Gaussian Distribution Approximation for Localized Effects of Input Parameters

Abstract

In the application of cycle-to-cycle control to manufacturing processes, the model of the process reduces to a gain matrix and a pure delay. For a general multiple input – multiple output process, this matrix shows the degree of influence each input has on each output. For a system of high order, determining this gain matrix requires excessive numbers of experiments to be performed, and thus a simplified, but non-ideal form for the gain matrix must be developed. In this paper, the model takes the form of a Gaussian distribution with experimentally determined standard deviation and scaling coefficients. Discrete die sheet metal forming, a multiple input-multiple output process with high dimensionality, is chosen as a test application. Results of the prediction capabilities of the Gaussian model, as well as those of two previously existing models, are presented. It is shown that the Gaussian distribution model does the best job of predicting the output for a given input. The model’s invariance over a set of different formed parts is also presented. However, as shown in the companion paper on cycle-to-cycle control, the errors inherent in this model will cause non-ideal performance of the resulting control system. However, this model appears to be the best form for this problem, given the limit of minimal experimentation.