Most of the uncertainty quantification analysis requires multiple tasks to be carried out in a sequence, which resembles scientific workflow with dataflow to achieve the objective of the analysis. Each task requires certain inputs and generates an output, which could become the input for the following task.
Both UQ Assessment Study and Calibration Study share common tasks in the scientific workflow. The details of the tasks for each study are outlined below with some references to demonstration cases.
Uncertainty Quantification Assessment Studies
The workflow typically consists of five steps performed in the following sequence:
- Identification and characterization of the sources of uncertainties and quantities of interest.
- Design simulation campaign to generate adequate data for surrogate model construction.
- Assessment of surrogate model to be employed for characterizing the relationship between uncertain input parameters and quantities of interest.
- Sensitivity study utilizing the surrogate model to identify the most influential input parameters.
- Forward propagation of the most influential uncertain input parameters on the quantities of interest to assess variability.
Demonstrations of the application of the above UQ workflow for multiphase flow problems can be found in several publications:
- Gel et al. (2013): The sensitivity of several input parameters in a Discrete Element Method (DEM) were investigated for central jet fluidized bed problem. Among six input parameters identified as uncertain, two were selected for the study (particle to particle and particle to wall restitution coefficients) with a uniform distribution and their effect on the quantities of interest (particle bed height and pressure drop across the bed) were investigated. MFiX-DEM software was utilized as the black-box simulation tool for performing fluidized bed simulations. PSUADE UQ software toolkit was employed for UQ studies. The effect of uncertainty in the restitution coefficients were demonstrated by forward propagation method, which enabled the construction of Cumulative distribution function (CDF) for average bed height and assessment of probability of achieving a certain bed height given the input uncertainties.
- Gel et al. (2014): Three input parameters (temperature, pressure and heating rate) were considered as uncertain and their effect on the quantities of interest were investigated, which were coal devolatilization product yields (i.e., mass fractions of CO, CO2, H2, tar, H2O, and CH4 along with total volatile yield). C3M software was utilized as the black-box simulation tool for performing the coal devolatilization simulations. PSUADE UQ software toolkit was employed for UQ studies. Sobol’ Indices based global sensitivity study was performed and temperature was quantitatively demonstrated to be the most influential parameter on the quantities of interest. The effect of uncertainty in input temperature parameters was demonstrated through forward propagation.
- Vaidheeswaran et al. (2021): Particle-In-Cell (PIC) methodology is suitable for modeling large-scale systems owing to its computational efficiency. However, several model parameters are involved due to its empiricism. In this study, PIC is applied to three distinct operating regimes common in chemical engineering applications, viz., settling bed, bubbling fluidized bed and circulating fluidized bed. A non-intrusive UQ-based approach is applied using Nodeworks to identify the most influential model parameters (a.k.a. sensitivity analysis). This knowledge would subsequently aid in developing an effective design of experiments for calibration. Finally, consistent ranking of PIC model parameters was achieved with grid refinement when statistical weight was scaled with the cell volume.
- Gel et al. (2013): Gel, A., R. Garg, C. Tong, M. Shahnam, and C. Guenther. "Applying uncertainty quantification to multiphase flow computational fluid dynamics." Powder technology 242 (2013): 27-39. https://doi.org/10.1016/j.powtec.2013.01.045
- Gel et al. (2014): Gel, Aytekin, Kiran Chaudhari, Richard Turton, and Philip Nicoletti. "Application of uncertainty quantification methods for coal devolatilization kinetics in gasifier modeling." Powder technology 265 (2014): 66-75. https://doi.org/10.1016/j.powtec.2014.01.024
- Vaidheeswaran, A., Gel, A., Clarke, M. A., & Rogers, W. A. (2021). Assessment of model parameters in MFiX particle-in-cell approach. Advanced Powder Technology, 32(8), 2962-2977. https://doi.org/10.1016/j.apt.2021.06.011
The workflow typically consists of six steps performed in the following sequence:
- Identification of model parameters to be calibrated, quantities of interest, available experimental datasets, and control variables.
- Assess the importance ranking of model parameters employing the insight gained from sensitivity analysis and reduce the number of model parameters to be calibrated if necessary.
- Design simulation campaign generate adequate data for surrogate model construction.
- Assessment of surrogate model for characterizing the relationship between uncertain input parameters and quantities of interest.
- Select and employ the type of the calibration study (deterministic or Bayesian calibration).
- Assess the improvement with calibrated model parameters using experimental data.
Application of the above calibration workflow for multiphase flow problems can be found in the following publications:
- Gel et al. (2021): Parcel-In-Cell methodology implemented in MFiX-PIC offers faster time-to-solution with a trade-off in accuracy. To improve the accuracy of MFiX-PiC simulations, deterministic calibration methodology was employed for one of the representative problems selected, i.e., settling of particles in a dense medium. Deterministic calibration was employed prior to adopting Bayesian calibration due to lesser complexity and computational burden. It was shown that deterministic calibration improved MFiX-PIC predictions substantially for the particle settling case.
- Gel et al. (2021): Gel, Aytekin, Avinash Vaidheeswaran, and Mary Ann Clarke. Deterministic Calibration of MFiX-PIC, Part 1: Settling Bed. No. DOE/NETL-2021/2646. National Energy Technology Laboratory (NETL), Pittsburgh, PA, Morgantown, WV, and Albany, OR (United States), 2021.