# Mathematical Models and Data Analysis

## Abstract

This chapter starts by introducing the benefits of applied data analysis and modeling methods through a case study example pertinent to energy use in buildings. Next, it reviews fundamental notions of mathematical models illustrates them in terms of sensor response, and differentiates between forward or simulation models and inverse models. Subsequently, various issues pertinent to data analysis and associated uncertainty are described, and the different analysis tools which fall within its purview are discussed. Basic concepts relating to white-box, black-box and grey-box models are then presented. An attempt is made to identify the different types of problems one faces with forward modeling as distinct from inverse modeling and analysis. Notions germane to the disciplines of decision analysis, data mining and intelligent data analysis are also covered. Finally, the various topics covered in each chapter of this book are described.

## Keywords

Inverse Modeling Biot Number Data Analysis Method Building Energy Intelligent Data Analysis## Supplementary material

## References

- Arsham, http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm, downloaded August 2008
- Berthold, M. and D.J. Hand (eds.) 2003. Intelligent Data Analysis, 2nd Edition, Springer, Berlin.CrossRefMATHGoogle Scholar
- Cha, P.D., J.J. Rosenberg and C.L. Dym, 2000. Fundamentals of Modeling and Analyzing Engineering Systems, 2
^{nd}Ed., Cambridge University Press, Cambridge, UK.Google Scholar - Claridge, D.E. and M. Liu, 2001.
*HVAC System Commissioning*, Chap. 7.1 Handbook of Heating, Ventilation and Air Conditioning, J.F. Kreider (editor), CRC Press, Boca Raton, FL.Google Scholar - Clemen, R.T. and T. Reilly, 2001. Making Hard Decisions with Decision Tools, Brooks Cole, Duxbury, Pacific Grove, CAGoogle Scholar
- Energy Plus, 2009. Energy Plus Building Energy Simulation software, developed by the National Renewable Energy Laboratory (NREL) for the U.S. Department of Energy, under the Building Technologies program, Washington DC, USA. http://www.nrel.gov/buildings/energy_analysis.html#energyplus.
- Edwards, C.H. and D.E. Penney, 1996. Differential Equations and Boundary Value Problems, Prentice Hall, Englewood Cliffs, NJMATHGoogle Scholar
- Eisen, M., 1988. Mathematical Methods and Models in the Biological Sciences, Prentice Hall, Englewood Cliffs, NJ.MATHGoogle Scholar
- Doebelin, E.O., 1995. Engineering Experimentation: Planning, Execution and Reporting, McGraw-Hill, New YorkGoogle Scholar
- Dunham, M., 2003. Data Mining: Introductory and Advanced Topics, Pearson Education Inc.Google Scholar
- Haimes, Y.Y., 1998. Risk Modeling, Assessment and Management, John Wiley and Sons, New York.MATHGoogle Scholar
- Heinsohn, R.J. and J.M.Cimbala, 2003, Indoor Air Quality Engineering, Marcel Dekker, New York, NYCrossRefGoogle Scholar
- Hoagin, D.C., F. Moesteller and J.W. Tukey, 1983. Understanding Robust and Exploratory Analysis, John Wiley and Sons, New York.Google Scholar
- Hodges, J.L. and E.L. Lehman, 1970. Basic Concepts of Probability and Statistics, 2nd Edition Holden DayGoogle Scholar
- Jochem, E. 2000. In Energy End-Use Efficiency in World Energy Assessment, J. Goldberg, ed., pp. 73–217, United Nations Development Project, New York.Google Scholar
- Masters, G.M. and W.P. Ela, 2008. Introduction to Environmental Engineering and Science,3
^{rd}Ed. Prentice Hall, Englewood Cliffs, NJGoogle Scholar - McNeil, D.R. 1977. Interactive Data Analysis, John Wiley and Sons, New York.Google Scholar
- PECI, 1997.
*Model Commissioning Plan and Guide Commissioning Specifications*, version 2.05, U.S.DOE/PECI, Portland, OR, February.Google Scholar - Reddy, T.A., 2006. Literature review on calibration of building energy simulation programs: Uses, problems, procedures, uncertainty and tools, ASHRAE Transactions, 112(1), JanuaryGoogle Scholar
- Sprent, P., 1998. Data Driven Statistical Methods, Chapman and Hall, London.MATHGoogle Scholar
- Stoecker, W.F., 1989. Design of Thermal Systems, 3
^{rd}Edition, McGraw-Hill, New York.Google Scholar - Streed, E.R., J.E. Hill, W.C. Thomas, A.G. Dawson and B.D. Wood, 1979. Results and Analysis of a Round Robin Test Program for Liquid-Heating Flat-Plate Solar Collectors,
*Solar Energy*, 22, p.235.CrossRefGoogle Scholar - Stubberud,A., I. Williams, and J. DiStefano, 1994. Outline of Feedback and Control Systems, Schaum Series, McGraw-Hill.Google Scholar
- Tukey, J.W., 1988. The Collected Works of John W. Tukey, W. Cleveland (Editor), Wadsworth and Brookes/Cole Advanced Books and Software, Pacific Grove, CAGoogle Scholar
- Weiss, N. and M. Hassett, 1982. Introductory Statistics, Addison-Wesley. NJ.Google Scholar