Instantaneous scale of fluctuation using Kalman-TFD and applications in machine-tool monitoring

P. G. Madhavan

doi:10.1117/12.279515

24 October 1997 Instantaneous scale of fluctuation using Kalman-TFD and applications in machine tool monitoring

P. G. Madhavan

Proceedings Volume 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII; (1997) https://doi.org/10.1117/12.279515
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

A new theory of random fields based on the concept of local averaging was developed in the 80s where the second-order properties of the random fields are characterized by the variance function. Certain asymptotic properties of the variance function lead to the definition of a scalar called the 'scale of fluctuation,' which has many interesting properties. A non- parametric method of estimating instantaneous scale of fluctuation is developed using the time-varying model-based time-frequency distribution. A wide range of random processes can be modeled by appropriate state-space models with white process noise. For properly defined state transition matrices and observation vectors, the states estimated using Kalman filtering or smoothing algorithms provide the estimated time-frequency distribution (Kalman-TFD). Using Kalman-TFD, the instantaneous scale of fluctuation is estimated. Performance of this estimator is compared to other instantaneous and block methods using the coefficient of variation of the estimators. The Kalman-TFD-based scale of fluctuation estimator has a coefficient of variation of 6% where as other methods yield coefficients of variation greater than 35%. The instantaneous scale of fluctuation quantifies the temporal variability of the underlying system and possible resultant limit- cycle oscillations. Tests with real vibration data from machine tools before and during chatter show that the estimated instantaneous scale of fluctuation may permit on-line prediction of chatter development many hundreds of milliseconds in advance. To explain the behavior of the estimated instantaneous scale of fluctuation during pre-chatter period, detailed simulations were undertaken which revealed that the random process during pre- chatter condition goes through an increase in 'degrees-of-freedom' or its unit standard deviation contour volume.

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P. G. Madhavan "Instantaneous scale of fluctuation using Kalman-TFD and applications in machine tool monitoring", Proc. SPIE 3162, Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, (24 October 1997); https://doi.org/10.1117/12.279515

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KEYWORDS

Process modeling

Autoregressive models

Filtering (signal processing)

Time-frequency analysis

Correlation function

Electronic filtering

Statistical analysis

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