Kalman Filtering for Manufacturing Processes

Abstract

where xk is the measurement at iteration k, x is the measurement average, and N is the number of samples. Noise due to the manufacturing process itself is often greater in magnitude than the electrical noise. Examples of process noise include: (1) high frequency cyclic variations due to tool eccentricity in a turning process, (2) low frequency variations due to discrete solidification of deposited material in Laser Metal Deposition (LMD) processes, and (3) chaotic mixing of materials in Friction Stir Welding (FSW) processes. Manufacturing process measurements must be filtered before the data can be used for dynamic modeling or control. First principle modeling is generally unable to capture inherent nonlinear dynamics such as non–uniform friction and system wear. Therefore, dynamic manufacturing process models are often developed empirically. Estimation techniques such as Recursive Least Squares and Particle Swarm Optimization are commonly used for system identification to create a “best fit” model based on collected measurements. However, the fidelity of an empirical model greatly depends upon the measurements used to create it and processes with high–magnitude variations in the measurement signals are often difficult to model due to the low signal–to–noise ratio. Manufacturing process models are often used to design process controllers. Process control is the on–line adjustment of process parameters to enhance operation productivity and improve part quality. Variations in the measurement signal are generally higher in frequency than the available actuator bandwidth, which can lead to increased actuator wear and possible instability. A filter must be developed for (1) post processing of data to compensate for large signal variations prior to use by a model identification method and (2) on–line filtering capable of preserving signal phase and magnitude with minimal computational burden. The fourth–order Butterworth filter is used in a number of manufacturing processes. Bhattacharyya and Sengupta (2007) used a fourth–order Butterworth filter on a face milling process to remove high frequency variation due to spindle rotation harmonics. Liang et al. (2002) employed a Butterworth filter on the spindle power signal of an end milling process for use in a fuzzy logic controller. Ghosh et al. (2007) used a Butterworth filter for neural– O pe n A cc es s D at ab as e w w w .in te ch w eb .o rg