scholarly journals Conservative model reduction for finite-volume models

2018 ◽  
Keyword(s):  
Model Reduction ◽  
Finite Volume ◽  
Optimization Problems ◽  
Posteriori Error ◽  
Galerkin Projection ◽  
Lower State ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Volume Models

We present a method for model reduction of finite-volume models that guarantees the resulting reduced-order model is conservative, thereby preserving the structure intrinsic to finite-volume discretizations [1]. The proposed reduced-order models associate with optimization problems characterized by (1) a minimum-residual objective function and (2) nonlinear equality constraints that explicitly enforce conservation over subdomains. Conservative Galerkin projection arises from formulating this optimization problem at the time-continuous level, while conservative least- squares Petrov–Galerkin (LSPG) projection associates with a time-discrete formulation. We note that other recent works have also considered ROMs that associate with constrained optimization problems [3, 2], although none are conservative. We equip these approaches with hyper-reduction techniques in the case of nonlinear flux and source terms, and also provide approaches for handling infeasibility. In addition, we perform analyses that include deriving conditions under which conservative Galerkin and conservative LSPG are equivalent, as well as deriving a posteriori error bounds. On a parameterized quasi-1D Euler equation problem, the proposed method not only conserves mass, momentum, and energy globally, but also has significantly lower state-space errors than nonconservative reduced-order models such as standard Galerkin and LSPG projection.

scholarly journals Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Imran ◽  
Abdul Ghafoor ◽  
Victor Sreeram
Keyword(s):  
Frequency Response ◽  
Model Reduction ◽  
Discrete Time ◽  
Error Bounds ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Discrete Time Systems ◽  
Weighted Model ◽  
Time Systems

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

scholarly journals Model reduction for a power grid model

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jing Li ◽  
Panos Stinis
Keyword(s):  
Model Reduction ◽  
Long Memory ◽  
Power Grid ◽  
The State ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Grid Model ◽  
Reduction Techniques ◽  
Short Memory ◽  
Better Than

<p style='text-indent:20px;'>We examine the complexity of constructing reduced order models for subsets of the variables needed to represent the state of the power grid. In particular, we apply model reduction techniques to the DeMarco-Zheng power grid model. We show that due to the oscillating nature of the solutions and the absence of timescale separation between resolved and unresolved variables, the construction of accurate reduced models becomes highly non-trivial because one has to account for long memory effects. In addition, we show that a reduced model that includes even a short memory is drastically better than a memoryless model.</p>

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.

Anisothermal Flow Control by Using Reduced-Order Models

2012 ◽  
Author(s):  
Alexandra Tallet ◽  
Cédric Leblond ◽  
Cyrille Allery
Keyword(s):  
Fluid Flow ◽  
Flow Control ◽  
Projection Method ◽  
Control Strategies ◽  
Pollutant Concentration ◽  
Galerkin Projection ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Optimal Projection ◽  
Fluid Flow Control

Despite constantly improving computer capabilities, classical numerical methods (DNS, LES,…) are still out of reach in fluid flow control strategies. To make this problem tractable almost in real-time, reduced-order models are used here. The spatial basis is obtained by POD (Proper Orthogonal Decomposition), which is the most commonly used technique in fluid mechanics. The advantage of the POD basis is its energetic optimality: few modes contain almost the totality of energy. The ROM is achieved with the recent developed optimal projection [1], unlike classical methods which use Galerkin projection. This projection method is based on the minimization of the residual equations in order to have a stabilizing effect. It enables moreover to access pressure field. Here, the projection method is slightly different from [1]: a formulation without the Poisson equation is proposed and developed. Then, the ROM obtained by optimal projection is introduced within an optimal control loop. The flow control strategy is illustrated on an isothermal square lid-driven cavity and an anisothermal square ventilated cavity. The aim is to reach a target temperature (or target pollutant concentration) in the cavity, with an interior initial temperature (or initial pollutant concentration), by adjusting the inlet fluid flow rate.

scholarly journals GENETIC ALGORITHM-BASED CALIBRATION OF REDUCED ORDER GALERKIN MODELS

2011 ◽  
Vol 16 (1) ◽  
pp. 233-247 ◽  
Author(s):  
Witold Stankiewicz ◽  
Robert Roszaka ◽  
Marek Morzyńskia
Keyword(s):  
Genetic Algorithm ◽  
Bluff Body ◽  
Calibration Procedure ◽  
Galerkin Projection ◽  
Reduced Order Models ◽  
Data Set ◽  
Reduced Order ◽  
Low Dimensional ◽  
Fluid Behaviour ◽  
Proper Orthogonal

Low-dimensional models, allowing quick prediction of fluid behaviour, are key enablers of closed-loop flow control. Reduction of the model's dimension and inconsistency of high-fidelity data set and the reduced-order formulation lead to the decrease of accuracy. The quality of Reduced-Order Models might be improved by a calibration procedure. It leads to global optimization problem which consist in minimizing objective function like the prediction error of the model. In this paper, Reduced-Order Models of an incompressible flow around a bluff body are constructed, basing on Galerkin Projection of governing equations onto a space spanned by the most dominant eigenmodes of the Proper Orthogonal Decomposition (POD). Calibration of such models is done by adding to Galerkin System some linear and quadratic terms, which coefficients are estimated using Genetic Algorithm.

scholarly journals NEW REGULARIZATION METHOD FOR CALIBRATED POD REDUCED-ORDER MODELS

2016 ◽  
Vol 21 (1) ◽  
pp. 47-62 ◽  
Author(s):  
Badr Abou El Majd ◽  
Laurent Cordier
Keyword(s):  
Regularization Method ◽  
Regularization Parameter ◽  
Weighted Average ◽  
Calibration Method ◽  
Wake Flow ◽  
Galerkin Projection ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Normalized Error ◽  
Curve Method

Reduced-order models based on Proper orthogonal decomposition are known to suffer from a lack of accuracy due to the truncation effect introduced by keeping only the most energetic modes. In this paper, we propose a new regularized calibration method aiming at minimizing a weighted average of normalized error, and a term measuring the change of the coefficients from their value obtained by Galerkin projection. We also determine the optimal value of the regularization parameter by analogy of the L-curve method. This paper is a sequel of [8] in which we compared various methods of calibration and introduced a Tikhonov-based regularization method. The proposed approach is assessed for a two dimensional wake flow around a cylinder, characteristic of the configurations of interest.

scholarly journals Multimodeling Control via System Balancing

2010 ◽  
Vol 2010 ◽  
pp. 1-20
Author(s):  
Nada Ratković Kovačević ◽  
Dobrila Škatarić
Keyword(s):  
Power Plants ◽  
Order Reduction ◽  
Reduced Order Models ◽  
Linear Quadratic ◽  
Linear Quadratic Gaussian ◽  
Reduced Order ◽  
Reduction Techniques ◽  
Balanced Model ◽  
Balancing Transformation ◽  
Different Order

A new approach in multimodeling strategy is proposed. Multimodel strategies in which control agents use different simplified models of the same system are being developed using balancing transformation and the corresponding order reduction concepts. Traditionally, the multimodeling concept was studied using the ideas of multitime scales (singular perturbations) and weak subsystem coupling. For all reduced-order models obtained, a Linear Quadratic Gaussian (LQG) control problem was solved. Different order reduction techniques were compared based on the values of the optimized criteria for the closed-loop case where the full-order balanced model utilizes regulators calculated to be the optimal for various reduced-order models. The results obtained were demonstrated on a real-world example: a multiarea power system consisting of two identical areas, that is, two identical power plants.

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