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Flow parameter estimation using laser absorption spectroscopy and approximate Bayesian computation

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Abstract

Given spatially sparse or lower dimensional experimental measurements, approximate Bayesian computation (ABC) and numerical simulations can be used to estimate unknown characteristics of complex multi-physics engineering systems. Here, we describe the ABC approach and use it to estimate the speed of high-temperature gases exiting an industrially relevant catalytic burner, as well as to estimate the completeness of combustion within the burner. Using vertical profiles of absorption-weighted average temperature from laser absorption spectroscopy (LAS) at three different burner operating conditions, we combine ABC and large eddy simulations (LES) to generate posterior distributions of inflow speeds and heat addition characteristics above the burner. We show that the ABC method correctly estimates trends in the inflow speed for different conditions, and we find that there is a strong likelihood of incomplete combustion for higher equivalence ratios. We evaluate the predictive capability of the approach using an observing system experiment, indicating that the ABC method, when combined with LES, is able to accurately predict LAS measurements. We thus demonstrate that ABC is an effective tool for obtaining additional insights from available experimental measurements, thereby improving understanding of real-world engineering systems.

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References

  • Abdessalem AB, Dervilis N, Wagg D, Worden K (2018) Model selection and parameter estimation in structural dynamics using approximate Bayesian computation. Mech Syst Signal Process 99:306

    Article  Google Scholar 

  • Adowski TR, Bauman PT (2018) A numerical study of bayesian inference of surface catalycity in low speed reacting flow using laser absorption spectroscopy. In: 2018 Joint Thermophysics and Heat Transfer Conference (American Institute of Aeronautics and Astronautics, Atlanta, Georgia, 2018). https://doi.org/10.2514/6.2018-4290

  • Beaumont MA (2010) Approximate Bayesian computation in evolution and ecology. Annu Rev Ecol Evol Syst 41(379–406):1

    Google Scholar 

  • Beaumont MA, Zhang W, Balding DJ (2002) Approximate Bayesian computation in population genetics. Genetics 162(4):2025

    Article  Google Scholar 

  • Bolshov MA, Kuritsyn YA, Romanovskii YV (2015) Tunable diode laser spectroscopy as a technique for combustion diagnostics. Spectrochim Acta Part B 106:45

    Article  Google Scholar 

  • Bonnie JM, Sanford G (1996) Computer program for calculation of complex chemical equilibrium compositions and applications. User’s Manual and Program Discription

  • Bouttier F, Kelly G (2001) Observing-system experiments in the ECMWF 4D-Var data assimilation system. Q J R Meteorol Soc 127(574):1469

    Article  Google Scholar 

  • Cai T, Tan T, Wang G, Chen W, Gao X (2009) Gas temperature measurements using wavelength modulation spectroscopy at \(1.39\,\mu \text{m}\). Opt Appl 39(1)

  • Chai T, Draxler RR (2014) Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature. Geosci Model Dev 7(3):1247

    Article  Google Scholar 

  • Christopher JD, Lapointe C, Wimer NT, Hayden TRS, Grooms I, Rieker GB, Hamlington PE (2017) Parameter Estimation for a Turbulent Buoyant Jet with Rotating Cylinder Using Approximate Bayesian Computation. AIAA Paper, AIAA-2017-3629

  • Christopher JD, Wimer NT, Hayden TRS, Lapointe C, Grooms I, Rieker GB, Hamlington PE (2017) Parameter estimation for a turbulent buoyant jet using approximate bayesian computation. AIAA Paper, AIAA-2017-0531

  • Christopher JD, Wimer NT, Lapointe C, Hayden TRS, Grooms I, Rieker GB, Hamlington PE (2018) Parameter estimation for complex thermal-fluid flows using approximate Bayesian computation. Phys Rev Fluids 3:104602

    Article  Google Scholar 

  • Constantine PG, Wang Q, Doostan A, Iaccarino G (2011) A surrogate accelerated Bayesian inverse analysis of the HyShot II flight data. AIAA Paper, AIAA-2011-2037

  • Cottilard SA (2011) Catalytic combustion. Nova Science Publ., New York

    Google Scholar 

  • Csilléry K, Blum MGB, Gaggiotti OE, François O (2010) Approximate Bayesian computation (ABC) in practice. Trends Ecol Evolut 25(7):410

    Article  Google Scholar 

  • Daily JW (1997) Laser induced fluorescence spectroscopy in flames. Prog Energy Combust Sci 23(2):133

    Article  Google Scholar 

  • Daun KJ, Grauer SJ, Hadwin PJ (2016) Chemical species tomography of turbulent flows: discrete ill-posed and rank deficient problems and the use of prior information. J Quant Spectrosc Radiat Transf 172:58

