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

Jakub Dokoupil,Pavel Václavek

doi:10.1088/1742-6596/633/1/012057

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.

Highlights

The problem of singular point detection of the atomic force microscope cantilever [1] can be viewed as the adaptive testing of hypotheses, each one matched to a certain model order
We extend the approach of the exponential forgetting scheme
The resulting formula is based on solving the statistical decision problem [3], [4], where the Kullback-Leibler divergence [5] is used to measure a distance between two mass functions

Summary

Introduction

The problem of singular point detection of the atomic force microscope cantilever [1] can be viewed as the adaptive testing of hypotheses, each one matched to a certain model order. The resulting formula is based on solving the statistical decision problem [3], [4], where the Kullback-Leibler divergence [5] is used to measure a distance between two mass functions. Dealing with the problem of which from competing models is more suitable to explain the data generating process a subjective measure of confidence for each model is evaluated to choose the most probable one. The given solution for the comparison of nonnested models produced by the Kalman based algorithms could not be put into practice. For this reason, the existing concept is reformulated preserving its Bayesian principle to be more beneficial in the case where on-line processing is needed. Published under licence by IOP Publishing Ltd doi:10.1088/1742-6596/633/1/012057

Adaptive model comparison

Conclusion