Optimal design of forest machine elements based on the theory of statistical catastrophe assembly

A solution of the optimal design problem of the roll-over protective structure (ROPS) for logging machine operators in terms of the catastrophe theory is provided. In the first part of the paper, a brief description of the catastrophe theory is presented; the cusp catastrophe is considered; control parameters are viewed as Gaussian stochastic quantities. The statement of the optimal design problem is given in the second part of the paper. It includes choices of the objective function and independent design variables, establishment of the system limits. The objective function is determined as an average total cost, which includes both the initial cost and the cost of failure according to the cusp catastrophe probability. The algorithm of the random search method with an interval reduction and functional constraints is provided in the last part of the paper. A suggested solution of the optimal design problem can be applied to choose rational ROPS parameters, which increase safety and reduce production and exploitation expenses.