Comparison of Traditional and Bayesian Calibration Techniques for Gray-Box Modeling
Publication: Journal of Architectural Engineering
Volume 20, Issue 2
Abstract
Bayesian and nonlinear least-squares methods of calibration were evaluated and compared for gray-box modeling of a retail building. Gray-box model calibration is one form of system identification and is examined here with perturbations to the simple yet popular European Committee for Standardization (CEN)-ISO thermal network model. The primary objective was to understand whether the computational expense of probabilistic Bayesian techniques is required to provide robustness to signal noise, specifically with regard to lower dimensional problems (physical or semiphysical), where model calibration is preferred over uncertainty quantification. The Bayesian approach allows parameter interactions and trade-offs to be revealed, one form of sensitivity analysis, but its full power for uncertainty quantification cannot be harnessed with gray-box or other simplified models. Surrogate data from a detailed building energy simulation program were used to ensure command over latent variables, whereas a range of signal-to-noise and noise colors were considered in the experimental study. The fidelity to the building zone temperature and thermal load was the basis for comparing results. Utilization of uniform priors showed that both methods performed similarly well. Bayesian calibration outperformed traditional methods on noisy data sets; however, traditional methods were adequate up to an approximately 25% noise level. The thermal gray-box model calibration has the intended application of embedded model predictive control, where speed, accuracy, and robustness are crucial. Traditional methods required approximately 100 times less CPU time and are recommended given the model simplicity, application, and expected system noise levels.
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Acknowledgments
This work has been sponsored through a research contract with QCoefficient, Inc., for which the authors express their sincere gratitude. Moreover, G. P. Henze discloses his role as technology advisor and cofounder of QCoefficient, Inc. This work utilized the Janus supercomputer, which is supported by the National Science Foundation (award No. CNS-0821794) and the University of Colorado Boulder. The Janus supercomputer is a joint effort of the University of Colorado Boulder, the University of Colorado Denver, and the National Center for Atmospheric Research.
References
Armstrong, P. R., Leeb, S. B., and Norford, L. K. (2006). “Control with building mass—Part I: Thermal response model.” Trans. Am. Soc. Heating Refrigerating Air Conditioning Eng., 112(1), 449–461.
Booth, A., Choudhary, R., and Spiegelhalter, D. (2012). “Handling uncertainty in housing stock models.” Build. Environ., 48, 35–47.
Braun, J., Montgomery, K., and Chaturvedi, N. (2001). “Evaluating the performance of building thermal mass control strategies.” HVAC&R Res., 7(4), 403–428.
Braun, J. E. and Chaturvedi, N. (2002). “An inverse gray-box model for transient building load prediction.” HVAC&R Res., 8(1), 73–100.
Cipra, B. A. (2000). “The best of the 20th century: Editors name top 10 algorithms.” SIAM News, 33(4), 1–2.
Clark, J. S. (2005). “Why environmental scientists are becoming Bayesians.” Ecol. Lett., 8(1), 2–14.
Clarke, J. (2001). Energy simulation in building design, Routledge, London.
Crawley, D. B., et al. (2001). “EnergyPlus: Creating a new-generation building energy simulation program.” Energy Build., 33(4), 319–331.
Dewson, T., Day, B., and Irving, A. (1993). “Least squares parameter estimation of a reduced order thermal model of an experimental building.” Build. Environ., 28(2), 127–137.
Dodier, R., and Kreider, J. (1999). “Whole building energy diagnostics.” ASHRAE Trans., 105(1), 579–589.
Dodier, R. H., Curtiss, P. S., and Kreider, J. F. (1998). “Small-scale on-line diagnostics for an HVAC system.” Trans. Am. Soc. Heating Refrigerating Air Conditioning Eng., 104(1), 530–539.
Fraisse, G., Viardot, C., Lafabrie, O., and Achard, G. (2002). “Development of a simplified and accurate building model based on electrical analogy.” Energy Build., 34(10), 1017–1031.
Fritzson, P. (2010). Principles of object-oriented modeling and simulation with Modelica 2.1, Wiley, Hoboken, NJ.
Halley, J. M., and Kunin, W. E. (1999). “Extinction risk and the family of noise models.” Theor. Popul. Biol., 56(3), 215–230.
Hensen, J. L., and Lamberts, R. (2011). Building performance simulation for design and operation, Spon Press, New York.
Heo, Y., Choudhary, R., and Augenbroe, G. (2012). “Calibration of building energy models for retrofit analysis under uncertainty.” Energy Build., 47, 550–560.
Higdon, D., Gattiker, J., Williams, B., and Rightley, M. (2008). “Computer model calibration using high-dimensional output.” J. Am. Stat. Assoc., 103(482), 570–583.
ISO. (2008). “Energy performance of buildings—Calculation of energy use for space heating and cooling.” ISO 13790, Geneva.
