A multi-mode cantilever singular point detection using adaptive hypothesis testing

Abstract

Fundamental analysis of a multi-mode model of the atomic force microscope cantilever shows that at some points; called here singular points, the mode is vanished. Consequently, the order of the input/output behavior is reduced. The singular points can be detected comparing possible candidates on the best model order. The detection is then naturally performed by applying the Bayesian model comparison. Since the exact position of the singular points is not available a priori, an explicit model of updating the probability of tested hypotheses in time is built. More specifically, a mechanism of suppressing absolute information is suggested based on the Bayesian decision problem where the Kullback-Leibler divergence is used.Fundamental analysis of a multi-mode model of the atomic force microscope cantilever shows that at some points; called here singular points, the mode is vanished. Consequently, the order of the input/output behavior is reduced. The singular points can be detected comparing possible candidates on the best model order. The detection is then naturally performed by applying the Bayesian model comparison. Since the exact position of the singular points is not available a priori, an explicit model of updating the probability of tested hypotheses in time is built. More specifically, a mechanism of suppressing absolute information is suggested based on the Bayesian decision problem where the Kullback-Leibler divergence is used.