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Figure 6.84. Online predictions for end-of-batch quality values for a normal batch. Dotted straight line indicates the average value of a quality variable based on reference batches.
Figure 6.84. Online predictions for end-of-batch quality values for a normal batch. Dotted straight line indicates the average value of a quality variable based on reference batches.
Figure 6.85. Online predictions for end-of-batch quality for the faulty batch.
to include the final product quality variables q,:
The size of the lifted output vector y may be too large to develop subspace models quickly. This high dimensionality problem can be alleviated by applying PCA prior to subspace identification [134], Since 34 may have a high degree of colinearity, there is a potential to reduce the number of variables significantly. If the number of principal components is selected correctly, the residuals are mostly noise that tends to be batchwise uncorrected, and the principal components will retain the important features of batch-to-batch behavior. Applying PCA to project y of length JK to a lower dimensional space y_ of size a such that a <C JK, the state-space model based on y is where y is defined by
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