Compensating data shortages in manufacturing with monotonicity knowledge

Systematic decision making in engineering requires appropriate models. In this article, we introduce a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints. Incorporating such information is particularly useful when the available datasets are small or do not cover the entire input space, as is often the case in manufacturing applications. We set up the regression subject to the considered monotonicity constraints as a semi-infinite optimization problem, and propose an adaptive solution algorithm. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It was tested and validated on two real-world manufacturing processes, namely, laser glass bending and press hardening of sheet metal. It was found that the resulting models both complied well with the experts monotonicity knowledge and predicted the training data accurately. The suggested approach led to lower root-mean-squared errors than comparative methods from the literature for the sparse datasets considered in this work.