Fidelity of reduced-order models for large-scale nonlinear orifice viscous dampers

2008 ◽  
Vol 15 (8) ◽  
pp. 1143-1163 ◽  
Author(s):  
R. W. Wolfe ◽  
H.-B. Yun ◽  
S. Masri ◽  
F. Tasbihgoo ◽  
G. Benzoni
Keyword(s):  
Large Scale ◽  
Reduced Order Models ◽  
Viscous Dampers ◽  
Reduced Order

Order Reduction of Nonlinear Systems Subjected to an External Periodic Excitation

2005 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
State Space ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Periodic Excitation ◽  
External Excitation ◽  
Reduced Order ◽  
Linear Approach

In this work, the basic problem of order reduction nonlinear systems subjected to an external periodic excitation is considered. This problem deserves attention because the modes that interact (linearly or nonlinearly) with the external excitation dominate the response. A linear approach like the Guyan reduction does not always guarantee accurate results, particularly when nonlinear interactions are strong. In order to overcome limitations of the linear approach, a nonlinear order reduction methodology through a generalization of the invariant manifold technique is proposed. Traditionally, the invariant manifold techniques for unforced problems are extended to the forced problems by ‘augmenting’ the state space, i.e., forcing is treated as an additional degree of freedom and an invariant manifold is constructed. However, in the approach suggested here a nonlinear time-dependent relationship between the dominant and the non-dominant states is assumed and the dimension of the state space remains the same. This methodology not only yields accurate reduced order models but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. Following this approach, various ‘reducibility conditions’ are obtained that show interactions among the eigenvalues, the nonlinearities and the external excitation. One can also recover all ‘resonance conditions’ commonly obtained via perturbation or averaging techniques. These methodologies are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control of large-scale externally excited nonlinear systems.

Order Reduction of Parametrically Excited Nonlinear Systems Subjected to External Periodic Excitations

2009 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Fundamental Solution ◽  
Invariant Manifold ◽  
Large Scale ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Reduced Order Models ◽  
Order Model ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems with periodic coefficients subjected to external periodic excitations are presented. The periodicity of the linear terms is assumed to be non-commensurate with the periodicity of forcing vector. The dynamical equations of motion are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the forcing and/or nonlinearity takes the form of quasiperiodic functions. The techniques proposed here; construct a reduced order equivalent system by expressing the non-dominant states as time-varying functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states in comparison with the large scale system. Specifically, two methods are outlined to obtain the reduced order model. First approach is a straightforward application of linear method similar to the ‘Guyan reduction’, the second novel technique proposed here, utilizes the concept of ‘invariant manifolds’ for the forced problem to construct the fundamental solution. Order reduction approach based on invariant manifold technique yields unique ‘reducibility conditions’. If these ‘reducibility conditions’ are satisfied only then an accurate order reduction via ‘invariant manifold’ is possible. This approach not only yields accurate reduced order models using the fundamental solution but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover ‘resonance conditions’ associated with the fundamental solution which could be obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to a typical problem and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems subjected to external periodic excitations.

Order Reduction of Nonlinear Systems With Periodic-Quasiperiodic Coefficients

2005 ◽  
Author(s):  
Sangram Redkar ◽  
S. C. Sinha
Keyword(s):  
Nonlinear Systems ◽  
Invariant Manifold ◽  
Large Scale ◽  
Evolution Equations ◽  
Linear Method ◽  
Dynamical Evolution ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Reduced Order ◽  
And Control

In this work, some techniques for order reduction of nonlinear systems involving periodic/quasiperiodic coefficients are presented. The periodicity of the linear terms is assumed non-commensurate with the periodicity of either the nonlinear terms or the forcing vector. The dynamical evolution equations are transformed using the Lyapunov-Floquet (L-F) transformation such that the linear parts of the resulting equations become time-invariant while the nonlinear parts and forcing take the form of quasiperiodic functions. The techniques proposed here construct a reduced order equivalent system by expressing the non-dominant states as time-modulated functions of the dominant (master) states. This reduced order model preserves stability properties and is easier to analyze, simulate and control since it consists of relatively small number of states. Three methods are proposed to carry out this model order reduction (MOR). First type of MOR technique is a linear method similar to the ‘Guyan reduction’, the second technique is a nonlinear projection method based on singular perturbation while the third method utilizes the concept of ‘quasiperiodic invariant manifold’. Order reduction approach based on invariant manifold technique yields a unique ‘generalized reducibility condition’. If this ‘reducibility condition’ is satisfied only then an accurate order reduction via invariant manifold is possible. Next, the proposed methodologies are extended to solve the forced problem. All order reduction approaches except the invariant manifold technique can be applied in a straightforward way. The invariant manifold formulation is modified to take into account the effects of forcing and nonlinear coupling. This approach not only yields accurate reduced order models but also explains the consequences of various ‘primary’ and ‘secondary resonances’ present in the system. One can also recover all ‘resonance conditions’ obtained via perturbation techniques by assuming weak parametric excitation. This technique is capable of handing systems with strong parametric excitations subjected to periodic and quasi-periodic forcing. These methodologies are applied to some typical problems and results for large-scale and reduced order models are compared. It is anticipated that these techniques will provide a useful tool in the analysis and control system design of large-scale parametrically excited nonlinear systems.

