A protocol is presented for the characterization of the in-field pedestrian behavior and the simulation of the resulting structural response. Field-tests demonstrate that the in situ identified pacing rate and synchronization rate among the participants constitute an essential input for the simulation and verification of the human-induced loads.
For slender and lightweight structures, vibration serviceability is a matter of growing concern, often constituting the critical design requirement. With designs governed by the dynamic performance under human-induced loads, a strong demand exists for the verification and refinement of currently available load models. The present contribution uses a 3D inertial motion tracking technique for the characterization of the in-field pedestrian behavior. The technique is first tested in laboratory experiments with simultaneous registration of the corresponding ground reaction forces. The experiments include walking persons as well as rhythmical human activities such as jumping and bobbing. It is shown that the registered motion allows for the identification of the time variant pacing rate of the activity. Together with the weight of the person and the application of generalized force models available in literature, the identified time-variant pacing rate allows to characterize the human-induced loads. In addition, time synchronization among the wireless motion trackers allows identifying the synchronization rate among the participants. Subsequently, the technique is used on a real footbridge where both the motion of the persons and the induced structural vibrations are registered. It is shown how the characterized in-field pedestrian behavior can be applied to simulate the induced structural response. It is demonstrated that the in situ identified pacing rate and synchronization rate constitute an essential input for the simulation and verification of the human-induced loads. The main potential applications of the proposed methodology are the estimation of human-structure interaction phenomena and the development of suitable models for the correlation among pedestrians in real traffic conditions.
Driven by the economic demand of efficiency and the increasing strength of (new) materials, architects and engineers are pushing the limits to build ever longer, taller and lighter structures. Typically, light and slender structures have one or more natural frequencies that lie within the dominant spectrum of common human activities such as walking, running or jumping. Likely to be subject to (near-)resonant excitation, they are often unduly responsive to human motion, resulting in disturbing or even harmful vibrations1. For these slender and lightweight structures, the vibration serviceability is a matter of growing concern, often constituting the critical design requirement.
The human motion and the resulting ground reaction forces (GRFs) are usually experimentally identified in laboratory conditions. Currently, designers are forced to rely on — what are assumed to be 'conservative' — equivalent load models, upscaled from single-person force measurements. With designs governed by the dynamic performance under high crowd densities, a strong demand exists for the verification and refinement of the currently available load models.
The present protocol employs a 3D inertial motion tracking technique for the characterization of the natural motion of pedestrians. It is shown how this information can be used to define the correlation among the pedestrians as well as the corresponding induced loads. In a subsequent step, the characterized pedestrian behavior is used to numerically simulate the induced structural response. Comparison with the registered structural response allows to quantify the effect of unaccounted human-structure interaction phenomena, e.g., the added damping due to the presence of the pedestrians. The methodology is illustrated for full-scale experiments on a real footbridge where the structural response and the motion of the participants are registered simultaneously.
All procedures were approved by the ethical committee of the university hospital of the KU Leuven and each subject gave a written informed consent prior to participation.
1. 3D Motion Tracking: Configuration and Data Acquisition
2. Force Plate: Setup and Configuration
Note: The present step discusses the application of a force plate to register the GRFs. In the case that a walking/running person is involved, a series of force plates or an instrumented treadmill is to be used to register the loading induced by subsequent steps3, the protocol itself is analogous.
3. Measurement of the Structural Accelerations
Note: The present steps aim to collect the structural vibrations at one or more relevant locations on the structure. The present application employs GeoSIG GMS recorders (Figure 3) to register the structural accelerations. Other sensor types with proper characteristics for the involved application, can be equally applied.
4. Experiments in a Controlled Laboratory Environment
5. Experiments In Situ
6. Data Analysis
7. Simulation and Analysis of the Structural Response
Note: The subsequent steps are performed using MATLAB7. The structural response is computed using the PediVib toolbox, a MATLAB toolbox developed by the authors8 (Figure 6): the human-induced forces are determined through application of the generalized load models of defined by Li et al.9 (walking) and Bachmann et al.1 (jumping, running and vandal loading), and the structural model is formulated in modal coordinates10. The accompanying manual includes tutorials that clearly illustrate the following steps.
