Profile monitoring via FSSM with application to scroll involute machining in air compressors

Profile monitoring is employed to check the stability of the functional relationship between process response variables and explanatory variables. A shift in this functional relationship indicates the presence of assignable causes. Due to the widespread adoption of sensors, manufacturers can now collect extensive data during production, making it feasible to model and monitor the functional relationship using profile monitoring techniques. However, in certain complex manufacturing processes, due to cost and technical limitations of sensors, some critical process information remains unmeasurable. To address this challenge, this study adopts a functional state-space model (FSSM) for process modeling, where the state equation describes the internal dynamic evolution of the system, while the observation equation characterizes the functional relationship between response and explanatory variables. In Phase I, a B-spline-based Expectation-Maximization algorithm is used to estimate the FSSM. For Phase II monitoring, an Exponentially Weighted Moving Average (EWMA)-type monitoring statistic is proposed, and its iterative computation formula is derived to enhance computational efficiency. Simulation results demonstrate that the proposed monitoring scheme delivers superior performance across various scenarios. Finally, the practical implementation of the scheme is validated through a case study on monitoring the machining process of scroll involutes in an air compressor.