Efficient Object-Oriented Modelling, Simulation and Parameter Estimation for Biomechanical Problems
We identify anthropometric parameter for models of human beings and the corresponding macroscopic movement. The models are based on rigid--body formalisms and formulated as mechanical DAEs. We use the Generalized Gauß--Newton method based on multiple shooting discretization to estimate the parameters of this dynamic nonlinear parameter estimation problem using measurement data taken from motion capturing. We adapt modelling, integration and optimization independently and in combination. The modelling based on Natural Coordinates is modified to efficiently evaluate the right-hand side of the DAE in linear time w.r.t. the number of bodies. The formulation does not introduce additional redundant constraints and we developed constraint partitioning to treat inherent singularities of the physical model. Furthermore, we include additional biomechanical elements like passive muscles and wobbling masses. As Natural Coordinates lead to a set of redundant coordinates, we have to relax to treat inconsistent variables during the optimization process. To efficiently generate the sensitivity information needed for the optimization algorithm, we apply reduced methods to evaluate a minimal number of directional derivatives and exploit the structure of the model equations to calculate each of them. Finally, we present parameter estimation results for a complex, full three-dimensional biomechanical model of the human body with 82 kinematic degrees of freedom. This is implemented in the object-oriented modelling tool MBSNAT and the parameter estimation package Parfit++.
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