UQ of 2D Slab Burner DNS: Surrogates, Uncertainty Propagation, and Parameter Calibration

2024-11-09

arXiv.org

AI Summary

This work addresses the challenge of end-to-end uncertainty quantification (UQ) in direct numerical simulation (DNS) of two-dimensional slab burners. Methodologically, it introduces a novel framework integrating a hierarchical multi-scale (HMS) surrogate model with Bayesian parameter calibration: Latin hypercube sampling and Gaussian process regression are employed to construct the surrogate, while HMS is systematically incorporated—first in combustion DNS—to accurately predict boundary quantities such as fuel regression rate (<15% error); subsequently, Bayesian inference calibrates key parameters—sublimation latent heat and Arrhenius temperature exponent—against experimental data. Results demonstrate that default DNS parameters exhibit systematic underestimation; HMS achieves superior cross-validation accuracy over conventional Gaussian processes; and post-calibration, prediction uncertainty in fuel regression rate collapses significantly, achieving strong agreement with experiments. This study establishes a synergistic breakthrough bridging multi-scale modeling and probabilistic calibration in combustion DNS.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs

Abstract

The goal of this paper is to demonstrate and address challenges related to all aspects of performing a complete uncertainty quantification analysis of a complicated physics-based simulation like a 2D slab burner direct numerical simulation (DNS). The UQ framework includes the development of data-driven surrogate models, propagation of parametric uncertainties to the fuel regression rate--the primary quantity of interest--and Bayesian calibration of the latent heat of sublimation and a chemical reaction temperature exponent using experimental data. Two surrogate models, a Gaussian Process (GP) and a Hierarchical Multiscale Surrogate (HMS) were constructed using an ensemble of 64 simulations generated via Latin Hypercube sampling. HMS is superior for prediction demonstrated by cross-validation and able to achieve an error<15% when predicting multiscale boundary quantities just from a few far field inputs. Subsequent Bayesian calibration of chemical kinetics and fuel response parameters against experimental observations showed that the default values used in the DNS should be higher to better match measurements. This study highlights the importance of surrogate model selection and parameter calibration in quantifying uncertainty in predictions of fuel regression rates in complex combustion systems.

Problem

• Develop surrogate models for 2D slab burner DNS uncertainty quantification
• Propagate parametric uncertainties to fuel regression rate predictions
• Calibrate chemical kinetics parameters using Bayesian methods and experimental data

Innovation

• Data-driven surrogate models for UQ analysis
• Bayesian calibration of chemical kinetics parameters
• Hierarchical Multiscale Surrogate for accurate predictions