Machine learning tools for improving energy transfer in nonlinear systems

Design and understanding of nonlinear models are required for optimal performance and for accurate reproduction of dynamical behaviour. One of the intriguing phenomena in nonlinear systems is Targeted Energy Transfer (TET), where the goal is to transfer energy within a nonlinear system between subsystems. 

The theory of linear dynamical systems is well-developed in the context of tuned mass dampers. This contrasts to nonlinear systems, where often individual nonlinear mechanisms are model-specific. Most of these approaches rely on perturbation theory, which is valid for weak nonlinearities over finite time. 

TET is a nonlinear alternative that can also be generalised to multi-degree-of-freedom systems. In the traditional TET formulation, the nonlinearities are given for all degrees of freedom (for instance of cubic order). The energy-transfer subsystem is tuned to an optimal set of parameters (coefficients) to mitigate undesirable dynamics of the primary system.

Based on the existing publications this leaves several gaps in the TET’s state-of-the-art:

• the typical approximate methods used to analyse TET are not applicable to fully nonlinear effects and are infeasible for necessary multi-degree-of-freedom (MDOF) systems
• a given nonlinearity in the system may not be optimal, and traditional methods do not scale to exploring the full range of potential nonlinear mechanisms
• there is no established framework for fast identification of the optimal nonlinear system for efficient TET from purely experimental data

You will work on these 3 points by combining ML optimization algorithms, such as Surrogate Optimization (SO), data-driven methods and SI.