scholarly journals Model Reduction in Large Chemical Systems- an Alternative Method Applying Discrete Approximation

2018 ◽  
Author(s):  
Magne Fjeld
Keyword(s):  
Model Reduction ◽  
Dynamic Model ◽  
Process Model ◽  
Tubular Reactor ◽  
Partial Differential Operator ◽  
Numerical Data ◽  
Stoichiometric Matrix ◽  
Chemical Systems ◽  
Reduction Techniques ◽  
In Series

No numerical data. <p><b><br> </b>Dynamic model reduction techniques based on the decomposition of the stoichiometric matrix to find the chemical invariant, break down if axial diffusion is present in a tubular reactor.</p> <p>Straightforward discretization of the partial differential operator does indeed show that the resulting discrete dynamic model cannot generally be partioned to obtain the reaction variant vector and the reaction invariant (asymptotic) vector. However, the paper demonstrate that, if the diffusional tubular reactor is discretely and approximatively represented by tanks-in-series, then matrix approaches to successfully find the chemical variant and invariant vectors of the resulting chemical process model is possible. </p>

scholarly journals Model Reduction in Large Chemical Systems- an Alternative Method Applying Discrete Approximation

2018 ◽  
Author(s):  
Magne Fjeld
Keyword(s):  
Model Reduction ◽  
Dynamic Model ◽  
Process Model ◽  
Tubular Reactor ◽  
Partial Differential Operator ◽  
Numerical Data ◽  
Stoichiometric Matrix ◽  
Chemical Systems ◽  
Reduction Techniques ◽  
In Series

No numerical data. <p><b><br> </b>Dynamic model reduction techniques based on the decomposition of the stoichiometric matrix to find the chemical invariant, break down if axial diffusion is present in a tubular reactor.</p> <p>Straightforward discretization of the partial differential operator does indeed show that the resulting discrete dynamic model cannot generally be partioned to obtain the reaction variant vector and the reaction invariant (asymptotic) vector. However, the paper demonstrate that, if the diffusional tubular reactor is discretely and approximatively represented by tanks-in-series, then matrix approaches to successfully find the chemical variant and invariant vectors of the resulting chemical process model is possible. </p>

Model Reduction in Chemical Systems- an Alternative Method Applying Discrete Approximation

2018 ◽  
Author(s):  
Magne Fjeld
Keyword(s):  
Model Reduction ◽  
Chemical Reactions ◽  
Tubular Reactor ◽  
Model Approximation ◽  
Diffusion Term ◽  
Diffusion Operator ◽  
Chemical Systems ◽  
Spatially Distributed ◽  
Derivative Term ◽  
Numerical Discretization

<div><div>This paper addresses model reduction in large or spatially distributed systems including diffusion of matter and chemical reactions. If diffusion is present, it would be represented by a diffusion operator (always including a spatial second derivative term). If diffusion is not present, spatial discretization is straightforward. In the latter case, applying the concept of chemical invariants, or the concept of asymptotic chemical invariants, paves the way for model reduction through elimination of the invariants. Inclusion of diffusion destroys the opportunity to obtain invariants , when numerical discretization of the diffusion term is applied. However, the paper demonstrates that application of the invariant concept may be applied even in the case of diffusion of matter in a chemical tubular reactor, if relying on an approximation in modelling of a tubular reactor by a tank-in-the series model. For nonreacting matter, the quality and numerical properties of the tanks-in-the-series model approximation of a tubular reactor is well documented in the literature. However, there is no general proof available for the quality and effectiveness of such an approximation when chemical reactions are present, although example cases show good approximation.<br></div></div><div><div><br></div></div>

scholarly journals Model Reduction in Chemical Systems- an Alternative Method Applying Discrete Approximation

2018 ◽  
Author(s):  
Magne Fjeld
Keyword(s):  
Model Reduction ◽  
Chemical Reactions ◽  
Tubular Reactor ◽  
Model Approximation ◽  
Diffusion Term ◽  
Diffusion Operator ◽  
Chemical Systems ◽  
Spatially Distributed ◽  
Derivative Term ◽  
Numerical Discretization

