Abstract
Engineering systems are often modeled as a large dimensional random process with additive noise. The analysis of such system involves a solution to simultaneous system of Stochastic Differential Equations (SDE). The exact solution to the SDE is given by the evolution of the probability density function (pdf) of the state vector through the application of Stochastic Calculus. The Fokker-Planck-Kolmogorov Equation (FPKE) provides approximate solution to the SDE by giving the time evolution equation for the non-Gaussian pdf of the state vector. In this paper, we outline a computational framework that combines linearization, clustering technique and the Adaptive Gaussian Mixture Model (AGMM) methodology for solving the Fokker-Planck-Kolmogorov Equation (FPKE) related to a high dimensional system. The linearization and clustering technique facilitate easier decomposition of the overall high dimensional FPKE system into a finite number of much lower dimension FPKE systems. The decomposition enables the solution method to be faster. Numerical simulations test the efficacy of our developed framework.
| Original language | English (US) |
|---|---|
| Title of host publication | 42nd Design Automation Conference |
| Publisher | American Society of Mechanical Engineers (ASME) |
| ISBN (Electronic) | 9780791850114 |
| DOIs | |
| State | Published - Jan 1 2016 |
| Event | ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 - Charlotte, United States Duration: Aug 21 2016 → Aug 24 2016 |
Publication series
| Name | Proceedings of the ASME Design Engineering Technical Conference |
|---|---|
| Volume | 2B-2016 |
Other
| Other | ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2016 |
|---|---|
| Country | United States |
| City | Charlotte |
| Period | 8/21/16 → 8/24/16 |
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All Science Journal Classification (ASJC) codes
- Mechanical Engineering
- Computer Graphics and Computer-Aided Design
- Computer Science Applications
- Modeling and Simulation
Cite this
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An adaptive Gaussian mixture model approach based framework for solving fokker-planck kolmogorov equation related to high dimensional dynamical systems. / Mukherjee, Arpan; Rai, Rahul; Singla, Puneet; Singh, Tarunraj; Patra, Abani.
42nd Design Automation Conference. American Society of Mechanical Engineers (ASME), 2016. (Proceedings of the ASME Design Engineering Technical Conference; Vol. 2B-2016).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
TY - GEN
T1 - An adaptive Gaussian mixture model approach based framework for solving fokker-planck kolmogorov equation related to high dimensional dynamical systems
AU - Mukherjee, Arpan
AU - Rai, Rahul
AU - Singla, Puneet
AU - Singh, Tarunraj
AU - Patra, Abani
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Engineering systems are often modeled as a large dimensional random process with additive noise. The analysis of such system involves a solution to simultaneous system of Stochastic Differential Equations (SDE). The exact solution to the SDE is given by the evolution of the probability density function (pdf) of the state vector through the application of Stochastic Calculus. The Fokker-Planck-Kolmogorov Equation (FPKE) provides approximate solution to the SDE by giving the time evolution equation for the non-Gaussian pdf of the state vector. In this paper, we outline a computational framework that combines linearization, clustering technique and the Adaptive Gaussian Mixture Model (AGMM) methodology for solving the Fokker-Planck-Kolmogorov Equation (FPKE) related to a high dimensional system. The linearization and clustering technique facilitate easier decomposition of the overall high dimensional FPKE system into a finite number of much lower dimension FPKE systems. The decomposition enables the solution method to be faster. Numerical simulations test the efficacy of our developed framework.
AB - Engineering systems are often modeled as a large dimensional random process with additive noise. The analysis of such system involves a solution to simultaneous system of Stochastic Differential Equations (SDE). The exact solution to the SDE is given by the evolution of the probability density function (pdf) of the state vector through the application of Stochastic Calculus. The Fokker-Planck-Kolmogorov Equation (FPKE) provides approximate solution to the SDE by giving the time evolution equation for the non-Gaussian pdf of the state vector. In this paper, we outline a computational framework that combines linearization, clustering technique and the Adaptive Gaussian Mixture Model (AGMM) methodology for solving the Fokker-Planck-Kolmogorov Equation (FPKE) related to a high dimensional system. The linearization and clustering technique facilitate easier decomposition of the overall high dimensional FPKE system into a finite number of much lower dimension FPKE systems. The decomposition enables the solution method to be faster. Numerical simulations test the efficacy of our developed framework.
UR - http://www.scopus.com/inward/record.url?scp=85007621929&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85007621929&partnerID=8YFLogxK
U2 - 10.1115/DETC2016-60312
DO - 10.1115/DETC2016-60312
M3 - Conference contribution
AN - SCOPUS:85007621929
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 42nd Design Automation Conference
PB - American Society of Mechanical Engineers (ASME)
ER -