OPEN ACCESS
This paper presents a proposed methodology for applying statistical techniques as the basis for validation activities of a computer model of heat transfer. To demonstrate this approach, a case study of a Ruggedized Instrumentation Package subject to heating from battery discharge and electrical resistance during normal operations is considered. First, the uncertainty in the simulation due to the discretization of the governing partial differential equations is quantified. This error is analogous to the measurement error in an experiment in that it is not representative of actual physical variation, and is necessary to completely characterize the range of simulation outcomes. Secondly, physical uncertainties, such as unknown or variable material properties, are incorporated into the model and propagated through it. To this end, a sensitivity study enables exploration of the output space of the model. Experiments are considered to be a realization of one of these possible outcomes, with the added complication of containing physical processes not included in the model. Statistical tests are proposed to quantitatively compare experimental measurements and simulation results. The problem of discrepancies between the computational model and tests is considered as well.
heat transfer, mesh resolution, numerical parameters, uncertainty quantification, validation, verification
[1] Sargent, R.G., Verification and validation of simulation models, Proceedings of the 2005 Winter Simulation Conference, pp. 130-143, 2005. doi: http://dx.doi.org/10.1109/ wsc.2005.1574246
[2] Babuska, I. & Oden, J.T., Verification and validation in computational engineering and science: basic concepts, Computer Methods in Applied Mechanics and Engineering, 193, pp. 4057-4066, 2004. doi: http://dx.doi.org/10.1016/j.cma.2004.03.002
[3] Roache, P.J., Verification and Validation in Computational Science and Engineering, Hermosa Publishers: Socorro, NM, 1998.
[4] Oberkampf, W.L. & Roy, C.J., Verification and Validation in Scientific Computing, Cambridge University Press: Cambridge, England, 2010. doi: http://dx.doi.org/10.1017/ cbo9780511760396
[5] Trucano, T.G., Pilch, M. & Oberkampf, W.L., General concepts for experimental vali- dation of ASCI code applications, Technical Report SAND2002-0341, Sandia National Laboratories: Albuquerque, NM, 2002. doi: http://dx.doi.org/10.2172/800777
[6] Oberkampf, W.L. & Trucano, T.G., Verification and validation in computational fluid dynamics, Progress in Aerospace Sciences, 38, pp. 209-272, 2002. doi: http://dx.doi. org/10.1016/s0376-0421(02)00005-2
[7] American Nuclear Society, Guidelines for the Verification and Validation of Scientific and Engineering Computer Programs for the Nuclear Industry, ANSI/ANS-10.4-1987, American Nuclear Society: La Grange Park, IL, 1987.
[8] Roy, C.J., Review of code and solution verification procedures in computational simu- lation, Journal of Computational Physics, 205, pp. 131-156, 2005. doi: http://dx.doi. org/10.1016/j.jcp.2004.10.036
[9] Scott, S.N., Templeton, J.A., Ruthruff, J.R., Hough, P.D. & Peterson, J.P., Computa- tional solution verification applied to a thermal model of a Ruggedized Instrumenta- tion Package, WIT Transactions on Modeling and Simulation, 55. doi: http://dx.doi. org/10.2495/cmem130021
[10] Logan, R.W. & Nitta, C.K., Comparing 10 methods for solution verification, and link- ing to model validation, Journal of Aerospace Computing, Information, and Communi- cation, 3, pp. 354-373, 2006. doi: http://dx.doi.org/10.2514/1.20800
[11] Oberkampf, W.L. & Barone, M.F., Measures of agreement between computation and experiment: validation metrics, Journal of Computational Physics, 217, pp. 5-36, 2006. doi: http://dx.doi.org/10.1016/j.jcp.2006.03.037
[12] Sierra Core Team, Sierra Thermal/Fluids Code, Sandia National Laboratories: Albu- querque, NM, 2012.
[13] Pro Engineer Core Team, Pro Engineer WildFire 5, PCT: Needham, MA, 2009.
[14] Cubit Core Team, Cubit: Geometry and Mesh Generation Toolkit, Sandia National Lab- oratories: Albuquerque, NM, 2011.
[15] Adams, B.M., Bohnhoff, W.J., Dalbey, K.R., Eddy, J.P., Eldred, M.S., Gay, D.M., Haskell, K., Hough, P.D. & Swiler, L.P., DAKOTA: a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis: version 5.0 user’s manual, Sandia Technical Report SAND2010- 2183, Sandia National Laboratories: Albuquerque, NM, 2011.
[16] Incropera, F.P. & Dewitt, D.P., Introduction to Heat Transfer, 4th edn., John Wiley and Sons: New York, NY, 2002.
[17] Hughes, T.J.R., The Finite Element Method, Dover Publications: Mineola, NY, pp. 52-56, 2000.
[18] R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing: Vienna, Austria, 2012.
[19] Pearson, K., On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling, Philosophical Magazine Series 5, 50, No. 302, pp. 157-175, 1900. doi: http://dx.doi.org/10.1080/14786440009463897
[20] Saltelli, A., Chan, K., Scott, E.M. eds., Sensitivity Analysis, Wiley Series in Probability and Statistics, Wiley: Chichester, West Sussex, England, 2000.
[21] Saltelli, A., Tarantola, S., Campolongo, F. & Ratto, M., Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models, John Wiley & Sons: Chichester, West Sussex, England, 2004.
[22] Speed, T.P., What is an analysis of variance? (with discussion), Annals of Statistics, 15, pp. 885-941, 1987. doi: http://dx.doi.org/10.1214/aos/1176350472
[23] Lehmann, E.L. & Romano, J.P., Testing Statistical Hypotheses, Springer Science and Business Media, New York, NY, 2005. doi: http://dx.doi.org/10.1007/0-387-27605-x
[24] Kolmogorov, A.N., On the empirical determination of a distribution function, Giornale dell’Istituto Italiano degli Attuari, 4, pp. 83-91, 1933.
[25] Smirnov, N.V., On the estimation of the discrepancy between empirical curves of distri- bution for two independent samples, Bulletin of Moscow, Vol. 2, pp. 3-16, 1939.
[26] Helton, J.C. & Davis, F.J., Sampling-based methods for uncertainty and sensitivity analysis, Technical Report SAND99-2240, Sandia National Laboratories: Albuquerque, NM, 2000. doi: http://dx.doi.org/10.2172/760743
[27] Iman, R.L. & Shortencarier, M.J., A Fortran 77 program and user’s guide for the gen- eration of Latin hypercube samples for use with computer models, Technical Report NUREG/CR-3624, SAND83-2365, Sandia National Laboratories: Albuquerque, NM, 1984. doi: http://dx.doi.org/10.2172/7091452