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

Summary

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.

Abstract

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.

Introduction

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.

Protocol

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

1. Ensure that the individual sensors are fully charged (Figure 1A). This step takes about 1 hr but can be performed on the days prior to the actual measurements. Follow the manufacturer's charging protocol.
2. MT Manager — Data acquisition²:
   1. Enable the wireless connection with the sensors and specify the desired sample rate (Wireless Configuration > Enable all wireless masters).
      Note: To allow for an accurate characterization of the pedestrian behavior, a sampling rate of at least 60 Hz is advised. The individual sensors record 3D linear acceleration, angular velocity (earth) magnetic field and atmospheric pressure data.
   2. Activate the operational mode and initiate the measurement mode: make slow movements with the sensors for about 1 min (Wireless Configuration > Start measurement on all wireless masters).
   3. Display inertial and magnetic data of all active sensors (View > Display > Inertial Data). Make sure that, while stationary, the orientation of the sensor does not chance.
      Note: A changing orientation of the stationary sensor would indicate a magnetically disturbed environment and, thereby, inaccurate orientation information.
3. Orientation reset: Apply an object/heading reset (Object/heading reset > Reset orientation) to define the global reference frame of the experiments (Figure 1B) ².
4. Place the sensor as close as possible to the body center of mass (CoM) located at the level of the fifth lumbar vertebrae (Figure 1C). Fasten a single sensor tightly and robustly onto each participant with specially designed click-in full body straps (Figure 1C).
5. Record data as required.
6. Load the records of interest (open file), specify the export settings (Tools > Preferences > Exporters) and export the acceleration (and orientation matrix) data for subsequent analysis² (File > Export).

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.

1. Ensure that the force plate is securely fixed to the laboratory floor (Figure 2).
2. Configure the device and acquisition settings⁴ (NDI Open Capture > Data > Device Settings > Settings). Select the proper "gain" and "sample rate". Configure and check the external trigger settings, if required⁴.
   1. Choose the gain and sample rate in accordance with the desired accuracy and the involved loading type. For the present application, use a gain of 128 (Maximum Force 4,879 N) and a sample rate 200 Hz.
3. Start and end each trial with an empty force plate: Tare the force plate when empty (NDI Open Capture > Data > Device Settings > Settings > Tare).
4. For verification purposes: Place a known weight on top of the force plate before and after each trial.
   Note: In the present application a mass of 5 kg is used, however, the use of another well-known rigid mass (> 2 kg) can equally serve this verification test.
5. Record and save the GRF data as required. Export the GRFs for subsequent analysis⁴.

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.

1. Ensure that the individual sensors are fully charged. This step can take several hours but can be performed on the days prior to the actual measurements. Follow the manufacturer's charging protocol.
2. Install the sensors on the desired locations of the primary structure: level the sensors and, if necessary, provide proper fixation to the primary structure (e.g., by using magnets).
   Note: given the high mass of the individual GMS recorders (> 6 kg) and the involved low-frequency oscillations (< 6 Hz), no additional fixation was necessary in this case.
3. For GeoDAS Data acquisition⁵: Configure and enable the wireless GMS network and connection with the sensors⁵. Check time settings and synchronization settings (if necessary) (right click on the sensor > More information).
4. Position the sensors on the desired location and level them in agreement with the global reference frame.
5. For GeoDAS Data acquisition⁵: Export the recorded data for subsequent analysis (right click on the sensor > Instrument Control > Send a request > User request > GETEVT⁵).

4. Experiments in a Controlled Laboratory Environment

1. Configure / Setup 3D motion tracking (as discussed in section 1).
2. Configure / Setup force plate (as discussed in section 2).
3. During operation: visually check the real-time measurements of both the wireless inertial sensors and the force plate to verify their operational mode.
4. Ask the participant to step onto the force plate and stand still for at least 30 sec: this allows to identify the weight of each individual.
5. Configure the metronome signal: select the desired rhythm, i.e., fundamental forcing frequency.
   Note: The metronome signal can be easily configured using free online or smartphone applications.
6. Start recording the data of both the force plate and the wireless inertial sensors.
7. Ask the participant to initiate the desired activity: walking, jumping or bobbing at the (targeted pacing) rate as indicated by the metronome signal (see Figure 4).
8. Record the chosen number of loading cycles, e.g., steps, jumps or bobbing cycles. Ask the participant to get off the force plate.
   Note: For validation purposes it is advised to consider some additional recording time in these unloaded conditions. In literature, there is no clear consensus about the minimum number loading cycles required to characterize the cycle-to-cycle variabilities⁶. Based on experience and the work presented in [⁶], the study presented here considers 60 consecutive cycles whereby the first and last five loading cycles are excluded from the further analysis to exclude irregularities in the loading pattern at the start and end of the trial.

