A Knowledge-Based Interval Modeling (KBIM) Method is introduced for global optimization and process tuning. A novel feature of the KBIM Method is its ability to take advantage of the a priori knowledge of the system by incorporating the linear/nonlinear sensitivity information between the objective function/constraints and the system variables in the form of an interval model. The interval model is then used to estimate the feasible/plausible region within the input space as the basis of search for the global optimum. The noted features of the KBIM Method are that (1) initial trials are not required to construct the interval model, (2) the interval model produces bounds for the objective function and constraints so that it may not be trapped into the local optima, and (3) learning is incorporated to update the interval model based on new input-output data that become available during the search. The updated interval model is shown to lead to more accurate estimates of the feasible/plausible region.
The utility of the KBIM Method is demonstrated in three different fields: global optimization, injection molding process tuning, and helicopter track and balance. In global optimization, the KBIM Method is used to search for the global optimum of both unconstrained and constrained benchmark problems. In tuning of injection molding, the method is used as an on-line tuning method to define the feasible region (process window) of the process and to search for a set of feasible machine setpoints in order to improve the production yield. In helicopter track and balance, the KBIM Method selects a set of blade modifications so as to reduce the vibration of the aircraft within the specification limits. The application results indicate that the method provides a viable means of incorporating the a priori knowledge for global optimization and process tuning.
