HYBRID COMPUTER UTILIZATION FOR THE OPTIMAL SMOOTHING FOR THE CONTROL OF A STOCHASTIC PROCESS

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

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On the equivalence of two stochastic approaches to spline smoothing

Journal of Applied Probability ◽

10.2307/3214367 ◽

1986 ◽

Vol 23 (A) ◽

pp. 391-405 ◽

Cited By ~ 7

Author(s):

Craig F. Ansley ◽

Robert Kohn

Keyword(s):

Stochastic Process ◽

Hilbert Space ◽

Minimization Problem ◽

Stochastic Models ◽

Conditional Expectation ◽

Smoothing Spline ◽

Computational Algorithms ◽

Spline Smoothing ◽

Optimal Smoothing ◽

Space Formulation

Wahba (1978) and Weinert et al. (1980), using different models, show that an optimal smoothing spline can be thought of as the conditional expectation of a stochastic process observed with noise. This observation leads to efficient computational algorithms. By going back to the Hilbert space formulation of the spline minimization problem, we provide a framework for linking the two different stochastic models. The last part of the paper reviews some new efficient algorithms for spline smoothing.

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An Investigation of Computer Control of Machining Chatter

Journal of Engineering for Industry ◽

10.1115/1.3439086 ◽

1976 ◽

Vol 98 (4) ◽

pp. 1209-1213 ◽

Cited By ~ 10

Author(s):

T. L. Subramanian ◽

M. F. DeVries ◽

S. M. Wu

Keyword(s):

Stochastic Process ◽

Process Modeling ◽

Feed Rate ◽

Computer Control ◽

Vibration Signal ◽

Process Variables ◽

Control Scheme ◽

Machining Chatter ◽

Hybrid Computer ◽

And Control

Based on stochastic process modeling, a scheme has been developed for the detection and control of machining chatter. The range of the tool vibration signal is computed by a hybrid computer and compared with permissible limits to exercise automatic change of the speed and feed rate. The control scheme was evaluated for its adaptability and effectiveness by forcing a chatter condition and subjecting the process to computer control. The scheme is sensitive to process variables.

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Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

Journal of Applied Probability ◽

10.1017/s0021900200003041 ◽

2007 ◽

Vol 44 (02) ◽

pp. 393-408 ◽

Cited By ~ 1

Author(s):

Allan Sly

Keyword(s):

Stochastic Process ◽

Brownian Motion ◽

White Noise ◽

Gaussian Process ◽

Discrete Data ◽

Hölder Exponent ◽

Scaling Properties ◽

Multifractional Brownian Motion ◽

Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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