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Concept
Grey box model
Summary
In mathematics, statistics, and computational modelling, a grey box model 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. 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. 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.
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, possibly using simulated annealing or genetic algorithms.
Within a particular model structure, parameters or variable parameter relations 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:
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 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.
Official source
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