<div><div>This paper addresses model reduction in large or spatially distributed systems including diffusion of matter and chemical reactions. If diffusion is present, it would be represented by a diffusion operator (always including a spatial second derivative term). If diffusion is not present, spatial discretization is straightforward. In the latter case, applying the concept of chemical invariants, or the concept of asymptotic chemical invariants, paves the way for model reduction through elimination of the invariants. Inclusion of diffusion destroys the opportunity to obtain invariants , when numerical discretization of the diffusion term is applied. However, the paper demonstrates that application of the invariant concept may be applied even in the case of diffusion of matter in a chemical tubular reactor, if relying on an approximation in modelling of a tubular reactor by a tank-in-the series model. For nonreacting matter, the quality and numerical properties of the tanks-in-the-series model approximation of a tubular reactor is well documented in the literature. However, there is no general proof available for the quality and effectiveness of such an approximation when chemical reactions are present, although example cases show good approximation.<br></div></div><div><div><br></div></div>

scholarly journals COMPARISON OF SIMPLE DYNAMIC MODEL REDUCTION TECHNIQUES

1976 ◽  
Vol 9 (3) ◽  
pp. 251-253
Author(s):  
Em NAKANISHI ◽  
HIROAKI YASUOKA
Keyword(s):  
Model Reduction ◽  
Dynamic Model ◽  
Reduction Techniques

Energy-Based Model Reduction Methodology for Automated Modeling

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Loucas S. Louca ◽  
Jeffrey L. Stein ◽  
Gregory M. Hulbert
Keyword(s):  
Model Reduction ◽  
Order Reduction ◽  
Process Models ◽  
Model Parameters ◽  
Automated Modeling ◽  
Reduced Models ◽  
System Models ◽  
Quarter Car Model ◽  
Reduction Techniques ◽  
Physical Phenomena

In recent years, algorithms have been developed to help automate the production of dynamic system models. Part of this effort has been the development of algorithms that use modeling metrics for generating minimum complexity models with realization preserving structure and parameters. Existing algorithms, add or remove ideal compliant elements from a model, and consequently do not equally emphasize the contribution of the other fundamental physical phenomena, i.e., ideal inertial or resistive elements, to the overall system behavior. Furthermore, these algorithms have only been developed for linear or linearized models, leaving the automated production of models of nonlinear systems unresolved. Other model reduction techniques suffer from similar limitations due to linearity or the requirement that the reduced models be realization preserving. This paper presents a new modeling metric, activity, which is based on energy. This metric is used to order the importance of all energy elements in a system model. The ranking of the energy elements provides the relative importance of the model parameters and this information is used as a basis to reduce the size of the model and as a type of parameter sensitivity information for system design. The metric is implemented in an automated modeling algorithm called model order reduction algorithm (MORA) that can automatically generate a hierarchical series of reduced models that are realization preserving based on choosing the energy threshold below which energy elements are not included in the model. Finally, MORA is applied to a nonlinear quarter car model to illustrate that energy elements with low activity can be eliminated from the model resulting in a reduced order model, with physically meaningful parameters, which also accurately predicts the behavior of the full model. The activity metric appears to be a valuable metric for automating the reduction of nonlinear system models—providing in the process models that provide better insight and may be more numerically efficient.

Application of projection-based model reduction to finite-element plate models for two-dimensional traveling waves

2016 ◽  
Vol 28 (14) ◽  
pp. 1886-1904 ◽  
Author(s):  
Vijaya VN Sriram Malladi ◽  
Mohammad I Albakri ◽  
Serkan Gugercin ◽  
Pablo A Tarazaga
Keyword(s):  
Finite Element ◽  
Model Reduction ◽  
Traveling Waves ◽  
Large Scale ◽  
Fe Model ◽  
Plate Model ◽  
Reduction Techniques ◽  
State Frequency ◽  
Scale Down ◽  
The Stability

A finite element (FE) model simulates an unconstrained aluminum thin plate to which four macro-fiber composites are bonded. This plate model is experimentally validated for single and multiple inputs. While a single input excitation results in the frequency response functions and operational deflection shapes, two input excitations under prescribed conditions result in tailored traveling waves. The emphasis of this article is the application of projection-based model reduction techniques to scale-down the large-scale FE plate model. Four model reduction techniques are applied and their performances are studied. This article also discusses the stability issues associated with the rigid-body modes. Furthermore, the reduced-order models are utilized to simulate the steady-state frequency and time response of the plate. The results are in agreement with the experimental and the full-scale FE model results.

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