Detection of global and local parameter variations using nonlinear feedback auxiliary signals and system augmentation

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 to 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-type 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 are common in most applications, and they 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, these benefits are refined to improve the robustness of detection using sensitivity enhancement. Also, the benefits of system augmentation are explored by using few actuators and sensors. An optimization algorithm is employed not only to maximize the sensitivity of resonant frequencies to added mass at particular locations, but also to detect uniform changes in mass and stiffness. 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. Additionally, a methodology is presented to accurately extract augmented frequencies from displacement and forcing data corrupted by noise. Numerical simulations of cantilevered beams are used to validate the approach and discuss the effects of noise.