A New Modelling Method With Hierarchies For Large-scale Systems

Hierarchy and structure of mode Is for large-scale System IS (L.S.S.) are important hierachical models are rather hard to be built without prior information, since a great number of variables are included in L.S.S. and phenomena of multicollinearity very often happen. The inherent reason of producing such phonomena is that there can hardly exist complete independence among variables which concentrates samples around a group of intersections of cylinders. The cylinder equations are considered as the first hierarchy for L.S.S. models. When several simple forms of function are used, these equations can be compounded into the models. The compound functions are taken as the second hierarchy. And that three criteria can be used to estimate the parameters of these compound functions. When more information is available, a few of intersections, on which samples focus, may be obtained. To handle the situation by using differential geometrical, algebraic, variational methods, three forms of a family of smooth surface are presented; which pass these lines and include more parameters suitable to be estimate using search method. This method can be used to establish hierarchical models for L.S.S. when prior information is lacked.