High fidelity mathematical model building with experimental data: A Bayesian approach

Blau, Gary; Lasinski, Michael; Orçun, Seza; Hsu, Shuo-Huan; Caruthers, James M.; Delgass, W. Nicholas; Venkatasubramanian, Venkat

doi:10.1016/j.compchemeng.2007.04.008

Cited by 51 publications

(44 citation statements)

References 14 publications

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“…Bayesian methods are based on a systematic probability‐theoretic treatment of all involved quantities including in particular experimental data as well as model parameters and center around applying Bayes' theorem to update knowledge represented in the form of distributions . Bayesian methods have been used in chemical kinetics for at least half a century , but their popularity in this and other fields has increased significantly in recent years due to an influential paper by Kennedy and O'Hagan . In particular, the use of Markov chain Monte Carlo (MCMC) sampling has become widespread, at least to some extent as a consequence of readily available powerful computers.…”

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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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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Section: The Quest For High-fidelity Experimental Datamentioning

confidence: 99%

“…Blau and coworkers [197] argued that although this approach is conceptually sound, yet there exist limitations to the approach. A key limitation is the paucity of high quality experimental data [197]. In other words, the quality of the experimental data available to the virtual testbed developer will significantly affect the validity of predictions from the testbed.…”

Section: The Quest For High-fidelity Experimental Datamentioning

confidence: 99%

Virtual testing of advanced composites, cellular materials and biomaterials: A review

Okereke

Akpoyomare

Bingley

2014

Composites Part B: Engineering

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Please cite this article as: Okereke, M.I., Akpoyomare, A.I., Bingley, M.S., Virtual testing of advanced composites, cellular materials and biomaterials: a review, Composites: Part B (2014), doi: http://dx.doi.org/10. 1016/ j.compositesb.2014.01.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. AbstractThis paper documents the emergence of virtual testing frameworks for prediction of the constitutive responses of engineering materials. A detailed study is presented, of the philosophy underpinning virtual testing schemes: highlighting the structure, challenges and opportunities posed by a virtual testing strategy compared with traditional laboratory experiments. The virtual testing process has been discussed from atomistic to macrostructural lengthscales of analyses. Several implementations of virtual testing frameworks for diverse categories of materials are also presented, with particular emphasis on composites, cellular materials and biomaterials (collectively described as heterogeneous systems, in this context). The robustness of virtual frameworks for prediction of the constitutive behaviour of these materials is discussed. The paper also considers the current thinking on developing virtual laboratories in relation to availability of computational resources as well as the development of multi-scale material model algorithms. In conclusion, the paper highlights the challenges facing developments of future virtual testing frameworks. This review represents a comprehensive documentation of the state of knowledge on virtual testing from microscale to macroscale length scales for heterogeneous materials across constitutive responses from elastic to damage regimes.

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“…Based on such a method, Gardoni et al (2002Gardoni et al ( , 2007 modeled both capacity and fragility in reinforced concrete columns or elastic modulus of concrete. This last method can be applied to heteroscedastic behaviours by transforming data in a homoscedastic space or by adding input dependent-noise to the model (Bansal and Aggarwal 2007;Blau et al 2008). Also, Yeh (2014) estimated the distribution of compressive strength of high-performance concrete which displayed a heteroscedastic behaviour, through the NN method.…”

Section: Introductionmentioning

confidence: 99%

Probabilistic Modeling of Heteroscedastic Laboratory Experiments Using Gaussian Process Regression

et al. 2018

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High fidelity mathematical model building with experimental data: A Bayesian approach

Cited by 51 publications

References 14 publications

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

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

Virtual testing of advanced composites, cellular materials and biomaterials: A review

Probabilistic Modeling of Heteroscedastic Laboratory Experiments Using Gaussian Process Regression

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