Grey-Box Modelling via Gaussian Process Mean Functions for Mechanical Systems

2021 ◽  
pp. 161-168
Author(s):  
Sikai Zhang ◽  
Elizabeth J. Cross
Keyword(s):  
Gaussian Process ◽  
Mechanical Systems ◽  
Process Mean

Radon-Nikodym derivatives, passages and maxima for a Gaussian process with particular covariance and mean

1975 ◽  
Vol 12 (4) ◽  
pp. 724-733 ◽  
Author(s):  
Israel Bar-David
Keyword(s):  
Parameter Estimation ◽  
Gaussian Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Multiple Reflections ◽  
Process Mean ◽  
First Passage ◽  
Estimation Problems ◽  
Rectangular Signal

We find expressions for the R–N derivative of the stationary Gaussian process with the particular covariance and mean, respectively, R(t, s) = max(1 – |t – s|, 0) and m(t)= aR(t, D), 0 ≦ D ≦ 1, within the time interval [0, 1]. We use these results, and a lemma on multiple reflections of the Wiener process, to find formulae for the probabilities of first passage time and maxima in [0, 1], and bounds on the former within [– 1, 1]. While previous work dealt extensively with the zero mean process, mean functions, as defined here, appear in signal detection and parameter estimation problems under the hypothesis that a rectangular signal centered at t = D is present in an observed process.

Radon-Nikodym derivatives, passages and maxima for a Gaussian process with particular covariance and mean

1975 ◽  
Vol 12 (04) ◽  
pp. 724-733 ◽  
Author(s):  
Israel Bar-David
Keyword(s):  
Parameter Estimation ◽  
Gaussian Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Multiple Reflections ◽  
Process Mean ◽  
First Passage ◽  
Estimation Problems ◽  
Rectangular Signal

We find expressions for the R–N derivative of the stationary Gaussian process with the particular covariance and mean, respectively, R(t, s) = max(1 – |t – s|, 0) and m(t)= aR(t, D), 0 ≦ D ≦ 1, within the time interval [0, 1]. We use these results, and a lemma on multiple reflections of the Wiener process, to find formulae for the probabilities of first passage time and maxima in [0, 1], and bounds on the former within [– 1, 1]. While previous work dealt extensively with the zero mean process, mean functions, as defined here, appear in signal detection and parameter estimation problems under the hypothesis that a rectangular signal centered at t = D is present in an observed process.

scholarly journals Control of Mechanical Systems via Feedback Linearization Based on Black-Box Gaussian Process Models

2021 ◽  
Author(s):  
Alberto Dalla Libera ◽  
Fabio Amadio ◽  
Daniel Nikovski ◽  
Ruggero Carli ◽  
Diego Romeres
Keyword(s):  
Gaussian Process ◽  
Feedback Linearization ◽  
Mechanical Systems ◽  
Black Box ◽  
Process Models ◽  
Gaussian Process Models

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
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.

A Stochastic Model for the Inheritance of the Cancer Proneness Phenotype

1987 ◽  
Vol 26 (03) ◽  
pp. 117-123
Author(s):  
P. Tautu ◽  
G. Wagner
Keyword(s):  
Stochastic Model ◽  
Gaussian Process ◽  
Covariance Function ◽  
Neoplastic Disease ◽  
Disease Phenotype ◽  
Probabilistic Representation ◽  
Temporal Behaviour ◽  
Continuous Trait ◽  
Continuous Parameter ◽  
Level Zero

SummaryA continuous parameter, stationary Gaussian process is introduced as a first approach to the probabilistic representation of the phenotype inheritance process. With some specific assumptions about the components of the covariance function, it may describe the temporal behaviour of the “cancer-proneness phenotype” (CPF) as a quantitative continuous trait. Upcrossing a fixed level (“threshold”) u and reaching level zero are the extremes of the Gaussian process considered; it is assumed that they might be interpreted as the transformation of CPF into a “neoplastic disease phenotype” or as the non-proneness to cancer, respectively.

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