    Article  Google Scholar 

  • Doronina OA, Christopher JD, Towery CAZ, Hamlington PE, Dahm WJA (2018) Autonomic closure for turbulent flows using approximate bayesian computation. AIAA Paper, AIAA-2018-0594

  • Doronina OA, Towery CAZ, Christopher JD, Grooms I, Hamlington PE (2019) Turbulence model development using Markov chain Monte Carlo approximate Bayesian computation. AIAA Paper, AIAA-2019-1883

  • Duraisamy K, Iaccarino G, Xiao H (2019) Turbulence Modeling in the Age of Data. Annu Rev Fluid Mech 51(1):357

    Article  MathSciNet  MATH  Google Scholar 

  • Dwight RP, Han Z (2009) Efficient uncertainty quantification using gradient-enhanced kriging. AIAA Paper, AIAA-2009-2276

  • Ebert V, Fernholz T, Giesemann C, Pitz H, Teichert H, Wolfrum J, Jaritz H (2000) Simultaneous diode-laser-based in situ detection of multiple species and temperature in a gas-fired power plant. Proc Combust Inst 28(1):423

    Article  Google Scholar 

  • Emmert J, Grauer SJ, Wagner S, Daun KJ (2019) Efficient Bayesian inference of absorbance spectra from transmitted intensity spectra. Opt Express 27(19):26893

    Article  Google Scholar 

  • Emmert J, Wagner S, Daun KJ (2020) Quantifying the spatial resolution of the maximum a posteriori estimate in linear, rank-deficient, Bayesian hard field tomography. Measur Sci Technol. https://doi.org/10.1088/1361-6501/abb550

  • Estumano DC, Hamilton FC, Colaço MJ, Leiroz AJK, Orlande HRB, Carvalho RN, Dulikravich GS (2015) Bayesian estimate of mass fraction of burned fuel in internal combustion engines using pressure measurements. Eng Optim IV, 997–1003

  • Fagundes NJR, Ray N, Beaumont MA, Neuenschwander S, Salzano FM, Bonatto SL, Excoffier L (2007) Statistical evaluation of alternative models of human evolution. Proc Natl Acad Sci 104(45):17614

    Article  Google Scholar 

  • Fox CW, Roberts SJ (2012) A tutorial on variational Bayesian inference. Artif Intell Rev 38(2):85

    Article  Google Scholar 

  • Frank J, Kaiser S (2008) High-resolution imaging of dissipative structures in a turbulent jet flame with laser Rayleigh scattering. Exp Fluids 44:221

    Article  Google Scholar 

  • Goldenstein CS, Hanson RK (2015) Diode-laser measurements of linestrength and temperature-dependent lineshape parameters for H2O transitions near \(1.4\,\mu \text{ m }\) using Voigt, Rautian, Galatry, and speed-dependent Voigt profiles. J Quant Spectrosc Radiat Transf 152:127

    Article  Google Scholar 

  • Goldenstein CS, Mathews GC (2020) Simulation technique enabling calibration-free frequency-modulation spectroscopy measurements of gas conditions and lineshapes with modulation frequencies spanning kHz to GHz. Appl Opt 59(5):1491

    Article  Google Scholar 

  • Goldenstein CS, Strand CL, Schultz IA, Sun K, Jeffries JB, Hanson RK (2014) Fitting of calibration-free scanned-wavelength-modulation spectroscopy spectra for determination of gas properties and absorption lineshapes. Appl Opt 53(3):356

    Article  Google Scholar 

  • Goldenstein CS, Spearrin RM, Jeffries JB, Hanson RK (2017) Infrared laser-absorption sensing for combustion gases. Prog Energy Combust Sci 60:132

    Article  Google Scholar 

  • Grauer SJ (2018) Bayesian methods for gas-phase tomography. PhD Thesis

  • Grauer SJ, Hadwin PJ, Daun KJ (2016) Bayesian approach to the design of chemical species tomography experiments. Appl Opt 55(21):5772

    Article  Google Scholar 

  • Grauer SJ, Hadwin PJ, Sipkens TA, Daun KJ (2017) Measurement-based meshing, basis selection, and prior assignment in chemical species tomography. Opt Express 25(21):25135

    Article  Google Scholar 

  • Grauer SJ, Tsang RW, Daun KJ (2017) Broadband chemical species tomography: measurement theory and a proof-of-concept emission detection experiment. J Quant Spectrosc Radiat Transf 198:145

