Assumption-free modeling of time-dependent processes
Batch processes are common in many industries. Typically, raw materials are combined in a suitable batch vessel before chemical, physical or biological transformations takes place, and ultimately resulting in an end product. In many cases the control of the batch process is recipe driven and the operations are not adjusted to accommodate raw material variation, changes in uncontrollable factors and other changing circumstances. The best possible end product quality is achieved by adapting batch operations according to any detectable changes during processing, thus providing a control mechanism to drive a product towards its desired state.
When building models across various batches one may often encounter varying batch lengths and the batches may start from various relative points of time in a chemical context. One example is granulation where the moisture content of the incoming material may differ between batches.
The data structure for a number of batches, samples and variables can be represented as a data cube. However, the batches may be of different lengths in terms of the number of samples, although the relative progression from start to end may be similar for the batches. Several situations may occur:
For the reasons above a line plot of individual variables represented as sample number on the x-axis does not reflect the chemical state of a number of batches.
CAMO has developed an improved batch modeling approach using Principal Component Analysis accommodating uneven batch lengths and different chemical or biological starting points. The method models the data in relative time and is also independent of the actual sampling rate between the batches.