Finite word-length optimal simulation for high-dimensional dynamical systems: Examples of tensegrity structures

This paper presents a model reduction technique to determine the optimal simulation model for high-dimensional systems within the confines of finite word-length computing. Such an optimal model is characterized by having minimal output error covariances in computational simulations when compared with the outputs of the physics model in reality. The round-off noise models for both floating- and fixed-point arithmetic are introduced first. Then, round-off error signals are incorporated into the dynamics models, representing the effects of finite precision. Analytical solutions for the simulation error covariance, perceived as a union of dynamics and round-off errors, are provided. Based on these insights, a general algorithm is developed to identify where the total simulation error is minimized, indicating the optimal model size. Two tensegrity structures, a two-dimensional morphing airfoil and a three-dimensional deployable tensegrity Levy cable dome, are analyzed to demonstrate this method. Our results show that large-scale models can be affected by increasing round-off errors in computational simulations, which might result in less accurate outcomes. However, by opting for a reduced-order simulation model, computational simulation performance can be improved considerably. Besides tensegrrity, the approach introduced in this research can be adapted to other high-dimensional dynamical system simulations.