Reduced Stochastic Data-Driven Approach to Modelling and Generating Vertical Ground Reaction Forces During Running

Abstract

This work presents a time-domain approach for characterizing the Ground Reaction Forces (GRFs) exerted by a pedestrian during running. It is focused on the vertical component, but the methodology is adaptable to other components or activities. The approach is developed from a statistical perspective. It relies on experimentally measured force-time series obtained from a healthy male pedestrian at eight step frequencies ranging from 130 to 200 steps/min. These data are subsequently used to build a stochastic data-driven model. The model is composed of multivariate normal distributions which represent the step patterns of each foot independently, capturing potential disparities between them. Additional univariate normal distributions represent the step scaling and the aerial phase, the latter with both feet off the ground. A dimensionality reduction procedure is also implemented to retain the essential geometric features of the steps using a sufficient set of random variables. This approach accounts for the intrinsic variability of running gait by assuming normality in the variables, validated through state-of-the-art statistical tests (Henze-Zirkler and Shapiro-Wilk) and the Box-Cox transformation. It enables the generation of virtual GRFs using pseudo-random numbers from the normal distributions. Results demonstrate strong agreement between virtual and experimental data. The virtual time signals reproduce the stochastic behavior, and their frequency content is also captured with deviations below 4.5%, most of them below 2%. This confirms that the method effectively models the inherent stochastic nature of running human gait.