(320f) Augmented Dynamic Pca Approach for Online Monitoring of Multi-Stage Batch Processes

Recently chemical industry and research community's focus has been shifted from large--volume continuous processing to low volume but high value-added batch operations. Manufacturing chemicals through batch processing is increasingly common in most of the major industries such as pharmaceuticals, fine and specialty, semiconductor, polymers etc. Hence monitoring of batch processes has become critically important. In addition, recent advances in online data acquisition make huge operation database available to analysis. These databases contain hundreds of measured variables recorded on a frequent basis for tens to hundreds of batches. Principal Component Analysis (PCA) - a multivariate statistical process control technique -- has been used successfully to capture the information contained in such database for monitoring purpose.

Online monitoring of batch processes using multivariate statistical process control (MSPC) techniques, PCA in particular, has been a challenging problem. The key issues include the 3?D nature of batch data, unequal batch lengths or variation in the timing for key dynamic events in reference database, and incomplete online data for evolving batch as first outlined by J. F. MacGregor and his co?workers (Nomikos and MacGregor, 1995a; Nomikos and MacGregor, 1995b; Nomikos and MacGregor, 1995c). In addition, difficult dynamics of batch processes (ie., highly nonlinear, time--varying, multi--stage/multi--phase) presents the extra challenges to their monitoring (Undey and Cinar, 2002). To deal with each of these issues, there has been a lot of research activity. Multiway Principal Component Analysis (MPCA)/ Multiway Partial Least Squares (MPLS) (Nomikos and MacGregor, 1995c), variable--wise unfolding (Wold et al., 1998) were proposed to deal with the issue of 3--D nature of batch data. Indicator variable technique (IVT) (Nomikos, 1995), dynamic time warping (DTW) technique (Kassidas et al., 1998) were adapted for dealing with the problem of unequal batch length in reference database. For online monitoring, a number of solutions, most of which involving estimating the missing batch data from the current time until the end of the evolving batch, were discussed in (Nomikos and MacGregor, 1995c). Alternatively, variable--wise unfolding technique (Wold et al., 1998; Lee et al., 2004) or hierarchical PCA (Rannar et al., 1998) could be employed. In addition, difficult dynamics (ie, highly nonlinear, time varying, multistage/multiphase), that are often encountered in batch processes was dealt with in (Lee et al., 2004, Chen and Liu, 2002).

However, we observe that no single method can handle all of the identified issues. Each of the methods was designed to specifically and particularly deal with one or two of the issues but not all and hence a combination of different methods is necessary. We propose a framework for such a combination by integrating dynamic feature synchronization and dynamic time warping (DTW) with Dynamic Principal Component Analysis (DPCA) (Chen and Liu, 2002). The strategy here is firstly identifying the singular points marking different process stages that are then aligned optimally by DTW and later analyzed by DPCA. We use the concept of singular points (SP) as defined in (Srinivasan and Qian, 2005) and observe that a SP breaks normal correlation of residuals from the best fit of recent moving window. The reason is because a SP carries more information content than adjacent points and hence it does not follow the best-fit line of the recent moving window. DTW is then used to warp corresponding process stages into equal time length. In offline analysis, optimal warping (in terms of distance measure) is achieved using asymmetric DTW algorithm as detailed in (Sakoe and Chiba, 1978). However, a similar algorithm, which requires end-point constraints, can not be implemented online because the end-points are not known in advance. In stead, we remove the constraints and consider the optimization of all possible end-point matching. Even though this could lead to sub-optimal warping, the modified DTW algorithm can be implemented online in a computationally efficient fashion. To obtain a DPCA model, we follow (Chen and Liu, 2002). However, in their paper, no scaling method was explicitly specified, without which the DPCA model can not work. Scaling against batch mean trajectory is selected because the goal is to detect deviations from the desired operation.

The proposed method, which is called augmented DPCA, is implemented on PenSim simulation - a dynamic simulation of fed-batch penicillin production (Undey and Cinar, 2002), as well as on experimental data from a crystallization process. Original DPCA as proposed in (Chen and Liu, 2002) is also implemented. Comparison between augmented DPCA and original DPCA shows that the augmented DPCA outperforms the original one in monitoring PenSim and in analyzing the crystallization data sets. The superiority of augmented DPCA demonstrates the need for integrating different methods for online monitoring of multi-stage batch processes.

Keywords: online monitoring, batch process, multi-stage process, feature synchronization, dynamic time warping, dynamic PCA

References

1. Birol, G., C. Undey and A. Cinar (2002). A modular simulation package for fed-batch fermentation: penicillin production. Computers and Chemical Engineering 26, 1553-1565.

2. Chen, J. and K. C Liu (2002). On-line batch process monitoring using dynamic PCA and dynamic PLS. Chemical Engineering Science 57, 63-75.

3. Kassidas, A., J. F. MacGregor and P. A. Taylor (1998). Synchronization of batch trajectories using dynamic time warping. AIChE J. 44, 864-875.

4. Lee, J. M., C. K. Yoo and I. B. Lee (2004). Enhanced process monitoring of fed-batch penicillin cultivation using time-varying and multivariate statistical analysis. Journal of Biotechnology 110, 119-136.

5. Nomikos, P. (1995). Statistical process control of batch processes. PhD thesis. McMaster University.

6. Nomikos, P. and J. F. MacGregor (1995a). Analysis, monitoring and fault diagnosis of batch processes using multiblock and multiway PLS. Journal of Process Control 5, 277-284.

7. Nomikos, P. and J. F. MacGregor (1995b). Multi-way partial least squares in monitoring batch processes. Chemometrics and Intelligent Laboratory Systems 30, 97-108.

8. Nomikos, P. and J. F. MacGregor (1995c). Multi-variate SPC charts for monitoring batch processes. Technometrics 37, 41-59.

9. Rannar, S., J. F. MacGregor and S. Wold (1998). Adaptive batch monitoring using hierarchical PCA. Chemometrics and Intelligent Laboratory Systems 41, 73-81.

10. Sakoe, H. and S. Chiba (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-26, 43-49.

11. Srinivasan, R. and M. S. Qian (2005). Online temporal signal comparison using singular points augmented time warping. Industrial & Engineering Chemistry Research (In press).

12. Undey, C. and A. Cinar (2002). Statistical monitoring of multistage, multiphase batch processes. IEEE Control Systems Magazine 10, 40-52.

13. Wold, S., N. Kettanhe, H. Friden and A. Holmberg (1998). Modelling and diagnostics of batch processes and analogous kinetic experiments. Chemom. Intell. Lab 44, 331-340.