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
The optimization problem is formulated, which consists in ensuring the maximum time of maintaining the pressure in the filled container in the range from the maximum reached to 70 ATM. A mathematical model of a system consisting of a solid-fuel gas generator and a constant-volume filling tank is constructed. The optimization problem was solved by the Hook-Jeeves method and a genetic algorithm with real coding. The results were compared. A software package has been developed with the help of which a system of ordinary differential equations describing the state of the object under consideration is solved.
Бушуев А.Ю., Ряузов С.С. Оптимизация конструкции твердотопливного модельного газогенератора. Математическое моделирование и численные методы, 2019, № 4, с. 3–14.
A software environment was developed for computer-aided design of optimal throttle hydraulic synchronization systems of actuators of various functional purposes operating under conditions of external alternating-sign force effects. The criterion of an optimization procedure was the minimization of a mismatch time of relative movement of actuators during operation. A compute core of an object-oriented code was constructed on the basis of a dynamic mathematical model of a synchronization system consisting of four power cylinders. A model problem was solved with the help of the created software environment. This model problem demonstrated the efficiency of the proposed multidimensional optimization process. The methodology was based on the use of the well-known heuristic method (binary coded genetic algorithm) and the subsequent improvement (in the sense of a given objective functional) of the obtained solution by a method on the basis of the Hooke-Jeeves algorithm. Recommendations on the practical application of the software and mathematical support for achieving the best convergence to the extreme value of a vector of controlled parameters were formulated.
Бушуев А.Ю., Иванов М.Ю., Коротаев Д.В., Реш Г.Ф. Программная среда dgsSynchCAD для моделирования и автоматизированной эвристической оптимизации дроссельных гидросистем синхронизации. Математическое моделирование и численные методы. 2020. № 1. с 103–117.
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.