Papers by Keyword: Recursion Method

Abstract: Lorenz system families contain Lorenz system, Chen system and Lu system, their accurate analytical solutions are not yet obtained now. The segmenting recursion method was put forward in this paper, the equations of Lorenz system families were reasonably linearized within small segment, the recursion formulas were obtained by solving the approximate analytical solutions within small segment, and all numerical solutions were got by the recursion formulas. The chaotic motion of Lorenz system families were numerically simulated by means of the segmenting recursion method, the simulation results were compared with Runge-Kutta method. The comparative results show that the segmenting recursion method is very effective to numerically simulate Lorenz system families, not only method is simple, programming is easy, but result is accurate. this method is a universal new method to numerically simulate similar system.

Abstract: Optimization method was designed via selecting a series of self calling functions on the basis of application of recursive algorithm method. An optimization method for unifying section of transmission tower’s chord member was testified from the example. The procedure to the feasible combination patterns for unifying section was put forward by recursion. Based on the hypothesis of static determination, the sections of the members in each pattern were shown, and the optimal design can be obtained by comparing existing patterns. Three different constraint inputs of transmission tower were checked by the recursion algorithm method in this paper. The comparison result shows that the design of unifying section save 123 Kg of steel after optimization under the condition of 5 division pattern of chord member. The number of possible combination of unifying section pattern was increased sharply, while the optimal weight of tower is decreased with the division of chord member.

Abstract: A unifying section problem of a double circuit power transmissions tower (DCPT)’s chord member was studied in this paper. The collision between the theoretic analysis and practical process in optimization of unifying section was proposed. The bourn of each chord member’s broken position was taken into consideration. The concept of dynamic programming was cited, and a procedure to get all the feasible combination patterns for unifying section was put forward by recursion. The object function which is the combination of the decision making and the state in every phase was set up. The object function value of whole structure can be obtained based on the previous decision of every phase. The optimization value in a decision of the weight of the tower’s chord member was set up though above object function value in a certain combination. At last, the optimization solution is designed via selecting a series of self calling functions on the basis of recursive idea.