Abstract
Artificial neural networks (ANNs) are primarily used in academia for their ability to model complex nonlinear systems. Though ANNs have been used to solve practical problems in industry, they are not typically used in nonacademic environments because they are not very well understood, complicated to implement, or have the reputation of being a “black-box” model. Few mathematical models exist that outperform ANNs. If a highly accurate model can be constructed, the knowledge should be used to understand and explain relationships in a system. Output surfaces can be analyzed in order to gain additional knowledge about a system being modeled. This paper presents a systematic approach to derive a “grey-box” model from the knowledge obtained from the ANN. A database for an automobile’s gas mileage performance is used as a case study for the proposed methodology. The results show a greater ability to generalize system behavior than other benchmarked methods.









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Young W, Weckman G, Thompson J, Brown M (2008) Artificial neural networks for knowledge extraction of concrete shear strength prediction. Int J Ind Eng 15(1):1–10
Hernandez S, Nesic S, Weckman G, Ghai V (2006) Use of artificial neural networks for predicting crude oil effect on CO2 corrosion of carbon steels. Corros J 62(6):1–35
Snow A, Weckman G, Chayanam K (2006) Modeling telecommunication outages due to power loss. Int J Ind Eng Theory Appl Pract 13(1):51–60
Weckman G, Lakshminarayanan S, Snow A, Marvel J (2008) An integrated stock market forecasting model using neural networks. Int J Business Forecast Mark Intell 1(1). doi:10.1504/IJBFMI.2008.020813
Millie D, Weckman G, Paerl H, Pinckney J, Bendis B, Pigg R et al (2006) Neural network modeling of estuarine indicators: hindcasting phytoplankton biomass and net ecosystem production in the Neuse (North Carolina) and Trout (Florida) Rivers. Ecol Indic 6:589–608. doi:10.1016/j.ecolind.2005.08.021
Ozesmi S, Ozesmi U (1999) An artificial neural network approach to spatial habitat modeling with interspecific interaction. Ecol Model 116:15–31. doi:10.1016/S0304-3800(98)00149-5
Box G, Draper N (1987) Empirical model-building and response surfaces. Wiley, New York
National Aeronautics Space Administration (2004) NASA cost estimation handbook. National Aeronautics and Space Administration, Washington, DC
Huysmans J, Baesens B, Vanthienen J (2006) Using rule extraction to improve the comprehensibility of predictive models. FETEW Internal Research. K.U.Leuven, Leuven
Xiong Q, Jutan A (2002) Grey-box modelling and control of chemical processes. Chem Eng Sci 57:1027–1039. doi:10.1016/S0009-2509(01)00439-0
Oussar Y, Dreyfus G (2001) How to be a gray box: dynamic semi-physical modeling. Neural Netw 14:1161–1172. doi:10.1016/S0893-6080(01)00096-X
Francisco C, Acuña G, Cubillos F (2007) Indirect training of grey-box models: application to a bioprocess. In: Cruz F, Acuña G, Cubillos F, Moreno V, Bassi D (eds) Lecture Notes in Computer Science. Springer, Berlin/Heidelberg, pp 391–397
Acuña G, Cubillos F, Thibault J, Latrille E (1999) Comparison of methods for training grey-box neural network models. Comput Chem Eng Suppl 23:561–564
Johannet A, Vayssade B, Bertin D (2007) Neural networks: from black box toward transparent box application to evapotranspiration modeling. Proc World Acad Sci Eng Technol 24:162–169
Tornøe C, Jacobsen J, Pedersen O, Hansen T, Madsen H (2004) Grey-box modelling of pharmacokinetic/pharmacodynamic systems. J Pharmacokinet Pharmacodyn 31(5):401–417. doi:10.1007/s10928-004-8323-8
Geeraerd AH, Herremans CH, Cenens C, Van Impe JF (1998) Application of artificial neural networks as a non-linear modular modeling technique to describe bacterial growth in chilled food products. Int J Food Microbiol 44:49–68. doi:10.1016/S0168-1605(98)00127-5
Reed RD, Marks RJ (1998) Neural smithing: supervised learning in feedforward artificial neural networks. MIT Press, Cambridge
Hornik H, Stinchcomb M, White J (1982) Multilayer feedforward networks are universal approximators. Neural Netw 2:359–366. doi:10.1016/0893-6080(89)90020-8
Meireles M, Almeida P, Simões M (2003) A comprehensive review for industrial applicability of artificial neural networks. IEEE Trans Ind Electron 50(3):585–601. doi:10.1109/TIE.2003.812470
Lek S, Guegan J (1999) Artificial neural networks as a tool in ecological modeling, an introduction. Ecol Modell 120:65–73. doi:10.1016/S0304-3800(99)00092-7
