A genetic algorithm based approach for robust evaluation of form tolerances

Abstract

Abstract This paper deals with the accurate interpretation of inspection data for various classes of form tolerances. The minimum zone (MZ) method (ANSI Y14.5M-1994) yields the lowest value (most accurate) for all the form tolerance errors. The MZ solution minimizes the maximum deviation of the inspected feature from a reference (normally an ideal state of the evaluated feature). An accurate evaluation of this solution for various form tolerances involves solving a nonlinear optimization problem. Evaluation algorithms incorporated in current coordinate measuring machines deal with minimizing the least-square error for the form feature being evaluated, resulting in higher values for form tolerances. This paper solves a nonlinear optimization problem for form tolerance evaluation by applying genetic algorithms. A unified genetics-based algorithm has been used to estimate the minimum zones of all form tolerance classes, namely straightness, flatness, circularity, and cylindricity. Multiple search zones are formed throughout the data set, simultaneously in each iteration, to arrive at a global optimal solution. This approach takes care of the inherent nonconvexity in the search surface and overcomes problems of local optima. The results of this approach, applied to some examples, are presented in this paper and compared with results from existing methods reported in the literature.