Mathematical modeling in the problem of selecting opti-mal control of obtaining alloys for machine parts in un-certainty conditions
Relevance of research, results of which are given in the paper concerns the development of methods for estimating the parameters of mathematical models in case they are built on the passive experiment results in conditions of small sample of fuzzy data. The first stage in this process is to develop...
Збережено в:
| Дата: | 2015 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Russian |
| Опубліковано: |
Інститут енергетичних машин і систем ім. А. М. Підгорного Національної академії наук України
2015
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| Теми: | |
| Онлайн доступ: | https://journals.uran.ua/jme/article/view/21309 |
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| Назва журналу: | Energy Technologies & Resource Saving |
Репозитарії
Energy Technologies & Resource Saving| Резюме: | Relevance of research, results of which are given in the paper concerns the development of methods for estimating the parameters of mathematical models in case they are built on the passive experiment results in conditions of small sample of fuzzy data. The first stage in this process is to develop a fuzzy clustering procedure, which allows to "spread" all experimental points in a multidimensional factor space, having "attributed" them to this or that hypercube top, forming a plan of full factorial experiment to implement the further orthogonalization procedure. The mathematical model of the process is the regression equation in the form of the Kolmogorov-Gabor polynomial, describing the influence of fuzzy input variables, i.e. alloy structure, on its properties. It is so-called "structure - property" model.As a result of realization of the proposed fuzzy clustering procedure, obligatory before building up the regression equation in case the planning area has an arbitrary shape, cluster, "nearest" to the considered experimental point can be installed and procedure of referring the corresponding point to this or that clustering center can be carried out. The results obtained can be used for the further construction procedure of the regression equation.The fuzzy clustering algorithm was proposed, and calculation examples of membership functions, used in the implementation of this algorithm were given. Using the proposed procedure is effective in estimating the parameters of mathematical models according to the passive experiment data in conditions of small sample of fuzzy data. |
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