Creating and Exploiting Nonlinear and Chaotic Dynamics for

System Interrogation in Sensing and Damage Detection

Bogdan I. Epureanu

Department of Mechanical Engineering

University of Michigan - Ann Arbor

ABSTRACT

Most current system interrogation approaches used in applications such as system identification, damage detection and structural health monitoring are passive in that they are based on passively observing the system dynamics. Other approaches are active in that they apply an auxiliary signal to the system (in the form of excitation). All such current techniques use predefined excitation signals, which can be of a variety of types, ranging from pulsed waves to frequency sweeps. Such auxiliary signals are designed off-line, and do not adapt to the particularities of the response of the system during its interrogation. A novel technique for interrogating systems by using nonlinear feedback auxiliary signals will be presented. The feedback nature of this form of excitation is an essential enabling feature for enhancing sensitivity and selectivity of the resulting novel interrogation paradigm. The proposed techniques are applied to sensing and damage detection, and exploit two radically new ideas.

The first idea is to actively induce desired nonlinear phenomena such as chaos and bifurcations in the dynamics of a system (which can be linear or nonlinear) by applying nonlinear feedback auxiliary signals. The morphology of bifurcation boundaries is then utilized to identify parameter variations indicative of damage. Moreover, the morphology (deformation) of the attractor of the nonlinear closed loop dynamics is used to identify multiple simultaneous parameter variations (e.g. damages) with very high sensitivity by employing a novel concept referred to as sensitivity vector fields. A unique perspective on the design of suitable attractors by means of nonlinear feedback auxiliary signals is discussed. In particular, the question of how to design a nonlinear controller that creates an attractor whose morphing reveals certain parameter variations most effectively is tackled. Most current studies of such problems are based on linear theories. In contrast, the proposed approaches exploit nonlinear phenomena, and can enhance accuracy and sensitivity (e.g. by monitoring attractor morphing).

The second key idea is based on a novel methodology for designing optimal nonlinear controllers for system interrogation. To design such controllers, the nonlinearity is accounted for by creating augmented linear models of higher order (in a higher dimensional state space). These augmented models have a specific forcing in the augmented degrees of freedom. The specific forcing ensures that the augmented models follow the trajectory of the nonlinear system when projected onto the original (physical) space. These augmented models open the door to using advanced (input/output) approaches for modal extraction and system identification which previously could be used only for linear systems. The input/output nature of the identification approach is particularly well suited for use in conjunction with nonlinear feedback auxiliary signals since there the input excitation is known (as the controller output is easily measured). This technique addresses three major limitations of existent frequency-based detection methods, namely the low sensitivity of the frequencies to damages, the limited number of parameters identifiable from frequency-only measurement data, and the need for enhanced sensitivity for nonlinear systems.

To demonstrate the applicability and the potential offered by the proposed approach, several systems are explored numerically and experimentally, including: various frame structures, a cantilever sensing beam, and an atomic force microscope in tapping mode.