Footbridge Dynamic Performance Assessment Using Inertial Measurement Units

Forced vibration testing of footbridges using calibrated human shaker and wireless sensors

Background/Purpose: The acquisition of three-dimensional ground reaction forces (3D-GRF) during running is crucial for monitoring and assessing running performance. However, limitations often arise in collecting 3D-GRF due to equipment and environmental constraints. Inertial sensors are gaining popularity in running applications because of their convenience, broad applicability, and cost-effectiveness. This study aimed to utilize an inertial sensor for gathering kinematic data during running, establish a high-precision neural network model for continuous 3D-GRF estimation, and investigate estimation variances across different body segments. Method: A total of thirty-three college students (17 male, 16 female) participated in this study. Kinematic and kinetic data were concurrently recorded using inertial sensors placed on the lower back, lateral thigh, anterior lower leg, and dorsum of the foot, while three-dimensional force plates were utilized during running at speeds of 8/10/12 km/h. The dataset was partitioned into training, validation, and test sets at a ratio of 24:3:6. A Long Short-Term Memory Neural Network (LSTM) was developed for training to predict 3D-GRF. Evaluation metrics included coefficients of determination, Root Mean Square Error (RMSE), and Normalized Root Mean Square Error (NRMSE). Models customized for specific body segments underwent a nine-fold cross-validation procedure, employing one-way ANOVA to evaluate estimation variances across different anatomical sites. Results: Estimation outcomes at different sites indicated optimal estimation accuracy at the right thigh. The coefficients of determination for Anteroposterior (AP)-GRF, Mediolateral (ML)-GRF, and Vertical (V)-GRF were 0.81±0.00, 0.55±0.14, and 0.97±0.02, respectively. RMSE values were 0.06±0.01BW, 0.06±0.01BW, and 0.14±0.03BW. Significant variances were observed between the right thigh and other sites in the horizontal plane (p < 0.05). The results from the test set showed correlation coefficients, RMSE, and NRMSE for AP-GRF, ML-GRF, and V-GRF: AP-GRF, 0.94±0.01, 0.06±0.01BW, 4.78%±0.50%; ML-GRF, 0.83±0.08, 0.10±0.01BW, 9.70%±2.41%; V-GRF, 0.99±0.00, 0.14±0.02BW, 2.79%±0.24%. Conclusion/Discussion: 1. The neural network model developed in this study demonstrated exceptional accuracy across three dimensions, facilitating continuous estimation of 3D ground reaction forces during running. Correlation coefficients surpassed 0.8 in every direction, with RMSE values below 0.2BW and NRMSE below 5%. 2. Estimation results from inertial sensors positioned at different sites exhibited diverse levels of disparity. The lateral thigh emerged as the most proficient location for estimation, with the lower back excelling in vertical ground reaction force estimation but displaying comparatively weaker performance in horizontal ground reaction force estimation.

The biomechanical-model-based approach with a contact model offers advantages in estimating ground reaction forces (GRFs) and ground reaction moments (GRMs), as it does not rely on the need for training data and gait assumptions. However, this approach faces the challenge of long computational times due to the inclusion of optimization processes. To address this challenge, the present study developed a new optical motion capture (OMC)-based method to estimate GRFs, GRMs, and joint torques without prolonged computational times. The proposed approach performs the estimation process by distributing external forces, as determined by a multibody model, between the left and right feet based on foot deformations, thereby predicting the GRFs and GRMs without relying on optimization techniques. In this study, prediction accuracies during level walking were confirmed by comparing a general analysis using a force plate with the estimation results. The comparison revealed excellent or strong correlations between the prediction and the measurements for all GRFs, GRMs, and lower-limb-joint torques. The proposed method, which provides practical estimation with low computational cost, facilitates efficient biomechanical analysis and rapid feedback of analysis results, contributing to its increased applicability in clinical settings.

Since the center of mass (CoM) is related to ground reaction force (GRF), the CoM position is expected to be used in evaluation of walking ability. The purpose of this study was to examine the possibilities of using the CoM acceleration calculated from the CoM trajectory estimated by inertial sensor signals to obtain similar information as the GRF. In this paper, 16 m straight walking measurements were performed under different walking speeds with healthy subjects. CoM acceleration, which was calculated from CoM positions estimated by signals measured with inertial sensors, were analyzed for the steady state gait. Waveforms of the CoM acceleration were similar among subjects. Four peak values (negative peak near the toe off (TO) and positive peak near the initial contact (IC) of the opposite lower limb in the anteroposterior component, and the positive peak before the TO of the opposite lower limb and the negative peak of the mid-stance phase) showed significant correlations with walking speed, which were similar to the relationships between GRF and walking speed in previous studies. These results suggest that anteroposterior and vertical components of CoM acceleration estimated from inertial sensor signals have a possibility of estimating similar information as the GRF during walking. The relationship between positive peak value of the vertical component near the IC of the opposite side and walking speed was seemed to be different from a previous study, although it showed significant correlation with walking speed. Simultaneous measurements with inertial sensors and GRF are expected in the next study.

