Application of Filters Theory for Analytical Description of Logical-Analytical Dependences
In this paper, we develop the approach combining local mathematical models into one comprehensive analytical mathematical model with its significant complications. Partial models are described using as simple analytical dependences as possible. The partial models obtained should be combined in one analytical model through multiplying them with the analytical ones in the whole range of weight functions of the object variables - equivalents of frequency filters. The single uniform analytical dependence is constructed by adding private models weighed by weight functions. The analyticity of the single model for the whole range remains at such statement. In this paper, we present the results confirming the possibility of developing the sufficiently simple analytical model by using the proposed method. Its accuracy of approximation meets modern methods and object-oriented modeling. The models developed by employing this method can be used for analytical calculations of optimum operating modes of non-stationary stochastic objects, diagnostics of their condition, interpolation and extrapolation of variables of object and for other purposes by identifying local mathematical models and their combining into full analytical model without essential complication both of mathematical model and natural experiment.