scholarly journals Balanced truncation for model reduction of biological oscillators

2021 ◽  
Author(s):  
Alberto Padoan ◽  
Fulvio Forni ◽  
Rodolphe Sepulchre
Keyword(s):  
Model Reduction ◽  
Biological Systems ◽  
Balanced Truncation ◽  
Differential Analysis ◽  
Diverse Range ◽  
Reduced Order ◽  
Classical Models ◽  
Reduction Methods ◽  
The Stability ◽  
Nonlinear Behaviors

AbstractModel reduction is a central problem in mathematical biology. Reduced order models enable modeling of a biological system at different levels of complexity and the quantitative analysis of its properties, like sensitivity to parameter variations and resilience to exogenous perturbations. However, available model reduction methods often fail to capture a diverse range of nonlinear behaviors observed in biology, such as multistability and limit cycle oscillations. The paper addresses this need using differential analysis. This approach leads to a nonlinear enhancement of classical balanced truncation for biological systems whose behavior is not restricted to the stability of a single equilibrium. Numerical results suggest that the proposed framework may be relevant to the approximation of classical models of biological systems.

scholarly journals Model Reduction Methods for Complex Network Systems

2020 ◽  
Vol 4 (1) ◽  
Author(s):  
X. Cheng ◽  
J.M.A. Scherpen
Keyword(s):  
Autonomous Systems ◽  
High Dimensional ◽  
Annual Review ◽  
Publication Date ◽  
Network Systems ◽  
Modeling And Control ◽  
Reduced Order ◽  
Reduction Methods ◽  
The Stability ◽  
And Control

Network systems consist of subsystems and their interconnections and provide a powerful framework for the analysis, modeling, and control of complex systems. However, subsystems may have high-dimensional dynamics and a large number of complex interconnections, and it is therefore relevant to study reduction methods for network systems. Here, we provide an overview of reduction methods for both the topological (interconnection) structure of a network and the dynamics of the nodes while preserving structural properties of the network. We first review topological complexity reduction methods based on graph clustering and aggregation, producing a reduced-order network model. Next, we consider reduction of the nodal dynamics using extensions of classical methods while preserving the stability and synchronization properties. Finally, we present a structure-preserving generalized balancing method for simultaneously simplifying the topological structure and the order of the nodal dynamics. Expected final online publication date for the Annual Review of Control, Robotics, and Autonomous Systems, Volume 4 is May 3, 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

scholarly journals MODEL REDUCTION METHODS APPLIED TO A NONLINEAR MECHANICAL SYSTEM

2019 ◽  
Vol 7 (7) ◽  
pp. 281-300
Author(s):  
Romes Antonio Borges ◽  
Daniel Gonçalves ◽  
Antônio Marcos De lima ◽  
Lázaro Fonseca Júnior
Keyword(s):  
Model Reduction ◽  
Point Of View ◽  
Time Saving ◽  
Computational Point ◽  
Reduced Models ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Reduction Methods ◽  
The Stability ◽  
High Flexibility

Modern structures of high flexibility are subject to physical or geometricnonlinearities, and reliable numerical modeling to predict their behavior is essential.The modeling of these systems can be given by the discretization of the problem usingthe Finite Element Method (FEM), however by using this methodology, it is a veryrobust model from the computational point of view, making the simulation processdifficult. Using reduced models has been an excellent alternative to minimizing thisproblem. Most model reduction methods are restricted to linear problems, whichmotivated us to maximize the efficiency of these methods considering nonlinearproblems. For better accuracy, in this study, adaptations and improvements aresuggested in reduction methods such as the Enriched Modal Base (EMB), the SystemEquivalent Reduction Expansion Process (SEREP), QUASI-SEREP and the IteratedImproved Reduced System (IIRS). The stability of a system is discussed according tothe calculation of the Lyapunov exponents and phase space. Numerical simulationsshowed that the reduced models presented a good performance, according to thecommitment of quality and speed of responses (or time saving).

Suboptimal Model Reduction by Multi-Point Padé Approximation

1994 ◽  
Vol 208 (2) ◽  
pp. 131-134 ◽  
Author(s):  
T N Lucas
Keyword(s):  
Transfer Function ◽  
Model Reduction ◽  
Approximation Method ◽  
Padé Approximation ◽  
Order Reduction ◽  
Pade Approximation ◽  
Reduced Order ◽  
Numerical Example ◽  
Integral Square Error ◽  
Reduction Methods

A novel Padé approximation method is used to obtain a reduced-order transfer function, with a predetermined denominator, such that the integral square error between the time responses of the full and reduced models is minimized. The method is seen to be easy to apply compared with existing suboptimal order reduction methods. A numerical example is given to illustrate its application.

Model reduction in power systems using a structure-preserving balanced truncation approach

2019 ◽  
Vol 177 ◽  
pp. 106002
Author(s):  
Johnny Leung ◽  
Michel Kinnaert ◽  
Jean-Claude Maun ◽  
Fortunato Villella
Keyword(s):  
Power Systems ◽  
Model Reduction ◽  
Balanced Truncation ◽  
Structure Preserving

scholarly journals Model reduction by balanced truncation of dominant Lure systems

2020 ◽  
Vol 53 (2) ◽  
pp. 5617-5622
Author(s):  
Alberto Padoan ◽  
Fulvio Forni ◽  
Rodolphe Sepulchre
Keyword(s):  
Model Reduction ◽  
Balanced Truncation

scholarly journals Model reduction methods based on Krylov subspaces

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 267-319 ◽  
Author(s):  
Roland W. Freund
Keyword(s):  
Large Scale ◽  
Krylov Subspace ◽  
Circuit Simulation ◽  
Krylov Subspaces ◽  
Lanczos Algorithm ◽  
Linear Dynamical Systems ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Reduction Methods ◽  
Modelling Techniques

In recent years, reduced-order modelling techniques based on Krylov-subspace iterations, especially the Lanczos algorithm and the Arnoldi process, have become popular tools for tackling the large-scale time-invariant linear dynamical systems that arise in the simulation of electronic circuits. This paper reviews the main ideas of reduced-order modelling techniques based on Krylov subspaces and describes some applications of reduced-order modelling in circuit simulation.

Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

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.

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