scholarly journals Invariant spectral foliations with applications to model order reduction and synthesis

2020 ◽  
Vol 101 (4) ◽  
pp. 2645-2669
Author(s):  
Robert Szalai
Keyword(s):  
Model Order Reduction ◽  
Model Identification ◽  
Order Reduction ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Vibration Data ◽  
Invariant Foliation ◽  
Order Components ◽  
Nonlinear Analogue

Abstract The paper introduces a technique that decomposes the dynamics of a nonlinear system about an equilibrium into low-order components, which then can be used to reconstruct the full dynamics. This is a nonlinear analogue of linear modal analysis. The dynamics is decomposed using Invariant Spectral Foliation (ISF), which is defined as the smoothest invariant foliation about an equilibrium and hence unique under general conditions. The conjugate dynamics of an ISF can be used as a reduced order model. An ISF can be fitted to vibration data without carrying out a model identification first. The theory is illustrated on a analytic example and on free-vibration data of a clamped-clamped beam.

scholarly journals Suboptimal Control Using Model Order Reduction

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Avadh Pati ◽  
Awadhesh Kumar ◽  
Dinesh Chandra
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Higher Order ◽  
Reduced Order Model ◽  
Suboptimal Control ◽  
Order Model ◽  
Model Order ◽  
Markov Parameters ◽  
Reduced Order ◽  
Partial Feedback

A Padé approximation based technique for designing a suboptimal controller is presented. The technique uses matching of both time moments and Markov parameters for model order reduction. In this method, the suboptimal controller is first derived for reduced order model and then implemented for higher order plant by partial feedback of measurable states.

scholarly journals Model order reduction of thermo-mechanical models with parametric convective boundary conditions: focus on machine tools

2020 ◽  
Author(s):  
Pablo Hernández-Becerro ◽  
Daniel Spescha ◽  
Konrad Wegener
Keyword(s):  
Boundary Conditions ◽  
Machine Tools ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Convective Boundary Conditions ◽  
Frequency Range ◽  
Order Model ◽  
Convective Boundary ◽  
Model Order ◽  
Reduced Order

Abstract Thermo-mechanical finite element (FE) models predict the thermal behavior of machine tools and the associated mechanical deviations. However, one disadvantage is their high computational expense, linked to the evaluation of the large systems of differential equations. Therefore, projection-based model order reduction (MOR) methods are required in order to create efficient surrogate models. This paper presents a parametric MOR method for weakly coupled thermo-mechanical FE models of machine tools and other similar mechatronic systems. This work proposes a reduction method, Krylov Modal Subspace (KMS), and a theoretical bound of the reduction error. The developed method addresses the parametric dependency of the convective boundary conditions using the concept of system bilinearization. The reduced-order model reproduces the thermal response of the original FE model in the frequency range of interest for any value of the parameters describing the convective boundary conditions. Additionally, this paper investigates the coupling between the reduced-order thermal system and the mechanical response. A numerical example shows that the reduced-order model captures the response of the original system in the frequency range of interest.

Model order reduction for quasi-magnetostatic problems

2017 ◽  
Vol 36 (6) ◽  
pp. 1783-1791
Author(s):  
Yuqing Xie ◽  
Lin Li ◽  
Shuaibing Wang
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Method ◽  
Computational Accuracy ◽  
Order Model ◽  
Model Order ◽  
Content Type ◽  
Reduced Order ◽  
Magnetostatic Problem

Purpose To reduce the computational scale for quasi-magnetostatic problems, model order reduction is a good option. Reduced-order modelling techniques based on proper orthogonal decomposition (POD) and centroidal Voronoi tessellation (CVT) have been used to solve many engineering problems. The purpose of this paper is to investigate the computational principle, accuracy and efficiency of the POD-based and the CVT-based reduced-order method when dealing with quasi-magnetostatic problems. Design/methodology/approach The paper investigates computational features of the reduced-order method based on POD and CVT methods for quasi-magnetostatic problems. Firstly the construction method for the POD and the CVT reduced-order basis is introduced. Then, a reduced model is constructed using high-fidelity finite element solutions and a Galerkin projection. Finally, the transient quasi-magnetostatic problem of the TEAM 21a model is studied with the proposed reduced-order method. Findings For the TEAM 21a model, the numerical results show that both POD-based and CVT-based reduced-order approaches can greatly reduce the computational time compared with the full-order finite element method. And the results obtained from both reduced-order models are in good agreement with the results obtained from the full-order model, while the computational accuracy of the POD-based reduced-order model is a little higher than the CVT-based reduced-order model. Originality/value The CVT method is introduced to construct the reduced-order model for a quasi-magnetostatic problem. The computational accuracy and efficiency of the presented approaches are compared.

