Since the minimum variance controller (MVC) provides the smallest achievable output variance, performance indices based on minimum variance benchmarking have been applied extensively to both univariate and multivariate systems. This paper extends the idea of minimum variance benchmarking to the performance monitoring of cross-directional (CD) processes in paper machines. A performance index is proposed based on the spatial and temporal minimum variance benchmark for the CD process. Computational complexity of the high dimensional time series estimation is reduced by taking advantage of the special structure in the coefficient matrices. Illustrative examples from a paper machine simulator and industrial data sets are provided to show the effectiveness of the techniques as well as the insensitivity of the performance index to high frequency spatial disturbances.
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