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## AN INCREMENTAL APPROACH FOR THE IDENTIFICATION OF REACTION KINETICS

### Citations

754 |
Regularization of inverse problems
- Engl, Hanke, et al.
- 2000
(Show Context)
Citation Context ...·) is used to denote a noisy quantity and εy represents the measurement noise contained in ỹ. This estimation problem represents an ill-posed inverse problem according to the definition of Hadamard (=-=Engl et al., 1996-=-). Since the measurement is noisy, the estimate f̂ ri (t) of f r i (t) can be arbitrarily large if no regularization of the solution is considered. Mhamdi and Marquardt (1999) used Tikhonov-Arsenin fi... |

738 |
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion, volume 4
- Hansen
- 1998
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Citation Context ...by the choice of the regularization parameter that weighs the tradeoff between noise reduction and bias in the estimate. Adequate regularization parameters can be determined by the L-curve criterion (=-=Hansen, 1998-=-), for example. Another approach to filtering is the use of smoothing splines (Craven and Wahba, 1979). Splines are piecewise polynomial functions that possess certain smoothness and differentiability... |

732 |
Smoothing noisy data with spline functions. Estimating the correct degree of smoothing by the method of generalized cross-validation
- Craven, Wahba
- 1978
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Citation Context ...ion and bias in the estimate. Adequate regularization parameters can be determined by the L-curve criterion (Hansen, 1998), for example. Another approach to filtering is the use of smoothing splines (=-=Craven and Wahba, 1979-=-). Splines are piecewise polynomial functions that possess certain smoothness and differentiability properties at the nodes. General cross validation (GCV) is often used to select a suitable regulariz... |

726 | Bayesian interpolation
- MacKay
- 1992
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Citation Context ...ng and improve the predictive capability of the model, regularization, model discrimination or data validation techniques are commonly used. Feed-forward neural networks with Bayesian regularization (=-=MacKay, 1992-=-) may serve as an automated regularization procedure for training. 4. ILLUSTRATIVE EXAMPLE 4.1 Simulated reaction system The incremental approach for identifying reaction kinetics is illustrated on th... |

58 | A hybrid neural network-first principles approach to process modeling - Psichogios, Ungar - 1992 |

29 |
Chemical Kinetics: The Study of Reaction Rates in Solution,
- Connors
- 1990
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Citation Context ...art in the modeling of chemical reactors. A reliable description is rarely available a priori. For example, it is well known that reaction kinetics cannot necessarily be derived from stoichiometries (=-=Connors, 1990-=-), in particular in the case of catalyzed reactions. Thus, a reliable kinetic model needs to be identified from experimental data. The model-based techniques used in process control and optimization r... |

17 |
Implementation of adaptive optimal operation for a semi-batch reaction system
- Ruppen, Bonvin, et al.
- 1997
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Citation Context ...ocedure for training. 4. ILLUSTRATIVE EXAMPLE 4.1 Simulated reaction system The incremental approach for identifying reaction kinetics is illustrated on the acetoacetylation of pyrrole with diketene (=-=Ruppen et al., 1997-=-): P+D K→ PAA (10a) D+D K→ DHA (10b) D→ oligomers (10c) PAA+D K→ F (10d) In addition to the desired reaction of diketene (D) and pyrrole (P) to 2-acetoacetyl pyrrole (PAA) (10a), there are several und... |

5 |
Model–based measurement of diffusion using Raman spectroscopy, AIChE
- Bardow, Marquardt, et al.
- 1995
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Citation Context ...feedforward neural network yielding the kinetic model. The approach is especially suited for nowaday’s high resolution measurement techniques such as IR (Alsmeyer et al., 2002) or Raman spectroscopy (=-=Bardow et al., 2003-=-), where concentration data can be obtained continuously in-situ. 2. PRELIMINARIES 2.1 Model of the reaction system Consider a homogeneous, not necessarily isothermal, chemical reaction system with R ... |

4 |
Target factor analysis for the identification of stoichiometric models',
- Bonvin, Rippin
- 1990
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Citation Context ... serve as inputs to the data-driven models rj = rj(ci) and rj = rj(ci, T ) for the isothermal and non-isothermal cases, respectively. If the reaction stoichiometry is unknown, target factor analysis (=-=Bonvin and Rippin, 1990-=-) can help identify the stoichiometry based on the estimated fluxes. Measurements BalancesModel 2 Model 1 Balances Stoichiometry Model 3 Rate law(conc. dep.)StoichiometryBalances Model 4 Rate law(conc... |

4 | An inversion approach to the estimation of reaction rates in chemical reactors - Mhamdi, Marquardt - 1999 |

2 |
A new method for phase equilibrium measurements in reacting mixtures. Fluid Phase Equilibria 203
- Alsmeyer, Marquardt, et al.
- 2002
(Show Context)
Citation Context ...e as input to a Bayesian algorithm to train a feedforward neural network yielding the kinetic model. The approach is especially suited for nowaday’s high resolution measurement techniques such as IR (=-=Alsmeyer et al., 2002-=-) or Raman spectroscopy (Bardow et al., 2003), where concentration data can be obtained continuously in-situ. 2. PRELIMINARIES 2.1 Model of the reaction system Consider a homogeneous, not necessarily ... |

2 | Neuralnetwork modeling and optimization of induced foreign protein production - Tholudur, Ramirez - 1999 |

1 |
Adaptivity in process systems modeling
- Marquardt
- 2002
(Show Context)
Citation Context ...entification process, the incremental identification approach features the stepwise identification of quantities as they are used in the modeling process. In an adaptive model identification context (=-=Marquardt, 2002-=-), the incremental approach allows the utilization of as much information as can be safely provided by first-principle modeling or sound empirical approaches. The process of identification then reduce... |