Method and apparatus for characterizing the unknown state of a physical system

A method and an apparatus are disclosed for characterizing the unknown state of a physical system having a time varying history, the characterization being made with reference to a known state of like physical systems. A response signature representative of the unknown system state is compared to a standard signature representative of the known system state. The standard signature includes a primary signature comprising a multi-dimensional region within a pre-defined, transformed coordinate system having an inner and outer boundary, and a secondary signature comprising at least one, but preferably two or more isoclines situated within the bounded region. If the response signature lies wholly within the bounded region and does not cross any of the region's isoclines, the system being characterized is deemed to be in the known state. Conversely, if both of these criteria are not satisfied the relative degree of departure of the system in the unknown state from the known system state is predicted using one or more point functions representative of the system being characterized. The ability to characterize the state of a physical system can be enhanced by adjusting the coordinate transformations of the standard signature and the response signature by and offset factor, and by subsequently subjecting both signatures to a topological transformation which produces a standard signature comprised of two concentric geometric figures.