Uncertainty quantification of fluidized beds using a data-driven framework

Abstract We carried out a nondeterministic analysis of flow in a fluidized bed. The flow in the fluidized bed is simulated with National Energy Technology Laboratory's open source multiphase fluid dynamics suite MFiX. It does not possess tools for uncertainty quantification. Therefore, we developed a C++ wrapper to integrate an uncertainty quantification toolkit developed at Sandia National Laboratory with MFiX. The wrapper exchanges uncertain input parameters and key output parameters among Dakota and MFiX. However, a data-driven framework is also developed to obtain reliable statistics as it is not feasible to get them with MFiX integrated into Dakota, Dakota-MFiX. The data generated from Dakota-MFiX simulations, with the Latin Hypercube method of sampling size 500, is used to train a machine learning algorithm. The trained and tested deep neural network algorithm is integrated with Dakota via the wrapper to obtain low order statistics of the bed height and pressure drop across the bed. In addition, it can be used to obtain statistics with various distributions of the uncertain input variables and various uncertainty quantification methods. In addition, sensitivity analysis is carried out for 9 input parameters and two output parameters.

[1]  V. M. Krushnarao Kotteda,et al.  Next Generation Exascale Capable Mutliphase Solver With Trilinos , 2016 .

[2]  John Red-Horse,et al.  Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach , 1999 .

[3]  Vinod Kumar,et al.  Performance of preconditioned iterative solvers in MFiX–Trilinos for fluidized beds , 2018, The Journal of Supercomputing.

[4]  Curtis B. Storlie,et al.  Numerical modeling and uncertainty quantification of a bubbling fluidized bed with immersed horizontal tubes , 2014 .

[5]  Lynn F. Gladden,et al.  Validation of a discrete element model using magnetic resonance measurements , 2009 .

[6]  R. Daniel Meyer,et al.  An Analysis for Unreplicated Fractional Factorials , 1986 .

[7]  Sergey Oladyshkin,et al.  Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion , 2012, Reliab. Eng. Syst. Saf..

[8]  Shane Legg,et al.  Massively Parallel Methods for Deep Reinforcement Learning , 2015, ArXiv.

[9]  Hugh W. Coleman,et al.  Uncertainties and CFD Code Validation , 1997 .

[10]  Yuan Yu,et al.  TensorFlow: A system for large-scale machine learning , 2016, OSDI.

[11]  S. Pannala,et al.  Open-source MFIX-DEM software for gas-solids flows: Part I – verification studies , 2012 .

[12]  J. Kuipers,et al.  Numerical study of segregation using a new drag force correlation for polydisperse systems derived from lattice-Boltzmann simulations , 2007 .

[13]  G. Grest,et al.  Granular flow down an inclined plane: Bagnold scaling and rheology. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Joaquín González-Rodríguez,et al.  Frame-by-frame language identification in short utterances using deep neural networks , 2015, Neural Networks.

[15]  Achintya Haldar,et al.  Probability, Reliability and Statistical Methods in Engineering Design (Haldar, Mahadevan) , 1999 .

[16]  Lynn F. Gladden,et al.  Granular temperature: Comparison of Magnetic Resonance measurements with Discrete Element Model simulations , 2008 .

[17]  Pol D. Spanos,et al.  Stochastic Finite Element Method: Response Statistics , 1991 .

[18]  Fei-Fei Li,et al.  Large-Scale Video Classification with Convolutional Neural Networks , 2014, 2014 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  W. Stahel,et al.  Log-normal Distributions across the Sciences: Keys and Clues , 2001 .

[20]  Habib N. Najm,et al.  Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics , 2009 .

[21]  S. Sundaresan,et al.  Effective particle diameters for simulating fluidization of non‐spherical particles: CFD‐DEM models vs. MRI measurements , 2017 .

[22]  Y. Tsuji,et al.  Discrete particle simulation of two-dimensional fluidized bed , 1993 .

[23]  Aytekin Gel,et al.  Applying uncertainty quantification to multiphase flow computational fluid dynamics , 2013 .

[24]  Masayuki Horio,et al.  DEM simulation of fluidized beds for gas-phase olefin polymerization , 1999 .

[25]  Danesh K. Tafti,et al.  Development of parallel DEM for the open source code MFIX , 2013 .

[26]  S. Baldwin,et al.  Hydrodynamic characteristics of particles with different roughness and deformability in a liquid fluidized bed , 2018, Chemical Engineering Science.

[27]  Anelia Angelova,et al.  Pedestrian detection with a Large-Field-Of-View deep network , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[28]  Indranil Pan,et al.  Incorporating uncertainty in data driven regression models of fluidized bed gasification: A Bayesian approach , 2016 .

[29]  Charles Tong.  Problem Solving Environment for Uncertainty Analysis and Design Exploration , 2008 .

[30]  Quoc V. Le,et al.  Sequence to Sequence Learning with Neural Networks , 2014, NIPS.

[31]  Prasad Saripalli,et al.  Semi-analytical approaches to modeling deep well injection of CO2 for geological sequestration , 2002 .

[32]  Christopher J. Roy,et al.  A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing , 2011 .

[33]  B. Kulkarni,et al.  Development of data-driven models for fluidized-bed coal gasification process , 2012 .

[34]  Vinod Kumar,et al.  A framework to integrate MFiX with Trilinos for high fidelity fluidized bed computations , 2016, 2016 IEEE High Performance Extreme Computing Conference (HPEC).

[35]  Michael S. Eldred,et al.  DAKOTA : a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Version 5.0, user's reference manual. , 2010 .