scholarly journals Mixed method of model reduction for uncertain systems

2007 ◽  
Vol 4 (1) ◽  
pp. 1-12 ◽  
Author(s):  
N. Selvaganesan
Keyword(s):  
Steady State ◽  
Model Reduction ◽  
Correction Factor ◽  
Interval Arithmetic ◽  
Mixed Method ◽  
Uncertain Systems ◽  
Uncertain System ◽  
Higher Order ◽  
Reduced Order ◽  
Denominator Polynomial

A mixed method for reducing a higher order uncertain system to a stable reduced order one is proposed. Interval arithmetic is used to construct a generalized Routh table for determining the denominator polynomial of the reduced system. The reduced numerator polynomial is obtained using factor division method and the steady state error is minimized using gain correction factor. The proposed method is illustrated using a numerical example.

scholarly journals Data-Driven Reduced-Order Modeling of Convective Heat Transfer in Porous Media

Fluids ◽  
2021 ◽  
Vol 6 (8) ◽  
pp. 266
Author(s):  
Péter German ◽  
Mauricio E. Tano ◽  
Carlo Fiorina ◽  
Jean C. Ragusa
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Steady State ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Data Driven ◽  
Reduced Order ◽  
Medium Formulation ◽  
Flow Resistances

This work presents a data-driven Reduced-Order Model (ROM) for parametric convective heat transfer problems in porous media. The intrusive Proper Orthogonal Decomposition aided Reduced-Basis (POD-RB) technique is employed to reduce the porous medium formulation of the incompressible Reynolds-Averaged Navier–Stokes (RANS) equations coupled with heat transfer. Instead of resolving the exact flow configuration with high fidelity, the porous medium formulation solves a homogenized flow in which the fluid-structure interactions are captured via volumetric flow resistances with nonlinear, semi-empirical friction correlations. A supremizer approach is implemented for the stabilization of the reduced fluid dynamics equations. The reduced nonlinear flow resistances are treated using the Discrete Empirical Interpolation Method (DEIM), while the turbulent eddy viscosity and diffusivity are approximated by adopting a Radial Basis Function (RBF) interpolation-based approach. The proposed method is tested using a 2D numerical model of the Molten Salt Fast Reactor (MSFR), which involves the simulation of both clean and porous medium regions in the same domain. For the steady-state example, five model parameters are considered to be uncertain: the magnitude of the pumping force, the external coolant temperature, the heat transfer coefficient, the thermal expansion coefficient, and the Prandtl number. For transient scenarios, on the other hand, the coastdown-time of the pump is the only uncertain parameter. The results indicate that the POD-RB-ROMs are suitable for the reduction of similar problems. The relative L2 errors are below 3.34% for every field of interest for all cases analyzed, while the speedup factors vary between 54 (transient) and 40,000 (steady-state).

Cyclic Breathing Simulations in Large Scale Models of the Lung Airway From the Oronasal Opening to the Terminal Bronchioles

2012 ◽  
Author(s):  
D. Keith Walters ◽  
Greg W. Burgreen ◽  
Robert L. Hester ◽  
David S. Thompson ◽  
David M. Lavallee ◽  
...  
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Large Scale ◽  
Whole Body ◽  
Patient Specific ◽  
Cfd Simulations ◽  
Reduced Order ◽  
Scale Models ◽  
Steady State Simulation ◽  
Conducting Zone

Computational fluid dynamics (CFD) simulations were performed for unsteady periodic breathing conditions, using large-scale models of the human lung airway. The computational domain included fully coupled representations of the orotracheal region and large conducting zone up to generation four (G4) obtained from patient-specific CT data, and the small conducting zone (to G16) obtained from a stochastically generated airway tree with statistically realistic geometrical characteristics. A reduced-order geometry was used, in which several airway branches in each generation were truncated, and only select flow paths were retained to G16. The inlet and outlet flow boundaries corresponded to the oronasal opening (superior), the inlet/outlet planes in terminal bronchioles (distal), and the unresolved airway boundaries arising from the truncation procedure (intermediate). The cyclic flow was specified according to the predicted ventilation patterns for a healthy adult male at three different activity levels, supplied by the whole-body modeling software HumMod. The CFD simulations were performed using Ansys FLUENT. The mass flow distribution at the distal boundaries was prescribed using a previously documented methodology, in which the percentage of the total flow for each boundary was first determined from a steady-state simulation with an applied flow rate equal to the average during the inhalation phase of the breathing cycle. The distal pressure boundary conditions for the steady-state simulation were set using a stochastic coupling procedure to ensure physiologically realistic flow conditions. The results show that: 1) physiologically realistic flow is obtained in the model, in terms of cyclic mass conservation and approximately uniform pressure distribution in the distal airways; 2) the predicted alveolar pressure is in good agreement with previously documented values; and 3) the use of reduced-order geometry modeling allows accurate and efficient simulation of large-scale breathing lung flow, provided care is taken to use a physiologically realistic geometry and to properly address the unsteady boundary conditions.