    Article  Google Scholar 

  • Greenshields C (2016) OpenFOAM | The OpenFOAM Foundation http://openfoam.org/

  • Hanson RK, Falcone PK (1978) Temperature measurement technique for high-temperature gases using a tunable diode laser. Appl Opt 17(16):2477

    Article  Google Scholar 

  • Hayden TRS, Rieker GB (2016) Large amplitude wavelength modulation spectroscopy for sensitive measurements of broad absorbers. Opt Express 24(24):27910

    Article  Google Scholar 

  • Hayden TRS, Malarich N, Petrykowski DJ, Nigam SP, Christopher JD, Lapointe C, Wimer NT, Hamlington P, Rieker GB (2019a) OH radical measurements in combustion environments using wavelength modulation spectroscopy and dual-frequency comb spectroscopy near 1491 nm. Appl Phys B 125

  • Hayden T, Petrykowski D, Sanchez A, Nigam S, Lapointe C, Christopher J, Wimer N, Upadhye A, Strobel M, Hamlington P, Rieker G (2019b) Characterization of OH, \(\text{ H}_2\text{ O }\), and temperature profiles in industrial flame treatment systems interacting with polymer films. Proc Combust Inst 37(2):1571

    Article  Google Scholar 

  • Hayden TRS, Wimer NT, Lapointe C, Christopher JD, Nigam SP, Upadhye A, Strobel M, Hamlington PE, Rieker GB (2020) Characterization of the Buoyant Jet above a Catalytic Combustor Using Wavelength Modulation Spectroscopy. Combust Sci Technol 192(6):997

    Article  Google Scholar 

  • Huang Q, Wang F, Zhang H, Yan J, Ni M, Cen K (2013) In-situ CO measurement of gas and oil combustion flame using near infrared tunable diode laser with direct and modulated absorption signals. Opt Commun 306:99

    Article  Google Scholar 

  • Jahn W, Rein G, Torero JL (2012) Forecasting fire dynamics using inverse computational fluid dynamics and tangent linearisation. Adv Eng Softw 47(1):114

    Article  Google Scholar 

  • Khalil M, Najm HN (2018) Probabilistic inference of reaction rate parameters from summary statistics. Combustion Theory and Modelling pp 1–31

  • Lintusaari J, Gutmann MU, Dutta R, Kaski S, Corander J (2017) Fundamentals and recent developments in approximate Bayesian computation. Syst Biol 66(1):e66

    Google Scholar 

  • Lucas DD, Gowardhan A, Cameron-Smith P, Baskett RL (2016) Impact of meteorological inflow uncertainty on tracer transport and source estimation in urban atmospheres. Atmos Environ 143:120

    Article  Google Scholar 

  • Ma L, Wu Y, Xu W, Hammack SD, Lee T, Carter CD (2016) Comparison of 2D and 3D flame topography measured by planar laser-induced fluorescence and tomographic chemiluminescence. Appl Opt 55(20):5310

    Article  Google Scholar 

  • Madsen H (2003) Parameter estimation in distributed hydrological catchment modelling using automatic calibration with multiple objectives. Adv Water Resour 26(2):205

    Article  Google Scholar 

  • Marin JM, Pudlo P, Robert CP, Ryder RJ (2012) Approximate Bayesian computational methods. Stat Comput 22(6):1167

    Article  MathSciNet  MATH  Google Scholar 

  • Marjoram P, Molitor J, Plagnol V, Tavaré S (2003) Markov chain Monte Carlo without likelihoods. Proc Natl Acad Sci 100(26):15324

    Article  Google Scholar 

  • Mcenally CS, Pfefferle LD, Schaffer AM, Long MB, Mohammed RK, Smooke MD, Colkei MB (2000) Characterization of a coflowing methane/air non-premixed flame with computer modeling, Rayleigh-Raman imaging, and on-line mass spectrometry. Proc Combust Inst 28(2):2063

    Article  Google Scholar 

  • McManus T, Sutton J (2020) Simultaneous 2D filtered Rayleigh scattering thermometry and stereoscopic particle image velocimetry measurements in turbulent non-premixed flames. Exp Fluids 61:134

    Article  Google Scholar 

  • Mosbach S, Braumann A, Man PLW, Kastner CA, Brownbridge GPE, Kraft M (2012) Iterative improvement of Bayesian parameter estimates for an engine model by means of experimental design. Combust Flame 159(3):1303

    Article  Google Scholar 

  • Nott DJ, Marshall L, Brown J (2012) Generalized likelihood uncertainty estimation (GLUE) and approximate Bayesian computation: What’s the connection? Water Resources Research 48(12)

