A Novel Approach to Robust Design Using Recent Advances in Robust and Multiobjective Optimization Methods
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Current advances in the fi eld of Robust Optimization (RO) from such authors as Azarm, Ben-Tal, Elishakoff , Zhang, Renaud and others have led to new and interesting approaches to the treatment of uncertainty in traditional engineering problems. This paper presents the Budget of Uncertainty (BoU) design method; a new method by which such approaches can be applied in a manner which balances the need for optimization with the desire for robust solutions. Where previous work has focused on immunizing an optimization problem against pre-set uncertainty ranges, the BoU method adds additional design variables in an eff ort to solve for an appropriate uncertainty range. The BoU method simultaneously determines an optimum solution and an allowed uncertainty budget within a restricted feasibility space. The result is a solution that guarantees fi rst order satisfaction of uncertain constraints and provides a measure of problem sensitivity to its uncertain parameters. This provides additional insight to early problem development, and can potentially create alternatives to traditional approaches such as Monte Carlo analysis. Within this work we will present a summary of current RO research and introduce the BoU method. We will then apply the BoU method to a simple 2D geometric problem to illustrate its application. Finally, we tackle two well-studied engineering design problems, the Golinksi Speed Reducer and the simple Helical Spring design problem to show a more realistic application of the new method.