Machine tool chatter is an unfavorable phenomenon during metal cutting, which results in heavy vibration of cutting tool. With increase in depth of cut, the cutting regime changes from chatter-free cutting to one with chatter. In this paper, we propose the use of permutation entropy (PE), a conceptually simple and computationally fast measurement to detect the onset of chatter from the time series using sound signal recorded with a unidirectional microphone. PE can efficiently distinguish the regular and complex nature of any signal and extract information about the dynamics of the process by indicating sudden change in its value. Under situations where the data sets are huge and there is no time for preprocessing and fine-tuning, PE can effectively detect dynamical changes of the system. This makes PE an ideal choice for online detection of chatter, which is not possible with other conventional nonlinear methods. In the present study, the variation of PE under two cutting conditions is analyzed. Abrupt variation in the value of PE with increase in depth of cut indicates the onset of chatter vibrations. The results are verified using frequency spectra of the signals and the nonlinear measure, normalized coarse-grained information rate (NCIR).

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Permutation Entropy (PE) statistic is a measure of self-similarity of the time series estimated from its ordinal patterns. This measure is used to detect the dynamical differences between patients with mild cognitive impairment (MCI) and normal controls. The comparison of PE values of Electroencephalograph (EEG) of the two groups in the resting eyes closed (EC) state and the short-term memory task (STM) state reveals altered efficiency of the different lobes of MCI brain in the compensational dynamical mechanism for task management. In resting EC state, PE values of MCI group is significantly (p †0:05) lower than that of controls in the frontal, temporal, and anterior parietal regions. In the STM task state, entropy levels of MCI group are significantly (p †0:05) lower than that of controls in the frontal region and the left parietal region. These findings suggest that nonlinear analysis of EEG using PE can provide important information about EEG characteristic of cognitively impaired condition that can lead to Alzheimer's Disease(AD).

In this Letter we numerically investigate the dynamics of a system of two coupled chaotic multimode Nd:YAG lasers with two mode and three mode outputs. Unidirectional and bidirectional coupling schemes are adopted; intensity time series plots, phase space plots and synchronization plots are used for studying the dynamics. Quality of synchronization is measured using correlation index plots. It is found that for laser with two mode output bidirectional direct coupling scheme is found to be effective in achieving complete synchronization, control of chaos and amplification in output intensity. For laser with three mode output, bidirectional difference coupling scheme gives much better chaotic synchronization as compared to unidirectional difference coupling but at the cost of higher coupling strength. We also conclude that the coupling scheme and system properties play an important role in determining the type of synchronization exhibited by the system.

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