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In mathematics, statistics, and computational modelling, a grey box model〔(【引用サイトリンク】year=2012 )〕〔Kroll, Andreas (2000). Grey-box models: Concepts and application. In: New Frontiers in Computational Intelligence and its Applications, vol.57 of Frontiers in artificial intelligence and applications, pp. 42-51. IOS Press, Amsterdam.〕 combines a partial theoretical structure with data to complete the model. The theoretical structure may vary from information on the smoothness of results, to models that need only parameter values from data or existing literature.〔Whiten, B., 2013. (Model completion and validation using inversion of grey box models ), ANZIAM J.,54 (CTAC 2012) pp C187–C199. 〕 Thus, almost all models are grey box models as opposed to black box where no model form is assumed or white box models that are purely theoretical. Some models assume a special form such as a linear regression or neural network.〔Heaton, J., 2012. Introduction to the math of neural networks, Heaton Research Inc. (Chesterfield, MO), ISBN 978-1475190878〕 These have special analysis methods. In particular linear regression techniques are much more efficient than most non-linear techniques. The model can be deterministic or stochastic (i.e. containing random components) depending on its planned use. == Model form == The general case is a non-linear model with a partial theoretical structure and some unknown parts derived from data. Models with unlike theoretical structures need to be evaluated individually,〔〔Mathworks, 2013. (Supported grey box models )〕〔.〕 possibly using simulated annealing or genetic algorithms. Within a particular model structure, parameters〔〔Nash, J.C. and Walker-Smith, M. 1987. Nonlinear parameter estimation, Marcel Dekker, Inc. (New York).〕 or variable parameter relations〔〔Whiten, W.J., 1971. Model building techniques applied to mineral treatment processes, Symp. on Automatic Control Systems in Mineral Processing Plants, (Australas. Inst. Min. Metall., S. Queensland Branch, Brisbane), 129-148.〕 may need to be found. For a particular structure it is arbitrarily assumed that the data consists of sets of feed vectors f, product vectors p, and operating condition vectors c.〔 Typically c will contain values extracted from f, as well as other values. In many cases a model can be converted to a function of the form:〔〔Whiten, W.J., 1994. Determination of parameter relations within non-linear models, SIGNUM Newsletter, 29(3–4,) 2–5. 10.1145/192527.192535.〕〔Whiten, B., 2014. (Determining the form of ordinary differential equations using model inversion ), ANZIAM J. 55 (EMAC2013) pp.C329–C347. 〕 : m(f,p,q) where the vector function m gives the errors between the data p, and the model predictions. The vector q gives some variable parameters that are the model's unknown parts. The parameters q vary with the operating conditions c in a manner to be determined.〔〔 This relation can be specified as q = Ac where A is a matrix of unknown coefficients, and c as in linear regression〔〔 includes a constant term and possibly transformed values of the original operating conditions to obtain non-linear relations〔Polynomial〕〔Spline (mathematics)〕 between the original operating conditions and q. It is then a matter of selecting which terms in A are non-zero and assigning their values. The model completion becomes an optimisation problem to determine the non-zero values in A that minimizes the error terms m(f,p,Ac) over the data.〔〔〔Kojovic, T., and Whiten W. J., 1994. Evaluation of the quality of simulation models, Innovations in mineral processing, (Lauretian University, Sudbury) pp 437–446. ISBN 088667025X〕〔Kojovic, T., 1989. The development and application of Model - an automated model builder for mineral processing, PhD thesis, The University of Queensland.〕〔Xiao, J., 1998. Extensions of model building techniques and their applications in mineral processing, PhD thesis, The University of Queensland.〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Grey box model」の詳細全文を読む スポンサード リンク
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