Sparse identification for improving energy transfer in nonlinear systems

The project output will have significant impacts in the area of 

• data-driven methods
• ML and SI
• vibration mitigation
• vibration isolation
• vibration energy harvesting

Design and understanding of nonlinear models are required for optimal performance and for accurate reproduction of dynamical behavior. One of the intriguing phenomenon 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 tuned mass dampers, in contrast to nonlinear systems, where often individual nonlinear mechanisms are considered to be a model-specific. A majority 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), and 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 a number of gaps in the TET’s state-of-the-art.

1. 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.
2. 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.
3. There is no established framework for fast identification of the optimal nonlinear system for efficient TET from purely experimental data.

To address these gaps the project will combine ML optimisational gorithms, such as Surrogate optimisation (SO), data-driven methods and SI.