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Changes in resonant frequencies of linear systems due to added mass and loss of stiffness have been explored extensively for applications such as sensing, system identification and damage detection. The benefits of using resonant frequencies are the small number of sensors required and their insensitivity to noise (as opposed to using other system properties such as mode shapes or mode shape curvatures). However, resonant frequencies are also insensitive to damages/perturbations in the system. To overcome this limitation, linear feedback excitations have been used to place the poles (and eigenvectors) of the system and to increase their sensitivity to changes in the system properties. Recently, system augmentation has been combined with optimal nonlinear feedback auxiliary signals (as applied to damage detection). That method extended the use of sensitivity enhancement of resonant frequencies to nonlinear systems. Linear systems were also considered by using nonlinear feedback to demonstrate the benefits of nonlinear feedback auxiliary signals with respect to traditional linear feedback excitation. Nonlinear feedback auxiliary signals have been designed to maximize the sensitivity of resonant frequencies to changes in stiffness (while minimizing the control effort). The nonlinearities of the closed loop system were handled by forming augmented linear systems. In this work, this approach is refined to improve its robustness. In particular, an optimization is employed not only to maximize the sensitivity of resonant frequencies to added mass at particular locations, but also to detect changes in temperature and humidity. Additionally, a methodology is presented to accurately extract augmented frequencies from displacement and forcing data corrupted by noise. Numerical simulations of a nonlinear cantilevered beam are performed and the effects of measurement noise are discussed.

Sensitivity Enhancement of Modal Frequencies for Sensing using System Augmentation and Optimal Feedback Auxiliary Signals