Time-varying parallel-cascade system identification of ankle stiffness from ensemble data

Measurement of joint dynamic stiffness during time-varying conditions is crucial to understand the role of joint mechanics during movement. Stiffness can be separated into intrinsic and reflex components, and are modeled as linear dynamic and Hammerstein systems, respectively. Time-varying identification methods using ensemble data have been developed previously for both pathways and were tested separately on simulated data. In this study, these algorithms were integrated into the time-varying, parallel-cascade identification method. Ankle dynamics were modeled during a ramp input and simulated impulse response functions (IRFs) were generated. Gaussian white noise was low-pass filtered and was convolved with the simulated systems over 500 realizations. The ensemble data was used to evaluate the new identification technique. The mean variances accounted for (VAFs) between the true and identified IRFs for the intrinsic and reflex pathways were 99.9% and 97.7%, respectively, demonstrating the technique's strong ability to predict the system's dynamics.