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Institute
BTU
Zhe paper introduces ideas from shape optimization to multibody system dynamics. A disk rolling down a given slope is taken as a simple example, for which it is the goal of the optimization to shape the rolling contour of the disk such that it takes a minimum time to cover a certain distance. The shape of the sontour is described by its radius of curvature. The governing equations of motion result from the kinematics of relative motion and the Nowton-Euler formalism. Three different kinds of spirals are defined and optimized.
The identification of parameters in dynamic systems usually first requires modeling the system as nonlinear differential equations based on physical principles, which then can be evaluated to search for a set of optimal parameters that enable the mathematical model to reproduce some desired behavior of the real system. To overcome the necessity of complex modeling and to possibly reduce the number of extensive experimental evaluations of the real system or numerical evaluations of the differential equations, strategies from machine learning may be applied. The proposed method uses recurrent architectures such as Long Short-Term Memory (LSTM) networks as core to predict the system development from initial conditions and parameter values. The trainable weights of the model are optimized based on a set of training data containing parameter values and corresponding solution trajectories generated by evaluation of the system to be investigated. The trained model may then be used to identify unknown system parameter values related to a specific solution trajectory by solving an optimization problem for the inputs of the machine learning model.