A fast uncertainty quantification methodology and sampling technique for joint probability distribution of the Arrhenius rate expression: a case study applied to H₂/CO kinetic mechanism

Abstract

This work proposes a fast, novel, mathematically robust, and elegant unconstrained Method of Uncertainty Quantification (MUQ) for the temperature-dependent Arrhenius rate constant using Cholesky Decomposition (CD) of the covariance matrix of the Arrhenius parameters. The Arrhenius parameters of a reaction are treated as normally distributed correlated random variables. The MUQ method lends itself to an approach for Sampling of Arrhenius Curves (SAC), which automatically ensures that the generated samples are consistent with the distribution of Arrhenius parameters. The Method of Uncertainty Quantification and Sampling of Arrhenius Curves (MUQ-SAC) is used to train a quadratic polynomial response surface (PRS). Three important classes of Arrhenius curves possible within the SAC method are identified. From the total set of targets, a small subset of targets is first used to study the combinations of different classes of Arrhenius curves and their proportions within the design matrix, which is used to train PRS. Based on this understanding, response surfaces are generated for 64 ignition delay targets (Tig), which comprises of a wide range of pressure (P: 1--32.7 atm), temperature (T: 916-DIFadd-2869 K), and equivalence ratio (ϕ: 0.5--6.11), as well as for 74 laminar flame speed targets (Fls), spanning P: 1--25 atm, T: 285--600 K, and ϕ: 0.6--5. The H${}_2$/CO sub-mechanism of FFCM1.0 is chosen for the case study in which 22 reactions (66 Arrhenius parameters) are considered active parameters. The quality of the generated PRS is measured using the relative Maximum Residual Error (MRE). The quality of PRS is also checked against the search iterations encountered during mechanism optimisation. Accurate PRS could be generated over the search iterations, validating that the SAC method is able to span the entire uncertainty domain while training the PRS. The implementation of the MUQ-SAC method is made available at https://github.com/KrunalPanchal1995/MUQ-SAC.git.

Keywords:

• chemical kinetic mechanism
• uncertainty quantification
• sampling technique
• response surface methodology
• Cholesky decomposition

Disclosure statement

No potential conflict of interest was reported by the author(s).

Supplemental data

Supplemental data for this article can be accessed at https://doi.org/10.1080/13647830.2024.2326413.

Additional information

Funding

Krithika Narayanaswamy acknowledges support from the Indian Institute of Technology, Madras [via NFSG project MEE/17-18/696/NFSC/KRII], for computing facilities. Sivaram Ambikasaran acknowledges the support of MATRICS grant from Science and Engineering Research Board, India [sanction number: MTR/2019/001241]. Krithika Narayanaswamy and Sivaram Ambikasaran acknowledge support from the CRG grant awarded by the Science and Engineering Research Board, India [sanction number: CRG/2019/004470].