Predicting the Quality of Production Processes with High-Dimensional Data via Tensor Regression

Advances in modern computer technologies and measurement systems embedded in various fields, there is a significant growth in the volume, variety and velocity of the data produced, which is a rich source of information. Tensor data is one of the most important types of complex structured data with high dimensions that traditional methods are not able to solve this type of data. Tensor regression models have many applications in optimizing problems in which there are a number of independent numerical variables as input to the problem that can be changed to create a better output. In this study, a regression model is presented in which the independent variables are numerical and the response variable is tensor. A set of linear algebraic methods and tensor approaches are proposed in order to find patterns within a set of points in space and their relationship to process variables. Friction stir welding (FSW) is a motivational example of this study to confirm the results. The proposed model is coded in R software. The results showed that the proposed model has a good performance in predicting the output of processes by dynamically adjusting its parameters