Orthogonal Polynomials Approximation and Balanced Truncation for a Lowpass Filter

2013 ◽  
Vol 11 (4) ◽  
pp. 2-16
Author(s):  
K. Perev
Keyword(s):  
Orthogonal Polynomials ◽  
Large Scale ◽  
Computational Effort ◽  
Balanced Truncation ◽  
Reduced Order Models ◽  
Lowpass Filter ◽  
Analog Filter ◽  
Reduced Order ◽  
System Properties ◽  
Balancing Transformation

Abstract This paper considers the problem of orthogonal polynomial approximation based balanced truncation for a lowpass filter. The proposed method combines the system properties of balanced truncation, the computational effectiveness of proper orthogonal decomposition and the approximation capability of the orthogonal polynomials approximation. Orthogonal polynomials series expansion of the reachability and observability gramians is used in order to avoid solving large-scale Lyapunov equations and thus, significantly reducing the computational effort for obtaining the balancing transformation. The proposed method is applied for model reduction of a lowpass analog filter. Different sets of orthonormal functions are obtained from Legendre, Laguerre and Chebyshev orthogonal polynomials and the corresponding reduced order models are compared. The approximation precision is measured by the relative mean square error between the outputs of the full order model and the obtained reduced order models.

Time-limited Gramians-based model order reduction for second-order form systems

2018 ◽  
Vol 41 (8) ◽  
pp. 2310-2318 ◽  
Author(s):  
Shafiq Haider ◽  
Abdul Ghafoor ◽  
Muhammad Imran ◽  
Fahad Mumtaz Malik
Keyword(s):  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Reduced Order Models ◽  
Infinite Time ◽  
Model Order ◽  
Reduced Order ◽  
Order Form ◽  
Second Order Systems

A new scheme for model order reduction of large-scale second-order systems in time-limited intervals is presented. Time-limited Gramians that are solutions of continuous-time algebraic Lyapunov equations for second-order form systems are introduced. Time-limited second-order balanced truncation procedures with provision of balancing position and velocity Gramians are formulated. Stability conditions for reduced-order models are stated and algorithms that preserve stability in reduced-order models are discussed. Numerical examples are presented to validate the superiority of the proposed scheme compared with the infinite-time Gramians technique for time-limited applications.

Interactive Thermo-Fluid Simulation by Using Reduced Order Models

2013 ◽  
Author(s):  
Sachio Kobayashi ◽  
Hiroki Kobayashi ◽  
Hiroshi Ikeda ◽  
Masayoshi Hashima ◽  
Yuichi Sato
Keyword(s):  
User Interfaces ◽  
Large Scale ◽  
Computational Models ◽  
Stokes Equations ◽  
Simulation Method ◽  
Dimensional Subspace ◽  
Fluid Simulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Advection Term

We present a new finite difference-based thermo-fluid simulation method by using reduced order models. Reduced order modeling technique is to project a high dimensional problem onto a lower dimensional subspace and then solve the problem in the reduced subspace. We solve the incompressible Navier-Stokes equations and the heat equation in their respective subspaces and join the two equations by projecting the advection term onto the joint reduced space. Our algorithm allows for fast thermo-fluid simulation of the large-scale computational models at a fraction of computational load. Our method shows more than one thousand times faster speed than usual mesh-based fluid simulation, while maintaining acceptable engineering accuracy. The real-time feature of our method enables interactive user interfaces for, e.g., assessing an immediate thermal field change in response to consecutive control of air-conditioning equipment in a data center.

scholarly journals Deep Learning-Based Accuracy Upgrade of Reduced Order Models in Topology Optimization

2021 ◽  
Vol 11 (24) ◽  
pp. 12005
Author(s):  
Nikos Ath. Kallioras ◽  
Alexandros N. Nordas ◽  
Nikos D. Lagaros
Keyword(s):  
Deep Learning ◽  
Topology Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Computational Effort ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Learning Techniques ◽  
Complex Models ◽  
Scale Design

Topology optimization problems pose substantial requirements in computing resources, which become prohibitive in cases of large-scale design domains discretized with fine finite element meshes. A Deep Learning-assisted Topology OPtimization (DLTOP) methodology was previously developed by the authors, which employs deep learning techniques to predict the optimized system configuration, thus substantially reducing the required computational effort of the optimization algorithm and overcoming potential bottlenecks. Building upon DLTOP, this study presents a novel Deep Learning-based Model Upgrading (DLMU) scheme. The scheme utilizes reduced order (surrogate) modeling techniques, which downscale complex models while preserving their original behavioral characteristics, thereby reducing the computational demand with limited impact on accuracy. The novelty of DLMU lies in the employment of deep learning for extrapolating the results of optimized reduced order models to an optimized fully refined model of the design domain, thus achieving a remarkable reduction of the computational demand in comparison with DLTOP and other existing techniques. The effectiveness, accuracy and versatility of the novel DLMU scheme are demonstrated via its application to a series of benchmark topology optimization problems from the literature.

Sign in / Sign up

Export Citation Format

Share Document