Interpretable Interval Constraint Solvers in Semantic Tolerance Analysis

A semantic tolerance modeling scheme based on generalized intervals was recently proposed to allow for embedding more tolerancing intents in specifications with a combination of numerical intervals and logical quantifiers. By differentiating a priori and a posteriori tolerances, the logic relationships among variables can be interpreted, which is useful to verify completeness and soundness of numerical estimations in tolerance analysis. In this paper, we present a semantic tolerance analysis approach to estimate tolerance stack-ups. New interpretable linear and nonlinear constraint solvers are developed to ensure interpretability of variation estimations. This new approach enhances traditional numerical analysis methods by preserving logical information during computation such that more semantics can be derived from numerical results.