We have built a mathematical model for deployment of multibody solar array with a cable system of deployment. On the basis of analysis of the kinematic scheme of deployment system we have chosen the dimensions of the radii of the rollers and gear ratio of the two types of gear mechanisms which provide the preset sequence of fixation of sections. We used Lagrange equation of the second kind for studying deployment of the solar battery array. A distinctive feature of this approach is application of iterative method for taking into account deformation of the cables of synchronizing system. The mathematical model can be used to choose optimal design factors and deployment system performance requirements. It is also valuable for dealing with worst-case situations and verifying the reliability of deployment procedure.
Bushuev A., Farafanov B. Mathematical modelling of deployment of large-area solar array. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 101-114
When dealing with many applications there is a problem of finding the global extremum. Of particular relevance are the optimization methods that allow solving problems effectively when the objective function depends on a complex mathematical model that requires large computing resources for its solution. In this paper, a comparison is made between the Ψ-transformation optimization method and the canonical particle swarm optimization method. The flaws of some known algorithms of the Ψ-transformation optimization method are revealed and a modification based on the replacement of a random law with uniform distribution for generating statistical realizations on the second and subsequent iterations of the standard algorithm by the normal distribution law with parameters determined by the results of the previous iteration is proposed. On the basis of the extensive computational experiment, the advantage of the modified algorithm of the Ψ-transformation optimization method is shown in comparison with algorithm of the canonical particle swarm method.
Бушуев А.Ю., Маремшаова А.А. Сравнение модифицированного метода Ψ-преобразования и канонического метода роя частиц. Математическое моделирование и численные методы, 2018, № 3, с. 22–37.