Hybrid simulation theory for a classical nonlinear dynamical system

Abstract

a b s t r a c tHybrid simulation is an experimental and computational technique which allows one to study the time evolution of a system by physically testing a subset of it while the remainder is represented by a numerical model that is attached to the physical portion via sensors and actuators. The technique allows one to study large or complicated mechanical systems while only requiring a subset of the complete system to be present in the laboratory. This results in vast cost savings as well as the ability to study systems that simply can not be tested due to scale. However, the errors that arise from splitting the system in two requires careful attention, if a valid simulation is to be guaranteed. To date, efforts to understand the theoretical limitations of hybrid simulation have been restricted to linear dynamical systems. In this work we consider the behavior of hybrid simulation when applied to nonlinear dynamical systems. As a model problem, we focus on the damped, harmonically-driven nonlinear pendulum. This system offers complex nonlinear characteristics, in particular periodic and chaotic motions. We are able to show that the application of hybrid simulation to nonlinear systems requires a careful understanding of what one expects from such an experiment. In particular, when system response is chaotic we advocate the need for the use of multiple metrics to characterize the difference between two chaotic systems via Lyapunov exponents and Lyapunov dimensions, as well as correlation exponents. When system response is periodic we advocate the use of L 2 norms. Further, we are able to show that hybrid simulation can falsely predict chaotic or periodic response when the true system has the opposite characteristic. In certain cases, we are able to show that control system parameters can mitigate this issue.

Application of Artificial Neural Networks in Hybrid Simulation

“…The division between both subsystems is defined by interface I. Boundary conditions for interface boundaries of subsystems: I A and I P are defined by actuators and force sensors. On the boundary I A , forces are known (measured by the sensors), and on the boundary I P , displacements are known (imposed by the actuators) [2,3,13]. Appl.…”

“…The main idea is that the physical subsystem is deformed during the simulation, exactly as it would be deformed as a part of the whole system under load. In order to achieve that, maintaining the full dynamical behavior of the system, all the finite element (FE) computations and data interchange between both subsystems must be performed in real-time [1,2].…”

A new nondeterministic method for optimal selection of master degrees of freedom for dynamic condensation based on evolutionary optimization

“…Apart from possible applications of the reduced models described above, another motivation for optimal model order reduction is real-time application of the finite element method (FEM), e.g. hybrid simulation (Drazin and Govindjee, 2017;Mucha, 2019;Ramos et al, 2016), surgery simulations (Audette et al, 2004;Berkley et al, 2004;Lapeer et al, 2010) and control of elastic soft robots (Duriez, 2013). In such cases, the finite element model must be reduced as much as possible, while remaining required accuracy, in order to enable or speed-up real-time computations where the calculation time is crucial.…”