Simulation in System-Level Based on Model Order Reduction for a Square-Wave Micromixer

2015 ◽  
Vol 16 (7-8) ◽  
pp. 307-314 ◽  
Author(s):  
Xueye Chen ◽  
Jienan Shen
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
System Level ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Square Wave ◽  
Bonding Method ◽  
Proper Orthogonal ◽  
Sodium Solution

AbstractWith the aim to optimize design, a simulation in system level has been presented for the square-wave micromixer in this article. The square-wave micromixer is divided into straight channels and square-wave units. The reduced-order model based on proper orthogonal decomposition is applied in calculating concentration of the sample in the straight channels, and numerical simulation is applied in calculating concentration of the sample in the square-wave units. The data can mutually be transferred between straight channels and square-wave units by data fitting and interpolation. The maximal relative deviation is 1.52% between simulation in system-level and only simulation. The computational efficiency will be improved significantly with the numbers of straight channels increasing. The Polymethyl methacrylate (PMMA) micromixer is fabricated with mill and hot bonding method. The mixing experiment of fluorescein sodium solution with different concentrations is carried out to verify simulation. The relative deviations between simulation in and experimental results are below 8.26%.

scholarly journals Model Order Reduction Technique Applied on Harmonic Analysis of a Submerged Vibrating Blade

2019 ◽  
Vol 24 (1) ◽  
pp. 131-142 ◽  
Author(s):  
E. Tengs ◽  
F. Charrassier ◽  
M. Holst ◽  
Pål-Tore Storli
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Reduction Technique ◽  
Reduced Order Model ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Speed Up ◽  
Speedup Factor ◽  
Fully Coupled

Abstract As part of an ongoing study into hydropower runner failure, a submerged, vibrating blade is investigated both experimentally and numerically. The numerical simulations performed are fully coupled acoustic-structural simulations in ANSYS Mechanical. In order to speed up the simulations, a model order reduction technique based on Krylov subspaces is implemented. This paper presents a comparison between the full ANSYS harmonic response and the reduced order model, and shows excellent agreement. The speedup factor obtained by using the reduced order model is shown to be between one and two orders of magnitude. The number of dimensions in the reduced subspace needed for accurate results is investigated, and confirms what is found in other studies on similar model order reduction applications. In addition, experimental results are available for validation, and show good match when not too far from the resonance peak.

scholarly journals Model Order Reduction for Lumped RC Transmission Lines

2020 ◽  
Author(s):  
Farid N. Najm
Keyword(s):  
Transmission Lines ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Detailed Review ◽  
Circuit Description ◽  
Rc Networks

<div>We start with a detailed review of the PACT approach for model order reduction of RC networks. We then develop a method that uses PACT as a preprocessing step to transform a generic lumped RC transmission line of some nominal order, based on a nominal (r,c) setting, into a parameterized circuit captured in a SPICE sub-circuit description. Then, given any other lumped RC line of the same order, we pass its (r,c) setting as parameters to this sub-circuit so as to automatically transform and reduce the line into a reduced order model without having to rerun PACT. In this way, we effectively characterize lumped RC transmission lines in a way that allows them to be reduced on-the-fly without any expensive processing.</div>

Firefly artificial intelligence technique for model order reduction with substructure preservation

2019 ◽  
Vol 41 (10) ◽  
pp. 2875-2885 ◽  
Author(s):  
Othman Alsmadi ◽  
Adnan Al-Smadi ◽  
Esra’a Gharaibeh
Keyword(s):  
Artificial Intelligence ◽  
Model Order Reduction ◽  
Fitness Function ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Model ◽  
Artificial Intelligence Technique ◽  
Model Order ◽  
Reduced Order ◽  
Intelligence Technique