First, it is shown how the accelerations registered near the CoM of the individuals can be used to characterize the consequent GRFs. The results are discussed here for a walking individual3. Fully comparable observations are made when rhythmical human activities, i.e., jumping and bobbing, are considered. Figure 7A and 7B show that the amplitude spectrum of the continuous vertical foot forces and the corresponding acceleration levels registered near the CoM of the pedestrian are qualitatively highly similar, i.e., in shape and frequency. The average pacing rate of the activity can be identified as the frequency of the first dominant peak in these spectra. Analysis of the registered GRFs and accelerations of the CoM shows that the same average pacing rate is in this way identified up to ±0.1%. Subsequently, the timing of nominally identical events is identified from the GRFs and the accelerations near the CoM, respectively. This procedure is illustrated in Figure 8 where the GRFs and the accelerations of the CoM are normalized to the weight of the person and gravity of Earth (g = 9.81 m/sec²), respectively. Analysis of the different trials shows that in this way, the period of each cycle and, thus, the time-variant pacing rate of the activity, can be identified from the accelerations of the person's CoM with a 95% confidence interval that is lower than 3% in comparison to the one as identified from the registered GRFs (see Table 1)3. Accounting in addition for the start time of the initial loading cycle, allows to compute the onset of all loading cycles.
Next, this information is applied to simulate the GRFs using the PediVib toolbox8. Figure 9 visualizes small quantitative and qualitative differences between the measured and simulated vertical single-step foot forces. These small dissimilarities are the result of applying a generalized single-step load model as defined in literature9 and could be minimized by applying the averaged vertical single-step foot force of the considered person for the corresponding walking speed. However, direct force measurements are generally not available for the persons involved in the experiments in situ. In addition, in comparison to small variations in the pacing rate, the sensitivity of the induced structural response to small variations in force amplitude or contact time can be considered neglegible3,11. Figure 9 also shows that the timing of the footsteps, and therefore, the time-variant pacing rate, is accurately identified from the registered motion of the pedestrian. Figure 10 presents the amplitude spectrum of the simulated and measured GRFs. In contrast to the perfectly periodic forces that are exclusively composed of the harmonics of the step frequency, the small variations in pacing rate result into a distribution of forces around the dominant harmonics12,13. By taking into account the identified variable pacing rate, these narrow band forces are also present in the simulated forces (Figure 10). Two scalar quantities are subsequently used to represent the similarity between the amplitude spectrum of the measured and the simulated forces : (1) the linear rank or correlation [-] which varies between 0 and 1 and for which 1 reflects a perfect correlation, and (2) the normalized 2-norm [%]:
The amplitude spectra are compared in the frequency range relevant for low-frequency civil structures (0-10 Hz). Figure 10 shows that a high correlation coefficient of more than 0.96 is found. Assuming the walking behavior to be perfectly periodic, results into a linear correlation of less than 0.5. The normalized 2-norm is approximately 20%, where this remaining discrepancy is primarily the result of applying a generalized single-step load model. For reference purposes it is noted that when the GRFs are simulated with the identified average single-step walking load, the correlation increases up to 0.99 and the corresponding 2-norm with respect to the actual registered forces decreases to less than 8 percent. In this way, analysis of the different trials shows that simulations based on the generalized load models and the identified time-variant pacing rate, allow for a good approximation of the imperfect real GRFs induced by the human motion.
In addition to the characterization of the individual induced loads, the time synchronization of the wireless motion trackers allows to analyze the synchronization rate among the participants. The synchronization rate [-] is defined as:
where Ts [sec] is the period of the activity and Δts [sec] is the time shift between the cycles of different participants. This synchronization rate is only relevant when comparable load cycles are involved. The time shifts Δts are therefore only considered for the cycles occurring within the relevant time window [t - ½Ts < t < t + ½Ts]. As a result, the synchronization rate can vary between zero and unity, whereby the latter depicts perfect synchronization. This procedure is illustrated for the experiments involving six pedestrians for which the same step frequency is imposed using a metronome (see Figure 5B). Figure 11A represents the identified onset of each loading cycle of every participant by a single vertical line. Coinciding lines, as observed during the first 40 sec, indicate a high rate of synchronization. Scattered lines, as observed between 50 and 60 sec of the considered trial, indicate a low rate or loss of synchronization among the participants. Similar observations can be made from Figure 11B presenting the corresponding synchronization rate and Figures 11C and 11D where the identified time-variant pacing rate is applied to simulate the induced vertical loads.
