Abstract
In this study, we consider the experimentally obtained, periodically forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions, while different levels of noise are injected into the system. Using these data, the robustness of the control-based continuation algorithm and its ability to capture the noise-free system response are assessed by identifying the parameters of an associated Duffing-like model. We demonstrate that control-based continuation extracts system information more robustly, in the presence of a high level of noise, than open-loop parameter sweeps and so is a valuable tool for investigating nonlinear structures.
Highlights
Studying physical structures experimentally can be a challenge if the measurements are polluted with a significant amount of noise
By investigating the steady-state response of a forced nonlinear oscillator under different levels of process noise, the robustness of control-based continuation was assessed by comparing it to open-loop measurements
We demonstrated that the ability of control-based continuation to capture both stable and unstable periodic solutions, and the fact that we have feedback control on the response, result in a more robust coverage of the solution branch than in case of parameter sweeps
Summary
Studying physical structures experimentally can be a challenge if the measurements are polluted with a significant amount of noise. One may find that a certain level of perturbation is tolerable and so the dynamics stay within the same basin of attraction, while a larger perturbation may lead the system to diverge from its originally observed steadystate behaviour This phenomenon means that by standard parameter sweeps, only stable solutions can be captured. Control-based continuation [27] is a method which incorporates the techniques of numerical continuation and bifurcation analysis to trace solutions of physical and numerical experiments where the governing equations are not explicitly available In principle, it is capable of capturing both stable and unstable steadystate solutions. While one could use the measured time profiles for the identification, here, we stick to the Sshaped amplitude response curves to assess the robustness of control-based continuation to noise directly on the bifurcation diagrams, which are frequently in the focus of studies on nonlinear systems. We assess if control-based continuation is capable to capture the response more accurately and if it is capable to reveal details from the system which would otherwise remain undetectable, providing a more robust basis for model building and parameter identification
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