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Numerical path integration of stochastic systems
| Title: | Numerical path integration of stochastic systems. |
 108 views 46 downloads |
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| Name(s): |
Yu, Jinshou. Florida Atlantic University, Degree grantor Lin, Y. K., Thesis advisor College of Engineering and Computer Science Department of Ocean and Mechanical Engineering |
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| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Issuance: | monographic | |
| Date Issued: | 1997 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 197 p. | |
| Language(s): | English | |
| Summary: | The present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed, which requires no explicit numerical interpolation. The probability evolution is represented in terms of the transition probabilities among Gauss points in various sub-intervals. Each transition probability is assumed to be Gaussian, and it can be obtained from the moment equations. Gaussian closure is used to truncate the moment equations in the case of a nonlinear system. The computation parameters of the new procedure, such as size of time-step and number of sub-intervals, can be determined in a systematic manner. The approximate Gaussianity of the transition probability obtained from the moment equations is first tested by comparing it with the simulation results, from which a proper time-step size is selected. The standard deviation of the transition probability in each direction of the state space can then be obtained from the moment equations, and is used to determine the size of the sub-intervals in that direction. The new numerical path integration procedure is applied to several one-dimensional and two-dimensional stochastic systems, for which the responses are homogeneous Markov processes. It is shown that the new procedure is not only accurate and efficient, but also numerically stable and highly adaptable. The new procedure is also applied to a nonlinear stochastic system subjected to both sinusoidal and random excitations. The system response in this case is a non-homogeneous Markov process. The algorithm is adapted for this case, so that re-computation of the transition probability density at every time step can be avoided. | |
| Identifier: | 9780591311143 (isbn), 12506 (digitool), FADT12506 (IID), fau:9398 (fedora) | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): |
College of Engineering and Computer Science Thesis (Ph.D.)--Florida Atlantic University, 1997. |
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| Subject(s): |
Stochastic systems Numerical integration Markov processes |
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| Held by: | Florida Atlantic University Libraries | |
| Persistent Link to This Record: | http://purl.flvc.org/fcla/dt/12506 | |
| Sublocation: | Digital Library | |
| Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
