Improving the efficiency of large scale topology optimization through on-the-fly reduced order model construction

2014 ◽  
Vol 101 (4) ◽  
pp. 281-304 ◽  
Author(s):  
Christian Gogu
Keyword(s):  
Topology Optimization ◽  
Large Scale ◽  
Reduced Order Model ◽  
Model Construction ◽  
Order Model ◽  
Reduced Order

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

scholarly journals Order Reduction based on Coulomb’s and Franklin’s laws Algorithm

2021 ◽  
Author(s):  
Ram Kumar ◽  
Afzal Sikander
Keyword(s):  
Large Scale ◽  
Linear Time ◽  
Order Reduction ◽  
Absolute Error ◽  
Search Space ◽  
Engineering Problem ◽  
Reduced Order Model ◽  
Order Model ◽  
Reduced Order ◽  
Linear Time Invariant

Abstract The Coulomb and Franklin laws (CFL) algorithm is used to construct a lower order model of higher-order continuous time linear time-invariant (LTI) systems in this study. CFL is quite easy to implement in obtaining reduced order model of large scale system in control engineering problem as it employs the combined effect of Coulomb’s and Franklin’s laws to find the best values in search space. The unknown coefficients are obtained using the CFLA methodology, which minimises the integral square error (ISE) between the original and proposed ROMs. To achieve the reduced order model, five practical systems of different orders are considered. Finally, multiple performance indicators such as the ISE, integral of absolute error (IAE), and integral of time multiplied by absolute error were calculated to determine the efficacy of the proposed methodology. The simulation results were compared to previously published well-known research.

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.

scholarly journals Sparse nonlinear models of chaotic electroconvection

2021 ◽  
Vol 8 (8) ◽  
pp. 202367
Author(s):  
Yifei Guan ◽  
Steven L. Brunton ◽  
Igor Novosselov
Keyword(s):  
Charge Density ◽  
Coherent Structures ◽  
Large Scale ◽  
Fluid Transport ◽  
Nonlinear Models ◽  
Original System ◽  
Reduced Order Model ◽  
Dimensional System ◽  
Order Model ◽  
Reduced Order

Convection is a fundamental fluid transport phenomenon, where the large-scale motion of a fluid is driven, for example, by a thermal gradient or an electric potential. Modelling convection has given rise to the development of chaos theory and the reduced-order modelling of multiphysics systems; however, these models have been limited to relatively simple thermal convection phenomena. In this work, we develop a reduced-order model for chaotic electroconvection at high electric Rayleigh number. The chaos in this system is related to the standard Lorenz model obtained from Rayleigh–Benard convection, although our system is driven by a more complex three-way coupling between the fluid, the charge density, and the electric field. Coherent structures are extracted from temporally and spatially resolved charge density fields via proper orthogonal decomposition (POD). A nonlinear model is then developed for the chaotic time evolution of these coherent structures using the sparse identification of nonlinear dynamics (SINDy) algorithm, constrained to preserve the symmetries observed in the original system. The resulting model exhibits the dominant chaotic dynamics of the original high-dimensional system, capturing the essential nonlinear interactions with a simple reduced-order model.

scholarly journals Circuit realization method for reduced order inductive PEEC modeling circuits

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Trung-Son Nguyen ◽  
Tung Le Duc ◽  
Son Thanh Tran ◽  
Jean-Michel Guichon ◽  
Olivier Chadebec
Keyword(s):  
Equivalent Circuit ◽  
Design Methodology ◽  
Large Scale ◽  
Circuit Simulation ◽  
Fast Multipole Method ◽  
Synthesis Method ◽  
Reduced Order Model ◽  
Order Model ◽  
Circuit Realization ◽  
Reduced Order

Purpose To synthesize equivalent circuit obtained from reduced order model of large scale inductive PEEC circuits. Design/methodology/approach This paper describes an original approach for reducing and synthesizing large parasitic RLM electrical circuits coming from inductive Partial Element Equivalent Circuit (PEEC) models. The proposed technique enables the re-use of the reduced order model in the time domain circuit simulation context. Findings The paper shows how to use a synthesis method to realize an equivalent circuit issued from compressed PEEC circuits. Originality/value The coupling between methods PEEC and a compressed method as Fast Multipole Method (FMM) in order to reduce time and space consuming are well-known. The innovation here is to realise a smaller circuit equivalent with the original large scale PEEC circuits to use in temporal simulation tools. Moreover, this synthesis method reduces time and memories for modelling industrial application while maintaining high accuracy.

A reduced-order model of the zonal jets problem in the Southern Ocean

2020 ◽  
Author(s):  
Elnaz Naghibi ◽  
Sergey Karabasov ◽  
Igor Kamenkovich
Keyword(s):  
Southern Ocean ◽  
Large Scale ◽  
Ocean Model ◽  
Reduced Order Model ◽  
Vorticity Equation ◽  
Order Model ◽  
Reduced Order ◽  
Multi Scale ◽  
Zonal Jets ◽  
Hybrid Coordinate Ocean Model

<p>We introduce a reduced-order model of the underlying dynamics of zonal jets in the Southern Ocean. The model is based on multi-scale decomposition in the vorticity equation and explains how large-scale forcing breaks down into mesoscale eddies and alternating zonal jets. In this reduced-order model, we average the vorticity equation both in time and in the zonal direction and utilize eddy viscosity parametrization for turbulence closure. For verification, we compare our results with two high-fidelity models: i) the quasi-geostrophic model of a shear-driven periodic channel flow and ii) primitive equation HYCOM (HYbrid Coordinate Ocean Model) simulations of the Southern Ocean.</p>

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