  • Oberkampf, WL, Trucano T (2000) Validation methodology in computational fluid dynamics. AIAA Paper, AIAA-2000-2549

  • Oberkampf WL, Roy CJ (2010) Verification and validation in scientific computing. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Oberkampf WL, Trucano TG (2002) Verification and validation in computational fluid dynamics. Prog Aerosp Sci 38(3):209

    Article  Google Scholar 

  • Oberkampf WL, Trucano TG, Hirsch C (2004) Verification, validation, and predictive capability in computational engineering and physics. Appl Mech Rev 57(5):345

    Article  Google Scholar 

  • Olson B (2016) Stochastic weather generation with approximate bayesian computation. Master’s thesis, University of Colorado at Boulder

  • Pan R, Daun KJ, Dreier T, Schulz C (2017) Uncertainty quantification and design-of-experiment in absorption-based aqueous film parameter measurements using Bayesian inference. Appl Opt 56(11):E1

    Article  Google Scholar 

  • Pandey S, Schumacher J, Sreenivasan KR (2020) A perspective on machine learning in turbulent flows. J Turbulence 0(0):1

  • Pemha E, Nyobe EN (2011) Genetic algorithm approach and experimental confirmation of a laser-based diagnostic technique for the local thermal turbulence in a hot wind tunnel jet. Progress Electromagn Res 28:325

    Article  Google Scholar 

  • Philippe LC, Hanson RK (1993) Laser diode wavelength-modulation spectroscopy for simultaneous measurement of temperature, pressure, and velocity in shock-heated oxygen flows. Appl Opt 32(30):6090

    Article  Google Scholar 

  • Qu Z, Ghorbani R, Valiev D, Schmidt FM (2015) Calibration-free scanned wavelength modulation spectroscopy-application to H 2 O and temperature sensing in flames. Opt Express 23(12):16492

    Article  Google Scholar 

  • Rieker GB, Jeffries JB, Hanson RK (2009) Calibration-free wavelength-modulation spectroscopy for measurements of gas temperature and concentration in harsh environments. Appl Opt 48(29):5546

    Article  Google Scholar 

  • Rohmer J, Rousseau M, Lemoine A, Pedreros R, Lambert J, Benki A (2018) Source characterisation by mixing long-running tsunami wave numerical simulations and historical observations within a metamodel-aided ABC setting. Stoch Environ Res Risk Assess 32:967–984. https://doi.org/10.1007/s00477-017-1423-y

  • Rothman LS, Gordon IE, Babikov Y, Barbe A, Benner DC, Bernath PF, Birk M, Bizzocchi L, Boudon V, Brown LR (2013) The HITRAN2012 molecular spectroscopic database. J Quant Spectrosc Radiat Transf 130:4

    Article  Google Scholar 

  • Sadegh M, Vrugt JA (2013) Bridging the gap between GLUE and formal statistical approaches: approximate Bayesian computation. Hydrol Earth Syst Sci 17(12)

  • Salinger AG, Pawlowski RP, Shadid JN, van Bloemen Waanders BG (2004) Computational analysis and optimization of a chemical vapor deposition reactor with large-scale computing. Ind Eng Chem Res 43(16):4612

    Article  Google Scholar 

  • Schmidt A, van der Kley S, Wagner S (2020) Optically accessible generic exhaust gas test bench for the investigation of fundamental SCR-relevant processes. Appl Opt 59(23):6953

    Article  Google Scholar 

  • Schulz C, Sick V (2005) Tracer-LIF diagnostics: quantitative measurement of fuel concentration, temperature and fuel/air ratio in practical combustion systems. Prog Energy Combust Sci 31(1):75

    Article  Google Scholar 

  • Scott DW (1979) On optimal and data-based histograms. Biometrika 66(3):605

    Article  MathSciNet  MATH  Google Scholar 

  • Sipkens TA, Hadwin PJ, Grauer SJ, Daun KJ (2018) Predicting the heat of vaporization of iron at high temperatures using time-resolved laser-induced incandescence and Bayesian model selection. J Appl Phys 123(9):095103

    Article  Google Scholar 

  • Smith RC (2013) Uncertainty quantification: theory, implementation, and applications, vol 12. SIAM, New Delhi

    Google Scholar 

  • Sousa J, García-Sánchez C, Gorlé C (2018) Improving urban flow predictions through data assimilation. Build Environ 132:282

    Article  Google Scholar 

  • Spearrin RM, Goldenstein CS, Jeffries JB, Hanson RK (2014) Quantum cascade laser absorption sensor for carbon monoxide in high-pressure gases using wavelength modulation spectroscopy. Appl Opt 53(9):1938

