Parametric Variation Identification Techniques in Nonlinear Dynamical Systems.

Nonlinear Systems;Parameter Variations;Mechanical Engineering;Engineering;Mechanical Engineering

Sloboda, Andrew R.Oldham, Kenn Richard ;

University of Michigan

关键词: Nonlinear Systems;    Parameter Variations;    Mechanical Engineering;    Engineering;    Mechanical Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/99892/asloboda_1.pdf?sequence=1&isAllowed=y

瑞士|英语

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

【 摘 要 】

Identification of parameter variations in dynamical systems is critical for many engineering applications. On the macro-scale, variation identification forms the basis of damage detection methods that monitor the integrity of infrastructure such as bridges and airframes. On the micro-scale, variation identification is the basis for sensing devices such as atomic force microscopes and micro-sensors. Thus, developing effective techniques for identifying parameter variations in a variety of dynamical systems is an important goal.Nonlinear systems are one subclass of systems for which traditional modal methods are often ineffective. This has spurred the development of alternative methodologies for use in such systems. In this dissertation, two methodologies for identifying parameter variations in nonlinear systems are presented. The first methodology, sensitivity vector fields (SVFs), examines how dynamical system attractors deform when a system undergoes parametric variations. This is accomplished by quantifying the separation of nominal and varied system trajectories in state space. Because SVFs are concerned with changes in attractor geometry, nonlinearity is something that can be exploited rather that avoided. The second identification methodology, system augmentation, casts a nonlinear system within the framework of a larger linear system, replacing system nonlinearities with additional variables and augmenting the original system equations with new equations having prescribed forcing. The advantage of this new, linear formulation is that modal methods are applicable.This work focuses on improving fundamental understanding of these two methodologies and developing additional techniques in order to make them applicable to real, physical systems. Specifically, a parametric study of the factors that influence SVF performance is presented, and two methods for providing feedback to improve SVF sensitivity are described. A method for using SVFs in time-delay embedding coordinates is also developed. Regarding system augmentation, some techniques are introduced that make the methodology amenable to a wider variety of systems and simplify the process of parameter identification. For both methodologies, experimental testing validates some of the more theoretical aspects of the work.