Finally, the protocol is applied to perform a detailed analysis of the vibrations induced by human activities on the Eeklo footbridge (see Figure 5). Figure 12 presents the modal characteristics of the first six modes of the structure. The experiments involve people walking3, jumping and bobbing with a pacing rate imposed by a metronome and targeted at the fundamental or second natural frequency. The response of the structure is registered using five triaxial sensors (see Figure 3 and 5B). Subsequently, the measured structural response is compared with the numerical simulations that account for the calibrated numerical model of the structure, the experimentally identified modal damping ratios and the characterized in-field pedestrian behavior.
First, the results are discussed for the experiments involving six pedestrians whose step frequency is chosen to match the first (fs = f1 = 1.71 Hz) and the second mode (fs = f2/2 = 1.49 Hz) of the structure. The pedestrians are arranged asymmetrically (all lined up one by one) or symmetrically (two by two) with respect to the longitudinal axis of the structure to maximize the excitation of the first and the second mode, respectively (see Figure 12). To illustrate the impact of the actual imperfect walking behavior of the participants, the structural response is first predicted assuming perfectly periodic walking forces. Second, intra- and inter-person variabilities are taken into account by considering the identified time-variant pacing rate and, thereby, also the true synchronization among the pedestrians.
Figure 13A presents the measured and simulated vertical acceleration at midspan for the persons walking two by two, with a pacing rate targeted at f2/2. This figure illustrates that when the walking behavior is assumed to be perfectly periodic, the structural response is overestimated by more than a factor of four. Accounting for the true imperfect walking behavior improves the agreement with the measured response significantly although the predicted vibration levels are three times larger.
Figure 13B presents the measured and simulated acceleration at midspan for the persons walking on one side of the bridge, with a pacing rate targeted at fs = f1. In this case, the registered and simulated lateral response at midspan is presented, i.e., the dominant component of the first mode. Figure 13B shows that when the moving force model is applied and perfectly periodic walking behavior is assumed, the peak value of the acceleration response is overestimated by a factor of two. A decrease in the measured acceleration is observed after about 40 sec due to a reduced synchronization of the pedestrians. A similar tendency is also reflected in the simulated response when accounting for the identified time-variant pacing rates. The latter leads to a much better qualitative agreement with the measured response that is, however, still slightly overestimated.
Figures 14 and 15 present a similar comparison of the measured and simulated structural response involving jumping and bobbing, respectively. Again, it is observed that the structural response is highly overestimated when the human-induced loads are assumed to be perfectly periodic. Accounting for the identified time-variant pacing rate leads to a much better qualitative agreement with the measured response.
The remaining discrepancy between the measured and simulated structural response may be due to errors in the model regarding (a) the structural behavior and (b) the pedestrian-induced load. Involving the structural model, the main uncertainty concerns the modal damping ratios. However, the covariance of the modal parameters as obtained from the SSI-cov14 were low and, in addition, the free decay analyses show that the modal damping ratios hardly depend on the vibration amplitudes3. Concerning the pedestrian excitation, the identified time-variant pacing rate is an approximation of the real imperfect walking behavior whereby small differences may arise due to the application of the generalized force model. The difference in amplitude between the predicted and the measured response in Figures 13-15 is striking and cannot simply result from these remaining uncertainties. It can, however, be explained by an increased damping, i.e., due to the changes in the dynamic properties of the coupled human-structure system in comparison to those of the empty structure. However, accounting for the involved time-variant pacing rates allows to quantify the remaining discrepancy that is due to these human-structure interaction (HSI) effects10,15-17. In this way, the methodology presented here provides essential input for the verification of the human-induced loads and quantification of HSI-effects.
