Empirical models of the decisive rules of the control for space vehicles on basis of orthonormal polynomial series
- Paper number
IAC-06-C2.1.11
- Author
Ms. Nataliya Lysenko, Dniepropetrovsk National University, Ukraine
- Year
2006
- Abstract
The forming of models of the recognition decisive rules of the nondestructive control objects is connected to necessity estimation of probability distribution laws on experimental data. It is supposed, that samplings measurements of parameters describing a condition of objects of the control (norm, spoilage) are known. It is necessary on this sampling to form analytical expressions for estimations of their laws of distribution and to form the recognition decisive rules. In the report the possibility of using for these purposes representation of functions by series of orthonormal polynomials is considered. The empirical laws of distribution of informative parameters were shaped on the basis of series of Hermite, Laguerre and Legendre. By realization of computing experiments the influence of a kind of a weigth function, sizes of sampling of measurements and number of terms of series on errors of estimation of the probability distribution laws by series of orthonormal polynomials was established. The selfdescriptiveness of the histogram and, therefore, regularity of selection of a weigth function depends on length of sampling. By unsuccessful selection of an error of recovery can bring up in 2 and more time. On number of terms of series and sizes of sampling of measurements depend a methodical and random error of recovery. With increase of number of terms of series the methodical error decreases, and random is augmented. The rule of limitation of orthonormal polynomials series is offered and by mathematical simulation its efficiency and functionability is confirmed. On experimental data the quantitative estimations of errors of recovery of the probability distribution laws by different series of orthonormal polynomials are obtained. On the basis of the rated laws of distribution the models of the decisive rules of the control were formed. Their efficiency was evaluated during computing experiments by matching with the optimum decisive rules. The methodical guidelines for formation of the decisive rules of the control are developed on the basis of orthonormal polynomials series in conditions of a disadvantage of an input information about statistical properties of measurements.
- Abstract document