Model order reduction (MOR) is a process of finding a lower order model for the original high order system with reasonable accuracy in order to simplify analysis, design, modeling and simulation for large complex systems. It is desirable that the reduced order model preserves the fundamental properties of the original system. This paper presents a new MOR technique of multi-input multi-output systems utilizing the firefly algorithm (FA) as an artificial intelligence technique. The reduction operation is proposed to maintain the exact dominant dynamics in the reduced order model with the advantage of substructure preservation. This is mainly possible for systems that are characterized as multi-time scale systems. Obtaining the reduced order model is achieved by minimizing the fitness function that is related to the error between the full and reduced order models’ responses. The new approach is compared with recently published work on firefly optimization for MOR, in addition to three other artificial intelligence techniques; namely, invasive weed optimization, particle swarm optimization and genetic algorithm. As a result, simulations show the potential of the FA for the process of MOR.

scholarly journals POD-DEIM Based Model Order Reduction for the Spherical Shallow Water Equations with Turkel-Zwas Finite Difference Discretization

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Pengfei Zhao ◽  
Cai Liu ◽  
Xuan Feng
Keyword(s):  
Computational Complexity ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Reduced Order Model ◽  
Order Model ◽  
Time Step ◽  
Model Order ◽  
Reduced Order

We consider the shallow water equations (SWE) in spherical coordinates solved by Turkel-Zwas (T-Z) explicit large time-step scheme. To reduce the dimension of the SWE model, we use a well-known model order reduction method, a proper orthogonal decomposition (POD). As the computational complexity still depends on the number of variables of the full spherical SWE model, we use discrete empirical interpolation method (DEIM) proposed by Sorensen to reduce the computational complexity of the reduced-order model. DEIM is very helpful in evaluating quadratically nonlinear terms in the reduced-order model. The numerical results show that POD-DEIM is computationally very efficient for implementing model order reduction for spherical SWE.

scholarly journals Model Reduction of Structured Dynamical Systems by Projecting onto the Dominant Eigenspace of the Gramians

2018 ◽  
Vol 10 (2) ◽  
pp. 94
Author(s):  
Shazzad Hasan ◽  
M. Monir Uddin
Keyword(s):  
Model Order Reduction ◽  
Krylov Subspace ◽  
Order Reduction ◽  
Second Order ◽  
Low Rank ◽  
Order Model ◽  
Model Order ◽  
Reduced Order ◽  
Second Order Systems ◽  
Theoretical Results

This paper studies the structure preserving (second-order to second-order) model order reduction of second-order systems applying the projection onto the dominant eigenspace of the Gramians of the systems. The projectors which create the reduced order model are generated cheaply from the low-rank Gramian factors. The low-rank Gramian factors are computed efficiently by solving the corresponding Lyapunov equations of the system using the rational Krylov subspace method. The efficiency of the theoretical results are then illustrated by numerical experiments.

scholarly journals An Improvement in LQR Controller Design based on Modified Chaotic Particle Swarm Optimization and Model Order Reduction

2021 ◽  
Vol 14 (1) ◽  
pp. 157-168
Author(s):  
Hadeel Abdullah ◽  
Keyword(s):  
Model Order Reduction ◽  
Order Reduction ◽  
Linear Quadratic Regulator ◽  
Reduced Order Model ◽  
Linear Quadratic ◽  
Order Model ◽  
Swarm Optimization ◽  
Model Order ◽  
Reduced Order ◽  
Lqr Controller

The diverse engineering and scientific applications are stated through complex and high-order systems. The significant difficulties of these systems are the complications of modeling, analyzing, and controlling. It is easier to examine simpler models for more physical insights than more complex models and result in lower-ordering controllers that are easier to implement. The model order reduction (MOR) was used to simplify the computational difficulty of such complications and was later developed intensively for use with increasingly CDS. In this paper, a new Modified Chaos Particle Swarm Optimization (MCPSO) technique is employed to get a reduced-order model of a large scale system and design a Linear Quadratic Regulator (LQR) based controller. The mod uses the combination of advantages of basic PSO algorithms and chaotic algorithms. It becomes an excellent algorithm with fast convergence, few control parameters, simple execution, and avoidance of local extremes. In addition to combining the chaotic algorithm, CPSO also improved the weight parameter w, adjusting it to the dynamic attenuation direction. First, efficient reduced-order model parameters are obtained for original higher-order systems based on the MCPSO. Then linear quadratic regulator (LQR (controller parameters optimized for the reduced-order model. The goodness of the proposed method is evaluated through a numerical example. The experimental results indicate that the proposed technique’s reduced order model provides an excellent close approximation to the original system.

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