The paper states that for a set of mathematical models, describing the same object, there primarily can be determined a meta-model, which is the result of evolution of convex combinations of those models. The evolution is actually the identification process that starts at the convex combination by coefficients, guaranteeing minimum of lacks. The purpose is to identify the machining tool wear theoretically under ultimate uncertainties, when there are no anticipatory data, determining how and in what ratio the abrasive, adhesive, diffusive, and oxidizing wear components constitute the wear value. The machining tool wear is considered as a time function of the single geometrical coordinate. There are four wear models, focusing on such specific features of the complicated wear process as abrasion, adhesion, diffusion, and oxidation. The aggregate of those four specificities of wear can be found as their convex combination, whose coefficients evolve as time goes by along with evolving values of wear models. Initially, these coefficients are set at minimaxed probabilities of applying the abrasive, adhesive, diffusive, and oxidizing wear models. Using a measure of accuracy for each wear model, the evolution through sampled time of the convex combination coefficients in every point of the single geometrical coordinate is expressed. That measure establishes the relative correspondence between a model wear value and the wear convex combination in the current time sample for any value of the geometrical coordinate. The stated procedure of weighting the wear models on their accuracy may be found as an identification process under uncertainties or unavailable anticipatory data. This will be used for identifying the model structure of a system or process primarily, when there are several approaches to model it, having unknown or uncertain significances.
Ключові слова: machining tool wear, abrasive wear, adhesive wear, diffusive wear, oxidizing wear, ultimate uncertainties, wear aggregate, measure of accuracy, convex combination, minimaxed probabilities
Identification of the machining tool wear model via minimax combining and weighting subsequently specific models,
Information Processing Systems,