By Michael Boudreau and Gregory McMillan, Emerson Process Management
If a control configuration does not exist, one can be created and tested in a virtual plant environment before the physical plant is completed. Batch recipes can be created and tested before clinical material is needed from pilot scale bioreactors. In a virtual environment, the process operation may be examined by running the process model and control faster than real time.
The fast execution allows users to play “what if” scenarios and design experiments that may reduce a process development batch schedule. [3] In production, the predictive capability of the virtual plant has the potential to infer unmeasured or unmeasureable process variables like product concentration. The accuracy of the inferential calculation can be maintained by adapting model parameters to changes in the actual plant.[4]
Data Analytics with Multivariate Statistical Models
Multivariate statistical models can monitor batch quality online, continuously. Monitoring can begin as early as the pilot scale clinical trial stage of product development. Alarm limits or univariate statistical techniques cannot be used to monitor quality since those techniques do not account for cross correlation and/or co-linearity present in cell culture or microbial batches.
Multivariate techniques for bioreactor quality monitoring and process control provide a solution by converting process variables that may be collinear and cross correlated to independent, uncorrelated variables called principal components. Based on principal component techniques, Squared Prediction Error (SPE), and Hotelling’s control charts can be developed to reflect overall batch operation.
Two types of multivariable analysis used online are Principal Component Analysis (PCA) and Partial Least Squares or Projection to Latent Structures (PLS). PCA monitors batch variables and states to verify the preservation of cross correlation and co-linearity upon which the model is based. PCA is most often used to detect process or measurement faults during a batch. PLS predicts output parameters based on input variables and the current process state. The output parameters may be the end of the batch or the endpoint product quality.
Both methods use empirical models based on a reference set of good batches. To be effective, these reference batches must capture the variability expected in the batch. Too little variation may lead to false alarms and too much variability can render the analysis insensitive. To build a model, the reference batches must be aligned so the data is synchronized at each point of the batch and all batches have common end points.
For example, a phase transition may wait for a tank to reach a predefined temperature. The time to reach that temperature and end the phase is not likely to be the same in any two batches. The method of synchronizing batches with the broadest application is Time Warping, [5], [6].
Time Warping is demonstrated as a feature match between two time series. The time series are non-linearly ‘warped” in the time dimension. The best results are obtained when a pattern or trajectory is optimized. Dynamic Programming is used to match elements of the time series so as to minimize discrepancies in each corresponding trajectory subject to constraints; hence the name Dynamic Time Warping. Constrains include sample beginning and end points, a monotonic solution and local continuity. Figures 1 and 2 compare batch data before and after alignment by Dynamic Time Warping.
Note how the oscillations are superimposed and the batch end points are equal after alignment. PCA and PLS techniques process continuous data in two dimensions; time and value. Batch data, on the other hand, is three dimensional; batch, value and time. Before PCA or PLS processing, batch data must be unfolded to two dimensions. There are several ways to unfold batch data.
Initially, batch-wise unfolding and variable-wise unfolding were considered separately. Batch-wise unfolding results in a two-dimensional matrix with each row containing all the data from a single batch. Variable-wise unfolding results in a two dimensional matrix segmented by time slices of the batch.
Each column of the variable-wise unfolded matrix contains all the values of a variable for all batches in that time segment. PCA and PLS analysis on batch-wise unfolded data can detect deviation from a desired operating trajectory. But in online application the data set is not complete until the end of the batch and prediction is necessary for batch-wise unfolding.
Online PCA and PLC analysis of variable-wise unfolded data does not require equal batch lengths or prediction of future values. However, nonlinear, time varying trajectories remain in the data matrix and calculated loadings contain correlations between variables. Lee, et al, [5], eliminated both the time dependency and need of prediction by mean centering and scaling batch-wise unfolded data and then re-arranging the data variable-wise.
Hybrid unfolding is used to generate the results shown in Figures 1 and 2. On line prediction of batch quality with PLS is achieved by partitioning the entire batch into equally spaced statistical scans. Since Dynamic Time Warping is used to match the measured data to the reference batches, they are labeled DTW scans. Each time the running batch completes a DTW scan, a PLS analysis is performed and the final product quality is predicted.
Summary
First order plus dead time, high fidelity and multivariate statistical models are valuable tools for batch operation improvement. First order plus dead time models can be identified automatically and high fidelity models can be generated from a library of composite block modules. Multivariate statistical analysis has been adapted to batch processes with dynamic time warping and hybrid unfolding. These online models can accelerate design of experiments and process design.
References
Authors
Corresponding author Michael Boudreau and Gregory McMillan are principal consultants for Emerson Process Management. Mr. Boudreau can be reached at michael.boudreau@emerson.com
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