Online Gaussian process regression for time-varying manufacturing systems

Model regression is vitally important for performance prediction and quality control in the manufacturing industry. Since manufacturing machines always suffer from random disturbances and unobservable model shift/drift due to component failure and tool wear in the daily production, online model regression techniques are required by the manufacturers to help increase productivity and reduce quality defects by tracking the system variations promptly. Though many different types of online regression methods exist in current literatures, very few of them have considered the regression of time-varying systems. This paper addresses the online model regression for time-varying manufacturing systems with random unknown model variations during production. We first extend the standard Gaussian process regression (GPR) method for time-varying systems, which provides the optimal model estimate with the minimum mean square error (MSE). Then, an iterative form of the extended method is derived which is computation efficient but maintains the optimality of estimation with the minimum MSE. However, such optimality is obtained at the cost of storage for continuously updating the covariances between the estimated model values and the measurements. This would make the storage unaffordable when an output can take infinite number of values. Due to such a limitation, a suboptimal GPR method is further proposed to make both computation and storage inexpensive, but with worse estimation performance. Finally, the effectiveness of the two proposed methods is demonstrated by simulations.