Objective gait analysis provides valuable information about the locomotion characteristics of sound and lame horses. Due to their high accuracy and sensitivity, inertial measurement units (IMUs) have gained popularity over objective measurement techniques such as force plates and optical motion capture (OMC) systems. IMUs are wearable sensors that measure acceleration forces and angular velocities, providing the possibility of a non-invasive and continuous monitoring of horse gait during walk, trot, or canter during field conditions. The present narrative review aimed to describe the inertial sensor technologies and summarize their role in equine gait analysis. The literature was searched using general terms related to inertial sensors and their applicability, gait analysis methods, and lameness evaluation. The efficacy and performance of IMU-based methods for the assessment of normal gait, detection of lameness, analysis of horse–rider interaction, as well as the influence of sedative drugs, are discussed and compared with force plate and OMC techniques. The collected evidence indicated that IMU-based sensor systems can monitor and quantify horse locomotion with high accuracy and precision, having comparable or superior performance to objective measurement techniques. IMUs are reliable tools for the evaluation of horse–rider interactions. The observed efficacy and performance of IMU systems in equine gait analysis warrant further research in this population, with special focus on the potential implementation of novel techniques described and validated in humans.

Gait parameters calculated from trunk acceleration reflect the features of gait; however, they cannot evaluate the gait pattern corresponding to the gait cycle. This study is aimed at investigating the differences in gait parameters calculated from trunk acceleration during gait corresponding to the gait cycle in healthy subjects with restricted knee extension. Participants included eight healthy volunteers who walked normally (NW) and with knee orthosis that restricted knee extension (ER). The ground reaction force (GRF), joint angles, and trunk acceleration during walking were measured using four force plates, a three-dimensional motion analysis system, and an inertial measurement unit. The peak GRF of the vertical components, joint ranges of motion, and moments of force were analyzed. The root mean square (RMS) and amplitude peak ratio (AR) of autocorrelation function were calculated from the trunk acceleration waveform. The first peak GRF and peak ankle dorsiflexion angles significantly increased during ER. The peak hip extension, knee flexion, knee extension angles, and the peak moment of knee extension significantly decreased during ER compared to that during NW. The acceleration AR significantly decreased during ER compared to that during NW. There was no significant difference in the RMS between the two conditions. The acceleration AR may show the temporal postural structure with restricted knee extension from the terminal stance phase for the ipsilateral limb to the initial stance phase for the contralateral limb. These results suggest that novel metrics for accelerometry gait analysis can reveal gait abnormalities, with restricted knee extension corresponding to the gait cycle.

Unlike baseball pitching, there currently is limited research on baseball batting to explain which biomechanical factors can best predict bat speed. Furthermore, an observational analysis has not been conducted to understand how ground reaction forces (GRF) and energy flow through the kinetic chain influence bat speed. PURPOSE: To understand how energy is generated, absorbed, and transferred through the kinetic chain and identify the best model of GRF and energy flow predictors of bat speed in the baseball swing. METHODS: Nine collegiate baseball players performed tee batting while their movements and GRF were recorded using a 3D motion capture system and two force platforms. Bat speed was recorded using an inertial measuring unit (IMU) sensor fixed to the knob of the bat. Biomechanical metrics were extracted from a total of 33 swings for energy flow and impulse analysis. A total of 27 energy flow and impulse discrete variables were inputted into a regression based on the LASSO regularization to determine the best model that predicts bat speed. Model performance was assessed using the root mean square error (RMSE) in units of m/s and an ordinary least squares (OLS) coefficient of determination. RESULTS: Players hit off the tee with a measured bat speed of 30.4 ± 1.3 m/s. The LASSO model predicted bat speed with a RMSE of 1.0 m/s (r2 = .597, p < .001) and included the back leg vertical impulse, lead leg propulsive impulse, lumbosacral (L5S1) energy absorption and transfer in the acceleration phase, and the lead hip energy absorption during follow-through. CONCLUSION: This study provides evidence that suggests that the key factors of determining bat speed during tee batting involve the momentum generated by the legs and the energy absorbed by the L5S1 and lead hip joints along with the energy transfer to and from the pelvis through these joints during the phases immediately before and after ball contact.

