Traditional Problem Definition - Computational Intelligence in Time Series Forecasting - page 67

their close relationship between the generation of the emission signal and the wear
condition of the tool.
The acoustic emission technique used is an adequate means for monitoring the
cutting tool wear condition (Liang and Dornfeld, 1989), because the frequency
band emitted by tool wear is much higher than the machine vibration frequency
band. Thus, the two frequency bands can be easily separated by a high-pass filter.
Also, the frequency signal emitted can be picked up directly from a sensor installed
on the tool holder.
Once the measured signal is obtained, the time series data sets can be built by
sampling the acoustic emission signal and thereafter its prediction can be made by
processing the time series data. The main difficulty here, however, is the high
sampling frequency required to build the time series of the emitted acoustic signal
having a frequency band of 100 kHz to 1 MHz and requiring a sampling frequency
of over 2 MHz.

2.10.5 Minimum Variance Control

Time series analysis and forecasting have been, since the earliest days of
engineering, powerful tools for problem solving in signal and system analysis and
prediction. Initially, the application of vibration analysis to machines and like
objects was the essential field of application, but later this was extended to
encompass most various application fields, including systems identification,
parameter estimation, and in self-tuning and predictive control.
An excellent representative application example is found in model building,
parameter estimation, and predictive control of dynamic systems. For this purpose,
the modifications of ARMA and ARIMA models are used, known as CARMA (or
CARMAX) and CARIMA (or CARIMAX), where C stands for control and X for
auxiliary input signal .
We would first like to use the CARIMA model

A zyt ()()

1

zBzut

k

()() ()()

1

Czet

1

(2.14)

to implement minimum variance control , designed to keep the output of a
stochastic system to the set point value. This requires that, for each time instant t ,
the value of the control signal u ( t ) should be determined to minimize the output
variance

J Ey t k

{(

}

Introducing the Diophantine equation

k
CAFzG (2.15)

with the polynomials