5. Experiments In Situ

1. Configure / Setup the network of 3D inertial sensors that track the motion of the participants (see section 2 and Figure 5).
2. Configure / Setup the GMS network of wireless accelerometers that register the structural accelerations (see section 4).
3. During operation: (visually) check the real-time measurements of the wireless inertial sensors to verify their operational mode.
4. Define a clear protocol that allows to synchronize the involved measurement systems, if required.
   Note: This step is necessary when the involved data acquisition systems do not allow for direct synchronization due to the lack of a trigger or common channel. The latter is the case for the wireless measurement systems applied in the in situ experiments (5.1 and 5.2). Therefore, a clear protocol has been adopted on site that allows to synchronize the datasets offline. In the present application, the involved measurement systems are synchronized through registration of an identical event, i.e., impact, at the beginning and end of each trial, registered by at least one sensor of each of the involved measurement systems. Properly aligned time vectors are subsequently obtained through offline alignment of these events.
5. Configure the metronome signal: in situ, the use of a megaphone to amplify the targeted beat is required.
6. Collect a sufficient number of trials to check the repeatability of the experiment. Based on experience, the authors recommend to record at least 3, or preferably 4, trials.

6. Data Analysis

1. Pre-process the raw data of the involved equipment as required: Apply the proper filters to remove undesired influences such as irrelevant high-frequency contributions and measurement noise, and retain the relevant time window according to manufacturer's protocol.
   Note: The filtering characteristics should be chosen in accordance with the application. In the present study, the MATLAB Signal Processing Toolbox⁷ is applied to perform a low-pass filtering with a cut-off frequency at 20 Hz for all involved signals.
2. For each participant: Compute the discrete Fourier transform of the registered accelerations of the CoM using MATLAB Signal Processing Toolbox⁷ and identify the average loading frequency as the frequency of the dominant peak of the fundamental harmonic in the obtained spectrum.
3. Identify the time in between any two nominally identical events of the load cycles using the method detailed in [³] or the lc_timing tool of the PediVib MATLAB toolbox⁸
   1. Load the data vector (lc_timing > Load).
   2. Specify the sampling rate and estimate the average loading frequency. Specify the relevant time window, if required. Save the identified timing of the nominally identical events, i.e., load cycles (lc_timing > Save).
4. Compute the average loading frequency as the inverse of the average time in between the subsequent load cycles (as identified in 6.3).
5. For the experiments in the laboratory: Apply the procedure detailed in 6.3 for both the resulting ground reaction forces and the accelerations registered at the CoM of each individual.
   Note: This step serves as validation for the procedure as applied for the in situ experiments where the GRFs cannot be measured directly. The method detailed in [³] shows how the time variant pacing rate of the pedestrian can be identified by characterizing the relation between the accelerations registered near the CoM of the individual and the consequent GRFs.
6. For the experiments in situ: Apply the procedure detailed in 6.3 for the accelerations registered at the CoM of each individual.

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.

1. Simulation of the structural response
   1. Define the modal parameters of the test structure: Natural frequencies, modal damping ratios, mass-normalized modal displacements, coordinates of the corresponding nodes (PediVib > Structural parameters > New). Visually check the modal input information (PediVib > Structural parameters > View).
   2. Define the characteristics of the pedestrian and the corresponding induced loads: load type, weight, walking path/location, average pacing rate, onset of each load cycle (PediVib > Single pedestrian > New). Run and save the simulated structural response for the involved participants. Visually check the results (PediVib > Single pedestrian > View).
2. Compute the total structural response through superposition of the individual responses, i.e., summation of the corresponding vectors, and compare the result with the measured structural response, e.g., by creating a figure which displays the measured and simulated structural response.

Results

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 r...

Discussion

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. Alter...

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
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).