Performance evaluation of an algorithm for the identification of time-varying joint stiffness

Abstract

Previously, we described a time-varying, parallel-cascade system identification algorithm that estimates intrinsic and reflex stiffness dynamics. It uses an iterative technique, in conjunction with established, time-varying, identification methods, to estimate the two pathways from ensembles of input and output realizations having the same time-varying behavior. This paper presents the results of a study that systematically evaluated the performance of the algorithm. Simulations were used to determine the algorithm's ability to track rapid changes in dynamic stiffness, and quantify its performance limits. There was close agreement between the simulated and estimated joint stiffness demonstrating that the algorithm estimates stiffness correctly even when it changes rapidly. However, the algorithm's ability to identify the reflex pathway was shown to depend on the relative contributions of the intrinsic and reflex pathways to the overall torque. As the intrinsic contribution to the output grew it became increasingly difficult to identify the reflex pathway accurately. The quality of the reflex identification greatly improved as the number of realizations in the data ensembles increased. More realizations were needed as the signal-to-noise ratio decreased and the relative contribution of the reflex pathway decreased. For good results, under typical time-varying experimental conditions, between 500 and 800 realizations are required.

Linear Parameter Varying Identification of Dynamic Joint Stiffness during Time-Varying Voluntary Contractions

“…Other studies have used ensemble-based method to evaluate the effect of activation level on joint stiffness. Visser ( 2010 ) studied ankle joint stiffness during a sinusoidal torque matching task, where a monotonic increase in elastic parameter with voluntary torque was observed similar to the observation of this study. The main difference with our results was that Visser ( 2010 ) found two peaks in the reflex gain at the lowest and highest activation levels.…”

“…Visser ( 2010 ) studied ankle joint stiffness during a sinusoidal torque matching task, where a monotonic increase in elastic parameter with voluntary torque was observed similar to the observation of this study. The main difference with our results was that Visser ( 2010 ) found two peaks in the reflex gain at the lowest and highest activation levels. Also, Ludvig and Perreault ( 2014 ) used a similar ensemble-based method to study knee stiffness during rapid activation and reported similar results for the elastic parameter.…”