IntroductionThe use of portable gait measurement systems in research is appealing to collect real-world data at low-cost, low participant burden, and without requirement for dedicated lab space. Most commercially available inertial measurement units (IMU’s) designed for running only capture temporospatial data, the ability to capture biomechanics data such as shock and motion metrics with the RunScribe IMU makes it the closest to a lab alternative. The RunScribe system has been validated in running, however, is yet to be validated for walking.MethodQualisys motion capture, AMTI force plates, and Delsys Trigno accelerometers were used as gold standard lab measures for comparison against the RunScribe IMU. Twenty participants completed 10 footsteps per foot (20 total) measured by both systems simultaneously. Variables for validation included: Vertical Ground reaction force (GRF), instantaneous GRF rate, pronation excursion, pronation velocity, total shock, impact force, braking force. Interclass correlation (ICC) was used to determine agreement between the measurement systems, mean differences were used to evaluate group level accuracy.ResultsICC results showed moderate agreement between measurement systems when both limbs were averaged. The greatest agreement was seen for GRF rate, pronation excursion, and pronation velocity (ICC = 0.627, 0.616, 0.539), low agreement was seen for GRF, total shock, impact shock, braking shock (ICC = 0.269, 0.351, 0.244, 0.180). However mean differences show the greatest level of accuracy for GRF, GRF rate, and impact shock.DiscussionResults show mixed agreement between the RunScribe and gold standard lab measures, and varied agreement across left and right limbs. Kinematic variables showed the greatest agreement, however GRF had the lowest relative mean difference for group results. The results show acceptable levels of agreement for most variables, however further work must be done to assess the repeatability and sensitivity of the RunScribe to be applied within areas such as footwear testing and gait retraining protocols.

Determination of joint moments with instrumented force shoes in a variety of tasks

The purpose of this study was to develop and validate an automatic procedure using accelerometers and angular rate sensors for detecting exact gait events: heel contact (HC), toe contact (TC), heel off (HO) and toe off (TO). For this purpose, two miniature-sized light sensors were attached to the right shoe which measured triaxial acceleration and biaxial angular velocity of various positions of the shoe while ground reaction force and marker data were recorded at the same time as reference measurements. Healthy men walked on a walkpath at self-selected normal speed with the instrumented shoes on. An automated algorithm was developed to detect HC, TC, HO and TO from the acceleration and angular velocity signals, which were compared with reference data from force plates and markers. The results showed that our method demonstrated similar HC and TO to those with force plates and markers. Moreover, this method well detected stance phase duration. However, TC and HO differed among the three methods (force plates vs. markers vs. sensors). We concluded that the system using inertia sensors can identify TC and HO accurately and be used in gait analysis.

Performing forced vibration tests on full-scale structures is the most reliable way of determining the relevant modal parameters in structural dynamics, such as modal frequencies, mode shapes, modal damping, and modal masses. This study describes the modal identification of a double-level curved cable-stayed bridge with separate deck systems for pedestrians and vehicles via forced vibration tests. The steady-state structural responses to sinusoidal excitations produced by an electrodynamic shaker are recorded under varying excitation frequencies, and the frequency response functions are established. The measured frequency response functions are curve fitted to estimate the modal parameters. The numerical simulation of frequency response function–based modal parameter identification of an elastically multi-supported continuous beam structure is carried out, and the emphasis has been placed on the evaluation of the effect of an additional shaker mass, excitation frequency step and range, multi-mode vibration, and noise on identification results. Finally, the modal parameters for the first lateral mode of a double-level curved cable-stayed bridge are identified by forced vibration experiments, and the results are compared with those from ambient vibration tests and free vibration tests. The effect of the unmeasured wind excitation on identification is discussed. It is shown that the effect of ambient vibration is minor for wind velocity of 3–5 m/s. The damping ratios identified by forced and free vibration tests are comparable, while those from ambient vibration are subject to large variations. The modal mass obtained from forced vibration tests is in good agreement with finite element prediction, which provides design basis for mass-type dampers.

