Effective conception of regresion analysis
Keywords:regression analysis, mathematical modeling, model structure, system of orthogonal normalized contrasts, statistical efficiency of the model, model stability
AbstractThe paper deals with the efficient conception of regression analysis, when modeling complex systems and processes. The work objective is the use of the method of formalized obtaining of the structure of multifactor regression model and stable estimation of its coefficient for construction of highly precise statistical models of the process of friction of a rubbing pair of a piston-cylinder in the internal combustion engine. It is supposed that the model structure is unknown for the author. Approximation of initial data is performed with the use of polynomial mathematical models. The idea of complete factor experiment is used as a theoretical ground of correct statistical modeling. The use of the complete factor experiment being impossible, it is recommended to use the multifactor regular plans on the basis of ЛПτ of uniformly distributed sequences. An extended conception of orthogonality of the obtained model has been proposed: the experiment design, model structure and structure elements of the model orthogonal to each other. The orthogonal structure of the multifactor statistical model allows obtaining statistically independent estimates of coefficients of the modeled function. Such a structure may be defined unambiguously with statistically significant coefficients. Normalization of orthogonal effects allows obtaining a maximally stable model structure, and, consequently, its coefficients. The solved problem will be well-posed The considered method of formalized obtaining of the structure of multifactor statistical model and stable estimation of its coefficients is used for constructing statistical models of tribotechnical characteristics of friction parameters of a pair cylinder-piston of the internal combustion engine. Three models have been obtained, which are characterized by good quality parameters: adequacy, informativeness, statistical efficiency, stability. The factors in the model structure are presented by orthogonal normalized contrasts. The models application allows analyzing the mechanisms of the going on phenomena and determining optimal operation conditions of the pair of piston-cylinder internal combustion engine. The results of using the extended conception of orthogonality, when constructing the models of friction parameters of the pair piston-cylinder, have confirmed the promising character of application of the considered approach, its efficiency and expediency in the design of regression statistical model of complex systems and processes.
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