Jaynes, E. T. (2003). Probability theory: The logic of science, Cambridge University Press, Cambridge, U.K.
Judkoff, R., and Neymark, J. (1995). “International energy agency building energy simulation test (bestest) and diagnostic method.” Report No. TP-472-6231, National Renewable Energy Laboratory, Golden, CO.
Kennedy, M. C., and O’Hagan, A. (2001). “Bayesian calibration of computer models.” J. R. Stat. Soc.: Series B (Stat. Method.), 63(3), 425–464.
Klein, S. A. (1979). TRNSYS, a transient system simulation program, Solar Energy Laboratory, Univ. of Wisconsin–Madison, Madison, WI.
Lauret, P., Miranville, F., Boyer, H., Garde, F., and Adelard, L. (2006). “Bayesian parameter estimation of convective heat transfer coefficients of a roof-mounted radiant barrier system.” J. Sol. Energy Eng., 128(2), 213–225.
Lee, W., and Yik, F. (2004). “Regulatory and voluntary approaches for enhancing building energy efficiency.” Prog. Energy Combust. Sci., 30(5), 477–499.
Ligges, U. (2011). tuneR: Analysis of music, 〈http://r-forge.r-project.org/projects/tuner/〉 (Aug. 1, 2013).
Maile, T. (2010). “Comparing measured and simulated building energy performance data.” Ph.D. thesis, Stanford Univ., Stanford, CA.
MATLAB 8.0.0.783 [Computer software]. Natick, MA, MathWorks.
Neumann, C., Jacob, D., Burhenne, S., Florita, A., Burger, E., and Schmidt, F. (2011). “Model-based methods for fault detection and optimization in building operations (modellbasierte methoden für die fehlererkennung und optimierung im gebäudebetrieb).” Rep. No. TAG-ChN/DJ-11-01, Fraunhofer Institute for Solar Energy Systems, Freiburg, Germany.
Newsham, G. R., Mancini, S., and Birt, B. J. (2009). “Do LEED-certified buildings save energy? Yes, but…” Energy Build., 41(8), 897–905.
O’Neill, Z., Narayanan, S., and Brahme, R. (2010). “Model-based thermal load estimation in buildings.” 4th National Conf. of the Int. Building Performance Simulation Association (IBPSA-USA), IBPSA-USA, 474–481.
R Development Core Team. (2008). “R: A language and environment for statistical computing.” R Foundation for Statistical Computing, 〈http://www.R-project.org〉 (Aug. 1, 2013).
Reddy, A. (2006). “Literature review on calibration of building energy simulation programs: Uses, problems, procedures, uncertainty, and tools.” ASHRAE Trans., 112(1), 226–240.
Sahlin, P., Eriksson, L., Grozman, P., Johnsson, H., Shapovalov, A., and Vuolle, M. (2004). “Whole-building simulation with symbolic DAE equations and general purpose solvers.” Build. Environ., 39(8), 949–958.
Sahlin, P., and Sowell, E. F. (1989). “A neutral format for building simulation models.” Proc., Int. Building Performance Simulation Association Building Simulation, IBPSA-USA, 147–154.
Scofield, J. H. (2009). “Do LEED-certified buildings save energy? Not really…” Energy Build., 41(12), 1386–1390.
Seem, J. (1987). “Modeling of heat transfer in buildings.” Ph.D. thesis, Univ. of Wisconsin–Madison, Madison, WI.
Sivia, D., and Skilling, J. (2006). “Parameter estimation II.” Chapter 3, Data analysis: A Bayesian tutorial, Oxford University Press, Oxford, U.K., 35–77.
Trčka, M., and Hensen, J. L. (2010). “Overview of HVAC system simulation.” Autom. Constr., 19(2), 93–99.
Wang, S., and Xu, X. (2006). “Parameter estimation of internal thermal mass of building dynamic models using genetic algorithms.” Energy Convers. Manage., 47(13–14), 1927–1941.
Witte, M. J., Henninger, R. H., Glazer, J., and Crawley, D. B. (2001). “Testing and validation of a new building energy simulation program.” Proc., 7th Int. IBPSA Conf., International Building Performance Simulation Association (IBPSA), 353–360.
Wright, J. A., and Hanby, V. I. (1987). “The formulation, characteristics and solution of HVAC system optimized design problems.” ASHRAE Trans., 93(2), 2133–2145.
Zhou, Q., Wang, S., Xu, X., and Xiao, F. (2008). “A grey-box model of next-day building thermal load prediction for energy-efficient control.” Int. J. Energy Res., 32(15), 1418–1431.
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Published In
Journal of Architectural Engineering
Volume 20 • Issue 2 • June 2014
Copyright
© 2013 American Society of Civil Engineers.
History
Received: May 16, 2013
Accepted: Dec 3, 2013
Published online: Dec 30, 2013
Discussion open until: May 30, 2014
Published in print: Jun 1, 2014
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