Modal analysis is a well developed field with many applications. The multi-output approaches in particular are
well suited for system identification and online damage detection because they use the natural excitations the
system undergoes in its normal operation. In this work two multi-output approaches are analyzed, compared,
and improved upon. The first method is smooth orthogonal decomposition (SOD). SOD was originally developed
as a tool for detecting features of chaotic dynamical systems. Recently, it has been used as a time-based multioutput
modal analysis approach. SOD has been demonstrated effectively for the free vibration case and for
random excitations. The second method is direct system parameter identification (DSPI). DSPI was developed
as a time-based multi-input multi-output modal analysis approach. When the inputs are not measured DSPI
can handle the free vibration case and random excitations like SOD. If the inputs are measured then DSPI works
with arbitrary excitations. In addition to comparing SOD and DSPI, novel filtering algorithms are introduced
to improve each method's performance when working with noisy data. Numerical simulations are carried out to
compare the two methods and demonstrate the effectiveness of the filtering algorithms in improving frequency
and mode shape extraction.
Recently, system augmentation has been combined with nonlinear feedback auxiliary signals to provide sensitivity
enhancement in both linear and nonlinear systems. Augmented systems are higher dimensional linear systems
that follow trajectories of a nonlinear system one at a time. These augmented systems are subject to a specialized
augmented forcing which enforces the augmented system will exactly reproduce the trajectory of the nonlinear
system when projected onto the lower dimensional (physical) system. Augmented systems have additional
benefits outside of handling nonlinear systems, which makes them more desirable than regular linear systems
for sensitivity enhancing control. One of the key advantages of augmented systems is the complete control over
the augmented degrees of freedom, and the additional sensor knowledge from the augmented variables. These
sensing and actuation features are very useful when only few physical actuators and sensors can be placed.
Such restrictions severely limit the usefulness of traditional linear sensitivity enhancing feedback approaches.
Another benefit of the augmentation is that the control exerted on the augmented degrees of freedom does not
require any physical energy, rather it is just signal processing. In this work, the benefits of system augmentation
are explored by using few actuators and sensors. In addition to increased sensitivity for both global and local
parameter changes, a study of increasing the sensitivity of local changes, while decreasing the sensitivity of global
changes is conducted. Numerical simulations for a linear cantilevered beam with a single piezo-actuator and two
sensors are used to validate the approach and discuss the effects of noise.
Recently, a sensitivity enhancement technique for damage detection using eigenstructure assignment has been
extended from linear to nonlinear systems. Nonlinearities have been accounted for by forming (higher dimensional)
augmented systems, which are designed for each trajectory of the nonlinear system, and are characterized
by a specific forcing that ensures that the augmented systems follow that trajectory (when projected onto the
original, lower dimensional space). The use of system augmentation for damage detection has several benefits
beyond its ability to handle nonlinearities. For example, sensitivity can be increased compared to existing linear
techniques through nonlinear feedback auxiliary signals because the constraint that the system is stable during
its interrogation has to be applied only to the linearized closed loop system, while the augmented linear system
does not have that constraint. In this work, the various benefits of <i>nonlinear</i> feedback auxiliary signals are
explored for damage detection in linear systems. System augmentation is used in a linear system because a
nonlinear controller is employed to enhance sensitivity. In addition to the increased sensitivity, fewer controller
actuator points and sensors are required compared to existing linear techniques due to the efficient use of added
(augmented) equations. Numerical simulations for a linear mass-spring and a linear mass-spring-damper system
are used to validate the approach and discuss the effects of noise.
Recently, a damage detection method for nonlinear systems using model updating has been developed by the authors. The method uses an augmented linear model of the system, which is determined from the functional form of the nonlinearities and a nonlinear discrete model of the system. The modal properties of the augmented system after the onset of damage are extracted from the system using a modal analysis technique that uses known but not prescribed forcing. Minimum Rank Perturbation Theory was generalized so that damage location and extent could be determined using the augmented modal properties. The method was demonstrated previously for cubic springs and Coulomb friction nonlinearities. In this work, the methodology is extended to handle large systems where only the first few of the augmented eigenvectors are known. The methodology capitalizes on the ability to create multiple augmentations for a single nonlinear system. Cubic spring nonlinearities are explored within a nonlinear 3-bay truss structure for various damage scenarios simulated numerically.