A Function-on-Function Regression Model for Monitoring the Manufacturing Process Performance with Application in Friction Stir Welding

Abstract— Friction stir welding is a relatively new way to join solid materials without melting using a nonconsumable tool, which has many applications in different industries including automotive, shipbuilding, and aerospace. Destructive testing is an integral part of engineering science, which costs a lot. Reducing the number of destructive tests via numerical calculations to determine the quality of welded parts is valuable. On the other hand, advances in computer technology and embedded sensing systems in different domains have made it possible to collect a variety of data in huge volume at an unbelievable velocity, which provides an opportunity and at the same time a challenge to engineers and practitioners to utilize this rich source of information efficiently. Functional data as a rich form of structured data allows for high dimensionality modeling and analysis of the data. In this paper, we develop a fully functional linear regression model to quantify and predict the quality of the process outputs by reducing the number of destructive tests and presenting a change-point detection model to avoid using the model when a change has occurred in one of the components of the process. Important issues such as autocorrelation and correlation are taken into account in the presented model. The functional variables of the model are solved by polynomial basis function expansions. The results of the experimental tests indicate that the proposed method performs well in detecting out-of-control conditions as well as estimating the change-point location. The obtained value of the multiple correlation coefficient 0.98 and the corresponding F-value equal to 652.95 support these results.