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In this paper, we present a novel tolerance allocation algorithm for theassessment and control of geometric variation on system performance that isapplicable to any system of partial differential equations. In particular, weparameterize the geometric domain of the system in terms of design parametersand subsequently measure the effect of design parameter variation on systemperformance. A surrogate model via a tensor representation is constructed tomap the design parameter variation to the system performance. A set ofoptimization problems over this surrogate model restricted to nestedhyperrectangles represents the effect of prescribing design tolerances, wherethe maximizer of this restricted function depicts the worst-case member, i.e.the worst-case design. Moreover, the loci of these tolerance hyperrectangleswith maximizers attaining, but not surpassing, the performance constraintrepresents the boundary to the feasible region of allocatable tolerances. Everytolerance in this domain is measured through a user-specified, weighted normwhich is informed by design considerations such as cost and manufacturability.The boundary of the feasible set is elucidated as an immersed manifold ofcodimension one, over which a suite of optimization routines exist and areemployed to efficiently determine an optimal feasible tolerance with respect tothe specified measure. Examples of this algorithm are presented withapplications to a plate with a hole described by two design parameters, a platewith a hole described by six design parameters, and an L-Bracket described byseventeen design parameters.

Physics-Informed Tolerance Allocation: A Surrogate-Based Framework for the Control of Geometric Variation on System Performance