Joint Center Estimation Using Single-Frame Optimization: Part 2: Experimentation

Human motion capture is driven by joint center location estimates, and error in their estimation can be compounded by subsequent kinematic calculations. Soft tissue artifact (STA), the motion of tissue relative to the underlying bones, is a primary cause of error in joint center calculations. A method for mitigating the effects of STA, single-frame optimization (SFO), was introduced and numerically verified in Part 1 of this work, and the purpose of this article (Part 2) is to experimentally compare the results of SFO with a marker-based solution. The experimentation herein employed a single-degree-of-freedom pendulum to simulate human joint motion, and the effects of STA were simulated by affixing the inertial measurement unit to the pendulum indirectly through raw, vacuum-sealed meat. The inertial sensor was outfitted with an optical marker adapter so that its location could be optically determined by a camera-based motion-capture system. During the motion, inertial effects and non-rigid attachment of the inertial sensor caused the simulated STA to manifest via unrestricted motion (six degrees of freedom) relative to the rigid pendulum. The redundant inertial and optical instrumentation allowed a time-varying joint center solution to be determined both by optical markers and by SFO, allowing for comparison. The experimental results suggest that SFO can achieve accuracy comparable to that of state-of-the-art joint center determination methods that use optical skin markers (root mean square error of 7.87–37.86 mm), and that the time variances of the SFO solutions are correlated (r =  0.58–0.99) with the true, time-varying joint center solutions. This suggests that SFO could potentially help to fill a gap in the existing literature by improving the characterization and mitigation of STA in human motion capture

Joint Center Estimation Using Single-Frame Optimization: Part 1: Numerical Simulation

The biomechanical models used to refine and stabilize motion capture processes are almost invariably driven by joint center estimates, and any errors in joint center calculation carry over and can be compounded when calculating joint kinematics. Unfortunately, accurate determination of joint centers is a complex task, primarily due to measurements being contaminated by soft-tissue artifact (STA). This paper proposes a novel approach to joint center estimation implemented via sequential application of single-frame optimization (SFO). First, the method minimizes the variance of individual time frames’ joint center estimations via the developed variance minimization method to obtain accurate overall initial conditions. These initial conditions are used to stabilize an optimization-based linearization of human motion that determines a time-varying joint center estimation. In this manner, the complex and nonlinear behavior of human motion contaminated by STA can be captured as a continuous series of unique rigid-body realizations without requiring a complex analytical model to describe the behavior of STA. This article intends to offer proof of concept, and the presented method must be further developed before it can be reasonably applied to human motion. Numerical simulations were introduced to verify and substantiate the efficacy of the proposed methodology. When directly compared with a state-of-the-art inertial method, SFO reduced the error due to soft-tissue artifact in all cases by more than 45%. Instead of producing a single vector value to describe the joint center location during a motion capture trial as existing methods often do, the proposed method produced time-varying solutions that were highly correlated (r > 0.82) with the true, time-varying joint center solution

Identification of the viscoelastic boundary conditions of Euler‐Bernoulli beams using transmissibility

A new method to identify the viscoelastic boundary conditions of Euler‐Bernoulli beams under forced response is here presented. The boundary conditions and transmissibility function with viscoelastic expressions in terms of the Green function are introduced in the identification process. Two distinct identification methods are proposed: the least squares method with singular value decomposition; and the pattern search optimization method. Three examples are reported to demonstrate the efficacy of the proposed methods. The results from the least squares method to provide accurate solutions under noise‐free conditions, but poorly perform with the addition of 1% noise. Conversely, the pattern search optimization method integrates the solutions from different frequencies and provides promising solutions, even with 50% noise. The capability of identifying complex boundary conditions under high levels of noise might open the door for the proposed method to be considered in real‐life applications of structural health monitoring and model updating with boundary conditions of beam‐like structures such as bridges

Effect of Directional Added Mass on Highway Bridge Response during Flood Events

This article presents a new analysis to determine the variation in modal dynamic characteristics of bridge superstructures caused by hydrodynamic added mass (HAM) during progressive flooding. The natural frequency variations were numerically and experimentally extracted in various artificial flood stages that included dry conditions, semi-wet conditions, and fully wet conditions. Three-dimensional finite element modeling of both subscale and full-scale models were simulated through a coupled acoustic structural technique using Abaqus®. Experiments were performed exclusively on a subscale model at a flume laboratory to confirm the numerical simulations. Finally, an approach to quantify the directional HAM in the dominant axes of vibration was pursued using the concept of effective modal mass. It is shown that specific vibrating modes with the largest effective mass are strongly affected during artificial flood events and are identified as the dominant modes. Numerical simulation shows that large directional HAM is introduced on those dominant modes during flood events. For the full-scale representative bridge, the magnitude of the HAM along the first structural mode was estimated to be over 5.8 times the bridge’s structural modal effective mass. It is suggested that directional HAM should be included during the design of bridges over streamways that are prone to flooding in order to potentially be appended to the AASHTO code