Figure 1. (A) The Xsens – Mtw Development Kit consisting of multiple wireless inertial units (MTw's)2, (B) platform designed to define the orientation reference frame, and (C) the specially designed click-in full body straps2. Please click here to view a larger version of this figure.
Figure 2. The force plate4 applied to register the GRFs during jumping/bobbing. Please click here to view a larger version of this figure.
Figure 3. Wireless triaxial Geosig sensors5 applied to register the structural accelerations. Please click here to view a larger version of this figure.
Figure 4. Configuration setup for the laboratory experiments involving human rhythmical experiments. Please click here to view a larger version of this figure.
Figure 5. (A) The Eeklo footbridge and (B) synchronized walking of six participants (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 6. The PediVib Toolbox8 applied to simulate the human-induced vibrations. Please click here to view a larger version of this figure.
Figure 7. The linear spectrum of (A) the vertical GRFs (sum of left and right foot) and (B) the corresponding acceleration levels near the CoM (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 8. The normalized (A-C) vertical single step (dashed) and continuous (solid) GRFs (B-D) the normalized accelerations near the CoM and (A-B) the identified timing of nominally identical events (vertical line) from the GRFs (solid) and the accelerations near the CoM (dashed) (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 9. The normalized measured (solid) and corresponding simulated (dashed) vertical GRFs during walking (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 10. The amplitude spectrum of the measured (black) and simulated (grey) vertical GRFs (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 11. The identified walking behavior of six pedestrians: (A) each step of every person indicated by a single vertical line (B) the synchronization rate, and (C-D) corresponding simulated vertical forces induced by left (grey) and right (black) foot (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 12. The experimentally identified modal parameters of the first six modes of the Eeklo footbridge: natural frequency (fj), modal damping ratio (ξj) and mode shape: (A) mode 1 (f1 = 1.71 Hz, ξ1 = 2.3%); (B) mode 2 (f2 = 2.99 Hz, ξ2 = 0.2%); (C) mode 3 (f3 = 3.25 Hz, ξ3 = 1.5%); (D) mode 4 (f4 = 3.46 Hz, ξ4 = 3.0%); (E) mode 5 (f5 = 5.77 Hz, ξ5 = 0.2%); and (F) mode 6 (f6 = 5.82 Hz, ξ6 = 0.2%). Please click here to view a larger version of this figure.
Figure 13. The accelerations at midspan for persons walking (A) two by two at a pacing rate targeted at fs = f2/2 and (B) in single file at a pacing rate fs = f1: measured (black) and predicted response without (grey) and with (blue) the in situ identified pacing rate (this figure has been modified from [3]). Please click here to view a larger version of this figure.
Figure 14. The accelerations at midspan for persons jumping at a pacing rate targeted at (A) fs = f2/2 and (B) fs = f1: measured (black) and predicted response without (grey) and with (blue) the in situ identified pacing rate. Please click here to view a larger version of this figure.
Figure 15. The accelerations at midspan for persons bobbing at a pacing rate targeted at (A) fs = f2/2 and (B) fs = f1: measured (black) and predicted response without (grey) and with (blue) the in situ identified pacing rate. Please click here to view a larger version of this figure.
Walking speed | Step frequency | # steps | CoM |
[km/hr] | [Hz] | [-] | 2σ [%] |
3.0 | 1.55 | 166 | 2.8 |
3.5 | 1.68 | 178 | 2.3 |
4.0 | 1.75 | 1.82 | 2.1 |
4.5 | 1.85 | 182 | 2.0 |
5.0 | 1.92 | 193 | 2.1 |
5.5 | 2.00 | 215 | 2.0 |
6.0 | 2.06 | 217 | 2.1 |
Table 1. For each trial: the different walking speeds, the mean step frequency, the number of registered steps and the 95% confidence interval of the identified onset of each step based on the motion registered near the CoM (this table has been modified from [3]).