    Article  Google Scholar 

  • Stroud JR, Katzfuss M, Wikle CK (2018) A Bayesian adaptive ensemble Kalman filter for sequential state and parameter estimation. Mon Weather Rev 146(1):373

    Article  Google Scholar 

  • Sun K, Chao X, Sur R, Goldenstein CS, Jeffries JB, Hanson RK (2013) Analysis of calibration-free wavelength-scanned wavelength modulation spectroscopy for practical gas sensing using tunable diode lasers. Meas Sci Technol 24(12):125203

    Article  Google Scholar 

  • Sunnåker M, Busetto AG, Numminen E, Corander J, Foll M, Dessimoz C (2013) Approximate Bayesian Computation. PLoS Comput Biol 9(1):e1002803

    Article  MathSciNet  Google Scholar 

  • Toni T, Welch D, Strelkowa N, Ipsen A, Stumpf MPH (2009) Approximate Bayesian computation scheme for parameter inference and model selection in dynamical systems. J R Soc Interface 6(31):187

    Article  Google Scholar 

  • Vakilzadeh MK, Beck JL, Abrahamsson T (2018) Using approximate Bayesian computation by Subset Simulation for efficient posterior assessment of dynamic state-space model classes. SIAM J Sci Comput 40(1):B168

    Article  MathSciNet  MATH  Google Scholar 

  • van der Kley S, Emmert J, Schmidt A, Dreizler A, Wagner S (2020) Tomographic spectrometer for the temporally-resolved 2D reconstruction of gas phase parameters within a generic SCR test rig. Proc Combust Inst. https://doi.org/10.1016/j.proci.2020.09.009

  • Vrbik I, Deardon R, Feng Z, Gardner A, Braun J (2012) Using individual-level models for infectious disease spread to model spatio-temporal combustion dynamics. Bayesian Anal 7(3):615

    Article  MathSciNet  MATH  Google Scholar 

  • Vrugt JA, Sadegh M (2013) Toward diagnostic model calibration and evaluation: approximate Bayesian computation. Water Resour Res 49(7):4335

    Article  Google Scholar 

  • Wagner S, Fisher BT, Fleming JW, Ebert V (2009) TDLAS-based in situ measurement of absolute acetylene concentrations in laminar 2D diffusion flames. Proc Combust Inst 32(1):839

    Article  Google Scholar 

  • Wang S, Xu X (2006) Parameter estimation of internal thermal mass of building dynamic models using genetic algorithm. Energy Convers Manag 47(13–14):1927

    Article  Google Scholar 

  • Wang Y, Chatterjee P, de Ris JL (2011) Large eddy simulation of fire plumes. Proc Combust Inst 33(2):2473

    Article  Google Scholar 

  • Weller HG, Tabor G, Jasak H, Fureby C (1998) A tensorial approach to computational continuum mechanics using object-oriented techniques. Comput Phys 12(6):620

    Article  Google Scholar 

  • Yamaguchi M, Iriguchi T, Nakazawa T, Wu CC (2009) An observing system experiment for Typhoon Conson (2004) using a singular vector method and DOTSTAR data. Mon Weather Rev 137(9):2801

    Article  Google Scholar 

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Acknowledgements

We acknowledge helpful discussions with Mark Strobel, Melvyn Branch, and Aniruddha Upadhye.

Funding

D.P., C.L., N.T.W., and T.R.S.H. acknowledge gift support from the 3M Company. O.A.D. was supported by NASA award NNX15AU24A-03. C.L. was supported by the NSF Graduate Research Fellowship Program under award DGE 1144083. P.E.H. was supported, in part, by AFOSR Award No. FA9550-17-1-0144. J.D.C. and G.B.R. were supported, in part, by NSF Award No. CBET 1454496 and AFOSR Award No. FA9550-17-1-0224. Computing resources were provided by DoD HPCMP under a Frontier project award and by the Air Force Research Laboratory.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Colorado, Boulder, CO, 80309, USA

    Jason D. Christopher, Olga A. Doronina, Dan Petrykowski, Torrey R. S. Hayden, Caelan Lapointe, Nicholas T. Wimer, Gregory B. Rieker & Peter E. Hamlington

  2. Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309, USA

    Ian Grooms

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  1. Jason D. Christopher
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Correspondence to Peter E. Hamlington.

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Christopher, J.D., Doronina, O.A., Petrykowski, D. et al. Flow parameter estimation using laser absorption spectroscopy and approximate Bayesian computation. Exp Fluids 62, 43 (2021). https://doi.org/10.1007/s00348-020-03122-2

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