Reduced-order steady-state descriptor Kalman fuser weighted by block-diagonal matrices

2008 ◽  
Vol 9 (2) ◽  
pp. 300-309 ◽  
Author(s):  
Zi-Li Deng ◽  
Yuan Gao ◽  
Gui-Li Tao
Keyword(s):  
Steady State ◽  
Reduced Order ◽  
Block Diagonal

Theoretical analysis of RNA polymerase fidelity: a steady-state copolymerization approach

2021 ◽  
Author(s):  
Wenbo Fu ◽  
Qiushi Li ◽  
Yongshun Song ◽  
Yaogen Shu ◽  
Zhongcan Ouyang ◽  
...  
Keyword(s):  
Steady State ◽  
Dna Replication ◽  
Theoretical Analysis ◽  
Rna Polymerase ◽  
Higher Order ◽  
Simplified Models ◽  
Rna Transcription ◽  
Dna Transcription ◽  
Polymerase Fidelity ◽  
Neighbor Effects

Abstract The fidelity of DNA transcription catalyzed by RNA polymerase (RNAP) has long been an important issue in biology. Experiments have revealed that RNAP can incorporate matched nucleotides selectively and proofread the incorporated mismatched nucleotides. However, systematic theoretical researches on RNAP fidelity are still lacking. In the last decade, several theories on RNA transcription have been proposed, but they only handled highly simplified models without considering the high-order neighbor effects and the oligonucleotides cleavage both of which are critical for the overall fidelity. In this paper, we regard RNA transcription as a binary copolymerization process and calculate the transcription fidelity by the steady-state copolymerization theory recently proposed by us for DNA replication. With this theory, the more realistic models considering higher-order neighbor effects, oligonucleotides cleavage, multi-step incorporation and multi-step cleavage can be rigorously handled.

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.

Temperature profiles in endothermic and exothermic reactions and the interpretation of experimental rate data

1970 ◽  
Vol 320 (1540) ◽  
pp. 71-100 ◽  
Keyword(s):  
Steady State ◽  
Correction Factor ◽  
Exothermic Reaction ◽  
Kinetic Studies ◽  
Activation Energies ◽  
Uniform Temperature ◽  
Exothermic Reactions ◽  
Arrhenius Function ◽  
Point To Point ◽  
Reacting Systems

Any endothermic or exothermic reaction is accompanied by self-cooling or self-heating. In reacting systems in which heat transfer is controlled by conduction, non-uniform temperature-position profiles are established. Examples of this situation are the exothermic decomposition of gaseous diethyl peroxide and the endothermic decomposition of nitrosyl chloride at low pressures (when convection is unimportant). In kinetic studies, allowance must be made for the non-uniform temperature to derive accurate isothermal velocity constants and Arrhenius parameters. In the present paper, the necessary corrections have been derived for a reactant in the steady state whose reaction rate varies exponentially with temperature and in which the temperature excess varies from point to point, being zero at the boundary (Frank-Kamenetskii’s conditions). The geometries considered are the slab, cylinder and sphere. The temperature gradient at the surface in the steady state ( Г ) occupies a key position, and this is exploited to find the correction factor required to convert 'observed’ rate constants to isothermal conditions, and thence to correct ‘observed’ activation energies and pre-exponential factors. The correction factor is found to be simply related to Frank- Kamenetskii’s δ (a dimensionless measure of heat-release rate). A similar analysis is given for systems hotter or cooler than their surroundings but uniform in temperature—such as well stirred fluid systems or small solid crystals (Semenov’s conditions). In these circumstances, systems of arbitrary geometry may be studied, and no approximation need be made to the Arrhenius function. For either type of boundary condition, uncorrected activation energies are overestimates in exothermic reactions and underestimates in endothermic reactions. Explicit relations are derived for making corrections. Boundary conditions intermediate between the two extremes investigated can also be treated though the resulting expressions are more cumbersome. In an appendix, an alternative ‘experimental’ approach is made to the elimination of errors from measured reaction velocities. This approach identifies the measured velocities with a temperature intermediate between those at centre and surface. The optimum choice, which weights the central and surface temperatures in the ratios 2:1 (slab), 1:1 (cylinder) and 2:3 (sphere), gives exactly correct results for the cylinder and acceptable precision for the slab and sphere even to within 5 K of the explosion limit. Other correction methods are also discussed.

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