It has been shown that short-leg walking boots alter kinematics, joint kinetics and ground reaction forces (GRFs) during gait. The altered GRF variables may be associated with the increased heel height on the walker side compared to the shoe side. By modifying the walking boots, it was hypothesized that the diminished heel height difference between the walker side and the shoe side would restore GRF characteristics closer to those in normal walking. PURPOSE: To examine effects of heel height modifications on the walker and shoe sides on GRF characteristics during level walking. METHODS: Ten (four males, six females) subjects performed five level walking trials in each of six randomized conditions: lab shoes (Shoe), Gait walker (GW), Gait Walker with heel insert (GWHI), Gait walker modified (GWM), Equalizer walker (EW), and Equalizer walker with heel insert (EWHI). A force platform (1200 Hz) and a seven-camera motion analysis system (120 Hz) were used to collect GRF during the testing session. Visual 3D and customized computer software were used to obtain GRF data. A two-way (2 × 6: side × condition) mixed design ANOVA was used to examine selected peak GRF related variables and post hoc comparisons with an alpha level (p < 0.05) adjusted for multiple comparisons through a Bonferroni procedure. RESULTS: The application of a walker created a peak GRF prior to the normal peaks associated with the loading response in both vertical and anteroposterior GRFs. Wearing a walker introduced an elevated minimum vertical GRF in GW (0.88 BW), GWHI (0.89 BW), GWM (0.89 BW) and EWHI (0.88 BW) compared to Shoe (0.82 BW) on the shoe (left) side. Peak propulsive GRFs were smaller in all five walker conditions (0.13 - 0.15 BW) compared to Shoe (0.20 BW) on the walker side. The same peak was smaller in GWHI, EW and EWHI on the walker side compared to the shoe side whereas it was greater on the right side than the left side in Shoe. CONCLUSION: The application of heel insert in GWHI and GWM (on shoe side) does not diminish the minimum vertical GRF as hypothesized. Wearing a walker decreases the peak propulsive ground reaction force on the walker side and induces asymmetrical loading.

IntroductionClinical assessment of upper limb sensorimotor function post-stroke is often constrained by low sensitivity and limited information on movement quality. To address this gap, recent studies proposed a standardized instrumented drinking task, as a representative daily activity combining different components of functional arm use. Although kinematic movement quality measures for this task are well-established, and optical motion capture (OMC) has proven effective in their measurement, its clinical application remains limited. Inertial Measurement Units (IMUs) emerge as a promising low-cost and user-friendly alternative, yet their validity and clinical relevance compared to the gold standard OMC need investigation.MethodIn this study, we conducted a measurement system comparison between IMUs and OMC, analyzing 15 established movement quality measures in 15 mild and moderate stroke patients performing the drinking task, using five IMUs placed on each wrist, upper arm, and trunk.ResultsOur findings revealed strong agreement between the systems, with 12 out of 15 measures demonstrating clinical applicability, evidenced by Limits of Agreement (LoA) below the Minimum Clinically Important Differences (MCID) for each measure.DiscussionThese results are promising, suggesting the clinical applicability of IMUs in quantifying movement quality for mildly and moderately impaired stroke patients performing the drinking task.

Background: Forward head posture is one of the most prevalent abnormal postures in patients with neck disorders. The aim of this study was to evaluate the effects of forward head posture on gait ground reaction force characteristics in children. Methods: Twelve children with forward head posture (age: 11.8±1.3 years) and sixteen healthy control children (age: 11.7±1.4 years) volunteered to participate in this study. Each participant was asked to walk 10 m in six trials with self-selected speed. The ground reaction force was measured by two Kistler Force Platforms at a frequency of 1000 Hz. MANOVA test ((version 16, SPSS Inc, Chicago, Il)) was used for between group comparisons. Results: In the non-dominant limb, the medio-lateral ground reaction force during push off phasein the forward head group was greater than that in the healthy group by 22.1% (P=0.049). In the dominant limb, time to peak for vertical ground reaction force during heel contact(by 13.7%; P=0.015) and push off(by 14.2%; P=0.004), mediolateral ground reaction force during heel contact (by 46.0%; P=0.006) and push off (by 15.1%; P=0.039) in the forward head group were significantly lower than those in the healthy group. Vertical loading, peak positive and negative free moment, and impulses in all axes were similar in the healthy and the forward head groups (P>0.05). Conclusion: Overall, the results reveal that gait ground reaction force components (especially time to peak for ground reaction forces) in forward head children may have clinical importance for the improvement of walking mechanics of these individuals. Rehabilitation protocols should be designed to increase time to reach peak ground reaction forces and decrease medio-lateral ground reaction force in forward head children during walking.

The effects of AFO footplate stiffness on foot and ankle push-off power in healthy persons