Forecasting bifurcations before they occur is a significant challenge and an important need in several fields. Existing approaches detect bifurcations before they occur by exploiting the critical slowing down phenomenon. However, the perturbations used in those approaches are limited to being very small and this represents a significant drawback. Large levels of perturbation have not been used mainly because of a lack of an adequate formulation that is robust to experimental noise. This paper provides such a formulation, and discusses how this approach to forecasting bifurcations is more accurate, especially when the dynamics are far from the bifurcation. Both numerical and experimental results are presented to demonstrate the technique and highlight its advantages over other prediction methods.

Two novel techniques are proposed to enhance the bifurcation morphing method as applied to cantilever-based sensors. First, nonlinear feedback excitations with added time delay are employed to minimize the sensitivity of the sensors to small variations in the unavoidable time delay. Second, a novel approach to forecast bifurcations is applied to the sensors. This approach significantly reduces the time required to obtain bifurcation diagrams. Both techniques are demonstrated experimentally in detecting mass variations of a test cantilever beam. This cantileverbased sensor operating based on the bifurcation morphing method is shown to be accurate, quick and robust when these techniques are utilized.

Bifurcation morphing created by means of nonlinear feedback excitation is a vibration-based method for sensing. In this work, several new studies are presented to connect previously demonstrated theory to increasingly more practical applications. In particular, in the process of designing nonlinear feedback auxiliary signals, time delays in the circuitry are unavoidable. Advantages as well as possible side e®ects and disadvantages of time delays are discussed. Furthermore, additional time delay is considered as a new design parameter. Increasing the time delay has advantages such as enhanced robustness and sensitivity, which are demonstrated computationally. Moreover, calibration using multiple sensor locations is discussed. A clampedfree cantilever beam structure is modeled and used for computational validation. The beam model resembles cantilever-based resonant sensor systems. Thus, potential applications of the new algorithm are discussed and the results stress the importance of nonlinear features for enhancing sensing performance in mechanical sensors without structural modi¯cations.

The application of the sensitivity vector fields (SVFs) for tip-sample interactions in the context of multi-mode tapping dynamics of atomic-force microscopes (AFM) is presented. SVFs represent a novel approach to accurately determine simultaneous parameter variations by exploiting the geometric features of observed chaotic dynamics. The paper also demonstrates that, in certain operating conditions, higher modes are essential to correctly predict the AFM dynamics, and they cannot be neglected. The accuracy of the SVF approach is discussed as applied to a multimode AFM model where mode shapes vary due to multiple parameter variations. The identifiability of various parameters based on SVF reconstruction is investigated. Several calibration issues for parameter reconstruction are observed and resolved by a specialized sample filtering and a novel correction factor.

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