When developing a PLS models for quality parameter prediction, the deviation of measurement values from their mean must be shifted in time to account for the time required for a change in the input to impact the quality parameter. Similarly, these delays should be taken into account in the processing of the deviation values used for on-line quality parameter prediction. As addressed in Advanced Control Foundation – Tools, Techniques, and Applications, the delay between a change in the process input value and when its impact is reflected in the quality parameter may be determined by doing a cross-correlation between the process input and the quality parameter. The identified delay is then used to create the time shifted data that is applied to the PLS model. For example consider the prediction of Kappa number at the output of a continuous digester shown below.
In a continuous digester, the chip meter speed is selected as the state parameter because it sets the process throughput. The Kappa number of the product output may be measured using an on-line analyzer or by analyzing a grab sample in the lab. The delay associated with each input that is reflected in the Kappa number is automatically determined by doing a cross-correlation between the process inputs and the Kappa number contained in a selected data set. For example, the transport delay between changes in the chip meter speed and its impact on the product Kappa number may be determined using cross correlation analysis as shown below.
The delay associated with a process input is established based on the time shift that provides maximum correlation. In this faster than real time simulation of a continuous digester, the delay between the change in chip meter speed and the change being reflected in the Kappa number is 175 seconds. In an actual process the delay is much longer.