Lange N (1999) New mathematical approaches in hydrological modeling—an application of artificial neural networks. Phys Chem Earth Part B Hydrol Oceans Atmos 24(1):31–35. doi:10.1016/S1464-1909(98)00007-0
Browne A, Hudson B, Whitley D, Ford M, Picton P, Kazemian H (2003) Knowledge extraction from neural networks. In: Proceedings of the 29th Annual Conference of the IEEE Industrial Electronics Society. Roanoke, Virginia, pp. 1909–1913
Garson D (1991) Interpreting neural-network connection weights. AI Expert 6(4):47–51
Zhang GP (2000) Neural networks for classification: a survey. IEEE Trans Syst Man Cybern 30(4):451–462. doi:10.1109/5326.897072
Cristea A, Cristea P, Okamoto T (1997) Neural networks knowledge extraction. Electrotech Eng 42(2):477–491
Towell G, Shavlik J (1993) The extraction of re¯ned rules from knowledge-based neural networks. Mach Learn 13(1):71–101
Setiono R, Liu H (1997) Neurolinear: from neural networks to oblique decision rules. Neural Comput 17(1):1–24
Setiono R, Leow W (2000) FERNN: an algorithm for fast extraction of rules from neural networks. Appl Intell 12(1–2):15–25. doi:10.1023/A:1008307919726
Saito K, Nakano R (2002) Extracting regression rules from neural networks. Neural Netw 15(10):1279–1288. doi:10.1016/S0893-6080(02)00089-8
Breiman L, Friedman H, Olshen R, Stone C (1984) Classification and regression trees. Wadsworth, Beltnont
Quinlan J (1988) C4.5: programs for machine learning. Morgan Kaufmann, USA
Craven M (1996) Extracting comprehensible models from trained neural networks. Ph.D. Dissertation, University of Wisconsin, Madison, Wisconsin
Schmitz G, Aldrich C, Gouws F (1999) ANN-DT: an algorithm for extraction of decision trees from artificial neural networks. IEEE Trans Neural Netw 10(6):1392–1401. doi:10.1109/72.809084
Timofeev R (2004) Classification and Regression Trees (CART) Theory and Applications. Masters Thesis, Humboldt University, Center of Applied Statistics and Economics, Berlin
Quinlan J (1986) Induction of decision trees. In: Mitchell T (ed) Mach Learn, vol 1. McGraw-Hill, New York, pp 81–106
Ziarko W, Yao Y (2001) A comparison of several approaches to missing values in data mining in Rough Sets and current trends in computing. Springer, Berlin
Rangwala M (2006) Empirical investigation of decision tree extraction from neural networks. Ohio University, Department of Industrial and Systems Engineering, Athens, OH, USA
Zhou ZH, Jiang Y, Chen SF (2003) Extracting symbolic rules from trained neural network ensembles. AI Commun 16(1):3–15
Nath R, Rajagopalan B, Ryker R (1997) Determining the saliency of input variables in neural network classifiers. Comput Oper Res 24(8):767–773. doi:10.1016/S0305-0548(96)00088-3
Thrun S (1995) Extracting rules from artificial neural networks with distributed representations. In: Tesauro G, Touretzky D, Leen T (eds) Advances in Neural Information Processing Systems 7. MIT Press, Cambridge
Lasdon L, Waren D, Jain A, Ratner M (1978) Design and testing of a generalized reduced gradient code for nonlinear programing. ACM Trans Math Softw 4(1):34–49. doi:10.1145/355769.355773
Watson J, Fylstra D (1996) Solver user’s guide. Frontline Systems, Incline Village
Windward Technolgies and Optimal Methods (1997) User’s guide for GRG2 optimization library. Retrieved April 7, 2007, from http://www.maxthis.com/Grg2ug.htm
Fylstra D, Lasdon L, Watson J (1998) Design and use of the microsoft excel solver. Interfaces 28(5):29–55. doi:10.1287/inte.28.5.29
Lasdon L, Smith S (1992) Solving largesparse nonlinear programs using GRG. ORSA J Comput 1:2–15
Newman D, Hettich S, Blake C, Merz C (1998) UCI repository of machine learning databases. (I. University of California, Producer, and Department of Information and Computer Sciences) Retrieved April 5, 2007, from ftp://ftp.ics.uci.edu/pub/machine-learning-databases/auto-mpg/
NeuroDimension (2006) Intelligent Software Solutions. Retrieved 2007, from http://www.nd.com/
Gill P, Murray W, Wright M (1981) Practical optimization. Academic Press, London
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Young, W.A., Weckman, G.R. Using a heuristic approach to derive a grey-box model through an artificial neural network knowledge extraction technique. Neural Comput & Applic 19, 353–366 (2010). https://doi.org/10.1007/s00521-009-0270-2
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DOI: https://doi.org/10.1007/s00521-009-0270-2