Dynamic analysis of a human leg model with a prosthetic foot in the presence of polymorphic uncertainty

When designing modern structural systems, such as the foot prosthesis con- sidered in this work, analysis of their behaviour via simulations is an essential part of the design process. This process assumes that the model and the procedure used in the simulation both accurately represent the real struc- ture as well as the physical laws governing its behaviour. Ideally, this would mean, that the model is absolutely accurate and the simulation algorithms used are without errors in their calculations. However, this is not possible for multiple reasons. Some stem from simulation limitations, i. e., computational limitations or numerical discretisations. Others are caused by missing infor- mation, like for instance measurement inaccuracies or missing data. Thus, to be feasible, a reduction in the model’s complexity is necessary although this introduces additional uncertainty into the simulation. This uncertainty has many sources and can either be implicitly considered when interpreting the results by adding safety margins to the results or it can be considered explic- itly, by modelling it and including it in the simulation. The goal of this work is to provide an efficient algorithm for considering polymorphic uncertainty in the simulation of human gait with a prosthetic foot and is part of the larger Priority Programme Schwerpunktprogramm (SPP) 1886 ‘Polymorphic uncer- tainty modelling for the numerical design of structures’.

To do this, three aspects have to be combined. Firstly, a suitable model needs to be developed. Here, the human leg with a prosthetic foot is modelled as a multibody system with rigid and flexible bodies. Secondly, the uncertainty that will be considered in the simulation has to be formalised, quantified and modelled. Then, the simulation procedure has to be expanded so it can propagate the uncertainty through the model. Finally, the results have to be visualised and interpreted. Two types of uncertainty are considered in this thesis. The Graph Follower algorithm is used to propagate epistemic uncer- tainty through the developed model, before expanding the uncertainty model to polymorphic uncertainty in the form of fuzzy random numbers which is propagated via the newly developed Fuzzy Random Variable Graph Follower algorithm (FRV-GFA). Thus, this thesis contributes a forward dynamics sim- ulation of the human leg with a flexible prosthesis for two distinct gait phases, namely the swing phase and stance phase, in which parametric uncertainty is explicitly considered. To do this, the existing Graph Follower algorithm’s effi- ciency is greatly improved so it can propagate epistemic uncertainty through the model. The main contributions of this thesis are the development of a new model for marker position errors during optical motion capture and an efficient algorithm, based on the Graph Follower algorithm, which can propagate polymorphic uncertainty modelled with fuzzy random variables through the complex non-linear multibody system of a human leg with a flexible prosthetic foot.