42 Characterising Randomness in Human Actions on Civil Engineering Structures 419 Time [s] 2.0 2.5 3.0 3.5 4.0 2.5 2.0 1.5 1.0 0.0 0.5 −0.5 Force / W Impulse CTi 2.0 a b 1.6 1.2 0.8 0.4 Force / W 0.0 3.0 5.0 Time [s] 4.0 2.0 Ti Ti Fig. 42.2 Ground reaction force waveforms measured whilst (a) walking and (b) jumping All data analysed in this paper are related to the vertical component of the force. The CoV is used as a key measure of the parameter randomness in each time history. 42.4 Randomness of Key Parameters 42.4.1 Walking Figure 42.3 shows the average and CoV parameters for step length as functions of treadmill (i.e. walking) speed. The figure demonstrates that the average step length increases with increase in walking speed (Fig. 42.3a). The mean and mean ˙one standard deviation (STD) lines are also shown in the figure, indicating that the STD does not change significantly across the studied population of test subjects. Figure 42.3b demonstrates that the CoV ranges between 1 and 5 %, with minimum variation achieved at the boundary between the normal (solid circles) and fast (crosses) walking speeds (1.6–1.8 m/s). While the probability distribution of the average step length (and averages of other parameters of interest) within a population of structural users is often available in literature [11–13], the detailed information regarding the intra-subject variability (i.e. CoV) is not frequently available. This is the reason that the CoV of different parameters is the main focus of this paper. The CoV of pacing frequency is shown in Fig. 42.4a. This is very similar to the CoV for step length, due to mutual dependence of the two parameters (the product between the pacing rate and the step length represents the walking speed). A much larger value of CoV (up to 40 %) is seen for the step width (Fig. 42.4b). Variation in this parameter is relatively independent from the walking speed. The CoV of three angular parameters (angle of attack, end-of-step angle and trunk angle) were also monitored during the experiments and they exhibited low variation (up to 2.3 %) [10]. 42.4.2 Jumping Figure 42.5a shows that the randomness in the frequency whilst jumping is larger than when walking (Fig. 42.4a), and therefore maintaining the cycle consistency is more difficult for the activity of jumping. The CoV values for the contact ratios (Fig. 42.5b) and the normalised impulse values (Fig. 42.5c) are in a similar range (up to 8 %). More detailed characterisation of the jumping action is available elsewhere [8]. All the data presented in this section could be used to develop and calibrate the models for humans walking and jumping, as well as develop an understanding of the level of variability in the parameters of interest frequently used to describe human actions.
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