Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior

The overall goal of this procedure is to use the tracked motion of pedestrians to characterize human-induced loads and subsequently, to verify the induced structural vibrations. This method can help to answer key questions in the field of human-induced vibrations, such as the characterization of the individual walking behavior, the identification of the correlation among pedestrians in a crowd, as well as the quantification of human-structure interaction phenomena. The main advantage of this technique is that it can be applied in-situ and thus allows us to analyze real traffic conditions.

In-field observations are the only way to obtain detailed and accurate information on representative loading data. Therefore, they are essential for the further development and validation of the load models used for pedestrian excitation. Demonstrating the procedure will be Klaus Lievens, Xinxin Wei, and Krumka Kasapova, three PhD students of our research group, and Bram Gezels, an academic assistant.

Use wireless motion trackers to register the motion of pedestrians. To configure the sensors, use the MT manager software to establish the wireless connection. Specify the desired sample rate, which should be at least 60 hertz to capture human motion.

Then, make slow movements with the motion trackers until they are connected, and then continue by activating the measurement mode. Next, display the inertial data of all the active motion trackers. Now, attach a motion tracker as closely as possible to each participant’s center of mass.

Robustly fasten the motion tracker onto the participant so it is snug and secure. Now, data can be recorded as required. When making measurements in the laboratory, the motion of the human subject can be tracked simultaneously with ground reaction forces measured with a force plate.

First, use the accompanying software to configure the force plate and acquisition settings. Select a gain and sample rate in accordance with the desired accuracy and the involved loading type. For human-induced loads, set the gain for a maximum force of 4, 879 newtons, and set the sample rate to 200 hertz.

Always start and end a measurement with an empty force plate. Use the tare function or the automatic offset correction to reset the force when the plate is empty. Once tared, data can be recorded as required.

For measurements performed on site, structural vibrations can be measured at relevant locations, such as at mid-span of a footbridge. To do this, use displacement, velocity, or acceleration sensing recorders. Configure the recorders according to the manufacturer’s instructions.

After placing the recorders at the desired locations, level them in agreement with a global reference frame. In the lab, after setting up motion trackers and the force plate, start the data recording. Then, ask the participant to step onto the force plate and stand still for at least 30 seconds.

Thus, weigh the participant. Next, start a metronome to dictate the fundamental forcing frequency. Then, ask the participant to move at the pace of the metronome signal, such as by walking, jumping, or bobbing.

Record this activity for a sufficient number of cycles, 60 cycles are recommended. When the cycles are complete, ask the participant to get off the plate. For experiments conducted on site on a civil structure of interest, set up the motion trackers and a network of sensors that will register the structural vibrations.

In an outdoor setting, a megaphone can be used to amplify the metronome signal. On site, repeat the test at least three times, preferably four times, to check the repeatability of the experiment. In any setting when multiple acquisition systems are used and no trigger or common channel is available, synchronize the devices using a single event that each system can register, such as a strong impact.

Add synchronizing events to the beginning and end of each test. Based on these events, the data of the different systems can be synchronized offline. When performing dynamic measurements with more than one type of sensor, synchronization of the data is essential.

Therefore, we either try to use a single data acquisition system or for the systems to record a common signal. Begin by identifying the time between the nominally identical events of the load cycles. For the reference lab experiments, perform this step on both the pedestrian motion data and the force plate data.

After loading the data, specify the sampling rate and estimate the average loading frequency. Also, specify the relevant time window if needed. The most critical step in this procedure lies in the identification of the onset of each load cycle from the tracked pedestrian motion.

It is this timing information which allows us to compute the time-variant pacing rate of the pedestrian. For the analysis of the experiments in the lab, exclude the first and last five cycles from the analysis and work with the remaining 50. Be sure to visually check the timing information before saving the data.

Now, compute the average fundamental loading frequency as the inverse of the average time in between the subsequent load cycles. When multiple pedestrians are involved, the identified timing information can be applied to analyze their correlation. For the analysis of the experiments on site, the next step is to use the identified timing information to simulate the induced structural response.

Firstly, define the modal parameters of the test structure. These include the natural frequencies, modal damping ratios, and the mass-normalized modal displacements. Be sure to visually check the modal input information before proceeding.

Secondly, define the characteristics of the pedestrians and their induced loads. These include the load type, weight, walking path or location, average pacing rate, and timing of the load cycles. Specify the solution parameters, such as the output locations, as well as the time parameters.

Then, run and save the simulated structural response for the involved participants. As before, visually check the results before proceeding. Thirdly, compute the total structural response through superposition of the individual responses by summing the corresponding vectors.

Then, compare the result with the measured structural response with a graphical representation of the data. From a single pedestrian tested in the lab, the onset of each load cycle was identified. This data is used to simulate the walking forces, shown in blue, and compare to the measured forces, shown in black.

A good approximation of real walking forces was obtained. Similarly, the walking behavior of six pedestrians on a footbridge was analyzed. Again, the onset of each load cycle was identified from the tracked pedestrian motion.

This load cycle information was then used to simulate the pedestrian-induced forces. After about 16 seconds, the pedestrians were walking in step, while after 50 seconds, a significant loss of synchronization was observed. By comparing the timing of the load cycles among the pedestrians, the synchronization rate was found to decrease to 60%after about 50 seconds.

The structural response was then simulated. When the pacing rate of the pedestrians was assumed to be constant and identical to the metronome signal, shown in gray, the result significantly overestimated the measurements, shown in black. When the simulation accounted for the identified time-variant pacing rate, shown in blue, it was clearly closer to the measured response.

This procedure can be applied to analyze the natural walking behavior of pedestrians. In this way, essential input is provided for the development of suitable models for the correlation among pedestrians. In addition, the comparison between the measured and the simulated structural response allows us to validate and calibrate the load models used for pedestrian excitation.

By doing so, also the impact of human-structure interaction phenomena, such as added damping, can be investigated.