Results 11 to 20 of about 106 (92)
A Unified Software Framework for Empirical Gramians [PDF]
Journal of Mathematics, 2013 A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical Gramians not only extended this concept to nonlinear systems but also provided a uniform computational method.
Christian Himpe, Mario Ohlberger
doaj +3 more sources
Adaptive Optimal PMU Placement Based on Empirical Observability Gramian [PDF]
2015 IEEE Power & Energy Society General Meeting, 2014 Accepted by IFAC NOLCOS 2016.
Qi, Junjian, Sun, Kai, Kang, Wei
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Empirical Observability Gramian for Stochastic Observability of Nonlinear Systems
CoRR, 2020 We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the empirical observability Gramian can be used to provide an equivalent condition for a definition of stochastic ...
Nathan D. Powel, Kristi A. Morgansen
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Empirical Computation of Reachability Gramian for Linear-Time Varying Systems
IFAC-PapersOnLine, 2021 Abstract This paper deals with the approximate computation of the reachability gramian for linear time-varying(LTV) systems over a finite time interval. To this end, we use state trajectory information obtained by simulating the system for various inputs and initial conditions. We propose three techniques for computing the reachability gramian.
Kasturi Das +2 more
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Comparing (Empirical-Gramian-Based) Model Order Reduction Algorithms [PDF]
, 2021 In this work, the empirical-Gramian-based model reduction methods: Empirical poor man's truncated balanced realization, empirical approximate balancing, empirical dominant subspaces, empirical balanced truncation, and empirical balanced gains are compared in a non-parametric and two parametric variants, via ten error measures: Approximate Lebesgue $L_0$
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The Empirical Cross Gramian for Parametrized Nonlinear Systems
IFAC-PapersOnLine, 2015 Abstract The cross gramian matrix can be used for model order reduction as well as system identification of linear control systems, which are frequently used in the sciences. The empirical cross gramian is solely computed from trajectories and hence extends beyond linear state-space systems to nonlinear systems.
Christian Himpe, Mario Ohlberger
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Nonlinear power system model reduction based on empirical Gramians
Journal of Electrical Engineering, 2017 Abstract An effective nonlinear model reduction approach, empirical Gramians balanced reduction approach, is studied, to reduce the computation complexity in nonlinear power system model application. The realization procedure is: firstly, computing the empirical controllable and observable Gramians matrices of nonlinear power system ...
Hongshan Zhao, Xiaoming Lan, Hui Ren
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IET Renewable Power Generation, Volume 20, Issue 1, January/December 2026.This work proposes an explainable, data‐driven methodology for early fault detection in wind turbine generators that relies solely on existing SCADA data, avoiding the need for additional sensors. The approach combines Gramian Angular Field encoding with a convolutional neural network and a two‐stage global and turbine‐specific training strategy ...
Kevin Barrera, Yolanda Vidal
wiley +1 more source
The Journal of Engineering, Volume 2026, Issue 1, January/December 2026.A steady state energy disaggregation and forecasting of appliance consumptions. ABSTRACT Poor energy conservation practices in residential settings due to reckless use of energy and faulty appliances account for the excess percentage of energy consumed daily.
Elvis Tamakloe +4 more
wiley +1 more source
On Efficient Iterative Algorithms and Conditioning for the Nonlinear Sylvester Equation
Computational and Mathematical Methods, Volume 2026, Issue 1, 2026.Nonlinear Sylvester‐type matrix equations arise in applications such as control theory, observer design, model reduction, and data‐driven systems, where they model higher order interactions in matrix transformations. Unlike the classical Sylvester equation, the presence of nonlinear terms introduces additional analytical challenges and increased ...
Constantino Mahinya +2 more
wiley +1 more source