TY - GEN
T1 - Non-negative Matrix Factorization based uncertainty quantification method for complex networked systems
AU - Mukherjee, Arpan
AU - Rai, Rahul
AU - Singla, Puneet
AU - Singh, Tarunraj
AU - Patra, Abani
N1 - Funding Information:
This material is based upon work partially supported by the National Science Foundation under Grant NSF CMMI #1301235. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Publisher Copyright:
Copyright © 2015 by ASME.
PY - 2015
Y1 - 2015
N2 - The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.
AB - The behavior of large networked systems with underlying complex nonlinear dynamic are hard to predict. With increasing number of states, the problem becomes even harder. Quantifying uncertainty in such systems by conventional methods requires high computational time and the accuracy obtained in estimating the state variables can also be low. This paper presents a novel computational Uncertainty Quantifying (UQ) method for complex networked systems. Our approach is to represent the complex systems as networks (graphs) whose nodes represent the dynamical units, and whose links stand for the interactions between them. First, we apply Non-negative Matrix Factorization (NMF) based decomposition method to partition the domain of the dynamical system into clusters, such that the inter-cluster interaction is minimized and the intra-cluster interaction is maximized. The decomposition method takes into account the dynamics of individual nodes to perform system decomposition. Initial validation results on two well-known dynamical systems have been performed. The validation results show that uncertainty propagation error quantified by RMS errors obtained through our algorithms are competitive or often better, compared to existing methods.
UR - http://www.scopus.com/inward/record.url?scp=84978945580&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84978945580&partnerID=8YFLogxK
U2 - 10.1115/DETC201546087
DO - 10.1115/DETC201546087
M3 - Conference contribution
AN - SCOPUS:84978945580
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 41st Design Automation Conference
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2015
Y2 - 2 August 2015 through 5 August 2015
ER -