Numerical investigation of the uncertainty of Arrhenius parameters

Varga, László; Szabó, Botond; Zsély, István Gy.; Zempléni, András; Turányi, Tamás

doi:10.1007/s10910-011-9859-7

Cited by 16 publications

(7 citation statements)

References 22 publications

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“…A specific case of the tradeoff of physical rigor for mathematical rigor has been the treatment of temperature-dependent rate uncertainty. As discussed in Section 2.1, the three rate coefficients each have their own uncertainty, which allows for a potentially elaborate description of the rate constant uncertainty with respect to temperature [172][173][174]. In principle, in an inverse-problem study, each of these three parameters would be subject to constraint, thereby constraining the temperature-dependent uncertainty.…”

Section: Balance Between Mathematical and Physical Rigormentioning

confidence: 99%

Combustion kinetic model uncertainty quantification, propagation and minimization

Wang

Sheen

2015

Progress in Energy and Combustion Science

282

150

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The current interest in the combustion chemistry of hydrocarbon fuels, including the various alcohol and biodiesel compounds, motivates this review of the methods and application of kinetic uncertainty quantification (UQ). Our intent is to provide a self-contained review about the mathematical principles and methods of uncertainty quantification and their application in highly complex, multi-parameter combustion chemistry problems. We begin by outlining the reasons why the kinetic uncertainty must be considered and treated as a part of the combustion chemistry development in order to make progress. This is followed by a brief discussion about the sources and classification of kinetic uncertainties and the meanings and definitions of model verification and validation. We discuss the histories of UQ studies with an emphasis on how the combustion community has a long tradition of UQ consideration through standard sensitivity analysis. Such efforts have motivated the advancements of UQ methods specifically tailored to combustion chemistry. They also led to the recent growing interests in applying UQ methods as a part of our recommended long-term solution to the chemical kinetic problem of combustion. We then review and classify the various UQ methods and illustrate their applications for problems involving forward uncertainty quantification and propagation, and as an inverse problem leading to model uncertainty constraining. For the inverse problem, the focus of discussion is in the use of methods originating from Bayes' Theorem. We show that, for combustion chemistry problems, while UQ alone cannot produce precise, individual rate parameters, it can be instrumental in measuring the progress of our understanding of combustion chemistry and in utilizing fundamental combustion property data beyond a simple "agreedisagree" statement. When treated as a Bayesian inference problem, UQ also aids the development of predictive kinetic models in two ways: the use of fundamental combustion property data, global or local, to provide a better constrained kinetic model, and along with forward kinetic uncertainty propagation, to yield estimates for the confidence of a model to make predictions outside of the thermodynamic regimes where the model has been tested. We provide several examples to illustrate the utility of the UQ methods discussed and to demonstrate that, in the field of combustion chemistry, further progress will be better achieved through a combination of fundamental studies of reaction rates through well-defined and designed experiments and ab initio theoretical calculations, and of analyses of global experimental measurements. These studies together must be supplemented by UQ analyses, in such a way that a measurable progress can be made over time.

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Section: Balance Between Mathematical and Physical Rigormentioning

confidence: 99%

Combustion kinetic model uncertainty quantification, propagation and minimization

Wang

Sheen

2015

Progress in Energy and Combustion Science

282

150

View full text Add to dashboard Cite

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“…Extensive work has been carried out on uncertainty bounds of Arrhenius parameters , feasible sets in such parameter spaces , and optimization of parameters beyond the basic Arrhenius ones, such as third‐body efficiencies . However, to explore the performance of the Bayesian methodology for parameter estimation and error propagation, which is the principal aim of this paper, it is sufficient to find any local minimum with respect to whichever parameters are considered.…”

Section: Methodsmentioning

confidence: 99%

“…For example, global sensitivity methods have been used to propagate uncertainties from parameters in first‐principles calculations to reaction rate coefficients . Uncertainties of the three parameters in the Arrhenius rate law, with particular emphasis on their joint distribution and its temperature dependence, have been investigated in detail . Given that error propagation is intrinsically part of parameter estimation, frequently in the sense of optimizing with respect to an objective function in one form or another, it is also natural to consider confidence regions defined by the contours of the objective function surface .…”

Section: Introductionmentioning

confidence: 99%

Bayesian Error Propagation for a Kinetic Model of n‐Propylbenzene Oxidation in a Shock Tube

Mosbach

Hong

Brownbridge

et al. 2014

Int J of Chemical Kinetics

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We apply a Bayesian parameter estimation technique to a chemical kinetic mechanism for n-propylbenzene oxidation in a shock tube to propagate errors in experimental data to errors in Arrhenius parameters and predicted species concentrations. We find that, to apply the methodology successfully, conventional optimization is required as a preliminary step. This is carried out in two stages: First, a quasi-random global search using a Sobol low-discrepancy sequence is conducted, followed by a local optimization by means of a hybrid gradient-descent/Newton iteration method. The concentrations of 37 species at a variety of temperatures, pressures, and equivalence ratios are optimized against a total of 2378 experimental observations. We then apply the Bayesian methodology to study the influence of uncertainties in the experimental measurements on some of the Arrhenius parameters in the model as well as some of the predicted species concentrations. Markov chain Monte Carlo algorithms are employed to sample from the posterior probability densities, making use of polynomial surrogates of higher order fitted to the model responses. We conclude that the methodology provides a useful tool for the analysis of distributions of model parameters and responses, in particular their uncertainties and correlations. Limitations of the method are discussed. For example, we find that using second-order response surfaces and assuming

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“…Because of the inherent correlation of the two Arrhenius parameters, k 0 and E A , the parameterization of the Arrhenius equation (Equation (25)) is challenging. That is, independently of the applied experimental setup the correlation cannot be reduced for the Arrhenius rate [62,63] expression. At best, a parameter transformation might be applied to mitigate the correlation effect but changes the meaning of the identified parameters alike [64].…”

Section: Synthesis Of An Api-scaffold (Dhbd)mentioning

confidence: 99%

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

et al. 2018

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In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients.Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

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Numerical investigation of the uncertainty of Arrhenius parameters

Cited by 16 publications

References 22 publications

Combustion kinetic model uncertainty quantification, propagation and minimization

Combustion kinetic model uncertainty quantification, propagation and minimization

Bayesian Error Propagation for a Kinetic Model of n‐Propylbenzene Oxidation in a Shock Tube

The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design

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