Parameter estimation from occupation times—a white noise approach

In this paper we investigate the parameter estimation of the fiber lay-down process in the production of nonwovens. The parameter estimation is based on the mass per unit area data, which is available at least on an industrial scale. We introduce a stochastic model to represent the fiber lay-down and through the model's parameters we characterize this fiber lay-down. Based on the occupation time, which is the equivalent quantity for the mass per unit area in the context of stochastic dynamical systems, an optimization procedure is formulated that estimates the parameters of the model. The optimization procedure is tested using occupation time data given by Monte-Carlo simulations. The feasibility of the optimization procedure on an industrial level is tested using the fiber paths simulated by the industrial software FYDIST. arXiv:1112.3550v1 [math.PR]

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“…The following theorem can be proven using the techniques of white noise analysis, see [1] for the one-dimensional case.…”

Section: Model and Theorymentioning

confidence: 99%

Parameter estimation of fiber lay-down in nonwoven production: an occupation time approach

Böck

Götz

Liyanage

2018

Int J Adv Eng Sci Appl Math

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“…The model is based on stochastic differential equations describing the resulting position of the fiber on the belt under the influence of turbulent air flows. In [1] parameter estimation of the Ornstein-Uhlenbeck process from available mass per unit area data, the occupation time in mathematical terms, was done. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

A White Noise Approach to Occupation Times of Brownian Motion

Suryawan

2022

Int.J.Appl.Sci.Smart Technol.

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Occupation times of a stochastic process models the amount of time the process spends inside a spatial interval during a certain finite time horizon. It appears in the fiber lay-down process in nonwoven production industry. The occupation time can be interpreted as the mass of fiber material deposited inside some region. From application point of view, it is important to know the average mass per unit area of the final fleece. In this paper we use white noise theory to prove the existence of the occupation times of one-dimensional Brownian motion and provide an expression for the expected value of the occupation times.

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Parameter estimation from occupation times—a white noise approach

Cited by 2 publications

References 7 publications

Parameter estimation of fiber lay-down in nonwoven production: an occupation time approach

Parameter estimation of fiber lay-down in nonwoven production: an occupation time approach

A White Noise Approach to Occupation Times of Brownian Motion

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