A New Theoretical Approach for Robust Truss Optimization with Uncertain Load Directions

Abstract

In the real-world truss optimization problems, the optimal performance obtained using conventional deterministic methods can be dramatically degraded in the presence of sources of uncertainty. The source of uncertainty may be the variability of applied loads, spatial positions of nodes, and section and material properties. In this paper, we present a new theoretical model and a problem-specific metaheuristic approach when the only source of uncertainty is the variability of the applied load directions. The essence of the novel conception is independent from the theoretical description of the uncertainty which may be either probabilistic (stochastic) or possibilistic (fuzzy). In the presented unified (nonprobabilistic and nonpossibilistic) approach, the varying load directions are handled as uncertain-but-bounded parameters. The result of the optimization is a robust minimal-weight truss design, which is invariant to the investigated load uncertainty type. The well-known ten-bar plane truss example with the most popular direction settings will be used to illustrate the validity and efficiency of the presented approach. In the presented example we replaced each nominal load direction by an angle set around the nominal value. The detailed description of the problem-specific robust metaheuristic based on the previously developed ANGEL metaheuristic will be presented in a forthcoming paper.

Keywords:

• Optimal truss design
• Robust truss optimization
• Uncertain load direction
• Uncertain-but-bounded parameters
• Unified uncertainty management

Notes

^#Communicated by Janos Logo.