Fourier Series Approximation of Vertical Walking Force-Time History through Frequentist and Bayesian Inference

Abstract

The increased ambition of architects coupled with advancements in structural materials, as well as the rapidly increasing pressure on civil engineering sector to reduce embodied carbon, have resulted in longer spans and more slender pedestrian structures. These structures often have one or more low natural frequencies in the range of human walking accompanied with low modal masses and damping ratios. Thus, they are prone to excessive and often resonant vibrations that may compromise the serviceability limit state. Principally the uncertainty in prediction of the vibration serviceability limit state mainly originates from unreliable estimates of pedestrian loading. The key rationale behind this situation is the limited mathematical characterisation featuring in current design codes and guidelines pertinent to pedestrian-induced loading. The Fourier approximation is typically used to describe individual walking forces. Historically, such models are based on limited experimental data and deterministic mathematical descriptions. Current industry used load models featured in design codes and guidelines have been shown to incorporate inherent bias through limited intra-subject variation and poor correlation with real walking loads. This paper presents an improved Fourier model of vertical walking force across multiple harmonics, presented in a Bayesian and Frequentist statistical parameterisation. They are derived using the most comprehensive dataset to date, comprising of over ten hours of continuous vertical walking force signals. Dissimilar to previous Fourier models, the proposed models attempt to encapsulate the surround energy leakage around harmonic integers with a singular value. The proposed models provide consistently lower force amplitudes than any previous model and is shown to be more representative of real walking. The proposed model provides a closer approximation of a structural acceleration than any other similar Fourier-based model. The proposed model provides further evidence to combine the so called high and low frequency load models.