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.
