Game theory approach for optimum design of an aged structure with multiple objectives

A mathematical procedure based on the concept of game theory is described for evaluating an optimal strategy for increasing the residual life of an aged structure subject to cyclic loading. To increase the residual life of the structure, it is proposed to attach additional sections with the critical members. A computational procedure for estimating residual life of structure based on Paris equation for crack growth propagation with number of cycle is described. The decision making problem is formulated as constrained optimization problem having two objectives of conflicting nature. The design variables are taken as the cross-sectional area of attached sections in the structure. Geometric constraints in the form of lower and upper bounds on the design variables and constraint on stress developed are considered in the formulation. Two objectives considered in the present investigation are: minimization of the mass of attached sections and maximization of the extra residual life of structure due to mass attachment. The design problem is formulated as a two-person game and the Nash non-cooperative solution is evaluated for irrational play to determine the starting point of the game. For the cooperative game, a supercriterion is formulated for the overall benefit of the players. The game is terminated when an optimal trade-off between the objectives is reached with the maximization of the supercriterion. Two different optimization methods, namely interior penalty function method and grid search method have been used for supercriterion maximization. The methodology is demonstrated by solving a problem of practical interest.