Abstract—The inclusion of uncertainty in design is of paramount practical importance because all real-life systems are affected by it. Designs that ignore uncertainty often lead to poor robustness, suboptimal performance, and higher build costs. This work proposes a novel framework to perform robust design optimization concurrently with optimal uncertainty apportionment for dynamical systems. The proposed framework considerably expands the capabilities of contemporary methods by enabling the treatment of both geometric and non-geometric uncertainties in a unified manner. Uncertainties may be large in magnitude and the governing constitutive relations may be highly nonlinear. Uncertainties are modeled using Generalized Polynomial Chaos and are solved quantitatively using a least-square collocation method. The computational efficiency of this approach allows statistical moments to be explicitly included in the optimization-based design process. The framework formulates design problems as constrained multi-objective optimization problems, thus enabling the characterization of a Pareto optimal trade-off curve that characterizes the entire family of systems within the probability space; consequently, designers are able to produce robust and optimally performing systems at an optimal manufacturing cost. A nonlinear vehicle suspension design problem, subject to parametric uncertainty, illustrates the capability of the new framework to produce an optimal design at an optimal manufacturing cost.

Index Terms—Uncertainty apportionment, tolerance allocation, robust design optimization, dynamic optimization, nonlinear programming, multi-objective optimization, multibody dynamics, uncertainty quantification, generalized polynomial chaos

Cite: Joe Hays, Adrian Sandu, Corina Sandu, and Dennis Hong, "Simultaneous Optimal Uncertainty Apportionment and Robust Design Optimization of Systems Governed By Ordinary Differential Equations," International Journal of Mechanical Engineering and Robotics Research, Vol. 3, No. 1, pp. 216-240, January 2014.