A genetic programming based fuzzy regression approach to modelling manufacturing processes

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Abstract
Fuzzy regression has demonstrated its ability to model manufacturing processes in which the processes have fuzziness and the number of experimental data sets for modelling them is limited. However, previous studies only yield fuzzy linear regression based process models in which variables or higher order terms are not addressed. In fact, it is widely recognised that behaviours of manufacturing processes do often carry interactions among variables or higher order terms. In this paper, a genetic programming based fuzzy regression GP-FR, is proposed for modelling manufacturing processes. The proposed method uses the general outcome of GP to construct models the structure of which is based on a tree representation, which could carry interaction and higher order terms. Then, a fuzzy linear regression algorithm is used to estimate the contributions and the fuzziness of each branch of the tree, so as to determine the fuzzy parameters of the genetic programming based fuzzy regression model. To evaluate the effectiveness of the proposed method for process modelling, it was applied to the modelling of a solder paste dispensing process. Results were compared with those based on statistical regression and fuzzy linear regression. It was found that the proposed method can achieve better goodness-of-fitness than the other two methods. Also the prediction accuracy of the model developed based on GP-FR is better than those based on the other two methods.