Statistical modelling of spatiotemporal variability of overground walking


The need to construct efficient yet economical public structures has over the years coerced researchers into investigating every aspect of various materials used, possible load combinations and even the effects of weather variations. In the field of civil engineering, researchers have embarked on intense research activity focused on characterizing the human walking loading, both experimentally and analytically. Contemporary models of walking loads are generally based on treadmill tests (i.e. treadmill walking). At present, the latter have evolved from deterministic periodic approaches to more sophisticated statistical formulations. These newer models include both the pedestrian-to-pedestrian and the step-to-step variability; in other words are referred to as inter- and intra-pedestrian variability, respectively. Suitable models of human walking loads are essential to check the vibration serviceability of lively structures under walking-induced excitation, particularly in the case of footbridges and long-span floors. For the case of the treadmill tests, a limitation in terms of variability of the pedestrian speed presents itself with regard to the real single-pedestrian walking (overground walking) format.

As a consequence of these potential discrepancies between treadmill and overground walking, the dynamic response of structures computed on the basis of treadmill walking data can differ from that corresponding to overground walking. Therefore, it is imperative that these discrepancies be thoroughly addressed. In this context, a research pair from the Department of Construction and Manufacturing Engineering, University of Oviedo, Gijón, Spain: Professor Marta García-Diéguez and Professor José Luis Zapico-Valle developed an innovative model describing the evolution of the spatiotemporal variables of unrestricted overground human walking. They aspired to compare the characteristic responses of low-frequency footbridges under both overground and treadmill walking excitations and establish some practical recommendations to obtain the characteristic response of low-frequency footbridges under single-pedestrian loading. Their work is currently published in the research journal, Mechanical Systems and Signal Processing.

The research approach and modeling technique employed by the two scholars was split into two: first, a statistical model reproducing the intra-pedestrian variability of the step speed was inferred and calibrated from experimental overground data. Secondly, a previously developed model by the same team was modified and combined with the first model so as to reproduce the variability of the step interval of overground walking.

The authors reported that based on the extensive database of simulated footbridge responses to single-pedestrian excitation, the treadmill models slightly overestimated the response of footbridges with natural frequencies within a certain range. The reported response was seen to depend on the footbridge length and corresponded to the central part of the inter-pedestrian distribution of walking frequencies considered in the simulations. Outside this range, i.e. in the tails of the walking frequency distribution, the response is underestimated up to 24%.

In summary, the study established that the variability of the walking speed in treadmills with a nominal length around 1m and conducted at constant speed was practically negligible when compared with that of free overground walking. In an interview with Advances in Engineering, Professor Marta García-Diéguez pointed out that their model presents an alternative to the contemporary related ones that are generally based on treadmill walking data. Overall, the results obtained from their study were in the form of characteristic response spectra and could be used to developed loadings for various structural systems i.e. footbridges and long span floors.


M. García-Diéguez, J.L. Zapico-Valle. Statistical modelling of spatiotemporal variability of overground walking. Mechanical Systems and Signal Processing, volume 129 (2019) page 186–200.

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