Model reduction for reduced order estimation in traffic models

2008 ◽  
Author(s):  
Joseph S. Niedbalski ◽  
Kun Deng ◽  
Prashant G. Mehta ◽  
Sean Meyn
Keyword(s):  
Model Reduction ◽  
Reduced Order ◽  
Traffic Models ◽  
Order Estimation

A Physics-Based Dynamic Model for Boilers: Part 2 — Model Reduction in a Cogeneration Application

2017 ◽  
Author(s):  
Matthew J. Blom ◽  
Michael J. Brear ◽  
Chris G. Manzie ◽  
Ashley P. Wiese
Keyword(s):  
Model Reduction ◽  
Gas Turbine ◽  
Dynamic Model ◽  
Reduction Process ◽  
Singular Perturbation Theory ◽  
Reduced Order Models ◽  
Reduced Order ◽  
One Dimensional ◽  
Time Scale Separation ◽  
Modelling Framework

This paper is the second part of a two part study that develops, validates and integrates a one-dimensional, physics-based, dynamic boiler model. Part 1 of this study [1] extended and validated a particular modelling framework to boilers. This paper uses this framework to first present a higher order model of a gas turbine based cogeneration plant. The significant dynamics of the cogeneration system are then identified, corresponding to states in the gas path, the steam path, the gas turbine shaft, gas turbine wall temperatures and boiler wall temperatures. A model reduction process based on time scale separation and singular perturbation theory is then demonstrated. Three candidate reduced order models are identified using this model reduction process, and the simplest, acceptable dynamic model of this integrated plant is found to require retention of both the gas turbine and boiler wall temperature dynamics. Subsequent analysis of computation times for the original physics-based one-dimensional model and the candidate, reduced order models demonstrates that significantly faster than real time simulation is possible in all cases. Furthermore, with systematic replacement of the algebraic states with feedforward maps in the reduced order models, further computational savings of up to one order of magnitude can be achieved. This combination of model fidelity and computational tractability suggest suggests that the resulting reduced order models may be suitable for use in model based control of cogeneration plants.

An Energy Closure Criterion for Model Reduction of a Kicked Euler–Bernoulli Beam

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Suparno Bhattacharyya ◽  
Joseph P. Cusumano
Keyword(s):  
Model Reduction ◽  
Mode Selection ◽  
Computational Cost ◽  
Impulsive Loading ◽  
Bernoulli Beam ◽  
Full System ◽  
Fixed Amount ◽  
Reduced Order ◽  
Proper Orthogonal ◽  
Euler Bernoulli Beam

Abstract Reduced order models (ROMs) can be simulated with lower computational cost while being more amenable to theoretical analysis. Here, we examine the performance of the proper orthogonal decomposition (POD), a data-driven model reduction technique. We show that the accuracy of ROMs obtained using POD depends on the type of data used and, more crucially, on the criterion used to select the number of proper orthogonal modes (POMs) used for the model. Simulations of a simply supported Euler–Bernoulli beam subjected to periodic impulsive loads are used to generate ROMs via POD, which are then simulated for comparison with the full system. We assess the accuracy of ROMs obtained using steady-state displacement, velocity, and strain fields, tuning the spatiotemporal localization of applied impulses to control the number of excited modes in, and hence the dimensionality of, the system’s response. We show that conventional variance-based mode selection leads to inaccurate models for sufficiently impulsive loading and that this poor performance is explained by the energy imbalance on the reduced subspace. Specifically, the subspace of POMs capturing a fixed amount (say, 99.9%) of the total variance underestimates the energy input and dissipated in the ROM, yielding inaccurate reduced-order simulations. This problem becomes more acute as the loading becomes more spatio-temporally localized (more impulsive). Thus, energy closure analysis provides an improved method for generating ROMs with energetics that properly reflect that of the full system, resulting in simulations that accurately represent the system’s true behavior.

Reduced-order deep learning for flow dynamics. The interplay between deep learning and model reduction

2020 ◽  
Vol 401 ◽  
pp. 108939 ◽  
Author(s):  
Min Wang ◽  
Siu Wun Cheung ◽  
Wing Tat Leung ◽  
Eric T. Chung ◽  
Yalchin Efendiev ◽  
...  
Keyword(s):  
Deep Learning ◽  
Model Reduction ◽  
Flow Dynamics ◽  
Reduced Order

scholarly journals H∞ Model Reduction of 2D Markovian Jump System with Roesser Model

2012 ◽  
Vol 6-7 ◽  
pp. 135-142
Author(s):  
Xue Song Han ◽  
Yu Bo Duan
Keyword(s):  
Model Reduction ◽  
Reduced Order Model ◽  
Markovian Jump Systems ◽  
Linear Matrix ◽  
Roesser Model ◽  
Markovian Jump ◽  
Order Model ◽  
Existence Of A Solution ◽  
Reduced Order ◽  
Jump Systems

This paper extends the results obtained for one-dimensional Markovian jump systems to investigate the problem of H∞model reduction for a class of linear discrete time 2D Markovian jump systems with state delays in Roesser model which is time-varying and mode-independent. The reduced-order model with the same randomly jumping parameters is proposed which can make the error systems stochastically stable with a prescribed H∞ performance. A sufficient condition in terms of linear matrix inequalitiesSubscript text(LMIs) plus matrix inverse constraints are derived for the existence of a solution to the reduced-order model problems. The cone complimentarity linearization (CCL) method is exploited to cast them into nonlinear minimization problems subject to LMI constraints. A numerical example is given to illustrate the design procedures.

Reduced-order estimation Part 1. Filtering

1987 ◽  
Vol 45 (6) ◽  
pp. 1867-1888 ◽  
Author(s):  
KRISHAN M. NAGPAL ◽  
RONALD E. HELMICK ◽  
CRAIG S. SIMS
Keyword(s):  
Reduced Order ◽  
Order Estimation

scholarly journals Empirical Reduced-Order Modeling for Boundary Feedback Flow Control

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Seddik M. Djouadi ◽  
R. Chris Camphouse ◽  
James H. Myatt
Keyword(s):  
Model Reduction ◽  
Reduction Method ◽  
Linear Subspace ◽  
Balanced Truncation ◽  
Order Model ◽  
Reduced Order ◽  
Domain Identification ◽  
Controllability And Observability ◽  
Obstacle Geometry ◽  
Proper Orthogonal

This paper deals with the practical and theoretical implications of model reduction for aerodynamic flow-based control problems. Various aspects of model reduction are discussed that apply to partial differential equation- (PDE-) based models in general. Specifically, the proper orthogonal decomposition (POD) of a high dimension system as well as frequency domain identification methods are discussed for initial model construction. Projections on the POD basis give a nonlinear Galerkin model. Then, a model reduction method based on empirical balanced truncation is developed and applied to the Galerkin model. The rationale for doing so is that linear subspace approximations to exact submanifolds associated with nonlinear controllability and observability require only standard matrix manipulations utilizing simulation/experimental data. The proposed method uses a chirp signal as input to produce the output in the eigensystem realization algorithm (ERA). This method estimates the system's Markov parameters that accurately reproduce the output. Balanced truncation is used to show that model reduction is still effective on ERA produced approximated systems. The method is applied to a prototype convective flow on obstacle geometry. AnH∞feedback flow controller is designed based on the reduced model to achieve tracking and then applied to the full-order model with excellent performance.

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