Solving interval constraints by linearization in computer-aided design

    Authors

    Y. Wang;B. O. Nnaji

    Comments

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    Abbreviated Journal Title

    Reliab. Comput.

    Keywords

    NONLINEAR-SYSTEMS; EXISTENCE VERIFICATION; GEOMETRIC CONSTRAINTS; DECOMPOSITION PLANS; BOUNDARY EVALUATION; MECHANICAL DESIGN; PARAMETRIC; DESIGN; SINGULAR ZEROS; BEZIER CURVES; NEWTON METHOD; Mathematics, Applied

    Abstract

    Current parametric CAD systems require geometric parameters to have fixed values. Specifying fixed parameter values implicitly adds rigid constraints on the geometry, which have the potential to introduce conflicts during the design process. This paper presents a soft constraint representation scheme based on nominal interval. Interval geometric parameters capture inexactness of conceptual and embodiment design, uncertainty in detail design, as well as boundary information for design optimization. To accommodate under-constrained and over-constrained design problems, a double-loop Gauss-Seidel method is developed to solve linear constraints. A symbolic preconditioning procedure transforms nonlinear equations to separable form. Inequalities are also transformed and integrated with equalities. Nonlinear constraints can be bounded by piecewise linear enclosures and solved by linear methods iteratively. A sensitivity analysis method that differentiates active and inactive constraints is presented for design refinement.

    Journal Title

    Reliable Computing

    Volume

    13

    Issue/Number

    2

    Publication Date

    1-1-2007

    Document Type

    Review

    Language

    English

    First Page

    211

    Last Page

    244

    WOS Identifier

    WOS:000252303100005

    ISSN

    1385-3139

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