ABSTRACT
Analysis of time series from stochastic processes governed by a Langevin equation is discussed. Several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the Fokker-Planck equation. The coefficients are estimated directly from a time series. The applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting.
ABSTRACT
Monitoring of a machining process on the basis of sensor signals requires a selection of informative inputs in order to reliably characterize and model the process. In this article, a system for selection of informative characteristics from signals of multiple sensors is presented. For signal analysis, methods of spectral analysis and methods of nonlinear time series analysis are used. With the aim of modeling relationships between signal characteristics and the corresponding process state, an adaptive empirical modeler is applied. The application of the system is demonstrated by characterization of different parameters defining the states of a turning machining process, such as: chip form, tool wear, and onset of chatter vibration. The results show that, in spite of the complexity of the turning process, the state of the process can be well characterized by just a few proper characteristics extracted from a representative sensor signal. The process characterization can be further improved by joining characteristics from multiple sensors and by application of chaotic characteristics.
