DOI: https://doi.org/10.22281/2413-9920-2017-03-04-400-414

УДК 625.54, 625.57

Лагерев А.В., Лагерев И.А.
Оптимальное проектирование линии канатного метро c унифицированными промежуточными опорами
Сформулирована и решена задача условной нелинейной технико-экономической оптимизации шага установки промежуточных опор, унифицированных по высоте, при проектировании линий канатного метро в условиях сильно урбанизированной городской среды. Задача оптимизации включает однокритериальную целевую функцию, выражающую стоимость строительства линии канатного метро (суммарную стоимость промежуточных опор, их фундамента, тягового и несущих стальных канатов и технологического оборудования). Указанная целевая функция подлежала минимизации путем нахождения оптимального сочетания шага установки промежуточных опор и усилия натяжения несущих канатов с учетом системы конструктивных, режимных, прочностных и градостроительных ограничений в виде нелинейных неравенств. Оптимизационный алгоритм был построен на основе прямого метода оптимизации типа Хука-Дживса, который был модифицирован с учетом необходимости варьирования высотой промежуточных опор с постоянным шагом, равным шагу унификации. При построении целевой функции были учтены три возможные формы провисания несущих канатов, которые могут быть реализованы для различных значений усилия их натяжения. Выполнен анализ влияния шага унификации и минимального типоразмера промежуточных опор по высоте на величину их оптимального шага в зависимости от конструктивных и стоимостных показателей промежуточных опор, а также на стоимость 1 км линии канатного метро при различных значениях угла продольного уклона поверхности рельефа вдоль линии канатного метро.
Ключевые слова: канатное метро, канатная дорога, промежуточная опора, шаг установки, унификация, канат несущий, канат тяговый, агрегатная прочность, технико-экономическая оптимизация, стоимость.

Lagerev A.V., Lagerev I.A.
Optimal design of the cable metro with unified intermediate supports
In article was formulated and solved the problem of conditional nonlinear technical and economic optimization of the distance between intermediate supports, uniform in height, during the design of the cable metro lines in highly urbanized city environment. The optimization problem involves a single-criterion objective function that expresses the cost of construction of the cable metro line (total cost of intermediate supports and their foundations, traction and carrying steel cables and technical equipment). The specified objective function subject to minimization by finding the optimal combination of the distance between intermediate supports and tension carrying ropes with accounting constructive, modal, structural and planning constraints in the form of nonlinear inequalities. The optimization algorithm was based on the direct method of optimization type, Hooke-Jeeves, which was modified taking into account the need of varying the height of intermediate supports with a constant step equal to the step of unification. When constructing the objective function were considered three possible forms sagging of carrying ropes, which can be implemented for various values of the efforts of their tension. Analysis was done of the influence of the step unification and minimum size of intermediate supports on their optimum step, the cost of intermediate supports, the cost of 1 km cable metro line for different values of the angle of the longitudinal slope of the surface relief along the cable metro line. The graph of height of unified supports from the angle of the longitudinal slope of the surface relief has discrete-step type. With the increase of the step unify the discreteness increases: the width of the range of angles of the longitudinal slope of the surface relief within which the height of the supports remains constant, increases. The graph of step installation of unified supports along the cable metro line from the angle of the longitudinal slope of the surface relief also has discrete-step type. The transition to a larger height unified intermediate supports determines the need for installation of supports with a large pitch. Its value then begins to decrease monotonically with further increase of the angle of the longitudinal slope of the surface relief until it needs to transition to the new size of supports. Synchronous change in the optimal values of the height and step of the installation of intermediate supports, depending on the angle of the longitudinal slope of the surface relief leads to the fact that the optimal cost characteristics of the cable metro lines are smooth functions. It has an extreme character with a minimum at angles of inclination of the surface elevation ~5 degrees, which is associated with the form of sagging of the load-bearing ropes. Unification of intermediate supports has little effect on the optimal cost characteristics of the cable metro lines. Even for a sufficiently large step of the unification the largest difference in optimal value is almost insignificant: it lies in the range of 2…3%, increasing with increasing the angle of the longitudinal slope of the surface relief and unit cost of the intermediate support. Unification of intermediate supports according to the height and their step practically does not affect the optimal value for horizontal tension on the load-bearing ropes. It determined mainly by the angle of the longitudinal slope of the surface relief. Deviation of horizontal tension on the load-bearing ropes for the nonstandard supports and the unified supports within the range of angles of inclination of the terrain surface 0…60 degrees is not more than 0.5 to 0.8 %.
Key words: cable metro, ropeway, intermediate support, installation step, unification, traction cable, carrying cable, strength of the cable, optimization, cost.

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