Variations in the application of a budget of uncertainty optimization approach

It is possible to consider uncertainty simultaneously with the design process. In fact, a Budget of Uncertainty(BoU) can be determined alongside the design solution, allowing the determination of uncertainty intervals for selected design variables and problem parameters. This paper presents a new strategy for optimization under uncertainty which provides for this simultaneous design and uncertainty determination. To test the theory, a simple Taylor series expansion strategy is used to propagate uncertainty in a design problem’s objectives and constraints and a new BoU design algorithm is formulated. Due to the need for competing objectives, nominal performance and robust design, the new formulation is a multiobjective problem with primary and secondary weights to allow for lexicographic weights of uncertain parameters and variation between optimal and robust solutions. This paper compares and contrasts three different Goal Programming techniques as solutions to the multiobjective problem. Within the paper, the term Budget of Uncertainty (BoU) is used to describe the fundamental idea of uncertainty allocation across design variables and problem parameters as well as for a shorthand to describe the presented formulation. An engineering design problem, that of a helical spring, is presented to further illustrate the new method, and an uncertainty budget is considered which trades uncertainty in coil diameter against uncertainty in wire diameter.