(251e) Online Maintenance of Multivariate Statistical Soft Sensors for Quality Monitoring in Batch Processes

Multivariate statistical models are powerful tools for batch process monitoring. However, they are assumed to be time-invariant [1]. This means that the online monitoring of future batches relies on the fact that every incoming batch belongs to the same (normal) distribution of the reference dataset. Unfortunately, special-cause variability is often present between batches. In fact, in the industrial practice a batch process is often subject to process and plant variations, because of maintenance intervention on the plant, recipe adjustment, raw materials alterations, catalyst deactivation, equipment aging, seasonal changes, etc... This causes a loss of the model performance, and for this reason a monitoring model should be updated on a regular basis to adapt to the new process/plant conditions.

The basic idea of the updating strategies proposed so far for multivariate statistical models is to recursively revise the values of mean, variance, and covariance, and to adapt the control limits of the models to the evolving conditions [2,3]. However, the model updating is commonly performed following a temporal order, while few criteria have been studied for selecting and updating an optimal set of batches to be included as a reference into the model regardless of the temporal order in which they have been run.

This work proposes a novel updating strategy for the recursive adaptation of multivariate statistical soft-sensors, in which the number of reference batches to include into the model is selected on a batch-to-batch basis. Namely, only the ?nearest neighbours? to the running batch are selected as references from an historical database of past completed batches, and a new soft sensor is built based on this adapting reference set. The selection of the most appropriate reference set is operated by evaluating the degree of similarity of the current batch to the past completed batches included into a historical database. The proposed procedure evolves through the following steps:

? evaluation of the current batch at the very beginning of the batch;

? selection of the nearest neighbours to the current batch from an historical database of past batches;

? calibration of the estimation model using the nearest neighbour batches;

? use of the estimation model for the online monitoring of the current batch.

The performance of the new adaptation technique is compared to a moving window recursive method where the reference set is selected on a temporal basis, and is tested in the case study of a PLS (partial least squares) soft-sensor for the quality estimation in an industrial batch polymerization processes for the production of resins [4] (34 process variables and 2 quality variables collected for 72 batches, i.e. more than 2.5 years of operational effort). Both the relative error of estimation and the rate of unreliable estimation of the proposed approach are lower then the ones of the moving window recursive approach, confirming superior performances of the proposed method.

References

[1] Zhao, C., F. Wang, F. Gao, N. Lu, and M. Jia (2007). Adaptive monitoring method for batch processes based on phase dissimilarity updating with limited modeling data. Ind. Eng. Chem.. Res., 46, 4943-4953.

[2] Rännar, S., J. F. MacGregor and S. Wold (1998). Adaptive batch monitoring using hierarchical PCA. Chemom. Intell. Lab. Sys., 41, 73-81.

[3] Qin, S. J., (1998). Recursive PLS algorithms for adaptive data modeling. Computers Chem. Eng., 22, 503-514.

[4] Facco, P., F. Doplicher, F. Bezzo and M. Barolo (2009). ?Moving-average PLS soft sensor for online product quality estimation in an industrial batch polymerization process?. J. Process Control, 19, 520-529.