This grant provides funding for developing systematic methodologies for effectively analyzing, monitoring, and inferring of cyclic functional sensing data for multiple embedded operation diagnosis in complex processes. The proposed functional data analysis methodology will be developed through the unique fusion of engineering knowledge with statistical wavelet analysis for data dimension reduction, data segmentation, feature extraction, and root causes diagnosis. The research will be conducted through (a) systematic (rather than subjective) data segmentation through process-oriented change-point detection; (b) engineering-driven wavelet thresholding (rather than only data-denoising) for efficient feature preserving data dimension reduction; (c) multiscale diagnostic mapping algorithms for effective feature extraction and root cause diagnosis (rather than only monitoring); and (d) optimal (rather than trial-and-error) wavelet basis selection to match with specific data characteristics and data analysis objectives. If successful, the results of this research will lead to improvements of the existing statistical process control (SPC) technology by adding a new set of monitoring and diagnostic tools for high dimensional functional data to achieve better process control and quality improvement. The implementation of the proposed methodology will facilitate the development of effective monitoring and diagnostic systems to significantly reduce process downtime and manufacturing cost, thus leading to significant benefits to the national economy. The proposed work will also extensively enhance the research and broaden the application domains of wavelet analysis to achieve better functional data analysis for diagnostic purposes. Meanwhile, it will contribute to the creation of a new workforce with multidisciplinary skills through new curriculum developments, involvement of undergraduate/K-12 students in the research activities, and close industrial collaborations.
