Forecasting bifurcation morphing: application to cantilever-based sensing

Abstract

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 Forecasting for Large Dimensional Oscillatory Systems: Forecasting Flutter Using Gust Responses

“…This is used for predicting the postbifurcation regime (namely the bifurcation diagram). Following Lim and Epureanu [5,6], suppose that we collect time series during recoveries at several different parameter values l 1 ; l 2 ; :::; l n . At a given parameter value l k (with k ¼ 1…n), we can choose a value r ¼r and compute k l k ;r ð Þusing the measurements.…”

“…The solution used in the past by Lim and Epureanu [5,6] for this problem is to fix the phase by selecting the local maxima of the recovery data and using only those measured values in the same procedure (as for the nonoscillating case). This is a good approximation in the cases where the system oscillates with high frequencies [5,6]. However, in the case of low frequency oscillations, there may not be enough samples available to have a good approximation.…”

“…Several forecasting methods using observing the recovery rate of the system from perturbations have been proposed [2][3][4][5][6] (see Ref. [7] for a review).…”

“…First, the system recovers to its equilibrium state with oscillations, and one cannot use all of the measured data for forecasting since adjacent points are at different phases. In this case, one can simply choose the local maxima of the oscillating recovery data, approximate the recovery rate, and use the method suggested by Lim and Epureanu [5,6]. However, that approach requires a large number of local peaks in the response during recovery and it is hard or impossible to use when there are only a few peaks in the measured recovery.…”

“…The approach is mainly based on the phenomenon of CSD which accompanies such bifurcations. We use the technique presented by Lim and Epureanu [5,6] as the basis of our method, and extend it for bifurcation forecasting of more complex oscillating systems.…”