Industrial & Engineering Chemistry Research, Vol.59, No.11, 5000-5009, 2020
Batch-to-Batch and Within-Batch Input Trajectory Adjustment Based on the Probabilistic Latent Variable Model
The input trajectory is critical to the output quality of batch processes; therefore, the input trajectory of an entire batch run should be designed according to the desired output before manufacturing. Moreover, in the middle of a batch run (within a batch run), the remaining trajectory should be adjusted if the predicted quality is not ideal. In this work, a method to guarantee the product quality via within-batch and batch-to-batch input trajectory adjustment is proposed based on the probabilistic latent variable model. For the batch-to-batch adjustment (product design), to obtain the desired output, the distribution of input trajectory may be computed by making the distribution of the latent variable conditioned on the input trajectory equal to that derived from the desired output. In the within-batch input trajectory adjustment, by minimizing the deviation between the latent variable derived from the desired output and that from the input trajectory, the remaining input trajectory is adjusted to overcome the influence of disturbances on the final quality. Different from the conventional method based on the partial-least-squares (PLS) model, the inherent probabilistic feature of the real industrial data is considered in this work, and both the product design and within-batch input trajectory adjustment are achieved by probabilistic inference. In addition, owing to the superiority of the probabilistic latent variable model over the PLS model, the proposed method can provide higher-dimensional design space and adjustment space within which any input adjustment can achieve the desired output. The application of the proposed method is illustrated by a numerical case and a beer fermentation process, and the application results indicate its validity in quality control of batch processes.