Application of fuzzy knowledge base for corrected measured point determination in coordinate metrology

This paper describes an application of fuzzy logic for corrected measured point determination in coordinate metrology. The correction method works on a series of indicated points obtained by contact scanning of the measured surface with a spherical tip probe. The outline of the probe ball defines an arc for each measured point, each such arc being delimited by the points of intersection with the preceeding and the following arcs. As a first approximation the corrected measured point is estimated as the mid-point of the arc. The refinement to the method consists in determining an angular compensation to be applied to the mid-point estimation and calculating the associated indicated measured point coordinate values. To determine an angular compensation a rule-based approach to decision making using fuzzy logic techniques is proposed. In this approach, we consider imprecise vague knowledge as a set of rules linking a finite number of conditions with a finite number of conclusions. The representation of such imprecise knowledge by means of fuzzy linguistic terms makes it possible to carry out quantitative processing in the course of inference based on the compositional rule of inference that is used for handling uncertain (imprecise) knowledge, often called approximate reasoning or fuzzy reasoning. Such knowledge can be collected and delivered by a human expert (e.g., decision maker, designer, process planner, machine operator, etc.). For our case, this knowledge is expressed by a finite number of heuristic fuzzy rules of the Multiple Input Single Output type (MISO). The paper will include a brief discussion of a new compensation procedure of probe radius tip and related test results of the same probe head carried out on a fixed bridge Mitutoyo Legex 910 CMM equipped with a MPP-300 scanning probe in the continuous scanning mode.