Attractor and Bifurcation Morphing Modes for High-Sensitivity Sensing.

Nonlinear Systems;Chaos;Bifurcation Morphing;Bifurcation Forecasting;Cantilever Sensors;Mechanical Engineering;Engineering;Mechanical Engineering

Lim, JoosupOldham, Kenn Richard ;

University of Michigan

关键词: Nonlinear Systems;    Chaos;    Bifurcation Morphing;    Bifurcation Forecasting;    Cantilever Sensors;    Mechanical Engineering;    Engineering;    Mechanical Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/84483/jooslim_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Novel techniques are developed to enhance the nonlinear approaches based on attractor morphing modes and bifurcation morphing modes for applications including atomic force microscopes (AFMs), and cantilever-based sensing. Furthermore, a novel approach of forecasting bifurcations is introduced and its applicability to a diversity of multidisciplinary systems is discussed. This forecasting approach is used as an essential tool to enhance the bifurcation morphing approach in applications using cantilever-based sensors for quick, robust and accurate sensing.Sensitivity vector fields (SVFs) are introduced to characterize the basic concept of attractor morphing modes. In this dissertation, the application of the SVF approach is discussed with a particular emphasis on cases where achieving proportionality of SVFs is challenging due to undesirable nonlinearities in the morphing of attractors. A filter for sample points is introduced to resolve strong nonlinearities. In addition, a correction factor is introduced for weak nonlinearities and shown to be very accurate.As an example, the nonlinear characteristics of a tapping-mode AFM is studied and the operation of the AFM is demonstrated in a chaotic regime using the SVF approach.Bifurcation morphing modes have been numerically shown to have high sensitivity to variations in the system parameters of interest. In this work, several issues of bifurcation morphing are discussed for practical applications. First, the effects of the unavoidable time delay to the bifurcation morphing modes are studied, and an approach to mitigate the undesirable side-effects of natural time delay is proposed. Second, a novel approach of forecasting bifurcations is introduced. A mathematical formulation is developed to forecast bifurcations based on large levels of perturbation to enhance current forecasting approaches (which are usually based only on small perturbations). The new forecasting approach can be applied to the bifurcation morphing method to significantly reduce the time required to detect the bifurcation diagram, and to ensure operation without driving the system into the post-bifurcation regime. Forecasting bifurcations (before they occur) is a significant challenge and an important need not only for methods based on bifurcation morphing, but also for other applications to a variety of engineered systems.