The human motion and resulting GRFs are usually identified by the application of force plates, instrumented treadmills as well as optical motion capture technology such as Vicon18 and CODA19. The application of these techniques is, however, restricted to the laboratory environment. In answer to this drawback, the potential of innovative techniques that permit the measurement of 'natural' person behavior over many repeated and uninterrupted cycles is currently investigated20. Alternative techniques include the use of pressure sensitive insole systems21 or instrumented shoes22. These systems allow for the direct measurement of contact forces on structures but generally only yield the vertical component and do not capture the global body behavior, e.g., the trunk motion20. Another ambulant technique employs combined magnetic-inertial sensors, i.e., accelerometry20,23. Although this wireless technology is also encountering some challenges (e.g., soft-tissue artefacts24, connectivity, etc.), it offers great potential for the indirect characterization of human-induced loading as well as for the analysis of individual, group and crowd behavior23,24. In the present study, a 3D inertial motion tracking technique developed for the movement science and entertainment industry is examined and a methodology is developed for the in-field characterization of the human motion and the resulting GRFs.
A first essential step in the method presented here consists of a comprehensive experimental study in laboratory conditions in which the human motion and the GRFs are registered simultaneously. This dataset should comprise a relevant set of pacing rates and individuals for each of the human activities in focus. Subsequently, this dataset can be applied to identify the relation between the registered motion of the participants and the resulting GRFs. Next, a procedure can be developed for the identification of the timing of nominally identical events in each loading cycle from both the registered motion and the corresponding GRFs. In this way, these datasets not only serve as validation for the procedure aiming to characterize the human-induced loads, but, also allows to quantify the corresponding accuracy.
Secondly, the synchronization between the involved measurement systems is of high importance. The latter is preferably accomplished by the use of a single data acquisition system or a shared trigger channel2. A well-designed and consistently executed protocol (as previously discussed) can serve as a useful alternative, especially for application in situ.
The procedure as discussed in the present work operates perfectly up to 10 or 12 participants. However, as the number of participants further increases and, thus, as the number of wireless motion tracking units increases, the corresponding data acquisition system requires the sampling rate to reduce significantly. Although cumbersome, the measurement system can be extended by multiple Xsens data acquisition stations for which, in turn, the data is synchronized through the application of a common trigger channel. When the aim is to monitor the behavior of larger groups and crowds, the application of alternative techniques such as video/image processing could be explored.
In situ observations are the only source of information to obtain detailed and accurate information on representative operational loading data. Further research will therefore include full-scale measurements on real footbridges involving large groups and crowds. The present technique can be applied to identify the natural walking behavior of the participants and, thereby, provide essential input for the development of suitable models for the correlation among pedestrians in real traffic conditions. In addition, the identified walking behavior, in combination with currently available load models, can be applied to simulate the induced structural response. Comparison with the corresponding measured structural vibrations allows to verify and calibrate the applied load models, e.g., by estimating the relevant human-structure interaction phenomena such as added damping.
The authors have nothing to disclose.
The experiments involving walking individuals are performed in cooperation with Movement & posture Analysis Laboratory Leuven (MALL)25. Their cooperation and support is gratefully acknowledged.
MTw Development Kit + MT Manager Software | Xsens | MTW-38A70G20-1 | Development kit with wireless, highly accurate, small and lightweight 3D human motion trackers and accompanying click-in full body straps. |
True Impulse Kinetic Measurement System + NDI Open Capture Data Acquisition and Visualization System | NDI Northern Digital Inc. | 791028 | TrueImpulse measures reaction forces exerted by humans during a wide variety of activities. |
GMS-24 | GeoSIG Ltd | Rev. 03.08.2010 | (Wireless) accelerometers to register the structural vibrations. |
GeoDAS GeoSIG Data Acquisition System | GeoSIG Ltd | Rev. 03.08.2010 | Graphical MS Windows application running under Windows 9x/NT/2000, providing a software interface between users and GeoSIG recorders GSR/GCR/GBV/GT. |
PediVib toolbox | KU Leuven | / | Software interface/toolbox to simulate the structural vibrations induced by pedestrians. |
Metronome | / | / | A device to indicate the targetted pacing rate of the activity (free applications are available online for pc/laptop/smartphone). |