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Abstract: Motivated by the existing models of wind and earthquake loading, speech recognition techniques and a method of replicating electrocardiogram (ECG) signals, this paper presents a mathematical model to generate synthetic narrow band lateral force signals due to individuals walking. The model is fitted to a database comprising many directly measured walking time series, yielding a random approach to generating their artificial – yet realistic counterparts. This multi-disciplinary modelling strategy offers a radical departure from traditional Fourier-based representations of lateral walking loads towards more reliable and more realistic vibration serviceability assessment of footbridges. [Copyright &y& Elsevier]

Abstract: A mathematical model has been developed to generate stochastic synthetic vertical force signals induced by a single person jumping. The model is based on a unique database of experimentally measured individual jumping loads which has the most extensive range of possible jumping frequencies. The ability to replicate many of the temporal and spectral features of real jumping loads gives this model a definite advantage over the conventional half-sine models coupled with Fourier series analysis. This includes modelling of the omnipresent lack of symmetry of individual jumping pulses and jump-by-jump variations in amplitudes and timing. The model therefore belongs to a new generation of synthetic narrow band jumping loads which simulate reality better. The proposed mathematical concept for characterisation of near-periodic jumping pulses may be utilised in vibration serviceability assessment of civil engineering assembly structures, such as grandstands, spectator galleries, footbridges and concert or gym floors, to estimate more realistically dynamic structural response due to people jumping. [ABSTRACT FROM AUTHOR]

Abstract: A mathematical modelling procedure has been developed to generate synthetic vertical force signals induced by a single person jumping. The ability to replicate much of the temporal and spectral features of real jumping loads give this model a definite advantage over the conventional half-sine models coupled with Fourier series analysis. This includes modelling of the omnipresent lack of symmetry of individual jumping pulses and jump-by-jump variations in amplitudes and timing. The model therefore belongs to a new generation of synthetic narrowband jumping loads that simulate reality better. The proposed mathematical concept for characterisation of irregular jumping pulses may be utilised in vibration serviceability assessment of civil engineering assembly structures, such as grandstands, footbridges and concert or gym floors, to estimate realistic dynamic structural response due to people jumping. [Copyright &y& Elsevier]

• Stochastic model of near-periodic walking force signals. • Variable walking speed on the step-by-step basis. • DLFs described as products of deterministic and random factors functions of speed. • Numerical simulations demonstrated a reliable performance of the model. • Neglecting intra-pedestrian DLF variability yields errors up to 22% in responses. This study presents a stochastic model of near-periodic walking force signals featuring variable walking speed on the step-by-step basis as the key input modelling parameter. This is a notable departure from traditional deterministic and periodic Fourier series models where the key modelling parameter is the average pacing rate in a walking trial. Walking speed instead of pacing rate is a more natural choice since human nervous system adopts speed of successive steps to the surrounding environment, including vibrations of the supporting structure. Starting from the previously developed models of variable walking speed and spatiotemporal parameters in a walking trial, this study derived a complementary model of variable dynamic loading factors (DLFs) corresponding to the first five dominant harmonics and subharmonics of the walking force. Both the mean and coefficient of variation of DLFs are described as the products of two factors. The first represents the deterministic dependence on the step speed and is modelled as a second-order polynomial. The second factor reproduces the random inter-pedestrian variability of the DLFs which is defined by a Beta distribution. Extensive vibration simulations of virtual footbridges due to measured and simulated walking forces showed a reliable performance of the model. Moreover, the results provided a strong evidence that the step-by-step variability of gait in a single-pedestrian walking trial yields up to 22% relative error in the simulated vibration response. [ABSTRACT FROM AUTHOR]

The key UK design guidelines published by the Concrete Society and Concrete Centre for single human walking excitation of high-frequency floors were introduced more than 10 years ago. The corresponding walking force model is derived using a set of single footfalls recorded on a force plate and it features a deterministic approach which contradicts the stochastic nature of human-induced loading, including intra- and inter- subject variability. This paper presents an improved version of this force model for high-frequency floors with statistically defined parameters derived using a comprehensive database of walking force time histories, comprising multiple successive footfalls that are continuously measured on an instrumented treadmill. The improved model enables probability-based prediction of vibration levels for any probability of non-exceedance, while the existing model allows for vibration prediction related to 75% probability of non-exceedance for design purposes. Moreover, the improved model shifts the suggested cut-off frequency between low- and high-frequency floors from 10 Hz to 14 Hz. This is to account for higher force harmonics that can still induce the resonant vibration response and to avoid possible significant amplification of the vibration response due to the near-resonance effect. Minor effects of near-resonance are taken into account by a damping factor. The performance of the existing and the improved models is compared against numerical simulations carried out using a finite element model of a structure and the treadmill forces. The results show that while the existing model tends to overestimate or underestimate the vibration levels depending on the pacing rate, the new model provides statistically reliable estimations of the vibration responses. Hence, it can be adopted in a new generation of the design guidelines featuring a probabilistic approach to vibration serviceability assessment of high-frequency floors. [ABSTRACT FROM AUTHOR]

The increasing number of reported vibration serviceability problems in newly built pedestrian structures, such as footbridges and floors, under walking load has attracted considerable attention in the civil engineering community over the past two decades. The key design challenges are: the inter- and intra-subject variability of walking people, the unknown mechanisms of their interaction with the vibrating walking surfaces and the synchronisation between individuals in a group. Ignoring all or some of these factors makes the current design methods an inconsistent approximation of reality. This often leads to considerable over- or under-estimation of the structural response, yielding an unreliable assessment of vibration performance. Changes to the dynamic properties of an empty structure due to the presence of stationary people have been studied extensively over the past two decades. The understanding of the similar effect of walking people on laterally swaying bridges has improved tremendously in the past decade, due to considerable research prompted by the Millennium Bridge problem. However, there is currently a gap in knowledge about how moving pedestrians affect the dynamic properties of vertically vibrating structures. The key reason for this gap is the scarcity of credible experimental data pertinent to moving pedestrians on vertically vibrating structures, especially for multi-pedestrian traffic. This paper addresses this problem by studying the dynamic properties of the combined human-structure system, i.e. occupied structure damping ratio, natural frequency and modal mass. This was achieved using a comprehensive set of frequency response function records, measured on a full-scale test structure, which was occupied by various numbers of moving pedestrians under different walking scenarios. Contrary to expectations, it was found that the natural frequency of the joint moving human-structure system was higher than that of the empty structure, while it was lower when the same people were standing still. The damping ratio of the joint human-structure system was considerably higher than that of the empty structure for both the walking and standing people – in agreement with previous reports for stationary people - and was more prominent for larger groups. Interestingly, it was found that the walking human-structure system has more damping compared with the equivalent standing human-structure system. The properties of a single degree of freedom mass-spring-damper system representing a moving crowd needed to replicate these observations have been identified. [ABSTRACT FROM AUTHOR]