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Mixed algorithm in searches of mechanical system steady‐state conditions for low precision of the state estimation
Author(s) -
Lipinski Krzysztof
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910293
Subject(s) - nonlinear system , algorithm , state (computer science) , newton's method , steady state (chemistry) , mechanical system , mathematics , numerical integration , computer science , mathematical optimization , mathematical analysis , physics , chemistry , quantum mechanics , artificial intelligence
This paper focuses on algorithms of numerical solution of nonlinear system of equations. Analytical formulas of their nonlinear functions my not be calculated with the requested precision. Additionally, analytical formulas of the partial derivatives are unknown. They are evaluated numerically by finite differences method. It effects in erroneous estimations. Described situation is critical when steady state conditions are searched for mechanical systems. According to the precision of the numerical procedures, their dynamic equations are known with limited precision. This same stands for the system's final conditions (obtained by a numerical integration). It the actual case, the classical Newton‐Raphson algorithm can be ineffective. As an alternative, a mixed search algorithm is proposed in the paper. By contrast to the classical algorithm, within the search direction defined by the Newton‐Raphson indication, (potentially erroneous) a local minimum is searched. Both the algorithms are tested on analytical functions; on randomized functions and on a model of a mechanical system. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)