Data-driven modelling of vertical dynamic excitation of bridges induced by people running

• A unique database of continuously measured running force signals is established.
• Traditional Fourier series model failed to represent the measurements reliably.
• A novel model can replicate temporal and spectral features of actual running forces.
• The model can be used in vibration serviceability assessment of bridges.

With increasingly popular marathon events in urban environments, structural designers face a great deal of uncertainty when assessing dynamic performance of bridges occupied and dynamically excited by people running. While the dynamic loads induced by pedestrians walking have been intensively studied since the infamous lateral sway of the London Millennium Bridge in 2000, reliable and practical descriptions of running excitation are still very rare and limited. This interdisciplinary study has addressed the issue by bringing together a database of individual running force signals recorded by two state-of-the-art instrumented treadmills and two attempts to mathematically describe the measurements. The first modelling strategy is adopted from the available design guidelines for human walking excitation of structures, featuring perfectly periodic and deterministic characterisation of pedestrian forces presentable via Fourier series. This modelling approach proved to be inadequate for running loads due to the inherent near-periodic nature of the measured signals, a great inter-personal randomness of the dominant Fourier amplitudes and the lack of strong correlation between the amplitudes and running footfall rate. Hence, utilising the database established and motivated by the existing models of wind and earthquake loading, speech recognition techniques and a method of replicating electrocardiogram signals, this paper finally presents a numerical generator of random near-periodic running force signals which can reliably simulate the measurements. Such a model is an essential prerequisite for future quality models of dynamic loading induced by individuals, groups and crowds running under a wide range of conditions, such as perceptibly vibrating bridges and different combinations of visual, auditory and tactile cues.