354 K. Van Nimmen et al. Fig. 44.1 The hollow-core pre-stressed concrete slab excited by a single pedestrian The experimental study considered a single pedestrian walking along the slab (see Fig. 44.1). The vertical acceleration response of the slab was recorded at 13 locations, uniformly distributed along its length. The pedestrian is instrumented with sensors allowing a 3D tracking of the motion. The registered pedestrian motion allows to identify the average step frequency and the onset of each step [6]. The location of the individual footsteps are identified from video processing (Fig. 44.1). The results show that the average step frequency of the pedestrian equals Qfs D1:98Hz. 44.3 Results The forces are estimated using a data set consisting of one displacement (nd;d D 1) and 13 acceleration measurements (nd;a D13. The noise covariance matrices Qand S used in the force identification are assumed to be zero as the force pŒk accounts for all excitation present. The matrix Rin this case accounts for sensor noise and is constructed from the (known) standard deviation of the measurement noise [4]. The initial state estimate vector xŒ0j 1 and its error covariance matrixPŒ0j 1 are both assumed zero. To verify the results of the joint input-state estimation algorithm, the estimated forces are ideally compared to the directly measured input force. Although direct measurements of the pedestrian load are not available in this case, a reasonable approximation of the real walking load is obtained using a generalized single-step load model characterized by the weight of the person and the identified pacing rate [6]. The average step frequency (Qfs D1:98Hz) and the onset of each step are identified from the tracked pedestrian motion [6]. The single-step walking load follows from previous research involving the same participant, whereby the ground reaction forces (GRFs) were measured directly by an instrumented split-belt treadmill [6]. The averaged vertical single-step walking load for a step frequency of 2.00 Hz was determined from more than 200 consecutive steps. The variations in amplitude of the single-step walking load resulting from small variations of the pacing rate (e.g. 1:98<fs <2:00Hz) are found to be negligible [7]. Moreover, the resulting forces and structural response are found to be much more sensitive to the timing of successive footfalls than to small variations in force amplitude or contact time of the single-step walking load [8]. Together, the averaged vertical single-step walking load (ps) and the identified onset of each step in time (tq), allow to reconstruct the force pq due to step q in time: pq.t/ D t tq ps t tq ; with .t/ D( 1 0 t tc 0 otherwise (44.1) with t [s] the general time of the experiment and tc the duration of contact between the foot and the supporting structure. Taking into account the identified location of each step and the mass-normalized mode shape, the modal load induced by the pedestrian is calculated. Figure 44.2 compares the numerically predicted modal load and individual foot traces with the results of the joint inputstate estimation algorithm. Both the comparison in time (Fig. 44.2a) and frequency domain (Fig. 44.2b) show a fairly good agreement between the numerical predictions and the vibration-based estimated input. The harmonics of the walking load can be clearly observed in the corresponding amplitude spectrum (see Fig. 44.2b).
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