CORRECT STATISTICAL MODELING IN CONDITIONS OF INCOMPLETE INITIAL INFORMATION
DOI:
https://doi.org/10.15588/1607-3274-2017-4-6Keywords:
Statistical modeling, ill-posed problems, stable structure of statistical model, extended conception of orthogonality.Abstract
Context. Urgent problem of statistical modeling of the complex systems and processes in conditions of incomplete initial information has been considered.
Objective. The work objective is the use of the method of formalized obtaining of the structure of multifactor statistical model and stable estimation of its coefficient for obtaining highly precise statistical models of elastic deformations of technological system of a lathe.
Methods. When solving applied problems, the analysis of initial data on obtaining statistical models has shown that they are often constructed in conditions of incomplete initial information and the problem which is solved is incorrectly formulated one. In such conditions the model structure obtaining and its stability prove to be the problems in models construction. The author proposes an extended conception of orthogonality of the obtained model: the experiment design, model structure and structure elements of the model are orthogonal. 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 permits obtaining a maximally stable model structure, and, consequently, its coefficients. The problem will be well-posed.
Results. Application of the considered method of formalized obtaining of the structure of multifactor statistical model and stable estimation of its coefficients is used for obtaining accurate statistical models of elastic deformations of a steel work-piece processed by a lathe. A complete factor experiment has been fulfilled; the factors were as follows: cutting force, work-piece length and diameter, and a response – the value of elastic deformations of the system. Statistical regression moments ˆy1 and ˆy2 were constructed as the experiment result. In the structure of models the factors are presented by orthogonal contrasts. Statistically significant effects are introduced in the model structure under its formation. The checks of the obtained models by quality criteria have shown their high informativeness, stability, adequacy, statistical efficiency. Using the models on lathes with numerical programmed control allows decreasing the number runs of the cutting tool and, consequently, the time of work-piece processing.
Conclusion. The results of the use of the extended conception of orthogonality and structure of the model of a complete factor experiment, when obtaining the models of elastic deformations of technological system of a lathe, have confirmed the great prospects of application of the considered approach, its effectiveness and expediency in constructing regression statistical models of complex systems and processes.References
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