Modeling and fractal parametrization

Abstract

Design - by definition - is the creation of a description of an object that does not yet exist [1]. This implies the main problem of the design process - the inability to assess the "correctness" of the selected option of the object until the design is fully completed, the object is manufactured and tested. Thus, optimization in design comes down to solving many inverse problems: from object to project. The solution of the contradictions connected with this problem is sought, as a rule, on the way of creating models of the future object and testing the latter with the help of simulation. This problem is especially relevant when designing complex systems, which include inter-acting elements that jointly solve a certain common problem and have the following properties in combination: the absence of a single functioning algorithm in the form of some consistent mathematical description; "noisy" model, which complicates the design and observation, due not so much to the presence of random noise generators, but to a large number of secondary processes; non-stationarity, expressed in the drift of characteristics, changes in parameters, evolution in time; irreproducibility of ex-periments with it [1]. As a rule, all this makes it difficult to use in CAD systems such "standard" back calculation from the required properties of the system to the parame-ters of its design or manufacturing technology. In the process of such calculations, using of the so-called fractal dimension of individual elements of the designed sys-tems can make a significant simplification of the applied models.