On parameters identification of computational models of vibrations during quiet standing of humans

Abstract

Vibration of the center of pressure (COP) of human body on the base of support during quiet standing is a very popular clinical research, which provides useful information about the physical and health condition of an individual. In this work, vibrations of COP of a human body in forward–backward direction during still standing are generated using controlled inverted pendulum (CIP) model with a single degree of freedom (dof) supplied with proportional, integral and differential (PID) controller, which represents the behavior of the central neural system of a human body and excited by cumulative disturbance vibration, generated within the body due to breathing or any other physical condition. The identification of the model and disturbance parameters is an important stage while creating a close-to-reality computational model able to evaluate features of disturbance. The aim of this study is to present the CIP model parameters identification approach based on the information captured by time series of the COP signal. The identification procedure is based on an error function minimization. Error function is formulated in terms of time laws of computed and experimentally measured COP vibrations. As an alternative, error function is formulated in terms of the stabilogram diffusion function (SDF). The minimization of error functions is carried out by employing methods based on sensitivity functions of the error with respect to model and excitation parameters. The sensitivity functions are obtained by using the variational techniques. The inverse dynamic problem approach has been employed in order to establish the properties of the disturbance time laws ensuring the satisfactory coincidence of measured and computed COP vibration laws. The main difficulty of the investigated problem is encountered during the model validation stage. Generally, neither the PID controller parameter set nor the disturbance time law are known in advance. In this work, an error function formulated in terms of time derivative of disturbance torque has been proposed in order to obtain PID controller parameters, as well as the reference time law of the disturbance. The disturbance torque is calculated from experimental data using the inverse dynamic approach. Experiments presented in this study revealed that vibrations of disturbance torque and PID controller parameters identified by the method may be qualified as feasible in humans. Presented approach may be easily extended to structural models with any number of dof or higher structural complexity.