28,357 research outputs found
An efficient null space inexact Newton method for hydraulic simulation of water distribution networks
Null space Newton algorithms are efficient in solving the nonlinear equations
arising in hydraulic analysis of water distribution networks. In this article,
we propose and evaluate an inexact Newton method that relies on partial updates
of the network pipes' frictional headloss computations to solve the linear
systems more efficiently and with numerical reliability. The update set
parameters are studied to propose appropriate values. Different null space
basis generation schemes are analysed to choose methods for sparse and
well-conditioned null space bases resulting in a smaller update set. The Newton
steps are computed in the null space by solving sparse, symmetric positive
definite systems with sparse Cholesky factorizations. By using the constant
structure of the null space system matrices, a single symbolic factorization in
the Cholesky decomposition is used multiple times, reducing the computational
cost of linear solves. The algorithms and analyses are validated using medium
to large-scale water network models.Comment: 15 pages, 9 figures, Preprint extension of Abraham and Stoianov, 2015
(https://dx.doi.org/10.1061/(ASCE)HY.1943-7900.0001089), September 2015.
Includes extended exposition, additional case studies and new simulations and
analysi
Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"
This special issue collects contributions from the participants of the
"Information in Dynamical Systems and Complex Systems" workshop, which cover a
wide range of important problems and new approaches that lie in the
intersection of information theory and dynamical systems. The contributions
include theoretical characterization and understanding of the different types
of information flow and causality in general stochastic processes, inference
and identification of coupling structure and parameters of system dynamics,
rigorous coarse-grain modeling of network dynamical systems, and exact
statistical testing of fundamental information-theoretic quantities such as the
mutual information. The collective efforts reported herein reflect a modern
perspective of the intimate connection between dynamical systems and
information flow, leading to the promise of better understanding and modeling
of natural complex systems and better/optimal design of engineering systems
Trajectory Synthesis for Fisher Information Maximization
Estimation of model parameters in a dynamic system can be significantly
improved with the choice of experimental trajectory. For general, nonlinear
dynamic systems, finding globally "best" trajectories is typically not
feasible; however, given an initial estimate of the model parameters and an
initial trajectory, we present a continuous-time optimization method that
produces a locally optimal trajectory for parameter estimation in the presence
of measurement noise. The optimization algorithm is formulated to find system
trajectories that improve a norm on the Fisher information matrix. A
double-pendulum cart apparatus is used to numerically and experimentally
validate this technique. In simulation, the optimized trajectory increases the
minimum eigenvalue of the Fisher information matrix by three orders of
magnitude compared to the initial trajectory. Experimental results show that
this optimized trajectory translates to an order of magnitude improvement in
the parameter estimate error in practice.Comment: 12 page
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