Статистический анализ для идентификации математической модели в прикладных задачах с целью экономии затрат
Abstract
Statistical analysis for the identification of the mathematical model in applied problems
with the purpose of cost savings
I.V. Stepakhno, Y.B. Gnuchiy, O.Y. Dyuzhenkova
In this article the method of multivariate statistical analysis is presented and the concept of identification of the mathematical statistical model is considered. The coefficients of the model parameters influence on the determined values of the maneuverability and economic characteristics of a complex technical system are calculated. The basic tool for processing input information is the apparatus of the theory of random matrices. Problems of constructing mathematical models in modern conditions when using a very large number of parameters require the development of approaches in which it’s possible to take into account all the necessary situations of life cycles without distorting the real functioning of multi-level systems and without losing important input information. World and native practice of navigation has a significant number of accidents and emergency situations arising from errors made by boatmasters during maneuvering, especially in difficult navigation conditions of navigation or mooring. This is primarily due to the fact that the choice of maneuver tactics is based mainly on the experience and intuition of the boatmaster and the visual assessment of the traffic situation. The decision to adjust the maneuver is implemented by trial and error, the price of which can be very high. Subjective assessment of the situation before the start of maneuver and after its initiation is the main source of errors leading to accidents. An alternative to this subjectivity can be only a good knowledge of the parameters of the mathematical model of the ship and computer playback of the expected maneuver based on this knowledge. There are two ways of obtaining such knowledge. The first way is to build a mathematical model of the ship once by the results of sea trials and in the future use of such a model with a correction for the conditions of navigation. The other way is to obtain the model parameters continuously during the operation of the vessel and use this updated model to predict the planned maneuvers. In this paper we use methods for proving theorems for random matrices, which have been studied in detail in the literature cited.
References
Girko, V. L., Stepahno, I. V. (1990). G–otsenka singulyarnyh sobstvennyh chisel matrits. [G-estimate of matrices singular eigenvalues]. Doklady AN USSR, 8(А), 14 – 17.
Girko, V. L. (1996). Theory of Linear Algebraic Equations with Random Coefficients. New York, 302.
Girko, V. L. (1996). An Introduction to Statistical Analysis of Random Arrays. VSP, 5–11.
Girko, V. L. (2001). Theory of stochastic canonical equations. Kluwer Publishers (Netherlands), 316.
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